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Discrimination and job search in imperfect labour markets Watts, Martin John 1976

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DISCRIMINATION AND JOB SEARCH IN IMPERFECT LABOUR MARKETS  by  MARTIN JOHN WATTS B.A. (Econ.), U n i v e r s i t y of Essex, 1970 M.A. (Econ.), U n i v e r s i t y of Manchester, 1971  A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY i n the Department of Economics  We accept t h i s thesis as conforming to the required standard  THE UNIVERSITY OF BRITISH COLUMBIA August, 1976 ©  Martin John Watts, 1976..  In presenting  t h i s thesis i n p a r t i a l f u l f i l m e n t of the requirements  f o r an advanced degree at the "University of B r i t i s h Columbia, I agree that the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r reference and study.  I f u r t h e r agree that permission f o r extensive  copying of  t h i s t h e s i s f o r s c h o l a r l y purposes may be granted by the Head of my Department or by h i s representatives.  I t i s understood that p u b l i -  c a t i o n , i n part o r i n whole, o r the copying of t h i s thesis f o r f i n a n c i a l gain s h a l l not be allowed without my w r i t t e n permission.  Martin John Watts  Department of Economics The U n i v e r s i t y of B r i t i s h Columbia Vancouver V6T1W5  ii ABSTRACT In t h i s study the behaviour of firms and workers i s modelled simultaneously  i n a labour market characterised by one imperfection,  namely the absence of complete information on the part of job seekers about job o f f e r s and wage rates over firms.  The necessary and s u f f i c i e n t  conditions f o r wage d i s p e r s i o n i n e q u i l i b r i u m i n t h i s model are examined. In the absence of perfect information,unemployed i n d i v i d u a l s search randomly f o r job o f f e r s .  Since t h e i r behaviour i s based on  general information acquired through search, workers' turnover and acceptance behaviour i s s t o c h a s t i c .  Firms make wage o f f e r and vacancy  c r e a t i o n d e c i s i o n s , based on t h e i r current l e v e l of employment,to maximise p r o f i t s over an i n f i n i t e horizon.  Firms enjoy intertemporal  monopsony power. E q u i l i b r i u m i n t h i s market i s s t o c h a s t i c .  I t i s characterised  by wage and employment d i s p e r s i o n and the simultaneous existence of f r i c t i o n a l unemployment and vacancies.  The l e v e l of vacancy c r e a t i o n  i s not consistent with s t a t i c p r o f i t maximisation. are defined as speculative.  Such vacancies  They do not represent desired net h i r e s .  Firms are speculating on the basis of i n d i v i d u a l s ' s t o c h a s t i c turnover and acceptance behaviour.  The aggregate measure of vacancy creation  represents job o f f e r s at d i f f e r e n t wage r a t e s . conventionally defined, does not e x i s t .  Excess demand, as  I n t h i s study the concept  of a vacancy and the construction of an index of market pressure are examined under d i f f e r e n t market s t r u c t u r e s .  Comparative s t a t i c  p r e d i c t i o n s are generated i n t h i s model, Model I .  iii The main c o n t r i b u t i o n of t h i s study i s i n the formulation of models of imperfect markets i n which there are two types of worker who d i f f e r s y s t e m a t i c a l l y i n t h e i r labour market behaviour.  Type  one i n d i v i d u a l s have a higher p r o b a b i l i t y of q u i t t i n g , i f employed, i n response to a p a r t i c u l a r wage o f f e r than type two i n d i v i d u a l s . To a firm,type two i n d i v i d u a l s are more valuable because, i n response to a stream of wage o f f e r s over time, the mean returns associated w i t h h i r i n g a type two i n d i v i d u a l exceed the returns associated w i t h h i r i n g a type one i n d i v i d u a l .  Two labour-market structures are considered.  In Model I I , f i r m s are unable to discriminate e x p l i c i t l y i n wage o f f e r and h i r i n g between i n d i v i d u a l s .  The important r e s u l t i s that,  although firms behave competitively, i n t e r - f i r m wage d i f f e r e n t i a l s are observed.  Firms make decisions based on t h e i r current l e v e l s and  compositions of employment.  Type one i n d i v i d u a l s , although less  valuable, earn a higher mean wage o f f e r than type two i n d i v i d u a l s . By contrast, i n Model I I I firms can discriminate e x p l i c i t l y between i n d i v i d u a l s i n h i r i n g and wage o f f e r .  Now firms make o f f e r s  d i r e c t l y r e l a t e d . t o the i n d i v i d u a l ' s value to the f i r m and i n t r a f i r m wage d i f f e r e n t i a l s are observed.  Comparative s t a t i c p r e d i c t i o n s  are derived w i t h respect to both models. Within t h i s framework, the arguments of economists, as to whether low turnover workers earn a higher or lower wage than high turnover workers, are evaluated. Furthermore, the impact of f a i r employment laws on t h i s labour market are examined.  iv  Excess demand, as c o n v e n t i o n a l l y d e f i n e d , does not e x i s t i n these models.  V a c a n c i e s do n o t r e p r e s e n t d e s i r e d n e t h i r e s and so a measure  o f market p r e s s u r e based on aggregate v a c a n c i e s ployment i s i n c o r r e c t .  and f r i c t i o n a l unem-  T h i s i m p o r t a n t r e s u l t from the models  the inadequacy o f u s i n g vacancy  demonstrates  and unemployment data to draw i n f e r e n c e s  about excess s u p p l y or demand i n a l a b o u r market.  A crude measure o f  market p r e s s u r e based on ex p o s t h i r e s and quits i s  developed and i t s  inadequacies  outlined.  TABLE OF CONTENTS Chapter 1.  Page THE PROBLEM AND.THE LITERATURE SURVEY I.  1  II.  An I l l u s t r a t i v e Model of the Labour Market . . .  3  III.  An Outline of the Models Developed i n the Thesis  10  IV.  Review of the L i t e r a t u r e on Imperfect Markets. .  15  The L i t e r a t u r e on D i s c r i m i n a t i o n  37  VI.  .  The Thesis  51  THE CONCEPTUAL FRAMEWORK I. II. III.  3.  1  Introduction  V.  2.  . . . . . . . .  53  I n d i v i d u a l Turnover and Acceptance Behaviour  53  Firms' Wage and Vacancy Creation Decisions and the Algorithm  72  The C h a r a c t e r i s t i c s of Stochastic E q u i l i b r i u m . .  87  THE DISTRIBUTION OF PERCEPTIONS, THE DATA, THE SIMULATION PROCEDURE AND THE METHOD OF COMPARATIVE STATICS , I. II. III. IV.  105  Summary The Gamma D i s t r i b u t i o n  105 . .  The Data  110  The Simulation Procedure  115  V. Problems A r i s i n g from the Simulation Procedure . VI.  105  Comparative S t a t i c Results ..  123 126  vi  4.  RESULTS FROM MODEL I I. II. III.  5.  Introduction Comparative S t a t i c  127 Predictions  . . . . .  Vacancy and Unemployment S t a t i s t i c s  RESULTS FROM MODELS I I AND I I I I.  .  .  .  .  132 168  173  Introduction . . . . .  173  II.  Results  o f Model I I  176  III.  Results  o f Model I I I  206  IV. V.  6.  127  A Comparison o f Models I I  and I I I  245  Conclusion  256  THE CONCEPT OF VACANCY CREATION AND EXCESS DEMAND IN AN IMPERFECT MARKET . I. II. III. IV.  258  Introduction  258  The Vacancy Concept  259  The Concept and Measure of Excess Conclusion  Demand  262 267  vii LIST OF TABLES Table  Page  1.  The I n i t i a l Exogeneous Parameter Values i n Model I . »  110  2.  The I n i t i a l Exogeneous Parameter Values i n Models I I and I I I . .  112  3.  The Basic S o l u t i o n to Model I  131  4.  Results and Comparative S t a t i c P r e d i c t i o n s f o r Misperceptions of the Reservation Wage  135  5.  Results and Comparative S t a t i c P r e d i c t i o n s f o r D i f f e r e n t Levels of Unemployment Compensation . . . .  144  6.  Results and Comparative S t a t i c P r e d i c t i o n s f o r D i f f e r e n t Horizons over which Returns from Search Accrue  149  7.  Results and Comparative S t a t i c P r e d i c t i o n s f o r D i f f e r e n t P e r i o d Lengths  153  8.  Results and Comparative S t a t i c P r e d i c t i o n s f o r D i f f e r e n t Values of the Perception Parameter,  9.  A Comparison of P a r t i a l and F u l l E q u i l i b r i u m  . . .  161  ....  167  10. 11.  The Basic S o l u t i o n to Model I I The S o l u t i o n to Model I I Corresponding to Perception Parameter Values [1.05,0.95]  12.  Summary S t a t i s t i c s f o r Unequal Values of the Perception Parameters  177 181  185  13. . Comparative S t a t i c Results f o r Model I I  200  14. 15.  210  16. 17.  The Basic S o l u t i o n to Model I I I The S o l u t i o n to Model I I I w i t h Perception :< •,Parameters, [1.05,0.95] . . . V . . . . . . . . . . ]' Summary S t a t i s t i c s f o r Unequal Values of the Perception Parameters i n Model I I . . . . . . . . . .  220  Comparative S t a t i c Results f o r Model I I I  241  222  viii  Table 18.  19.  20.  Page Comparison o f S t o c h a s t i c E q u i l i b r i a i n Models I I and I I I c o r r e s p o n d i n g t o the B a s i c Parameter Values  247  Comparison o f S t o c h a s t i c E q u i l i b r i a i n Models I I and I I I c o r r e s p o n d i n g to Parameter V a l u e s [1.05,0.95]  248  Comparison o f Summary S t a t i s t i c s o f Models I I and I I I  250  ix  LIST OF FIGURES  Figure  1.  Page  The F i r m ' s D e c i s i o n Problem i n the model .  Illustrative .  6  2.  The Labour Market S t r u c t u r e s  Modelled  12  3.  S t o c h a s t i c E q u i l i b r i u m i n Reder's  4.  The F i r m ' s D e c i s i o n Problem i n A r c h i b a l d ' s Model  5.  The Gamma D i s t r i b u t i o n  6.  Gamma D i s t r i b u t i o n s w i t h D i f f e r e n t  Means  7.  Gamma D i s t r i b u t i o n s w i t h D i f f e r e n t  Variancies  8.  The M a t r i x of Employment S t a t e s  Model  27 .  .  32 107 108  . . . .  109 175  X  ACKNOWLEDGEMENTS  I would l i k e to extend my g r a t i t u d e my i n t e r e s t  i n this  t o C u r t i s Eaton who s t i m u l a t e d  t o p i c and h e l p e d c o n s i d e r a b l y i n i t s  Thanks a r e due t o C h r i s A r c h i b a l d f o r h i s his  formulation.  comments on the t e x t and  encouragement.  To my w i f e , forbearance.  Linda,  I express my a p p r e c i a t i o n f o r h e r p a t i e n c e  F i n a l l y , I am i n d e b t e d t o Ann MacLeod f o r h e r  i n t r a n s l a t i n g s c r a w l to the f i n a l ,  typed p r o d u c t .  and  alacrity  1 CHAPTER 1 THE PROBLEM AND THE LITERATURE SURVEY  I.  Introduction  Economists argue that the existence of wage d i s p e r s i o n and f r i c t i o n a l unemployment as e q u i l i b r i u m phenomena i n labour markets i s c e r t a i n l y r e l a t e d t o , and perhaps caused by, imperfect information on the part of market participants."*" An i n d i v i d u a l seeking a job i n a p a r t i c u l a r industry lacks s p e c i f i c information about job o f f e r s and wage r a t e s .  Consequently,  he samples o f f e r s by searching and contacting d i f f e r e n t f i r m s . According to h i s perception of the wage d i s t r i b u t i o n i n the i n d u s t r y , the i n d i v i d u a l computes an estimate of h i s r e s e r v a t i o n wage. The 2 reservation wage i s that wage o f f e r at which the expected returns from search are zero.  marginal  Thus, i f o f f e r e d that wage, the  i n d i v i d u a l would be i n d i f f e r e n t between search and accepting the offer.  On the basis of t h i s r e s e r v a t i o n wage,he evaluates each  o f f e r and decides whether to accept the p a r t i c u l a r o f f e r or indulge i n f u r t h e r search.  I t i s sometimes a l l e g e d that r a t i o n a l d e c i s i o n  making on the part of firms i n response to t h i s search behaviour i s 3 s u f f i c i e n t to generate wage d i s p e r s i o n and f r i c t i o n a l unemployment. Unfortunately,the micro-theoretic foundations of t h i s behaviour have not been s p e l t out.  The l i t e r a t u r e f a i l s to model simultaneously  the r a t i o n a l behaviour of both sets of p a r t i c i p a n t s i n t h i s imperfect market. 1.  This l i t e r a t u r e can be divided i n t o four d i s t i n c t areas : S t i g l e r [1961] and Gronau [1971] model the optimal search rules f o r i n d i v i d u a l s who sample from a known d i s t r i b u t i o n of product p r i c e s and wage o f f e r s , respectively.  Dispersion i s asserted to e x i s t due to  imperfect information of searchers ,but there i s no 4 formal a n a l y s i s of firms' behaviour i n e i t h e r model. 2.  Mortenson  [1970] and Salop [1973b] analyse optimal  f i r m decision making f o r prescribed non-stochastic turnover and acceptance behaviour by i n d i v i d u a l s . The micro-foundations of workers' behaviour are not developed and i t i s not c l e a r that wage d i s p e r s i o n and consequently job search are e q u i l i b r i u m phenomena. 3.  Reder [1969] develops a model of an imperfect market i n which the nature of e q u i l i b r i u m i s described but again r a t i o n a l behaviour by market p a r t i c i p a n t s i s not s p e c i f i e d .  4.  Archibald [1954] develops a s t a t i c model of an imperfect market.  He attempts to define the concept of a vacancy,  but i n d i v i d u a l search behaviour i s not formally modelled. Rothschild [1973] argues that a s a t i s f a c t o r y model of the adjustment to e q u i l i b r i u m of a market must have three components, namely :  3 1.  A d e s c r i p t i o n of how market p a r t i c i p a n t s behave i n disequilibrium;  2.  A set of rules as to how  the market operates i n  response to p a r t i c i p a n t s ' behaviour; and 3.  A theorem demonstrating convergence to e q u i l i b r i u m . 5  A cursory glance at t h i s l i t e r a t u r e i n d i c a t e s that these c r i t e r i a have not been s a t i s f i e d .  In my thesis I wish to model  simultaneously and analyse the behaviour of firms and workers i n a labour market characterised by imperfect information.  The main  c o n t r i b u t i o n i s i n the extension of t h i s framework to  incorporate  two types of worker who behaviour.  d i f f e r s y s t e m a t i c a l l y i n t h e i r labour market  The i m p l i c a t i o n s for f i r m behaviour of t h i s heterogeneous  workforce are examined. In order.to i n d i c a t e the e s s e n t i a l elements of my model of an imperfect labour market and motivate the close examination of the l i t e r a t u r e , I now  develop a simple i l l u s t r a t i v e model.  II.  An I l l u s t r a t i v e Model of the Labour Market  The labour market i s assumed to consist of a number of t e c h n i c a l l y homogeneous firms who  enjoy d i f f e r e n t l e v e l s of employment.  Firms h i r e  from a labour force homogeneous i n i t s capacity to do the job.  Each  f i r m makes a wage and vacancy d e c i s i o n to maximise p r o f i t s over a one period horizon.  This assumption s i m p l i f i e s the a n a l y s i s but  still  allows the examination of the e s s e n t i a l elements of an imperfect market. These decisions w i l l be r e l a t e d to the l e v e l of employment the f i r m c u r r e n t l y faces.  Wage dispersion and dispersion i n the l e v e l of  employment over firms are assumed to e x i s t , i n i t i a l l y .  The  labour  4 market environment i s characterised by the d i s t r i b u t i o n of firms over d i f f e r e n t l e v e l s of employment and t h e i r corresponding wage and vacancy decisions. An unemployed i n d i v i d u a l has imperfect information about where the most remunerative searches randomly. f o r job o f f e r s .  job o f f e r s may be found.  Consequently,he  Other unemployed i n d i v i d u a l s are a l s o searching  Thus an i n d i v i d u a l searcher i s not assured of a job  offer,even i f he samples a f i r m which has created vacancies.  Through  h i s knowledge of the labour market environment, which i s generated through search, the i n d i v i d u a l evaluates the p r o b a b i l i t y of an o f f e r at each f i r m .  He then computes the mean and variance of t h i s wage  offer distribution. For any wage o f f e r received,the i n d i v i d u a l computes the returns from search.  I f he accepts t h i s offer,he assumes he w i l l enjoy t h i s  wage r a t e f o r the rest of h i s working horizon.  Otherwise,  remaining  unemployed, he searches f u r t h e r and assumes he w i l l receive an o f f e r equal to the mean wage o f f e r i n the industry a f t e r one search.  He  accepts t h i s o f f e r and assumes that he w i l l enjoy t h i s wage rate f o r the rest of h i s working horizon.  By comparing these income streams,  he estimates the returns from search.  H i s perceived r e s e r v a t i o n wage  i s that current o f f e r which makes h i s returns from search zero. I f the i n d i v i d u a l receives an o f f e r less than h i s perceived r e s e r v a t i o n wage, the returns from search are p o s i t i v e and he searches Otherwise,he accepts the job o f f e r .  further.  5 I f the i n d i v i d u a l has complete i n f o r m a t i o n about t h e d i s t r i b u t i o n of wage o f f e r s over f i r m s and t h e p r o b a b i l i t y o f o f f e r d i s t r i b u t i o n over f i r m s ,  then he can e s t i m a t e the t r u e mean wage o f f e r and thus  the  true reservation  wage.  On the b a s i s  of t h i s reservation  the  i n d i v i d u a l makes acceptance d e c i s i o n s .  wage,  The i n d i v i d u a l ' s  p e r c e p t i o n o f t h i s l a b o u r market environment i s i n c o m p l e t e , however, since the  i t i s generated through non-exhaustive j o b s e a r c h .  individual's perceived reservation  distribution.  From the p r o p e r t i e s  wage i s s u b j e c t t o a p r o b a b i l i t y  o f random sampling, the p r o b a b i l i t y  d i s t r i b u t i o n o f the perceived reservation t r u e wage o f f e r d i s t r i b u t i o n . of the r e s e r v a t i o n the  F o r s i m p l i c i t y , the mean and v a r i a n c e  wage and the t r u e v a r i a n c e o f o f f e r s  perceived reservation  (from the p o i n t  wage w i l l be r e l a t e d t o t h e  wage d i s t r i b u t i o n a r e assumed t o be f u n c t i o n s o f  true reservation The  Consequently,  respectively.  wage f o r an i n d i v i d u a l can be regarded  o f view o f t h e employer) as a random drawing from  t h i s density  function.  and  an o f f e r , then the p r o b a b i l i t y o f acceptance i s g i v e n  by  receives  the p r o b a b i l i t y  that  I f an i n d i v i d u a l samples a p a r t i c u l a r  the i n d i v i d u a l ' s p e r c e i v e d r e s e r v a t i o n  i s l e s s than o r e q u a l t o the wage o f f e r .  is stochastic.  wage  T h i s equals the c u m u l a t i v e  p r o b a b i l i t y d i s t r i b u t i o n of the perceived reservation a t the wage o f f e r .  firm  wage e v a l u a t e d  Thus acceptance b e h a v i o u r by unemployed  The expected flow s u p p l y o f unemployed  individuals  individuals  ( s e a r c h e r s ) t o a p a r t i c u l a r f i r m which o f f e r s a wage w i s S^(w), where  1 dw  > 0.  6 Likewise, a currently employed i n d i v i d u a l has  imperfect  information about other job o f f e r s and wage rates.  Thus h i s  perception of the reservation wage i s also subject to a p r o b a b i l i t y d i s t r i b u t i o n whose parameters are functions wage and the true variance of o f f e r s . stochastic.  of the true  reservation  His q u i t decision i s therefore  The p r o b a b i l i t y that an i n d i v i d u a l quits i n response to  a wage o f f e r i s given by the p r o b a b i l i t y that the perceived wage exceeds the wage o f f e r . and o f f e r s a wage, w,  reservation  I f the f i r m c u r r e n t l y employs e i n d i v i d u a l s  then the expected number of i n d i v i d u a l s who dS dS 2  do  not  2  q u i t i s S2(e,w), where ~j^7~ > 0 and  > 0.  The  t o t a l expected flow  supply of i n d i v i d u a l s to a f i r m which c u r r e n t l y faces employment, e, and o f f e r s a wage, w, i s given by the h o r i z o n t a l sum  of S^(w)  and  S2(e,w) and i s denoted by S(e,w). Labour i s the only v a r i a b l e f a c t o r of production.  The  f i r m faces  an unchanging downward sloping marginal revenue product function, MR(e). This s p e c i f i c a t i o n . o f the marginal revenue product function cuts the l i n k between p r i c e and the aggregate output of the industry but, i n order to i s o l a t e the elements of an imperfect labour market, i t i s necessary to abstract from the impact of changes i n the product p r i c e on f i r m behaviour.  l ^ 2 * 3' Figure 1 - The Firm's Decision Problem i n the I l l u s t r a t i v e Model e  e  e  e  e  7 The marginal cost of labour schedule facing the f i r m i s denoted by MS(e,e).  This function i s obtained from the d e r i v a t i v e of the wage  b i l l , wS(e,w), w i t h respect to t o t a l employment, e.  To maximise one  period p r o f i t s , t h e f i r m chooses the l e v e l of employment at which the marginal revenue product equals marginal cost. i n d i v i d u a l s at wage, w*. behaviour,more than workers, may w*.  Due  to s t o c h a s t i c search and acceptance  i n d i v i d u a l s , the mean flow supply of unemployed  contact the f i r m and be prepared to accept the wage o f f e r ,  At wage r a t e , w*,  the f i r m would choose to employ e^ i n d i v i d u a l s ,  i f they were forthcoming.  At employment l e v e l , e^, the marginal revenue  product equals the wage, w*, at wage, w*,  I t hopes to employ e*  and so i f the f i r m can employ e^ i n d i v i d u a l s  then p r o f i t s are maximised.  Correspondingly, the f i r m would  not choose to employ more than e^ workers. The  f i r m a n t i c i p a t e s that e - e^ i n d i v i d u a l s w i l l q u i t .  Consequently, the f i r m w i l l create e^ - e^ vacancies but i t expects that only e* - e^ vacancies w i l l be f i l l e d . i n i t s vacancy creation. Figure 1.  The  Thus the f i r m speculates  firm's decision problem i s shown i n  This model c l o s e l y follows Archibald's model [1954].  I t i s evident that, i f wage dispersion e x i s t s i n i t i a l l y and  firms  face d i f f e r e n t l e v e l s of employment, wage dispersion w i l l p e r s i s t as w i l l dispersion i n firms' employment l e v e l s .  I n d i v i d u a l s w i l l indulge  i n job search and there w i l l be f r i c t i o n a l unemployment. that industry e q u i l i b r i u m , however defined, may  This suggests  be characterised  wage dispersion and employment dispersion over firms.  by  8 In  g e n e r a l , t h e maximising  the i n i t i a l  d e c i s i o n s of firms w i l l not regenerate  l a b o u r market environment.  I f t h e environment changes,  then workers' s e a r c h and q u i t b e h a v i o u r w i l l change and so the environment w i l l once a g a i n change as f i r m s make a new s e t o f optimal d e c i s i o n s . T h i s i n d i c a t e s t h e fundamental s i m u l t a n e i t y o f the problem. S e a r c h e r s ' d e c i s i o n s t o accept j o b o f f e r s and employed  individuals'  d e c i s i o n s to q u i t a r e dependent upon the d i s t r i b u t i o n o f wage r a t e s and v a c a n c i e s over f i r m s i n the i n d u s t r y . w i t h r e s p e c t t o wage r a t e s and vacancy the s e a r c h and q u i t b e h a v i o u r meaningful it  But, f i r m s ' d e c i s i o n s  d e c i s i o n s a r e dependent upon  o f the l a b o u r f o r c e .  To say a n y t h i n g  about wage d i s p e r s i o n , v a c a n c i e s and f r i c t i o n a l  i s necessary  t o r e s o l v e these simultaneous  unemployment,  r e l a t i o n s h i p s and examine  the n a t u r e o f e q u i l i b r i u m i n t h i s model. T h i s i l l u s t r a t i v e model then demonstrates the n a t u r e o f t h e problem I am l o o k i n g a t . comings, however. i n Chapter  T h i s model has severe t h e o r e t i c a l s h o r t -  Model I , t h e b a s i c model, which i s developed f o r m a l l y  2, remedies these d i f f i c u l t i e s  makes t h e problem much more complex.  t o some e x t e n t but p r e d i c t a b l y  The p r i n c i p a l d e f i c i e n c i e s o f  t h i s i l l u s t r a t i v e model a r e examined below. Firm behaviour  i s unconvincing.  I n t a k i n g the expected  flow  s u p p l y o f l a b o u r t o the f i r m t h e s t o c h a s t i c elements o f j o b s e a r c h }  have been purged and f i r m s a r e n o t maximising  expected p r o f i t s .  the flow s u p p l y o f l a b o u r i s known w i t h c e r t a i n t y , then the f i r m c r e a t e s e* - e.. v a c a n c i e s which a r e i n s t a n t a n e o u s l y  filled.  If  9 It  i s evident  t h a t an i n d i v i d u a l h i r e d l a s t p e r i o d has some  v a l u e to the f i r m t h i s p e r i o d , b e c a u s e the f i r m ' s c u r r e n t wage and vacancy  d e c i s i o n s depend on the number o f employees  last period.  T h e r e f o r e , i n h i r i n g an i n d i v i d u a l , the f i r m  a flow o f r e t u r n s over t i m e . the f i r m , power.  It  MS(e,e),  anticipates  S i n c e the m a r g i n a l c o s t f u n c t i o n  i s upward s l o p i n g , t h e  firm exhibits  facing  s t a t i c monopsony  may be demonstrated t h a t , under p l a u s i b l e a s s u m p t i o n s ,  marginal cost function s h i f t s i n e,  i n h e r i t e d from  to the r i g h t i n response to an i n c r e a s e  the c u r r e n t l e v e l of employment.^  dynamic monopsony power.  the  Then, i t  Thus, the f i r m  exhibits  i s a p p r o p r i a t e to model  b e h a v i o u r i n a m u l t i - p e r i o d framework.  In a d d i t i o n , i n  a one p e r i o d h o r i z o n , the model a b s t r a c t s  firm  specifying  from the dynamic i n t e r -  dependence o f f i r m s r e s u l t i n g from the impact o f each f i r m ' s  decisions  on the s t a t e o f the l a b o u r market, n o t a b l y such parameters as the mean and v a r i a n c e o f the wage o f f e r ment.  d i s t r i b u t i o n and the l e v e l of unemploy-  These parameters i n f l u e n c e the n a t u r e o f i n d i v i d u a l s ' job In s h o r t , a s a t i s f a c t o r y  model o f an i m p e r f e c t  requires both formal s p e c i f i c a t i o n  l a b o u r market  of i n d i v i d u a l b e h a v i o u r ,  that  s e a r c h r u l e s f o r i n d i v i d u a l s faced w i t h a d i s t r i b u t i o n of wage and, i n a d d i t i o n , choice t h e o r e t i c namely wage and vacancy  foundations of f i r m s '  is  offers,  decisions,  d e c i s i o n s which maximise expected p r o f i t s  an i n f i n i t e h o r i z o n i n response to the s t o c h a s t i c  search.  over  flow s u p p l y o f l a b o u r .  These elements a r e f u r t h e r emphasised i n the b r i e f o u t l i n e o f Model I which  follows.  10  III.  A.  An O u t l i n e of the Models Developed i n the T h e s i s  Model I I n the b a s i c model, Model I ,  which i s f u l l y  2, workers are assumed t o maximise expected t h e i r job h o r i z o n .  the most remunerative job  they a r e f o r c e d to s e a r c h randomly.  do not n e c e s s a r i l y offers,  s e a r c h the same firms or r e c e i v e  they have d i f f e r e n t  t u r n o v e r and acceptance  d e c i s i o n s i n the l i g h t  stochastic.  wage r a t e which i s  less  They make  of t h e i r  perceptions  a  than h i s p e r c e p t i o n o f the r e s e r v a t i o n wage,  v a l u e o f expected p r o f i t s  for a better  position. to maximise the  The f i r m makes at most as many o f f e r s  acceptance by job as v a c a n c i e s  must employ any i n d i v i d u a l a c c e p t i n g an o f f e r . s e a r c h e r s may c o n t a c t  i s n e c e s s a r i l y s p e c u l a t i v e because  This  They are faced by s t o c h a s t i c  over by t h e i r employees and s t o c h a s t i c  and because n o t a l l o f f e r s  present  d i s c o u n t e d over an i n f i n i t e h o r i z o n .  the net worth o f the f i r m .  insufficient  the same job  Thus, t h e i r l a b o u r market  Firms make wage and vacancy d e c i s i o n s  however,  offers.  An employed i n d i v i d u a l , who i s o f f e r e d  q u i t s h i s job and searches  equals  they do  Since i n d i v i d u a l s  l a b o u r market e x p e r i e n c e s .  of the t r u e l a b o u r market environment. behaviour i s  income d i s c o u n t e d over  Due to i m p e r f e c t i n f o r m a t i o n , however,  not know where they w i l l r e c e i v e Consequently,  a n a l y s e d i n Chapter  it  seekers.  creates  and i t  Through random s e a r c h ,  the f i r m .  Vacancy c r e a t i o n  the flow o f s e a r c h e r s i s  may be a c c e p t e d .  turn-  stochastic  These wage and vacancy  d e c i s i o n s depend on the l e v e l o f employment the f i r m c u r r e n t l y  faces  11 and  a l s o how  i t perceives  the l a b o u r market environment.  The  level  of  employment a t t a i n e d i s s t o c h a s t i c . T h i s model i s t r u l y simultaneous i n t h a t each s e t of market p a r t i c i p a n t s responds to h i s p e r c e p t i o n  of the environment and  how  the o t h e r s e t of p a r t i c i p a n t s behaves. E q u i l i b r i u m i n t h i s model i s s t o c h a s t i c and  i s characterised  by  a steady s t a t e d i s t r i b u t i o n of f i r m s over d i f f e r e n t l e v e l s of employment.  I f the s t o c h a s t i c p r o c e s s occurs f o r a l o n g p e r i o d of  the expected p r o p o r t i o n ment i s given by given  of time any  f i r m faces  a given  time,then  l e v e l of employ-  the c o r r e s p o n d i n g element o f the d i s t r i b u t i o n .  a l a r g e number of f i r m s , t h e  employment s t a t e i s given by  proportion  of f i r m s  Or,  in a particular  the element of the d i s t r i b u t i o n .  the s t o c h a s t i c n a t u r e of the p r o c e s s , t h e a c t u a l p r o p o r t i o n  Given  of  firms  h a v i n g a p a r t i c u l a r employment l e v e l e x h i b i t s v a r i a t i o n about  the  c o r r e s p o n d i n g element. The and,  e q u i l i b r i u m i s c h a r a c t e r i s e d by  s p e c u l a t i v e vacancy  creation  i n a d d i t i o n , i f t h i s steady s t a t e d i s t r i b u t i o n i s non-degenerate,  wage d i s p e r s i o n and Two imperfect 1.  f r i c t i o n a l unemployment.  important q u e s t i o n s emerge from the m o d e l l i n g of t h i s l a b o u r market which I hope t o answer i n my Under what l a b o u r  market s t r u c t u r e s  an e q u i l i b r i u m phenomenon?  thesis.  i s wage d i s p e r s i o n  12 2.  What i s models?  the i n t e r p r e t a t i o n , of vacancy  c r e a t i o n i n such  In p a r t i c u l a r , i s i t p o s s i b l e  to c o n s t r u c t  an  index o f l a b o u r market t i g h t n e s s o r excess demand u s i n g l a b o u r market p a r a m e t e r s , unemployment,  such as aggregate v a c a n c i e s  such t h a t when the market i s i n  e q u i l i b r i u m the index has a zero value? the concept  B.  stochastic  In short,  is  o f excess demand v a l i d i n an i m p e r f e c t  market?  Models of D i s c r i m i n a t i o n U s i n g the same g e n e r a l framework as Model I ,  d i s c r i m i n a t i o n are f o r m u l a t e d . consists differing  two models  I n these models, the l a b o u r  o f two types of i n d i v i d u a l s w i t h the same  d i f f e r i n g perceptions  can i d e n t i f y  of  overt  young and o l d workers d i f f e r i n g i n t h e i r  o f time p r e f e r e n c e  from s e a r c h accrue)  to  the n a t u r e  each i n d i v i d u a l & s l a b o u r market b e h a v i o u r through some (e.g.  force  o f r e s e r v a t i o n wage.  C r u c i a l t o the f i r m i s whether i t  characteristics  of  skills,but  i n t h e i r t u r n o v e r and acceptance b e h a v i o u r , d u e  systematically  rates  and  o r h o r i z o n s over which they b e l i e v e  and, f u r t h e r m o r e , whether i t  is  legally  returns allowed  t o d i s c r i m i n a t e i n wages p a i d and i n h i r i n g . There a r e f o u r d i s t i n c t The a p p r o p r i a t e model i s  Figure 2  l a b o u r market s t r u c t u r e s  i n d i c a t e d by the elements  RC  RC  III  II  II  II  considered.  of a 2 x 2 matrix.  The Labour Market S t r u c t u r e s M o d e l l e d  13 In state RC, each f i r m can recognise the c h a r a c t e r i s t i c s of an i n d i v i d u a l searcher's labour market behaviour p r i o r to h i r i n g , i n addition to knowing the c h a r a c t e r i s t i c s of each employee's behaviour and the general composition of the stock of unemployed workers. In s t a t e RC, no f i r m i s able t o recognise d i f f e r e n t i n d i v i d u a l s p r i o r to h i r i n g but, at any p o i n t i n time, i t knows the general composition of i t s work force and the stock of unemployed workers. In state DI, each f i r m i s l e g a l l y allowed to discriminate e x p l i c i t l y between the d i f f e r e n t types of worker through i t s wage o f f e r and vacancy creation decision.  I t makes an ex ante wage and  vacancy decision f o r each type of worker. In state DI, e x p l i c i t wage and h i r i n g d i s c r i m i n a t i o n are i l l e g a l . Each f i r m makes o f f e r s randomly to those searchers who sample i t and pays a l l i n d i v i d u a l s the same wage. In Model I I firms do not discriminate i n wage o f f e r or h i r i n g between d i f f e r e n t i n d i v i d u a l s e i t h e r because the p r a c t i c e i s i l l e g a l (row 2 of the matrix) or because they are unable to recognise the c h a r a c t e r i s t i c s of each i n d i v i d u a l ' s behaviour (column 2 of the matrix). Each of these states i s a s u f f i c i e n t condition  f o r no i n t r a - f i r m  d i s c r i m i n a t i o n , but neither i s a necessary condition. the general composition of i t s workforce  Each f i r m knows  and the stock of unemployed  individuals. I n Model I I I each f i r m i s able t o recognise the c h a r a c t e r i s t i c s of i n d i v i d u a l searchers and each member of i t s workforce  (column 1  14 of  the m a t r i x ) .  o f the m a t r i x ) .  Furthermore, i t  i s a l l o w e d to d i s c r i m i n a t e  Then, i n response  (row 1  to the p e r c e i v e d l a b o u r market  environment and the number of and c o m p o s i t i o n o f i t s w o r k f o r c e , makes an ex ante wage and vacancy  it  c r e a t i o n d e c i s i o n f o r each type o f  worker. Through the examination o f t h e s e two models, I w i s h t o the f o l l o w i n g q u e s t i o n s 1.  If  employment 2.  :  each f i r m r e c o g n i s e s  worker and i s  the d i f f e r e n t  types o f i n d i v i d u a l  a l l o w e d to d i s c r i m i n a t e i n wage o f f e r  (Model I I I ) ,  Assuming t h a t ,  answer  w i l l f i r m s ' workforces  ex a n t e ,  and  be segregated?  type one i n d i v i d u a l s have a h i g h e r  p r o b a b i l i t y o f q u i t t i n g than type two i n d i v i d u a l s i n to a g i v e n wage o f f e r ,  response  w i l l type one i n d i v i d u a l s earn lower  wages as argued by Sanborn (1964), or w i l l firms o f f e r  high-  t u r n o v e r i n d i v i d u a l s h i g h e r wages? 3.  What i s  the impact o f  industry profits different 4.  If  ' f a i r employment'  and on expected  types o f  laws on  lifetime  expected  incomes of  the  individuals?  i n t r a f i r m d i s c r i m i n a t i o n i s i l l e g a l , w i l l wage J  differentials  persist  over firms w i t h the same  but d i f f e r e n t  c o m p o s i t i o n o f employment?  w i l l a n t i - d i s c r i m i n a t i o n laws be e f f e c t i v e wage and employment  discrimination?  level  I n o t h e r words, in abolishing  15  IV.  A.  Review o f the L i t e r a t u r e oh Imperfect  Markets  A Summary As a l r e a d y n o t e d the l i t e r a t u r e on i m p e r f e c t markets can be  sub-divided i n t o four areas, 1.  namely  :  Models o f o p t i m a l s e a r c h b e h a v i o u r by i n d i v i d u a l s i n markets  2.  c h a r a c t e r i s e d by i m p e r f e c t  information;  Models o f i n t e r t e m p o r a l f i r m behaviour i n response prescribed non-stochastic  t u r n o v e r and  to  acceptance  b e h a v i o u r by i n d i v i d u a l s ; 3.  Models o f a l a b o u r market which i s viewed as a process;  4.  Static  stochastic  and  monopsony models which examine the concept  of a  vacancy.  B.  Optimal Search In S t i g l e r ' s  and h e t e r o g e n e i t y He develops  fundamental a r t i c l e o f goods o r s e r v i c e s  [1961], he argues generate  is applicable  o f unknown p r i c e s  f o r a homogeneous  good.  l a b o u r market where j o b s  offered.  If  This  there  analysis  a r e ranked s o l e l y  on the wage  the consumer knows the d i s t r i b u t i o n o f p r i c e s , but n o t  the p a r t i c u l a r p r i c e at each s t o r e ,  then he searches  s e a r c h i s a drawing from the d i s t r i b u t i o n o f p r i c e s . the  given that  t o i n d i v i d u a l s s e a r c h i n g f o r the h i g h e s t wage i n an  imperfect  that  ignorance  price dispersion.  a t h e o r y o f how consumers ought to behave,  is a variety  that  consumer d e c i d e s ,  ex a n t e ,  randomly. Stigler  on the o p t i m a l number o f  Each argues  searches  16 and then p i c k s the minimum p r i c e .  The expected minimum p r i c e from  a sample of n observations each w i t h cumulative p r o b a b i l i t y d i s t r i b u t i o n F(p) i s  CO p  =  /  (l-F(p) " pnF'(p)dp. n  0  . . . . (1)  1  The expected gain from a f u r t h e r search i s  00 ' g  n  =  P  n  - P  = /' ( l - F ( p ) ) F ( p ) d p n  n + 1  ....  (2)  which i s a decreasing f u n c t i o n of n. I f the cost of one search i s c^then n i s the optimal number of searches where S  n ±  C  - n+l • g  • • • •  ( 3 )  The marginal returns from the next search are equalled or exceeded by the cost of another search.  S t i g l e r has s i m p l i f i e d the  problem by assuming that one unit of the good i s purchased of the p r i c e charged.  irrespective  In t h i s framework, i t i s not c l e a r how returns  from search are computed when quantity demanded v a r i e s w i t h p r i c e . Several authors, notably McCall [1965], [1960], Nelson [1970] and Rothschild [1973] argue that the d e c i s i o n r u l e that S t i g l e r devised 9 i s sub-optimal and that the optimal r u l e of search i s s e q u e n t i a l . I f s i s the minimum p r i c e of those sampled,.then the expected returns from one f u r t h e r search are  17 (s-p)dF(p) = [ ( s - p ) F ( p ) ] ^ + f  S  0  F(p)dp  = g(p)«  ....  (4)  I n d i v i d u a l s w i l l continue to search, i f the lowest p r i c e observed exceeds R, where R i s the s o l u t i o n to g(R) = c.  In contrast to S t i g l e r ' s  ex ante d e c i s i o n r u l e , the sequential r u l e does not require the c o l l e c t i o n of o f f e r s .  This r e s u l t i s p a r t i c u l a r l y u s e f u l when modelling search i n  a labour market, where the t e c h n i c a l homogeneity of workers makes o f f e r c o l l e c t i o n implausible. I t i s important to note that R i s independent of the number of searches already undertaken, i f the marginal cost of search i s constant. Thus, an i n d i v i d u a l may search many stores u n t i l a p r i c e l e s s than R i s observed, although h i s d e c i s i o n r u l e i s based on the computation of the returns from one f u r t h e r search. A s i m i l a r one search d e c i s i o n r u l e can be developed f o r job search i n a labour market.  This d e c i s i o n r u l e , however, i s generally not the  optimum r u l e of search. Gastwirth [1971] examines the robustness of these optimal d e c i s i o n rules when the searcher i n c o r r e c t l y estimates the d i s t r i b u t i o n of p r i c e s . He demonstrates that even a modest s p e c i f i c a t i o n e r r o r d r a m a t i c a l l y increased the expected number of searches.  He proposes a mixed r u l e  which i s both robust and preserves the r e s e r v a t i o n p r i c e property.  18  The r u l e i s t h a t  the i n d i v i d u a l keeps  searching u n t i l either n  til observations  have been taken o r the lowest  observation i s less Rothschild  observation after  than some p r e s c r i b e d R .  [1974] d e r i v e s  the o p t i m a l s e a r c h r u l e s  f o r an  i n d i v i d u a l who l e a r n s about an unknown d i s t r i b u t i o n of p r i c e s search.  the k  He concludes  that economists  can c o n s i d e r w i t h o u t  through  great  loss  t h a t s e a r c h r u l e s from unknown d i s t r i b u t i o n s do have the same qualitative Telser  properties  as the o p t i m a l r u l e s  [1973] adopts a d i f f e r e n t  techniques,he  calculates  the gains  from known d i s t r i b u t i o n s . " ' " ^  approach.  U s i n g Monte C a r l o  a r i s i n g from an o p t i m a l s e a r c h r u l e  as compared w i t h a n a i v e s e a r c h r u l e o f p i c k i n g the f i r s t p r i c e sampled, for different  known d i s t r i b u t i o n s of p r i c e s .  His results  show t h a t  the  gains a r e an i n c r e a s i n g f u n c t i o n o f the r a t i o o f the range o f each d i s t r i b u t i o n to i t s minimum p r i c e and a d e c l i n i n g f u n c t i o n o f the cost  o f one s e a r c h .  He c o n c l u d e s ,  however,  that  the gains  from the  o p t i m a l r u l e over the n a i v e r u l e a r e s m a l l . In the r e s t about  of h i s a r t i c l e ,  the i n t e n s i t y  of p r i c e d i s p e r s i o n .  S t i g l e r makes some l o o s e  of s e a r c h and the determinants I n the absence  f i r m b e h a v i o u r which generates  d i s p e r s i o n , these remarks l a c k  conviction.  consumers' b e h a v i o u r i n  response t o p r i c e v a r i a t i o n i s s p e c i f i e d , b u t i s not explained.  o f the magnitude  o f any formal s p e c i f i c a t i o n o f  I t i s a p a r t i a l e q u i l i b r i u m model i n that  generated  assertions  how such d i s p e r s i o n i s  19 S t i g l e r models an i n d i v i d u a l store's behaviour when i t b e l i e v e s that consumers make n searches from a rectangular d i s t r i b u t i o n of store p r i c e s on the u n i t i n t e r v a l [0,1].  The expected number of  customers buying from a store charging p r i c e , p, i s D(p)  =  k(l-p)  . . . . (5)  n _ 1  where k i s a p o s i t i v e constant.  Given that other s t o r e p r i c e s are  fixed,then D(p) represents the store's demand function. p r o f i t s by  Denoting  II, the f i r m maximises n  =  D(p)p - C[D(p)]  . . . . (6)  where C[D(p)] i s the store's cost function.  I f each store has the  same cost function,then each w i l l choose the same p r i c e and the uniform d i s t r i b u t i o n which was supposed to generate the demand function w i l l shrink to a point. follows Rothschild's review  The preceding d i s c u s s i o n c l o s e l y  [1973].  This s t a t i c framework i s  inappropriate to model the d i s p e r s i o n . interdependance.  Stores have no intertemporal  Stores have no intertemporal monopoly power because  no customers are attached to them over time.  Thus, they are i d e n t i c a l  i n a l l respects and no p r i c e d i s p e r s i o n i s generated. In a l a t e r a r t i c l e [1962], S t i g l e r discusses the amount of wage d i s p e r s i o n observed i n d i f f e r e n t professions and the determination of the returns from search.  He points out that t o compute the returns  from search requires that the firm's perceived wage o f f e r has a c o r r e l a t i o n of one over time.  He argues that, even with r a t i o n a l  search and i n the absence of exogeneous s h i f t s i n supply and demand,  20 wage d i s p e r s i o n w i l l p e r s i s t i n the labour market.  He c i t e s changes  i n jobs due to changes i n workers' tastes and a b i l i t i e s  and employees'  i d e n t i t i e s as i n s u f f i c i e n t to generate s u f f i c i e n t search to eliminate dispersion.  These phenomena, he s t a t e s , set a minimum to the amount  of wage d i s p e r s i o n . These changes surely can be regarded as exogeneous to the labour market.  I f the labour market i s c o n t i n u a l l y i n flux,so that i n d i v i d u a l s  a c t u a l l y leave the labour force and new firms appear,then d i s p e r s i o n i s l i k e l y to p e r s i s t .  S t i g l e r argues that costs of search prevent s u f f i c i e n t  search and thus d i s p e r s i o n p e r s i s t s . not generate d i s p e r s i o n .  Costs of search alone, however, do  There are two s u f f i c i e n t but not necessary  conditions f o r zero d i s p e r s i o n . 1.  Firms are t e c h n i c a l l y homogeneous and have no intertemporal monopoly power,as S t i g l e r u n w i t t i n g l y demonstrated [1961]; and  2.  I n d i v i d u a l s are homogeneous i n t h e i r search behaviour i n the sense that, ex post, they respond i n the same way to any p a r t i c u l a r p r i c e or wage o f f e r , that i s , they e i t h e r accept or r e j e c t the p r i c e with a p r o b a b i l i t y o f one. I f a l l i n d i v i d u a l s adopt the same sequential d e c i s i o n rule,then a l l i n d i v i d u a l s have the same r e s e r v a t i o n or c r i t i c a l p r i c e and there w i l l be no d i s p e r s i o n .  I f firms e x h i b i t dynamic  monopsony power and i n d i v i d u a l s adopt a non-exhaustive ex ante d e c i s i o n r u l e f o r search, such as the one proposed by S t i g l e r , then d i s p e r s i o n p e r s i s t s , as shown below.  The  21 magnitude of d i s p e r s i o n seems to be p o s i t i v e l y related, to the cost of search. These conditions suggest that i n some c a s e s , i n d i v i d u a l s ' expectations about the nature of the p r i c e or wage d i s t r i b u t i o n are s e l f r e a l i s i n g .  I n my model of an imperfect labour market,  i n d i v i d u a l s ' s t o c h a s t i c turnover and acceptance behaviour i s motivated by t h e i r b e l i e f that the wage d i s t r i b u t i o n e x h i b i t s non-zero variance and thus non-zero d i s p e r s i o n which j u s t i f i e s search.  This s t o c h a s t i c  behaviour i n t u r n r e i n f o r c e s d i s p e r s i o n as firms experience d i f f e r e n t l e v e l s of employment.  I f i n d i v i d u a l s b e l i e v e that there i s no d i s -  persion and each has the same perception of the r e s e r v a t i o n wage, then a l l firms w i l l o f f e r that r e s e r v a t i o n wage and there w i l l be no d i s persion and no search.  Thus, non-exhaustive  search, per se, i s not  s u f f i c i e n t to generate d i s p e r s i o n . Gronau [1971] develops a model of intertemporal sequential search i n which the t o t a l time devoted to work and search i s constant. further search leads to a shorter working horizon.  Thus,  The i n d i v i d u a l has  a perception of the wage d i s t r i b u t i o n over the horizon.  For each period  over the f i x e d horizon,the i n d i v i d u a l computes a r e s e r v a t i o n wage such that the discounted income stream associated with t h i s wage i s equal to the discounted income stream associated w i t h the best a l t e r n a t i v e . This expression takes the form of a recurrence r e l a t i o n s h i p .  The  optimal current r e s e r v a t i o n wage depends on the sequence of optimal r e s e r v a t i o n wages over the remainder of the horizon.  I f unemployed  22 p r i o r to the l a s t it  p e r i o d , ah i n d i v i d u a l a c c e p t s any wage o f f e r  i s exceeded by h i s a l t e r n a t i v e  compensation.  I n d i v i d u a l s assume t h a t  a f i r m ' s wage o f f e r  is unity.  Gronau demonstrates  that,  tribution, of t i m e .  e a r n i n g s , namely the  temporal c o r r e l a t i o n o f  s e q u e n t l y , the acceptance  little  wage d e c l i n e s v e r y  c a p i t a l markets.  Gronau takes wage d i s p e r s i o n as g i v e n and f a i l s  Salop  o f f i r m b e h a v i o u r to generate  [1973a] a l s o d i s c u s s e s  at that  Consearch  assumed  wage i s  A more that  Like S t i g l e r  [1961],  to p r o v i d e any f o r m a l  dispersion.  The i n d i v i d u a l has  job  knowledge  d i s t r i b u t i o n and the p r o b a b i l i t y of an  f i r m at each p o i n t i n t i m e .  s e a r c h o r d e r and sequence  to  the i n d i v i d u a l ' s s y s t e m a t i c  s e a r c h i n an i n t e r t e m p o r a l framework. of each f i r m ' s wage o f f e r  over the  (see C h a p t e r ^ I B ) .  p l a u s i b l e e x p l a n a t i o n f o r the d e c l i n i n g acceptance  specification  to work.  the h o r i z o n of job tenure i s  the i n d i v i d u a l faces i m p e r f e c t  function  the time devoted  devoted  independent o f the d u r a t i o n of s e a r c h  dis-  wage i s a d e c l i n i n g  search i s normally a small f r a c t i o n of that  constants i f  relations,  g i v e n a time i n v a r i a n t wage o f f e r  T h i s argument i s m i s l e a d i n g i n t h a t  p e r i o d and i s  unemployment  S o l v i n g the r e c u r r e n c e  the r e s e r v a t i o n o r acceptance  unless  He has to choose the  of acceptance  offer  optimal  wages over time to maximise  the p r e s e n t v a l u e of expected wealth over an i n f i n i t e h o r i z o n .  Re-  s a m p l i n g any p a r t i c u l a r f i r m i s not p e r m i t t e d .  that  He demonstrates  an i n d i v i d u a l w i l l sample a h i g h wage-low p r o b a b i l i t y o f o f f e r b e f o r e a low wage-high are  identical.  p r o b a b i l i t y of o f f e r  f i r m , i f mean wage  firm rates  23 Again, r a t i o n a l f i r m behaviour which generates d i s p e r s i o n i s not s p e c i f i e d .  I f searchers are homogeneous i n t h e i r knowledge of  wage o f f e r s , then a l l w i l l sample the same f i r m f i r s t and a l l have the same acceptance wage.  Dispersion w i l l disappear according to  the second s u f f i c i e n t c o n d i t i o n discussed above. C.  Firms' Intertemporal Behaviour Mortenson [1970] develops a non-stochastic model of f i r m  behaviour i n a labour market characterised by imperfect information. Information i s incomplete because i t has to be acquired s e q u e n t i a l l y through search, which i s time consuming and c o s t l y , and because o l d information becomes r a p i d l y obsolete.  Workers' preferences over firms  are ranked by the wage o f f e r e d , so there i s no psychic income associated w i t h employment at a p a r t i c u l a r f i r m .  I n d i v i d u a l s have perceptions  about the mean wage o f f e r which they update through t h e i r own  experience.  This i s modelled by s p e c i f y i n g that each i n d i v i d u a l has a perception of the mean wage which i s subject to a p r o b a b i l i t y d i s t r i b u t i o n . Each i n d i v i d u a l appears homogeneous, ex ante, i n h i s perception of the mean wage and h i s labour market experiences are captured by s p e c i f y i n g s t o c h a s t i c misperceptions of the mean wage. Search behaviour i s not formally specified,but firms can expect the number of unemployed searchers who sample them to be i n proportion to t h e i r r e l a t i v e s i z e i n the labour market.  Unemployed searchers have  a higher p r o b a b i l i t y of contact, that i s r e c e i v i n g an o f f e r , than employed searchers.  This r e f l e c t s the lower opportunity costs of  search when unemployed.  The p r o b a b i l i t y of contact i s assumed constant,  24 but i s c l e a r l y a f u n c t i o n o f the d i s t r i b u t i o n o f v a c a n c i e s o f unemployment. they a r e o f f e r e d market wage a f t e r  and l e v e l  Both employed and unemployed s e a r c h e r s assume a job w i t h c e r t a i n t y  that  a t t h e i r n o t i o n o f the mean  t h e i r mean l e n g t h o f s e a r c h , namely the i n v e r s e o f  the p r o b a b i l i t y of making a c o n t a c t .  T h e i r q u i t , acceptance and  i n t e r - f i r m t u r n o v e r d e c i s i o n s are a l l made through comparing these c e r t a i n income s t r e a m s .  Summing the i n d i v i d u a l components and t a k i n g  the mathematical e x p e c t a t i o n , l a b o u r to the f i r m .  Mortenson d e r i v e s the flow s u p p l y of  The p r o p o r t i o n a l r a t e of change o f the  labour force i s a f u n c t i o n of i t s  own r e l a t i v e wage and the  of unemployment,but i s independent of the s i z e of i t s  labour  firm's level force.  Assuming the form o f the wage d i s t r i b u t i o n and t a k i n g the of unemployment as c o n s t a n t ,  he o b t a i n s  level  the o p t i m a l time path o f  wages f o r the f i r m by s o l v i n g the i n t e r t e m p o r a l p r o f i t maximising problem.  W h i l e r e c o g n i s i n g the e x p l i c i t  dynamic interdependence  firms i n the h i r i n g o f l a b o u r , Mortenson f i n e s s e s making these p a r t i a l e q u i l i b r i u m assumptions.  the problem by  Adopting a non-stochas-  t i c l a b o u r s u p p l y s c h e d u l e , he has s u p p r e s s e d any ex p o s t of w o r k e r s '  l a b o u r market b e h a v i o u r generated by s t o c h a s t i c  o f the mean wage. contact,  F u r t h e r m o r e , by assuming  he has a v o i d e d the s t o c h a s t i c  of  heterogeneity misperceptions  a f i x e d p r o b a b i l i t y of  elements  o f job s e a r c h i n a  market c h a r a c t e r i s e d by changing d i s t r i b u t i o n s of wages and v a c a n c i e s over t i m e . vacancies,  A l l p o s i t i o n s .> c r e a t e d a r e i n s t a n t a n e o u s l y as c o n v e n t i o n a l l y d e f i n e d ,  excess demand.  f i l l e d so  do n o t e x i s t , and n e i t h e r  does  25 Since,  ex p o s t ,  s t a t u s i s homogeneous second s u f f i c i e n t heterogeneity  labour of in its  the same employment  l a b o u r market b e h a v i o u r ,  of firms.  initial  t h e n , from the  c o n d i t i o n n o t e d above, wage d i s p e r s i o n r e q u i r e s I n t h i s p a r t i a l e q u i l i b r i u m framework,  r e q u i r e s t h a t firms face e i t h e r different  or unemployment  different  l e v e l s o f employment.  the  this  t e c h n i c a l c o n d i t i o n s or If  the l a t t e r  is true,  i n the l i m i t , wage d i s p e r s i o n d i s a p p e a r s as firms move towards  then, the  s a d d l e p o i n t s o l u t i o n to t h e i r i n t e r t e m p o r a l maximization p r o b l e m . W h i l e M o r t e n s o n ' s model i s i l l u m i n a t i n g i n t h a t i t that,  given i m p e r f e c t  power,  it  i n f o r m a t i o n , firms e x h i b i t  i s p a r t i a l and does not r e f l e c t  of an i m p e r f e c t Salop  i n t e r t e m p o r a l monopsony  the i n h e r e n t  an i n t e r t e m p o r a l model of f i r m ' s  when faced w i t h a known q u i t r a t e which i s s o l e l y  l e v e l s of v a c a n c i e s  behaviour  a f u n c t i o n of  Formal s e a r c h b e h a v i o u r o f workers i s  L i k e M o r t e n s o n ' s model,the affect  stochasticity  l a b o u r market.  [1973b] develops  wage o f f e r .  demonstrates  a g a i n not  specified.  and unemployment, which  the q u i t r a t e and wage b e h a v i o u r o f o t h e r firms i n the  are c o n s t a n t . instantaneously  Also positions  of s t o c h a s t i c  r e q u i r e s t h a t firms face d i f f e r e n t a g a i n such d i s p e r s i o n d i s a p p e a r s  they are  behaviour.  t h i s d e t e r m i n i s t i c b e h a v i o u r on the p a r t of a l l p a r t i c i p a n t s ,  point solution.  industry,  c r e a t e d are not v a c a n c i e s , s i n c e  f i l l e d i n the absence  its  Given dispersion  l e v e l s of employment i n i t i a l l y and  as firms move towards  their  saddle  26 The c r u c i a l shortcoming of these models then i s t h a t , despite imperfect information and thus job search by i n d i v i d u a l s , the labour supply to the i n d i v i d u a l f i r m i s d e t e r m i n i s t i c .  Vacancy creation  and excess demand do not e x i s t . For u n f i l l e d p o s i t i o n s t o e x i s t , j o b creation must be s p e c u l a t i v e , that i s , the supply of labour to the f i r m must be subject to s t o c h a s t i c variation. D.  The Labour Market Viewed as a S t o c h a s t i c Process Reder [1968] develops a s t o c h a s t i c model of the labour market  characterised by imperfect information. Workers are faced w i t h a choice of heterogeneous jobs o f f e r i n g the same wage r a t e .  They q u i t  t h e i r jobs i n order to search f o r a p r e f e r a b l e one,but, through i n complete information,,they are not i n s t a n t l y re-employed.  Since there  i s no systematic preference f o r p a r t i c u l a r j o b s , each f i r m faces e s s e n t i a l l y the same labour supply schedule.  Firms create vacancies  i n a n t i c i p a t i o n of workers' turnover and acceptance behaviour. Aggregating over firms and i n d i v i d u a l s y i e l d s an e f f e c t i v e demand schedule f o r labour, D, and an e f f e c t i v e supply schedule, S. speculative demand f o r labour i s denoted by D'.  The  I t measures the  number of vacancies that must be created on average at a given wage, i n order t o generate employment given by the corresponding point on the e f f e c t i v e demand schedule.  Analogously, the S' schedule i n d i c a t e s  the number of workers who must search f o r a j o b at a given wage r a t e , i n order that the number represented by the S schedule be employed.  In t h i s  static  framework,  firms r e h i r e t h e i r l a b o u r f o r c e at  b e g i n n i n g of each p e r i o d and, i g n o r i n g p r e v i o u s experience,  they  offer  the same wage.  is  l a b o u r market  In s t o c h a s t i c  ON i n d i v i d u a l s a r e employed at wage r a t e , cW. g i v e n by N ^ - N , a n d aggregate v a c a n c i e s  the  equilibrium  Aggregate unemployment  by ^ - N .  Stochastic  e q u i l i b r i u m r e q u i r e s t h a t on average the number of  individuals  s  q u i t t i n g t h e i r jobs A priori,  equals  the number of new v a c a n c i e s  the average l e n g t h o f time a vacancy  i s open i s  r e l a t e d i n any p a r t i c u l a r way to the average p e r i o d o f Thus s t o c h a s t i c existence  equilibrium is  consistent  o f unemployment and v a c a n c i e s ,  them b e i n g i n d e t e r m i n a t e .  F i g u r e 3.  filled.  w i t h the  not  unemployment.  simultaneous  the r e l a t i o n s h i p  between  The model i s i l l u s t r a t e d i n F i g u r e  Stochastic  E q u i l i b r i u m i n R e d e r ' s Model  3.  28 Reder provides considerable i n s i g h t i n t o the nature of e q u i l i b r i u m i n an imperfect market,but the s t a t i c framework i s inappropriate.  He  f a i l s to formulate e x p l i c i t l y the behaviour of market p a r t i c i p a n t s or discuss how the market converges to e q u i l i b r i u m .  Search and thus  f r i c t i o n a l unemployment i n t h i s model are generated by non-systematic job  preferences rather than wage dispersion. Holjtj and David [1966] and Holt [1970] a l s o discuss the nature  of s t o c h a s t i c e q u i l i b r i u m i n the labour market without i n d i c a t i n g the  choice t h e o r e t i c foundations of market p a r t i c i p a n t s ' behaviour. Bergman [1973] develops a simulation model of an imperfect  labour market.  To test hypotheses about the impact of d i f f e r i n g  behaviour by male and female workers, she incorporates ideas from H o l t and David [1960], namely, that an unemployed person becomes l e s s fussy about the c h a r a c t e r i s t i c s of a job o f f e r as the period of unemployment increases and, l i k e w i s e , firms become less fussy about the c h a r a c t e r i s t i c s of job candidates and more w i l l i n g to increase the wage o f f e r , the longer a vacant p o s i t i o n remains u n f i l l e d . The labour market i s a d a i l y process. of job s l o t s .  Each employer has a f i x e d number  Each day a random s e l e c t i o n of employed workers q u i t  and become unemployed.  A number of candidates, dependent on the number  of unemployed workers, parade randomly past each vacant s l o t .  The  p r o b a b i l i t y that an employer w i l l o f f e r a candidate the vacant p o s i t i o n i s a function of the employer's length of search.  Likewise, the  p r o b a b i l i t y that an unemployed i n d i v i d u a l accepts a p o s i t i o n i s a function of h i s length of search.  Thus, some s l o t s remain open t i l l  the next day and some i n d i v i d u a l s remain unemployed.  Parameter v a l u e s number o f s l o t s ,  a r e chosen f o r the l a b o u r f o r c e s i z e ,  the  the t u r n o v e r and acceptance f u n c t i o n s o f workers  and the p r o b a b i l i t y o f o f f e r  f u n c t i o n o f employers.  The system  is  then s i m u l a t e d and each month a survey taken to measure unemployment and vacancy  rates  and the d u r a t i o n o f unemployment.  Bergman d e f i n e s  the s l o t  position available  (i.e.,  the l a b o u r f o r c e .  If  r a t e as the r a t i o o f the  both f i l l e d  the s l o t  the l e v e l o f unemployment i s  and u n f i l l e d )  total  to the s i z e  r a t e i s l e s s than 100 p e r c e n t ,  of  then  an i n c o r r e c t measure o f the l e v e l o f  f r i c t i o n a l unemployment, s i n c e n o t a l l i n d i v i d u a l s can be employed. The vacancy  rate i s  If  r a t e i s e q u a l to 100 p e r c e n t o r more, t h e n , she  all  the s l o t  the c o r r e c t measure o f f r i c t i o n a l unemployment. argues,  i n d i v i d u a l s i n the l a b o u r f o r c e c o u l d be employed and t o t a l  unemployment i s  the a p p r o p r i a t e measure o f f r i c t i o n a l unemployment.  She s t a t e s t h a t t h e amount o f unemployment a t t r i b u t a b l e s e a r c h i s low,even when t h e r e i s a h i g h r a t e o f t u r n o v e r . l a b o u r market, a s e p a r a t i o n  (when the s l o t  rate i s  fixed)  to  In  makes one  i n d i v i d u a l unemployed,but immediately opens up an o p p o r t u n i t y one o f the c u r r e n t l y unemployed, s i n c e s e p a r a t i o n s f i r m attempts t o f i l l  vacant s l o t s .  argues  rates  occur before  exhibiting different  d i s c r i m i n a t i o n i n h i r i n g by f i r m s .  t h a t the r a t i o o f unemployment r a t e s  of people i s  f o r the d i f f e r e n t  given by the r a t i o o f the p r o d u c t s o f the  and the employment r a t e s  for the  She c o n s i d e r s an i n t e g r a t e d  l a b o u r market w i t h groups o f i n d i v i d u a l s o f t u r n o v e r and no e x p l i c i t  this  o f each t y p e .  13  rates She types  separation  In some o c c u p a t i o n s ,  30 women have a higher turnover rate than men but, i f women compete equally with men f o r vacant p o s i t i o n s , these d i f f e r e n t rates of turnover are i n s u f f i c i e n t to generate the observed d i f f e r e n c e i n unemployment r a t e s .  She concludes that labour markets are to a  large degree segmented, so that i t i s the higher overcrowding or lower s l o t rates i n women's labour markets which generate t h e i r s i g n i f i c a n t l y higher rates of unemployment. Bergman points out that, i n t h i s world of s t o c h a s t i c behaviour, firms would speculate i n s l o t c r e a t i o n i n order t o secure t h e i r desired employment.  Thus^ Holt's measure of labour market tightness  [Holt, 1970] namely, vacancies/unemployment i s inappropriate and (desired-actual employment)/unemployment i s a b e t t e r measure of t i g h t n e s s , since the speculative elements of vacancy c r e a t i o n are purged.  There are, however, considerable sampling problems i n  obtaining such a measure. In arguing that an imperfect labour market behaves as a s t o c h a s t i c process and that conventional measures of excess demand are inappropriate due to speculative behaviour, Bergman has made an important c o n t r i b u t i o n . micro foundations  She f a i l s , however, to provide  explicit  of f i r m and worker behaviour and so her conclusions  must be subject to doubt.  I n the absence of wage and vacancy decisions  by f i r m s , i n response to t h e i r own experience and current labour market conditions, i t i s not evident that i n d i v i d u a l s choose t o remain unemployed, unless somehow wage d i s p e r s i o n e x i s t s or i n d i v i d u a l s e x h i b i t s p e c i f i c preferences  f o r d i f f e r e n t firms.  Likewise, unless workers  31 appear to be heterogeneous i n t h e i r capacity to perform the j o b , firms do not choose to leave vacant p o s i t i o n s u n f i l l e d .  A model  i n which firms, aware of d i f f e r e n c e s i n labour market behaviour by recognisable groups of i n d i v i d u a l s , are able to d i s c r i m i n a t e , generates d i f f e r e n t conclusions, perhaps.  In Model I I I , which i s  analysed i n Chapter 2 IC3, firms can recognise systematic d i f f e r e n c e s i n i n d i v i d u a l s ' labour market behaviour and d i s c r i m i n a t e . A l l these models are characterised by the absence of any choice t h e o r e t i c foundations f o r i n d i v i d u a l market p a r t i c i p a n t s ' behaviour. As Rothschild [1973] points out, models of d i s e q u i l i b r i u m behaviour do not make sense,unless they meet c e r t a i n standards of coherence and consistency.  He argues that e x i s t i n g models of adjustment to  e q u i l i b r i u m s a c r i f i c e a d i s c u s s i o n of rules that market p a r t i c i p a n t s adopt out of e q u i l i b r i u m , f o r a d e s c r i p t i o n of how the market operates 14 i n response t o i n d i v i d u a l behaviour and a convergence theorem. E.  The Vacancy Concept A r c h i b a l d [1954] develops a simple monopsony model i n which the  f i r m maximises short run p r o f i t s .  He a t t r i b u t e s the r i s i n g labour  supply schedule faced by the f i r m , e i t h e r to the preference of workers f o r p a r t i c u l a r j o b s , or to the large s i z e of the f i r m .  Short  run p r o f i t maximisation leads the f i r m to h i r e labour up to the point at which marginal revenue product equals marginal c o s t s . The f i r m h i r e s L workers a t wage, w, and e x p l o i t s labour through not paying i t i t s marginal revenue product, namely w*. i s shown i n Figure 4.  The firm's d e c i s i o n problem  32  w MC  0  L  Figure 4  if  L  The F i r m ' s D e c i s i o n Problem i n A r c h i b a l d ' s model  A r c h i b a l d argues  t h a t the  could r e c r u i t  costlessly  it  demonstrate  f i r m would c r e a t e at wage r a t e , w.  vacancies, He was  t h a t e q u i l i b r i u m i n the l a b o u r market a t  was c o n s i s t e n t Hansen's  L  x  w i t h an excess of v a c a n c i e s  Burgess  full  employment was  [1969] argues  trying  offer.  incorrect.  t h a t the concept  it  t o improve s e a r c h e r s '  Given t h a t the f i r m i s  has some knowledge  argues prefers  of i t s  of v a c a n c i e s  is  advertising  p r o f i t maximising p o s i t i o n , (w,L),  labour supply schedule.  supply of  incorrect.  i n f o r m a t i o n , n o r i n c r e a s i n g t h e wage  at i t s  t h a t measuring v a c a n c i e s a more e l a s t i c  Thus,  inflationary  The f i r m i s u n w i l l i n g t o i n c u r c o s t s of r e c r u i t i n g , n e i t h e r expenditure  to  the r u l i n g wage  over unemployment.  [1953] use o f excess demand as a measure of  p r e s s u r e at  L^-L,  as L ^ - L labour.  is  to i n f e r  Myers  [1968]  t h a t the  firm  33 Devine and Marcus [1967] demonstrate t h a t , i n t h i s s t a t i c framework, i f the f i r m can choose both i t s wage o f f e r and l e v e l of r e c r u i t i n g costs, then Archibald's r e s u l t s t i l l holds.  Job vacancies  are consistent w i t h monopsony e q u i l i b r i u m , both w i t h respect to wage o f f e r and recruitment costs.  Now S i s i n t e r p r e t e d as the schedule  r e l a t i n g the wage o f f e r to the number of i n d i v i d u a l s prepared to work, given that at each l e v e l of employment the f i r m chooses i t s cost minimising combination of wage o f f e r and recruitment costs (advertising).  MC represents the o v e r a l l marginal costs, namely  marginal wage costs and marginal recruitment costs.  Vacancies,  L^-L, w i l l be created and the f i r m i s u n w i l l i n g to o f f e r a higher wage or spend more on recruitment.  Burgess again claims that such  vacancies are i l l u s i o n a r y , since firms w i l l not even i n c u r costs of an i n t e r v i e w .  In the absence of p r o h i b i t i v e i n t e r v i e w costs,  t h i s a s s e r t i o n i s untrue.  The desired employment l e v e l i s that  l e v e l bf employment at which the marginal cost of h i r i n g  another  worker, namely the p r o f i t maximising wage, w, plus the interview costs, equals the marginal revenue product.  In t h i s model, reported  vacancies equal desired employment minus the p r o f i t maximising  level  of employment. I t i s questionable whether t h i s concept of vacancies i s l e g i t i m a t e i n t h i s framework.  The supply schedule i n the A r c h i b a l d  and Devine and Marcus models shows the number of workers who would show up at the f i r m and are hired,given the wage o f f e r and the l e v e l of r e c r u i t i n g costs.  The f i r m makes i t s optimal wage o f f e r and the  34 number of i n d i v i d u a l s represented by the corresponding p o i n t on the supply schedule are h i r e d . Both authors are now asking the question:i f some v a r i a t i o n i n h i r e s i s p o s s i b l e at t h i s wage r a t e , what l e v e l of vacancies would the f i r m create?  I t i s wrong to consider s t o c h a s t i c  v a r i a t i o n i n h i r e s at the optimal wage r a t e alone.  I f there i s im-  perfect information i n the market, then the whole schedule would be subject t o s t o c h a s t i c v a r i a t i o n and the r e s u l t i n g optimal wage d e c i s i o n may w e l l be d i f f e r e n t . These models h i g h l i g h t a severe p r a c t i c a l problem i n d e f i n i n g a vacancy.  I t i s agreed that employers should be a c t i v e l y r e c r u i t i n g  to f i l l a p o s i t i o n i n order that i t should c l a s s i f y as a vacancy. I n the Devine and Marcus model, firms are spending a f i x e d sum on r e c r u i t ment to improve workers' information,but the volume of expenditure does not i n d i c a t e the number of p o s i t i o n s f o r which i t i s a c t i v e l y r e c r u i t i n g . The marginal cost of a d v e r t i s i n g another vacancy i s zero. Attempts to formalise the vacancy concept i n t h i s s t a t i c framework are u n s a t i s f a c t o r y and misleading. interdependence  Since there i s no intertemporal  i n a one period model, firms are forced to r e h i r e t h e i r  labour forces each p e r i o d .  These s o - c a l l e d vacancies represent the  magnitude of the misperceptions of the f i r m about the labour supply forthcoming at the p a r t i c u l a r wage. I t creates  p o s i t i o n s based on  i t s perception of the labour supply schedule and L are f i l l e d .  If i t  knew about the nature of the labour supply schedule w i t h c e r t a i n t y , then i t would create L p o s i t i o n s which would be instantaneously f i l l e d .  35 Hold and David [1966] define a vacancy as a job w i t h requirements s p e c i f i e d f o r which the f i r m i s a c t i v e l y r e c r u i t i n g .  Vacancies equal  the number of men who would be h i r e d today, but not n e c e s s a r i l y to s t a r t , i f they had the same s k i l l and wage requirements as those the company recently h i r e d to f i l l corresponding p o s i t i o n s .  There i s the  small problem of t e c h n i c a l change generating job vacancies representing new s k i l l requirements. The unemployed i n d i v i d u a l i s one who : 1.  I s a c t i v e l y searching; and  2.  I f asked i s prepared to work at h i s best previous job.  The l a t t e r condition ensures that the concept of unemployment r e l a t e s to job search alone rather than a l l instances of i n a b i l i t y to f i n d work at reasonable wages.  P r o v i s i o n must be made that the  m a n . s t i l l q u a l i f i e s f o r h o l d i n g the o l d job, i f offered.  Gilpatrick  [1966] points out that t h i s d e f i n i t i o n implies that workers displaced by t e c h n o l o g i c a l change do not q u a l i f y as unemployed,since w i l l not be offered to them.  the o l d job  I f the 'best previous job' should s t i l l  e x i s t , then those s t r u c t u r a l l y unemployed are not included i n the Holt and David d e f i n i t i o n , and G i l p a t r i c k i s correct. Hold and David require that the i n d i v i d u a l be searching f o r employment at reasonable wages.  This appears to exclude those  i n d i v i d u a l s who q u i t t h e i r jobs b e l i e v i n g that the general l e v e l of wages i s higher than t h e i r current wage.  At best, t h e i r d e f i n i t i o n  36 covers those searchers with reasonable wage demands who are unemployed through inadequate demand or s t r u c t u r a l changes or because of imperfect information as to the existence of s u i t a b l e vacancies.  An i n d i v i d u a l  who a c t i v e l y searches, can be f r i c t i o n a l l y unemployed through sampling firms w i t h no vacancies, or through misperceiving the wage d i s t r i b u t i o n , or both.  Holt and David's d e f i n i t i o n , then, seems to exclude searchers  with unreasonable wage requirements. At the p r a c t i c a l l e v e l , then, H o l t and David's measures of unemployment and vacancies r e q u i r e extensive sampling of firms to obtain information about wage o f f e r s and the number of p o s i t i o n s they wish to f i l l a t that wage o f f e r .  A homogeneous measure of t o t a l vacancies  requires that the vacancies aggregated over firms be homogeneous both i n the wage offered and the s k i l l s r e q u i r e d . Thus, i f any wage d i s persion e x i s t s i n a labour market, homogeneous i n the s k i l l s of i t s labour f o r c e , i t i s necessary to construct some measure of a market wage.  The unemployed are asked the h y p o t h e t i c a l question as t o  whether they would a c t i v e l y search given t h i s market wage. L i k e w i s e , firms are asked how many vacancies they would create at t h i s market wage r a t e . For p r a c t i c a l purposes, i n d i v i d u a l s without work f o r seven days are c l a s s i f i e d as unemployed.  A compatible d e f i n i t i o n of a vacancy  i s required. While unemployment i s a d i s t i n c t and recognisable s t a t e for the i n d i v i d u a l (again ignoring the a c t i v e search d e f i n i t i o n ) , the existence of a vacancy i s l e s s w e l l defined. An employer, not a c t i v e l y recruiting,may create a p o s i t i o n f o r a w e l l q u a l i f i e d a p p l i c a n t .  37 A l t e r n a t i v e measures are open to an employer with an i n s u f f i c i e n t labour force, namely : 1.  He can i n s t i g a t e overtime;  2.  He can subcontract the work elsewhere;, and  3.  He can purchase a d d i t i o n a l machinery, that i s c a p i t a l deepening, and make h i s labour force more productive.  F.  Conclusion As i n d i c a t e d throughout the s e c t i o n , the l i t e r a t u r e on im-  p e r f e c t markets has f a i l e d t o model i n d i v i d u a l behaviour based on micro-theoretic foundations, i n response to the perceived environment and the behaviour of other market p a r t i c i p a n t s .  Furthermore, how the  market operates i n response t o such behaviour i s not s p e c i f i e d .  The  shortcomings w i l l be f u r t h e r examined and emphasised i n the next chapter i n which the b a s i c t h e o r e t i c a l framework i s discussed. V. A.  The L i t e r a t u r e on D i s c r i m i n a t i o n  A Summary The l i t e r a t u r e on models of d i s c r i m i n a t i o n can be sub-divided  i n t o three areas : 1.  Models examining the impact of f a i r employment laws on wage rates and employment;  2.  Models of d i s c r i m i n a t i o n based on employer p r e j u d i c e ; and  3.  Models of d i s c r i m i n a t i o n based on imperfect information.  38 B.  The Impact of F a i r Employment Laws In h i s model of f i r m behaviour, Salop [1973] presents two  explanations of the impact of d i f f e r e n t turnover rates by i n d i v i d u a l s on t h e i r respective wage o f f e r s .  He suggests that workers w i t h a low  q u i t rate command high wages because t h e i r f i x e d costs of employment may be amortised over a longer period of time.  On the other hand,  i n d i v i d u a l s w i t h a low marginal q u i t rate w i l l be d i s c r i m i n a t e d against i n wage o f f e r because they have fewer a l t e r n a t i v e job opportunities. The p a r t i a l e q u i l i b r i u m framework he adopts i s inappropriate to model d i s c r i m i n a t i n g f i r m behaviour whence h i s arguments cannot be evaluated.  These explanations are, however, the ad hoc arguments  presented by economists  to e x p l a i n wage d i f f e r e n t i a l s generated by  d i f f e r e n t i a l rates of turnover by members of the labour force. I t i s a l l e g e d , f o r example, by Women's Bureau [1969], that women factory operatives have a higher rate of turnover than t h e i r male counterparts.  Sanborn [1964] attempts to analyze the factors causing  the observed wage d i f f e r e n t i a l s between men and women. He argues, l i k e Salop, that,since men have a longer period of job tenure, t h e i r f i x e d costs of employment are amortised over a longer period of time. Consequently, i n the absence of d i s c r i m i n a t i o n , through prejudice or ignorance, men should earn more than women, i f firms behave r a t i o n a l l y and d i s c r i m i n a t e .  Unfortunately, Sanborn does not present a formal  model t o support h i s conclusions.  39 Demsetz who s u f f e r welfare  [1965] argues  t h a t some laws designed t o a i d m i n o r i t i e s  from d i s c r i m i n a t i o n have the o p p o s i t e e f f e c t .  of these i n d i v i d u a l s i s r e d u c e d .  The economic  He c o n s i d e r s a w o r l d i n  which employers have a s y s t e m a t i c  preference  f o r h i r i n g from a  p a r t i c u l a r group of i n d i v i d u a l s .  A n o n - p r e f e r r e d job a p p l i c a n t  a lower wage than i s r e c e i v e d by h i s p r e f e r r e d , but e q u a l l y f e l l o w worker.  productive,  The employer r e c e i v e s w e a l t h compensation f o r employing  a non-preferred i n d i v i d u a l .  If  a minimum wage law i s imposed, then  employer cannot h i r e a n o n - p r e f e r r e d worker at l e s s wage.  earns  the  than the minimum  He i s p r o h i b i t e d from r e c e i v i n g w e a l t h compensation from a n o n -  preferred i n d i v i d u a l . on the b a s i s  Consequently,  he w i l l choose between  of t h e i r p e r s o n a l c h a r a c t e r i s t i c s .  applicants  N o n - p r e f e r r e d workers  w i l l be f o r c e d t o seek l e s s d e s i r a b l e p o s i t i o n s i n o c c u p a t i o n s c o v e r e d by the law,  or w i l l become unemployed.  Those n o n - p r e f e r r e d  i n d i v i d u a l s who e a r n above minimum wages, but l e s s w o r k e r s , do not b e n e f i t to r e c e i v e w e a l t h  not  from the minimum wage laws.  than t h e i r  fellow  Firms c o n t i n u e  compensation f o r employing them.  Demsetz then c o n s i d e r s the f a i r employment laws enacted i n some s t a t e s i n the U . S . A .  S i n c e u p h o l d i n g the law i s expensive  dependent on s u b j e c t i v e that the p e n a l t i e s  e v a l u a t i o n o f a f i r m ' s b e h a v i o u r , he  to v i o l a t o r s w i l l be s m a l l .  i m p o s i t i o n of such laws w i l l have l i t t l e practices  of f i r m s .  and argues  He suggests that  impact on the  employment  He s u p p o r t s t h i s c o n c l u s i o n w i t h evidence  over t i m e , the r a t i o s of the unemployment r a t e s  the  that,  of b l a c k and w h i t e  40 workers i n states i n which f a i r employment have been enacted do not s i g n i f i c a n t l y d i f f e r from the r a t i o s of unemployment rates i n other states. In Model III, firms a c t i v e l y d i s c r i m i n a t e i n both wage o f f e r and h i r i n g against type one i n d i v i d u a l s who are l e s s valuable to them. I n Model I I , firms are forced t o make ex ante wage and vacancy c r e a t i o n decisions and make job o f f e r s randomly t o searchers. employment' laws do r e s u l t i n non-discriminatory  Thus, the ' f a i r  hiring practices.  Both types of i n d i v i d u a l s earn higher wages and incomes i n Model I I . The question a r i s e s as to whether the non-preferred type one i n d i v i d u a l s enjoy an increase i n t h e i r share of labour income under f a i r employment laws. C.  Employer D i s c r i m i n a t i o n based on Prejudice Most t h e o r e t i c a l models of labour market d i s c r i m i n a t i o n are developed  i n a s t a t i c u t i l i t y maximising framework ( f o r example, Becker [1956]; Arrow [1972]; and Freeman [1973]).  Black employees are discriminated  against i n the wage offered because of the d i s u t i l i t y experienced by whites employing them or working with them.  This s e c t i o n w i l l focus on  models of employer d i s c r i m i n a t i o n . Becker [1956] argues that, i f an i n d i v i d u a l has a taste f o r d i s c r i m i n a t i o n , then he must be prepared t o pay f o r i t . He states that d i s c r i m i n a t i o n a r i s e s through a lack of o b j e c t i v i t y i n the market place.  He distinguishes between prejudice and ignorance.  I f , f o r example, employers b e l i e v e erroneously  that negroes have a  lower p r o d u c t i v i t y than whites, then t h e i r behaviour would be d i s -  41  criminatory but caused by ignorance. eliminate t h i s d i s c r i m i n a t i o n .  The spread of knowledge would  I f employers d i s c r i m i n a t e ,  t h e i r knowledge that blacks are equally productive, prejudiced.  despite  then they are  This preference i s independent of knowledge about the  p r o d u c t i v i t y of the workforce. By t h i s d e f i n i t i o n , a more appropriate  d e s c r i p t i o n of Models I I  and I I I might be "Models of I n t e r and Intra-Firm E x p l o i t a t i o n " . I n d i v i d u a l s are exploited.or discriminated against not through prejudice or ignorance on the part of firms, but because of the objective evidence that they d i f f e r s y s t e m a t i c a l l y i n t h e i r market behaviour and can be recognised. Becker q u a n t i f i e s the tastes and preferences of d i s c r i m i n a t o r s by d e f i n i n g a d i s c r i m i n a t i o n c o e f f i c i e n t , d.  A f i r m f a c i n g a money  wage, I T , f o r a f a c t o r of production behaves as i f the wage was Tf(l+d). He considers a labour force c o n s i s t i n g of two groups, negroes, and whites, who are p e r f e c t s u b s t i t u t e s i n production and receive wages T T ^ and ir^ r e s p e c t i v e l y .  The i " * 1  1  employer has a f i x e d c o e f f i c i e n t of  d i s c r i m i n a t i o n , d^, against i n d i v i d u a l s i n group N.  Then, i f the  market wage, T T ^ , i s l e s s than ir^Cl+d^ , the i * " * employer w i l l 1  h i r e group W workers.  only  I f ir^. exceeds ir^Cl+d^), then only group N th  workers are h i r e d by the i  employer.  I f ir^ equals ir^(l+d^) , the  til  i  employer i s i n d i f f e r e n t as t o the composition of h i s labour force.  The market d i s c r i m i n a t i o n c o e f f i c i e n t d s a t i s f i e s (7)  42 If  the d i s c r i m i n a t i o n c o e f f i c i e n t s  vary over e m p l o y e r s ,  then  most firms w i l l be s e g r e g a t e d and m a r g i n a l f i r m s , whose d i s c r i m i n a t i o n coefficient  equals  the market d i s c r i m i n a t i o n c o e f f i c i e n t ,  mixed l a b o u r f o r c e s .  The market d i s c r i m i n a t i o n  w i l l have  coefficient  r e l a t e d t o the d i s t r i b u t i o n of d i s c r i m i n a t i o n c o e f f i c i e n t s  w i l l be  and the  supplies  of each f a c t o r .  The demand curve f a c i n g the d i s c r i m i n a t e d  group i s  downward s l o p i n g as a d d i t i o n a l workers seek employment w i t h  i n c r e a s i n g l y d i s c r i m i n a t i n g employers. If  the supply of  group N workers i n c r e a s e s ,  then IT w i l l  fal\.  because d i s c r i m i n a t i n g firms have to be compensated f o r employing group N w o r k e r s .  A segregated white  firm,  f i r m i , s a y , w i l l now  d i s c o v e r t h a t the r e a l c o s t o f h i r i n g group N w o r k e r s , namely TT (l+d^), N  is  l e s s than the wage p a i d t o a w h i t e w o r k e r .  Consequently,  the f i r m w i l l f i r e a l l i t s white workers and employ s o l e l y b l a c k w o r k e r s . T h i s ad hoc approach i s an u n s a t i s f a c t o r y phenomena.  way to model any economic  An economic model of d i s c r i m i n a t i o n s h o u l d attempt to e x p l a i n  the e x i s t e n c e of d i s c r i m i n a t i o n through the f o r m u l a t i o n o f i n d i v i d u a l and firm behaviour.  Becker has imposed the e x i s t e n c e of wage d i s c r i m i n a t i o n  through the s p e c i f i c a t i o n  of the c L ' s which are n o t j u s t i f i e d by any  r a t i o n a l b e h a v i o u r on the p a r t of l a b o u r market p a r t i c i p a n t s . i s p a r t i a l i n t h a t the b e h a v i o u r o f firms and workers i s n o t specified.  H i s model formally  In a d d i t i o n , the p r e d i c t i o n s of t h i s model are n o t  with casual observation.  compatible  The l a b o u r f o r c e i s n o t s e g r e g a t e d by f i r m and  firms do n o t f i r e one w o r k f o r c e ,  say  group i f workers a n d ' h i r e a new group  N workforce i n response to a change i n f a c t o r  :  prices."^  43 Arrow [1972] formally models d i s c r i m i n a t i o n i n the labour market,, but he too adopts ah ad hoc approach.  I n adopting t h i s s p e c i f i c a t i o n ,  however, he demonstrates the i n t e r n a l c o n t r a d i c t i o n s of the model.  He  argues that the i n d i v i d u a l employer's d i s c r i m i n a t i o n c o e f f i c i e n t depends on the number of black and white employees, rather than being f i x e d and independent of the number of black and white employees.  He assumes  that firms face the same production functions, produce one commodity and h i r e black and white labour who  are p e r f e c t s u b s t i t u t e s i n  production and i n e l a s t i c a l l y supplied.  The a n a l y s i s i s short run  and labour i s the only v a r i a b l e f a c t o r of production.  I f W and N are  the amounts of white and black labour h i r e d by the f i r m , then output i s given by f(W + N). n where  =  P r o f i t s of the f i r m are  f (W + N) - W W - W N W N T T  and  ....  (8)  are the wages of white and black workers r e s p e c t i v e l y .  The representative f i r m wishes to maximise a u t i l i t y function whose arguments are p r o f i t s and the degree of a s s o c i a t i o n with black and white workers. %  >  W  >  0  U  <  0 .  U  N  U(jl , W, N) denotes the u t i l i t y function and ;  0  ....  (9)  Since firms are i d e n t i c a l , each w i l l choose the same number of W and N i n e q u i l i b r i u m . S o l v i n g the f i r s t order conditions f o r a maximum y i e l d s  44  V ' "V f  V ' -V f  +  U  +  W  U  =  N  =  0  0  • • • •  < >  • • • '  < >  10  U  and so  f  1  =  W + ^ w  =  W +  . . . .  N  (12)  where  ^  =  " v  —  N = - fj- .  ( 1 3 )  U  djj  . . . .  (14)  •it}  d^ and d^ a r e B e c k e r ' s d i s c r i m i n a t i o n c o e f f i c i e n t s . efficient  because firms h i r e an e q u a l number of w o r k e r s .  assumption o f i d e n t i c a l p r o d u c t i o n f u n c t i o n s condition for efficiency  is relaxed,  If  the  then a  i s t h a t cL^ and d^ a r e the same f o r a l l  who employ a mixed l a b o u r f o r c e i n e q u i l i b r i u m . is  Production i s  A sufficient  firms  condition  t h a t d^ and dL^ a r e c o n s t a n t and independent of the arguments o f  utility  function.  This i s equivalent  to s p e c i f y i n g  the  a linear u t i l i t y  f u n c t i o n , w h i c h i s p r e c i s e l y the model developed by B e c k e r . D i s c r i m i n a t i o n by white employers thus l e a d s t o a p e c u n i a r y r e d i s t r i b u t i o n from b l a c k workers to the white d i s c r i m i n a t i n g employers.  community o f workers and  White workers earn an a d d i t i o n a l - d ^ per  man, w h i l e d i s c r i m i n a t i n g employers face a change i n p r o f i t s  of  N*d^ + W*d^,where N * and W* denote the number o f b l a c k and white workers employed by the f i r m i n e q u i l i b r i u m .  The e x p r e s s i o n f o r  the  45 change i n p r o f i t s has indeterminate  sign.  E q u i l i b r i u m i n t h i s model  then i s characterised by mixed labour forces.  In a response to a  change i n f a c t o r p r i c e s , f i r m s change the r e l a t i v e composition of t h e i r workforce. I t i s assumed t h a t , i n the long run, firms have access to perfect c a p i t a l markets.  For a given labour force, the f i r m borrows optimally  at the long run rate of i n t e r e s t to purchase c a p i t a l .  I f the production  function displays constant returns to c a p i t a l and labour, then the c a p i t a l labour r a t i o i s a unique function of the rate of i n t e r e s t . Let the production f u n c t i o n , f-(W + N), represent output a f t e r the optimal a c q u i s i t i o n of c a p i t a l .  Then, t h i s derived function displays  constant returns to labour. I f firms have d i f f e r e n t u t i l i t y f u n c t i o n , then implausible conclusions emerge. types of labour.  f  '  f•  <  w  w  < W  N  +  *w  E q u i l i b r i u m conditions become  w  i f  + djj  I t i s no longer necessary that firms employ both  if  =  N  0  =  f  0  '  =  f*  w  w  =  +  ^  i f  Wjj+djj  w  if  > °* N>0,  •• •  ( 1 5 a )  . ._.  (15b)  Since e q u i l i b r i u m implies f u l l employment, these e q u a l i t i e s hold f o r at l e a s t one f i r m .  Hence, a l l whites are employed i n firms i n which  d*^ i s the algebraic minimum and blacks are employed i n firms i n which i f i s a minimum. then d^j = 0. d^ = 0.  I f some firms do not discriminate against b l a c k s ,  Therefore from (15b),for a l l firms who employ b l a c k s ,  Then, there i s a black and white wage d i f f e r e n t i a l , i f  < 0.  46 But, i t i s reasonable to postulate that any preference a f i r m has f o r h i r i n g whites a r i s e s as a r e s u l t of the presence of d i s l i k e d blacks.  Furthermore, i t can be argued that, i f a f i r m does not  discriminate against black workers, i t does not pay whites any more. Then, N = 0 o r cL = 0 implies ci^ = 0. firms, d^ = 0 f o r a l l firms. f  =  W  w  =  Since cL = 0 o r N = 0 f o r a l l  Thus,  W  . . . . (16)  N  and there i s no d i s c r i m i n a t i o n . A more concise but s i m i l a r argument for no d i s c r i m i n a t i o n i n the long run i s that, given constant returns to labour, the non-discriminating but more p r o f i t a b l e firms drive out d i s c r i m i n a t i n g firms, i f c a p i t a l markets are p e r f e c t . Freeman [1973] argues t h a t , i f owners of firms who discriminate are prepared to accept a lower r e t u r n , then d i s c r i m i n a t i o n p e r s i s t s . This i s c l a s s i f i e d as a c a p i t a l market imperfection. In a s i m i l a r framework, i t i s p o s s i b l e to model f i r m behaviour given white employees' d i s c r i m i n a t i o n against f e l l o w black workers. White workers demand a wage r e l a t e d to the degree of a s s o c i a t i o n with black workers.  I f whites and blacks are s u b s t i t u t e s i n production  and employees do not d i s c r i m i n a t e , then e q u i l i b r i u m i s characterised by segregation and no wage d i s c r i m i n a t i o n .  Employers minimise the  cost of h i r i n g white workers by segregating the labour force.  In  e q u i l i b r i u m they are i n d i f f e r e n t between h i r i n g a black or a white •labour force.  Thus, there are no wage d i f f e r e n t i a l s .  I f black and  47 white workers are complementary i n production and white employers or workers d i s c r i m i n a t e , then wage d i f f e r e n t i a l s p e r s i s t . The existence of wage d i f f e r e n t i a l s provides a return t o nond i s c r i m i n a t i n g behaviour.  The higher p r o f i t s or incomes earned by  non-discriminating employers or employees c o n s t i t u t e an i n c e n t i v e to increase t h e i r respective supplies over time.  I n p a r t i c u l a r , the  supply of black employers and employees w i l l increase.  I f the supply  of non-discriminating employers and employees increases,then wage d i f f e r e n t i a l s w i l l disappear i n the long run.  Freeman argues that  the problem of. e x p l a i n i n g economic d i s c r i m i n a t i o n i n the long run t r a n s l a t e s i n t o the problem of .explaining l i m i t a t i o n s on the supply of non-discriminating (black) employers or l i m i t a t i o n s on t h e i r market behaviour.  He argues that there are three ways i n which governmental  d i s c r i m i n a t i o n and p o l i c i e s can influence the r e l a t i v e p o s i t i o n of blacks i n the labour market, namely : 1.  By a f f e c t i n g black human c a p i t a l formation through d i s c r i m i n a t i o n i n p u b l i c education;  2.  By d i s c r i m i n a t i o n f o r and against blacks i n p u b l i c employment, and, l e s s d i r e c t l y , i n employment by p u b l i c contractors, and  3.  By l e g a l regulations of d i s c r i m i n a t o r y p r a c t i c e s i n the market and a p p l i c a t i o n s of laws p e r t a i n i n g to employment and income."^  48 D.  D i s c r i m i n a t i o n based on Imperfect  Information  In the models formulated by Becker and Arrow and Freeman, i t i s assumed that black and white workers are p e r f e c t s u b s t i t u t e s i n production and that firms have p e r f e c t information about p r i c e s , marginal products and other relevant v a r i a b l e s .  Such information i s not  a c t u a l l y possessed by employers producing i n an environment characterised by uncertainty and costs of search.. I f i t i s b e l i e v e d that the producti v i t y of blacks and whites d i f f e r , but not i n a systematic fashion, then an assessment of an i n d i v i d u a l ' s p r o d u c t i v i t y may be expensive.  McCall  argues that firms w i l l attempt to u t i l i z e r e l a t i v e l y c o s t l e s s information devices such as age, sex and race i n the h i r i n g d e c i s i o n .  This  screening  by employers leads to d i s c r i m i n a t i o n i n h i r i n g . In Models I I and I I I , by contrast, firms know that i n d i v i d u a l s d i f f e r i n t h e i r labour market behaviour i n a systematic fashion.  Intra-  f i r m wage and h i r i n g d i s c r i m i n a t i o n i s p r a c t i s e d , i f the f i r m recognises d i f f e r e n t i n d i v i d u a l s p r i o r t o h i r i n g and i f they are allowed t o discriminate. In McCall's model,the f i r m wishes t o minimise the cost of h i r i n g one s u c c e s s f u l employee, that i s an employee with a marginal product i n excess of some prescribed m*.  Using h i s n o t a t i o n , i f the expected  costs of f i n d i n g and evaluating a white and a black worker are c^ and C 2 , r e s p e c t i v e l y , and i f p^, p  2  r e s p e c t i v e l y denote the expected p r o b a b i l i t y  of h i r i n g a s u i t a b l e candidate, then the f i r m chooses i t o minimise _ i i = 1, 2.  The expected number of candidates of type i a f i r m  ^  must interview i s 1/p.. and each interview costs c_.. The f i r m r e v i s e s  i  49 its  estimates of  and  i n B a y e s i a n f a s h i o n by i n c o r p o r a t i n g the  i n f o r m a t i o n gained by employing d i f f e r e n t At any p o i n t i n t i m e , t h e n , t h e M c C a l l argues productivity will  that,  individuals.  f i r m makes a [ 0 , 1 ] • d e c i s i o n .  as the l a b o u r market t i g h t e n s ,  the  average  o f the w h i t e unemployed p o o l w i l l f a l l , s i n c e the p o o l  c o n t a i n an i n c r e a s i n g number o f i n d i v i d u a l s who have f a i l e d  be employed i n o t h e r firms or have been f i f e d .  to  At some p o i n t ,  experiments w i t h non-white employees w i l l b e g i n as p r i o r  assessments  are r e v i s e d .  is  If  the e x p e r i e n c e w i t h non-white employees  successful,  then the use o f c o l o u r as a s c r e e n i n g d e v i c e may be d i s c o n t i n u e d . T h i s model, though i n t e r e s t i n g , ants  of c^ and  i s p a r t i a l i n t h a t the  are not f o r m u l a t e d .  The r e s p e c t i v e  e v a l u a t i n g i n d i v i d u a l s a r e random v a r i a b l e s  costs of  and are determined by  the i n t e r a c t i o n of f i r m and i n d i v i d u a l s e a r c h b e h a v i o u r . w i l l depend on the r e l a t i v e  supplies  absence o f t h e f u l l s p e c i f i c a t i o n  determin-  These  of unemployed s e a r c h e r s .  costs In  o f the l a b o u r m a r k e t , i t i s n o t  how t h i s d i s c r i m i n a t i o n i n h i r i n g i n f l u e n c e s  the clear  the wages o f white and  black workers. M c C a l l models s e p a r a t e l y  the s e a r c h b e h a v i o u r of i n d i v i d u a l s .  A g a i n u s i n g h i s n o t a t i o n ^ c denotes x is  the c o s t p e r p e r i o d of  a random v a r i a b l e d e n o t i n g the wage o f f e r f u n c t i o n of o f f e r s .  search,  and <f>(x) i s the p r o b -  ability  density  Then, the r e s e r v a t i o n or  wage e,  f o r an unemployed i n d i v i d u a l s , s a t i s f i e s  the  acceptance  equation  oo c  = /  (x-e)<Kx)dx. e  where H ' ( e )  < 0.  =  H(e)  . . . .  (17)  50. L e t e^ denote C Q = HCeg).  If  the r e t u r n s from r e m a i n i n g unemployed and s e t  the c o s t  of search,  at a l l i s  the b e s t s t r a t e g y .  c > CQ is  less  to accept  an o f f e r  than e^.  c,  > e*,is  c  =  and the wage o f f e r  account  that  costs of search are higher for  d i s t r i b u t i o n for blacks  o f white  (18)  blacks  18  i s i n f e r i o r to t h a t  He s t a t e s t h a t  t h e r e a r e no s y s t e m a t i c  w i l l not p e r s i s t .  in their productivity,  t h i s k i n d resembles two f a c t o r s  labour  these  of  factors  dropouts.  differences  19  in  the  and b l a c k w o r k e r s , t h e n s c r e e n i n g w i l l cease  and wage d i f f e r e n t i a l s  Clearly,  i f whites  and  then a l o n g run model o f  a model o f f i r m b e h a v i o u r i n which t h e r e  are  of p r o d u c t i o n .  In the absence search behaviour, It  . . . .  of d i s c r i m i n a t i o n .  do d i f f e r  Thus,  remain f r i c t i o n a l l y unemployed, u n t i l  H(e*)  I n the l o n g r u n , i f  blacks  t o drop out of the  f o r the d i s p r o p o r t i o n a t e number o f non-white  productivity  for  r e c e i v e d where  McCall asserts  w h i t e s because  (17)  than the r e t u r n s from n o t s e a r c h i n g .  c > C Q , otherwise,  an o f f e r , x  searching  the i n d i v i d u a l i s p r e p a r e d  the d e c i s i o n r u l e f o r the i n d i v i d u a l i s force,if  then not  The v a l u e o f e s a t i s f y i n g  Consequently,  less  exceeds e^,  i s evident  of simultaneous m o d e l l i n g o f f i r m and i n d i v i d u a l  it  i s i m p o s s i b l e to d i s c u s s market e q u i l i b r i u m .  though t h a t  t o the amount t h a t  the wage d i f f e r e n t i a l  firms on average b e l i e v e  between b l a c k and white  workers.  observed i s  related  that p r o d u c t i v i t i e s  differ  51. E.  Conclusion In conclusion, most models of d i s c r i m i n a t i o n are based on a  u t i l i t y theory approach.  This approach i s u n s a t i s f a c t o r y because  the existence of any economic phenomenon can be j u s t i f i e d by the s p e c i f i c a t i o n of a u t i l i t y f u n c t i o n . I t does provide a framework, however, i n which simple models can be formulated and p r e d i c t i o n s compared to observation. the models.  Arrow underlines the i n c o n s i s t e n c i e s of  In p a r t i c u l a r , given p e r f e c t c a p i t a l markets and  unlimited supplies of non-discriminating i n d i v i d u a l s , wage d i f f e r e n t i a l s disappear i n the long run.  These aire models of d i s c r i m i n a t i o n through  prejudice.  M c C a l l s model i s a model of d i s c r i m i n a t i o n generated by  ignorance.  I n the long run, i n the absence of exogeneous changes i n  1  the labour market, wage d i f f e r e n t i a l s w i l l r e f l e c t true d i f f e r e n c e s in productivity. VI.  The Thesis  In my t h e s i s , I wish t o answer the questions posed i n I I I , by s p e c i f y i n g and s o l v i n g the three models o f an imperfect labour market. A simple model i s developed and the l i t e r a t u r e i s reviewed i n t h i s chapter and the conceptual framework adopted i s o u t l i n e d i n Chapter 2 1. The complexity of the model precludes a n a l y t i c s o l u t i o n , so i n order 20 to perform the desired comparative s t a t i c experiments,  I solve the  model numerically using the algorithm described i n Chapter 2 I I B . The r e s u l t s from Model I are presented i n Chapter 4.  52.  An i n t e r e s t i n g  t h e o r e t i c a l extension i s  the development  o f models  of d i s c r i m i n a t i o n i n which t h e r e are two types o f l a b o u r , w i t h  the  same p e r c e i v e d s k i l l s but d i f f e r i n g i n t h e i r t u r n o v e r and acceptance b e h a v i o u r through d i f f e r i n g p e r c e p t i o n s t o r i s k , r a t e of time p r e f e r e n c e f i r m i s whether i t characteristics  can i d e n t i f y  (e.g.  of market p a r a m e t e r s ,  or l e n g t h o f h o r i z o n .  o r i n vacancy  young and o l d workers d i f f e r i n g i n t h e i r  creation.  2 and Appendix I and r e s u l t s static  C r u c i a l to  each type of l a b o u r through some  o f working h o r i z o n ) , and, f u r t h e r , whether i t offer  attitudes  Models I I  the  overt  length  can d i s c r i m i n a t e i n wage  and I I I  are examined i n Chapter  are p r e s e n t e d i n Chapter 5.  p r e d i c t i o n s are d e r i v e d from these two models.  Comparative  53 CHAPTER 2 THE CONCEPTUAL FRAMEWORK,  I.  A.  I n d i v i d u a l Turnover and Acceptance Behaviour  A Summary This simultaneous model of an imperfect labour market was  formulated by C u r t i s Eaton and myself.  I t provides the conceptual  framework f o r the a n a l y s i s of other s t r u c t u r e s examined i n my t h e s i s . Modelled simultaneously i s the search behaviour of workers and the profitJmaximising behaviour of firms i n a labour market characteri s e d by one imperfection, the absence o f complete information.  This  simultaneity complicates the development and a n a l y s i s of the model. I n d i v i d u a l s , faced w i t h imperfect information, are forced to search. Their search behaviour i s determined by the perceived wage and vacancy c r e a t i o n behaviour of firms.  Wage and vacancy decisions of firms are  determined by t h e i r notions of i n d i v i d u a l s ' search behaviour.  Firms  make wage and vacancy decisions to maximise expected p r o f i t s discounted over an i n f i n i t e horizon,while workers' search behaviour i s motivated by the maximisation of expected discounted income over the job horizon. The labour force i s constant and homogeneous i n i t s capacity to do the job.  This general assumption ensures that any wage d i s p e r s i o n ,  c h a r a c t e r i s i n g e q u i l i b r i u m , i s generated by imperfect information on the part of market p a r t i c i p a n t s , rather than i n d i v i d u a l d i f f e r e n c e s in productivity.  54 Each i n d i v i d u a l i n the l a b o u r f o r c e has g e n e r a l i n f o r m a t i o n about the l a b o u r market environment,  such as the mean and v a r i a n c e of  p r e v a i l i n g wage d i s t r i b u t i o n , but must generate s p e c i f i c o r job o f f e r s  through random s e a r c h .  No s e a r c h e r a c c e p t s an o f f e r  unemployment  l e s s than the l e v e l o f  compensation which i s a c e r t a i n r e t u r n . individual quits  and searches  information  He must be unemployed to  When unemployed, each i n d i v i d u a l r e c e i v e s  the  search.  compensation.  unemployment  L i k e w i s e , each employed  f o r a more remunerative job o f f e r ,  o f f e r e d a wage r a t e l e s s than the l e v e l o f unemployment In o r d e r to secure some employees,  if  compensation.  then, a l l firms o f f e r  a wage at  l e a s t as h i g h as the l e v e l of unemployment compensation.  Thus,  there  1 are e x p l i c i t  costs of  search.  Each i n d i v i d u a l , s e a r c h e r samples On the b a s i s an e s t i m a t e  o f h i s g e n e r a l l a b o u r market i n f o r m a t i o n , he o f h i s r e s e r v a t i o n wage.  wage, c u r r e n t l y o f f e r e d , further search zero. recently  sampled,  wage was o f f e r e d ,  Likewise,  that  which makes the expected n e t r e t u r n s  from  offer  from the f i r m most  the s e a r c h e r would be i n d i f f e r e n t the o f f e r .  If  offer.  between c o n t i n u i n g  a wage l e s s than the  he would c o n t i n u e s e a r c h i n g .  s e a r c h e r a c c e p t s the job  computes  The r e s e r v a t i o n wage i s  I f he r e c e i v e d t h i s  to s e a r c h and a c c e p t i n g  the expected  one f i r m p e r d e c i s i o n p e r i o d .  Otherwise,  reservation the unemployed  2  each i n d i v i d u a l , who i s  c u r r e n t l y employed,  evaluates  r e t u r n s and c o s t s a s s o c i a t e d w i t h q u i t t i n g and s e a r c h i n g  f o r a new j o b ,  next p e r i o d .  He computes h i s r e s e r v a t i o n wage.  If  the  55 wage o f f e r  from h i s f i r m f o r n e x t p e r i o d i s  wage, then he q u i t s and searches  less  than h i s  f o r another j o b .  reservation  Otherwise,  he  remains employed. I t w i l l be demonstrated i n the next s e c t i o n t h a t , i n d i v i d u a l i n the l a b o u r f o r c e ,  each  i r r e s p e c t i v e o f employment s t a t u s ,  the same p e r c e p t i o n o f the d i s t r i b u t i o n o f wage o f f e r s , risk,  if  has  attitudes  to  r a t e o f d i s c o u n t and time h o r i z o n over which he b e l i e v e s wage  differentials  persist,  then each i n d i v i d u a l has  the same r e s e r v a t i o n  wage. To c h a r a c t e r i s e i n c o m p l e t e s p e c i f i c  i n f o r m a t i o n i n the l a b o u r  market, each i n d i v i d u a l ' s p e r c e p t i o n o f the r e s e r v a t i o n wage i s to be s u b j e c t  t o a p r o b a b i l i t y d i s t r i b u t i o n whose parameters are  o f the t r u e r e s e r v a t i o n wage and t r u e v a r i a n c e o f wage o f f e r s industry.  assumed  A l l i n d i v i d u a l s , i r r e s p e c t i v e o f l a b o u r market  functions  i n the  experience,  have the same p r o b a b i l i t y d i s t r i b u t i o n o f the r e s e r v a t i o n wage.  The  p e r c e i v e d r e s e r v a t i o n wage f o r an i n d i v i d u a l can be r e g a r d e d as a random drawing from t h i s  distribution.  Turnover and acceptance  decisions  a r e made by comparing the wage o f f e r w i t h the p e r c e i v e d r e s e r v a t i o n wage. Consequently,  t u r n o v e r and acceptance  f i r m ' s p o i n t o f view. probability,  ex a n t e ,  d e c i s i o n s are s t o c h a s t i c  from the  C e t e r i s p a r i b u s , each i n d i v i d u a l has a h i g h e r o f a c c e p t i n g a job o f f e r ,  q u i t t i n g a p o s i t i o n , i f employed,  i f unemployed, or n o t  the h i g h e r the wage  The i n d u s t r y has a f i x e d number of t e c h n i c a l l y h i r e from a f i x e d l a b o u r f o r c e .  offer.  i d e n t i c a l firms who  Each f i r m faces the same  p r o d u c t demand.  It  industry p r i c e .  T h i s assumption i s  exogeneous  can s e l l any l e v e l o f output a t the p r e v a i l i n g general,  i n the sense  that i t  cuts  56 the l i n k between i n d u s t r y output and p r i c e , but i t and focus on the f e a t u r e s forced to disentangle  a l l o w s me to  isolate  of an i m p e r f e c t l a b o u r market, r a t h e r than be  the i n f l u e n c e s  o f the p r o d u c t market.  The f i r m ' s m a r g i n a l revenue p r o d u c t and the wage o f f e r  are both  expressed as r a t e s p e r p e r i o d of time e q u a l to the f i r m ' s d e c i s i o n p e r i o d which i s c o i n c i d e n t and e q u a l to  the i n d i v i d u a l ' s d e c i s i o n p e r i o d .  At the b e g i n n i n g of each p e r i o d , t h e f i r m makes i t s wage and vacancy decisions  f o r the succeeding p e r i o d .  q u i t s and new h i r e s o c c u r . and s t o c h a s t i c  In view of the s t o c h a s t i c  creation is necessarily  The f i r m makes a t most as many o f f e r s searchers  accept an o f f e r .  show up.  i t has c r e a t e d . . decision reflects  as v a c a n c i e s  searchers  speculative.  i t has c r e a t e d ,  s e a r c h e r s s a m p l i n g the f i r m o r  the f i r m may f a i l  to f i l l  a l l the p o s i t i o n s the f i r m ' s  the d e s i r e d number o f net h i r e s , the number of  to q u i t and the expected p r o p o r t i o n of those  d e c i s i o n depends on i t s  individ-  searchers  c u r r e n t l e v e l of employment.  F o r any wage and stochastic.  C o n s i d e r i n g l e v e l s o f employment faces by firms as s t a t e s ,  then  e v o l u t i o n of the l a b o u r market i s a n o n - s t a t i o n a r y Markov p r o c e s s .  Markov p r o c e s s .  vacancy  Ceteris paribus, a f i r m ' s optimal  d e c i s i o n , the l e v e l o f employment a t t a i n e d i s  reaching stochastic  if  must employ a l l those i n d i v i d u a l s who  F o r any p a r t i c u l a r l e v e l of employment,  o f f e r e d a p o s i t i o n who a c c e p t .  vacancy  It  Through i n s u f f i c i e n t  s e a r c h e r s r e f u s i n g job o f f e r s ,  u a l s expected  flow o f  t u r n o v e r and acceptance generated through m i s p e r c e p t i o n  of t h e r e s e r v a t i o n wage, vacancy  sufficient  At the end o f the p e r i o d , a l l  the On  e q u i l i b r i u m , the l a b o u r market behaves as a s t a t i o n a r y  E q u i l i b r i u m i s c h a r a c t e r i s e d by wage d i s p e r s i o n ,  and f r i c t i o n a l unemployment.  vacancies  57 I t i s now behaviour.  a p p r o p r i a t e to a n a l y s e f o r m a l l y i n d i v i d u a l and  The s i m u l t a n e i t y o f the model c o m p l i c a t e s t h i s .  firm Each  s e t o f market p a r t i c i p a n t s makes d e c i s i o n s i n response to t h e i r p e r c e p t i o n s o f the o t h e r s e t of p a r t i c i p a n t s ' b e h a v i o u r and the g e n e r a l l a b o u r market environment. model i n d i v i d u a l b e h a v i o u r f i r s t B.  I t appears t o be e a s i e r to  r a t h e r than f i r m b e h a v i o u r .  I n d i v i d u a l Turnover and Acceptance Behaviour i n Model I I n t h i s s e c t i o n , i n d i v i d u a l s ' t u r n o v e r and acceptance b e h a v i o u r  i n response to a 'labour market environment', x, i s modelled.  This  environment may be c h a r a c t e r i s e d by the d i s t r i b u t i o n o f f i r m s over employment s t a t e s , 3 v ( n = 0,1,...,n),and a c o r r e s p o n d i n g s e t o f d e c i s i o n s , 6 (n = 0,1,...,n), where 6 = (w , v ) , ( n = 0,1 n). ' n n n n Then $ denotes the a c t u a l p r o p o r t i o n o f f i r m s c u r r e n t l y employing n  n individuals. creates v  n  Each o f these f i r m s makes a wage o f f e r , w , and  vacancies.  fL i s the maximum p o s s i b l e l e v e l o f employment  t h a t the f i r m chooses.  x=  (3,6) = ( 3  0 >  3  Then,  ,...,B , . . . , B , 6 , 6 , . . . , 6 , . . . 6 ) . f l  0  1  n  f t  . . . . (1)  There are N f i r m s and L i n d i v i d u a l s i n the l a b o u r f o r c e . i s the number o f unemployed _ U  =  L - E  _ =  L-N  If U  workers, then, n . E ' n.g. n  n=0 > n  where E i s the l e v e l o f employment.  . . . .  (2)  58 Individuals have general information about the labour market environment, such as the mean and variance of the wage o f f e r d i s t r i b u t i o n , which they generate through t h e i r perceptions of the number of searchers, the number of firms and the p r o b a b i l i t y d i s t r i b u t i o n of wage rates and job vacancies over firms.  To  generate  s p e c i f i c information or job o f f e r s , however, i n d i v i d u a l s search randomly. F i r s t , i t i s necessary to compute the true mean and variance of the wage o f f e r d i s t r i b u t i o n f a c i n g the searcher. searchers each making one contact during the p e r i o d .  There are U Then, each  searcher contacts a p a r t i c u l a r f i r m w i t h p r o b a b i l i t y , 1/N, the period.  during  To exclude the searcher's previous f i r m of employment  or the f i r m he searched p r e v i o u s l y , greatly complicates the analysis without s u b s t a n t i a l l y changing the conclusions, given that N i s large. The f i r m creates v  n  vacancies and at the end of the period the f i r m  makes o f f e r s to at most v I f less than v  of the searchers who have contacted i t .  n searchers have contacted the f i r m , a l l the searchers  n  receive o f f e r s .  Then, the p r o b a b i l i t y that a searcher, having contacted  a p a r t i c u l a r f i r m with n employees, w i l l obtain an o f f e r i s Y„ = V (V) j=0 2  1/N  j  (1-1/N) " U  1_;i  min fc£=-, 1). 3  ....  (3)  59 The expression i n the f i r s t set of parentheses  i n d i c a t e s the  p r o b a b i l i t y that j other searchers contact the f i r m .  The second  expression denotes the p r o b a b i l i t y that the searcher receives an o f f e r , given that j other i n d i v i d u a l s sample the f i r m .  I f j+1, the  t o t a l number of searchers sampling the f i r m , exceeds v , the number of vacancies created, then the p a r t i c u l a r i n d i v i d u a l obtains an v offer with probability  „ Qtherwise he obtains an o f f e r with }  certainty. The p r o b a b i l i t y of contacting a f i r m with n employees i n one search i s simply B n  Hence, the p r o b a b i l i t y of r e c e i v i n g an o f f e r  from a f i r m with n employees i n one search i s 3 Y ' n  n employees o f f e r s a wage, w wage o f f e r w , n  n  I f a f i r m with  then the p r o b a b i l i t y of o b t a i n i n g a  n>  namely <jT \, i s 3 Y n  n  The searcher w i l l get no o f f e r  from a f i r m with n employees with p r o b a b i l i t y , 8 (1-y )• i s denoted as a zero o f f e r . _ <f> = Let EW*  Then the p r o b a b i l i t y of a zero o f f e r i s  n E 8Y „ n n n=0  1 -  No o f f e r  .  denote the mean o f f e r obtained i n one search.  ....  (4)  As noted above,  an o f f e r of l e s s than the l e v e l of unemployment compensation, w, i s unacceptable.  Then, n  EW*  =  Z  n=0  W  <i>  w  n  + wd> .  . . . .  (5)  60  I f VW denotes  the v a r i a n c e of o f f e r s ,  0 2 Z (w -EW*) 4> + (w-EW*) <> | . n=0 n n  VW* =  L e t W-j. denote the wage o f f e r receive  then,  from h i s f i r m next p e r i o d .  . . . .  (6)  the employed i n d i v i d u a l w i l l Then, ,the expected  gross r e t u r n s ,  R, from the d e c i s i o n to q u i t and commence s e a r c h i n g next p e r i o d a r e  H R =  .  S i=l  where D i s  (.^~)  1  (Etf^Wj)  . . . .  the i n d i v i d u a l ' s own r a t e o f d i s c o u n t and  over which the i n d i v i d u a l expects to enjoy i n d i v i d u a l assumes t h a t his offer,  the d i s t r i b u t i o n o f o f f e r s  The  and, i n p a r t i c u l a r , How much i n f o r m a t i o n  contained- i n a c u r r e n t wage o f f e r  by the temporal c o r r e l a t i o n of wage o f f e r s ,  the h o r i z o n  the wage d i f f e r e n t i a l .  W^., w i l l p e r s i s t o v e r t h e h o r i z o n H ^ .  about f u t u r e wage r a t e s  is  (7)  can be measured  defined i n H I E .  The c o s t s  o f s e a r c h f o r one p e r i o d a r e g i v e n by the d i f f e r e n c e between h i s wage offer  and the l e v e l o f unemployment compensation, namely W^- w.  d e c i s i o n to q u i t i s based on the comparison o f expected c o s t s from one s e a r c h .  R  >  r e t u r n s and  The i n d i v i d u a l w i l l q u i t i f  (W -w).  . . . .  I  The s e a r c h e r ' s  d e c i s i o n to accept  continue searching, i s  His  analogous.  an o f f e r ,  or r e j e c t  (8)  i t and  D u r i n g the c u r r e n t p e r i o d the  i n d i v i d u a l samples a f i r m and r e c e i v e s  a wage o f f e r ,  W , which may be y  61 zero.  Then, the i n d i v i d u a l w i l l choose to remain unemployed and search  f u r t h e r , i f the i n e q u a l i t y i n (8) i s s a t i s f i e d . There e x i s t s some -value of W , say W*, such that (8) becomes an equality.  W* i s the true reservation wage. The reservation wage i s  that wage o f f e r which makes an i n d i v i d u a l i n d i f f e r e n t between accepting the o f f e r and e i t h e r indulging i n : f u r t h e r search., i f currently unemployed, 3 or q u i t t i n g , i f c u r r e n t l y employed. The r e l a t i o n s h i p represents the decision rule of an i n d i v i d u a l who has a perfect perception of the p r o b a b i l i t y d i s t r i b u t i o n of o f f e r s  facing  him and i s attempting to maximise the present value of expected future income.  This decision r u l e has the same general form as the one period  sequential decision r u l e developed i n Chapter 1 IVB f o r search i n product markets.  The r u l e i s based on the. choice between acceptance of  the current o f f e r , and a further search, and acceptance of the corresponding offer. An i n d i v i d u a l ' s a c t u a l turnover and acceptance behaviour, however, i s based on the comparison of the reservation wage determined by t h i s r u l e and h i s current wage o f f e r .  Since the horizon over which the  i n d i v i d u a l expects t o enjoy the wage d i f f e r e n t i a l , which determines the returns from a f u r t h e r search, i s assumed constant, the reservation wage i s constant and independent of the i n d i v i d u a l ' s actual duration of search. Such, a search r u l e i s not optimal, however, because the mean duration 4 of search associated with, the reservation wage i s not u n i t y .  Thus, the  i n d i v i d u a l ' s a c t u a l labour market behaviour i s not consistent with the decision r u l e .  62 Telser  [1973] i n d i c a t e s ,  however,  t h a t the gains  from s e a r c h i n  product markets a s s o c i a t e d w i t h such a one p e r i o d s e q u e n t i a l over the gains  to a n a i v e s e a r c h r u l e are s m a l l . ^  Then, i t  rule is  plausible  t h a t the gains a s s o c i a t e d w i t h the o p t i m a l s e a r c h r u l e  over t h i s  one p e r i o d r u l e , d e r i v e d i n the t e x t , would be s m a l l .  Consequently,  i n the i n t e r e s t s  of c o m p u t a t i o n a l economy,  the one  p e r i o d s e a r c h r u l e i s used i n the s i m u l a t i o n p r o c e d u r e . If  a l l i n d i v i d u a l s were i d e n t i c a l w i t h r e s p e c t  discount,  to t h e i r r a t e  time h o r i z o n , b e h a v i o u r towards r i s k and each  the t r u e d i s t r i b u t i o n o f o f f e r s  i n the l a b o u r market,  of  perceived  then any  firm  o f f e r i n g a wage r a t e l e s s than the t r u e r e s e r v a t i o n wage, W*, would l o s e a l l employees  and would be unable to a t t r a c t  T h i s i m p l i e s t h a t no f i r m o f f e r s no f i r m o f f e r s  any new  a wage l e s s than W* a n d ,  a wage h i g h e r than W*.  employees. likewise,  Thus, t h e r e i s no d i s p e r s i o n  and no s e a r c h . Indeed, perceive  if  i n d i v i d u a l s are i d e n t i c a l l y m o t i v a t e d b u t do n o t  the t r u e d i s t r i b u t i o n of o f f e r s ,  then e q u i l i b r i u m i s  c h a r a c t e r i s e d by no d i s p e r s i o n and no s e a r c h . computes  If  still  each i n d i v i d u a l  the r e s e r v a t i o n wage as W*, not e q u a l to W*, then a l l  firms  w i l l o f f e r W*. Wage d i s p e r s i o n , t h e n ,  i s n o t a p r o p e r t y o f models i n which  i n d i v i d u a l s are i d e n t i c a l l y m o t i v a t e d and p e r c e i v e necessarily  true,  d i s t r i b u t i o n of wage o f f e r s ,  substantial  costs of search.  Rothschild  the same, but n o t  even though t h e r e  [1973], i n  discussing  are  63 Stigler's se,  c o n t r i b u t i o n , makes the same p o i n t .  are i n s u f f i c i e n t  heterogeneity  of search,  to generate p r i c e o r wage d i s p e r s i o n .  o f market p a r t i c i p a n t s  I n the absence different  Costs  of exhaustive  is  Some  required.  s e a r c h each p e r i o d and due  l a b o u r market e x p e r i e n c e s ,  per  to  an i n d i v i d u a l ' s p e r c e p t i o n s  the l a b o u r market environment may n o t c o i n c i d e w i t h the r e a l i t y the l a b o u r market.  Consequently,  r e s e r v a t i o n wage. wage.  of  he may i n c o r r e c t l y compute the  L e t wc r e p r e s e n t h i s p e r c e p t i o n o f the  of  true  reservation  Then, wc i s the minimum wage o f f e r which would i n d u c e h i m to  remain at h i s  c u r r e n t job or accept a p o s i t i o n , i f unemployed.  phenomena o f m i s p e r c e p t i o n s  o f the l a b o u r market environment  m o d e l l e d most e a s i l y by assuming t h a t each i n d i v i d u a l ' s  The  are  perception  of h i s r e s e r v a t i o n wage i s drawn from some p r o b a b i l i t y d e n s i t y  function,  p(wc),  density  defined f o r non-negative  function allows  The s p e c i f i c a t i o n  of t h i s  the computation o f the p r o b a b i l i t y o f q u i t t i n g ,  a wage, o f f e r ,  w.  t(w)  =  where t(w)  wc.  /  oo w  p(wc)dwc  t'(w)  <  0  t"(w)  >  0  i s the p r o b a b i l i t y o f  (9)  turnover.  given  64 If  the i n d i v i d u a l r e c e i v e s an o f f e r , w, then, he w i l l q u i t , i f  he p e r c e i v e s t h e r e s e r v a t i o n wage, wc, as e x c e e d i n g w. by the cumulative  d e n s i t y f u n c t i o n i n (9).  Analogously, i s accepted  a(w)  The  This i s given  t h e p r o b a b i l i t y , a(w), t h a t a f i r m ' s wage o f f e r , w,  by a s e a r c h e r i s g i v e n by  =  p(wc)dwc  a'(w)  > 0  a"(w)  < 0.  =  l-t(w)  . . . . (10)  s p e c i f i c a t i o n of misperceptions,  formulated  6  i n (9) and (10)  i s p l a u s i b l e because i n d i v i d u a l s ' knowledge o f the l a b o u r market i s generated through random s e a r c h and o f f e r c o l l e c t i o n .  Thus, t h e i r  p e r c e p t i o n of l a b o u r market parameters w i l l show s t o c h a s t i c v a r i a t i o n . T h e i r p e r c e p t i o n s , based on incomplete to  s p e c i f i c information, are related  the t r u e l a b o u r market environment.  Then, the mean o f t h e d e n s i t y  f u n c t i o n should be r e l a t e d t o t h e t r u e r e s e r v a t i o n wage and t h e v a r i a n c e o f t h e d e n s i t y f u n c t i o n s h o u l d be r e l a t e d t o t h e v a r i a n c e o f the wage offer distribution.  L e t M, VP r e p r e s e n t  the mean and v a r i a n c e ,  r e s p e c t i v e l y , o f t h e d e n s i t y f u n c t i o n of i n d i v i d u a l p e r c e p t i o n s r e s e r v a t i o n wage, then these  M  VP  r e l a t i o n s may be w r i t t e n  =  c,W*  (ID  =  c VW*  (12)  2  o f the  65 where W* i s the t r u e r e s e r v a t i o n wage, W * i s the t r u e v a r i a n c e o f offers  and c^,  are constants.  an unbiased e s t i m a t e h i s estimate All but,  If  c^ = 1, then the i n d i v i d u a l has  o f the t r u e r e s e r v a t i o n wage.  function of  perceptions,  through t h e i r s t o c h a s t i c misperceptions, i n d i v i d u a l s  may behave d i f f e r e n t l y environment.  c^ < 1, then  of t h e r e s e r v a t i o n wage i s b i a s e d downward.  i n d i v i d u a l s have the same d e n s i t y  ex p o s t ,  If  i n response to a p a r t i c u l a r l a b o u r market  S i n c e each i n d i v i d u a l ' s b e h a v i o u r i s  does n o t d i f f e r  systematically  stochastic,  it  over time from another i n d i v i d u a l ' s  b e h a v i o u r i n response to the same l a b o u r market p a r a m e t e r s . The assumption o f a f i x e d p e r i o d o v e r w h i c h r e t u r n s from s e a r c h accrue ensures t h a t an i n d i v i d u a l ' s t r u e r e s e r v a t i o n wage, g i v e n an unchanging l a b o u r market environment, i s c o n s t a n t and independent o f h i s d u r a t i o n o f search., i f unemployed, and p r e v i o u s o f f e r s , employed. ex a n t e ,  Thus, the s t o c k o f unemployed i n d i v i d u a l s i s  if  homogeneous,  i n t h e i r acceptance b e h a v i o u r , a l t h o u g h composed of i n d i v i d u a l s  w i t h d i f f e r e n t h i s t o r i e s o f unemployment. If zero,  t h e r e i s no p e r c e i v e d wage d i s p e r s i o n , i . e .  then i n d i v i d u a l s a c c e p t or r e j e c t  an o f f e r  p e r c e p t i o n of the r e s e r v a t i o n wage, c^W*. offers  o r VW* i s  according to  In t h i s  c a s e , each  a wage e q u a l t o the p e r c e i v e d r e s e r v a t i o n wage, c^w*.  the r e s e r v a t i o n wage i s always l e s s than the mean o f f e r , wage f a l l s . so on.  Next p e r i o d ,  In f u l l  each firm offers  industry equilibrium,  firm Since reservation  the new r e s e r v a t i o n wage and  each f i r m o f f e r s  the l e v e l o f unemployment compensation.  the  their  a wage e q u a l  to  There i s no wage d i s p e r s i o n , no  66 s e a r c h and thus zero unemployment. over firms i s  The d i s t r i b u t i o n o f  employment  indeterminate.  The c r u c i a l element o f t h i s model, which d i s t i n g u i s h e s the p e r f e c t l y  c o m p e t i t i v e model, i s the absence o f f u l l  i n f o r m a t i o n about wage o f f e r s  and v a c a n c i e s  and vacancy  from  specific  on the p a r t of i n d i v i d u a l s .  As a r e s u l t , no f i r m i s a b l e to i n f l u e n c e i t s through i t s wage o f f e r  it  supply of  creation behaviour.  searchers If  it  offers  a wage e q u a l to or g r e a t e r than the r e s e r v a t i o n wage, then a l l who randomly sample i t ,  accept the o f f e r .  If  the f i r m o f f e r s  searchers, a wage l e s s  than the r e s e r v a t i o n wage, then no s e a r c h e r s w i l l a c c e p t a job o f f e r .  In  i n d u s t r y e q u i l i b r i u m , t h e r e i s no s e a r c h and so no f i r m i s a b l e to communicate  its  excess demand f o r l a b o u r .  The e q u i l i b r i u m corresponds to  c o l l u s i v e monopsony s o l u t i o n i n which f i r m s c o l l u d e i n t h e i r wage to i n d i v i d u a l s .  Firms are u n a b l e , however,  to choose the j o i n t  the  offers  profit  maximising l e v e l o f employment because t h e r e i s no s e a r c h . If  a l l individuals believe  t h e r e i s no wage d i s p e r s i o n , then  e q u i l i b r i u m i n the l a b o u r market i s c h a r a c t e r i s e d by zero wage d i s p e r s i o n . The assumptions o f t h i s p a r t i c u l a r model are c o n s i s t e n t w i t h the c o n d i t i o n f o r z e r o d i s p e r s i o n o u t l i n e d i n Chapter Equations  (9)  and (10)  second  1.  show the t u r n o v e r and acceptance r e l a t i o n s  which c o n s t r a i n the f i r m ' s market b e h a v i o u r .  67 C.  Systematic Differences  1.  S t a t e s o f Employment  iii Individual  I n Models I I and I I I , i n d i v i d u a l s l a b o u r market b e h a v i o u r .  Behaviour  d i f f e r systematically  Firms make wage and vacancy  i n their  decisions  based  on both t h e l e v e l and c o m p o s i t i o n o f employment. Thus, p o s s i b l e  states  o f employment f a c i n g t h e f i r m a r e enumerated  b o t h by number and type o f employee i n these models. that  the labour force consists  I t i s assumed  o f two types o f i n d i v i d u a l .  Thus, i f  the f i r m can e x p e r i e n c e l e v e l s of employment 0 , 1 , . . . , f i , t h e r e a r e M possible  employment s t a t e s  where  n+l M  =  E  i  i=l  (n+2)(n+l) . 2  (13)  I f the f i r m employs n i n d i v i d u a l s , then i t w i l l be i n any one o f n+l d i s t i n c t employment s t a t e s , type o f i n d i v i d u a l employed. which r e l a t e s s t a t e under Let j,  depending  on the number o f each  I t i s n e c e s s a r y t o impose a mapping  t h e number o f each type o f employee t o t h e p a r t i c u l a r consideration.  e ^ be the number o f type i i n d i v i d u a l s i n employment  and l e t s(e^,e2)  denote t h e s t a t e  employees and e„ type two employees.  j  =  sf.e^, e ) . J  2  r  state  c o r r e s p o n d i n g to e^ type one Then,  (14)  68 It i s u s e f u l to define this point.  then  F o r any s t a t e j ^ , i f  1  =  m  =  j  e ^ l  s(m,l)  and J  2  . . . . (17)  a r e r e f e r r e d t o as ' s t a t e complements'.  I f L^.U^ ( i the  . . . . (15)  . . . . (16)  =  2  the concept o f a ' s t a t e complement' a t  =  1»2) denote,  the number o f type i i n d i v i d u a l s i n  l a b o u r f o r c e and t h e number unemployed, r e s p e c t i v e l y ,  then  M U. 1  2.  = L.- N 1  E g.e. j=l 2  J  II.  . . . . (18)  Workers' Behaviour i n Model I I Firms a r e n o t p e r m i t t e d  the  i = 1,2.  1  ( o r a r e unable) t o d i s c r i m i n a t e  against  d i f f e r e n t types o f workers i n wage o f f e r and i n h i r i n g i n Model Each f i r m , however, makes a wage o f f e r and vacancy  creation  d e c i s i o n which i s dependent both on the s i z e and composition of i t s workforce.  T h i s wage o f f e r i s made b o t h to e x i s t i n g employees and  to p o t e n t i a l new employees.  Thus, w h i l e wage d i f f e r e n t i a l s a r e  observed between f i r m s employing the same number b u t a d i f f e r e n t c o m p o s i t i o n of i n d i v i d u a l s , each i n d i v i d u a l f a c e s market environment because e x p l i c i t d i s c r i m i n a t i o n The  the same l a b o u r i s illegal.  l a b o u r market environment i n which i n d i v i d u a l s and f i r m s  make d e c i s i o n s  may be w r i t t e n as  69 x  (6,6) = ( B , B , . . . , e  =  2  1  Individuals  m  systematically  B ,6 ,6 ,...,6 ,...,5 ) M  1  differ  b e h a v i o u r due to t h e i r s y s t e m a t i c a l l y t r u e mean o f f e r  2  and h o r i z o n s over which they b e l i e v e  (19)  M  i n t h e i r l a b o u r market different  from s e a r c h , EW*, and thus  I n d i v i d u a l s have the same a t t i t u d e s  m  perceptions  of  the  the r e s e r v a t i o n wage.  to r i s k , r a t e s  o f time  wage d i f f e r e n t i a l s  preference  persist.  There  i s no d i s c r i m i n a t i o n i n h i r i n g , whence a l l unemployed i n d i v i d u a l s t h e same p r o b a b i l i t y of a j o b o f f e r the  and the same mean o f f e r .  Therefore,  t r u e r e s e r v a t i o n wage, W*, i s t h e same f o r a l l i n d i v i d u a l s .  and VP^ denote the mean and v a r i a n c e  o f the d i s t r i b u t i o n o f  have  If  perceptions  o f the r e s e r v a t i o n wage f o r each type i i n d i v i d u a l , then  M  ±  VP  l  c  °2  ±  1  =  M (c EW*)  i = 1,2.  . . . .  (20)  =  ^^VW*  i = 1,2.  . . . .  (21)  i  J l  1  1  2  c  =  °2  =  where the argument,  C  2  c ^ E W * ( i = 1,2)  denotes  . . . .  (22)  . . . .  (23)  the p e r c e i v e d mean  f a c i n g a type i i n d i v i d u a l from one s e a r c h and c^  x  ( i = 1,2)  the c o r r e s p o n d i n g p e r c e p t i o n parameter of the v a r i a n c e o f  offer  denotes  offers.  70 I f c ^ i s unity, then the mean of the d i s t r i b u t i o n of perceptions, 1  M^,equals the true reservation wage, W*. L i k e w i s e , i f  i s unity,  the perceived variance of the d i s t r i b u t i o n of perceptions, V P ^ , equals the true variance, VW*. Type i i n d i v i d u a l s have s t o c h a s t i c misperceptions of the reservation wage represented by a density function whose parameters are JX and V P ^ . Turnover and acceptance functions may be w r i t t e n ,  t  ±  a^  f o r the d i f f e r e n t types of i n d i v i d u a l  respectively  t (w;  =  a^(w; x,U; N , D , H , c ^ , C 2 )  ±  x,U;  N.D.H.Cj ,^)  =  1  1  i =  1,2  i = 1,2  .  .  .  . (24)  . . . .  (25)  where the argument before the f i r s t semicolon denotes a v a r i a b l e endogeneous  t o the firm.  are endogeneous  The v a r i a b l e s between the semicolons  to the labour market and the remaining arguments  are exogeneous. 3.  Workers' Behaviour i n Model I I I In Model I I I , the f i r m can recognise the c h a r a c t e r i s t i c s of both  i t s employees and those searchers who sample i t .  A f i r m can d i s c r i m -  inate by o f f e r i n g d i f f e r e n t wages to d i f f e r e n t types of i n d i v i d u a l s and creating vacancies f o r one type of i n d i v i d u a l and not the other. Again, firms are forced t o make wage and vacancy decisions, ex ante. This s t i p u l a t i o n prevents the f i r m d r i v i n g out one type of employee i n one period through a low wage o f f e r , i n response to a large number  71 o f s e a r c h e r s o f the o t h e r t y p e .  I n t h i s model, the f i r m makes a  wage and vacancy c r e a t i o n d e c i s i o n f o r each type o f i n d i v i d u a l . Thus, the two types o f worker f a c e d i f f e r e n t l a b o u r market e n v i r o n ments . The  l a b o u r market environment f a c i n g a type i worker ( i = 1,2)  may be w r i t t e n  x.  =  where  ( M  1  )  denotes the wage o f f e r and vacancy c r e a t i o n d e c i s i o n f o r a  type i i n d i v i d u a l from a f i r m f a c i n g employment s t a t e m. Based on the d i s t r i b u t i o n o f wage o f f e r s and v a c a n c i e s and the l e v e l o f unemployment f a c i n g each type o f i n d i v i d u a l , the mean o f t h e d i s t r i b u t i o n of p e r c e p t i o n s i s computed, as i n I B . i  The mean o f a type  i n d i v i d u a l ' s d i s t r i b u t i o n o f p e r c e p t i o n s may be w r i t t e n  M. 1  =  M. (c/EW*) x 1 1  i = 1,2  . . . . (27)  '  and t h e v a r i a n c e o f the d i s t r i b u t i o n ,  VP  ±  =  c  2  X  VW*  i = 1,2.  Each type o f i n d i v i d u a l has s t o c h a s t i c m i s p e r c e p t i o n s  . . . . (28)  of t h e  r e s e r v a t i o n wage, which i s r e p r e s e n t e d by a d e n s i t y f u n c t i o n w i t h mean, M^, and v a r i a n c e , VP^.  A g a i n , i n d i v i d u a l s a r e assumed t o d i f f e r  systematic misperceptions  o f t h e i r r e s p e c t i v e r e s e r v a t i o n wages.  through Thus,  72 Cj  c  4  1  = 2  . . . . (29)  c . ±  c  2  2  =  c  2-  . . . . (30)  I t i s easy to model i n d i v i d u a l d i f f e r e n c e s generated by d i f f e r e n t discount r a t e s , a t t i t u d e s t o r i s k o r horizons over which returns from search accrue. Turnover and acceptance rates f o r the d i f f e r e n t types of i n d i v i d u a l may be w r i t t e n , r e s p e c t i v e l y , t  a  ±  ±  II. A.  =  t ( w ; x ,V; N . D . H ^ C p C p  i = 1,2  . . . . (31)  =  a^w;  i = 1,2.  . . . . (32)  ±  ±  x ,U; N.D.H^cJ,^) ±  Firms' Wage arid Vacancy Creation Decisions and the Algorithm  Firms' Behaviour i n Model I Returning t o the b a s i c model i n which i n d i v i d u a l s behave i d e n t i c a l l y ,  ex ante, i t i s now appropriate to model f i r m behaviour. Each f i r m can vary only i t s labour i n p u t , whence each has a w e l l defined marginal revenue product f u n c t i o n , MRP(n), where n i s the l e v e l of employment.  This a n a l y s i s of f i r m behaviour i s a p p l i c a b l e to the  c l a s s i c a l short run. Allowing v a r i a t i o n of other f a c t o r s of production severely comp l i c a t e s the s o l u t i o n to the problem.^ unable t o hold i n v e n t o r i e s .  By assumption, firms are  73  Given an unchanging l a b o u r market environment, x,  individual  turnover and acceptance f u n c t i o n s f a c i n g the f i r m , which o f f e r s wage, w,  may  be w r i t t e n as  t = t dw  (w,x)  ^  <  0 < t < 1.  a = a da ^ dw  . . . .  (33)  . . . .  (34)  (w,x)  < 0  0 < a < 1.  C o n s i d e r i n g a f i r m whose employment l e v e l i s n, l e t the p r o b a b i l i t y  p.  = ()  p  =  The  n  (1-t)  1  Then,  t  0  1 1  "  1  i < n  i > n .  flow of new  hires  . . . .  1/N.  one  (35)  to the f i r m i s q u i t e complex.  be U s e a r c h e r s and assume each s e a r c h e r makes one Then, any  denote  t h a t e x a c t l y i o f the n employees do n o t q u i t i n  response to the o f f e r , w.  ±  a  Let  contact per p e r i o d .  of the U s e a r c h e r s w i l l c o n t a c t the f i r m w i t h  probability  D u r i n g the p e r i o d , the f i r m makes o f f e r s to a t most v of  i n d i v i d u a l s who  there  c o n t a c t i t , where v i s the number of v a c a n c i e s  the i t has  74  created.  If  denotes the p r o b a b i l i t y of i new h i r e s , then  consists of two expressions. or l e s s sample the f i r m .  In the f i r s t expression, v i n d i v i d u a l s  I n the second expression  more than v  i n d i v i d u a l s , sample the f i r m .  a. =  E (^)(|) (l-l/N) ~ 3=1 j  +  U  j  ( ^ ( l - a ^  U . E (")(1/N) 3 (1-1/N) j=v+l 3  U 3  -  1  (Y)a (l-a) 1  V  1  . . . .  \  The terms enclosed i n the f i r s t s e t of parentheses  (36)  i n each  expression compute the p r o b a b i l i t y that j i n d i v i d u a l s contact the f i r m . The f i r m creates v vacancies.  The f i r m makes j o f f e r s , i f the number  of i n d i v i d u a l s contacting the f i r m i s l e s s than or equal to v. The remaining terms i n the f i r s t expression i n d i c a t e the p r o b a b i l i t y that, of the j o f f e r s made to searchers, i are accepted.  I f more than v  i n d i v i d u a l s contact the f i r m , then v o f f e r s are made randomly t o the searchers.  The remaining terms i n the second expression compute the  p r o b a b i l i t y that i of the v o f f e r s are accepted.  This r e l a t i o n may be  w r i t t e n more simply as P ( i hires) = P ( i hires  | j < v contacts) P ( j contacts where j < v)  + P ( i h i r e s | j > v contacts) P ( j contacts where j > v) . . (37)  75 Relations of employment  (35) and (36) determine the p r o b a b i l i t y f o r the f i r m next p e r i o d .  o f employment i s c o n d i t i o n a l be the p r o b a b i l i t y n employees i n p e r i o d  distribution  The p r o b a b i l i t y  distribution  on the c u r r e n t l e v e l o f employment.  o f employing k i n d i v i d u a l s  i n period  Let  z+1, g i v e n  z.  J  6  nk  =  £  . i=I T  a; p. . l k-i  J = min(k,v)  I = k-n i f n+v > k > n  = 0 if k < n,  nk  =  8 . (38)  0 i f k > n+v .  I f k, the number o f i n d i v i d u a l s the  l e v e l o f vacancy c r e a t i o n ,  summation J w i l l be v s i n c e , k-v  employed i n p e r i o d  z+1, exceeds  v, then the upper bound f o r the  t o a t t a i n employment l e v e l k, a t l e a s t  i n d i v i d u a l s must n o t q u i t . The maximum number o f p o s s i b l e  employees n e x t p e r i o d  I f k exceeds n+v then the t r a n s i t i o n p r o b a b i l i t y ,  8  i s n+v.  i s zero.  If  k i s l e s s than c u r r e n t employment, n, then the lower bound f o r the summation i s z e r o .  I t i s consistent  k employees n e x t p e r i o d .  t o n o t h i r e anyone b u t s t i l l have  I f k l i e s between the maximum number o f  76  p o t e n t i a l employees next period, n+v, and the current l e v e l of employment, n, then at l e a s t k-n new employees must be h i r e d .  Thus,  the lower bound f o r the summation i s k-n. I f n i s the highest employment l e v e l a f i r m can p o s s i b l e choose to face, then a wage and vacancy decision f o r each p o s s i b l e l e v e l of employment generates a set of c o n d i t i o n a l p r o b a b i l i t i e s which describe a Markov process, where l e v e l s of employment c o n s t i t u t e the s t a t e s . Let P be the n+l by fi+1 Markovian t r a n s i t i o n matrix,  P  =  [9  n k  ] n,k = 0,1,...,n.  . . . . (39).  For any given labour market environment, x, and s e t of d e c i s i o n s , 6^(n = 0,1,...,n), a Markov t r a n s i t i o n matrix can be generated i n which the i n d i v i d u a l element, 0 ( 6 ),(n,k = 0,1,... ,n), denotes the p r o b a b i l i t y v  that a f i r m with n employees paying a wage r a t e , w , and c r e a t i n g v n  vacancies w i l l have k employees one period l a t e r .  Since the evolution  of the labour market i s a s t o c h a s t i c process, e q u i l i b r i u m i n the labour market i s n e c e s s a r i l y s t o c h a s t i c . I t i s now p o s s i b l e to formulate the firm's o b j e c t i v e .  Let II(n,k)  denote the one period p r o f i t s of a f i r m which pays a wage r a t e , w^, and creates v  n  vacancies and as a r e s u l t of the s t o c h a s t i c process occurring  i n the labour market ends up with k employees.  n(n,k)  =  Then,  k Z MRP ( i ) - k.w.-c '1=0. n  where MRP(O)  =  0  and MRP(i) i s f i n i t e  i=l,2,...,n.  . . . . (40)  77 The f i r s t term i n d i c a t e s t o t a l revenue, while the second represents t o t a l labour cost and c represents f i x e d non-labour costs of production.  Then, the firm's expected one period p r o f i t s  are n Z 6 . (6 ) n(n,k)... k=0  f(n,S ) =  . . . . (41)  A p o l i c y i s defined as a wage and vacancy d e c i s i o n f o r a l l p o s s i b l e l e v e l s of employment.  y  r  =  Let y  denote a p o l i c y then,  r  • ( o l *"' fP * 6  , 5  ,  . . . . (42)  6  Let I now denote the number of d i f f e r e n t p o l i c i e s that a f i r m could adopt and Y be the s e t of a l l such p o l i c i e s , then,  Y  =  { y : r == 1,2,...,I}.  . . . . (43)  r  I t i s assumed that same p o l i c y , y eY, y e t to be determined, i s r  adopted by the f i r m f o r ever.  Then, the wage and vacancy decision  made at any p o i n t i n time corresponds to the p a r t i c u l a r l e v e l of employment the f i r m then experiences. The f i r m assumes that market parameters are unchanging, that i s the 'labour market environment', x, remains the same. Then, turnover and acceptance are time i n v a r i a n t functions of the wage o f f e r .  Then, the firm's state to s t a t e t r a n s i t i o n  78  matrix i s time i n v a r i a n t when the p o l i c y , y , i s adopted f o r ever. The f i r m regards the e v o l u t i o n of the labour market to be a s t a t i o n a r y Markov process.. This may be w r i t t e n  P(y,r)  = .[8 («n)] nk  n,k = 0 , l , . . . , r i  r = 1,2,...,1.  . . . . (44)  Let F(n,y ) denote the expected p r o f i t over an i n f i n i t e horizon r  discounted t o the beginning of the f i r s t p e r i o d , when a f i r m commences with n employees and adopts p o l i c y , . y , f o r ever.  I f the labour market  environment i s unchanging, then F(n,y ) i s also time i n v a r i a n t . r  I f the f i r m wishes to maximise expected discounted p r o f i t s over an i n f i n i t e horizon given an unchanging environment, then i t may be demonstrated that t h i s requires the adoption of a p o l i c y , say y*eY, f o r ever.  L e t F*(n) denote the maximum expected p r o f i t discounted  over an i n f i n i t e horizon when the f i r m commences i n employment s t a t e , n. I t s f u n c t i o n a l equation may be w r i t t e n  F*(n)  =  max [f(n,6*) + ^ Y  l  ^  S nk k=0 9  ( < S  n * ) F  ( k ) 1  • • • • < >  where R now denotes the i n d i v i d u a l firm's r a t e of discount.  45  Solving  such f u n c t i o n a l equations i s not easy and i t defies a n a l y t i c s o l u t i o n . Hadley [1964] has demonstrated that t h i s problem i s i n the c l a s s of dynamic s t o c h a s t i c programming problems, however, and can be solved 9 u s i n g an algorithm or l i n e a r programming. problem i s o u t l i n e d below.  The algorithm to solve the  79 B.  The A l g o r i t h m L e t x denote the unchanging l a b o u r market environment i n which  i n d i v i d u a l and f i r m d e c i s i o n s a r e made.  x -  (3,6) -  Then, r e w r i t i n g (1) and (2)  ( I 6 Q , B ^ , . . . ,3 ,... ,3^,6Q,5^, . . . , 6 ^ , . . . , 6 ^ )  . . . .  ii U = L - E = L - N E & . n  (1)  ....(2)  n=0  where L i s t h e s i z e of the l a b o u r f o r c e , U i s the number o f s e a r c h e r s and E the number o f i n d i v i d u a l s employed.  The t u r n o v e r and acceptance  f u n c t i o n s may be c a l c u l a t e d , namely t(w) and a ( w ) . L e t G ( n , x ) denote expected p r o f i t s h o r i z o n , when the f i r m adopts p o l i c y employment s t a t e n .  G (n,x) r  f o r ever and commences i n  Then,  f(n,6*)  =  d i s c o u n t e d over an i n f i n i t e  , + 3^  fi Z  e ( 6 * , x ) G (k,x)  k=0  and x i s i n c l u d e d as an argument t o i n d i c a t e the c o n s t a n t Writing  (46)  environment.  (G (0,5), G ( l , x ) , . . . , G ( i i , x ) ) as G ( x ) , and ( f ( 0 , s j ) , r  r  f(l,6 ),...,f(n,6.)) 1  ( n , k = 0,1,...,fi),  G (x) r  . . . .  r  n k  =  r  r  as f ( x ) and d e f i n i n g f ^ x ) as [0 . ( 6 , x ) ] r  r  (460 may be w r i t t e n as  f ( x ) + T 5 R ? ( X ) G (x). r  r  . . . .  (47)  80  Solving for G (x) y i e l d s  G() r  X  where 1 ^  =  / i  (i)  +  i ,  f  t  i - l i i ^ ^ " "  +  f (^).:  1  w  • • • •  r  i s the fi+1 by n+l i d e n t i t y matrix.  +1  The  n  algorithm may  be described i n the following  way  Select an a r b i t r a r y p o l i c y , say y eY, and set the p o l i c y s index, j ,at the value zero. Calculate the t r a n s i t i o n matrix, P (x), and  the p r o f i t vector, f (x).  From  (48)  —s — 1 — 1 — solve for G (x). Define a vector, H (x), and set H (x) => J  G (x). (ii) (iii)  J  Set the value of a scalar r to s.  Increment the p o l i c y index, so j =  j+1.  Assume the firm uses p o l i c y , y-, from period two onwards forever and s e l e c t a new  set of decisions, p o l i c y r, to  be adopted i n period one which maximises the present value of expected p r o f i t s . y  =  r  ( { . . { . . I . . J . )  0' 1'  f T  ^iv)  ' n  ^ > lk 6  }  n  k=0  This requires  choosing  which maximises  6  n k ^ >  H^Vx).  I f p o l i c y r and p o l i c y r are identical,then outlined i n (45) has been solved. ' N  and v^ = v^ converged.  r r That i s , i f w = v ' n n  f o r a l l n = 0,1,...,n. , the algorithm has I f the p o l i c i e s r and r are not  set r = r , calculate G (x) r  and  the problem  return to step ( i i ) .  identical,  fronts (48), set H (x) = J  G (x) r  81 Hadley demonstrates that i f there i s a f i n i t e number of p o s s i b l e p o l i c i e s , then the algorithm converges i n a f i n i t e number of steps. In choosing t h e i r optimal p o l i c y , f i r m s assume that i n d i v i d u a l s evaluate t h e i r o f f e r s i n the context of the f i x e d environment, x = (3,6).  I n d i v i d u a l s make decisions about turnover and acceptance  i n the l i g h t of the d i s t r i b u t i o n of current o f f e r s , however.  Thus,  i f y^ denotes the p o l i c y adopted, then i n d i v i d u a l s respond to the environment, x = ( 3 , y ) .  Furthermore, i f a l l firms i n the industry-  r  adopt the optimal wage and vacancy d e c i s i o n corresponding to t h e i r current l e v e l s of employment, then the s t o c h a s t i c forces i n the labour market w i l l , except i n e q u i l i b r i u m , generate a new environment charact e r i s e d by a d i f f e r e n t d i s t r i b u t i o n of firms over employment states and thus d i f f e r e n t l e v e l s of aggregate unemployment and vacancies and a new d i s t r i b u t i o n of wage o f f e r s .  Generally, the o l d p o l i c y w i l l be sub-  optimal w i t h respect to the new environment.  Thus, the algorithm  described can be regarded as s o l v i n g the p a r t i a l optimisation problem, namely choosing a p r o f i t maximising p o l i c y given a constant environment. The feedback of i n d i v i d u a l firms decisions on the labour market environment i s ignored. The approach adopted to solve the f u l l optimisation problem i s to p a r t i a l l y optimise given a p a r t i c u l a r environment, s a y i ^ . Let y^ denote the optimal p o l i c y and l e t x denote the environment, ( B ^ , y ) . r  Compute the t r a n s i t i o n matrix, P ( y ) , where x i s the unchanging labour r  market environment. s t a t e s , 3^ ^> +  Define the new d i s t r i b u t i o n of firms over employment  as  h+1  =  *i  P ( y  r  }  ....  (49)  82 and the new labour market environment as  =  ^i+l'V*  . . . . (50)  Using the p a r t i a l optimisation algorithm y i e l d s a new optimal p o l i c y i n response to the labour market environment, ^ -^«  This new p o l i c y  x  +  i s again used to generate a new environment and so on. of  Convergence  the algorithm to a f u l l y optimal solution occurs when consecutive,  labour market environments d i f f e r by a vector of a r b i t r a r y small constants.  This convergence c r i t e r i o n i s stringent enough to ensure  that consecutive p o l i c i e s are i d e n t i c a l , since the vacancy decision i s integer and the wage decision i s considered i n fixed  increments.  The f u l l optimisation algorithm may be written  Choose an i n i t i a l labour market environment X  (i)  Q  = (3Q>YQ) •  Set the loop index, j , at zero. (ii)  Solve the p a r t i a l optimisation algorithm as described, subject to the environment, x... Denote the optimal p o l i c y by y.  (iii)  Define x* as (y,3..) and c a l c u l a t e P\ = [ k(^ »x*)], e  n  (n,k = 0,1,...,n). •  Increment the loop index, j , by  1 and define 3. = 3. ,P. , and x. = (y,3.). 3  (iv)  n  Compare x^. and of  3-1  3-1  3  V  J  "  2  .  I f Abs|x_.-x^_^| < e, rwhe.xe.-e i s a vector  small a r b i t r a r y constants, go to (v). Otherwise,  return to ( i i ) .  83 (v)  Calculate 8 = 8 Lim P. I f Abs|B-3I < e, then f u l l m-*=° optimisation has been achieved, and so set x* = x. and 3  3  8* = 6.  I f not, return to ( i i ) .  The s t o c h a s t i c turnover and acceptance behaviour guarantees that the flows of i n d i v i d u a l s i n and out of employment w i l l be s t o c h a s t i c and so there w i l l be v a r i a t i o n i n the l e v e l of employment over firms.  Consequently, e q u i l i b r i u m i s s t o c h a s t i c and i s characterised  by a p r o b a b i l i t y d i s t r i b u t i o n of employment, 8* = (3*,3*,...,g|). d i s t r i b u t i o n , 3*,is conceptually  The  d i f f e r e n t from the d i s t r i b u t i o n , 3-  d e s c r i b i n g the labour market environment.  3 r e f e r s t o the a c t u a l  d i s t r i b u t i o n of firms a t a p a r t i c u l a r point i n time.  In equilibrium,  the a c t u a l d i s t r i b u t i o n of f i r m s , 8, e x h i b i t s v a r i a t i o n about the d i s t r i b u t i o n , 8 * , due to the s t o c h a s t i c forces operating i n the market. Since the process described i s a Markov process, the steady s t a t e d i s t r i b u t i o n e x i s t s , i f the t r a n s i t i o n matrix i s regular. d i s t r i b u t i o n i s given by 8 as c a l c u l a t e d i n (v).  This  This r e s u l t i s  approximate, since the convergence c r i t e r i a i n ( i v ) and (v) does not require that 8.. = 8..  Since e > 0 adopting the optimal p o l i c y ,  y*, does not exactly recreate the same expected labour market environment.  The accuracy of the r e s u l t depends on the magnitude of e.  I f y* i s the optimal p o l i c y , . t h e n the true steady state d i s t r i bution 8* i s given by  where  B  j " Vl  [ e  nk  ( 6  £'Vl -' ) ]  (51)  84 If  f i r m s a r e d i s t r i b u t e d a c c o r d i n g to (3*, then a d o p t i o n o f  optimal p o l i c y exactly recreates the p a r t i a l l y  optimal p o l i c y i s  The e x p l i c i t  the l a b o u r market environment. optimal for  Thus,  ever.  f o r m u l a t i o n o f f i r m b e h a v i o u r and d i s c u s s i o n o f  a l g o r i t h m t o s o l v e Models I I  C.  the  and I I I  can be found i n Appendix  the  I.  An Overview of Model I H a v i n g developed  the b e h a v i o u r o f market p a r t i c i p a n t s  the market responds t o t h i s b e h a v i o u r , the r e l a t i o n s h i p s .  it  i s now p o s s i b l e  and how t o summarise  T h i s i s a model o f the l a b o u r market i n which  there  are N firms each h a v i n g the same m a r g i n a l revenue p r o d u c t f u n c t i o n , MRP(n), and the same r a t e o f d i s c o u n t , v a l u e of p r o f i t s  R.  Firms maximise the expected  over an i n f i n i t e h o r i z o n .  I n d i v i d u a l workers maximise the expected p r e s e n t v a l u e over a working h o r i z o n o f H p e r i o d s . differential H^ < H .  They b e l i e v e  associated with search w i l l p e r s i s t  T h e i r r a t e o f d i s c o u n t i s D.  job o f f e r s ,  of income  t h a t the wage  for H^ p e r i o d s ,  I n o r d e r to generate  workers must engage i n a p r o c e s s  worker can make one c o n t a c t If  o f random s e a r c h .  unemployed, the worker i s  ment compensation,,w.  Individuals'  perceptions  c^ and  in  Each search  guaranteed  of t h e r e t u r n s  s e a r c h are assumed i m p e r f e c t but n o t u n r e l a t e d to the a c t u a l The parameters  specific  p e r p e r i o d and he r e c o n s i d e r s h i s  d e c i s i o n each p e r i o d .  from s e a r c h .  present  unemployfrom  returns  (11) and (12) determine  r e l a t i o n s h i p between the i n d i v i d u a l ' s p e r c e p t i o n o f the o f f e r  the  distri-  85 bution and the a c t u a l d i s t r i b u t i o n .  Each i n d i v i d u a l ' s perception of  the r e s e r v a t i o n wage i s drawn from a gamma d i s t r i b u t i o n , p(wc), whose parameters are r e l a t e d t o the true r e s e r v a t i o n wage and the variance of o f f e r s .  The supply of labour to the i n d u s t r y , L, i s constant.  Thus, N, D, R, H^, L, H are exogeneous constants and MRP (n) and p(wc) are exogeneously determined r e l a t i o n s h i p s ,  c^ and  can be regarded  as s h i f t parameters. I f an i n d i v i d u a l searches randomly, then h i s perception of the mean and variance of the wage d i s t r i b u t i o n i s unbiased. The unknowns i n the model are t * , (n = 0,1,...,n), the rate of turnover f o r a f i r m w i t h n employees. n  a n  *> (n = 0,1,...,n), the rate of accession f o r a f i r m w i t h n employees.  6 k*,(n,k = 0,1,...,n), the p r o b a b i l i t y that a f i r m w i t h n employees n  In one p e r i o d w i l l have k employees i n the next period. <$* = ( w * , v * ) , ( n =_ 0,1,... ,fi) , the wage o f f e r and vacancy c r e a t i o n n  n  d e c i s i o n made by a f i r m with n employees. 8* , (n = 0,1,...,n), the steady state p r o b a b i l i t y of a f i r m f a c i n g n employees. E* ,the l e v e l of employment. U*, the l e v e l of unemployment, and x* = (8*,<5*),  the labour market environment.  2 There are (n+l) + 4(fi+l) + 3 unknowns.  86 I n d i v i d u a l s e a r c h b e h a v i o u r g i v e s r i s e to the t u r n o v e r  rates  to the f i r m which may be w r i t t e n ,  V  W  =  5  X  *' * U  N.D.H^CJ^CJ)  ;  n = 0,1,...,n.  The t u r n o v e r r a t e  . . . .  f a c i n g a f i r m i s a f u n c t i o n of i t s  (52)  own wage r a t e ;  the l a b o u r market environment and the l e v e l of unemployment; the number o f f i r m s , the i n d i v i d u a l ' s own r a t e o f d i s c o u n t , time h o r i z o n over whichwage d i f f e r e n t i a l s  persist  and the  and the  perception  parameters. Likewise,  a  n*  =  a  n  ( w  the acceptance  n*  ;  X  *' * U  ;  f u n c t i o n may be w r i t t e n  N.^IL^c^)  n = 0,1,...,n.  The t r a n s i t i o n p r o b a b i l i t i e s may be w r i t t e n  nk  nk^n ' n ' n '  '  '  3  =  (53)  . . . .  (54)  as  N )  n,k = 0 , 1 , . . . , n .  The steady  . . . .  state distribution, B (n = 0 , 1 , . . . , n ) ,  [1,0,...,Q:]. l i m [ 0 t-*»  n  r f c  ]  t  f  is  . . . .  determined  (55)  87  The wage and vacancy the s o l u t i o n to  (45),  r  + ^  r r r r = (6 ,6,,...,5 , . . . , < S O o 1 n n  t h a t c o u l d be  (w^*,v^*)(n  = 0,1,...,fi),  are  namely  F*(n) = max [ f ( n , S * ) Y  where y  decisions,  E 9 (<^)F*(k) ] k=0  . . . .  nk  and t h e r e a r e I p o s s i b l e  (45.)  policies  adopted.  The expected  l e v e l o f employment  is  n E* = N  Z  n  n=0  n.g  * n  . . . .  (56)  . . . .  (57)  and the expected l e v e l o f unemployment,  Tj* = L - E * .  III. A.  The C h a r a c t e r i s t i c s o f S t o c h a s t i c  Equilibrium  The Mean Wage o f the Employed I n d i v i d u a l Unemployed i n d i v i d u a l s computing the r e t u r n s from s e a r c h  the mean wage by e v a l u a t i n g  the p r o b a b i l i t y o f an o f f e r .  measure can be computed f o r those c u r r e n t l y employed. the mean wage b i l l  calculate  A similar  I f WB i n d i c a t e s  i n c u r r e d by the i n d u s t r y d u r i n g the p e r i o d , and mean  employment i s E * , then the mean wage f o r those employed i s MW where  (58)  88 Denoting the steady s t a t e t r a n s i t i o n matrix by T* where X* = [T„*],(i,j = 0,1,..., n) , then a f i r m c u r r e n t l y facing employment l e v e l n w i l l pay a wage, w *, t o j employees next period w i t h n  p r o b a b i l i t y , T^*.  Then, the mean wage b i l l incurred by a f i r m i n  employment s t a t e n i s computed as  WB  «  n  Z T *.j.w *. J=0 nj  . . . . (59)  n  There are N.3^* firms f a c i n g employment l e v e l n.  Thus the mean  industry wage b i l l , WB, i s given by n n n WB =N E WB .3 * = E N.3 * £ T .*.j.w *. „ n n n . ni n n=0 n=0 j=0 J  n  . . . . (60)  J  n  In s t o c h a s t i c e q u i l i b r i u m the l e v e l of mean employment,E*,is constant and E*  =  N  Z  ii=0  n.3 * •  . . . . (61)  n  Then, MW =  n N E W Bn. 3n*  n E W Bn. 3n*  n  =  n  N Z n.3 * „ n n=0  .  n Z n.3 * n n=0  T h i s measure o f the mean wage i s another summary s t a t i s t i c be used f o r comparing s t o c h a s t i c  e q u i l i b r i a generated  under  which may different  89 values of the exogeneous parameters.  The mean wage for each type  of employed i n d i v i d u a l can be computed i n Models I I and I I I . Comparison of these measures gives some indication of the impact of e x p l i c i t discrimination B.  Mean Lifetime  on r e l a t i v e wage o f f e r s .  Income for the Worker  When the labour market i s i n stochastic possible  equilibrium,  it is  to calculate three d i f f e r e n t measures of l i f e t i m e mean  income for an i n d i v i d u a l .  At the beginning of each period an  i n d i v i d u a l i s i n one of three d i s t i n c t states.  He may be unemployed  and have j u s t received and accepted a wage o f f e r , j * ( j w  0,1,...,n),  =  for next period, from a firm facing employment l e v e l , j , states UA = ( 0 , 1 , . . . , n ) . an o f f e r , j*>(j w  He may be already employed and j u s t about to accept 1,2,... ,fi), from his firm which faces employment l e v e l  =  j , states EA = (fi+l,n+2,... ,2n) .  I f already employed, he cannot receive  a wage o f f e r , w^*, from his firm.  These states are i d e n t i f i e d then  according to whether the individual was previously employed or unThe t h i r d category, state 2fi + 1 ,  employed and the wage rate accepted.  i s that the currently unemployed i n d i v i d u a l has decided to search further next period and receive unemployment compensation, w. The  individual's state to state t r a n s i t i o n matrix i s closely  related to his own probability of receiving an o f f e r , 3 *Y *» accepting n  i t , a^* = ( a  n  w n  n  * » x*,U*; N , D , H ^ , c ^ , C 2 ) , q u i t t i n g when employed,  t * = t (w'*; x*,U*; N J D J H , , C , , C ) , and the firm's t r a n s i t i o n matrix, n n n ' 1' 1' 2 ' ' 0  =  9  k^ n*' n*' n*'^*'' ' a  n  t  V  n  determines the wage o f f e r .  s:  *"  nce  t  *  ie  f  i r m  '  s  state of employment  The f i r s t two categories of state, UA and EA,  90  are conceptually d i f f e r e n t i n that the t r a n s i t i o n vector f o r a f i r m , f a c i n g employment l e v e l , j , and o f f e r i n g wage, j*» depends on whether w  the p a r t i c u l a r i n d i v i d u a l , who has j u s t received and accepted an o f f e r , W j * , f o r the next p e r i o d , i s now unemployed or already employed by the firm.  I f S denotes the returns from each s t a t e then  S  =  (WQ.W^  ... ,w ,w ,w ,... ,w ,w) . fl  1  2  . . . .  ft  (63)  The three measures of l i f e t i m e mean income are : 1.  Income gained from the s t o c h a s t i c turnover and acceptance behaviour modelled i n t h i s chapter, YS;  2.  Income derived from never q u i t t i n g a f i r m , YQ;  and  3.  Income gained from turnover and acceptance behaviour based on knowledge of the true reservation wage, YC.  I t must be understood that the l a s t two measures are h y p o t h e t i c a l i n that they are c a l c u l a t e d on the b a s i s of one i n d i v i d u a l ' s nons t o c h a s t i c behaviour i n a world where a l l other i n d i v i d u a l s and a l l firms behave i n the manner described i n Section I I I .  This i n d i v i d u a l  i s not recognised by firms. These measures y i e l d i n t e r e s t i n g i n s i g h t s i n t o the nature of s t o c h a s t i c forces i n the labour market.  I f the f i r m i s subject to  s i g n i f i c a n t changes i n employment from one period to the next, then the search behaviour modelled i n I I I w i l l be sub-optimal, because wage d i f f e r e n t i a l s f a i l to p e r s i s t .  Expected income from such  91 behaviour, that i s the f i r s t measure, w i l l be l e s s than f o r some other search r u l e .  Herein l i e s the c o n t r a d i c t i o n , however.  Assuming that i n  t h i s stochastic environment an i n d i v i d u a l i s b e t t e r o f f i f he quits and accepts o f f e r s according to the reservation wage, then i t seems p l a u s i b l e that a l l i n d i v i d u a l s should adopt t h i s non-stochastic behaviour. I f firms were aware of such behaviour, however, then each would o f f e r s l i g h t l y more than the l e v e l of unemployment compensation, the c o l l u s i v e monopsony s o l u t i o n , and there would be no dispersion and no search.  I n d i v i d u a l s are homogeneous i n t h e i r search behaviour,, then-.  Thus, w h i l e these measures do y i e l d i n s i g h t s i n t o the ranking of search r u l e s , these measures are p a r t i a l e q u i l i b r i u m measures i n that firms are assumed not t o respond optimally to the rules s p e c i f i e d . This underlines the importance of the expectations of each set of market p a r t i c i p a n t s about the behaviour of the other set o f p a r t i c i p a n t s . The forward.  computation of mean income from s t o c h a s t i c behaviour i s s t r a i g h t I f an i n d i v i d u a l behaves s t o c h a s t i c a l l y , then he accepts a wage  offer,w^*, when unemployed, with p r o b a b i l i t y , a^* =  a k  (  w k  * ; x*,U*; N,D,H^,  c^j^),and,once employed,he remains employed i n response t o a wage o f f e r , w *, w i t h p r o b a b i l i t y ( l - t * ) = 1 - t ( w * ; x*,U*; N.D,^,^,^) . k  k  fc  k  Consider an i n d i v i d u a l who has received and accepted h i s f i r s t job o f f e r , w^*, at the beginning of h i s job horizon.  Then, the p r o b a b i l i t y  that he receives and accepts an o f f e r , w *, next period i s the product k  of the p r o b a b i l i t y of accepting the o f f e r , l - t * , and a c o n d i t i o n a l k  p r o b a b i l i t y , namely, that the f i r m f a c i n g employment l e v e l n and o f f e r i n g  92 a wage, * » moves to employment l e v e l k next period, w  n  p a r t i c u l a r searcher accepted the o f f e r , w^*. ployment l e v e l k next period, i f creating  v  The firm achieves em* l -  n  given that one  vacancies and facing  h currently employed individuals and U * - l searchers i t can employ k-1 of them.  Denoting t h i s t r a n s i t i o n p r o b a b i l i t y by'TS ^, then  TS . = (l-.t. *)6 . ,(a * , t *,v * - l ; U*-l,n; N) ni - k nk-1 n ' n ' n ' ' ' where  i e E A n e U A  i = k + n'..  If an i n d i v i d u a l , previously  . . . .  (64a)  unemployed, has j u s t accepted an  o f f e r , then i n the following period he either becomes unemployed or enters a state denoted by EA.  TSn i.  =0  Then  n E EA or n E UA and i e UA .  . . . .  (64b)  An i n d i v i d u a l , already employed with a firm which offers a wage, w *, n  say, has a d i f f e r e n t p r o b a b i l i t y of receiving and accepting an  offer, w^*,  next period.  remain employed.  The firm has one employee who i s certain to  Thus, facingU* searchers and n-1 other employees and  creating v * vacancies the firm must h i r e k-1 i n d i v i d u a l s .  TS' . mx where  =  Then  (l-t*)6 Aa * , t *,v *; U*,n-1,N) k n-lk-1 n n ' n ' ' '  m,isEA  n i  m=n  + n  i = k. + n .  . . . .  (64c)  93  From (64a) the p r o b a b i l i t y that an i n d i v i d u a l i n s t a t e , n e UA, becomes unemployed next period i s simply  T S  n,2fi l  =  "  1  +  * ni leEA T S  n  e  U A  "  • • • • < > 64d  Likewise, from (64c) the p r o b a b i l i t y that an i n d i v i d u a l who i s c u r r e n t l y employed and r e c e i v i n g a wage, w^*, w i l l q u i t i n response to the new wage o f f e r next p e r i o d i s  TS  =  1 -  m,2n+l  TS . me leEA mi  EA, m = n+n.. '  .Z_.  ....  (64e)  An i n d i v i d u a l , who i s currently unemployed, w i l l receive an o f f e r , w^*,  from a f i r m w i t h p r o b a b i l i t y , 3 *Y *« n  n  He w i l l accept  the o f f e r w i t h p r o b a b i l i t y , a * = a (w *; x*,U*; N,D,H ,c ,c ). n  T S  T S  Zn+l-,n  ?A+I  OA_I_I  n  =  n  zn+1,n  =  Y„*  n  Pj}*  0  n  n  n  fl  n  e  UA.  e  EA.  ;L  1  2  . . . .  . . . .  Then  (64f)  (64g)  An i n d i v i d u a l , who i s c u r r e n t l y employed, can only enter one of the UA states or remain unemployed.  This explains (64g).  From (64f) an i n d i v i d u a l has a p r o b a b i l i t y T ^ ^ ^ remaining unemployed where  2n+l' °^  94  TS  2n+l,2fi+l  "  1  ~  2n+l,n * neUA '  Z  . . . . (64h)  T S  T T A  The i n d i v i d u a l i s assumed t o search f o r one period p r i o r t o h i s job horizon.  Then, he has a p r o b a b i l i t y T ^ ^ + i » °^ securing and n  accepting a wage o f f e r , w^*, at the beginning of h i s job horizon and a p r o b a b i l i t y ^2fi+l  2n+l' °^  c o m m e n c : L n  8  n i s  work horizon unemployed.  He has a zero p r o b a b i l i t y of commencing h i s work horizon i n one of the th EA s t a t e s .  Denoting the 2ii+l  row of TS (the t r a n s i t i o n matrix) by  TS2^ ^ then expected income, YS, i s given by +  YS = T S  C.  [S + (TS)S + (TS) S + ... + ( T S ) 2  2 f i + 1  H - 1  S]. . . . .  (65)  1 0  Labours' Share of Output I f both sets of p a r t i c i p a n t s gain i n response to a change i n an  exogeneous parameter, f o r example, the period length, then a u s e f u l summary s t a t i s t i c i s labours' share of t o t a l output. A f i r m f a c i n g employment l e v e l , n, has mean one p e r i o d p r o f i t s , f(n,6 ). n  Denoting t o t a l mean one p e r i o d industry p r o f i t s by Til, then,  * E 6 .f(n,6 ).. „ n n n=0 fi  Til  =  N  From (60), WB denotes the mean industry wage b i l l . LS denotes labours' share of t o t a l output,  . . . . (66)  Then, i f  95 D.  The C o r r e l a t i o n of Wage Rates Over Time In computing t h e i r returns from job search,individuals assume  that, i f they accept a p a r t i c u l a r wage o f f e r , then they w i l l enjoy the same wage over the horizon, H^.  I f firms face s t o c h a s t i c t u r n -  over and acceptance behaviour on the part of workers, then they w i l l face d i f f e r e n t l e v e l s of employment over time and thus o f f e r d i f f e r e n t wage rates over time. Of i n t e r e s t , then, i s the c o r r e l a t i o n of firms' wage o f f e r s over time.  E v i d e n t l y , i f the temporal c o r r e l a t i o n of wage rates i s low then  i n d i v i d u a l s should never q u i t to search but should remain employed, i r r e s p e c t i v e of the wage o f f e r . This c o r r e l a t i o n c o e f f i c i e n t i s computed i n the f o l l o w i n g way. Let W  denote the vector of wage r a t e s , defined over states of employ-  1  ment, i n period i . Then, since the labour market i s i n s t o c h a s t i c equilibrium,  rW i = (w^w^... /i i f\) ,wi,... ,w T  n  = w  fi  i + k  = W*  i = 0,1,... k = - i , - i + l ...  . . . .(68)  _* where W  denotes the vector of wage o f f e r s c h a r a c t e r i s i n g s t o c h a s t i c  equilibrium.  L e t g* denote the steady s t a t e d i s t r i b u t i o n of employment.  Then, the mean wage o f f e r facing an i n d i v i d u a l , i f he i s employed i n period i , i s w  1  where  96  ft  1  Let v  n E j=0  =  J  =  w  =  w*.  J  i = 0,1,...  K  k = -i,-i+l,  . . . . (69)  denote t h e v a r i a n c e o f wage o f f e r s , g i v e n  1  i s employed,  v  B* w?  1  t h a t the i n d i v i d u a l  then,  =  E j-0 n E j-0  B*(wT) - ( w ) 2  J  2  i+k  =  v  =  v* .  2  J  B* w* J  1  2 - w  J  i = 0,1,...  k = -1,-i+l,  . . . . (70)  L e t 6 *Xk,n = 0 , 1 , . . . . ,fi) denote t h e elements nk  matrix, P * , characterising equilibrium. matrix i s stationary  i s stationary.  the j o i n t p r o b a b i l i t y t h a t a f i r m , i n p e r i o d i and w^* i n p e r i o d i+1. written  S i n c e both t h e t r a n s i t i o n  and the d i s t r i b u t i o n o f o f f e r s  then the c o r r e l a t i o n c o e f f i c i e n t  o f the t r a n s i t i o n  i s time i n v a r i a n t ,  Let P( j» w  taken a t random, o f f e r s  w  k  +  ^ denote  a wage,  w  j*>  Then, t h i s j o i n t p r o b a b i l i t y may be  97  P  (  w  j '  W  k  ±  +  1  )  =  p  (  j '  w  W  k  }  =  3  j* jk*-  . . . . (71)  9  Then, the c o v a r i a n c e between wage o f f e r s i n p e r i o d cov(W"*",W'''""'") , may be w r i t t e n r  _. _. cov(W ,W ) =  If  i and p e r i o d i+1,  as  fi fi „ E E g * 9* w* w* - w . j=0 k=0 J j k j k  . . . . (72)  cc(W^,W '" ^) denotes t h e c o r r e l a t i o n c o e f f i c i e n t , then :  +  ccCW ,^* ) 1  =  1  c  °v(w%W  i + 1  )  cov(W*,W*)  =  /.i.i+1 V  To  ( 7 3 )  v*  V  determine the c o r r e l a t i o n o f wage o f f e r s over s a y , T  p e r i o d s , i t i s n e c e s s a r y t o compute  p  and  T  =  [ 0  nk*  . . . . (74)  ] T  r e p l a c e t h e elements, 0 * ( n , k = 0 , l , . . . ,fi) , i n the computation k  -T w i t h t h e c o r r e s p o n d i n g elements from P .  E.  The Mean D u r a t i o n of Employment and the Mean D u r a t i o n of Search P r i o r t o a Wage O f f e r Two o t h e r summary s t a t i s t i c s ,  e a s i l y computed, a r e the mathematical  e x p e c t a t i o n o f t h e d u r a t i o n o f unemployment and the m a t h e m a t i c a l expectation  o f the d u r a t i o n of s e a r c h p r i o r t o a wage o f f e r .  denote the p r o b a b i l i t y  of r e c e i v i n g a j o b o f f e r i n one s e a r c h and l e t  PA* denote the p r o b a b i l i t y one  search.  L e t PO*  of r e c e i v i n g  Then, u s i n g t h e normal  and a c c e p t i n g a wage o f f e r i n  notation,  98 PO*  =  n E 0* y* n=0  . . . . (75)  n E g* Y*a*.. n n n n=0  . . . . (76)  n  PA*  =  n  n  In s t o c h a s t i c e q u i l i b r i u m these p r o b a b i l i t i e s are time i n v a r i a n t . Then, the mean duration of search p r i o r to an o f f e r , D , may be w r i t t e n g  as  D  s  PO*  . . . . (77)  and the mean duration of employment, D^, may be w r i t t e n as  D  F.  u  PA* '  =  ' ' ' '  ( 7 8 )  Mean P r o f i t s of a Firm I t i s also possible to compute the p r o f i t s of a f i r m taken a t  random.  I f $* denotes the p r o b a b i l i t y of a f i r m a t t a i n i n g employment  s t a t e n andF*(n)is the mean p r o f i t s discounted over an i n f i n i t e horizon of a f i r m commencing i n employment state n$ then mean p r o f i t s , EII, are  En  =  n E g *F*(n). n=0  . . . . (79)  n  This measure can be used as an i n d i c a t i o n of the industry p r o f i t a b i l i t y under d i f f e r e n t labour market s t r u c t u r e s .  99 G.  Speculative It  i s evident  in stochastic static  Vacancy  Creation  t h a t i n t h i s model the l e v e l  e q u i l i b r i u m i s at  p r o f i t maximisation,  The q u e s t i o n a r i s e s  l e a s t the l e v e l  of vacancy  creation  consistent  with  assuming no c u r r e n t employees  as t o whether  the f i r m would choose  quit.  to h i r e  more i n d i v i d u a l s i n the c u r r e n t p e r i o d , i n o r d e r to e x p l o i t i n t e r t e m p o r a l monopsony power. the f o l l o w i n g  denote  e q u i l i b r i u m a f i r m employing n i n d i v i d u a l s  and o f f e r s  a wage, w^*.  single period profits n  denote mean p r o f i t s  for  U s i n g the u s u a l n o t a t i o n ,  i n s t a t e n , and adopts  denotes  individuals let  F*(n)  the o p t i m a l s e t  of  ever.  Assume the f i r m faces employment F(n,k)  w i t h employing k  d i s c o u n t e d over an i n f i n i t e h o r i z o n earned by  the f i r m , which commences 6*,  creates  L e t iUkjW^*), ( n , k = 0,1,...,n)  associated  and p a y i n g them a wage, w * .  decisions,  can be t e s t e d by  procedure.  In s t o c h a s t i c v * vacancies  This hypothesis  its  the t o t a l mean p r o f i t s  h o r i z o n of a f i r m , which commences  l e v e l k next p e r i o d , d i s c o u n t e d over an  then  if  infinite  i n s t a t e n and then moves  to  employment s t a t e k n e x t p e r i o d ,  F ( n , k ) = n(k,w  *). +  F*(k)  1+R  k < n + v * ., n  (80)  }  100  If,  after  choose i t s  adopting i t s  initial  d e c i s i o n , 8*, the f i r m c o u l d n  l e v e l o f employment, next p e r i o d , then i t would choose  employment l e v e l , L ,  where  n  F(n,L ) n  = max(n(k,w *) k n  +  )  . . . .  Denote the s i n g l e p e r i o d p r o f i t maximising l e v e l of a s s o c i a t e d w i t h a wage, w * , b y n ( w * ) , n  L  n  n  -  ft  employment  then  ( *> w  (81)  . . . .  n  (82)  s i n c e the f u n c t i o n , F * ( k ) , i s a n o n - d e c r e a s i n g f u n c t i o n o f k . T h i s demonstrates  t h a t f i r m s may choose t o c r e a t e more v a c a n c i e s  than i s c o n s i s t e n t w i t h s i n g l e p e r i o d p r o f i t m a x i m i s a t i o n , i n o r d e r t o exploit  t h e i r i n t e r t e m p o r a l monopsony power.  In a d d i t i o n , however,  n + v *• n  that i s  >  L  over some s t a t e s ,  . . . .  n  firms create vacancies  (83)  i n excess o f the l e v e l d e s i r e d h i r e s  which a r e c o n s i s t e n t w i t h the e x p l o i t a t i o n o f i n t e r t e m p o r a l monopsony power.  Such vacancy  stochastic  c r e a t i o n . c a n be d i r e c t l y a t t r i b u t e d to  t u r n o v e r and acceptance  behaviour of i n d i v i d u a l s .  the By  101  definition,  vacancy  creation is speculative.  f i l l i n g any p o s i t i o n s  c r e a t e d due to s t o c h a s t i c  b e h a v i o u r by i n d i v i d u a l s . describe  those v a c a n c i e s  b e h a v i o u r by w o r k e r s . can be c o n s t r u c t e d .  No f i r m i s a s s u r e d o f s e a r c h and  acceptance  I n t h i s work, the word w i l l be used which can be a t t r i b u t e d  to  stochastic  A measure o f aggregate s p e c u l a t i v e I f .V  denotes  to  aggregate s p e c u l a t i v e  vacancies vacancies,  then  n V  s  =  N  Z  (n+v * - L )3 * . n n n  n=0 n  The approach adopted t o a n a l y s e i s analogous  to t h a t  o p t i m a l wage o f f e r market.  d e s c r i b e d by A r c h i b a l d [1954].  of vacancy  creation  the  is  c r e a t i o n would  T h i s i s a s i n g l e p e r i o d model and so the o p t i m a l c r e a t i o n i s e q u a l to the l e v e l of employment  which the w o r k e r s '  m a r g i n a l revenue product e q u a l s  minus the c u r r e n t l e v e l  of  c o m p l i c a t e d because  at  the o p t i m a l wage,  employment.  I n the i l l u s t r a t i v e model, the problem i s made s l i g h t l y  last  decision  imperfect  i f the s u p p l y o f l a b o u r  what l e v e l o f vacancy  (84)  He d e r i v e s  f o r the f i r m p r o f i t maximising i n an  at the wage o f f e r ,  the f i r m c r e a t e ? level  the f i r m ' s vacancy  He then asks t h e q u e s t i o n :  stochastic  . . . .  the f i r m i s  more  assumed t o i n h e r i t a workforce  p e r i o d , b u t s t i l l p r o f i t maximises i n a s i n g l e p e r i o d  from  framework.  102 In t h i s model,  the f i r m chooses a wage o f f e r and l e v e l o f  vacancy c r e a t e d t o maximise p r o f i t s over an i n f i n i t e h o r i z o n  subject  to s t o c h a s t i c v a r i a t i o n i n the whole l a b o u r s u p p l y s c h e d u l e . q u e s t i o n i s then posed  The  : what l e v e l o f employment would t h e f i r m  c h o o s e , i f able to i n f l u e n c e i n d i v i d u a l s ' behaviour?  Does t h i s  employment l e v e l exceed the s t a t i c p r o f i t maximising l e v e l o f employment?  I f s o , then the f i r m chooses a l e v e l o f employment above the  s t a t i c p r o f i t maximising l e v e l o f employment, i n o r d e r t o e x p l o i t i t s i n t e r t e m p o r a l monopsony power.  H.  The C o l l u s i v e R e s e r v a t i o n Wage I f f i r m s were t o c o l l u d e i n t h e i r wage o f f e r , they would o f f e r a  wage j u s t above the l e v e l o f unemployment i n s u r a n c e , w.  There would be  no d i s p e r s i o n , no s e a r c h and z e r o unemployment. A n a l o g o u s l y , i t i s p o s s i b l e to compute t h e c o l l u s i v e  reservation  wage f o r workers such t h a t t h e i r j o i n t e a r n i n g s a r e maximised,  under  the assumption of p r o f i t maximising b e h a v i o u r on the p a r t o f f i r m s . Assume t h a t each f i r m has an exogeneous m a r g i n a l revenue p r o d u c t f u n c t i o n o f the form  MRP  (n)  =  a - -n  where n denotes t h e l e v e l o f employment.  . . . . (85)  There a r e N f i r m s i n the  i n d u s t r y and s o , i f w denotes t h e r e s e r v a t i o n wage, j o i n t J E , may be w r i t t e n  earnings,  103 JE = N ( a - w)w + (L-N(a - w))\w.  . . . . (86)  Q  Each firm p r o f i t maximises and chooses a l e v e l of employment at which the marginal revenue product equals the wage, w. ignoring i n d i v i s i b i l i t i e s , remaining (L-N(a ~ w))-  Then,  each firm hires ( - w) workers and the a  Q  individuals earn unemployment compensation,  o  w.  D i f f e r e n t i a t i n g with respect to w y i e l d s  Na  -2Nw + Nw  Q  . . . . (87)  and so t o t a l labour income i s maximised by a c o l l u s i v e reservation wage, w, where  N(a w  o  + w) ^  =  a + w o ^— *  Ignoring i n d i v i s i b i l i t i e s ,  ,„„. . . . . (88)  the c o r r e s p o n d i n g l e v e l o f employment  is  a + w L o ( a - w)N = ( a Q  Q  -^j—  a -w )  N  != (  ) N..  . . . . (89)  An i n t e r e s t i n g question i s whether the mathematical expectation of the discounted stream of wage offers (including unemployment compensation) enjoyed by an i n d i v i d u a l over h i s job horizon i s p o s i t i v e l y related to the mean wage o f f e r enjoyed by an employed worker i n a single  104 period.  I f , i n a labour market i n which information i s perfect, the  wage rate exceeds the c o l l u s i v e reservation wage, then the j o i n t earnings of labour i n the single period f a l l below the j o i n t earnings associated with the c o l l u s i v e reservation wage.  Then, ignoring the  impact of the stochastic forces i n the labour market, i t seems plausible that an individual's mean discounted  income over h i s work  horizon i s p o s i t i v e l y correlated with the single mean wage o f f e r up to the c o l l u s i v e reservation wage,ft,and i s negatively correlated to the mean wage o f f e r above the c o l l u s i v e reservation wage.^  105 CHAPTER 3 THE DISTRIBUTION OF PERCEPTIONS, THE DATA, THE SIMULATION PROCEDURE AND THE METHOD OF COMPARATIVE STATICS  I. A Summary In t h i s chapter the properties of the density function of perception o f the reservation wage, which i s adopted i n the s i m u l t i o n s , are analysed.  The parameter values adopted i n each  model are s p e c i f i e d . The p a r t i a l optimisation procedure i s outl i n e d and the convergence and c y c l i n g c r i t e r i a are examined.  The  problemsarising from the simulation procedure are discussed, and f i n a l l y the approach adopted i n organizing the comparative s t a t i c r e s u l t s i s described. II.  The Gamma D i s t r i b u t i o n  A p r i o r i , the density function of i n d i v i d u a l perceptions o f the reservation wage has no p a r t i c u l a r form, except that i t be defined on the p o s i t i v e quadrant.  The gamma d i s t r i b u t i o n was chosen because i t  has two u s e f u l p r o p e r t i e s , 1.  I t i s a two parameter d i s t r i b u t i o n defined on the whole p o s i t i v e quadrant; and  2.  Through d i f f e r e n t values o f the parameters i t can look Gaussian or skew.  L  f \ / \ exp —r~. (~wc) P(wc) = , 1B+1 (wc) B  B  A  . . . . (1)  106 2 This d i s t r i b u t i o n has mean, (B+1)A, and variance, (B+1)A . From Chapter 2 IB, MP and VP represent the mean and variance, r e s p e c t i v e l y , of the density f u n c t i o n of i n d i v i d u a l perceptions of the r e s e r v a t i o n wage, where  MP = CjW*  c  > 0  . . . . (2)  VP = c EW*  c > 0  . . . . (3)  1  2  2  and W*, VW* denote, r e s p e c t i v e l y , the true r e s e r v a t i o n wage and variance of wage o f f e r s i n the industry.  For consistency, then, i t i s necessary  that MP = (B+1)A  . . . . (4)  and VP = (B+1)A . 2  . . . . (5)  In order to determine the p r o b a b i l i t i e s of turnover and acceptance i n response to a given wage o f f e r , w, and given labour market parameters, i t i s necessary to evaluate the cumulative of the gamma d i s t r i b u t i o n , P(w), which may be w r i t t e n P(w) =  p(wc) dwc..  . . . . (6)  Turnover and acceptance p r o b a b i l i t i e s are given by t(w) = l-P(w)  . . . . (7)  a(w) = P(w) ..  . . . . (8)  107 2 Mood [1950] demonstrates that a close approximation to this cumulative p r o b a b i l i t y i s  P(w)  = 1.0 - e x p ( ^ ) A  J B •(-) Z -4r* J=l '  . . . . . (9)  3  J  The i n t e g r a l part of B i s used i n the summation u n i t .  I t i s easy to  M demonstrate that the mode, WC , i s given by M VP WC = AB = MP - ^ •  , , i . . . . (IO)*  The general shape of the gamma d i s t r i b u t i o n i s shown i n Figure 5.  P  WC Figure 5 -  The Gamma D i s t r i b u t i o n  Changes i n MP o r VP change the parameter values, A and B, and the d e r i v a t i v e of the cumulative distribution,P(w), with respect to B i s not defined.  Thus, i t i s not possible to determine a n a l y t i c a l l y the impact  of changes i n the mean and variance on the shape of the gamma d i s t r i b u t i o n .  108 If  increases so that MP increases, however, then from (10) the mode, M  WC , s h i f t s to the r i g h t and i t i s p l a u s i b l e to assert that the r e l a t i o n ship between the new marginal gamma distribution,p^(wc), and the d i s t r i b u t i o n , p(wc), i s as shown i n Figure 6.  Figure 6 - Gamma D i s t r i b u t i o n s with D i f f e r e n t Means.  For values of wc greater than or equal to the new mode, WC^, then p^(wc) exceeds p(wc) and so the marginal rates of turnover and acceptance are higher.  Furthermore, f o r a l l values of w the new  cumulative d i s t r i b u t i o n P^(w) i s less than P(w).  Then, c e t e r i s paribus,  109 dP(w) dc,  < 0  • (ID  dt(w) dc.  > 0  • (12)  da(w) dc.  <  and s o ,  An  Increase  0 .  . . . . (13)  i n the v a l u e o f o.^ i n c r e a s e s t h e p e r c e i v e d  of the d i s t r i b u t i o n  of perceptions.  o f t h e d i s t r i b u t i o n became f a t t e r . d i s t r i b u t i o n s h i f t s t o the l e f t . f i d e n c e t h a t an i n c r e a s e i n manner shown i n F i g u r e 7.  to  variance  I t can be argued t h a t the t a i l s From above, t h e mode o f the  Then,it  can be a s s e r t e d w i t h  changes t h e d i s t r i b u t i o n  coni n the  p(wc) denotes t h e new d i s t r i b u t i o n o f per-  c e p t i o n s o f the r e s e r v a t i o n wage. Pl»P  WC  1  WC  MP  F i g u r e 7 - Gamma D i s t r i b u t i o n s w i t h D i f f e r e n t  wc  Variances  110 Then, f o r r e l a t i v e l y low o f f e r s , the cumulative p r o b a b i l i t y of acceptance increases, w h i l e , f o r r e l a t i v e l y high o f f e r s , the cumulative p r o b a b i l i t y of acceptance d e c l i n e s .  For values of the wage approximately  equal to MP, the change i n the cumulative p r o b a b i l i t y i s indeterminate because the points of i n t e r s e c t i o n of the two curves are indeterminate as are the p o s i t i o n s of the respective medians."' III. A.  The Data  Model I The exogeneous constants i n Model I are given the i n i t i a l values  as shown i n Table 1. TABLE 1 The - Initial.:Exogeneous- Parameter Values i n Model I • , V  —  ~  N  R  D  L  w  30  5.26  5.26  120  0.75  ~  : — —  H 10  "  l  H  10  n 8  N denotes the number of f i r m s , " R and D are the respective discount rates f o r each f i r m and each i n d i v i d u a l , L i s the labour 7  force s i z e , w i s the l e v e l of unemployment compensation, H,  denote  the respective horizons of job tenure and the returns from search and fi denotes the maximum l e v e l of employment a f i r m chooses to face.  The  marginal revenue product f u n c t i o n , MRP(n), i s given the f o l l o w i n g form MRP(n) =  5 - n  ....  (14)  Ill  where n i s perfectly  the l e v e l o f employment. competitive  F i r m s , p r o f i t maximising i n a  i n d u s t r y , w i l l h i r e i n d i v i d u a l s up to the p o i n t  at which m a r g i n a l revenue p r o d u c t equals competitive'  the wage.  Thus, i n  'perfectly  e q u i l i b r i u m , each f i r m would h i r e 4 workers and pay a  g wage 1.00.  The l e v e l o f unemployment compensation i s  below the e q u i l i b r i u m wage.  thus  set  MDI over the work h o r i z o n , H , f o r each 9  i n d i v i d u a l i s approximately 8.028. h o r i z o n f o r each f i r m a r e If  Discounted p r o f i t s  over an i n f i n i t e  160.0."^  i n d i v i d u a l s c o u l d c o l l u d e t o maximise t h e i r j o i n t  by f i x i n g a r e s e r v a t i o n wage,then they would choose the  earnings,  reservation  wage, w, where a + w « = — £  5  =  2.875.  The c o r r e s p o n d i n g l e v e l o f employment, L ,  a - w L =(- —)N 2  2  =  MDI f o r an employed i n d i v i d u a l i s 23.081 and mean p r o f i t  at  8.  . . . .  (16)  1 1  discounted  45.157.  The t o t a l number of employment s t a t e s i s s e t set  (15)  is  64 ,  over an i n f i n i t e h o r i z o n i s  . . . .  a t 9 , s i n c e fl i s  T h i s v a l u e o f fi ensures t h a t no p r o f i t maximising f i r m  to create s p e c u l a t i v e vacancies  chooses  such t h a t t h e r e i s a n o n - z e r o p r o b a b i l i t y  o f the r e s u l t i n g l e v e l of employment e x c e e d i n g fi.  112 The parameters c^, c^y  t n e  form of the density function of  perceptions of the r e s e r v a t i o n wage are conceptually d i s t i n c t from the exogeneous labour market parameters shown i n Table 1. The former can be regarded as behavioural parameters while the l a t t e r , although i n f l u e n c i n g labour market behaviour, are t e c h n i c a l parameters and do not r e f l e c t q u a l i t a t i v e aspects of behaviour. The values of the exogeneous constants s p e c i f i e d i n Table 1 and u n i t values of the perception parameters c^,  c o n s t i t u t e the  set of parameter values from which, using the simulation procedure, the 'basic' s o l u t i o n to Model I i s obtained.  Comparative s t a t i c  p r e d i c t i o n s are derived by varying one parameter value and maintaining the remaining parameters a t these s p e c i f i e d values.  Comparative s t a t i c  p r e d i c t i o n s are derived w i t h respect to the perception parameters c^, C 2 » the l e v e l of unemployment compensation, w, the horizon over which returns from search are computed, H^, and the length of the period over which decisions are made. B.  Models I I and I I I Table 2 shows the i n i t i a l values of the labour market parameters  adopted. TABLE 2 The I n i t i a l Exogeneous Parameter Values i n Models I I and I I I N  R  D  50  5.26  5.26  L  l  50  L  2  50  w  0.75  H  10  H  l 10  n  4  113 Using the usual notation, N denotes the number of firms, R and D are the respective discount rates f o r each f i r m and each i n d i v i d u a l , and  are the s i z e s of each labour f o r c e , w denotes the l e v e l of un-  employment compensation, H i s the horizon of job tenure,  i s the  horizon over which returns from search accrue and n denotes the maximum employment l e v e l the f i r m chooses to face. In both models, states of employment are enumerated by both number and composition.  Given the complexity of the s i m u l a t i o n  procedures and the increased number of s t a t e s , i t was decided to reduce the s c a l e of the problem by s e t t i n g the exogeneous marginal revenue product to MRP(n) =  3.0-n . •  ....  (17)  In a ' p e r f e c t l y competitive' world, each f i r m h i r e s two i n d i v i d u a l s and pays a wage of 1.0.  MDI i s again 8.028, but mean  p r o f i t s over an i n f i n i t e h o r i z o n are 40.0.  I f i n d i v i d u a l s could  collude t o maximise t h e i r j o i n t earnings, then they would choose a reservation wage, ft, where ft =  a + w - ° 2 — = 1.875.  ....  (18)  The corresponding l e v e l of employment, L, i s given by x L  a - w = (~ 2—)N 2  1 9  =  56.  . . . . (19)^  114  The c o r r e s p o n d i n g l e v e l o f MDI i s over an i n f i n i t e h o r i z o n are 12.656. number o f s t a t e s , M, i s set  at 15.  15.053 and p r o f i t s Since n i s set  It  influences  i n Models I I  the  creation decisions  III.  Comparisons o f the g e n e r a l c h a r a c t e r i s t i c s  of  stochastic  e q u i l i b r i u m i n Model I w i t h t h e c h a r a c t e r i s t i c s  of  stochastic  e q u i l i b r i u m i n these models suggest t h a t the o b j e c t o f  firms'  d e c i s i o n s over most employment s t a t e s a r e n o t i n f l u e n c e d by r e s t r i c t i o n on the l e v e l o f In Models I I  total  imposed by the parameter,  t h e c h o i c e o f f i r m s ' wage and vacancy and  a t 4,  i s p o s s i b l e t h a t the r e s t r i c t i o n  on the l e v e l o f employment faced by the f i r m , fi,  discounted  and I I I ,  employment.  this  13  over a l l s e t s of parameter v a l u e s  and over a l l o p t i m a l wage d e c i s i o n s ,  the l e v e l o f employment  adopted consistent  w i t h the e x p l o i t a t i o n o f i n t e r t e m p o r a l monopsony power c o i n c i d e s w i t h t h e s t a t i c p r o f i t maximising l e v e l o f employment. i t s wage o f f e r ,  the f i r m n e v e r chooses  above t h a t c o n s i s t e n t w i t h s t a t i c  t o face a l e v e l o f  p r o f i t maximisation.  c u r r e n t l y employing 4 i n d i v i d u a l s and vacancy f i r m can always choose t o s p e c u l a t e The parameter v a l u e s parameters  with respect  i n vacancy  employment  Except when  creation i s  zero,  the  creation.  s p e c i f i e d and u n i t v a l u e s o f the p e r c e p t i o n  generate a ' b a s i c '  simulation procedure.  Thus, h a v i n g made  s o l u t i o n to each model u s i n g  In Model I ,  comparative s t a t i c  to the t e c h n i c a l p a r a m e t e r s , w ^ U  the  predictions  and the p e r i o d  length  115  and the b e h a v i o u r a l parameters  c^,  are d e r i v e d .  g e n e r a l tenor o f such comparative s t a t i c i n Models I I  and I I I .  Consequently,  results  to c ^ ( i =  The C a l c u l a t i o n o f the P a r t i a l O p t i m i s a t i o n P o l i c y  1.  Model I  is  predictions 1,2).  The S i m u l a t i o n Procedure  A.  The f i r s t  the  s h o u l d be the same  the comparative s t a t i c  d e r i v e d f o r those models are s o l e l y w i t h r e s p e c t  IV.  A priori,  s t e p i n the s o l u t i o n o f the f u l l  optimisation algorithm  the s o l u t i o n o f the p a r t i a l o p t i m i s a t i o n a l g o r i t h m , which i s  o u t l i n e d i n Chapter 2 I I B .  The f i r m ,  briefly  faced w i t h an unchanging l a b o u r  market environment, must choose a p o l i c y to be adopted f o r ever which > maximises  the p r e s e n t v a l u e o f mean p r o f i t s  d i s c o u n t e d over an i n f i n i t e  horizon. Hadley's s o l u t i o n procedure i s s a  Y  to s p e c i f y  an a r b i t r a r y  policy,  y~» which i s adopted by the f i r m from p e r i o d two onwards.  firm,  i n employment s t a t e n and f a c i n g  the f i x e d l a b o u r market e n v i r o n -  ment, x , must choose a wage and vacancy  creative  decision,  f i r s t p e r i o d which maximises mean d i s c o u n t e d p r o f i t s horizon,  The  5 , in  the  over an i n f i n i t e  namely,  VVy-.x)  where f ( n , 6 ) n  decision',;  ;  = f(n,6 ) n  denotes  +3^  £ e k=0  n k  (S ,x)ll(k,x) n=0,l,...,n n  mean one p e r i o d p r o f i t s  5 , i n employment s t a t e  .  f o r the f i r m which  n , 9 , (6 ,x)  denotes  •  (20)  adopts  the corresponding  116 s t a t e to s t a t e t r a n s i t i o n vector, R i s the rate of discount and H(k,x) denotes mean p r o f i t s discounted over an i n f i n i t e horizon of a f i r m , enjoying employment s t a t e k, which adopts the a r b i t r a r y p o l i c y , y-, for ever i n the labour market environment, x. The s e t of optimal f i r s t period decisions from the maximisation of Q (^ »y^» ^ (n=0,l,... ,fi) may be denoted as y . The procedure, x  n  n  as o u t l i n e d i n Chapter 2 IIB, i s t o adopt y  r  as the a r b i t r a r y second  period p o l i c y , by s e t t i n g r = r , and then choose a new set of optimal f i r s t period decisions which maximises Q 0$ ,y.-,x) • Wh n  n  en t n e  optimal  f i r s t period p o l i c y and the a r b i t r a r y p o l i c y are i d e n t i c a l , the p a r t i a l optimisation problem has been solved. The e f f i c i e n c y of Hadley's algorithm a r i s e s from the reduction of the p a r t i a l optimisation problem from the determination of a p o l i c y c o n s i s t i n g of 2(n+l) unknowns to a sequence of problems each r e q u i r i n g the  s o l u t i o n of fi+1 sub-problems i n v o l v i n g the choice of a one period  d e c i s i o n , c o n s i s t i n g of two unknowns, f o r each s t a t e of employment. I wish t o o u t l i n e i n some d e t a i l the s o l u t i o n of the sub-problem namely the choice of 6 to maximise Q (6 ,y-,x) because i t i s i n the n n n'^r' J  x  s o l u t i o n of t h i s sub-problem where p o s s i b l e inaccuracies i n the simulation procedure appear.  This might explain some of the i n c o n s i s t e n t  comparative s t a t i c r e s u l t s . The form of the maximand precludes the use of t r a d i t i o n a l calculus techniques.  The approach adopted i s a non-exhaustive search over a g r i d  of values of the wage o f f e r and the i n t e g r a l vacancy d e c i s i o n .  117  o  I n i t i a l l y , the f i r s t period decision adopted, § , i s equal t o n' r the corresponding decision of the second period p o l i c y , 6^. The value o A  of the objective f u n c t i o n , Q (5  »y~»x), i s computetd.  The maximum  value of the objective function corresponding to the wage d e c i s i o n , w  n  for  , i s found by comparing d i f f e r e n t values of the objective function d i f f e r e n t vacancy creation decisions. 14  i s i n i t i a l l y reduced by u n i t y  The vacancy c r e a t i o n d e c i s i o n  and the objective function evaluated.  I f the objective function has increased, then the l e v e l of vacancy c r e a t i o n i s reduced f u r t h e r and the o b j e c t i v e function again evaluated. The optimal vacancy creation decision i s found where the objective function i s maximised, that i s the l e v e l of vacancy c r e a t i o n such that a lower l e v e l of vacancy c r e a t i o n y i e l d s a lower value of the o b j e c t i v e ~ o function.  I f reducing the i n i t i a l l e v e l of vacancy c r e a t i o n from v  n  reduces the value of the objective f u n c t i o n , then t h i s i n i t i a l l e v e l of vacancy c r e a t i o n i s incremented by unity and the o b j e c t i v e function re-evaluated.  I f the objective function i s i n c r e a s i n g , then the l e v e l  of vacancy creation i s incremented again, and so on. This procedure y i e l d s the optimal vacancy c r e a t i o n decision f o r ~ o the prescribed wage o f f e r , w^ . The wage o f f e r i s reduced by i t s prescribed increment"''"' and the optimal vacancy c r e a t i o n d e c i s i o n i s computed according to the approach elaborated above.  I f t h i s lower  wage o f f e r and corresponding optimal l e v e l of vacancy c r e a t i o n y i e l d s a higher value of the objective f u n c t i o n , then the wage o f f e r i s reduced f u r t h e r by the prescribed increment, Qtherwise,the wage o f f e r i s incremented above i t s i n i t i a l v a l u e , w^, 0  d e c i s i o n computed.  and the optimal vacancy  118 The search procedure i s thus non-exhaustive i n that only values of the decision v a r i a b l e s i n the neighbourhood of the i n i t i a l decision are considered  and only then when the o b j e c t i v e function i s i n c r e a s i n g .  To summarise, then, to f i n d the optimal f i r s t period p o l i c y , when a p a r t i c u l a r p o l i c y i s adopted from period two onwards and the labour market environment i s unchanging over time, can be reduced to n+1 problems r e q u i r i n g the choice of a d e c i s i o n f o r each s t a t e of employment. Each such problem i s a two step procedure. (i)  Choose the optimal l e v e l of vacancy c r e a t i o n associated with a  p a r t i c u l a r wage o f f e r by incrementing the vacancy c r e a t i o n d e c i s i o n i n the d i r e c t i o n of i n c r e a s i n g the value of the objective function u n t i l a l o c a l maximum i s determined. ( i i ) Use the same technique to f i n d the wage d e c i s i o n corresponding t o a l o c a l maximum by adopting ( i ) and varying the wage d e c i s i o n . This procedure i s computationally  more e f f i c i e n t than an  exhaustive search over two space,but w i l l only c o n s i s t e n t l y y i e l d the correct s o l u t i o n when the objective function i s a monotonic function of both v a r i a b l e s .  Otherwise, i t i s p o s s i b l e that the  optimal f i r s t period p o l i c y c o n s t i t u t e s a l o c a l maximum rather than a g l o b a l maximum of the objective function over a l l states of employment. 2.  Model I I The p a r t i a l optimisation procedure i s the same i n Model I I because,  while the t r a n s i t i o n vector computations are more complex (see Appendix I ) and states of employment are defined over both l e v e l of employment and  119 type of i n d i v i d u a l , the f i r m s t i l l chooses a s i n g l e wage and vacancy creation d e c i s i o n f o r each state of employment, given a p a r t i c u l a r p o l i c y i n period two and an unchanging labour market environment, to maximise mean p r o f i t s discounted over an i n f i n i t e horizon. 3.  Model I I I The computation of the p a r t i a l optimisation p o l i c y i n Model I I I  i s more complicated because the f i r m has to choose a wage and vacancy c r e a t i o n f o r each type of i n d i v i d u a l . The labour market environment -  - -1 -2  x = (3,6 ,6 ) i s unchanging over time. The p a r t i a l optimisation procedure remains b a s i c a l l y the same. The a r b i t r a r y second period i s now defined as a wage and vacancy creation d e c i s i o n f o r each type of i n d i v i d u a l oyer a l l states of employment. The p a r t i a l optimisation procedure reduces to a sequence of problems each r e q u i r i n g the s o l u t i o n of M sub-problems, over 4 v a r i a b l e s . Thus, a f i r m i n employment s t a t e m must choose wage and 1 2 vacancy creation d e c i s i o n s , (6 - ,6 ) , to maximise mean discounted m ' m '' p r o f i t s over an i n f i n i t e horizon J  M Y, Q . (6 ,6 ,x)H(k,x) 1+R , . mk m ' m ' ' k=0  Q (6 ,6 ,y-,x) = f(m,6 ,6 ) + m m'm'-'r' 'm 'm 1  2  1  2  1  x  m = 0,1, .. .  2  v  ,  M  .  .  .  .  (21)  The s o l u t i o n procedure i s again a non-exhaustive stepwise search procedure.  The value of the objective function i s computed when the  * 1 " 2 a r b i t r a r y decisions (6^ ,6^ ) are adopted i n period one. The wage  120 " 1 ~ 2 o f f e r s t o type one and type two i n d i v i d u a l s , c o n s t a n t and t h e o p t i m a l vacancy  (w  ,w  m  ) , are kept  c r e a t i o n d e c i s i o n s a r e found by  an e x h a u s t i v e s e a r c h over the f e a s i b l e non-negative two-space o f v a l u e s o f the vacancy c r e a t i o n d e c i s i o n . d e f i n e d by the requirement e^  + e  where v^, v  2  2  m , *• * + v^.+ v  That i s the vacancy  that f-  2  space  /ION  < n  a r e the vacancy c r e a t i o n d e c i s i o n s .  . . . . (22)  The wage t o type one  i n d i v i d u a l s i s kept c o n s t a n t and the wage t o type two i n d i v i d u a l s i s v a r i e d a c c o r d i n g t o the p r i n c i p l e s e l a b o r a t e d i n A ( l ) . the o p t i m a l type two wage o f f e r and vacancy c r e a t i o n  Having  chosen  decisions  c o r r e s p o n d i n g t o t h e wage o f f e r to type one i n d i v i d u a l s , the type one wage o f f e r i s v a r i e d i n the same manner t o f i n d the l o c a l maximum. T h i s t h r e e s t e p procedure may be summarised (i)  Given wage o f f e r s t o each type o f i n d i v i d u a l , c h o o s e the o p t i m a l  vacancy  c r e a t i o n d e c i s i o n t o each type o f i n d i v i d u a l by the e x h a u s t i v e  s e a r c h o v e r t h e g r i d o f i n t e g r a l v a l u e s o f vacancy c r e a t i o n  decisions  i n two space. ( i i ) A d o p t i n g step ( i ) ,  increment the wage o f f e r t o type two i n d i v i d u a l s  i n the d i r e c t i o n o f i n c r e a s i n g the v a l u e o f the o b j e c t i v e f u n c t i o n  until  a l o c a l maximum i s found. ( i i i ) U s i n g ( i ) and ( i i ) ,  increment the wage o f f e r to type one i n d i v i d u a l s  i n the d i r e c t i o n o f i n c r e a s i n g the v a l u e o f the o b j e c t i v e f u n c t i o n a l o c a l maximum i s a c h i e v e d . " ^  until  121 B.  Convergence C r i t e r i a As n o t e d i n Chapter 2 I I B ,  the p a r t i a l o p t i m i s a t i o n p o l i c y , environments to t e s t f o r f u l l  the approach adopted i s ,  on s e c u r i n g  to compare c o n s e c u t i v e  l a b o u r market  convergence  l a b o u r market environments d i f f e r by l e s s  o f the a l g o r i t h m . than a v e c t o r o f  If  the  constants,  o e,  set  at  0.001, then a steady s t a t e d i s t r i b u t i o n o f employment i s  computed which i s compared w i t h the employment d i s t r i b u t i o n c o n s t i t u t i n g the l a b o u r market environment. than the v e c t o r , . e ,  then f u l l  If  these two d i s t r i b u t i o n s d i f f e r by  less  o p t i m i s a t i o n o f the a l g o r i t h m has been  achieved. T h i s convergence  c r i t e r i o n was t i g h t e n e d by r e q u i r i n g t h a t  c o n s e c u t i v e p a r t i a l o p t i m i s a t i o n p o l i c i e s be i d e n t i c a l b e f o r e d i s t r i b u t i o n s of employment  (the o t h e r v e c t o r s  l a b o u r market environments)  are compared.  If  o p t i m i s a t i o n p o l i c i e s a r e i d e n t i c a l , so t h a t  constituting consecutive  4 consecutive  consecutive  partial  the o p t i m a l p o l i c y i n  response to an unchanging l a b o u r market environment c o i n c i d e s w i t h the p o l i c y c o n s t i t u t i n g t h a t l a b o u r market environment, then the l a b o u r market i s s a i d t o be i n a s t a t e o f temporary e q u i l i b r i u m .  If  employment d i s t r i b u t i o n s d i f f e r e d by l e s s  e,  than the v e c t o r ,  i d e n t i c a l p a r t i a l optimisation p o l i c i e s , t h e n consecutive environments are i d e n t i c a l up t o an e r r o r , employment v e c t o r i s  e,  consecutive after  4  l a b o u r market  and the steady  state  computed.  Tests w i t h the procedure demonstrate that such a s t r i n g e n t convergence  criterion is essential.^  Otherwise,  it  is possible  that  122  a number o f p a r t i a l o p t i m i s a t i o n p o l i c i e s  are i d e n t i c a l ,  l a b o u r market i s i n temporary e q u i l i b r i u m , d e s p i t e d i s t r i b u t i o n s over f i r m s .  and so  changing  the  employment  F i n a l l y , a new l a b o u r market environment c o u l d  be generated which rendered these p a r t i a l o p t i m i s a t i o n s o l u t i o n s optimal.  sub-  ^  I t was hoped that  the a d o p t i o n o f an i n t e g r a l vacancy  d e c i s i o n and  a wage d e c i s i o n d e f i n e d i n increments of 0.1 would be s u f f i c i e n t ensure convergence.  Unfortunately,  p r o c e d u r e f a i l e d to converge The approach adopted i s wage increments o f 0 . 1 . ment shows s i g n s If  at  this  degree  of  the s i m u l a t i o n  accuracy.  t o commence the s i m u l a t i o n by  When i t  of s t a b i l i z i n g ,  the a l g o r i t h m f a i l s  i n most c a s e s ,  appears  that  after  adopting  the l a b o u r market e n v i r o n -  the wage increment i s  to converge  to  a significant  reduced to  0.05.  number o f  19 iterations, necessary, C.  to  where  0.005.  Cycling It  that  then the increment i s reduced to 0.01 and f i n a l l y ,  is  cycle.  set at  frequently  observed t h a t  T h i s means t h a t  the a l g o r i t h m generates  f o r some i > m, where m i s  results  arbitrarily  6, (P-  x  j + i  )  < TI  . . . .  where x^ i s  the l a b o u r market environment generated a f t e r  o f the f u l l  optimisation algorithm  T h i s means t h a t  20  and n i s a v e c t o r  of  j  (23)  iterations constants.  the same l a b o u r market environment i s b e i n g  21  recreated  123  d u r i n g the s i m u l a t i o n . iterations i s set  is  Consequently,  the same as that a f t e r  the o p t i m a l p o l i c y a f t e r j  iterations  m  a t a h i g h number to ensure t h a t the s i m u l a t i o n p r o c e d u r e  c y c l i n g r a t h e r than c o n v e r g i n g v i a a sequence If  and so on.  j+i  the s i m u l a t i o n procedure c y c l e s ,  iterations  to converge  at the 0.005 l e v e l ,  of temporary e q u i l i b r i a .  then the wage increments  a g a i n reduced and t h e procedure i s r e s t a r t e d . procedure c y c l e s o r f a i l s  after  If  The f u l l y  at  are  the s i m u l a t i o n  a s i g n i f i c a n t number o f  then a new a r b i t r a r y i n i t i a l  labour  market environment i s i n t r o d u c e d and the procedure r e s t a r t e d the wage increments s e t  is  with  0.05.  o p t i m a l p o l i c y and the a s s o c i a t e d  l a b o u r market e n v i r o n -  22 ment are g e n e r a l l y  unique f o r a p r e s c r i b e d increment i n the wage  23 decision. percentage  T h i s means t h a t the s i m u l a t i o n p r o c e d u r e , i n a h i g h of c a s e s ,  generates a f u l l y  o p t i m a l p o l i c y and  l a b o u r market environment, i n d e p e n d e n t l y l a b o u r market environment. and a s s o c i a t e d  associated  o f the c h o i c e o f the  T h i s suggests t h a t the f u l l y  initial  optimal p o l i c y  l a b o u r market environment are u n i q u e , when d e f i n e d to an  a r b i t r a r y number o f d e c i m a l p l a c e s . V. Problems A r i s i n g from the S i m u l a t i o n P r o c e d u r e A.  Non-Convergence Most s e t s o f parameter v a l u e s ,  optimal s o l u t i o n , cycle ments.  I n the absence  which do not generate a  fully  at one or more o f the p r e s c r i b e d wage i n c r e o f i n f i n i t e computing r e s o u r c e s ,  it  is  impossible  to use the s i m u l a t i o n procedure over a t i g h t g r i d of parameter v a l u e s  to  124 delineate the parameter space between sets of parameter values which generate a s o l u t i o n to the algorithm and those which d i d not. A p r i o r i , there i s no reason why the problem should be badly behaved f o r some sets of parameter values and not f o r others.  While  i t i s u n s a t i s f a c t o r y that some r e s u l t s are missing, so that some comparative s t a t i c comparisons are impossible, t h i s problem i s l e s s s i g n i f i c a n t than would be the case i f I wished to examine the nature of dynamic adjustment i n the labour market by the use of a modified version of the model.  Then, the d e l i n e a t i o n of the parameter space  i s necessary. An obvious explanation of the f a i l u r e of the simulation procedure to converge i s simply that the increment i n the wage decision i s too large.  The true s e t of f u l l y optimal wage decision i s defined t o a  greater degree of accuracy than the minimum wage increment 0.005. A second p o s s i b l e explanation, as already mentioned, i s that the non-exhaustive search procedure f o r the p a r t i a l - o p t i m i s a t i o n problem, i n some cases, y i e l d s a p o l i c y which i s associated with a l o c a l maximum rather than a g l o b a l maximum. B.  Inconsistent Results Results are considered i n c o n s i s t e n t when comparison of the f u l l y  optimal p o l i c i e s r e s u l t i n g from d i f f e r e n t values of a p a r t i c u l a r parameter y i e l d d i f f e r e n t comparative s t a t i c p r e d i c t i o n s when, a p r i o r i , the p r e d i c t i o n s should be the same.  Some of the explanations presented  125  to e x p l a i n non-convergence be i n a c c u r a t e  are also r e l e v a n t here.  due t o i n s u f f i c i e n t l y  s m a l l increments i n the wage  d e c i s i o n and, i n a d d i t i o n , the n o n - e x h a u s t i v e A further d i f f i c u l t y  arises  solutions  degree o f a c c u r a c y i n the wage  T h i s occurs because of c y c l i n g and non-convergence.  noted i n I I I B ,  the c o n v e n t i o n adopted i s  when the s o l u t i o n c y c l e s . fully  search procedure.  through the comparison o f  which are d e f i n e d t o a d i f f e r e n t decision.  The s o l u t i o n may  optimal solutions  As  to reduce the wage increment  Some s e t s of parameter v a l u e s may y i e l d  at,  say,  the wage increment 0.01 and  at the lower wage increment 0 . 0 0 5 , w h i l e  cycle  o t h e r s e t s of parameter  may generate the o p p o s i t e  result.  are b e i n g made from f u l l y  o p t i m a l p o l i c i e s which a r e d e f i n e d to  degrees of accuracy  Thus, comparative s t a t i c  i n the wage d e c i s i o n .  values  predictions different  E v i d e n t l y n o t h i n g can be done  t o cure t h i s problem o t h e r than to p e r s i s t i n u s i n g the s i m u l a t i o n procedure w i t h the same s e t s o f parameter v a l u e s l a b o u r market  but d i f f e r i n g  environments.  In a d d i t i o n , i t  i s possible  t h a t s m a l l changes i n c e r t a i n  market parameters may l e a d t o such s m a l l changes i n the t r u e policy  initial  labour  optimal  t h a t the combination o f the i n a c c u r a c y o f the wage d e c i s i o n and  the n o n - g l o b a l p a r t i a l o p t i m i s a t i o n procedure may l e a d t o results.  F o r example,  incorrect  a 10% change i n the h o r i z o n over which r e t u r n s  from s e a r c h a c c r u e from 10 to 11 has a s m a l l impact on the  computation  of t h e r e t u r n s from s e a r c h and thus on the o p t i m a l p o l i c y , w h i l e a 10%  126  change i n the v a l u e o f c^,  the p e r c e p t i o n parameter, has a  impact on the n a t u r e o f s t o c h a s t i c r e v e a l e d i n the r e s u l t s . seeking q u a l i t a t i v e  e q u i l i b r i u m and t h i s i s  Comparative S t a t i c  Comparative s t a t i c constants,  consistently  s h o u l d be emphasised, however,  and n o t q u a n t i t a t i v e  VI.  exogeneous  It  significant  t h a t I am  24 predictions. Results  r e s u l t s a r e generated over d i f f e r e n t  namely the p e r c e p t i o n parameters  c^,  values  of  the  c^,  l e v e l o f unemployment compensation, w, the h o r i z o n over which the r e t u r n s from s e a r c h are computed, H ^ , and the p e r i o d l e n g t h . frequency w i t h which a p a r t i c u l a r comparative s t a t i c a change i n a summary s t a t i s t i c  to 'weak' comparative r e s u l t s .  statistic, constant,  constant.  F o r example,  The  frequencies  i f a summary  S S , i s p o s t u l a t e d to be a d e c l i n i n g f u n c t i o n o f the c^,  prediction  p r e d i c t i o n of  i s upheld i s p r e s e n t e d i n a T a b l e  c o r r e s p o n d i n g to the p a r t i c u l a r exogeneous refer  The  then the exogeneous  constant  c^ generates  exogeneous  one c o r r e c t  if  SSCc^) < S S ^ -  A  C ; L  )  . . . .  where Ac^ i s the increment i n the v a l u e o f the exogeneous If k different  values  (24)  constant.  o f c^ are adopted i n increments ' o f Ac^, then  25 k - 1 p r e d i c t i o n s are g e n e r a t e d . •'  ;  127  CHAPTER 4 RESULTS FROM MODEL I  I• A.  Introduction  The C h a r a c t e r i s t i c s of Stochastic E q u i l i b r i u m The f o l l o w i n g features of s t o c h a s t i c e q u i l i b r i u m are observed  f o r a l l values of the exogeneous constants adopted.  Stochastic  misperceptions of the reservation wage generate s i g n i f i c a n t wage and employment dispersion i n e q u i l i b r i u m .  The d i s t r i b u t i o n of wage  rates over employment states l i e s above the p e r f e c t l y  competitive  e q u i l i b r i u m wage rate."*" The mean wage o f f e r s to searchers and employed i n d i v i d u a l s exceed the p e r f e c t l y competitive wage but are l e s s than the average 2 marginal product. Firms e x h i b i t dynamic monopsony power i n that the wage o f f e r i s a d e c l i n i n g function of the l e v e l of employment.  This r e l a t i o n s h i p  between the wage o f f e r and the l e v e l of employment can be demonstrated 3 i n the i l l u s t r a t i v e model by comparative s t a t i c a n a l y s i s .  The l e v e l  of vacancy creation i s also a d e c l i n i n g function of the l e v e l of employment.  I f a l l firms f i l l the vacancies that they create and no  workers q u i t , then a l l firms pay t h e i r workforces a wage above t h e i r respective marginal products. In a one period framework, i f behaviour i s non-stochastic,  firms  h i r e i n d i v i d u a l s up to the point at which the worker's marginal product  128  e q u a l s the wage o f f e r . s t a t e s , however,  In some s o l u t i o n s , over c e r t a i n employment  the l e v e l o f employment c o n s i s t e n t w i t h the  ex-  p l o i t a t i o n of i n t e r t e m p o r a l monopsony power (as d e f i n e d i n Chapter 2 IIIG) exceeds the s t a t i c , employment. vacancy  one p e r i o d , p r o f i t maximising l e v e l of  But,in a l l solutions,the  l e v e l o f aggregate  speculative  c r e a t i o n , which i s d e f i n e d as aggregate v a c a n c i e s  i n excess  of those c o n s i s t e n t w i t h the e x p l o i t a t i o n o f i n t e r t e m p o r a l monopsony power,  is a significant  i n every s o l u t i o n .  component o f vacancy  Thus, the s p e c i f i c a t i o n o f s t o c h a s t i c  and acceptance b e h a v i o u r causes the p a r t o f  c r e a t i o n , e x c e e d i n g 30%  s u b s t a n t i a l vacancy  turnover  s p e c u l a t i o n on  firms.  The aggregate mean l e v e l o f vacancy c r e a t i o n exceeds aggregate mean unemployment.  E q u i l i b r i u m i n a market i s c h a r a c t e r i s e d by  excess demand, as c o n v e n t i o n a l l y d e f i n e d . formation i s p e r f e c t , to increase i t s  l e v e l o f employment and unemployment i s  of aggregate vacancy vacancies  I n a market i n which i n -  at the e q u i l i b r i u m wage r a t e , no f i r m  t h i s i m p e r f e c t market, e q u i l i b r i u m i s  wishes  zero.  In  c h a r a c t e r i s e d by n o n - z e r o  c r e a t i o n and aggregate unemployment.  exceed aggregate unemployment.  As Reder  levels  Aggregate  [1969] a r g u e s ,  a l a b o u r market c h a r a c t e r i s e d by i m p e r f e c t i n f o r m a t i o n , the l e n g t h of time a vacancy  zero  in  average  i s open i s n o t r e l a t e d i n any p a r t i c u l a r way  4 to the average  d u r a t i o n of unemployment, a p r i o r i .  not s u f f i c i e n t  condition for stochastic  is  that  on average  A necessary,  e q u i l i b r i u m i n the l a b o u r market  the number o f i n d i v i d u a l s q u i t t i n g t h e i r j o b s  the number o f v a c a n c i e s  filled."'  but  Convergence o f the f u l l  equals  optimisation  129 a l g o r i t h m demonstrates  t h a t s t o c h a s t i c e q u i l i b r i u m has been a t t a i n e d  in  the l a b o u r market.  The q u e s t i o n remains  of  excess demand can be developed which r e g i s t e r s a c o n s t a n t v a l u e  as t o whether a measure  when the l a b o u r market i s i n s t o c h a s t i c e q u i l i b r i u m , i r r e s p e c t i v e o f the v a l u e s o f exogeneous parameters.  The concept and measure o f  excess demand i s d i s c u s s e d i n Chapter  6.  Comparison o f the measures o f mean d i s c o u n t e d income i n d i c a t e s t h a t , i n t h i s environment,  an i n d i v i d u a l e n j o y s t h e h i g h e s t mean  income by a c c e p t i n g the f i r s t j o b o f f e r e d and r e m a i n i n g employed over h i s working h o r i z o n , i r r e s p e c t i v e o f t h e wage o f f e r . I n d i v i d u a l s , who q u i t and a c c e p t o f f e r s a c c o r d i n g t o t h e t r u e r e s e r v a t i o n wage, e a r n a lower mean income over t h e i r j o b h o r i z o n and i n d i v i d u a l s , who behave s t o c h a s t i c a l l y , enjoy the lowest d i s c o u n t e d income.  The f i r s t  two measures a r e h y p o t h e t i c a l , s i n c e they a r e com-  puted on the b a s i s o f one i n d i v i d u a l ' s n o n - s t o c h a s t i c b e h a v i o u r , when a l l o t h e r i n d i v i d u a l s behave s t o c h a s t i c a l l y . The comparison  o f these measures, however, does suggest  that  i n d i v i d u a l s ' s t o c h a s t i c b e h a v i o u r generates s i g n i f i c a n t v a r i a t i o n i n the l e v e l o f employment f a c e s by a f i r m over time.  Thus, a low c u r r e n t  wage enjoyed by a n , i n d i v i d u a l w i l l n o t p e r s i s t , i f he remains w i t h the same f i r m .  employed  T h i s h y p o t h e s i s i s confirmed by the o b s e r v a t i o n o f  the temporal c o r r e l a t i o n o f wage o f f e r s over the d i f f e r e n t  solutions.  The temporal c o r r e l a t i o n i s a d e c l i n i n g f u n c t i o n o f time and, i n some c a s e s , assumes a n e g a t i v e v a l u e which i s s m a l l , however, i n a b s o l u t e terms.  130  T h i s demonstrates t h a t t h e r e i s l i t t l e i n f o r m a t i o n i n a c u r r e n t wage o f f e r about the f u t u r e stream of wage o f f e r s f a c i n g an i n d i v i d u a l accepts  who  the o f f e r .  These remarks must be q u a l i f i e d because the f i r m makes d e c i s i o n s on the b a s i s of i t s p e r c e p t i o n s  of i n d i v i d u a l s ' behaviour.  Ifa l l  i n d i v i d u a l s adopted the same ex ante [0,1] d e c i s i o n r u l e f o r s e a r c h , then the i n d u s t r y e q u i l i b r i u m would be c h a r a c t e r i s e d by the c o l l u s i v e monopsony s o l u t i o n . ^  The term, 'mean d i s c o u n t e d  income', or MDI  now always r e f e r t o l i f e t i m e income from s t o c h a s t i c Mean d i s c o u n t e d p r o f i t f u n c t i o n o f the i n i t i a l  behaviour.  over an i n f i n i t e h o r i z o n i s a p o s i t i v e  l e v e l o f employment.  T h i s r e s u l t can be  j u s t i f i e d on the grounds t h a t the g r e a t e r i s the i n i t i a l employment the g r e a t e r i s t h e f i r m ' s monopsony power. to  will  l e v e l of  While unable  f i r e employees, a f i r m , f a c e d w i t h a h i g h l e v e l of employment, can  always e x p l o i t i t s monopsony power by o f f e r i n g a r e l a t i v e l y low wage, so t h a t t h e r e i s a r e l a t i v e l y h i g h p r o b a b i l i t y o f s e c u r i n g a l e v e l o f employment c o n s i s t e n t w i t h i n t e r t e m p o r a l p r o f i t m a x i m i s a t i o n a t the p r e v a i l i n g wage. Mean d i s c o u n t e d p r o f i t over an i n f i n i t e h o r i z o n i n c r e a s e s a t a decreasing  r a t e as the i n i t i a l  l e v e l of employment i n c r e a s e s .  r e f l e c t s the d i m i n i s h i n g m a r g i n a l  This  p r o d u c t i v i t y of workers as employment  increases. B.  An I l l u s t r a t i v e S o l u t i o n T a b l e 3 shows the f u l l o p t i m i s a t i o n s o l u t i o n generated by the  131  basic parameter values, that i s those values s p e c i f i e d i n Table 1 and u n i t values of perception parameters. TABLE 3 The Basic Solution to Model I  Stochastic E q u i l i b r i u m Level of Employment  Steady State Distribution  Wage Offer  Vacancy Creation  Mean One Period Profits  0 1 2 3 4 5 6 7 8  0.020 0.126 0.284 0.317 0.196 0.051 0.006 0.000 0.000  2.165 2.085 1.975 1.825 1.710 1.655 1.580 1.520 1.505  4 3 2 2 2 1 1 1 0  2.04 3.26 4.00 4.43 4.69 4.86 4.98 5.08 5.13  ! i  P r o f i t s over an I n f i n i t e Horizon 80.03 82.34 83.61 84.26 84.60 84.83 84.96 85.06 85.11  Summary S t a t i s t i c s EW* 1.722  V  LS  MW  W*  VW*  1.852  1.609  0.173  63  0.546  V s 45  U  PA*  38  1.561  po*  1 period 0.379  i •-  I...  .1  I  .  ....  , ••  -  2 periods j 3 periods j 4 periods 0.151 1 0.032 1 0.012  ~  5 periods 0.011  Mean Discounted Income No q u i t t i n g  True Perception  14.446  14.354  Stochastic Behaviour 11.998  En  1.166 j 83.843  Correlation of Offers •T — „ • • • - — ,  j  132 Steady State Transition Matrix 0.314 0.043 0.012 0.009 0.009 0.008 0.010 0.011 0.011  0.369 0.333 0.121 0.079 0.070 0.061 0.064 0.067 0.068  0.212 0.352 0.366 0.252 0.209 0.188 0.181 0.179 0.178  0.080 0.197 0.341 0.360 0.319 0.306 0.283 0.269 0.268  0.024 0.076 0.160 0.231 0.261 0.278 0.265 0.253 0.252  0.0 0.0 0.0 0.069 0.111 0.133 0.147 0.151 0.152  As can be observed the solution exhibits employment dispersion. 1.505.  0.0 0.0 0.0 0.0 0.021 0.026 0.045 0.056 0.057  0.0 0.0 0.0 0.0 0.0 0.0 0.006 0.012 0.012  0.0 0.0 o 0o . 0 o.o 0 0 o.o  !  1 I! i! !  o.oov  0.001  s i g n i f i c a n t wage and  The wage offers l i e i n the ranges 2 . 1 6 5 to  Over 90% of firms face employment l e v e l s of between 1 and 4  workers.  II. A.  Comparative S t a t i c Predictions  An Introduction In order to organise and analyse the comparative s t a t i c r e s u l t s ,  summary s t a t i s t i c s are defined.  The changes i n the values of these  summary s t a t i s t i c s describe the impact on stochastic  equilibrium i n  the labour market of a change i n the value of the p a r t i c u l a r exogeneous parameter.  The summary s t a t i s t i c s are the following :  g (a)  the l e v e l of the general wage o f f e r d i s t r i b u t i o n ;  (b)  the mean wage o f f e r facing a searcher;  (c)  the variance of the wage o f f e r d i s t r i b u t i o n facing a searcher;  (d) (e)  the mean wage enjoyed by an employed i n d i v i d u a l ; mean discounted income enjoyed by an i n d i v i d u a l ;  (f)  the l e v e l of aggregate vacancy  creation;  133 (g)  the l e v e l of aggregate vacancy speculation;  (h)  the l e v e l of aggregate unemployment;  (i)  the mean duration of search p r i o r t o an o f f e r ;  (j)  the mean duration of unemployment;  (k)  mean p r o f i t s discounted over an i n f i n i t e horizon earned by the f i r m ;  (1)  labour's share of t o t a l output; and  (m)  the one period c o r r e l a t i o n of wage o f f e r s .  B.  Systematic Misperceptions of the Reservation Wage  1.  The Results Solutions to Model I are obtained f o r d i f f e r e n t values of the  parameter, c^. The values of c^ adopted l i e i n the range 0.90 t o 1.25 i n increments of 0.05. The comparative s t a t i c  predictions,  generated f o r d i f f e r e n t values of c^, are consistent with respect to the a l g e b r a i c signs of most of the changes of the summary s t a t i s t i c s computed. An increase i n the parameter, c^, leads t o a s h i f t t o the r i g h t of the wage o f f e r d i s t r i b u t i o n .  Indeed, the wage o f f e r over a l l  employment states increases. The mean wage o f f e r f a c i n g an unemployed searcher and the mean wage rate earned by an employed worker both increase. The variance of the wage o f f e r d i s t r i b u t i o n i s p o s i t i v e l y r e l a t e d to the value of c^, up to the value 1.25. The one period c o r r e l a t i o n between wage o f f e r s decreases as c^ increases.  The other temporal c o r r e l a t i o n  c o e f f i c i e n t s do not show any systematic r e l a t i o n over d i f f e r e n t values  134 MDI i s p o s i t i v e l y 1.15.  r e l a t e d w i t h the v a l u e of  up to the  value  The mean wage f a c i n g an employed i n d i v i d u a l o n l y exceeds  c o l l u s i v e r e s e r v a t i o n wage when c^ e q u a l s 1.25. behaviour,  Thus, due t o  the  stochastic  the r e l a t i o n s h i p of the one p e r i o d c o l l u s i v e r e s e r v a t i o n wage  and the mean wage f o r the employed does not i n d i c a t e the r e l a t i o n s h i p of MDI t o the mean wage, over d i f f e r e n t An i n c r e a s e i n c^ l e a d s  values  of  c^.  to an i n c r e a s e i n the l e v e l of  vacancy  c r e a t i o n over some s t a t e s o f employment and the same l e v e l o f c r e a t i o n over a l l the o t h e r Aggregating creation.  states.  over f i r m s y i e l d s measures o f unemployment and vacancy  Both these measures are p o s i t i v e l y  correlated with  v a l u e o f c^, but  t h e r e appears  these measures.  The l e v e l o f aggregate s p e c u l a t i v e  positively  vacancy  to be no simple r e l a t i o n s h i p  r e l a t e d t o the v a l u e of  the  between  vacancies  is  also  c^.  The mean d u r a t i o n of unemployment i s p o s i t i v e l y  c o r r e l a t e d to  9 the v a l u e of c^,  w h i l e the mean d u r a t i o n o f s e a r c h p r i o r to an  shows no s y s t e m a t i c  r e l a t i o n s h i p t o c^.  appears to i n c r e a s e or decrease  than aggregate vacancy  of c^ a r e adopted and so i t  seven s e t s o f comparative s t a t i c of the summary s t a t i s t i c s  search  a c c o r d i n g to whether aggregate u n -  employment i n c r e a s e s more o r l e s s Eight values  The mean d u r a t i o n o f  offer  predictions.  creation.  i s p o s s i b l e to  generate  T a b l e 4 shows the  values  c o r r e s p o n d i n g to each v a l u e o f c^ and the  frequency w i t h which the comparative s t a t i c p r e d i c t i o n s are u p h e l d . The f r e q u e n c i e s  r e f e r to  'weak'  comparative s t a t i c  results.  TABLE 4 Results arid Comparative S t a t i c P r e d i c t i o n s for Misperceptions of the Reservation Wage  Summary Statistic  0.90  0.95  The Perception Parameter, c, 1.10 1715 1.05 1.00  1.20  1.25  _  _  _  _  _  _  —  —  (b)  1.494  1.560  1.722  1.833  1.894  2.099  2.348  2.757  (c)  0.137  0.163  0.173  0.232  0.291  0.311  0.358  (d)  1.614  1.697  1.852  2.005  2.108  2.292  (e)  11.119  11.528  11.998  12.255  12.318  (f)  53  53  63  67  (g)  20  20  45  (h)  30  32  38  (a)  Comparative S t a t i c s Sign Frequency/7 7 7  0.331  + +  2.549  2.909  +  6  12.568  12.383  11.868  68  81  93  119  +  7(-l)  45  43  51  54  95  +  6 (-2)  45  50  56  67  79  +  7  7  5  7  (i)  1.215  1.227  1.166  1.184  1.211  1.164  1.136  1.081  (j)  1.484  1.533  1.561  1.708  1.843  1.956  2.298  2.930  +  7  (k)  ^100.949  94.668  83.843  73.854  67.425  56.254  42.798  27.039  +  7  (1)  0.488  0.512  0.546  0.575  0.593  0.632  0.678  0.742  +  7  (m)  0.365  0.555  0.379  0.333  0.304  0.310  0.232  0.200  . —  5  136 An E x p l a n a t i o n  2.  I n the i l l u s t r a t i v e model, i t ceteris  c u r r e n t employees  ance on the p a r t of job seekers then a s u f f i c i e n t increase i s  that  and a lower p r o b a b i l i t y o f  i n response  the m a r g i n a l r a t e o f  I n Chapter 3 I I ,  or it  increases.  13  i s argued t h a t ,  ceteris c^,  p a r i b u s , i n response firms o f f e r i n g  and m a r g i n a l r a t e o f t u r n o v e r by employees  r a t e of acceptance  to  accept-  a wage  the mean o f the d i s t r i b u t i o n of r e s e r v a t i o n wages, MP, face  higher absolute  and a h i g h e r m a r g i n a l acceptance  a  and a lower  r a t e on the p a r t o f  seekers. The m a j o r i t y  of  offer,  t u r n o v e r (and t h e r e f o r e  to an i n c r e a s e i n the p e r c e p t i o n parameter,  job  to a g i v e n wage  accept-  c o n d i t i o n f o r i t s p r o f i t maximising wage o f f e r  remains c o n s t a n t  above  if,  p a r i b u s , a f i r m faces a h i g h e r p r o b a b i l i t y o f t u r n o v e r on  the p a r t o f i t s  ance)  can be demonstrated t h a t  o f f i r m s i n the i n d u s t r y o f f e r s  the d i s t r i b u t i o n o f p e r c e p t i o n s ,  choose to adopt the the s y s t e m a t i c  MP.  If  same wage and vacancy  wages above the mean  a l l firms i n the  industry  creation decisions,  change i n i n d i v i d u a l b e h a v i o u r ,  then the steady  despite state  l e v e l o f unemployment would be h i g h e r . If  a f i r m r a i s e s i t s wage o f f e r  change i n i n d i v i d u a l b e h a v i o u r , high,  that  wage o f f e r )  i n response to t h i s  systematic  then the p r o b a b i l i t y o f a c h i e v i n g a  i s o p t i m a l , l e v e l o f employment  (which i s dependent  i s i n c r e a s e d and thus h i g h e r mean p r o f i t s  by a d o p t i n g the p r e v i o u s wage decision."''"'  on the  a r e earned than  137 I f the majority of firms increase wage o f f e r s , however, the true reservation wage r i s e s and so there i s a systematic change i n i n d i v i d u a l s ' behaviour as noted i n Chapter 3. Thus,the higher mean p r o f i t s enjoyed by a f i r m , i f i t alone r a i s e s i t s wage o f f e r , i s o f f s e t , i f a majority of firms i n the industry increase t h e i r wage o f f e r s and thus the general d i s t r i b u t i o n of o f f e r s . Firms, who i n i t i a l l y o f f e r a wage below the r e s e r v a t i o n wage, face a higher p r o b a b i l i t y of maintaining a high l e v e l of employment i n response to the change i n i n d i v i d u a l s ' behaviour.  The r i s e i n the  general wage d i s t r i b u t i o n , however, caused by decisions of high wage firms, forces these low wage firms to increase t h e i r wage o f f e r s . Thus, the wage d i s t r i b u t i o n s h i f t s to the r i g h t . The l e v e l of aggregate unemployment r i s e s f o r two reasons. F i r s t l y , i n a labour market i n which i n d i v i d u a l s behave s t o c h a s t i c a l l y , given a higher d i s t r i b u t i o n of wage o f f e r s , firms choose to employ fewer i n d i v i d u a l s i n the aggregate,due to the d e c l i n i n g productivity  of labour.  marginal  I t i s p l a u s i b l e , then, that since firms  increase the general d i s t r i b u t i o n of wage o f f e r s i n response to the increase i n c^, the mean l e v e l of unemployment would be higher. Secondly, an i n d i v i d u a l i s l e s s valuable t o the f i r m because the mean returns over time associated with any given stream of wage o f f e r s i n response t o t h i s systematic change i n behaviour.  falls  Thus, firms do not  increase wage o f f e r s s u f f i c i e n t l y t o ensure that the previous aggregate l e v e l of employment i s maintained.  138 I n a d d i t i o n t o o f f e r i n g h i g h e r wages t o lower the p r o b a b i l i t y of e x i s t i n g employees q u i t t i n g and to i n c r e a s e searchers accepting  the p r o b a b i l i t y o f  o f f e r s , the f i r m can i n c r e a s e  the number o f  p o s i t i o n s o f f e r e d t o s e a r c h e r s by i n c r e a s i n g t h e l e v e l o f vacancy creation.  An i n c r e a s e  i n the l e v e l o f vacancy c r e a t i o n r a i s e s t h e  p r o b a b i l i t y of achieving  a high  l e v e l o f employment and thus  high  profits.  While t h e r e a r e d i r e c t c o s t s o f i n c r e a s i n g t h e wage o f f e r ,  increased  vacancy c r e a t i o n p e r se i s c o s t l e s s , except t h a t t h e  s p e c u l a t i v e n a t u r e o f vacancy c r e a t i o n may l e a d t o f i r m s h i g h e r l e v e l o f employment than they would choose i n a labour  market.  There i s a t r a d e o f f , t h e r e f o r e , between  vacancy c r e a t i o n and an i n c r e a s e d wage o f f e r . mean l e v e l o f employment. increase  non-stochastic increased  Both l e a d t o a h i g h e r  I t i s quite consistent  f o r the f i r m t o  i t s wage o f f e r and the l e v e l o f vacancy c r e a t i o n i n response  to t h i s s y s t e m a t i c The  facing a  increase  change i n b e h a v i o u r . i n aggregate unemployment means t h a t the steady  s t a t e d i s t r i b u t i o n o f employment has s h i f t e d towards low employment states.  Vacancy c r e a t i o n i s a d e c l i n i n g f u n c t i o n o f the l e v e l o f  employment.  Thus, even i n the absence o f i n c r e a s e d  over some s t a t e s , aggregate vacancy c r e a t i o n S i n c e the wage o f f e r d i s t r i b u t i o n s h i f t s  vacancy  creation  rises. t o t h e r i g h t , the  l e v e l o f employment a s s o c i a t e d w i t h each wage o f f e r , which i s c o n s i s t e n t w i t h the e x p l o i t a t i o n o f i n t e r t e m p o r a l remains c o n s t a n t or f a l l s .  monopsony power,  I n response t o an i n c r e a s e  i n c^,  vacancy c r e a t i o n over each employment s t a t e remains c o n s t a n t o r rises.  Thus, i t i s p l a u s i b l e t h a t aggregate vacancy  i s an i n c r e a s i n g f u n c t i o n of' c. .  speculation  139 The increase i n aggregate vacancy creation and the s h i f t i n the wage o f f e r d i s t r i b u t i o n leads to an increase i n the mean wage o f f e r f a c i n g a searcher, despite the increase i n unemployment. This r e s u l t i s p l a u s i b l e but d i f f i c u l t to prove, since the mean wage o f f e r i s dependent on the d i s t r i b u t i o n of vacancies and wage o f f e r s over firms and the l e v e l of unemployment. Since the wage o f f e r d i s t r i b u t i o n r i s e s , the mean wage enjoyed by an employed i n d i v i d u a l , MW, r i s e s .  Despite the increase i n  aggregate unemployment, MDI enjoyed by an i n d i v i d u a l r i s e s up to the point that c^ equals 1.15. The aggregate l e v e l of unemployment i n s t o c h a s t i c e q u i l i b r i u m , associated with a p a r t i c u l a r value of MW, always exceeds the h y p o t h e t i c a l measure of unemployment, computed under the assumption that a l l firms o f f e r the wage, MW, and p r o f i t maximise i n a labour market, characterised by p e r f e c t information. Thus, the comparison on the mean wage, MW, i n t h i s m u l t i - p e r i o d s t o c h a s t i c model of the labour market with the s t a t i c c o l l u s i v e acceptance wage i s not an accurate i n d i c a t o r of the magnitude of MDI.  I t i s consistent that the s h i f t of the d i s t r i b u t i o n of o f f e r s  to the r i g h t should be accompanied by an increase i n the variance of offers. The duration of unemployment r i s e s and again the r e s u l t i s p l a u s i b l e but d i f f i c u l t to prove.  I f i n d i v i d u a l s faced the same  p r o b a b i l i t y d i s t r i b u t i o n of o f f e r s whether employed or unemployed, then i t follows that, i f turnover and acceptance behaviour are com-, plementary, a higher rate of unemployment implies a higher p r o b a b i l i t y  140 of q u i t t i n g a job and a lower p r o b a b i l i t y of accepting an o f f e r and a longer duration of unemployment.  In t h i s model, the state of un-  employment can be regarded as a t r a n s i t o r y state f o r the i n d i v i d u a l between low wage, high employment states and high wage,low employment states.  Thus, while turnover and accpetance behaviour are complementary,  searchers have a higher p r o b a b i l i t y of r e c e i v i n g a high o f f e r i f they receive a non-zero o f f e r , than i n d i v i d u a l s c u r r e n t l y employed, since both wage o f f e r and vacancy c r e a t i o n are d e c l i n i n g functions of the l e v e l of employment. There i s no systematic r e l a t i o n s h i p between the mean duration of search arid c^.  The duration of search i s p o s i t i v e l y correlated w i t h  the sign of the change of the measure of aggregate vacancies minus aggregate unemployment.  This i s quite p l a u s i b l e , since an increase  i n the l e v e l of vacancy creation increases,  and an increase i n the  l e v e l of unemployment decreases the p r o b a b i l i t y of an o f f e r , c e t e r i s paribus. Over each employment s t a t e , firms earn lower p r o f i t s , since they o f f e r higher wage rates.  The steady state d i s t r i b u t i o n of firms has  s h i f t e d t o low employment, low p r o f i t firms. are lower.  Thus,mean industry p r o f i t s  Labour's share of t o t a l output therefore r i s e s .  As c^ increases,  firms choose to employ l e s s workers i n the  aggregate, since they receive higher wage o f f e r s and are l e s s  valuable.  Then the p r o b a b i l i t y that an i n d i v i d u a l accepts a job from a f i r m o f f e r i n g a wage, w , f a l l s .  Likewise, the p r o b a b i l i t y increases that an i n d i v i d u a l ,  141 c u r r e n t l y employed at a f i r m o f f e r i n g a wage,w , q u i t s . n  Thus, there  i s , i n some sense, more s t o c h a s t i c v a r i a t i o n i n the labour market. Then,it i s p l a u s i b l e that the one period c o r r e l a t i o n c o e f f i c i e n t declines as c^ increases. C.  The Level of Unemployment Compensation  1.  The Results Comparative s t a t i c p r e d i c t i o n s are derived f o r values of unem-  ployment compensation, w, l y i n g between 0.60 and 0.95 i n increments of 0.05. I n a d d i t i o n , a s o l u t i o n f o r a zero l e v e l of unemployment compensation i s derived. are generated.  S i x sets of comparative s t a t i c p r e d i c t i o n s  The r e s u l t s are somewhat ambiguous.  An increase i n  the l e v e l of unemployment compensation leads to a s h i f t of the wage o f f e r d i s t r i b u t i o n to the r i g h t .  The mean wage earned by an employed  i n d i v i d u a l r i s e s as does the mean wage of a searcher. of o f f e r s f a l l .  The variance  The l e v e l of MDI enjoyed by an i n d i v i d u a l f a l l s .  The changes i n the l e v e l s of aggregate unemployment and aggregate vacancy c r e a t i o n are not systematic.  Both measures simultaneously  r i s e twice, f a l l twice and remain constant twice.  The measure of  aggregate speculative vacancy increases twice, remains constant three times and f a l l s once.  1  Changes i n the mean duration of search are negatively r e l a t e d to changes i n the aggregate measure of vacancies minus unemployment. The mean duration of unemployment generally f a l l s i n response to an increase i n unemployment compensation.  The l e v e l of mean industry  142 p r o f i t s generally f a l l s , w h i l e labour's share of t o t a l output generally r i s e s .  The one period c o r r e l a t i o n c o e f f i c i e n t of wage  o f f e r s f a l l s as the l e v e l of unemployment compensation r i s e s . When the model i s solved f o r a zero l e v e l of unemployment compensation, s t o c h a s t i c e q u i l i b r i u m i s characterised by wage d i s p e r s i o n , vacancy c r e a t i o n and f r i c t i o n a l unemployment.  The wage  o f f e r d i s t r i b u t i o n l i e s above the p e r f e c t competitive wage r a t e . The average marginal product exceeds the mean wage of employees. The summary s t a t i s t i c s corresponding to a l l these r e s u l t s are shown i n Table 5. 2.  An Explanation C e t e r i s paribus, an increase i n the l e v e l of unemployment  compensation reduces the opportunity costs of search, W^. - w, where W-j. denotes the most recent o f f e r received by a searcher or an employed i n d i v i d u a l , and also increases the mean o f f e r , EW*, f a c i n g a searcher given an unchanging o f f e r d i s t r i b u t i o n .  From [7] and [8] i n Chapter  2 IB the true r e s e r v a t i o n wage i s given by  W*  =  w +  l 1  H  E  x  (^)  i  (EW* - W*).  . . . . (2)  i=l W* - w are the costs of search.  The i n d i v i d u a l w i l l receive a wage  o f f e r , EW*, a f t e r one search, which he w i l l enjoy over a h o r i z o n , H .  143 W*  =  w + Z.EW* 1 + Z  (3)  1 i (1 + D) i=l  (4)  1 + Zcj) > 0 1 + Z  (5)  where Z Then dW*  df?  where cj> denotes the p r o b a b i l i t y of a zero o f f e r .  Rewriting (6) i n  Chapter 2, (6)  dVW* = dw  2(w - EW*) $ < 0  (7)  16  since w c o n s t i t u t e s the f l o o r of the d i s t r i b u t i o n of o f f e r s . Then, c e t e r i s paribus, an increase i n w, the l e v e l of unemployment compensation, increases the true r e s e r v a t i o n wage but reduces the true variance of o f f e r s .  The o v e r a l l impact on the shape of the p r o b a b i l i t y  d i s t r i b u t i o n of perceptions of the r e s e r v a t i o n wage i s unclear.  The  increase i n the mean of the perceptions d i s t r i b u t i o n i m p l i e s that i n d i v i d u a l s have a lower p r o b a b i l i t y , ex ante, of accepting a r e l a t i v e l y high wage o f f e r , w h i l e the reduction i n the variance of the perceptions d i s t r i b u t i o n means that i n d i v i d u a l s have a higher p r o b a b i l i t y , ex of accepting a r e l a t i v e l y high o f f e r .  ante,  TABLE 5 Results and Comparative S t a t i c P r e d i c t i o n s for D i f f e r e n t Levels of Unemployment Compensation Summary Statistic  0.0  -  (a)  0.65  JFJie_L§yel .Qf_Une.mp.lQymen.tL_a,nd. Comp.ensarJ.on^_w 0.70 } 0.75 0.80 0.85 0.90 i i 1  -  —  — •  —  —  0.95 —  Comparative S t a t i c s Sign Frequency/6  +  4  (b)  1.456  1.547  1.689  1.722  1.625  1.675  1.704  1.709  +  5  (c)  0.270  0.206  0.178  0.173  0.178  0.180  0.174  0.153  -  4  .(d)  1.581  1.714  1.821  1.852  1.788  1.841  1.864  1.858  +  4  (e)  9.114  11.185  11.702  11.998  11.880  12.175  12.445  12.591  +  5  69  55  63  63  56  57  57  56  +  4  (8)  32  22  36  45  30  30  30  30  +  5 (-3)  (h)  33  35  38  38  36  38  38  37  +  4 (-2)  (i)  1.117  1.237  1.166  1.166  1.242  1.247  1.249  1.246  ?  6(-2)  (j)  1.440  1.590  1.563  1.561  1.600  1.646  1.642  1.619  (k)  99.235  92.655  85.368  83.843  88.759  84.799  83.814  84.621  0.478  0.510  0.537  0.546  0.529  0.541  0.548  0.548  +  0.441  0.509  0.391  0.379  0.373  0.432  0.449  0.397  . -  . ( f ) .  (1) (m)  \  -  4 4 5(-l) 4  145 The Increase i n MDI and the mean o f f e r f a c i n g a searcher and the decrease i n the variance of o f f e r s can be d i r e c t l y a t t r i b u t e d to the increase i n the l e v e l of unemployment compensation.  The  s h i f t of the wage o f f e r d i s t r i b u t i o n to the r i g h t and the r e s u l t a n t increase i n the mean wage o f f e r enjoyed by an employed i n d i v i d u a l suggest that the impact on the perception d i s t r i b u t i o n of the reservation wage of the increase i n the mean dominates the impact of the decrease i n variance.  But, n e i t h e r the mean duration of un-  employment nor the aggregate l e v e l of unemployment increase systema t i c a l l y , as the l e v e l of unemployment compensation increases. I t must be concluded, therefore, that the impact of an increase i n the l e v e l of unemployment compensation on the nature of s t o c h a s t i c e q u i l i b r i u m i n the labour market i s indeterminate,due t o the conf l i c t i n g influences of increased mean and decreased variance on the form of the perception d i s t r i b u t i o n of the r e s e r v a t i o n wage.  These  r e s u l t s c o n f l i c t w i t h the t r a d i t i o n a l p o s i t i o n taken by economists. For example, Grubel, Maki and Sax [1973] develop a model to i n v e s t i g a t e the impact of i n s t i t u t i n g unemployment compensation.  They argue that  an increase i n unemployment compensation lowers the e x p l i c i t costs of being unemployed. Then, assuming l e i s u r e and unemployment are equivalent, the p r i c e of l e i s u r e i s reduced. a normal good.  More l e i s u r e i s consumed because i t i s  The a n a l y s i s i s p a r t i a l , because f i r m s ' behaviour i n  response to t h i s reduced labour-force p a r t i c i p a t i o n i s not analysed.  146 The c r u c i a l d i f f e r e n c e market i s  i n f o r m u l a t i o n i n my model o f the  t h a t the p e r c e i v e d v a r i a n c e o f o f f e r s  t u r n o v e r and acceptance b e h a v i o u r .  influences  imperfect  individuals  1  The l e v e l of unemployment compen-  s a t i o n i s an element o f the d i s t r i b u t i o n o f o f f e r s . the s i m p l e model developed by G r u b e l , Maki and Sax  In c o n t r a s t  to  [1973], unemployment  compensation does n o t unambiguously i n c r e a s e the ex ante q u i t p r o b a b i l i t y o r reduce the ex ante p r o b a b i l i t y o f acceptance i n response to a p a r t i c u l a r wage  offer.  I n a d d i t i o n , by s p e c i f y i n g g e n e r a l e q u i l i b r i u m framework.  f i r m b e h a v i o u r the model i s s e t Firms,  therefore,  respond to changes  i n i n d i v i d u a l s ' l a b o u r market b e h a v i o u r by a d j u s t i n g and vacancy  creation decisions.  Consequently,  in a  t h e i r wage  offer  i n t h i s model, the  level  of unemployment does n o t unambiguously r i s e i n response t o an i n c r e a s e i n unemployment compensation. The s o l u t i o n to Model I ,  c o r r e s p o n d i n g to a zero l e v e l o f unem-  ployment compensation, i s s i g n i f i c a n t  i n that i t  demonstrates  that  it  i s n o t the r e l a t i v e l y h i g h l e v e l of unemployment compensation which accounts  f o r b o t h wage d i s p e r s i o n and the wage o f f e r  l y i n g above the p e r f e c t l y  c o m p e t i t i v e wage.  distribution  Thus, i r r e s p e c t i v e  the l e v e l of unemployment compensation, firms do not choose to a l a r g e number o f v a c a n c i e s  and o f f e r  a wage below the  of create  perfectly  c o m p e t i t i v e wage such t h a t the l e v e l of employment c o n s i s t e n t  with  s t a t i c n o n - s t o c h a s t i c p r o f i t maximisation, and, perhaps, a l s o with the e x p l o i t a t i o n of i n t e r t e m p o r a l monopsony power, r i s e s above t h a t consistent with f u l l  employment.  147 D.  The Horizon over which Returns from Search Accrue  1.  The Results Comparative s t a t i c p r e d i c t i o n s are derived f o r values of H^  between 5 and 12 i n increments of u n i t y .  The algorithm d i d not  converge f o r H^ set a t 6 despite exhaustive t e s t i n g .  Although  s o l u t i o n s t o an accuracy of 0.005 i n the wage o f f e r were obtained i n 6 of the 7 s o l u t i o n s , the r e s u l t s obtained are not consistent for one period changes i n H^.  This can be confirmed by observation  of Table 6. I f comparative s t a t i c p r e d i c t i o n s are made over 2 p e r i o d changes i n H^, then the r e s u l t s are more s a t i s f a c t o r y .  An increase i n the  horizon, over which i n d i v i d u a l s b e l i e v e the returns from search accrue, leads to a s h i f t t o the r i g h t of the wage o f f e r d i s t r i b u t i o n .  Mean  wage o f f e r s to both searchers and employed i n d i v i d u a l s r i s e along w i t h the  variance of the o f f e r d i s t r i b u t i o n .  wage o f f e r s f a l l s , but not c o n s i s t e n t l y .  The one period c o r r e l a t i o n of MDI increases and mean p r o f i t s  discounted over an i n f i n i t e horizon f a l l s . Labour's share of t o t a l output rises. Aggregate measures o f vacancy c r e a t i o n , speculative vacancy c r e a t i o n and unemployment r i s e .  Changes i n the duration of search p r i o r t o an  o f f e r are not c o r r e l a t e d i n a consistent way to changes i n aggregate vacancies minus unemployment. to an o f f e r increases.  The mean duration of unemployment p r i o r  148 2.  An Explanation Increasing the horizon over which returns from search are b e l i e v e d  to accrue increases the perceived returns f o r an unemployed i n d i v i d u a l . From ( 3 ) ,  dW* ffi  EW*_  =  (w ••+ ZEW*) , dZ  r  i"  "  1 + 2  -  (1+Z)  f (1+Z) ^ 1  2  >  0  (8)  2  since EW* > w and dZ dH value of  > 0.  Then, c e t e r i s paribus, an increase i n the  1  increases the mean of the perceptions d i s t r i b u t i o n of the  r e s e r v a t i o n wage.  Consequently, the comparative s t a t i c p r e d i c t i o n s  should coincide w i t h r e s u l t s obtained f o r systematic  misperceptions  of the reservation wage. There are two r e l a t e d explanations that can e x p l a i n the incons i s t e n t r e s u l t s obtained from u n i t changes i n H^. (a)  The u n i t change i n  does not s u b s t a n t i a l l y change the nature  of i n d i v i d u a l behaviour and, given the inherent inaccuracy of the s o l u t i o n algorithm, due (  to the a r b i t r a r y s i z e of the wage increment,  the s o l u t i o n s are not consistent. (b)  The non-exhaustive search procedure has generated non-optimal  solutions. The second explanation i s not too convincing, however, i n that such i n c o n s i s t e n t s o l u t i o n s were not generated i n other comparative static  experiments.  TABLE 6 Result3 and Comparative S t a t i c P r e d i c t i o n s f o r D i f f e r e n t Horizons over which Returns from Search Accrue  Summary Statistic  5  The Horizon over which Returns Accrue, H. 10 9 " 8 7  11  Comparative S t a t i c s Frequency/5 Frequency/5 Sign U n i t P e r i o d Two Periods  12  i  (a)  +  3  5  3  5  2  5  (b)  1.567  1.577  1.712  1.594  1.722  1.607  1.780  (c)  0.168  0.176  0.169  0.182  0.173  0.191  0.190  + +  (d)  1.714  1.734  1.840  1.753  1.852  1.778  1.921  +  3  5  (e)  11.486  11.527  11.934  11.633  11.998  11.632  12.143  3  4  (f)  55  55  63  55  63  56  65  + +  3  5 (-3)  (g)  18  22  36  22  45  30  46  +  3  5(-l)  (h)  34  35  38  35  38  37  41  +  -3  5(-2)  1.233  1.166  1.166  1.237  1.166  1.244  1.163  ?  4  2(-l)  (j) (k)  1.567  1.583  1.561  1.584  1.561  1.624  1.612  +  2  5(-l)  ^ 93.162  91.901  84.438  90.774  83.843  88.636  79.252  3  5  (1)  0.512  0.516  0.542  0.521  0.546  0.524  0.559  -  +  3  5  (m)  0.482  0.832  0.370  0.439  0.379  0.405  0.358  —  3  3  150 E.  The Period Length  1.  The Results Comparative s t a t i c p r e d i c t i o n s are derived from Model I f o r  d i f f e r e n t values of the period  length.  The parameter, F, denotes  the new period length i n terms of the standard period. i n F then implies an increase i n the period length.  An increase  For consistency,  the number of new periods which c o n s t i t u t e the work and search horizons are defined as H  H  l  =  1  H  =  |  ....  (9)  ....  (10)  where H^, H denote the new search and work horizons r e s p e c t i v e l y , expressed i n terms of the new period length.  Thus, the a c t u a l  horizons of search, H^F, and work, HF, are equal to the horizons of search and work i n the b a s i c s o l u t i o n .  A value of F greater than unity  implies that both firms and i n d i v i d u a l s make decisions l e s s frequently. Likewise, the respective rates of discount and the l e v e l of unemployment compensation are adjusted according to the period length, whence R  =  RF  ....  (11)  D  =  DF  ....  (12)  w  =  wF  ....  (13)  where R and D represent the new rates of discount f o r firms and  151 i n d i v i d u a l s , r e s p e c t i v e l y , a n d w i s the adjusted rate of unemployment compensation. An increase i n F, the length of the d e c i s i o n p e r i o d , increases the l e v e l of unemployment compensation and also the respective rates of discount f o r firms and workers.  As a r e s u l t , future returns are  discounted a t a. higher r a t e , but l e s s frequently. The procedure adopted i s t o simulate the model given the new period length.  The sample s t a t i s t i c s d e s c r i b i n g s t o c h a s t i c e q u i l i b r i u m  are a l l defined i n terms of the new period length.  For purposes of  comparison,, with the standard p e r i o d , the mean wage o f f e r f o r an unemployed i n d i v i d u a l and the mean wage f o r an employed i n d i v i d u a l are then adjusted by a f a c t o r , ^ , the variance of o f f e r s i s adjusted r  by the f a c t o r , — , and both the mean duration of unemployment and the F mean duration of search p r i o r to an o f f e r are adjusted by the f a c t o r , F. The measures of aggregate vacancy c r e a t i o n and unemployment are constant over time,once s t o c h a s t i c e q u i l i b r i u m i s achieved,and are compatible, therefore, f o r d i f f e r e n t values of F.  I t i s necessary t o w r i t e a  simple computer program t o convert measures of MDI and mean p r o f i t s discounted over an i n f i n i t e horizon t o equivalent measures based on 18 the standard period length and discount r a t e .  These new sample  s t a t i s t i c s are compatible and thus comparable. Values of ^ are adopted.  l y i n g between 0.85 and 1.20 i n increments of 0.05  An increase i n the period lengthy,which  corresponds to  a f a l l i n — , leads t o a s h i f t to the r i g h t of the unadjusted wage offer distribution.  Adjusted measures of the mean o f f e r to searchers,  152 the mean wage o f employed i n d i v i d u a l s , MDI and the v a r i a n c e o f however,  all fall.  The one p e r i o d c o r r e l a t i o n of wage o f f e r s  The a d j u s t e d measure of mean p r o f i t s output  rises.  offers, rises.  L a b o u r ' s share of  total  falls.  Aggregate l e v e l s o f vacancy  creation, speculative  and unemployment do n o t change i n a s y s t e m a t i c  vacancy  fashion,but  measure o f the mean d u r a t i o n o f unemployment r i s e s .  the  creation adjusted  Changes i n the  unadjusted measure of mean d u r a t i o n o f s e a r c h p r i o r to an o f f e r n e g a t i v e l y c o r r e l a t e d t o changes i n the aggregate measure o f  are  vacancies  minus unemployment. T a b l e 7 shows the r e s u l t s and the frequency w i t h which these comparative s t a t i c 2..  p r e d i c t i o n s are u p h e l d .  An E x p l a n a t i o n Through the s p e c i f i c a t i o n o f a l o n g e r d e c i s i o n p e r i o d , market  p a r t i c i p a n t s make d e c i s i o n s l e s s  frequently  over a p e r i o d of time and  thus t h e r e i s an i n c r e a s e i n the i m p l i c i t c o s t s of the market i m p e r f e c t i o n , namely i n c o m p l e t e i n f o r m a t i o n , to b o t h s e t s o f p a r t i c i p a n t s . T h i s can be regarded as a symmetric i n c r e a s e i n the c o s t s o f  the  imperfection. The o p p o r t u n i t y c o s t s of s e a r c h f o r an i n d i v i d u a l a r e i n c r e a s e d and, i n a d d i t i o n , the i n d i v i d u a l r e c o n s i d e r s h i s s e a r c h d e c i s i o n l e s s frequently.  L i k e w i s e , f o r the f i r m the foregone p r o f i t s  w i t h a s u b o p t i m a l l e v e l o f employment are i n c r e a s e d .  If  associated the i n d i v i d u a l ' s  d e c i s i o n p e r i o d remains c o n s t a n t and the f i r m ' s d e c i s i o n p e r i o d i n c r e a s e s ,  TABLE 7 Results and Comparative S t a t i c P r e d i c t i o n s 19 f o r D i f f e r e n t P e r i o d Lengths Summary Statistic  1.20  1.15  The Inverse of the Period Length 1/F 0.95 1.00 1.05 i . 10  0.90  •1 0.85  (a) (b) *  1.768  1.766  1.714  1.753  1.722  1.607  1.591  1.587  (c) *  0.202  0.173  0.174  0.171  0.173  0.184  0.181  0.181  (d) *  1.919  1.892  1.850  1.883  1.852  1.767  1.751  1.749  (e) *  12.137  12.137  11.926  12.011  11.998  11.775  11.613  11.534  64  65  63  65  63  55  55  56  (g)  27  28  27  37  45  30  30  (h)  41  39  39  40  38  34  35  () f  Comparative S t a t i c s Sign Frequency/7  +  7  -  6 4(-l)  -  6 4(-l)  30  -  +  5(-l)  36  -  4(-l)  -  6(-l)  (i)  1.180  1.151  1.171  1.155  1.166  1.234  1.237  1.241  ?  5  (j) *  1.356  1.363  1.439  1.514  1.561  1.649  1.759  1.887  +  7  (k) *  , 79.341  81.238  83.642  81.421  83.843  90.229  91.000  90.648  +  5  (1)  0.559  0.554  0.544  0.550  0.546  0.528  0.521  0.518  -  6  (m)  0.359  0.360  0.377  0.365  0.379  0.436  0.394  0.415  +  5  154.  then the i n c r e a s e i n the i m p l i c i t c o s t s o f the i m p e r f e c t i o n a r e asymmetric and a m u l t i p l e s e a r c h model o f the l a b o u r market  is  appropriate. It  i s m i s t a k e n , however,  ticipants  enjoy  to conclude t h a t b o t h s e t s o f p a r -  a s m a l l e r income, i f the d e c i s i o n p e r i o d i s  The two s e t s o f p a r t i c i p a n t s a r e b o t h a t t e m p t i n g income, g i v e n the o t h e r s e t  increased.  to s e c u r e the maximum  o f p a r t i c i p a n t s ' b e h a v i o u r , and so f o r any  f i x e d l e v e l of aggregate p r o d u c t i o n the market p a r t i c i p a n t s are p l a y i n g a f i x e d . s u m game. frequently,  it  I f both s e t s o f p a r t i c i p a n t s make d e c i s i o n s more  does n o t f o l l o w t h a t the l e v e l o f employment and thus  aggregate p r o d u c t i o n a r e i n c r e a s e d i n s t o c h a s t i c if  F decreases  towards  equilibrium.  Indeed,  z e r o , t h i s d i s c r e t e model approximates a c o n -  tinuous model of the l a b o u r market.  D e c i s i o n making i s  instantaneous,  but p a r t i c i p a n t s s t i l l face i m p e r f e c t i n f o r m a t i o n . To demonstrate the p l a u s i b i l i t y o f these r e s u l t s , necessary  it  is  again  to examine the impact on the cumulative f u n c t i o n , P ( w ) ,  the change i n the exogeneous parameter, F .  If  of  the wage d i s t r i b u t i o n  i s s c a l e d upwards i n accordance w i t h the l o n g e r d e c i s i o n p e r i o d and i n d i v i d u a l s make d e c i s i o n s l e s s f r e q u e n t l y ,  then the p e r c e i v e d r e t u r n s  from s e a r c h , R^,, may be w r i t t e n =1  E Rp = where W i s  1 (3^)  x  (EW*.F-W)  the c u r r e n t wage o f f e r  . . . . (14) f a c i n g the i n d i v i d u a l and i s  i n terms of the new d e c i s i o n p e r i o d , F > 1.  defined  155 Then, i f C_, denotes the opportunity costs of search, r CL, = W - w.F. r  . . . . (15)  Since F i s the new d e c i s i o n period, i n d i v i d u a l s expect t o receive a . wage, EW*.F, i f they search one period.  They w i l l enjoy unemployment  compensation, w.F. The reservation wage, W„, associated with the longer d e c i s i o n r period, i s the s o l u t i o n to 1  W  - wF  p  =  E i=l  1 ( p ^ ) (EW*.F-W ). 1  p  . . . . (16)  Hence, Z .EW.F + wF W  F "  1 + Z„  ' • ' '  ( 1 7 )  where, 1  Z  =  p  E  i=l  1 (—). x  . . . . (18)  1+5  I t i s easy to demonstrate that Z„ < Z, where Z denotes the value r  of a stream of u n i t returns discounted over the standard horizon at 20 the standard discount rate and F > 1. Then, denoting the reservation wage associated with the standard period by W^., W  p  < FW  I  .  ....  (19)  2 1  156 Then, i f firms r a i s e t h e i r wage o f f e r s i n proportion to the longer period length of employment and i n d i v i d u a l s evaluate the returns from search from adopting the longer d e c i s i o n period, the r e s e r v a t i o n wage falls relatively.  C e t e r i s paribus, i n d i v i d u a l s have a lower p r o b a b i l i t y ,  ex ante, of q u i t t i n g i n response to a p a r t i c u l a r wage, i f employed, and a higher p r o b a b i l i t y , ex ante, of accepting an o f f e r , i f unemployed. Despite l e s s frequent d e c i s i o n making, the f i r m faces t h i s systematic change i n i n d i v i d u a l behaviour.  The formal s t r u c t u r e of the model i s  unchanged so the f i r m adjusts i t s wage o f f e r . This change i n i n d i v i d u a l behaviour which r e s u l t s from lengthening the d e c i s i o n p e r i o d and r a i s i n g the wage o f f e r d i s t r i b u t i o n proportiona t e l y i s equivalent t o a f a l l i n the perception parameter, c^. In the model of systematic misperceptions a f a l l i n the parameter c^ leads to a f a l l i n the mean of the perception d i s t r i b u t i o n .  In  response to t h i s systematic change i n behaviour, the wage o f f e r d i s t r i b u t i o n s h i f t s to the l e f t .  The l e v e l of vacancy c r e a t i o n over each  employment s t a t e remains constant or f a l l s . The increase i n the length of the d e c i s i o n period leads to an increase i n the length of the period i n which i n d i v i d u a l s are committed to work f o r a f i r m p r i o r to reconsidering t h e i r q u i t d e c i s i o n .  It is  p l a u s i b l e that firms increase t h e i r l e v e l of wage o f f e r s over a l l states of employment, due to the increase i n labour p r o d u c t i v i t y associated w i t h the longer work period, but i n l e s s than proportion to the increase i n the period length.  157  Therefore, the unadjusted measures of mean wages to searchers and employees and the variance of o f f e r s r i s e , b u t the adjusted measures a l l f a l l .  I n d i v i d u a l s earn a lower l e v e l of adjusted MDI.  The one p e r i o d c o r r e l a t i o n of wage o f f e r s r i s e s with, a longer d e c i s i o n period,but not c o n s i s t e n t l y .  The change i n the c o r r e l a t i o n c o e f f i c i e n t  depends on the r e l a t i v e i n f l u e n c e of the increased range of the unadjusted wage o f f e r d i s t r i b u t i o n on the covariance of successive wage o f f e r s as compared w i t h i t s i n f l u e n c e on the variance of the wage o f f e r distribution. The comparative s t a t i c p r e d i c t i o n s , a r i s i n g from systematic misperceptions of the r e s e r v a t i o n wage, show that firms reduce t h e i r l e v e l of wage o f f e r s and, i n some cases, the l e v e l of vacancy c r e a t i o n i n response to a decrease i n c^, i n order t o reduce the p r o b a b i l i t y of l o s i n g p r o f i t s due to an above optimal workforce. Lengthening  the p e r i o d length means that p r o f i t s foregone from a  low l e v e l of employment are increased and, l i k e w i s e , the p r o f i t s l o s t from a high l e v e l of employment are increased.  Thus, i t i s not evident  t h a t , i n response t o a lengthening of the period length, a f i r m w i l l decrease the l e v e l of vacancy c r e a t i o n i n a d d i t i o n to decreasing the adjusted wage o f f e r . Thus, the l e v e l of vacancy c r e a t i o n over employment states does not change i n a systematic fashion i n response to a change i n the decision p e r i o d .  Aggregate vacancy c r e a t i o n and therefore aggregate  158  unemployment do not change s y s t e m a t i c a l l y . is  longer,  rises. is  the a d j u s t e d  S i n c e the d e c i s i o n p e r i o d  measure o f the mean d u r a t i o n o f  unemployment  The change i n the mean d u r a t i o n o f s e a r c h p r i o r t o an  offer  a g a i n n e g a t i v e l y c o r r e l a t e d t o the change i n the measure o f aggregate  vacancy c r e a t i o n minus unemployment. When i n f o r m a t i o n i s p e r f e c t , and no s e a r c h .  A l l f i r m s employ f o u r i n d i v i d u a l s and pay the  c o m p e t i t i v e wage 1.0.  Aggregate output and t o t a l p r o f i t s  Due to the s p e c i f i c a t i o n firm,  t h e r e i s no f r i c t i o n a l unemployment perfectly  a r e maximised.  of a n o n - l i n e a r production function f a c i n g  each  t o t a l l a b o u r income i s maximised when some i n d i v i d u a l s a r e unem-  ployed.  Unwittingly  h i g h e r mean incomes.  through i m p e r f e c t  i n f o r m a t i o n , i n d i v i d u a l s earn  Although the i m p l i c i t c o s t s o f t h i s  are i n a sense symmetric to b o t h f i r m s and i n d i v i d u a l s , b r u n t of the c o s t s .  imperfection  firms bear  When d e c i s i o n p e r i o d s are s i m u l t a n e o u s l y  the g a i n can be regarded as symmetric to p a r t i c i p a n t s y e t ,  increased,  due to  specification  o f the p e r c e p t i o n d i s t r i b u t i o n , firms a l o n e b e n e f i t  l e s s frequent  d e c i s i o n making.  These r e s u l t s  can be j u s t i f i e d  the  the from  on the  grounds t h a t , d u e to a l o n g e r p e r i o d d u r i n g which employed i n d i v i d u a l s are committed t o work f o r a p a r t i c u l a r f i r m , the q u i t If firms,  decision,  p r i o r to reconsidering  f i r m s enjoy g r e a t e r i n t e r t e m p o r a l monopsony power.  i n d i v i d u a l s a r e a b l e t o make d e c i s i o n s more f r e q u e n t l y then a m u l t i p l e s e a r c h model i s a p p r o p r i a t e .  can c o l l e c t  offers  If  individuals  over t h e f i r m ' s d e c i s i o n p e r i o d , then i t  t h a t the new s t o c h a s t i c  than  is  likely  e q u i l i b r i u m would be c h a r a c t e r i s e d by a h i g h e r  159  g e n e r a l d i s t r i b u t i o n o f wage o f f e r s d i s t r i b u t i o n o f wage o f f e r s ,  and l e s s d i s p e r s i o n .  the mean o f f e r  s e a r c h model, because o n l y the b e s t o f f e r possible  t h a t i n d i v i d u a l s might enjoy  and thus MDI might f a l l .  Thus, t h i s  Given any  i s higher i n a multiple  i s considered.  longer periods of  It  unemployment  asymmetrical r e d u c t i o n i n  i m p l i c i t c o s t s of the market i m p e r f e c t i o n to p a r t i c i p a n t s t o reduce f i r m s ' p r o f i t s . the p e r f e c t l y  competitive  is  When s e a r c h becomes  exhaustive,  is  the  likely  however,  model i s a g a i n a p p r o p r i a t e and f i r m s e a r n  maximum p r o f i t s . The i n f o r m a t i o n s t r u c t u r e i s t h e r e f o r e v e r y i m p o r t a n t i n m o d e l l i n g o f any market. workers b e n e f i t  It  the  appears t h a t i n t h i s l a b o u r market  unambiguously  from i m p e r f e c t  appears t h a t i n d i v i d u a l s enjoy  relatively  i n f o r m a t i o n and  h i g h e r wage o f f e r s  it when  c e r t a i n symmetric o r asymmetric changes i n the i m p l i c i t c o s t s o f the i m p e r f e c t i o n o c c u r , or i f  such as a r e d u c t i o n i n the d e c i s i o n p e r i o d  i n d i v i d u a l s engage i n m u l t i p l e  F.  Systematic  1.  The  search.  M i s p e r c e p t i o n s o f the V a r i a n c e  Results  Comparative s t a t i c of the parameter,  c^.  i n increments o f 0 . 0 5 .  p r e d i c t i o n s are derived for d i f f e r e n t The v a l u e s  of  For i n e x p l i c a b l e  p r o c e d u r e does not converge w i t h the comparative s t a t i c  experiments.  comparative p r e d i c t i o n s  l i e i n the range 0.85 to  I n a d d i t i o n , two o t h e r v a l u e s  0.25 and 0 . 5 0 , a r e adopted.  frequency  reasons,  o f c^,  1.10  namely  the s i m u l a t i o n  t h a t occurs w i t h  T h i s l i m i t s the number o f  available.  values  other  possible  160  O b s e r v a t i o n o f T a b l e 8 shows t h a t the comparative p r e d i c t i o n s a r e not systematic.  static  I n d i v i d u a l s and f i r m s enjoy a  lower l e v e l of MDI and p r o f i t s r e s p e c t i v e l y , b u t the measures o f mean wages f a l l i n three o r l e s s cases out o f f i v e .  The wage o f f e r  d i s t r i b u t i o n does n o t s h i f t s y s t e m a t i c a l l y over d i f f e r e n t v a l u e s o f and,  f u r t h e r m o r e , wage o f f e r s a s s o c i a t e d w i t h any s t a t e do n o t  move i n a s y s t e m a t i c  way over d i f f e r e n t v a l u e s  Labour's s h a r e o f t o t a l output i n c r e a s e s  o f C2« i n three cases out o f  f i v e which cannot be r e g a r d e d as a s i g n i f i c a n t r e s u l t . n e i t h e r the variance  o f o f f e r s n o r t h e one p e r i o d c o r r e l a t i o n o f  wage o f f e r s change i n a s y s t e m a t i c i n the v a r i a n c e The  perception  f a s h i o n i n response t o an i n c r e a s e  parameter,  l e v e l s o f aggregate vacancy c r e a t i o n and aggregate  vacancy c r e a t i o n both remain c o n s t a n t  speculative  o r i n c r e a s e , w h i l e the l e v e l o f  unemployment does n o t change i n a s y s t e m a t i c  fashion.  d u r a t i o n o f s e a r c h p r i o r t o an o f f e r a r e n e g a t i v e l y changes i n the aggregate measure o f v a c a n c i e s The  Likewise,  Changes i n the  correlated to  minus unemployment.  d u r a t i o n o f unemployment does n o t change s y s t e m a t i c a l l y i n response  t o an i n c r e a s e i n c^. The  i n t e r e s t i n g r e s u l t s are obtained  reduced s u b s t a n t i a l l y .  when the v a l u e  o f C2 i s  I t i s argued i n Chapter 2 IB t h a t , i f t h e  parameter C2 i s z e r o , wage d i s p e r s i o n d i s a p p e a r s and s t o c h a s t i c e q u i l i b r i u m c o i n c i d e s w i t h the c o l l u s i v e monopsony e q u i l i b r i u m . Workers' e x p e c t a t i o n s  about wage d i s p e r s i o n a r e s e l f  realising.  TABLE 8 Results and Comparative S t a t i c P r e d i c t i o n s f o r D i f f e r e n t Values of the Perception Parameter, c Summary Statistic  0.25  Values of the Variance Paramete r . i C 0.85 0.90 0.95 " 1.00 0.50  1  1.05  1.10  !  |Comparative S t a t i c s j Sign Frequency/5 j  j  (a)  ^  (b)  0.750  1.404  1.618  1.627  1.645  1.722  1.721  1.696  -  (c). (d)  0.000  0.160  0.194  0.200  0.215  0.173  0.177  0.163  0.750  1.605  1.790  1.805  1.833  1.852  1.850  1.821  (e)  6.021  11.164  11.768  11.778  11.730  11.998  11.943  11.819  -  (f)  0  40  56  56  58  63  63  63  +  .(g)  0  11  30  30  30  45  36  36  (h)  0  27  36  37  40  38  39  3  i  2  \  2  |  3  |  % i  j  +  5(-4) 4(-3)  |  38  +  3  j  5  f  3  |  (i)  0.000  1.353  1.242  1.244  1.254  1.166  1.171  1.165  ?  (j) (k)  0.000  1.595  1.604  1.620  1.686  1.561  1.587  1.564  +  \ 178.598  103.869  88.669  87.407  84.618  83.843  83.319  85.301  -  (1)  0.252  0.487  0.530  0.532  0.535  0.546  0.545  0.536  +  3  j  (m)  1.000  0.584  0.464  0.363  0.419  0.379  0.469  0.381  -  3  |  ON  162 If  the p e r c e p t i o n parameter i s s e t  a t 0 . 5 0 , then  stochastic  e q u i l i b r i u m i s c h a r a c t e r i s e d by wage d i s p e r s i o n , f r i c t i o n a l unem22 ployment and v a c a n c i e s .  If  i s s e t at 0.25 o r below,  then  stochastic  equilibrium is  solution.  A l l firms pay a wage e q u a l to the l e v e l o f unemployment  compensation. or s e a r c h .  c h a r a c t e r i s e d by the c o l l u s i v e monopsony  There i s no f r i c t i o n a l unemployment, wage d i s p e r s i o n ,  The d i s t r i b u t i o n of f i r m s over employment s t a t e s i s  determinate.  Each f i r m employing l e s s than f o u r workers  vacancies,but  i s unable to communicate i t s  in-  creates  excess demand because  t h e r e are no s e a r c h e r s . T h i s r e s u l t i s most i m p o r t a n t .  It  demonstrates  that i f  individuals  base t h e i r g e n e r a l l a b o u r market i n f o r m a t i o n on a sample o f f o u r o r more wage o f f e r s  sampled over time and they compute an u n b i a s e d e s t i m a t e  the v a r i a n c e of the sample mean, then s t o c h a s t i c  equilibrium is  t e r i s e d by zero d i s p e r s i o n .  The c r i t i c a l v a l u e ,  four, clearly  on the exogeneous parameters  chosen.  T h i s r e s u l t demonstrates  that, i f  individuals search  over time f o r i n f o r m a t i o n about j o b o f f e r s t h e i r l a b o u r market b e h a v i o u r i s t e r i s e d by zero d i s p e r s i o n . sample mean decreases  characdepends  extensively  and wage r a t e s  stochastic,  of  then,  the e q u i l i b r i u m i s  although charac-  T h i s i s s i m p l y because t h e v a r i a n c e o f a  as the sample  increases.  T h i s r e s u l t i s n o t dependent on i n d i v i d u a l s s e a r c h i n g o r i n d u l g i n g i n m u l t i p l e searches per d e c i s i o n p e r i o d . r e q u i r e s t h a t a l l i n f o r m a t i o n about wage o f f e r s  It  exhaustively simply  gathered i n the p a s t  i s i n c o r p o r a t e d i n t o the i n d i v i d u a l s ' g e n e r a l i n f o r m a t i o n .  163 2.  An Explanation An increase i n c^, c e t e r i s paribus, has a non-systematic e f f e c t  on the ex ante p r o b a b i l i t i e s of turnover and acceptance i n response to any wage o f f e r .  From Chapter 3 I I , i t appears that, i f an i n d i v i d u a l  faces a r e l a t i v e l y high o f f e r , than an increase i n C2 leads t o a higher p r o b a b i l i t y of q u i t t i n g , when employed, and a lower p r o b a b i l i t y of acceptance, when unemployed.  The converse i s true, i f the i n d i v i d u a l  faces a r e l a t i v e l y low o f f e r . The r e s u l t s r e f l e c t t h i s non-systematic i n f l u e n c e of a change i n C2«  Both p r o f i t s discounted over an i n f i n i t e horizon and MDI f a l l as  the parameter, C2, r i s e s .  I n contrast, when c^ increases, i n d i v i d u a l s  earn higher wage rates over a l l employment states and, despite increased search unemployment and vacancy c r e a t i o n i n s t o c h a s t i c e q u i l i b r i u m , they earn higher MDI.  Firms do not increase wage o f f e r s over a l l employment  states and the combination of higher aggregate unemployment and lower wage o f f e r s over some states of employment leads to lower MDI f o r some changes i n C2, i n a d d i t i o n to lower mean p r o f i t s discounted over an i n f i n i t e horizon. G.  Conclusion In t h i s Chapter, the general c h a r a c t e r i s t i c s of s t o c h a s t i c  e q u i l i b r i u m i n the labour market have been described f o r d i f f e r e n t values of the exogeneous parameters.  Comparative s t a t i c p r e d i c t i o n s ,  derived w i t h respect to the exogeneous parameters, c. , w, H-, F, and  164 i n d i c a t e t h e a l g e b r a i c s i g n of t h e changes i n these summary 23 s t a t i s t i c s which describe' e q u i l i b r i u m . I t i s argued t h a t a s u f f i c i e n t c o n d i t i o n f o r t h e e x i s t e n c e o f wage and employment d i s p e r s i o n i n e q u i l i b r i u m i s t h a t workers, although equally productive geneously.  and i n d i s t i n g u i s h a b l e , behave h e t e r o -  I n t h i s model, i n d i v i d u a l s ' l a b o u r market b e h a v i o u r i s  s t o c h a s t i c and thus heterogeneous, ex p o s t , i f t h e wage o f f e r d i s t r i b u t i o n e x h i b i t s non-zero v a r i a n c e employment d i s p e r s i o n .  initially,  and i f t h e r e i s  I f the value of the perception  parameter  exceeds 0.25, then s t o c h a s t i c e q u i l i b r i u m i s c h a r a c t e r i s e d by wage and  employment  dispersion.  I f no wage d i s p e r s i o n e x i s t s i n i t i a l l y  then, i r r e s p e c t i v e o f  whether employment d i s p e r s i o n e x i s t s , f i r m s w i l l be f o r c e d by i n d i v i d u a l s ' homogeneous n o n - s t o c h a s t i c ,  ex p o s t t u r n o v e r and  acceptance b e h a v i o u r t o o f f e r a wage e q u a l t o the p e r c e i v e d v a t i o n wage.  reser-  C o n v e r s e l y , wage d i s p e r s i o n w i l l o n l y p e r s i s t , i f  employment d i s p e r s i o n c u r r e n t l y e x i s t s . I f individuals incorporate i n t o t h e i r 'general disappear.  labour  information  about p a s t wage o f f e r s  market i n f o r m a t i o n '  then d i s p e r s i o n  will  Then, i n t h i s model, a s u f f i c i e n t c o n d i t i o n f o r h e t e r o -  geneous b e h a v i o u r by i n d i v i d u a l s and thus wage and employment d i s persion  i n e q u i l i b r i u m i s the i n i t i a l e x i s t e n c e  o f wage and employment  d i s p e r s i o n and t h e n o n - c o l l e c t i o n o f p a s t wage o f f e r s t o generate market  information.  labour  165 Firms e x p l o i t t h e i r intertemporal monopsony power by making wage o f f e r s r e l a t e d to t h e i r current l e v e l s of employment.  Thus, i t i s  not i n d i v i d u a l s ' s t o c h a s t i c behaviour, per se, that causes wage d i s p e r s i o n , but rather that firms, f a c i n g d i f f e r e n t l e v e l s of employment, choose to o f f e r d i f f e r e n t wage rates and i n d i v i d u a l s ' s t o c h a s t i c behaviour allows them to do so. Firms speculate i n vacancy c r e a t i o n .  I f a l l vacancies  are f i l l e d ,  and nobody q u i t s , then the l e v e l of employment attained exceeds that consistent w i t h intertemporal p r o f i t maximisation.  This speculation  i s based on i n d i v i d u a l s ' s t o c h a s t i c search, acceptance and behaviour.  turnover  There appears to be a trade-off between the wage o f f e r and  the l e v e l of vacancy c r e a t i o n .  Rather than create vacancies  equal to  desired net h i r e s and o f f e r a high wage, whence there i s a high probabi l i t y that the current workforce i s r e t a i n e d , the f i r m o f f e r s a lower wage and speculates i n vacancy c r e a t i o n . Although the model i s not intended to represent the labour market as behaving as a dynamic process, the explanations of the comparative s t a t i c r e s u l t s are formulated  i n a dynamic context.  The  explanations  are n e c e s s a r i l y h e u r i s t i c due to the simultaneity of the model.  In  response to a change i n an exogeneous parameter, both sets of part i c i p a n t s ' behaviour changes and the nature of the labour market environment changes.  This, i n t u r n , generates new decisions on the part of  market p a r t i c i p a n t s and so on.  I t i s assumed that the instantaneous  166 changes  i n the summary s t a t i s t i c s  caused by the change i n the  exogeneous  parameter a r e an i n d i c a t i o n o f how the n a t u r e o f s t o c h a s t i c e q u i l i b r i u m i s i n f l u e n c e d by the parameter change. of the r e s u l t s  I n o t h e r words,  i s merely s u g g e s t i v e because  it  attempts  the d i s c u s s i o n to e x p l a i n  n a t u r e o f the new p a r t i a l e q u i l i b r i u m i n the l a b o u r market the parameter change,  r a t h e r than the new f u l l  One o f the s i g n i f i c a n t is  that  following  stochastic equilibrium.  t h e o r e t i c a l c o n t r i b u t i o n s o f t h i s model  the l a b o u r market i s m o d e l l e d i n a g e n e r a l e q u i l i b r i u m c o n t e x t .  I n t h i s m o d e l , i n r e s p o n s e to a change i n an exogeneous adopt new d e c i s i o n s .  t h e i r d e c i s i o n s and so on.  generated,  i n which f i r m s a g a i n  W h i l e the c h a r a c t e r i s t i c s  e q u i l i b r i u m s o l u t i o n i n d i c a t e the c h a r a c t e r i s t i c s e q u i l i b r i u m s o l u t i o n , they F o r example,  parameter,firms  Workers respond t o these new d e c i s i o n s and a new  l a b o u r market environment i s  change  o f the p a r t i a l  o f the new  stochastic  are n o t i d e n t i c a l .  the f o l l o w i n g t a b l e shows the s t o c h a s t i c e q u i l i b r i u m  s o l u t i o n s . f o r two v a l u e s  o f c^,  1.20  and 1.25,  and the p a r t i a l  e q u i l i b r i u m s o l u t i o n i n response to an i n c r e a s e o f c^ from 1.20 1.25.  the  In t h i s example,  it  does seem t h a t  the comparison o f the p a r t i a l  e q u i l i b r i u m s o l u t i o n w i t h the i n i t i a l s t o c h a s t i c the q u a l i t a t i v e stochastic  changes  equilibrium indicates  i n the summary s t a t i s t i c s  describing  e q u i l i b r i u m , a s s o c i a t e d w i t h the i n c r e a s e i n  In c o n t r a s t ,  b o t h Salop and Mortenson a n a l y s e  a p a r t i a l e q u i l i b r i u m context.  to  full  c^.  firm behaviour i n  The f i r m ' s d e c i s i o n s over time a r e  assumed to n o t change the g e n e r a l l a b o u r market environment.  167 TABLE 9 A Comparison o f P a r t i a l and F u l l E q u i l i b r i u m  Stochastic Equilibrium P e r c e p t i o n P a r a m e t e r , c ^ = 1.20  Level of Employment  0 1 2 3 4 5 6 7 8  Steady S t a t e Distribution  Wage Offer  0.127 0.306 0.318 0.182 0.057 0.008 0.000 0.000 0.000  2.715 2.650 2.535 2.440 2.365 2.305 2.275 2.260 2.255  Vacancy Creation  Mean One Period Profits  Profits Over an Infinite Horizon  4 3 3 3 3 3 2 1 0  1.55 1.98 2.25 2.45 2.60 2.71 2.80 2.84 2.85  42.04 42.60 42.95 43.19 43.36 43.50 43.60 43.65 43.66  1.53 1.94 2.21 2.40 2.54 2.65 2.73 2.77 2.78  40.98 41.52 41.86 42.09 42.26 42.39 42.48 42.53 42.54  Partial Equilibrium Perception Parameter,c = 1.25  o 1 2 3 4 5 6 7 8  0.143 0.323 0.313 0.166 0.048 0.006 0.000 0.000 0.000  | j  1  I  1 1  2.720 2.665 2.550 2.460 2.385 2.325 2.300 2.285 2.280  4 3 3 3 3 3 2 1 0  ;  I  Stochastic Equilibrium P e r c e p t i o n Parameter, c . = 1.25 i  0 1 2 3 4 5 6 7 8  0.231 0.369 0.263 0.107 0.026 0.003 0.000 0.000 0.000  3.025 2.940 2.865 2.800 2.750 2.720 2.700 2.695 2.690  4 4 4 4 4 3 2 1 0  -  1.09 1.32 1.48 1.60 1.69 1.76 1.81 1.83 1.83  26.73 27.01 27.19 27.33 27.43 27.51 27.56 27.59 27.59  1 '  ! !  168  The  c r u c i a l element i n t h e model i s t h e p r o b a b i l i t y d i s t r i b u t i o n  of perceptions  o f t h e r e s e r v a t i o n wage f a c i n g each i n d i v i d u a l .  the impact o f the change i n the exogeneous parameter on t h i s bution  o f perceptions  s t a t i c results:.  which i s the key to a n a l y s i n g  It is  distri-  t h e comparative  The market i s s e g r e g a t e d , so a l l i n d i v i d u a l s a r e  i d e n t i c a l , ex ante.  No f a c t o r s u b s t i t u t i o n i s p o s s i b l e .  f i r m s a r e f o r c e d t o respond d i r e c t l y  Consequently,  through t h e i r wage o f f e r and  v a c a n c y c r e a t i o n d e c i s i o n t o changes i n the n a t u r e o f the d i s t r i b u t i o n of perceptions.  O t h e r w i s e , they w i l l f a c e inadequate o r e x c e s s i v e  l e v e l s o f employment w i t h g r e a t e r An  frequency.  i m p o r t a n t c o n t r i b u t i o n o f Model I I , o u t l i n e d i n Chapter I I and  Appendix I , i s t h a t f i r m s a r e a b l e t o s u b s t i t u t e i m p l i c i t l y between d i f f e r e n t types o f i n d i v i d u a l s , a l t h o u g h wage and employment ination i s i l l e g a l  2 4  III. A.  discrim-  Vacancy and Unemployment S t a t i s t i c s  Model I In Model I , f i r m s a r e t e c h n i c a l l y homogeneous and each member of  the w o r k f o r c e i s e q u a l l y p r o d u c t i v e .  Due t o s t o c h a s t i c m i s p e r c e p t i o n s  o f t h e r e s e r v a t i o n wage, however, i n d i v i d u a l s ' t u r n o v e r and a c c e p t a n c e b e h a v i o u r , i n response t o the same wage and l a b o u r market environment, i s heterogeneous, ex p o s t , but t h e i r b e h a v i o u r does n o t . d i f f e r i n a systematic  fashion.  E q u i l i b r i u m i s s t o c h a s t i c and i s c h a r a c t e r i s e d by  wage d i s p e r s i o n and t h e simultaneous unemploymen t .  existence  o f v a c a n c i e s and f r i c t i o n a l  169 Although representing  p o s i t i o n s r e q u i r i n g the same s k i l l s , the  aggregate measure o f vacancy c r e a t i o n i s heterogeneous because i t represents u n f i l l e d p o s i t i o n s  created  a t d i f f e r e n t wage rates."  Furthermore, t h e aggregate measure o f vacancy c r e a t i o n r e p r e s e n t d e s i r e d n e t h i r e s because i t r e f l e c t s f i r m s '  does n o t speculation  about i n d i v i d u a l s ' t u r n o v e r and acceptance b e h a v i o u r . In a non-stochastic world, positions,which instantaneously  filled.  In t h i s stochastic  are created, are  framework, i n s u f f i c i e n t  workers may sample the f i r m due t o random s e a r c h , l e a v i n g unfilled,  o r , s i n c e t u r n o v e r and acceptance d e c i s i o n s  some o f f e r s may n o t be a c c e p t e d by c u r r e n t Reder argues t h a t , a p r i o r i ,  unfilled. by  are stochastic,  employees and j o b s e a r c h e r s .  the d u r a t i o n  r e l a t e d i n any p a r t i c u l a r way t o the d u r a t i o n 26  positions  o f unemployment i s n o t o f time a vacancy i s '•>  ;  Then, s t o c h a s t i c e q u i l i b r i u m , which i s c h a r a c t e r i s e d ,  d e f i n i t i o n , by zero excess demand, i s c o n s i s t e n t w i t h t h e s i m u l -  taneous e x i s t e n c e  o f v a c a n c i e s and unemployment, the r e l a t i o n s h i p  between them b e i n g i n d e t e r m i n a t e . These r e s u l t s demonstrate t h a t the use o f a f u n c t i o n o f aggregate v a c a n c i e s and unemployment as a proxy f o r excess demand i n such a 27homogeneous l a b o u r market i s i n c o r r e c t .  Thus, any unemployment and  vacancy s t a t i s t i c s must be c a r e f u l l y i n t e r p r e t e d . B.  Heterogeneous Labour Markets In the r e a l w o r l d o f heterogeneous l a b o u r markets, t h e r e a r e  s e v e r a l f a c t o r s which f u r t h e r c o m p l i c a t e t h e i n t e r p r e t a t i o n o f vacancy statistics.  170 F i r s t l y , as n o t e d i n the L i t e r a t u r e Review, Chapter 1 t h e r e i s the c o n c e p t u a l  HIE,  problem o f d e f i n i n g and measuring the  of vacancy c r e a t i o n which i s c o m p a t i b l e , i n some sense, w i t h d e f i n i t i o n of unemployment.  An  level the  i n d i v i d u a l w i t h o u t work f o r seven  days i s c l a s s i f i e d as unemployed b u t , w h i l e unemployment i s a d i s t i n c t . and  recognisable  s t a t e f o r the i n d i v i d u a l , ( i g n o r i n g the problem of  defining active search), defined.  An  the e x i s t e n c e  employer, n o t  a c t i v e l y r e c r u i t i n g , may  for a well qualified applicant. an employer may  of a vacancy i s l e s s w e l l create a p o s i t i o n  Faced w i t h an i n s u f f i c i e n t w o r k f o r c e  adopt a l t e r n a t i v e measures, namely :  (a)  The  i n s t i g a t i o n o f overtime;  (b)  Subcontracting  (c)  The  the work elsewhere;  and  purchase of a d d i t i o n a l machinery, t h a t i s c a p i t a l  deepening, to make h i s l a b o u r A f i r m may  f o r c e more  productive.  choose to a d v e r t i s e i n a newspaper or t r a d e p a p e r ,  but  28'  f  not  s p e c i f y the number o f p o s i t i o n s a v a i l a b l e . Secondly, a f i r m i s n o t  l e g a l l y compelled t o n o t i f y a manpower 29  office  (a source o f job vacancy s t a t i s t i c s ) of the e x i s t e n c e  I t may  not  of v a c a n c i e s .  choose t o do so i f , f o r example, i t b e l i e v e s t h a t n o t i f i c a t i o n  of u n f i l l e d p o s i t i o n s w i l l a t t r a c t a l a r g e number o f a p p l i c a n t s who  will  require interviews  filled  at c o n s i d e r a b l e  by a l o c a l worker, the a p p l i c a n t who  has  f i r m may  cost.  Or,  i f the vacancy i s not  f e e l committed to o f f e r the p o s i t i o n to  t r a v e l l e d a l o n g way  to the  interview.  an  1  171 The f i r m may regard informal contacts as more e f f i c i e n t .  I t may  be able t o d i s c r i m i n a t e against the p o t e n t i a l employee i n wage o f f e r or c o n d i t i o n s , or indeed, choose t o not h i r e him, which may be imp o s s i b l e , i f Manpower i s n o t i f i e d of the c h a r a c t e r i s t i c s of the job and number of vacancies. T h i r d l y , the existence of an i n t e r n a l labour market w i t h i n a f i r m , as described by Dunlop [1966] and Doeringer and P i o r e [1971], the i n t e r p r e t a t i o n of a vacancy.  complicates  Employers develop an elaborate s e t of  r u l e s , whether or not subject to c o l l e c t i v e bargaining, r e l a t i n g to promotions, t r a n s f e r s , l a y o f f s , and retirements f o r various job classifications.  Entry from outside the organisation i s confined to  a few c l a s s i f i c a t i o n s .  Each 'port of entry' i s the bottom rungrdf a  family of s i m i l a r s k i l l r e q u i r i n g operations. job,  I n d i v i d u a l s , on the  receive t r a i n i n g to enable them to be promoted w i t h i n a family  of jobs.  The r u l e s of s e n i o r i t y s p e c i f y the i n t e r n a l movement of  i n d i v i d u a l s between these jobs.  The concept of the supply of labour  i n t h i s market i s thus inappropriate.  A vacancy i n a top p o s i t i o n may  be f i l l e d by a s e r i e s of promotions throughout the family of jobs, such that the vacancy created i n the e x t e r n a l labour market i s f o r a 'bottom rung' p o s i t i o n ,  w h i l s t maintaining a t r a d i t i o n of i n t e r n a l promotion,  firms may n o t i f y the e x t e r n a l labour market of such a vacancy. I f each such vacancy down the ladder i s advertised, the number of vacancies advertised w i l l exaggerate the number of i n d i v i d u a l s required.  The s k i l l  requirements of these 'port of entry' p o s i t i o n s may w e l l be higher than  172  f o r m a l l y r e q u i r e d , s i n c e such a p p l i c a n t s w i l l be expected t o be promoted w i t h i n t h i s f a m i l y o f j o b s . F o u r t h l y , even w i t h i n  the same i n d u s t r y , the exact  skills  r e q u i r e d and the non-monetary b e n e f i t s of t h e j o b a r e n o t homogeneous over f i r m s .  Thus the unemployed worker has i m p e r f e c t  information  30 about a v e c t o r o f c h a r a c t e r i s t i c s of the j o b . A s i d e from the problem o f wage d i s p e r s i o n and s p e c u l a t i o n i n vacancy c r e a t i o n , demonstrated i n Model I,'; the use o f j o b vacancy and unemployment s t a t i s t i c s market i s s u b j e c t  to considerable  siderable disaggregation of job v a c a n c i e s ,  t o a n a l y s e the f u n c t i o n i n g o f the difficulties,  i s required.  d e t a i l e d information  labour  t h e r e f o r e , and con-  I n a d d i t i o n t o the c h a r a c t e r i s t i c s i s r e q u i r e d about the s k i l l s and  a s p i r a t i o n s of unemployed workers.  Otherwise, any l o o s e comparison o f  vacancy and unemployment s t a t i s t i c s  may  friction  i n the o p e r a t i o n  o v e r e s t i m a t e the degree bf  o f the l a b o u r market and d i s g u i s e t h e degree  3d of s t r u c t u r a l unemployment:  1  173  CHAPTER 5 RESULTS FROM MODELS I I AMD I I I  I.  Introduction  I n t h i s chapter the r e s u l t s from Models I I and I I I are presented. S o l u t i o n s to each model are generated f o r d i f f e r e n t combinations of 1 2 values o f the perception parameter v a l u e s , c^ , c^ . 1 2 A r b i t r a r i l y , the value of c^ i s assumed to equal o r exceed c^ . I n response to the same labour market environment^" and a p a r t i c u l a r wage o f f e r , each type one i n d i v i d u a l has a lower p r o b a b i l i t y o f accepti n g a p o s i t i o n and a higher p r o b a b i l i t y of t u r n o v e r , i f employed, ex ante, than a type two i n d i v i d u a l .  Even when employed, type one i n d i v i d u a l s ,  although equally productive over a s i n g l e p e r i o d , are l e s s v a l u a b l e to the f i r m i n an i n t e r t e m p o r a l sense than type two i n d i v i d u a l s because, i n response t o the same stream of wage o f f e r s over time from the f i r m , the mean returns from employing a type one i n d i v i d u a l are lower than the mean r e t u r n s from employing a type two i n d i v i d u a l . For the purpose of e x p l a i n i n g both sets of r e s u l t s , i t i s u s e f u l to d i v i d e the employment states i n t o f i v e d i s t i n c t subgroups.  The  exogeneous parameters adopted are such t h a t , f o r a l l values o f the perception parameters chosen, the s i n g l e p e r i o d p r o f i t maximising l e v e l of employment coincides w i t h the intertemporal p r o f i t maximising 2 l e v e l of employment next period  f o r wage o f f e r s l y i n g between 0.75 and  174 1.50.  A s i n g l e p e r i o d p r o f i t maximising  f i r m i s i n d i f f e r e n t as t o the  composition o f employment i t a t t a i n s , s i n c e , given the wage o f f e r , s i n g l e p e r i o d p r o f i t s a r e determined  by l e v e l o f employment a l o n e .  A  f i r m o f f e r i n g a wage i n t h i s range chooses t o employ two i n d i v i d u a l s . Two then c o n s t i t u t e s t h e ' o p t i m a l ' l e v e l o f employment. A f i r m , which maximises p r o f i t s d i s c o u n t e d over an i n f i n i t e h o r i z o n , chooses t o employ type two i n d i v i d u a l s who a r e more v a l u a b l e , i n the sense d e s c r i b e d . two  3  Thus, the ' o p t i m a l w o r k f o r c e '  i s d e f i n e d as two type  i n d i v i d u a l s , i f the f i r m o f f e r s a wage between 0.75 and 1.50.  4  Given the c h o i c e o f the l e v e l and composition Of employment, t h e f i r m employs the ' o p t i m a l w o r k f o r c e ' .  I n d i v i d u a l s ' l a b o u r market  b e h a v i o u r i s s t o c h a s t i c , however, and the l e v e l and c o m p o s i t i o n o f employment the f i r m f a c e s n e x t p e r i o d i s n e c e s s a r i l y s t o c h a s t i c .  An  'outcome' i s d e f i n e d as the l e v e l and composition o f employment t h a t a f i r m faces next p e r i o d .  Mean p r o f i t s a r e d e f i n e d as p r o f i t  discounted  over an i n f i n i t e h o r i z o n a s s o c i a t e d w i t h each outcome, weighted p r o b a b i l i t y o f a t t a i n i n g t h a t outcome.  by the  A f i r m , which maximises mean  p r o f i t s , w i l l make d e c i s i o n s such t h a t t h e r e i s a h i g h ex ante probability  o f a t t a i n i n g an outcome i n the neighbourhood o f the ' o p t i m a l work-  force'.~*  The o p t i m a l l e v e l o f employment i s independent  of employment  o f the composition  over the v a l u e s o f t h e p e r c e p t i o n parameters adopted.  Thus,  f i r m s make d e c i s i o n s such t h a t t h e r e i s a r e l a t i v e l y h i g h ex ante p r o b a b i l i t y of a c h i e v i n g t h e o p t i m a l l e v e l o f employment.  A f i r m , which c u r r e n t l y employs  175 s o l e l y type two i n d i v i d u a l s , has the 'optimal' composition of employment, when analysing firms' decisions i n both Models II and I I I , i t proves' easiest to group employment states i n t o  subgroups according to t h e i r  r e l a t i o n s h i p to the 'optimal workforce'.  The f i v e conceptually d i s t i n c t  subgroups constitute the elements of 2 x 3 matrix, as shown i n Figure 8.  BO  00  AO  OC  b  a  d  SC  b  c  e  Figure 8  The Matrix of Employment States  In state OC, the firm faces a workforce with the optimal composition of employment, that i s s o l e l y type two employees.  In state SC, the f i r m  faces a workforce which has a suboptimal composition of employment. type one i n d i v i d u a l s are employed. than optimal l e v e l of employment. optimal l e v e l of employment.  Some  In state BO, the firm faces a less In state AO, the firm faces an above  The f i v e d i s t i n c t subgroups which are  denoted by l e t t e r s (a) to (e) are the following : a.  The firm currently employs the 'optimal workforce', that i s state [ 0 , 2 ] ; 6  b.  The firm currently employs a less than optimal l e v e l of employment, states [0,0], [1,0], and [0,1];  c.  The firm currently employs the optimal l e v e l but sub-optimal composition of employment, states [2,0] and [1,1];  176  d.  The f i r m c u r r e n t l y employs an above o p t i m a l l e v e l o f employment but the subset [1,3]  e.  'optimal workforce'  o f those employed, s t a t e s and [ 0 , 4 ] ;  constitutes  [1,2],  [0,3],  The f i r m c u r r e n t l y employs an above o p t i m a l l e v e l o f suboptimal i n composition.  o p t i m a l workforce does n o t c o n s t i t u t e a subset c u r r e n t employees,  II.  states  [3,0],  [2,1],  The of  [4,0] and  [3,1].  R e s u l t s o f Model I I  B a s i c Parameter Values The parameter v a l u e s  of  [2,2],  and  employment which i s  A.  a  s p e c i f i e d i n Chapter 3 I I I B and u n i t  the p e r c e p t i o n parameters c o n s t i t u t e  values.  Ex a n t e ,  behaviour. values  the  'basic'  set  Thus, Model I I  Firms,  simplifies  facing  to Model I .  Indeed,if  The steady  s t a t e complements.  1  2  If  J  the  simplifies  to  the same l e v e l o f employment, make i d e n t i c a l  wage and vacancy c r e a t i o n d e c i s i o n s , o f employment.  of parameter  i n d i v i d u a l s are i d e n t i c a l i n t h e i r l a b o u r market  of the p e r c e p t i o n parameters a r e e q u a l , Model I I  Model I .  values  i n d e p e n d e n t l y o f the c o m p o s i t i o n  s t a t e d i s t r i b u t i o n i s symmetric about and j  2  are s t a t e complements,  then  (1)  2  S o l v i n g the s i m u l a t i o n p r o c e d u r e i n Model I I the p e r c e p t i o n parameters c o n s t i t u t e s b a s i c s o l u t i o n t o Model I I  the  for i d e n t i c a l values  a t e s t of i t s  i s shown i n T a b l e  10.  consistency.  of The  177 TABLE 10 The  B a s i c S o l u t i o n t o Model I I Stochastic  i  Type One Employment  Equilibrium  |  j  Type Two ! Employment  0 1 0 2 1 0 3 2 1 0 4 3 2 1 0  i  Steady S t a t e Distribution  j  0 0 1 0 1 2 0 1 2 3 0 1 2 3 4  0.156 0.213 0.213 0.087 0.175 0.087 0.008 0.025 0.025 0.008 0.000 0.000 0.000 0.000 0.000  j  Wage Offer  1.455 1.420 1.420 1.245 1.245 1.245 1.185 1.185 ! 1.185 ! 1.185 1.085 1.085 1.085 1.085 1.085  EW  MW  1.323  vw*  W*  !  2 1 1 1 1 1 0 o 0 0 o 0 0 0 0  i  ! ! !  •  !  P r o f i t s Over Infinite Horizon.  0.45 1.01 1.01 1.21 1.21 1.21 1.29 1.29 1.29 1.29 1.33 1.33 1.33 1.33 1.33  19.13 20.29 20.29 20.61 20.61 20.61 20.72 20.72 20.72 20.72 20.74 20.74 20.74 20.74 20.74  Statistics  LS  i 1.145 j 0.081  Mean One Period Profits  ; Vacancy ; Creation  i  Summary  ;  V*  0.634  V *  54  U*  s 17  32  PO*  PA*  En  1.737 j 1.377  20.250  Correlation of Offers ;1 P e r i o d  0.395  !  !  2 Periods  0.167  | |  3 Periods  0.035  i  j  4 Periods  '  5 Periods!  !  !  q. 001  - 0.003 !  Mean D i s c o u n t e d Income •  No Q u i t t i n g  10.215  True  Perception  • 10.215  Stochastic  Behaviour!  9.070  !  TABLE 10 (continued) Steady State T r a n s i t i o n M a t r i x 0.570 0.091 0.091 0.069 0.069 0.069 0.061 0.061 0.061 0.061 0.081 0.081 0.081 0.081 0.081  0.164 0.536 0.031 0.310 0.163 0.017 0.283 0.188 0.094 0.0 0.283 0.213 0.142 0.071 0.0  0.164 0.031 0.536 0.017 0.163 0.310 0.0 0.094 0.188 0.283 0.0 0.071 0.142 0.213 0.283  0.025 0.171 0.0 0.384 0.035 0.0 0.434 0.145 0.0 0.0 0.372 0.186 0.062 0.0 0.0  0.052 0.171 0.171 0.070 0.384 0.070 0.0 0.289 0.289 0.0 0.0 0.186 0.248 0.186 0.0  0.025 0.0 0.171 0.0 0.035 0.384 0.0 0.0 0.145 0.434 0.0 0.0 0.062 0.186 0.372  0.0 0.0 0.0 0.075 0.0 0.0 0.222 0.0 0.0 0.0 0.217 0.054 0.0 0.0' 0.0  0.0 0.0 0.0 0.0 0.0 0.0 0.075 0.0 0.075 0.075 0.0 0.075 0.0 0.0 0.222 • 0.0 0.0 0.222 0.0 0.0 0.0 0.0 0.163 0.0 0.108 0.108 0.0 0.163 0.0 0.0  0.0 0.0 0.0 0.0 0.0 0.075 0.0 0.0 0.0 0.222 0.0 0.0 0.0 0.054 0.217  0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.047 0.0 0.0 0.0 0.0  0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.047 0.0 0.0 0.0  0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.047 0.0 0.0  0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.047 0.0  0.0 i 0.0 0.0 0.0 0.0 0.0 o.o : 0.0 ; 0.0 0.0 0.0 • 0.0 0.0 : o.o : 0.047  oo  179' The general c h a r a c t e r i s t i c s of s t o c h a s t i c e q u i l i b r i u m with these exogeneous parameters conform to the s o l u t i o n s to Model I .  Stochastic  e q u i l i b r i u m i s characterised by wage and employment dispersion over l e v e l s of employment.  The d i s t r i b u t i o n of wage o f f e r s l i e s above the  p e r f e c t l y competitive e q u i l i b r i u m wage but the mean wage o f f e r s to searchers and employed i n d i v i d u a l s are l e s s than average marginal product.  Firms e x h i b i t dynamic monopsony power i n that the wage  o f f e r i s a d e c l i n i n g function of the l e v e l of employment and mean p r o f i t s discounted  over an i n f i n i t e horizon are an i n c r e a s i n g function  of the l e v e l of employment.  Curiously, although able to create vacancies  when f a c i n g an employment l e v e l of three, firms do not choose t o do so. I f i n d i v i d u a l s are i d e n t i c a l , and the common perception parameter, c^, exceeds 1.00, however, then firms do create vacancies, when employing three i n d i v i d u a l s . This r e s u l t r e f l e c t s the trade o f f between the wage o f f e r and l e v e l of vacancy c r e a t i o n .  The f i r m earns higher mean p r o f i t s  by c r e a t i n g a vacancy and i n c r e a s i n g the wage o f f e r rather than i n c r e a s i n g the wage o f f e r alone, i f c^ increases. The comparative s t a t i c p r e d i c t i o n s generated by d i f f e r e n t sets of equal values of the perception parameters conform exactly t o those generated i n Model I . An important feature of a l l s o l u t i o n s of Model I I i s that speculative vacancy c r e a t i o n i s a s i g n i f i c a n t l y smaller percentage of t o t a l vacancy creation than i n Model I .  This r e s u l t can be a t t r i b u t e d to the reduction  i n the number of employment l e v e l s , i n p a r t i c u l a r these exceeding the  180 s t a t i c p r o f i t maximising l e v e l of employment.  This r e s t r i c t i o n of  the maximum l e v e l of employment, however, does not seem to change the e s s e n t i a l nature of firms' d e c i s i o n making. B.  Unequal Values of the Perception Parameters  1.  The Results Solutions to Model I I are obtained f o r 7 sets of unequal values 1  2  of the perception parameters, c^ , c^ , l y i n g i n the range 0.90 to 1.15 i n increments of 0.05.  Table 11 shows the s o l u t i o n to Model I I  f o r perception parameters values, [1.05,0.95], Stochastic e q u i l i b r i u m i n Model I I i s characterised by wage dispersion and dispersion both i n the l e v e l and composition of employment facing a f i r m .  The d i s t r i b u t i o n of wage o f f e r s l i e s above  the p e r f e c t l y competitive wage.  Both searchers' and employees' mean  o f f e r s are exceeded by the average marginal product.  The wage o f f e r  i s a d e c l i n i n g function of the l e v e l of employment faced by the f i r m , i r r e s p e c t i v e of the composition of employment.  Over each l e s s than  optimal l e v e l of employment, the wage o f f e r i s an i n c r e a s i n g function of the number of type one i n d i v i d u a l s employed.  The l e v e l of vacancy  creation i s independent of the composition of employment over l e s s than optimal l e v e l s of employment and i s a d e c l i n i n g function of these l e v e l s of employment.  A f i r m , c u r r e n t l y f a c i n g the optimal workforce, creates  a vacancy i n one case out of seven.  I  181 TABLE  11  The S o l u t i o n to Model I I  Corresponding  To P e r c e p t i o n Parameter V a l u e s  Stochastic  Type One j Type Two Employment ]. Employment 0 1 0 2 1 0 3 2 1 0 4 3 2 1 0  0  Steady S t a t e Distribution ! ! 1 !  0 1 0 1 2 0 1 2 3 0 1 2 3 4  0.143 0.180 0.247 0.079  I  j|  0.158 0.147 0.008 0.022 0.014 0.0 0.0 0.001 0.0 0.0 0.0  ! •  Equilibrium  Wage Offer  ; ;  :  j|  [1.05,0.95]  1.45 1.43 i.38 1.26 1.22 1.29 1.14 1.11 1.14 1.12 1.10 1.08 1.05 1.03 1.01  j  2 1 1 1 1 0 1 1 0 0 0 0  :  : '  !  :'  i  0  |  j  j  j v * 'V I  |49  s  MW  W*  VW*  LS  1.323  1.310  1.100  0.089  0.274  j V *  *  13  Statistics  MW  1  1.146  Summary 2  PA *  u *  2  20  12  2.058  ;  1.783  C o r r e l a t i o n of  J.  19.77 20.76 21.34 21.04 21.49 21.92 21.12 21.49 21.83 22.09 21.12 21.46 21.74 21.96 22.13  j  1  0.351  PO*  En  1-532  21.105  1  Offers  i  1 Period  2 Periods  0.422  0.187  j  3 Periods  4 Periods  5 Periods  0.048  0.005  -  Mean D i s c o u n t e d No Q u i t t i n g Type  1  PA *  1  2  J  1.17 1.26 1.32 1.25 1.33 1.39 1.43 1.30 1.36 1.42 1.45 1.48  1  0  .  P r o f i t s Over Infinite Horizon  0.45 0.98 1.08  i  0  EW  Mean One Period Profits  Vacancy Creation  0.008  Income  True P e r c e p t i o n  1  10.015  9.629  JType 2  10.143  10.143  "1  Stochastic 8.682  I  9.287  Behaviour  TABLE 11 (continued) Steady State T r a n s i t i o n M a t r i x i  0.573 0.108 0.072 0.080 0.063 0.031 0.090 0.076 0.049 0.039 0.093 0.075 0.069 0.059 0.052  0.197 0.531 0.027 0.324 0.113 0.0 0.291 0.144 0.050 0.0 0.302 0.164 0.085 0.032 0.0  0.130 0.030 0.558 0.017 0.219 0.289 0.015 0.153 0.215 0.227 0.0 0.120 0.188 0.217 0.228  0.036 0.199 0.0 0.371 0.025 0.0 0.330 0.079 0.0 0.0 0.367 0.118 0.026 0.0 0.0  0.050 0.133 0.204 0.065 0.391 0.0 0.046 0.288 0.216 0.0 0.0 0.260 0.230 0.118 0.0  0.015 0.0 0.139 0.0 0.041 0.681 0.0 0.022 0.234 0.444 0.0 0.0 0.128 0.264 0.374  0.0 0.0 0.0 0.083 0.0 0.0 0.148 0.010 0.0 0.0 0.198 0.029 0.0 0.0 0.0  0.0 0.0 0.0 0.061 0.084 0.0 0.046 0.156 0.0 0.0 0.0 0.188 0.070 0.0 0.0  0.0 0.0 0.0 0.0 0.064 0.0 0.0 0.038 0.235 0.0 0.0 0.0 0.156 0.144 0.0  0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.291 0.0 0.0 0.0 0.108 0.273  0.0 0.0 0.0 0.0 0.0 0.0 0.019 0.0 0.0 0.0 0.040 0.0 0.0 0.0 0.0  0.0 0.0 0.0 0.0 0.0 0.0 0.015 0.019 0.0 0.0 0.0 0.046 0.0 0.0 0.0  0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.016 0.0 0.0 0.0 0.0 0.048 0.0 0.0  0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.058 0.0  0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 ' 0.0 j 0.075  M CD ro  183 A l s o , a f i r m , c u r r e n t l y employing three type one i n d i v i d u a l s , does not create a vacancy i n one case out of seven.  I n some cases,  firms employing a mixed workforce of three employees w i l l also create vacancies.  Thus, the vacancy c r e a t i o n decisions are reasonably  consistent over d i f f e r e n t sets of the perception parameters. Then, over the optimal or above optimal l e v e l s of employment, the vacancy c r e a t i o n d e c i s i o n i s not independent of the composition of employment.  These e x i s t s a t r a d e o f f between the wage o f f e r and  vacancy c r e a t i o n decision and i f , i n p a r t i c u l a r , a f i r m employs the optimal workforce, i t creates zero vacancies and o f f e r s a higher wage than a f i r m f a c i n g an optimal l e v e l , but suboptimal composition of employment. Type one employees' mean wage exceeds the mean wage of type two employees but type two i n d i v i d u a l s enjoy a higher MDI and a l a r g e r share of output.  Type one i n d i v i d u a l s enjoy both a higher l e v e l and  a longer duration of unemployment than type two i n d i v i d u a l s . For each l e v e l of employment, mean p r o f i t s discounted over an i n f i n i t e horizon are a d e c l i n i n g function of the number of type one i n d i v i d u a l s employed.  Discounted p r o f i t s are not, however, an i n -  creasing f u n c t i o n of the l e v e l of employment independently of the composition.  This i s quite p l a u s i b l e and i s shown i n Table 11 where  higher discounted p r o f i t s are enjoyed by a f i r m i n s t a t e [0,1] than a f i r m i n state [2,0].  184 The v a l u e s  of these summary s t a t i s t i c s  over the seven  solutions  and the frequency w i t h which the s p e c i f i e d r e l a t i o n s h i p between summary s t a t i s t i c s  c o r r e s p o n d i n g to each type o f i n d i v i d u a l i s upheld  are shown i n T a b l e 2.  the  12.  An E x p l a n a t i o n Again,  it  i s p o s s i b l e to demonstrate the p l a u s i b i l i t y of  r e s u l t s by an a p p l i c a t i o n o f the i l l u s t r a t i v e model.  If  these  high-turnover  type one i n d i v i d u a l s have a h i g h e r m a r g i n a l turnover r a t e than l o w t u r n o v e r type two i n d i v i d u a l s , then i t initial  l e v e l o f employment,  can be shown t h a t ,  the wage o f f e r  for a given  i s an i n c r e a s i n g f u n c t i o n  o f t h e number o f type one i n d i v i d u a l s employed.  Most f i r m s i n  the  9 industry offer  a wage above the mean o f the d i s t r i b u t i o n o f  perceptions  and thus f a c e a h i g h e r m a r g i n a l t u r n o v e r r a t e on the p a r t o f type one individuals,  ceteris  paribus.  In the i l l u s t r a t i v e model, however, vacancy  creation decisions.  f i r m s do n o t make e x p l i c i t  Firms maximise p r o f i t s a s s o c i a t e d w i t h  the mean l e v e l o f employment c o r r e s p o n d i n g to the wage o f f e r . t a k i n g t h e mathematical e x p e c t a t i o n ,  therefore,  the flow s u p p l y o f  l a b o u r t o the f i r m i s reduced t o a n o n - s t o c h a s t i c l a b o u r dependent on the wage o f f e r . sheds  flow s u p p l y of  T h u s , the i l l u s t r a t i v e model o n l y  l i g h t on the r e s u l t s , when f i r m s , f a c i n g the same l e v e l  different decision.  c o m p o s i t i o n o f employment, make the same vacancy In t h i s  case,  between  firms.  but  creation  each f i r m faces the same s t o c h a s t i c  s u p p l y o f workers who r e c e i v e an o f f e r b u t the p r o b a b i l i t y o f differs  By  flow acceptance  TABLE 12 Summary S t a t i s t i c s f o r Unequal Values of the Perception Parameters 1 c  l  C  . 2 l  MW  2  MDI^  MDI  2  U  l  U  2  PA*  PA*  0.95  0.90  1.237  1.214  8.524  8.913  16  9  1.890  1.752  1.00  0.90  1.244  1.235  8.534  8.968  17  10  1.987  1.00  0.95  1.288  1.308  8.776  9.087  17  14  1.05  0.95  1.323  1.310  8.682  9.287  20  1.05  1.00  1.353  1.366  8.852  9.154  1.10  0.90  1.355  1.328  8.658  1.10  1.00  1.424  1.392  8.982  Freq/7  5  .  \  7  !  L  S  LS  i  i  2  | 0.271  0.321  1.791  ! 0.268  0.329  1.917  1.869  | 0.292  0.328  12  2.058  1.783  | 0.274  0.351  20  17  2.051  1.979  ! 0.303  0.337  9.559  22  10  2.181  1.746  : 0.264  0.370  9.452  22  16  2.035  1.723  ' 0.303  0.360  7  7  7  186  As i n Model I , the wage i s a d e c l i n i n g f u n c t i o n o f the l e v e l o f employment the f i r m c u r r e n t l y f a c e s , i n d e p e n d e n t l y o f the c o m p o s i t i o n o f employment."^  T h i s r e f l e c t s the f i r m ' s i n t e r t e m p o r a l  monopsony power.  The wage o f f e r d i s t r i b u t i o n l i e s above the p e r f e c t l y c o m p e t i t i v e  equilibrium  wage. T h i s r e s u l t i s p l a u s i b l e , because, s i n c e the l e v e l o f f r i c t i o n a l unemployment i s non-zero, a m a j o r i t y  o f f i r m s i n the i n d u s t r y  face  l e v e l s o f employment below t h a t c o n s i s t e n t w i t h p r o f i t m a x i m i z a t i o n and payment o f the s t a t i c e q u i l i b r i u m wage.  By o f f e r i n g a wage above  the s t a t i c e q u i l i b r i u m wage, the f i r m r a i s e s the ex ante p r o b a b i l i t y o f i n c r e a s i n g i t s w o r k f o r c e and thus i n c r e a s i n g i t s p r o f i t s S i n c e a majority  o f f i r m s o f f e r a wage above t h e s t a t i c e q u i l i b r i u m wage, h i g h  employment f i r m s a r e f o r c e d t o o f f e r a wage above the s t a t i c wage because the t r u e r e s e r v a t i o n wage i s r e l a t i v e l y I t i s now a p p r o p r i a t e  equilibrium  high.  t o a n a l y s e t h e f i r m s ' wage d e c i s i o n s by  c o n s i d e r i n g each o f t h e f i v e s e t s o f employment s t a t e s d e f i n e d i n I : (a)  The f i r m c u r r e n t l y employs the 'optimal workforce'. I t s d e c i s i o n s a r e such t h a t t h e r e i s a h i g h ex ante p r o b a b i l i t y of r e t a i n i n g that workforce.  I t does n o t w i s h  to employ any more workers s o , assuming t h a t i t c r e a t e s vacancies,  i t o f f e r s a r e l a t i v e l y low wage, s p e c u l a t i n g  about s t o c h a s t i c turnover  and acceptance b e h a v i o u r by  c u r r e n t employees and s e a r c h e r s .  Then, i t f a c e s the  p o s s i b i l i t y o f l o s i n g e i t h e r o r both v a l u a b l e employees.  Given s t o c h a s t i c s e a r c h  type two  and acceptance  187  b e h a v i o u r by unemployed i n d i v i d u a l s , any vacancy may n o t be f i l l e d .  created  More type one i n d i v i d u a l s than type 12  two i n d i v i d u a l s a r e unemployed.  Then, t h e r e i s a h i g h e r  p r o b a b i l i t y t h a t a type one s e a r c h e r w i l l r e c e i v e than a type two s e a r c h e r . a higher probability^  an  A l t h o u g h a type one s e a r c h e r has  ex a n t e ,  o f r e f u s i n g the o f f e r ,  has a h i g h e r p r o b a b i l i t y o f r e c e i v i n g and a c c e p t i n g offer  than a type two i n d i v i d u a l (see  firm creates  vacancies,  offer  it  (b)  ).  he  an  Hence, i f  faces a h i g h p r o b a b i l i t y  a  of  a t t a i n i n g a suboptimal l e v e l or suboptimal composition of employment.  In o t h e r words,  the f i r m faces a g r e a t e r  variance  i n the l e v e l and c o m p o s i t i o n o f employment n e x t p e r i o d , and 13 thus lower mean p r o f i t s . Then, to maximise mean p r o f i t s , vacancies  and o f f e r s  h i g h wage, so t h a t quitting. elements  its  the f i r m c r e a t e s  c u r r e n t workforce a  the p r o b a b i l i t y t h a t the w o r k f o r c e ,  the  'optimal workforce'  i n the t r a n s i t i o n m a t r i x , shown i n T a b l e 11.  retains  employees  i s supported by o b s e r v a t i o n o f  o f the row c o r r e s p o n d i n g to the  workforce'  relatively  there i s a small p r o b a b i l i t y of  This hypothesis  which i n d i c a t e s  zero  The  element,  a f i r m f a c i n g the  assumes  'optimal  the g r e a t e s t v a l u e  the m a t r i x . The f i r m faces a l e s s  than o p t i m a l l e v e l of  Therefore,  vacancies  it  creates  and o f f e r s  than h i g h e r employment f i r m s , so t h a t  employment. a h i g h e r wage  i t has a h i g h p r o b a b -  in  188  ility  o f i n c r e a s i n g the s i z e o f i t s w o r k f o r c e .  o f vacancy  c r e a t i o n f o r these t h r e e s t a t e s o f  The  levels  employment  are consistent with intertemporal p r o f i t maximization, d e f i n e d i n Chapter 2 IIIiG, creation is  and thus s p e c u l a t i v e  as  vacancy  zero.  A f i r m i n employment s t a t e a firm i n state  [1,0]  offers  a h i g h e r wage than  [ 0 , 1 ] , s i n c e t y p e one i n d i v i d u a l s have a  h i g h e r p r o b a b i l i t y o f q u i t t i n g i n response t o a p a r t i c u l a r wage o f f e r ,  ex a n t e ,  than type two i n d i v i d u a l s and these  firms wish to r e t a i n t h e i r e x i s t i n g The f i r m i n employment s t a t e i n the i n d u s t r y . Model I .  workforces.  [0,0] o f f e r s  the h i g h e s t wage  T h i s conforms to the r e s u l t o b t a i n e d i n  The f i r m enjoys  zero i n t e r t e m p o r a l monopsony power.  These f i r m s c o u l d choose a lower wage o f f e r the l e v e l o f vacancy  creation.  and i n c r e a s e  Type one i n d i v i d u a l s  have  a h i g h e r p r o b a b i l i t y o f sampling the f i r m and a c c e p t i n g  an  14 offer  than type two i n d i v i d u a l s .  low p r o b a b i l i t y ,  however,  sampling the same f i r m .  of say,  There i s  an  extremely  even two i n d i v i d u a l s  In a d d i t i o n , a f i r m c u r r e n t l y  employing a more v a l u a b l e  type two i n d i v i d u a l faces a h i g h  p r o b a b i l i t y o f a t t a i n i n g a s u b o p t i m a l c o m p o s i t i o n as as a s u b o p t i m a l l e v e l o f employment i n response to s p e c u l a t i o n and a low wage  offer.  well  vacancy  189  Then, summarising,a f i r m , c u r r e n t l y f a c i n g an u n d e r - s i z e w o rkforce,  c r e a t e s v a c a n c i e s e q u a l to d e s i r e d n e t h i r e s  and o f f e r s a h i g h e r wage t o a c u r r e n t type one employee than a type two employee i n the s t a t e complement. The f i r m f a c e s t h e o p t i m a l l e v e l b u t s u b o p t i m a l o f employment.  composition  I n each o f t h e s o l u t i o n s , the f i r m c r e a t e s  a s i n g l e vacancy f o r b o t h s t a t e s o f employment.  Observation  of the r e l e v a n t rows o f t h e t r a n s i t i o n m a t r i x shows t h a t the f i r m has a r e l a t i v e l y h i g h p r o b a b i l i t y o f m a i n t a i n i n g t h e same composition accessions.  o f employment, d e s p i t e some q u i t s and  Ex ante, a type one i n d i v i d u a l has a h i g h e r  p r o b a b i l i t y o f q u i t t i n g i n response  t o a p a r t i c u l a r wage  o f f e r b u t a type one i n d i v i d u a l a l s o has a h i g h e r p r o b a b i l i t y o f r e c e i v i n g and a c c e p t i n g an o f f e r . Thus, as i n Model I , t h e r e e x i s t s a t r a d e o f f between the wage o f f e r and vacancy c r e a t i o n d e c i s i o n .  Firms w i l l n o t  o f f e r a r e l a t i v e l y h i g h wage and c r e a t e zero v a c a n c i e s , so that there i s a high p r o b a b i l i t y of maintaining the e x i s t i n g workforce  which has s u b o p t i m a l  c o m p o s i t i o n , because t h e r e i s  a r e l a t i v e l y low ( i n the case o f s t a t e [2,0], zero) of a c h i e v i n g a worse c o m p o s i t i o n  o f employment.  probability  Indeed, t h e r e  i s a low p r o b a b i l i t y o f a c h i e v i n g a b e t t e r c o m p o s i t i o n o f employment. Then, t o summarise, f i r m s who f a c e t h e o p t i m a l l e v e l b u t subo p t i m a l composition  o f employment c r e a t e a s i n g l e s p e c u l a t i v e  190  vacancy.  T h i s r e f l e c t s t h e t r a d e o f f between the wage  o f f e r and vacancy d e c i s i o n , n o t e d i n Model I , and a l s o the  s m a l l p r o b a b i l i t y t h a t such an o f f e r may l e a d t o a  s u b s t i t u t i o n i n employment between a type one i n d i v i d u a l and  a type two i n d i v i d u a l through one q u i t and one  accession.  The wage o f f e r over these two s t a t e s o f  employment i s an i n c r e a s i n g  function  o f the number o f  type one i n d i v i d u a l s employed. The f i r m employs an o v e r s i z e workforce c o n s t i t u t e s the  w o r k f o r c e , but t h e ' o p t i m a l '  a subset o f t h a t w o r k f o r c e .  For  reasons s p e c i f i e d i n ( a ) , t h e f i r m c r e a t e s zero v a c a n c i e s .  I t s wage d e c i s i o n of a t t a i n i n g  i s such that  there i s a high  the o p t i m a l l e v e l o f employment.  probability Thus, a t a  g i v e n c u r r e n t l e v e l o f employment, the wage o f f e r i s an increasing  function  o f the number o f type one i n d i v i d u a l s  employed.  Individuals'  l a b o u r market b e h a v i o u r , i n some  sense, i s compatible w i t h the f i r m ' s d e c i s i o n s . v a l u a b l e type one i n d i v i d u a l s have a h i g h e r ex and  Less  probability,  ante, of q u i t t i n g i n response t o a p a r t i c u l a r wage o f f e r , so t h e r e i s a r e l a t i v e l y h i g h p r o b a b i l i t y o f a c h i e v i n g  the o p t i m a l c o m p o s i t i o n o f employment. The f i r m f a c e s an above o p t i m a l l e v e l and a s u b o p t i m a l c o m p o s i t i o n o f employment.  I t s decisions  there i s a high p r o b a b i l i t y of a t t a i n i n g  a r e such  that  the o p t i m a l  191 employment l e v e l .  I f the f i r m c u r r e n t l y employs four workers,  then i t i s constrained to create zero vacancies and i t s wage o f f e r i s , therefore, an i n c r e a s i n g f u n c t i o n of the number of type one i n d i v i d u a l s employed. The r e s u l t s associated with an employment l e v e l of three are not consistent.  A f i r m , i n employment s t a t e [3,0], creates  a speculative vacancy and o f f e r s a r e l a t i v e l y low wage i n s i x cases out of seven.  Creating a speculative vacancy  enables the f i r m to o f f e r a lower wage. There i s a non-zero p r o b a b i l i t y of achieving a superior composition of employment and a zero p r o b a b i l i t y of a t t a i n i n g a worse composition of employment. In employment s t a t e [2,1] the r e s u l t s are not systematic, since the f i r m creates a vacancy i h three cases out of seven. A p r i o r i , there i s no reason to b e l i e v e that the vacancy d e c i s i o n should be consistent over the seven sets of perception parameters. -  The choice of wage and vacancy decisions  may w e l l be influenced by the magnitude of the perception parameters and the d i f f e r e n c e between them.^ 3.  A Summary of Firm's Decisions i n Model I I The key to analysing the r e s u l t s i s to note the s i g n i f i c a n c e of the  composition of employment and the supply of searchers on firms' decisions. F i r s t l y , the p r o b a b i l i t y of r e t a i n i n g the e x i s t i n g workforce i n response to a p a r t i c u l a r o f f e r depends on the composition of employment.  Thus,  192 over a l l employment s t a t e s which c o n s t i t u t e a p a r t i c u l a r l e v e l o f employment, i f the vacancy c r e a t i o n d e c i s i o n i s the same, then wage o f f e r i s an i n c r e a s i n g f u n c t i o n o f the number of type  the  one  i n d i v i d u a l s employed. Secondly,  by c o n t r a s t t o Model I , f i r m s a r e n o t  between r e t a i n i n g c u r r e n t employees and, one  accession.  indifferent  say, f a c i n g one q u i t  and  T h u s , s p e c u l a t i v e v a c a n c i e s a r e c r e a t e d and lower wage  16 o f f e r s made  by f i r m s i n the s t a t e s c o r r e s p o n d i n g  to o p t i m a l or above  l e v e l s o f employment i n which t h e r e i s a low o r zero p r o b a b i l i t y a c h i e v i n g a worse composition  of employment.  s p e c u l a t i n g on the b a s i s of type one behaviour  alone. ^  the o p t i m a l  L  Firms a r e  of  essentially  i n d i v i d u a l s ' t u r n o v e r and  acceptance  Firms do n o t c r e a t e v a c a n c i e s when c u r r e n t l y employing  workforce.  T h i r d l y , vacancy d e c i s i o n s a r e i n f l u e n c e d by the s u p p l y of s e a r c h e r s . S p e c u l a t i v e v a c a n c i e s a r e n o t c r e a t e d by f i r m s i n s t a t e s c o r r e s p o n d i n g low  to  l e v e l s of employment because t h e r e i s a low p r o b a b i l i t y t h a t s u f f i c i e n t  s e a r c h e r s w i l l sample the  firm.  These t h r e e f a c t o r s e x p l a i n f i r m d e c i s i o n s which appear i n comparison to d e c i s i o n s i n Model I .  non-systematic  In Model I , f i r m s ' wage and  vacancy c r e a t i o n d e c i s i o n s demonstrate t h e i r i n t e r t e m p o r a l monopsony power and i n d i f f e r e n c e between c u r r e n t employees and 4.  searchers.  An E x p l a n a t i o n o f the Summary S t a t i s t i c s Type one employees enjoy a h i g h e r d i s t r i b u t i o n of wage o f f e r s  type one employees.  T h i s r e f l e c t s t h e i r h i g h e r ex ante p r o b a b i l i t y  t u r n o v e r i n response  t o a p a r t i c u l a r o f f e r and,  than of  i n a d d i t i o n , the g r e a t e r  193 s u p p l y of type one s e a r c h e r s . and the  Both the c o m p o s i t i o n o f the  c o m p o s i t i o n o f the unemployed i n f l u e n c e  Thus, type one employees  the f i r m ' s wage  e a r n a h i g h e r mean wage than type two  S i n c e each s e a r c h e r faces  then,  t h a t a type one i n d i v i d u a l , d e s p i t e  mean wage, when employed,  It  a type is  earning a higher  unemployment.  Type one i n d i v i d u a l s a r e l e s s  valuable  to the f i r m and earn h i g h e r  T h u s , f i r m s i n the aggregate w i l l employ fewer  individuals.  employees.  earns a lower MDI than a type two i n d i v i d u a l ,  due to a l o n g e r mean d u r a t i o n o f  mean wages.  offer.  the same d i s t r i b u t i o n o f o f f e r s ,  one i n d i v i d u a l has a l o n g e r mean d u r a t i o n o f unemployment. plausible,  workforce  T h u s , type one i n d i v i d u a l s enjoy  employment than type two i n d i v i d u a l s .  type one  a higher l e v e l of un-  A l t h o u g h type one employees  a h i g h e r mean wage, they e a r n a lower share o f output due t o t h e i r l e v e l of  earn higher  unemployment.  Type one i n d i v i d u a l s a r e l e s s  valuable  than type two i n d i v i d u a l s .  Then, f o r any g i v e n l e v e l o f employment, mean p r o f i t s  discounted  over  an i n f i n i t e h o r i z o n a r e a d e c l i n i n g f u n c t i o n o f the number o f type one individuals i n i t i a l l y Individuals' so f i r m s face  t u r n o v e r and acceptance  different  wage and vacancy of wage o f f e r s  employed.  levels  behaviour i s  stochastic  o f employment over time and make  creation decisions.  Consequently,  i s a d e c l i n i n g function of  and different  the temporal c o r r e l a t i o n  time.  S i n c e employment d i s p e r s i o n e x i s t s i n i t i a l l y and i n d i v i d u a l s imperfect  i n f o r m a t i o n about wage o f f e r s ,  t u r n o v e r and  acceptance  have  194 behaviour i s s t o c h a s t i c and f r i c t i o n a l unemployment i s non-zero i n s t o c h a s t i c equilibrium.  Search i s random and therefore  stochastic  e q u i l i b r i u m cannot be characterised by segregated workforces. Even i n Model I I I , when firms can e x p l i c i t l y  discriminate  between i n d i v i d u a l s i n wage o f f e r and employment, mixed workforces  7  characterise e q u i l i b r i u m , although i n d i v i d u a l s evaluate wage o f f e r s i n r e l a t i o n to t h e i r own wage o f f e r d i s t r i b u t i o n . 5.  The Concepts of Vacancy Creation and Excess Demand In Model I , although a s i g n i f i c a n t component of vacancy c r e a t i o n  represents desired net h i r e s , firms speculate i n vacancy c r e a t i o n .  By  i n c r e a s i n g the number of i n d i v i d u a l s , i n t o t a l , to whom o f f e r s are made the f i r m i s able t o o f f e r a lower wage r a t e . The f i r m i s i n d i f f e r e n t between r e t a i n i n g current employees and f a c i n g , say, one accession and one q u i t , because i n d i v i d u a l s , ex ante, are i d e n t i c a l i n t h e i r labour market behaviour and p r o d u c t i v i t y , i r r e s p e c t i v e of employment status. In Model I I , the composition of the current workforce and the l i k e l i h o o d of achieving a superior composition through new h i r e s assumes key importance.  Speculative vacancy creation i s only undertaken  by firms who c u r r e n t l y employ an optimal or above optimal s i z e d workforce, and who have a low p r o b a b i l i t y of a t t a i n i n g a worse composition of employment.  Below the optimal l e v e l of employment, vacancy c r e a t i o n  decisions are not speculative and represent desired net h i r e s .  195 This non-systematic nature of vacancy creation over some l e v e l s of employment further undermines i t s use as a proxy f o r firms' excess demand f o r labour.  I t seems u n l i k e l y that, even i n a labour market  i n which vacancies represent p o s i t i o n s r e q u i r i n g i d e n t i c a l s k i l l s , a homogeneous measure of vacancies can be created. Vacancies are heterogeneous,since they represent job o f f e r s at d i f f e r e n t wage rates. 6.  Theoretical Contribution  of Model I I  Both Salop and Sanborn i n f e r that a necessary condition f o r wage d i f f e r e n t i a l s i s that firms recognise d i f f e r e n t types of i n d i v i d u a l and are allowed to discriminate  i n wage o f f e r and h i r i n g .  The r e s u l t s  of Model I I i n d i c a t e the contrary. I n t e r - f i r m wage d i f f e r e n t i a l s a t the same l e v e l of employment e x i s t , even when the firm'" i s not allowed to discriminate.  I n response to the p r e v a i l i n g wage o f f e r d i s t r i b u t i o n ,  type one i n d i v i d u a l s have a higher p r o b a b i l i t y of q u i t t i n g , ex ante, and a higher ex ante marginal p r o b a b i l i t y of q u i t t i n g than type two individuals.  Firms, unable to discriminate e x p l i c i t l y between i n d i v i d u a l s  i n wage o f f e r and h i r i n g , make wage o f f e r and vacancy creation  decisions  which are dependent on both the l e v e l and composition of employment. Over those states of employment which correspond t o the same l e v e l of employment and the same vacancy c r e a t i o n d e c i s i o n , the wage o f f e r i s an increasing function of the number of type one i n d i v i d u a l s employed. Low-turnover type two i n d i v i d u a l s , who also have a low marginal p r o b a b i l i t y of turnover, are discriminated  against i n the wage o f f e r .  This i s essen-  196 t i a l l y Salop's argument.  A low-turnover, type two i n d i v i d u a l , however,  i s more valuable to the f i r m , because the mean returns associated w i t h h i r i n g him and then o f f e r i n g him a stream of wage rates over time are higher than the returns associated w i t h h i r i n g a type one i n d i v i d u a l and o f f e r i n g him the same stream of wage r a t e s .  Not only does the type  one i n d i v i d u a l have a higher p r o b a b i l i t y of q u i t t i n g , ex ante, but he has a lower p r o b a b i l i t y of acceptance i n response to a given wage o f f e r . Consequently, i f the f i r m faces the 'optimal workforce', then i t attempts to r e t a i n t h i s optimal workforce by o f f e r i n g a r e l a t i v e l y high wage r a t e , as argued by Sanborn.  This wage rate i s higher than any wage rate offered  by a f i r m f a c i n g an optimal or above l e v e l of employment. Thus, Sanborn's and Salop's arguments are p a r t i a l l y correct when firms cannot e x p l i c i t l y discriminate i n wage o f f e r and employment.  In  the aggregate, however, firms' i n a b i l i t y to discriminate e x p l i c i t l y i n wage o f f e r s becomes c r u c i a l .  Although type two i n d i v i d u a l s are more  valuable t o a f i r m , the mean wage enjoyed by a type two i n d i v i d u a l i s 18 l e s s than the mean wage enjoyed by a type one employed i n d i v i d u a l . By contrast, i n Model I I I , more valuable type two workers earn a higher mean wage than type one workers. C. Comparative S t a t i c P r e d i c t i o n s of Model I I 1.  An Introduction There are twenty summary s t a t i s t i c s whose changes describe the  impact on s t o c h a s t i c e q u i l i b r i u m i n the labour market of a change i n the value of perception parameters.  They are :  197 (a)  The l e v e l of the g e n e r a l wage o f f e r d i s t r i b u t i o n ;  (b)  The mean of the o f f e r  (c)  The v a r i a n c e of a s e a r c h e r ' s  (d)  The mean wage earned by a type  one employed i n d i v i d u a l ;  (e)  The mean wage earned by a type  two employed i n d i v i d u a l ;  (f)  MDI enjoyed by a type  one i n d i v i d u a l ;  (g)  MDI enjoyed by a type  two i n d i v i d u a l ;  (h)  Aggregate  unemployment;  (i)  Aggregate  type one unemployment;  (j)  Aggregate  type  (k)  Aggregate  vacancy  (1)  Aggregate  s p e c u l a t i v e vacancy  (m)  The mean d u r a t i o n of s e a r c h p r i o r t o an  d i s t r i b u t i o n facing a searcher; d i s t r i b u t i o n of wage  offers;  two unemployment; creation; creation; offer  for a searcher; (n)  The mean d u r a t i o n o f unemployment f o r a type  one  individual; (o)  The mean d u r a t i o n of unemployment f o r a type  two  individual; (p)  Mean f i r m p r o f i t s ;  (q)  Type one i n d i v i d u a l s ' share o f t o t a l  output;  (r)  Type two i n d i v i d u a l s ' share o f t o t a l  output;  (s)  L a b o u r ' s t o t a l share of o u t p u t ;  (t)  The one p e r i o d c o r r e l a t i o n c o e f f i c i e n t  and of wage  offers.  198  2.  The R e s u l t s Eleven different  c^  2  combinations o f the p e r c e p t i o n parameters,  are adopted i n the range 0.90 to 1.15.  A l l other  1 parameters remain c o n s t a n t ,  c^  exogeneous 2  equals o r exceeds c^  a t i o n s o f the p e r c e p t i o n parameters chosen.  i n a l l combin-  These s o l u t i o n s y i e l d t e n  19 weak comparative s t a t i c p r e d i c t i o n s , f i v e a s s o c i a t e d w i t h an i n c r e a s e 1 2 i n c^ and f i v e a s s o c i a t e d w i t h an i n c r e a s e i n c^ . W h i l e the r e s u l t s are more s y s t e m a t i c evidence  2 i n the case o f an i n c r e a s e of c^ , t h e r e i s no  to suggest t h a t  the q u a l i t a t i v e  would be d i f f e r e n t when c ^ 2 c^ . c  1 1  in  The a n a l y s i s  change i n l a b o u r market b e h a v i o u r  i s i n c r e a s e d as compared w i t h an i n c r e a s e i n  o f the r e s u l t s  relates  to an i n c r e a s e i n the parameter  , but a s i m i l a r d i s c u s s i o n i s a p p r o p r i a t e i n the case o f an i n c r e a s e 2 c^ An i n c r e a s e i n the v a l u e o f the p e r c e p t i o n parameter,  a non-systematic  shift  i n the wage o f f e r  g e n e r a l tendency  f o r wage o f f e r s  distribution.  leads  There i s  to i n c r e a s e over s t a t e s o f  to  a  employment,  20 u n l e s s the p a t t e r n o f vacancy c r e a t i o n d e c i s i o n s changes. and v a r i a n c e o f the o f f e r  d i s t r i b u t i o n facing searchers  The mean  generally  and the mean wages earned by b o t h employed type one and type two u a l s always i n c r e a s e .  MDI o f type one i n d i v i d u a l s g e n e r a l l y  o f type two i n d i v i d u a l s r i s e s . individuals' falls.  rise individ-  f a l l s but MDI  B o t h t o t a l unemployment and type one  unemployment r i s e w h i l e type two i n d i v i d u a l s ' unemployment  Aggregate vacancy  creation  rises.  199 The mean duration of search p r i o r to an o f f e r i s again negatively c o r r e l a t e d t o the change i n the aggregate measure of vacancies minus unemployment.  The mean duration of unemployment f o r type one i n d i v i d u a l s  r i s e s , while changes i n the duration of unemployment of type two i n d i v i d uals are not r e l a t e d i n a systematic way to changes i n the perception parameter. The mean l e v e l of p r o f i t s discounted over an i n f i n i t e horizon f a l l s . Type one i n d i v i d u a l s  1  share of output f a l l s , but type two i n d i v i d u a l s '  share of t o t a l output r i s e s .  Labour's share of t o t a l output r i s e s .  The  one period c o r r e l a t i o n of wage o f f e r s f a l l s when c ^ r i s e s . The values of the summary s t a t i s t i c s over a l l combinations of the perception parameters adopted and the frequency w i t h which the comparative 1  2  s t a t i s p r e d i c t i o n s are upheld f o r increases i n c^ and c^ are shown i n Table 13. 3.  An Explanation (a)  An Introduction  I t seems that the absolute magnitudes of the parameter values are unimportant i n the explanation of the r e s u l t s . Some r e s u l t s , however, have to be explained i n the context of the r e l a t i v e parameter 1 values chosen.  2  I n p a r t i c u l a r , i f c^ and c^ are equal, then a l l  i n d i v i d u a l s are i d e n t i c a l , ex ante, so Model I i s appropriate and firms make the same wage and vacancy c r e a t i o n decisions over each l e v e l of employment,irrespective of the composition of employment.  I n t h i s case,  TABLE 13 Comparative Static Results for Model II  1 2 Different Combinations of cx and c\ Sign  Freq/ j Freq/ 1 10  0.95 | 0.95  1.00  1.00  1.00  1.05  1.05  1.05  1.10  1.10  1.10  Sign  0.90  0.90  0.95  1.00  0.95  1.00  1.05  0.90  1.00  1.10  (cJ+>  Freq/ 5  +  1  +  3  0.95  a)  I i i  }  (c "0 2  i  5  ' j  i  i  2  b)  1.079  1.169  1.085  1.133  1.196  1.146  1.169  1.249  1.160  1.257  1.283! +  3  c)  0.067  0.071  0.073  0.085  0.081 ''0.089  0.100  0.091  0.099  0.101  0.112| +  5  + +  d)  1.237  1.276  1.244  1.288  1.323  1.323  1.353  1.386  1.355 J 1.424  1.455  5  +  5  10  e)  1.214  1.276  1.235  1.308  1.323  1.310  1.366  1.386: 1.328  1.392  1.455  5  +  5  10  f)  8.524  8.988  8.534  8.776  9.070 8.682  8.852  9.133  8.658  8.982  9.143  3  +  g)  8.913  8.988  8.968  9.087 9.070 9.287 9.154  9.133  9.559  9.452  9.143  +  5  -  h)  25  28  27  31  32  32  37  38  32  38  | 44  !*>  16  1.4  \ 17  17  16  20  20  19  22  22  I  + +  9  14  j 10  14  16  12  17  19  10  16  |22  k)  44  52  ; 48  54  49  51  59  48  58  j  61  +  1)  14  19  17  13  12  18  13  17  \ 16  -  1.377  1.532  1.541  1.335  1.553  1.368 }1.374  ?  2.181 2.035 12.022  +  1.723 j2.022  -  p) 24.674 (22.020 24.147J21.526 20.250 21.105 19.182 17.912 20.592 .7.439 15.612 1 0.268 ! 0.292 0.317 0.274 0.303 0.327 0.264 0.303 IJ 0.337 q) 1 0.271 0.310 0.317 0.351 0.337 0.327 0.370 0.360 tj0.337 r) \ 0.321 0.310 | 0.329 j 0.328 s) \ 0.592 0.620 ! 0.597 0.620 0.634 0.625 0.640 0.654 0.634 0.663 |0.674  -  I1 !  43  | 13 1.608 1.541 m) | 1.570 1.369 n) ! 1.890  j 1.654 I  1.987| 1.917 1.737 I 2.058  o) \ 1.752; 1.654 1.79li 1.869  1.737  1.783  2.051 1.825 1.979  1.825  1.746  i  t)  0.455  0.452 | 0.485 0.437  0.395  0.422  0.361  0.342  0.481  22  +  +  \1  I  5  5  10  5  5 (-2)  10(-2)  5  8(-l)  2  4(-l) 4 4 i  2  5  i  5  +  5(-l) 3  +  | +  •  1 "  5 2(-l)  7 6 (-2)  5  9  j i ~ j +  5  9  2  4  {  _  5  10  +  5  | -  5  +  5  10(-1)  5  8  i ? S  5(-l) |  +  0.386 j0.300 i. - . . .  8 8  ;  i  8  3  3(-l)  \  8  10(-1) 10  201  1 an i n c r e a s e i n c^  2 above c^  leads to a d i f f e r e n t p a t t e r n o f  vacancy  c r e a t i o n and wage d e c i s i o n s .  Some o f the c o r r e s p o n d i n g changes  the summary s t a t i s t i c s  from those a r i s i n g from the comparison  differ  in  o f two s o l u t i o n s when b o t h s e t s o f p e r c e p t i o n parameters a r e u n e q u a l . (b)  P r e d i c t i o n s a r i s i n g from an i n c r e a s e i n Given any f u t u r e stream o f wage o f f e r s ,  the mean r e t u r n s  a f i r m a s s o c i a t e d w i t h h i r i n g a type one i n d i v i d u a l f a l l , ceteris  because,  p a r i b u s , he has a h i g h e r p r o b a b i l i t y o f t u r n o v e r , ex  ante.  A l t h o u g h type one i n d i v i d u a l s are as p r o d u c t i v e , when employed, are both l e s s valuable  dividuals r i s e s .  when unemployed.  If  f i r m s make the same  then the r a t e o f unemployment o f type one i n -  More f i r m s face  s u b o p t i m a l , i n the sense d e f i n e d .  levels  o f employment which are  Firms c o u n t e r t h e . i n c r e a s e  one unemployment by an i n c r e a s e i n wage o f f e r s employment.  they  to the f i r m , once employed,and have a lower  p r o b a b i l i t y of acceptance, d e c i s i o n s as b e f o r e ,  to  S i n c e type  in  type  over some s t a t e s o f  one i n d i v i d u a l s are l e s s v a l u a b l e ,  firms i n  the aggregate w i l l n o t choose to h i r e as many at h i g h e r wage r a t e s and t h i s d e c i s i o n i s r e i n f o r c e d by type one i n d i v i d u a l s ! b e h a v i o u r . Thus, d e s p i t e  the i n c r e a s e i n the g e n e r a l wage o f f e r d i s t r i b u t i o n ,  aggregate type one unemployment  rises.  Type two i n d i v i d u a l s now f a c e a h i g h e r d i s t r i b u t i o n o f and are l i k e l y  to have a h i g h e r p r o b a b i l i t y o f acceptance  p r o b a b i l i t y of q u i t t i n g i n response t o an o f f e r  offers  and a lower  from a f i r m i n a  21 p a r t i c u l a r employment s t a t e . two i n d i v i d u a l s g e n e r a l l y  falls.  Thus, aggregate unemployment o f The analogy  of a simple s t a t i c  type two  202 f a c t o r model of f i r m behaviour i s appropriate.  A s h i f t to the l e f t  of the supply of one f a c t o r leads to both a s u b s t i t u t i o n e f f e c t and a scale e f f e c t .  P r e c i s e l y the same phenomenon i s observed i n t h i s  dynamic s t o c h a s t i c model of f i r m behaviour. decisions  Firms' wage and vacancy  r e i n f o r c e d by each type of i n d i v i d u a l ' s labour market  behaviour leads i n the aggregate to s u b s t i t u t i o n i n employment between type one and type two i n d i v i d u a l s .  The scale e f f e c t of the systematic  change i n type one i n d i v i d u a l s ' market behaviour i s measured by the increase i n aggregate unemployment.  At t h i s higher l e v e l of wage o f f e r s  firms choose t o employ fewer i n d i v i d u a l s i n the aggregate. This increase i h unemployment means that there i s a s h i f t i n the d i s t r i b u t i o n of employment to low employment, high wage firms. a d d i t i o n , firms' wage o f f e r s over employment states generally and, i n some cases, vacancy creation as w e l l . enjoyed by searchers generally r i s e s .  In increase  Thus, the mean o f f e r  The mean o f f e r s enjoyed by each  type of employed i n d i v i d u a l always increase.  The higher l e v e l of wage  o f f e r s over some employment states and the unchanged l e v e l of unemployment compensation lead to an increase i n the variance of the wage o f f e r distribution. Type two i n d i v i d u a l s f a c i n g a higher d i s t r i b u t i o n of wage o f f e r s and, enjoying a lower l e v e l of unemployment, earn a higher MDI. The influence on the MDI of type one i n d i v i d u a l s of an increase i n c ^ i s not systematic.  I n contrast t o Model I , i n which an increase i n c^ i s  analysed, MDI of type one i n d i v i d u a l s f a l l s i n three cases out of f i v e .  203 These r e s u l t s a r e q u i t e p l a u s i b l e . a n a l y s e d i n Model I ,  type one i n d i v i d u a l s alone enjoy  d i s t r i b u t i o n of o f f e r s behaviour.  a r i s i n g from t h e i r s y s t e m a t i c  market  a higher change i n  Thus, d e s p i t e an i n c r e a s e i n the i n c i d e n c e o f unemploy-  ment, they enjoy of 1.15.  In the s e g r e g a t e d  a h i g h e r MDI up to and i n c l u d i n g the v a l u e o f  I n Model I I ,  of o f f e r s ,  type  however,  c^  i n response t o the h i g h e r d i s t r i b u t i o n  two i n d i v i d u a l s enjoy  a h i g h e r l e v e l o f employment and  thus s t e a l some o f the p o t e n t i a l g a i n s a c c r u i n g to type one i n d i v i d u a l s from h i g h e r wage o f f e r s .  T h u s , these n o n - s y s t e m a t i c  t e n t i n that  the i n d e t e r m i n a t e e f f e c t  they r e f l e c t  r e s u l t s are  on type one i n d i v i d u a l s '  MDI o f an i n c r e a s e d mean d u r a t i o n o f unemployment o f f s e t h i g h e r d i s t r i b u t i o n o f wage There i s a s h i f t firms.  vacancy  and so s p e c u l a t i v e  by a  i n employment to low wage, h i g h vacancy  creation i s vacancy  creation  creation generally  zero a t below o p t i m a l l e v e l s  creation generally  of  increases. employment,  falls.  The change i n the d u r a t i o n of s e a r c h p r i o r to an o f f e r negatively  generally  offers.  T h u s , t h e l e v e l o f aggregate vacancy  Speculative  consis-  r e l a t e d to the change i n the aggregate measure o f  is  again  vacancies  minus unemployment. The mean d u r a t i o n o f unemployment f o r type one i n d i v i d u a l s increases.  The mean d u r a t i o n o f unemployment enjoyed by type two  u a l s decreases  i n two cases out o f f i v e .  type two i n d i v i d u a l s ' unemployment r e s u l t s vacancy  generally individ-  A f a l l i n the mean d u r a t i o n o f from the r i s e i n aggregate  c r e a t i o n and the r e d u c t i o n i n type two unemployment which reduces  the mean d u r a t i o n o f s e a r c h and the h i g h e r d i s t r i b u t i o n o f wage which i n c r e a s e s  the p r o b a b i l i t y o f  acceptance.  offers  204 In response t o the systematic change i n type one i n d i v i d u a l s ' behaviour, wage o f f e r s r i s e and aggregate unemployment r i s e s and so a firm's mean p r o f i t discounted over an i n f i n i t e horizon f a l l s . Despite the increase i n mean wage o f f e r , type one i n d i v i d u a l s ' share of t o t a l output f a l l s , due t o t h e i r lower l e v e l of employment. By contrast, type two employees enjoy higher wages and employment and a l a r g e r share of t o t a l output.  U n s u r p r i s i n g l y , labour's t o t a l  share of output increases. The one period c o r r e l a t i o n of wage o f f e r s generally f a l l s .  This  can be explained by the greater s t o c h a s t i c i t y associated w i t h type one i n d i v i d u a l s ' turnover and acceptance behaviour. (c)  P r e d i c t i o n s a r i s i n g from Equal Values of the Perception Parameters The counter i n t u i t i v e r e s u l t s can be explained by n o t i n g that  two of the f i v e comparative s t a t e p r e d i c t i o n s a r i s e from an increase i n c^  1  2 above e q u a l i t y w i t h c^ . I n each case, the pattern of vacancy  c r e a t i o n changes.  When the perception parameters are equal, firms create  the same number of vacancies over the optimal employment l e v e l and zero 1 vacancies above the optimal l e v e l of employment.  2  When c^ exceeds c^ ,  firms create zero vacancies f o r the optimal workforce and a vacancy f o r the employment s t a t e corresponding to three type one i n d i v i d u a l s . r e s u l t s i n a f a l l i n the l e v e l of aggregate vacancy c r e a t i o n .  This  Together  w i t h the r i s e i n unemployment, t h i s leads to a f a l l i n the mean o f f e r a r i s i n g from search.  In both cases, the mean duration of unemployment  for type two i n d i v i d u a l s increases.  205  The r e m a i n i n g i n c o n s i s t e n t r e s u l t s a r e n o t r e a d i l y except i n the case o f p e r c e p t i o n parameter v a l u e s , [1.05,1.00].  and above o p t i m a l l e v e l s  [0,2],  o f employment.  unemployment i s matched by a s i g n i f i c a n t  offer  creation.  offsets  the tendency  s i n c e they enjoy  wage o f f e r s  the  vacancy  'optimal workforce'  The i n c r e a s e i n type one r i s e i n the l e v e l of aggregate  T h i s r e d u c t i o n i n the d u r a t i o n of s e a r c h p r i o r  to an  f o r the mean d u r a t i o n o f unemployment o f  one i n d i v i d u a l s to i n c r e a s e . rises,  [ 1 . 1 0 , 1 . 0 0 ] and  The r i s e i n c^" i s accompanied by s i g n i f i c a n t  s p e c u l a t i o n , both i n employment s t a t e  vacancy  comprehensible,  Consequently,  type  MDI o f type one i n d i v i d u a l s  a s h o r t e r d u r a t i o n o f unemployment and h i g h e r  when employed.  22 2  (d)  P r e d i c t i o n s a r i s i n g from an i n c r e a s e i n c^ 2 When c^  increases  the r e s u l t s  c o r r e s p o n d i n g to an i n c r e a s e i n  generally  accord with  those  again w i t h the e x c e p t i o n o f  those  r e s u l t s a s s o c i a t e d w i t h e q u a l v a l u e s o f the p e r c e p t i o n parameters. 2 two o f the t h r e e cases i n which c^ C j \  the v a r i a n c e o f wage o f f e r s  In  i n c r e a s e s and becomes e q u a l w i t h  falls.  This r e s u l t i s  plausible,  because t h e r e i s no wage d i s p e r s i o n o v e r s t a t e s o f employment c o r r e s p o n d i n g t o the same l e v e l but d i f f e r e n t  c o m p o s i t i o n o f employment, when the p e r -  c e p t i o n parameters are e q u a l . The change i n the p a t t e r n o f vacancy c r e a t i o n o v e r employment s t a t e s 2 1 a r i s i n g from the i n c r e a s e i n c^ i n t o e q u a l i t y w i t h c^ generates an i n c r e a s e i n aggregate vacancy c r e a t i o n and aggregate s p e c u l a t i v e vacancy c r e a t i o n i n each c a s e . The r e s u l t i n g f a l l i n the d u r a t i o n o f s e a r c h p r i o r  206 to an o f f e r  offsets  the tendency  type two i n d i v i d u a l s to r i s e .  f o r the d u r a t i o n o f unemployment o f  This r e s u l t  MDI of type two i n d i v i d u a l s r i s e s of  [0.95,0.95]  and [ 0 . 9 5 , 0 . 9 0 ]  occurs i n a l l t h r e e  f o r p e r c e p t i o n parameter  and [ 1 . 0 0 , 0 . 9 5 ]  a r e s u l t i s n o t i m p l a u s i b l e , because  cases. values  and [ 1 . 0 0 , 0 . 9 0 ] .  Such  type two i n d i v i d u a l s earn h i g h e r  wages when employed and, i n the f i r s t  case,  have a s h o r t e r d u r a t i o n o f  23 unemployment.  III. A.  B a s i c Parameter  1.  An I n t r o d u c t i o n In Model I I I ,  f o r Model  and h i r i n g  parameters s p e c i f i e d i n Chapter 3  o f the p e r c e p t i o n parameters  o f parameter v a l u e s  constitute  the  ex a n t e ,  t o d i s c r i m i n a t e between  type o f i n d i v i d u a l , then i t w i l l c r e a t e  the firms have  them.  f i r m c u r r e n t l y employs a below o p t i m a l workforce  F o r example, solely  vacancies  and o f f e r  higher value  to the f i r m o f i n d i v i d u a l s c u r r e n t l y employed than an  then i t  i s evident  that  a  This r e f l e c t s  the  searchers,  offer.  t h e s o l u t i o n c o r r e s p o n d i n g t o the b a s i c s e t  i s unique,  if  a higher  type o f i n d i v i d u a l than the o t h e r t y p e .  who may o r may not sample the f i r m and accept  the  of a p a r t i c u l a r  wage t o t h i s  If  basic  III.  Although i n d i v i d u a l s a r e i d e n t i c a l , economic i n c e n t i v e  III  d i s c r i m i n a t i o n i n wage o f f e r s  The exogeneous  I I I B and u n i t v a l u e s  o f Model  Values  explicit  by f i r m s i s l e g a l .  set  Results  the s o l u t i o n i s  o f parameter symmetric.  24  values  207 Then, f o r any employment s t a t e j , i f w , 3  and vacancy  creation decisions  and, i f employment s t a t e k i s  w  2  v 2  3  k  =  w  =  v  =  w  2  2  v|, w , 3  v  3  denote the wage  f o r each type of i n d i v i d u a l , the s t a t e  respectively,  complement,  J  . . . .  (2)  j  . . . .  (3)  i  •  . . . .  (4)  =V  ....  -  Bj  . . . .  (6)  =  s(e  . . . .  (7)  (5)  where k  2  J  ,  e^)  .  N e i t h e r s o l u t i o n c o r r e s p o n d i n g to e q u a l v a l u e s parameters i s symmetric. reasons to e x p l a i n these (a)  If  There are b o t h c o n c e p t u a l and c o m p u t a t i o n a l results.  the f i r m faces  workers of each t y p e ,  it  o f the p e r c e p t i o n  a mixed workforce w i t h the same number o f  i s possible  that,  due to the i n t e g r a l  vacancy  c r e a t i o n d e c i s i o n , i t might choose t o make a d i f f e r e n t wage o f f e r  and  vacancy  to a  c r e a t i o n d e c i s i o n f o r each type  p a r t i c u l a r l a b o u r market environment. these  d e c i s i o n s as a step  o f i n d i v i d u a l i n response  R e g a r d i n g the d e t e r m i n a t i o n o f  i n the s i m u l a t i o n p r o c e d u r e , t h i s means  the parameters o f each i n d i v i d u a l ' s d i s t r i b u t i o n of p e r c e p t i o n s differ.  Consequently,  individuals w i l l differ systematically  that  will  in their  208  l a b o u r market b e h a v i o u r i n subsequent generated w i l l be n o n - s y m m e t r i c ,  iterations  given  and the  solution  t h a t t h e r e i s some degree  of  i n a c c u r a c y i n the s i m u l a t i o n p r o c e d u r e . (b)  Likewise,  decision i s  only d e f i n e d to an accuracy  s t a t e j , where e ^ decisions,  a c o m p u t a t i o n a l problem may a r i s e because  it  =  For example,  and the f i r m makes the same vacancy  is possible  two s u c c e s s i v e  of 0 . 0 0 5 .  the wage  that  produced by the s i m u l a t i o n , w^ and w , 2  w-  <  w  w  -  w  <  w  =  0.005  in  creation  the o p t i m a l wage d e c i s i o n l i e s  p o s s i b l e wage d e c i s i o n s .  if  between  The o p t i m a l wage d e c i s i o n s t h e n , may be such  2  that  . . . .  (8)  . . . .  (9)  and  where w denotes  2  1  the o p t i m a l s o l u t i o n f o r b o t h types of i n d i v i d u a l .  a non-symmetric p a r t i a l o p t i m i s a t i o n s o l u t i o n , procedure, w i l l r e s u l t Again, of  i n subsequent  generated by the s i m u l a t i o n  i n individuals facing different  simulations,  the s y s t e m a t i c a l l y  offer  distributions.  different  type one and type two i n d i v i d u a l s may be r e i n f o r c e d by f i r m  given  Such  behaviour decisions,  the i n a c c u r a t e s i m u l a t i o n p r o c e d u r e . (c)  The non-symmetric s e a r c h p r o c e d u r e , adopted i n the s o l u t i o n o f  Model I I I ,  may be the cause of the non-symmetric r e s u l t ,  although,  each c a s e ,  the o p t i m a l d e c i s i o n generated by t h e s e a r c h procedure  compared w i t h the o p t i m a l d e c i s i o n c o r r e s p o n d i n g to the s t a t e  in is  complement.  209. 2.  The Results Stochastic e q u i l i b r i u m i s characterised by d i s p e r s i o n both i n the  l e v e l and composition of employment.  I n t r a - f i r m wage d i f f e r e n t i a l s  e x i s t , although i n d i v i d u a l s are i d e n t i c a l , ex ante, and there i s d i s persion i n each wage o f f e r d i s t r i b u t i o n both over the l e v e l and comp o s i t i o n of employment.  Over each l e v e l of employment, the wage o f f e r  to each type of i n d i v i d u a l i s generally an i n c r e a s i n g f u n c t i o n of the number of that type employed.  Firms create vacancies a t l e s s than  optimal l e v e l s of employment which, i n t o t a l , exceed desired net h i r e s . Facing the optimal l e v e l of employment c o n s i s t i n g of one type of i n d i v i d u a l , the f i r m creates s p e c u l a t i v e vacancies f o r the other type of i n d i v i d u a l at a low wage o f f e r . Vacancy c r e a t i o n i s zero f o r above optimal l e v e l s of employment.  Table 14 shows the b a s i c s o l u t i o n to  Model I I I . 3.  An Explanation In analysing firms d e c i s i o n s , i t i s e a s i e s t to group employment  states according to whether the employment l e v e l i s l e s s than, equal t o , or greater than the optimal l e v e l of employment. (a)  The f i r m faces an undersize workforce.  increase the s i z e of i t s workforce.  The f i r m wishes to  Thus, i t creates vacancies.  Although able t o d i s c r i m i n a t e i n h i r i n g , the f i r m creates vacancies f o r both types of i n d i v i d u a l .  I f the f i r m creates vacancies f o r type  one i n d i v i d u a l s alone, say, then, due to s t o c h a s t i c search, the f i r m faces a r e l a t i v e l y high p r o b a b i l i t y of not being sampled by a type one searcher.  Then, i t faces a high p r o b a b i l i t y of continuing to face a  TABLE 14. The Basic S o l u t i o n t o Model I I I  Stochastic E q u i l i b r i u m Type One Employment  Type Two Employment  Steady State Distribution  Type One Wage  Type Two Wage  Type One Vacancy  Type Two Vacancy  Mean One Period Profits  0 1 0 2 1 0 3 2 1 0 4 3 2 1 0  0 0 1 0 1 2 0 1 2 3 0  0.106 0.210 0.209 0.116 0.211 0.115 0.0 0.017 0.016 0.0 0.0 0.0 0.0 0.0 0.0  1.270 1.260 1.090 1.180 1.165 0.755 1.045 1.060 0.940 0.745 0.955 1.015 0.990 0.745 0.745  1.270 1.090 1.260 0.750 1.165 1.180 0.745 1.005 1.085 1.050 0.745 0.750 0.910 1.050 0.955  2 1 1 0 0 2 0 0 0 0 0 0 0 0 0  2 1 1 2 0 0 0 0 0 0 0 0 0 0 0  0.502 1.241 1.238 1.510 1.515 1.506 1.579 . 1.582 1.580 1.569 1.590 1.590 1.600 1.569 1.591  2 3 4  P r o f i t s Over Infinite Horizon 24.069 25.817 25.786 26.360 26.269 26.313 26.461 26.420 26.388 26.415 26.443 26.448 26.396 26.415 26.395  211  TABLE 14 (continued) Summary S t a t i s t i c s EW  EW  1  MW  2  0.962  0.959  V* 1  v*  43  43  MW  1  V  1.189  1.200  1  S  12  W*  2  W*  0.937  2  VW*  vw*  LSj^  LS  0.935  0.053  0.053  0.282  0.283  U*  U*  PA*  PA*  PO*  PO*  En  14  15  2.402  2.435  1.703  1.711  25.861  ._  12  2  C o r r e l a t i o n of Offers j  1 Period  2 Periods  3 Periods  4 Periods  5 Periods'  Type One  0.658  0.443  0.188  - 0.053  - 0.217 |  Type Two  0.729  0.567  0.388  0.242  !  0.155  Mean Discounted Income No Q u i t t i n g  True Perception  S t o c h a s t i c Behaviour  Type One  9.094  9.064  8.270  Type Two  9.125  9.080  8.268  TABLE 14  (Continued)  Steady S t a t e T r a n s i t i o n M a t r i x  0.590 0.065 0.067 0.026 0.035 0.028 0.038 0.038 0.041 0.035 0.054 0.045 0.053 0.035 0.057  0.152 0.584 0.015 0.262 0.155 0.001 0.224 0.172 0.041 0.0 0.231 0.221 0.151 0.0 0.0  0.163 0.015 0.581 0.001 0.150 0.269 0.0 0.056 0.203 0.217 0.0 0.010 0.084 0.217 0.238  0.019 0.160 0.0 0.659 0.0 0.000 0.444 0.195 0.0 0.0 0.374 0.358 0.107 0.0 0.0  0.042 0.137 0.128 0.014 0.660 0.014 0.0 0.253 0.205 0.0 0.0 0.049 0.239 0.0 0.0  0.022 0.0 0.171 0.000 0.0 0.653 0.0 0.0 0.254 0.444 0.0 0.0 0.033 0.444 0.375  0.0 0.0 0.0 0.0 0.0 0.0 0.293 0.0 0.0 0.0 0.269 0.193 0.0 0.0 0.0  0.005 0.038 0.0 0.036 0.0 0.000 0.0 0.286 0.0 0.0 0.0 0.080 0.170 0.0 0.0  0.006i 0.0 ' 0.038 0.000 0.0 0.034 0.0 0.0 0.256 0.0 0.0 0.0 0.095 0.0 0.0  0.0 j 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.304 0.0 0.0 0.0 0.304 0.262  0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.073 0.0 0.0 0.0 0.0  0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.043 0.0 0.0 0.0  0.001 0.0 0.0 0.001 0.0 0.001 0.0 0.0 0.0 0.0 0.0 0.0 0.067 0.0 0.0  0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0  0.0 0.0 0.0 0.0 o.oo 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.069  ro  213 below optimal l e v e l of employment. f o r both types of searcher.  Therefore, i t creates vacancies  The l e v e l of vacancy c r e a t i o n f o r each  type of i n d i v i d u a l equals t o t a l desired net h i r e s .  Then, i n t o t a l ,  the firm's vacancy c r e a t i o n d e c i s i o n does not represent desired net hires.  Search i s s t o c h a s t i c , however, so there i s a low p r o b a b i l i t y  that a l l vacancies w i l l be f i l l e d .  I f the f i r m c u r r e n t l y has no  employees, then i t makes the same wage o f f e r t o each type of searcher. I f the f i r m faces a non-zero l e v e l of employment, then the wage o f f e r t o each type of i n d i v i d u a l i s an i n c r e a s i n g f u n c t i o n of the number c u r r e n t l y employed. a current employee.  This r e f l e c t s the value to the f i r m of  I f the f i r m chooses to o f f e r a r e l a t i v e l y low  wage to a current employee, then there i s a high p r o b a b i l i t y that the individual quits.  Then the f i r m i s forced to increase the l e v e l of  vacancy c r e a t i o n f o r each type of i n d i v i d u a l , so that there i s a high p r o b a b i l i t y of securing the optimal l e v e l of employment.  The r e l a t i v e l y  low wage t o an employee i s a l s o a wage o f f e r to a searcher.  Thus,  despite increased vacancy c r e a t i o n , the f i r m faces a high p r o b a b i l i t y of f a c i n g a below optimal workforce next p e r i o d .  The variance of the  l e v e l of employment the f i r m faces next period i n c r e a s e s , because of increased vacancy c r e a t i o n . I n short, due to the s t o c h a s t i c elements of job search, the i m p l i c i t costs of vacancy c r e a t i o n , which are measured by foregone p r o f i t s , have r i s e n to the f i r m , despite i t s a b i l i t y t o d i s c r i m i n a t e in hiring.  Consequently, current employees are more valuable to the  f i r m i n Model I I I , i n some sense, than i n Model I and earn a higher wage than that o f f e r e d t o searchers alone.  214  (b) [1,1],  The f i r m faces  the f i r m o f f e r s  and c r e a t e s then i t  the o p t i m a l l e v e l o f employment.  the same r e l a t i v e l y h i g h wage to each i n d i v i d u a l  zero v a c a n c i e s .  faces  In state  If  i t offers  a low wage t o one i n d i v i d u a l ,  a h i g h p r o b a b i l i t y of l o s i n g an employee.  It  is  again  forced to create vacancies  f o r each type o f i n d i v i d u a l and face  stochastic  search.  elements  In s t a t e s  o f job  [2,0],  [ 0 , 2 ] , the f i r m o f f e r s  r e l a t i v e l y h i g h wage and c r e a t e s  zero v a c a n c i e s .  p r o b a b i l i t y of r e t a i n i n g i t s workforce. i n d i v i d u a l a wage e q u a l o r s l i g h t l y compensation and c r e a t e s in  c u r r e n t employees  It  the  a  The f i r m has a h i g h  offers  the o t h e r type  of  above the l e v e l of unemployment  vacancies.  Such vacancy  the sense d e f i n e d i n Chapter 2 I I I G ,  creation i s  speculative,  and t h e r e i s a low p r o b a b i l i t y  26 t h a t such p o s i t i o n s w i l l be f i l l e d . then, of  the wage o f f e r  Over these  employment  states,  t o a c u r r e n t employee i s an i n c r e a s i n g f u n c t i o n  the number employed. (c)  creates  The f i r m c u r r e n t l y employs an o v e r s i z e w o r k f o r c e . zero vacancies  and adopts wage d e c i s i o n s such t h a t  The  firm  there i s  a  h i g h p r o b a b i l i t y o f a t t a i n i n g the o p t i m a l l e v e l o f employment. A f i r m c u r r e n t l y employing one type of i n d i v i d u a l i n i t s workforce makes a wage o f f e r  oversize  t o those i n d i v i d u a l s , which i s a d e c l i n i n g  f u n c t i o n o f the number employed.  The wage o f f e r  t o the o t h e r type  of  i n d i v i d u a l i s a r b i t r a r y because none of these i n d i v i d u a l s a r e employed and vacancy  creation i s  zero.  A f i r m employing a mixed workforce of t h r e e i n d i v i d u a l s , [1,2]  and [ 2 , 1 ] , makes wage o f f e r s  states  such t h a t t h e r e i s a r e l a t i v e l y  high  215  p r o b a b i l i t y of r e t a i n i n g a mixed w o r k f o r c e , b u t o p t i m a l l e v e l o f employment. By c o n t r a s t ,  a f i r m employing a mixed workforce o f f o u r  individ-  u a l s w i t h an unequal number o f each type o f i n d i v i d u a l , s t a t e s and [ 1 , 3 ] ,  offers  [3,1]  a wage a p p r o x i m a t e l y e q u a l l i n g the l e v e l o f unem-  ployment compensation to the m i n o r i t y group. firm i s d i r e c t l y exploiting i t s  In these c a s e s ,  the  a b i l i t y t o d i s c r i m i n a t e i n wage  offers  i n o r d e r t o d r i v e out one type o f i n d i v i d u a l and reduce the v a r i a n c e o f employment  next p e r i o d .  wage o f f e r s , but,in this  The f i r m has the o p p o r t u n i t y to make s i m i l a r  when employing a mixed workforce o f three i n d i v i d u a l s , case,  a low wage o f f e r  to the type o f i n d i v i d u a l c o n s t i t u t i n g  the m i n o r i t y o f the workforce l e a v e s the f i r m w i t h the o p t i m a l l e v e l employment, and so i t  is  forced to o f f e r  t h i s l e v e l o f employment. which o f f e r s  a v e r y h i g h wage to m a i n t a i n  L i k e w i s e , a f i r m i n employment s t a t e  one type o f i n d i v i d u a l a low wage, f o r c e s  and has t o o f f e r  a r e l a t i v e l y h i g h wage t o r e t a i n o t h e r  In a l l cases,  the wage o f f e r  all  This r e f l e c t s  out these  employees.  the v a l u e t o the f i r m o f r e t a i n i n g some or  o f the type o f i n d i v i d u a l s who predominate i n the w o r k f o r c e ,  A Summary of F i r m s ' If  ex a n t e ,  vacancies.  rather  27  Decisions  the p e r c e p t i o n parameters are e q u a l ,  identical,  employees  to the o t h e r type o f  than o f f e r i n g low wages and c r e a t i n g s p e c u l a t i v e 4.  [2,2],  to the type o f i n d i v i d u a l who p r e -  dominates i n the workforce exceeds the o f f e r individual.  of  then i n d i v i d u a l s a r e  i n t h e i r l a b o u r market b e h a v i o u r .  Firms d i s c r i m i n a t e  216  i n h i r i n g and wage o f f e r between i n the workforce  and the o t h e r type o f i n d i v i d u a l , who i s a c u r r e n t  employee o r s o l e l y less  a searcher.  than o p t i m a l l e v e l s  c o s t s of vacancy in hiring.  the type o f employee who predominates  Such d i s c r i m i n a t i o n i s p r a c t i s e d  o f employment because  o f the h i g h i m p l i c i t  c r e a t i o n a r i s i n g from the a b i l i t y  To attempt  to c r e a t e v a c a n c i e s  to h i r e a s i n g l e  at  to  discriminate  i n d i v i d u a l , t h e firm i s  f o r b o t h types o f i n d i v i d u a l .  T h i s leads  forced to a  g r e a t e r v a r i a n c e o f employment i n the n e x t p e r i o d and thus lower mean profits.  T h u s , the  facing a less  f i r m attempts  than o p t i m a l l e v e l  workforce  o f the o p t i m a l s i z e ,  to c r e a t e  speculative  i n d i v i d u a l not  to r e t a i n c u r r e n t employees, o f employment.  the f i r m uses  vacancies  its  segregated  d i s c r i m i n a t o r y power f o r the type o f  employed.  to d i s c r i m i n a t e i n wage o f f e r  ability  When f a c i n g a  at a low wage o f f e r  F a c i n g an above o p t i m a l l e v e l o f employment,  constitute  when  allows  it  the  firm's  to d r i v e out employees,  a m i n o r i t y o f the w o r k f o r c e , w i t h a low wage.  to d i s c r i m i n a t e i n wage o f f e r  ability  Thus,  who the  l e a d s t o a reduced v a r i a n c e o f  employment next p e r i o d . The f i r m ' s a b i l i t y manifests of  itself,  to d i s c r i m i n a t e i n wage o f f e r  and h i r i n g  t h e n , i n d i f f e r e n t ways, a c c o r d i n g t o t h e  level  employment.  B.  Unequal V a l u e s of the P e r c e p t i o n  1.  An I n t r o d u c t i o n Seven s o l u t i o n s  to Model I I I 1  parameter v a l u e s ,  c  1  Parameters  c o r r e s p o n d i n g to unequal p e r c e p t i o n  2 and c^  are generated.  These j o i n t v a l u e s  lie  217 i n the range 0.90 to 1.15 i n increments of 0.05. I n order to organise and analyse the r e s u l t s associated w i t h d i f f e r e n t combinations of parameter values, eleven summary s t a t i s t i c s associated with each i n d i v i d u a l are computed f o r each s o l u t i o n .  Then, the consistency of  the solutions i s checked by comparing the summary s t a t i s t i c s c o r r e s ponding t o each s o l u t i o n . The summary s t a t i s t i c s are :  2.  (a)  The mean of the wage o f f e r d i s t r i b u t i o n facing a searcher;  (b)  The variance of the wage o f f e r d i s t r i b u t i o n f a c i n g a searcher;  (c)  The mean wage o f f e r enjoyed by an employee;  (d)  MDI;  (e)  Aggregate unemployment;  (f)  Aggregate vacancy c r e a t i o n ;  (g)  Aggregate vacancy s p e c u l a t i o n ;  (h)  The mean duration of search p r i o r t o an o f f e r ;  (i)  The mean duration of unemployment;  (j)  The share of t o t a l output; and  (k)  The one period c o r r e l a t i o n of wage o f f e r s .  Results 1 2 Again, c^ i s set a r b i t r a r i l y above c^ . Then, type one i n d i v i d u a l s  have a higher p r o b a b i l i t y of r e j e c t i n g a p a r t i c u l a r o f f e r , i f unemployed, and a higher p r o b a b i l i t y of q u i t t i n g , i f employed, than type two i n d i v i d u a l s , assuming they face the same labour market environment.  Each type  of i n d i v i d u a l , however, evaluates an o f f e r i n the context of h i s own d i s t r i b u t i o n of o f f e r s .  218 Stochastic  e q u i l i b r i u m i n a l a b o u r market,  employment d i s c r i m i n a t i o n i s p r a c t i s e d ,  i n which wage and  i s c h a r a c t e r i s e d by d i s p e r s i o n  both i n the l e v e l and c o m p o s i t i o n o f employment. differentials  exist,  I n t r a - f i r m wage  and t h e r e i s d i s p e r s i o n i n each wage  d i s t r i b u t i o n b o t h over the l e v e l and c o m p o s i t i o n o f The wage o f f e r systematically Indeed,  d i s t r i b u t i o n facing  h i g h e r than t h a t  the t r u e mean o f f e r  f a c i n g a type two s e a r c h e r and t h e mean  though,  f a c i n g a type two s e a r c h e r .  corresponding  The p e r c e i v e d mean wage  exceeds the p e r c e i v e d mean  The v a r i a n c e of the wage o f f e r  b u t i o n f a c i n g a type one s e a r c h e r exceeds the v a r i a n c e o f f a c i n g a type two s e a r c h e r .  Then, ex a n t e ,  a lower p r o b a b i l i t y o f a c c e p t i n g searcher.  offer  offer distrioffers  type one i n d i v i d u a l s  a p a r t i c u l a r offer  have  than a type two  Type two i n d i v i d u a l s earn a h i g h e r MDI than type one i n d i v i d u a l s .  Aggregate unemployment i s h i g h e r and aggregate vacancy  creation  lower f o r type one i n d i v i d u a l s than f o r type two i n d i v i d u a l s . i n d i v i d u a l s enjoy  Type two employees  is  Type one  a l o n g e r mean d u r a t i o n o f unemployment and a l o n g e r  mean d u r a t i o n o f s e a r c h p r i o r to an o f f e r  employees.  not  enjoyed by type two i n d i v i d u a l s .  f a c i n g type one i n d i v i d u a l s .  of a type one s e a r c h e r ,  employment.  type one i n d i v i d u a l s i s  wage earned by a type two employee b o t h exceed the offers  offer  enjoy  than type two i n d i v i d u a l s .  a l a r g e r share o f t o t a l output  The c o r r e l a t i o n o f type one wage o f f e r s  h i g h e r i n f o u r cases out o f  seven.  than type one  over one p e r i o d i s  219  Over each employment l e v e l except  four, profits  d i s c o u n t e d over  an i n f i n i t e h o r i z o n a r e an i n c r e a s i n g f u n c t i o n o f t h e number o f  type  two i n d i v i d u a l s employed. The s o l u t i o n to the s i m u l a t i o n p r o c e d u r e f o r p e r c e p t i o n parameter values  [ 1 . 0 5 , 0 . 9 5 ] i s shown i n T a b l e  T a b l e 16 shows the v a l u e s  15.  o f the summary s t a t i s t i c s  f o r each  type  o f i n d i v i d u a l , and the frequency w i t h which the p r e d i c t e d r e l a t i o n s h i p between  c o r r e s p o n d i n g summary s t a t i s t i c s  i n the seven 3.  f o r each i n d i v i d u a l i s u p h e l d  cases.  An E x p l a n a t i o n The a n a l y s i s  o f the r e s u l t s  is  c o m p l i c a t e d by the endogeneity  each d i s t r i b u t i o n o f p e r c e p t i o n s o f the r e s e r v a t i o n wage so t h a t i n d i v i d u a l evaluates o f wage o f f e r s . ility if  a wage o f f e r  i n the c o n t e x t  Thus, w h i l e a type  of acceptance,  of  each  o f h i s own d i s t r i b u t i o n  two i n d i v i d u a l has a h i g h e r p r o b a b -  i f unemployed, and a lower p r o b a b i l i t y of t u r n o v e r ,  employed, i n response to a p a r t i c u l a r wage o f f e r  and the same l a b o u r  market environment, type two i n d i v i d u a l s may face a h i g h e r d i s t r i b u t i o n of wage It  offers. i s i m p l a u s i b l e , however,  s h o u l d enjoy  a h i g h e r wage o f f e r  s t a t e complement. offered  It  t h a t over a l l s t a t e s type  than type one i n d i v i d u a l s r e c e i v e i n the  i s p r e c i s e l y t h a t type two i n d i v i d u a l s can be  a lower stream o f wage o f f e r s  over time than type one i n d i v i d u a l s ,  but w i t h the same mean d u r a t i o n of employment, which i s t h e i r greater value.  two i n d i v i d u a l s  Type two s e a r c h e r s do enjoy  the s o u r c e o f  a h i g h e r t r u e mean wage  o f f e r b u t compute a lower mean o f t h e i r d i s t r i b u t i o n o f p e r c e p t i o n s o f  TABLE 15 The S o l u t i o n to Model I I I with Perception Parameters, [ 1 . 0 5 , 0 . 9 5 ] Stochastic E q u i l i b r i u m i Mean One j P r o f i t s Over i |Infinite ! Type One | Type Two P e r i o d ] Vacancy P r o f i t s | Horizon i Vacancy  1  Type One Employment 0 1 0 2 1 0 3 2 1 0 4 3 2 1 0  0 0 1 0 1 2 0 1 2 3 0  i• I \ ! 1  t  I ;' 1  2  !  3  I  4  Type One Wage  Steady State Distribution  Type Two Employment  0.095 0.182 0.229 0.123 0.150 0.184 0.0 0.014 0.024 0.0 0.0 0.0 0.000 0.0 0.0  I i 1 | ;  1.315 1.290 1.085 1.205 1.145 0.745 1.070 1.020 0.750 0.745 0.980 0.905 0.750 0.750 0.745  Type Two Wage 1.275 1.100 1.285 0.830 1.170 1.215 0.750 1.145 1.190 1.065 , 0.745 • 1.175 1.160 \ 1.055 ! 0.970  1  i !  2 1 1 o  1 i i !  I ;  • =  !  i i  •  ;  2 1  !  I  o 0  1 i i 1  0  !  2 1 0 1 o 0 o o o o 0 0  0  1  1  I  o o o o 0 o  I I  1 i i  0.478 1.197 1.234 1.458 1.469 ! 1.481 ! 1.519 i 1.539 ! 1.507 ' 1.544 ! 1.538 j 1.539 \ 1.535 1.512 1.553 :  ;  ! | 1 | | i i ; | : j ! ! i'  23.546 25.223 25.497 25.703 25.870 26.131 25.794 25.947 26.153 26.219 25.778 25.940 26.155 26.186 26.179  !  1 i | j i !  ro o  r 221 TABLE 15  (continued)  Summary S t a t i s t i cs  EW  1  0.951 V*  2  MW  1.039_  1.210  E W  v* 2 49  31  j .  V V  V  i  1  S  '1  v V  W*  MW„  1  2  S  20  2  W  ...  1.221 U* 18  VW*  l  0.970 , 0.960 ,0.056 U* ;  PA*  92.786  PA*  1.793  C o r r e l a t i o n of  VW*  j  LS  1  0.049 | 0.252 PO*  PO*  2.168  1.362  LS  2  0.326 En 25.482  Offers  1 Period  2 Periods  3 Periods  4.Periods  5 Periods:  Type One  0.474  0.305  0.161  0.047  - 0.053  Type Two  0.735  0.571  0.376  0.182  0.021  Mean D i s c o u n t e d Income |No Q u i t t i n g  True P e r c e p t i o n  Stochastic  Behaviour  Type One  8.807  8.909  8.118  Type Two .  9.545  9.501  8.869  TABLE 15  (Continued)  Steady S t a t e T r a n s i t i o n M a t r i x  0.609 0.068 0.054 0.028 0.034 0.016 0.036 0.033 0.018 0.026 0.051 0.036 0.022 0.026 0.042  0.203 0.594 0.014 0.272 0.111 0.0 0.217 0.094 0.004 0.0 0.225 0.071 0.009 0.005 0.0  0.102 0.010 0.626 0.002 0.175 0.223 0.001 0.135 0.203 0.187 0.0 0.183 0.207 0.169 0.204  0.035 0.213 0.0 0.648 0.0 0.0 ;0.432 0.068 0.000 0.0 0.373 0.047 0.001 0.0 0.0  0.034 0.085 0.166 0.014 0.565 0.0 0.006 0.390 0.049 0.0 0.0 0.362 0.079 0.032 0.0  0.008 0.0 0.111 0.000 0.027 0.761 0.0 0.0 0.578 0.441 0.0 0.0 0.475 0.372 0.369  0.0 0.0 0.0 0.0 0.0 0.0 0.287 0.0 0.0 0.0 0.275 0.010 0.0 0.0 0.0  0.006 0.030 0.0 0.034 0.0 0.0 0.012 0.280 0.002 0.0 0.0 0.238 0.008 0.0 0.0  0.003 0.0 0.029 0.000 0.088 0.0 0.0 0.0 0.141 0.0 0.0 0.0 0.182 0.071 0.0 -  0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.346 0.0 0.0 0.0 0.272 0.29.6'  0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.076 0.0 0.0 0.0 0.0  0.0 0.0 0.0 0.0 0.0 0.0 0.008 0.0 0.0 0.0 0.0 0.052 0.0 0.0 0.0  0.000 0.0 0.0 0.001 0.0 0.0 0.0 0.0 0.006 0.0 0.0 0.0 0.017 0.0 0.0  0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0*0 0.0 0.0 0.0 0.0 0.052 0.0  0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.089  N5 N3  TABLE 16 Summary S t a t l 8 t l c a  f o rUnequal Values o f t h e P e r c e p t i o n Parameters I n Model I I I  Perception  *  Parameters  0^  tMj  1.00  0.90  0.934  1.033  1.05  0.95  0.951  1.10  0.90  0.950  1.10  0.95  1.001  1.10  1.00  1.10  1.05  1.15  1.10  Frequency/7  tt^  V»  2  Mt^  K»  1.190  1.207  2  MDIj  MDI  8.104  8.849  U  2  16  2  8  *  *  *  Vj^ V j  POj  P02  PAj^  PA  35  1.795  1.359  2.639  1.702  48  2  LSj^  LS  0.256  0.320  2  CC^  0.722  CCj  0.054  0.049  0.751  1.039  0.056  0.049  1.210  1.221  8.118  8.869  18  9  31  49  2.168  1.362  2.786  1.793  0.252  0.326  6.474  0.735  1.083  0.063  0.052  1.257  1.246  8.220  9.284  19  6  27  42  2.446  1.354  2.971  1.588  0.249  0.345  0.484  0.666  1.108  0.076  0.066  1.286  1.301  8.426  9.233  19  11  49  51  1.537  1.342  2.602  1.801  0.271  0.345  0.729  0.694  1.007  1.109  0.076  0.067  1.289  1.309  8.454  9.192  19  12  50  51  1.531  1.343  2.574  1.863  0.276  0.341  0.721  0.700  1.029  1.057  0.080  0.077  1.313  1.321  8.633  8.935  18  15  47  45  1.616  1.628  2.545  2.288  0.294  0.324  0.696  0.667  1.050  1.078  0.089  0.086  1.356  1.363  8.744  9.067  19  16  49  46  1.551  1.590  2.607  2.347  0.301  0.334  0.708  0.684  224 the r e s e r v a t i o n wage  28  than type one  The d e t e r m i n a t i o n of r e l a t i v e  individuals.  offers  i s made more c o m p l i c a t e d by the a b i l i t y wage o f f e r  and h i r i n g and i n d i v i d u a l s '  behaviour. ante,  individual  of f i r m s to d i s c r i m i n a t e heterogeneous  and firms a r e unable t o d i s c r i m i n a t e , It  is  indifferent  and l o s i n g c u r r e n t employees  workers..  It  offers  a f i r m enjoys  between r e t a i n i n g i t s  workforce  in  l a b o u r market  I n a market i n which a l l i n d i v i d u a l s a r e i d e n t i c a l ,  monopsony power.  of  to each type of  and s i m u l t a n e o u s l y  ex  considerable existing h i r i n g new  a wage which i s a d e c l i n i n g f u n c t i o n o f i t s  level  employment. The b a s i c  s o l u t i o n to Model I I I  d i s c r i m i n a t e has a n o n - s y s t e m a t i c decisions  over employment  states.  p o s i t i o n s has i n c r e a s e d ,  vacancies  mixed f o r c e ,  d i s m i s s e d by a low wage It  proves  easiest  one type of employee  If  firms'  the f i r m c u r r e n t l y employs  decisions  the  ' o p t i m a l workforce'  a r e such t h a t t h e r e i s  m a t r i x i n T a b l e 15).  can be  and, i n a effectively  offer. to a n a l y s e  its  to  workforces  low wage r a t e s  decisions  c u r r e n t l e v e l and c o m p o s i t i o n of employment (a)  new  s e a r c h , but the a b i l i t y  means t h a t i n segregated  to  creation  The i m p l i c i t c o s t s of f i l l i n g  can be c r e a t e d a t  i f necessary,  t h a t the a b i l i t y  impact on wage and vacancy  due t o s t o c h a s t i c  d i s c r i m i n a t e i n wage o f f e r s speculative  demonstrates  If  (see  the  by comparing  to the o p t i m a l  its  workforce.  'optimal workforce',  a high p r o b a b i l i t y  the a p p r o p r i a t e row o f the  the f i r m c r e a t e s v a c a n c i e s  of  then  retaining  transition  and o f f e r s  a lower  225 wage, then, as argued i n the explanation of the r e s u l t s to Model I I , there i s a high p r o b a b i l i t y that the f i r m faces a suboptimal l e v e l or composition of employment.  Although firms can d i s c r i m i n a t e i n h i r i n g ,  vacancies have to be created f o r both types of worker,due t o the s t o c h a s t i c elements of job search.  I t follows then that the f i r m w i l l  not create vacancies, because i t c u r r e n t l y faces a l e v e l and composition of employment which i s optimal i n both a s i n g l e period and m u l t i p e r i o d framework.  Thus, i t o f f e r s a r e l a t i v e l y high wage t o type two employees  and creates no vacancies. (b)  The f i r m faces a l e s s than optimal l e v e l of employment. I t s  decisions are such that there i s a high p r o b a b i l i t y of achieving the optimal l e v e l of employment. i t creates vacancies.  This can be observed i n Table 15. Thus,  Due to the s t o c h a s t i c elements of job search,  the f i r m i s forced to create vacancies f o r each type of searcher.  The  l e v e l of vacancy c r e a t i o n f o r each type of i n d i v i d u a l i s equal to the l e v e l of desired net h i r e s consistent w i t h p r o f i t maximisation.  These  vacancies, i n t o t a l , are s p e c u l a t i v e . I f the f i r m faces zero employment, then i t wishes to h i r e 2 workers. Type one i n d i v i d u a l s have a lower p r o b a b i l i t y , ex ante, of accepting a particular offer.  Given s t o c h a s t i c search, there i s a low p r o b a b i l i t y  that type two searchers w i l l sample the f i r m .  Thus, the f i r m o f f e r s a  higher wage t o type one searchers than type two searchers. A type one i n d i v i d u a l i n employment s t a t e [1,0], receives a higher wage than a type two i n d i v i d u a l receives i n the s t a t e complement [0,1].  226 These decisions r e f l e c t the heterogeneous  labour market behaviour  of d i f f e r e n t types of i n d i v i d u a l s and the higher i m p l i c i t costs of vacancy creation and thus the greater value of current employees r e s u l t i n g from the a b i l i t y t o discriminate i n h i r i n g . I t i s i n the wage o f f e r to searchers alone that firms are able to demonstrate t h e i r preference f o r type two employees.  A firm i n  state [1,0], i s prepared to o f f e r a type two searcher a higher wage than a type one searcher receives i n the state complement.  Type one  i n d i v i d u a l s are l e s s valuable when h i r e d and t h i s i s r e f l e c t e d i n the r e l a t i v e o f f e r s to searchers alone over these s t a t e s . Despite the higher o f f e r to type two searchers, there i s a lower p r o b a b i l i t y that a type two searcher, w i l l sample a p a r t i c u l a r f i r m and accept an o f f e r than a type one searcher i n the state complement, because type two i n d i v i d u a l s have a lower incidence of unemployment. Over suboptimal l e v e l s of employment, then, the f i r m creates vacancies f o r both types of i n d i v i d u a l .  The wage o f f e r to each type  of worker i s an increasing function of the number employed at each l e v e l of employment. (c)  The f i r m faces an optimal l e v e l but suboptimal composition  of employment.  The f i r m employs at l e a s t one type one worker.  Again,  because the i m p l i c i t costs of f i l l i n g vacancies are h i g h , the f i r m makes wage o f f e r decisions such that there i s a high ex ante p r o b a b i l i t y of r e t a i n i n g i t s workforce, (see Table 15).  Thus,the wage o f f e r to both  type one and type two employees over t h i s l e v e l of employment i s an increasing function of the number employed.  227 At t h i s optimal l e v e l of employment, firms create speculative vacancies f o r type two i n d i v i d u a l s .  The l e v e l of vacancy creation  corresponds to current employment of type one i n d i v i d u a l s and thus represents desired net h i r e s of type two i n d i v i d u a l s consistent with a t t a i n i n g the optimal workforce. In Model I , there i s a s u b s t i t u t i o n between the wage o f f e r and vacancy c r e a t i o n d e c i s i o n .  Ceteris paribus, a higher l e v e l of vacancy  creation e n t a i l s a lower wage o f f e r .  I f a f i r m c u r r e n t l y employs a  mixed workforce, s t a t e [1,1], and creates zero vacancies, the wage o f f e r to type one i n d i v i d u a l s can be expected t o exceed the wage o f f e r to type two i n d i v i d u a l s .  This r e f l e c t s type one i n d i v i d u a l s higher  ex ante p r o b a b i l i t y of turnover.  By c r e a t i n g vacancies f o r type two  i n d i v i d u a l s , however, there e x i s t s a non-zero p r o b a b i l i t y of a t t a i n i n g the 'optimal workforce'.  Consequently, i n a mixed workforce,the o f f e r  to type one i n d i v i d u a l s i s l e s s than the o f f e r to type two i n d i v i d u a l s . Employing a segregated workforce, s t a t e [2,0], the firm's wage o f f e r to type two searchers i s r e l a t i v e l y low.  The p r o b a b i l i t y of  f i l l i n g such vacancies i s s m a l l , however, due to the s t o c h a s t i c elements of job search.  Thus, the f i r m o f f e r s r e l a t i v e l y high wages to type one  i n d i v i d u a l s , so that there i s a high p r o b a b i l i t y that they do not t u r n over.  The a b i l i t y to d i s c r i m i n a t e enables speculative vacancies to be  created f o r type two searchers at lower wage rates than are offered to current type one employees. (d)  The f i r m faces an above optimal l e v e l of employment but the  'optimal workforce' c o n s t i t u t e s a subset of the current workforce,  228  states  [1,2],  [0,3],  [2,2],  [1,2]  and [ 0 , 4 ] .  independent o f the p e r c e p t i o n parameter For j o i n t v a l u e s [1.10,0.90], type  The r e s u l t s are n o t  values.  o f the p e r c e p t i o n p a r a m e t e r s ,  the f i r m c r e a t e s  of i n d i v i d u a l such t h a t  zero v a c a n c i e s  [1.00,0.90]  and makes o f f e r s  there i s a h i g h p r o b a b i l i t y of  the o p t i m a l l e v e l o f employment.  The f i r m o f f e r s  and  to each  securing  a wage e q u a l to or  29 below the l e v e l of unemployment compensation  over a l l these  to type one employees.  two employees  The wage o f f e r  t o type  states over  each employment l e v e l i s a d e c l i n i n g f u n c t i o n of the number employed. The f i r m wishes  to r e t a i n two o f the c u r r e n t type  For h i g h e r j o i n t v a l u e s creates  a vacancy  f o r a type  two w o r k e r s .  o f the p e r c e p t i o n p a r a m e t e r s , one s e a r c h e r i n s t a t e  the  [ 1 , 2 ] , and  firm offers 30  a wage e q u a l to or e x c e e d i n g The o f f e r  the l e v e l of unemployment compensation.  to type one i n d i v i d u a l s i n s t a t e  [2,2]  l e v e l o f unemployment compensation, but the o f f e r equal to or l e s s p a t t e r n of o f f e r s  equals  or exceeds  i n state  [1,3]  than the l e v e l of unemployment compensation. to type  two employees  over the f i v e  the  is  The  states i s un-  changed. For low v a l u e s type one employees, offer  o f the p e r c e p t i o n p a r a m e t e r s , zero vacancy  the low wage o f f e r  c r e a t i o n d e c i s i o n and r e l a t i v e l y  the  high  to type two employees a r e c o n s i s t e n t w i t h t h e r e b e i n g a low  v a r i a n c e o f employment next p e r i o d and h i g h p r o b a b i l i t y of 'optimal workforce'.  to  attaining  229  Higher j o i n t values of the perception parameters correspond to 2  higher values of the perception parameter, c^ . Then, i n order to r e t a i n two type two employees, the f i r m must o f f e r a higher wage to type two workers.  I f the f i r m c u r r e n t l y employs only two type two  i n d i v i d u a l s , however, rather than o f f e r type two i n d i v i d u a l s a r e l a t i v e l y high wage, i t chooses to o f f e r type one i n d i v i d u a l s a wage equal to or exceeding unemployment compensation to e x p l o i t t h e i r higher marginal p r o b a b i l i t y of acceptance, and, i n a d d i t i o n , i f not constrained by the employment l e v e l , . c r e a t e a speculative vacancy f o r type one i n d i v i d u a l s .  This enables the f i r m to o f f e r a s l i g h t l y lower  wage to type two i n d i v i d u a l s than otherwise. I f the f i r m currently employs three or more type two i n d i v i d u a l s , then a low wage w i l l drive out any current type one employee, but the wage o f f e r to type two i n d i v i d u a l s i s lower than i n a workforce of two type two i n d i v i d u a l s , because the f i r m only wishes to r e t a i n two type 31 two i n d i v i d u a l s .  Thus, the f i r m does not choose to create speculative  vacancies or attempt to r e t a i n i t s current type one employee. (e)  The f i r m faces an above optimal l e v e l and a suboptimal compos-  i t i o n of employment.  The wage decisions by firms r e f l e c t t h e i r desire  to a t t a i n the optimal l e v e l of employment.  I n most cases, the wage o f f e r  to type one and type two i n d i v i d u a l s i s an i n c r e a s i n g function of the number employed f o r any given t o t a l l e v e l of employment.  I f the f i r m  c u r r e n t l y employs a mixed workforce, then i t s wage o f f e r to type one i n d i v i d u a l s i s less than the o f f e r to type two i n d i v i d u a l s i n eleven  230  cases out o f a p o s s i b l e f o u r t e e n .  32  The f i r m wishes  to r e t a i n  the  type two i n d i v i d u a l and l o s e a l l but one o f the type one i n d i v i d u a l s . In a segregated  type one w o r k f o r c e , by c o n t r a s t ,  r e t a i n two of the workforce and o f f e r s three cases, state  [3,1]  the f i r m d r i v e s out type w i t h a low wage o f f e r .  the f i r m wishes  a h i g h e r wage.  In the  to  other  two i n d i v i d u a l s from employment  T h i s reduces  the v a r i a n c e o f em-  ployment. I n s i x cases out o f s e v e n , f o r type  the f i r m c r e a t e s  a speculative  two i n d i v i d u a l s a t a wage e q u a l to or j u s t  of unemployment compensation i n employment s t a t e i s quite plausible,  above the  [3,0].  level  Such b e h a v i o u r  s i n c e the f i r m would p r e f e r to employ type  i n d i v i d u a l s and the vacancy i s c r e a t e d a t a low wage  vacancy  two  offer.  I n a mixed workforce of t h r e e i n d i v i d u a l s , the f i r m does n o t vacancies,  because  any wage o f f e r  made i s an o f f e r  to current  create  employees  as w e l l .  The p r o b a b i l i t y o f a type two s e a r c h e r s a m p l i n g t h e f i r m i s  The o f f e r  t o c u r r e n t type  to t h i s vacancy  low.  one employees would n e c e s s a r i l y be lower due  creation.  Consequently,  the v a r i a n c e o f the l e v e l and  c o m p o s i t i o n of employment n e x t p e r i o d would be h i g h e r and mean p r o f i t s lower. 4.  A Summary o f F i r m s ' It  that  Decisions  i s i m p o r t a n t to n o t e t h a t , i n a n a l y s i n g f i r m b e h a v i o u r ,  firms a r e a t t e m p t i n g to a t t a i n  a l t h o u g h the c l a s s i f i c a t i o n  the  'optimal workforce'  of employment s t a t e s i s u s e f u l .  to  argue  is misleading, F i r m s ' wage  231  and  vacancy c r e a t i o n d e c i s i o n s r e f l e c t  the value  of r e t a i n i n g current  employees and h i r i n g new employees i n the l i g h t o f t h e i r turnover and acceptance b e h a v i o u r and t h e r e l a t i o n s h i p between the c u r r e n t and  optimal  l e v e l o f employment.  level  I n d i v i d u a l s ' b e h a v i o u r may be such  that there i s a high p r o b a b i l i t y that the 'optimal workforce' i s indeed  attained.  The  seemingly n o n - s y s t e m a t i c wage and vacancy c r e a t i o n  decisions  f o r each i n d i v i d u a l over employment s t a t e s o c c u r , because o f a number of c o n f l i c t i n g f a c t o r s a r i s i n g from t h e f i r m s ' a b i l i t y  to discriminate  i n b i r i n g - and wage o f f e r . The  costs  to the f i r m o f c r e a t i n g and f i l l i n g v a c a n c i e s ,  which  are measured i n terms o f foregone p r o f i t s , have r i s e n due t o h i r i n g d i s c r i m i n a t i o n and s t o c h a s t i c s e a r c h .  Thus, a t l e s s than  optimal  l e v e l s , vacancy c r e a t i o n f o r each type o f i n d i v i d u a l i s n o t s p e c u l a t i v e > but  i s speculative i n total. As  i n the case when the p e r c e p t i o n  parameters a r e e q u a l ,  i t i s the  a b i l i t y o f f i r m s t o d i s c r i m i n a t e between t h e type o f employee who c o n s t i t u t e s the m a j o r i t y  o f the w o r k f o r c e and the o t h e r  who i s i n the m i n o r i t y  o r i s s o l e l y a searcher,  portance.  to d i s c r i m i n a t e gives  The a b i l i t y  type o f worker  which assumes key im-  the f i r m e x t r a degrees o f  freedom i n i t s d e c i s i o n making, but i t s u f f e r s a l o s s o f i n t e r t e m p o r a l and, it  indeed, s t a t i c monopsony power because, due t o s t o c h a s t i c  search,  i s f o r c e d t o make s e p a r a t e vacancy c r e a t i o n d e c i s i o n s f o r each type  of i n d i v i d u a l .  At l e s s than the o p t i m a l  l e v e l o f employment, f o r example,  232 each vacancy  c r e a t i o n d e c i s i o n i s n o n - z e r o and the f i r m faces  r e l a t i v e l y h i g h v a r i a n c e o f employment next p e r i o d . using i t s  d i s c r i m i n a t o r y power, i t  offers  a  Consequently,  r e l a t i v e l y h i g h wages  to  the type o f i n d i v i d u a l who predominates i n i t s workforce and reduces i t s vacancy  creation.  individual is by f i l l i n g  The l e v e l of vacancy  c r e a t i o n f o r each type  c o n s i s t e n t w i t h o b t a i n i n g the o p t i m a l l e v e l o f  e i t h e r type o f vacancy  therefore,  c u r r e n t employees,  predominate i n the w o r k f o r c e , a r e r e l a t i v e l y more v a l u a b l e o f the h i g h e r i m p l i c i t c o s t  Model I I I ,  it  can be argued t h a t  employment  and assuming no q u i t s .  I n c o n t r a s t to Models I and I I ,  because  of  of vacancy  to  who  firms  c r e a t i o n . ' Hence, i n  the f i r m enjoys  less  intertemporal  monopsony power. At e q u a l or above o p t i m a l l e v e l s b e h a v i o u r changes.  Now d e s i r e d n e t h i r e s are zero a n d , i n some  f i r m s w i s h to d i s c a r d w o r k e r s . offer  of employment, the n a t u r e of  In s e g r e g a t e d w o r k f o r c e s ,  a h i g h e r wage to c u r r e n t employees  vacancies  are  firms  than to s e a r c h e r s ,  cases, still speculative  created.  I n mixed w o r k f o r c e s ,  however,  type  two i n d i v i d u a l s e a r n a h i g h e r  wage than type one i n d i v i d u a l s .  I n some employment s t a t e s ,  to type one i n d i v i d u a l s a c t u a l l y  equals  pensation or l e s s ,  because  the f i r m wishes  than o p t i m a l l e v e l s  the  offer  the l e v e l of unemployment comto d i s c a r d these  Thus, as compared w i t h the b a s i c s o l u t i o n to Model I I I , and l e s s  if  firms'  o f employment,  differences  u a l s are r e f l e c t e d by the comparison o f r e s p e c t i v e  employees. at optimal  between  offers  individ-  i n state  233 complements, and the firm's a b i l i t y to discriminate between employees and searchers remains important.  I n mixed workforces, i n d i v i d u a l  differences dominate firms' a b i l i t y to discriminate between searchers and employees.  Consequently, over these s t a t e s , type two employees  earn higher wages than type one employees. 5.  An Explanation of the Summary S t a t i s t i c s Generally, type one searchers only receive o f f e r s from firms  c u r r e n t l y employing undersize workforces.  Then, the p r o b a b i l i t y that  a type one searcher receives a zero wage o f f e r i s higher than f o r a type two searcher.  Thus, the variance of o f f e r s facing a type one  searcher exceeds the variance of o f f e r s facing a type two searcher. Type two i n d i v i d u a l s enjoy a higher mean wage, when employed, and have a lower p r o b a b i l i t y , ex ante, of q u i t t i n g i n response to a p a r t i c u l a r wage o f f e r than type one i n d i v i d u a l s .  Thus, type two  i n d i v i d u a l s enjoy a higher MDI than type one i n d i v i d u a l s , although, over some states of employment, type one employees enjoy a higher wage rate. In Models I and I I , i n d i v i d u a l s , who do not q u i t , enjoy the largest MDI.  I n t h i s model, firms can discriminate i n wage o f f e r s ,  whence, i f a type one i n d i v i d u a l i s a member of an oversize workforce, the f i r m e f f e c t i v e l y lays him o f f w i t h a low wage o f f e r .  I f , hypo-  t h e t i c a l l y , the i n d i v i d u a l never q u i t s , then i t i s p o s s i b l e that he also receives the same low wage o f f e r , since the f i r m wishes to r e t a i n  234 the other employees.  I f he quits because the o f f e r i s lower than h i s  reservation wage, then he receives unemployment compensation, searches and faces a non-zero p r o b a b i l i t y of r e c e i v i n g an o f f e r i n excess of h i s reservation wage. Thus, i n f i v e out of the seven cases, the measure of MDI associated w i t h turnover and acceptance according t o the true reservation wage i s higher than that associated w i t h never q u i t t i n g . Most vacancies f o r type one i n d i v i d u a l s are created by firms c u r r e n t l y f a c i n g undersize workforces.  Thus, aggregate vacancy creation  f o r type one i n d i v i d u a l s i s lower than aggregate vacancy creation f o r type two i n d i v i d u a l s because speculative  type two vacancies are created  at optimal and above optimal employment l e v e l s .  Type one i n d i v i d u a l s  are less valuable than type two i n d i v i d u a l s a t a p a r t i c u l a r wage o f f e r and thus fewer are employed i n s t o c h a s t i c e q u i l i b r i u m , since type one i n d i v i d u a l s do not receive s y s t e m a t i c a l l y  lower o f f e r s .  Type one i n d i v i d u a l s enjoy a higher unemployment r a t e and fewer vacancies.  Then type one searchers have a longer mean duration of  search p r i o r t o an o f f e r . Type one i n d i v i d u a l s wait longer before r e c e i v i n g an o f f e r and have a lower p r o b a b i l i t y of accepting a p a r t i c u l a r o f f e r .  Then, i t  i s p l a u s i b l e that type one i n d i v i d u a l s enjoy a longer duration of unemployment.  Type two i n d i v i d u a l s enjoy a higher mean wage when em-  ployed and a higher rate of employment.  Thus, they enjoy a l a r g e r  share of t o t a l output than type one i n d i v i d u a l s . A p r i o r i , the respective  c o r r e l a t i o n s of each i n d i v i d u a l ' s wage  o f f e r over one period have no p a r t i c u l a r r e l a t i o n .  235 6i.  The Concept of Vacancy C r e a t i o n and Excess Demand In Models I and I I ,  identified.  two motives b e h i n d vacancy  F i r s t l y , vacancies  a r e c r e a t e d which r e p r e s e n t d e s i r e d  n e t h i r e s of f i r m s c u r r e n t l y f a c i n g a l e s s employment. offers reflect  Secondly,  than o p t i m a l l e v e l  speculative vacancies  of  are c r e a t e d at low wage  which demonstrate the f i r m s ' monopsony power.  Such v a c a n c i e s  s p e c u l a t i o n about i n d i v i d u a l s ' t u r n o v e r and acceptance  and f i r m s ' d e c i s i o n s r e p r e s e n t an attempt employment a t a r e l a t i v e l y  low wage.  r e p r e s e n t the d e s i r e to s u b s t i t u t e uals.  c r e a t i o n can be  A l t h o u g h vacancy  to a t t a i n  I n Model I I ,  between  behaviour  the o p t i m a l l e v e l these v a c a n c i e s  type one and type two  speculation increases  of  also  individ-  the v a r i a n c e o f the  level  of employment, t h e r e i s a low p r o b a b i l i t y of a c h i e v i n g an i n f e r i o r comp o s i t i o n o f employment next p e r i o d . In Model I I I , t h e n a t u r e o f f i r m s ' due to i t s  a b i l i t y t o d i s c r i m i n a t e i n wage o f f e r  noted, vacancies due to s t o c h a s t i c behaviour.  d e c i s i o n making i s more c o m p l i c a t e d , and h i r i n g .  r e p r e s e n t i n g d e s i r e d net h i r e s are s p e c u l a t i v e s e a r c h , r a t h e r than s t o c h a s t i c  t u r n o v e r and  f o r each, type o f i n d i v i d u a l .  the v a r i a n c e of employment, however, c r e a t e these v a c a n c i e s . employment l e v e l s net h i r e s .  in  total,  acceptance  The f i r m i s c o n s t r a i n e d by the r e s t r i c t i o n o f the maximum  l e v e l of employment from o f f e r i n g a lower wage and c r e a t i n g vacancies  As a l r e a d y  it  Given the r e s u l t i n g i n c r e a s e i n i s u n l i k e l y that  Aggregate vacancy  then r e p r e s e n t s  twice  speculative  the f i r m would  c r e a t i o n a t below o p t i m a l  the aggregate measure o f d e s i r e d  236 At the o p t i m a l l e v e l o f employment and above, generally vacancy  speculative  vacancies,  f o r type two s e a r c h e r s , are c r e a t e d at low wage o f f e r s .  c r e a t i o n demonstrates  Such  the a b i l i t y to d i s c r i m i n a t e i n wage  between s e a r c h e r s and c u r r e n t employees  offer  r a t h e r than the f i r m s ' monopsony  power a l o n e . T h i s vacancy  c r e a t i o n b e h a v i o u r u n d e r l i n e s the problem o f  a homogeneous measure o f d e s i r e d n e t h i r e s . are created at d i f f e r e n t  constructing  I n Models I and I I ,  wage r a t e s a c c o r d i n g to the c u r r e n t employment  l e v e l b u t , w i t h the e x c e p t i o n o f the f i r m f a c i n g a zero l e v e l of ment, these o f f e r s  vacancies  are a l s o made t o c u r r e n t employees.  Model I I I , some s p e c u l a t i v e  vacancies  employ-  By c o n t r a s t , i n  a r e accompanied by wage  offers  which are made t o s e a r c h e r s alone o r to an i n d i v i d u a l type who c o n stitutes  a m i n o r i t y of the workforce and whom the f i r m may w i s h to  out o f i t s  employment.  Since vacancies speculative  drive  in total,  r e p r e s e n t i n g d e s i r e d net h i r e s can be regarded as due to s t o c h a s t i c  s e a r c h , r a t h e r than  stochastic  t u r n o v e r and acceptance b e h a v i o u r , a more a p p r o p r i a t e measure of speculative  vacancies  may be those v a c a n c i e s  a r e unequal between i n d i v i d u a l s . firms  That i s  c r e a t e d by f i r m s which  those v a c a n c i e s  c r e a t e d by  f a c i n g the o p t i m a l o r above o p t i m a l l e v e l of employment f o r one  type o f i n d i v i d u a l which c l e a r l y do n o t r e p r e s e n t d e s i r e d n e t h i r e s . 7.  The T h e o r e t i c a l C o n t r i b u t i o n o f Model The c o n t r i b u t i o n o f t h i s model i s  firms'  discriminatory behaviour.  It  33  III  i n the e x p l i c i t  is possible  formulation of  to s e t t l e some o f  the  debates between economists as to which type of worker earns t h e h i g h e r wage.  237 Salop argues  that,  q u i t r a t e than a n o t h e r ,  if  one type o f employee has a h i g h e r m a r g i n a l  then he earns a h i g h e r wage, i f  d i s c r i m i n a t e s i n i t s wage o f f e r .  Unfortunately,  an o f f e r offer  is  that  i s based on the e v a l u a t i o n o f the o f f e r  Chapter I VD, i f  the e x p l i c i t  specify  The assumption  an i n d i v i d u a l ' s ex ante p r o b a b i l i t y o f  d i s t r i b u t i o n f a c i n g him.  firm  he does not  how i n d i v i d u a l s ' q u i t p r o b a b i l i t i e s , a r e determined. i n Model I I I  the  accepting  i n the context  I n M c C a l l ' s model d e s c r i b e d i n c o s t s o f s e a r c h and the r e t u r n s  of  the  the from  b e i n g unemployed and not s e a r c h i n g a r e the same f o r b o t h white and b l a c k w o r k e r s , more b l a c k i n d i v i d u a l s would drop out o f the force,  if  they e v a l u a t e  d i s t r i b u t i o n o f wage In a s t r i c t  their offers  i n the c o n t e x t  sense,  Salop i s  incorrect.  The wage o f f e r  d i s t r i b u t i o n f a c i n g a type two i n d i v i d u a l .  Under c e r t a i n c i r c u m s t a n c e s , between  offers  i t pays  i n d i v i d u a l s on the b a s i s  employment.  o f t h e i r own  offers.  f a c i n g a type one i n d i v i d u a l i s n o t s y s t e m a t i c a l l y offer  h i g h e r than the wage  of t h e i r d i f f e r e n t  type one s e a r c h e r i n the s t a t e complement o r , i f  mean r e t u r n s  to s e a r c h e r s ,  more v a l u a b l e  h i g h e r wage.  It  i s when the f i r m wishes  one employees  are r e t a i n e d that S a l o p ' s  offer  from a  firm  [1,0] than to a  the f i r m  employs a mixed workforce which i s e q u a l to or above offers  simple.  firms to d i s c r i m i n a t e i n wage  a h i g h e r wage t o a type two s e a r c h e r i n s t a t e  then, again?, i t  distribution  The reason i s  In p a r t i c u l a r , i n making wage o f f e r s  ployment l e v e l ,  labour  currently  the o p t i m a l em-  type two workers a  to ensure t h a t arguments a r e  c u r r e n t type  correct.  34  238 Although the wage o f f e r d i s t r i b u t i o n s are such that type one i n d i v i d u a l s do indeed have a higher marginal q u i t r a t e , i n response to a p a r t i c u l a r o f f e r , than type two i n d i v i d u a l s i n the s t a t e complement, the mean wage enjoyed by a type two employee i s higher than that enjoyed by a type one i n d i v i d u a l .  I n an o v e r a l l sense, then, Salop i s i n c o r r e c t .  Sanborn argues that, i n the absence of d i s c r i m i n a t i o n through ignorance or p r e j u d i c e , low q u i t i n d i v i d u a l s w i l l enjoy a higher wage o f f e r than h i g h q u i t i n d i v i d u a l s because t h e i r costs of turnover are amortised over a longer period of time.  I n the aggregate, employed  type two i n d i v i d u a l s do, indeed, enjoy a higher mean wage o f f e r b u t , as i n d i c a t e d , type two i n d i v i d u a l s do not enjoy s y s t e m a t i c a l l y higher wage o f f e r s than type one i n d i v i d u a l s . C.  Comparative S t a t i c P r e d i c t i o n s of Model I I I  1.  An Introduction  Nine d i f f e r e n t combinations of the perception parameters, c ^ 2 and c^ are adopted i n the range 0.90 t o 1.15. A l l other exogeneous constants are kept constant. ^^> a r b i t r a r i l y , i s assumed to exceed 2 c^ . S i x comparative s t a t i c p r e d i c t i o n s are generated, four associated 2 1 with an increase i n c^ and two w i t h an increase i n c^ . Most q u a l i t a t i v e c  p r e d i c t i o n s are independent of the absolute or r e l a t i v e values of the perception parameters and, indeed, independent of which perception parameter increases. There are twenty-five summary s t a t i s t i c s whose changes describe the impact on s t o c h a s t i c e q u i l i b r i u m of a change i n the value of an exogeneous parameter.  They are the f o l l o w i n g :  (a)  The wage o f f e r d i s t r i b u t i o n facing type one i n d i v i d u a l s ;  (b)  The wage o f f e r d i s t r i b u t i o n facing type two i n d i v i d u a l s ;  (c)  The mean wage o f f e r enjoyed by a type one searcher;  (d)  The mean wage o f f e r enjoyed by a type two searcher;  (e)  The variance of o f f e r s facing a type one i n d i v i d u a l ;  (f)  The variance of o f f e r s facing a type two i n d i v i d u a l ;  (g)  The mean wage earned by a type one employed i n d i v i d u a l ;  (h)  The mean wage earned by a type two employed i n d i v i d u a l ;  (i)  MDI enjoyed by a type one i n d i v i d u a l ;  (j)  MDI enjoyed by a type two i n d i v i d u a l ;  (k)  Aggregate unemployment;  (1)  Aggregate type one unemployment;  (m) Aggregate type two unemployment; (n)  Aggregate vacancy creation  f o r type one searchers;  (o)  Aggregate vacancy creation  f o r type two searchers;  (p)  Aggregate type one speculative vacancy  creation;  (q)  Aggregate type two speculative vacancy  creation;  (r)  The mean duration of search p r i o r t o an o f f e r f o r a type one searcher;  (s)  The mean duration of search p r i o r to an o f f e r f o r a type two searcher;  (t)  The mean duration of type one unemployment;  (u)  The mean duration of type two unemployment;  (v)  Mean f i r m p r o f i t s discounted over an i n f i n i t e h o r i z o n ;  240 (w)  Type one labours' share of t o t a l output;  (x)  Type two labours' share of t o t a l output; and  (y)  Labours' t o t a l share of output.  The values of the summary s t a t i s t i c s over combinations of the perception parameters are shown i n Table 17. The a n a l y s i s of the 2 r e s u l t s r e l a t e s to an increase i n c^ . 2.  The Results 2 In response to an increase i n c^ , the wage o f f e r d i s t r i b u t i o n s  f a c i n g both type one and type two i n d i v i d u a l s generally s h i f t t o the right.  For some parameter changes, however, there i s a change i n the  p a t t e r n of vacancy c r e a t i o n over employment states and so not a l l wage o f f e r s over a l l states increase. The mean wage o f f e r facing each type of unemployed i n d i v i d u a l and the variances of the respective d i s t r i b u t i o n s a l l increase.  The mean  wage f o r both type one and type two employed i n d i v i d u a l s r i s e .  Type  one i n d i v i d u a l s enjoy an increase i n MDI, but MDI of a type two individual f a l l s . T o t a l mean unemployment r i s e s . type one unemployment f a l l s .  Type two unemployment r i s e s w h i l e  Aggregate mean vacancy c r e a t i o n f o r both  types of i n d i v i d u a l generally r i s e s , but there i s no systematic change i n aggregate speculative vacancy c r e a t i o n f o r e i t h e r type of i n d i v i d u a l . The mean duration of search p r i o r to an o f f e r i s again negatively r e l a t e d to the aggregate measure of vacancies minus unemployment. Consequently, type one i n d i v i d u a l s ' mean duration of search f a l l s ,  TAJoLE 1/  Comparative S t a t i c Results f o r Model I I I -  1.00  1.00  0.90  1.00  -  c  l s  !  1  a)  1.00  x  1.10  ; l.io  1.05  1.10  b)  1  c)  0.934  d)  1.035  0.959  1.039  1.083  1.001 | 1.007 | 1.029 i 1.030 1.108 \ 1.109 ' 1.057 I 1.050  e)  0.054  0.053  0.056  0.063  0.076 | 0.076 1 0.080 \ 0.084  0.962  0.951  •  0.950  1  1 • 1.15 [  1.078 0.089  j> !g)  1.190  h)  1.207  1.200  1.221  1.246  1.301 ; 1.309  1.321 . 1.325  1.363  i)  8.104  8.270  8.118  8.220  8.426 j 8.45,4  8.633  8.744  j)  8.849  9.268  8.869  9.284  9.233  k)  24