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An ethically flexible evaluation of unemployment insurance reform with constrained and unconstrained… Phipps, Shelley Ann 1987

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AN ETHICALLY FLEXIBLE EVALUATION OF UNEMPLOYMENT REFORM WITH CONSTRAINED AND UNCONSTRAINED  INSURANCE  MODELS'OF LABOUR  SUPPLY by SHELLEY A . PHIPPS B . A . ( H o n o u r s ) , The U n i v e r s i t y of V i c t o r i a , M.A.,  The U n i v e r s i t y  of B r i t i s h Columbia,  1981 1982  A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY  in THE FACULTY OF GRADUATE STUDIES Department  of  Economics  We accept t h i s t h e s i s as to the  required  THE UNIVERSITY  conforming  standard  OF BRITISH COLUMBIA  October  1987  © S h e l l e y A . Phipps,  1987  In  presenting  degree  this  thesis in partial fulfilment of the  for  of  department  this thesis for scholarly or  by  his  or  her  I further agree that permission for  purposes  permission.  Department of  6C0r>gYvvtcS  The University of British Columbia 1956 Main Mall Vancouver, Canada V6T 1Y3  DE-6f 3/811  advanced  Q-f>  ISS^-  extensive  may be granted by the head of  representatives.  It  is  understood  that  publication of this thesis for financial gain shall not be allowed without  Date  an  at the University of British Columbia, I agree that the Library shall make it  freely available for reference and study. copying  requirements  copying  my or  my written  ABSTRACT  The  goal  of  this  dissertation  importance and f e a s i b i l i t y which  pay  attention  Introducing  an  i n t r o d u c i n g value can be  both  h i s own  judgements,  the  values  dissertation  ethically  flexible  the p r o p o s a l s f o r Insurance  by  explicitly  illustrates  the reform of  (UI) programme  the  3.  an  'ethically imposing  conducting  ethical  the  positions.  feasibility  the Canadian  made by the  B e h a v i o u r a l models which take  The models are estimated data  objectivity  of  an  approach by c a r r y i n g out an e v a l u a t i o n of  of unemployment and UI are 2.  involves  an a n a l y s t can a v o i d  Commissions. The e v a l u a t i o n proceeds 1.  equity.  necessarily  e v a l u a t i o n from a number of d i f f e r e n t  This  and  adoption of  the  evaluations  but I suggest that  approach. That i s , particular  illustrate  efficiency  criterion  maintained through  flexible'  to  of c o n d u c t i n g p o l i c y  to  equity  is  Unemployment  Macdonald and  Forget  i n four stages:  account of the  existence  developed. u s i n g an a p p r o p r i a t e  Canadian  set.  The estimated models  are used  to simulate  behavioural  responses to UI reform. 4.  E s t i m a t i o n and s i m u l a t i o n r e s u l t s the e t h i c a l l y  flexible  welfare i i  are used to c a r r y  evaluation.  out  Two household  labour-supply  assumes  observed  that  utility-maximizing possibility  The  used.  is  the  first  outcome  of the  that demand-side c o n s t r a i n t s may i n t e r f e r e  with  A form  'constrained'  second  The  introduces  sample s e p a r a t i o n unknown i s  of switching  n o n - l i n e a r as a r e s u l t  regression  developed to allow  labour-supply  problems for e s t i m a t i o n  variable,  are  unemployment  choices.  supply-side choices.  of  models  functions.  with  estimation Additional  i n c l u d e a budget c o n s t r a i n t which of  the UI programme and a  weeks of l e i s u r e  to v a l u e s between zero and  (unemployment),  dependent  which i s  limited  fifty-two.  Both u n c o n s t r a i n e d and c o n s t r a i n e d models are estimated single  men,  expenditure Consumer  single  women  systems  and  Finance.  and  data  couples, from  Estimation  the  f u n c t i o n s are  unconstrained  that  difference women in important  between the  the  behaviour of c o u p l e s .  model, and  determination  no  of that than  observable of men  and  that c r o s s - e f f e c t s  are  of  the  labour-supply  Estimated p r o b a b i l i t i e s of  take an average value of  Survey  less elastic is  for  linear  suggest  l a b o u r - s u p p l y behaviour  a constrained in  there  using 1982  results  constrained labour-supply functions,  is  (approximately)  The s i m u l a t i o n of b e h a v i o u r a l responses  constraint  80 p e r c e n t .  to UI reform  using  the estimated that  unconstrained l a b o u r - s u p p l y f u n c t i o n s  large reductions  S i m u l a t i o n using suggests that  i n unemployment might be  the  constrained  responses may be  Welfare  evaluation  ethical  perspectives:  Utilitarianism; theory of  of  justice;  order  utilities.  r  the  r  in  constructed  for  is  spirit  in  the  is  the  over  the  the  i n the  is  poverty l i n e  of  to  individual  required  of  of  incomes,  focus a t t e n t i o n  the d i s t r i b u t i o n  a  individual  The ' R a w l s i a n ' measure i s a mean  distribution  between  Robert  measure  of  of  Rawls'  s p i r i t of  distribution  group. The ' E n t i t l e m e n t ' measure  the d i s t a n c e  three  the s p i r i t of John  ( E x p l i c i t i n t e r p e r s o n a l comparisons are  censored at worst-off  first  third  over  functions  negligible.  are  is  anticipated.  labour-supply  t h e o r y . The ' U t i l i t a r i a n '  for these e v a l u a t i o n s . ) order  The  the second  Nozick's entitlement mean  measures  suggests  on  the  i s a measure individual  of  costs  (premiums) and b e n e f i t s d e r i v e d from U I .  Three f a c t o r s  are important  welfare-evaluation adopted  matters.  welfare-reducing  results. Both from  w e l f a r e - i m p r o v i n g from an for the Rawlsian  in  First, UI  a  the- determination the  reform  Utilitarian  ethical  iv  appear  perspective  evaluations,  the  the  position  proposals  Entitlement perspective.  and U t i l i t a r i a n  of  and  Second, assumed  degree  of  inequality  assumptions critical. results.  made  aversion  about  the  utility-maximizing  then  appear w e l f a r e - i m p r o v i n g : poor incomes  r e s u l t of  demand-side  increase.  If  then  i l l u s t r a t e the  and the e f f i c i e n c y thesis  demonstrates  objective  the  that  Rawlsian  to work may  more  be  in  results  group.  of both the  of  equity This  conducting  p o l i c y e v a l u a t i o n which pays a t t e n t i o n  v  the  increases  of a p o l i c y e v a l u a t i o n .  feasibility  of  proposals  UI reform merely  importance  dimensions  reform  unemployment so  are  the outcome  people choose  i n r e d u c t i o n s i n income for the w o r s t - o f f  These r e s u l t s  unemployment  to be both  constraints  employment are not p o s s i b l e ,  of  Finally,  i l l u s t r a t e d by the  i s assumed  choices,  and t h e i r  important.  nature  T h i s i s most c l e a r l y I f unemployment  is  to b o t h .  an  TABLE OF CONTENTS Abstract  ii  L i s t of Tables  viii  L i s t of F i g u r e s  xi  Acknowledgements  xii  I. II.  III.  Introduction  1  The Unconstrained Labour-Supply Model 15 1. The Basic Model of Household Behaviour . . . . 15 2. I n c o r p o r a t i o n of UI in Budget C o n s t r a i n t s . 19 3. L i n e a r i z a t i o n of the Non-linear Budget Constraint 22 4. Formal Model 27 5. S t o c h a s t i c S p e c i f i c a t i o n of the Model 32 a . Share F o r m u l a t i o n 33 b. N o n - l i n e a r Budget Constraint with S t o c h a s t i c Model 35 c . T r u n c a t i o n due to N o n - p a r t i c i p a t i o n . . 38 d. Censoring due to F u l l - y e a r Workers . . . 42 e. D e r i v a t i o n of the L i k e l i h o o d Functions . . 43 The C o n s t r a i n e d Labour-Supply Model 1. The Basic Model of Household Behaviour . . . . 2. Survey of Previous S t u d i e s of C o n s t r a i n t s . 3. The Formal Model of C o n s t r a i n e d Behaviour . 4. D e r i v a t i o n of the L i k e l i h o o d F u n c t i o n . . . . .  IV. E s t i m a t i o n R e s u l t s 1 . Data 2. Model 1 E s t i m a t i o n R e s u l t s 3. Model 2 E s t i m a t i o n R e s u l t s 4. E l a s t i c i t y Estimates 5. Conclusions V. S i m u l a t i o n R e s u l t s 1. Previous S t u d i e s of UI 2. P o l i c y Changes Simulated 3. S i m u l a t i o n Methodology 4. M o d e l l i n g UI Reform 5. P r e d i c t e d Labour-Supply Responses to UI 6.  Conclusions  V I . Welfare E v a l u a t i o n  46 46 50 59 64 69 69 74 84 88 98  100 101 109 113 119 Reform 124 132 135  vi  1. Methodology 135 2. Methodology 3. Methodology 150  for the U t i l i t a r i a n E v a l u a t i o n s  ..  for the Rawlsian E v a l u a t i o n s . for the E n t i t l e m e n t E v a l u a t i o n s  146 ..  4. Welfare E v a l u a t i o n R e s u l t s VII.  Conclusions  154 162  Bibliography  172  Appendix 1 Appendix 2  193 195  Appendix 3  198  vii  List  of  Tables  Table 4 . 1 :  B a s i c Data Averages  199  Table 4.2:  O c c u p a t i o n a l Averages  200  Table 4.3:  P r o v i n c i a l Averages  201  Table 4.4:  D i s t r i b u t i o n of Weeks Across Budget Segments  Table 4.5: Men  Mean V a r i a b l e  Values. Single  Women and  .202  Single . . .203  Table 4.6:  Mean V a r i a b l e V a l u e s . Couples  Table 4.7:  Model  1 Parameter E s t i m a t e s .  S i n g l e Women.  Table 4.8:  Model  1 Parameter E s t i m a t e s .  S i n g l e Men  206  Table 4.9:  Model  1 Parameter E s t i m a t e s .  Couples  207  Table 4.10:  204 ...205  Model 2 Parameter Estimates  208  Table 4.11: P r o b a b i l i t i e s of C o n s t r a i n t in Unemployment. S i n g l e Women  209  Table 4.12: P r o b a b i l i t i e s of C o n s t r a i n t in Unemployment. S i n g l e Men  210  Table 4.13:  P r o b a b i l i t i e s of C o n s t r a i n t . Couples  211  Table 4.14:  Model  Table  4.15: Women  1 Labour-Supply E l a s t i c i t i e s .  Model  1  Labour-Supply  Single  Elasticities.  Men. 212 Single 213  Table 4.16: Model 1 Labour-Supply E l a s t i c i t i e s . Men. Wives F u l l - t i m e Workers  Married  Table 4.17: Model 1 Labour-Supply E l a s t i c i t i e s . Men. Wives P a r t - t i m e Workers  Married  Table 4.18: Model 1 Compensated E l a s t i c i t i e s . Men. Wives F u l l - t i m e Workers  Married  Table 4.19: Model 1 Compensated E l a s t i c i t i e s . Men. Wives P a r t - t i m e Workers  Married  viii  214 215 216 217  Table 4.20: Model 1 Labour-Supply E l a s t i c i t i e s . Women. Husbands Seasonal Workers  Married  Table 4.21: Model 1 Labour-Supply E l a s t i c i t i e s . Women. Husbands C y c l i c a l Workers  Married  218 219  Table 4.22: Model 1 Labour-Supply E l a s t i c i t i e s . Married Women. Husbands N e i t h e r Seasonal nor C y c l i c a l Workers. 220 Table 4.23: Model 1 Compensated E l a s t i c i t i e s . Women. Husbands Seasonal Workers  Married  Table 4.24: Model 1 Compensated E l a s t i c i t i e s . Women. Husbands C y c l i c a l Workers  Married  221 222  Table 4.25: Model 1 Compensated E l a s t i c i t i e s . Married Women. Husbands N e i t h e r Seasonal nor C y c l i c a l Workers. 223 Table 4.26:  Model 2 Labour-Supply E l a s t i c i t i e s  Table 4.27:  Model 2 Labour-Supply E l a s t i c i t i e s .  224 Couples.  Rationed and Unrationed Table 5.1:  Model 1.  .225  Labour-Supply Responses. S i n g l e Men.  226  Table 5.2: Model 1. Labour-Supply Responses. S i n g l e Men. Unemployed P o p u l a t i o n 227 Table 5.3: Model 1. Labour-Supply Responses. S i n g l e Women. 228 Table 5.4: Model 1. Women. Unemployed Table 5.5:  Model  1.  Labour-Supply Population  Labour-Supply  Table 5.6: Model 1. Labour-Supply Men. Unemployed Population Table 5.7:  Model 1.  Model 2.  Single 229  Responses. M a r r i e d Responses.  Men. 230  Married 231  Labour-Supply Responses. M a r r i e d  Table 5.8: Model 1. Labour-Supply Women. Unemployed P o p u l a t i o n Table 5.9:  Responses.  Responses.  Women. 232  Married  Labour-Supply Responses. S i n g l e Men.  233 234  Table 5.10: Model 2. Labour-Supply Men. Unemployed P o p u l a t i o n Table 5.11:  Model 2.  Responses.  235  Labour-Supply Responses. S i n g l e  Table 5.12: Model 2. Labour-Supply Women. Unemployed p o p u l a t i o n Table 5.13:  Model 2.  Responses.  Model 2.  6.1a: Cut-offs  Single  Labour-Supply Responses. Married  Men. 238  Married 239  Labour-Supply Responses. M a r r i e d Women. 240  Table 5.16: Model 2. Labour-Supply Responses. Women. Unemployed P o p u l a t i o n Table  Women. 236 237  Table 5.14: Model 2. Labour-Supply Responses. Men. Unemployed P o p u l a t i o n Table 5.15:  Single  Equivalence  Scales  Implicit  in  Married 241 Low-income 242  Table 6.1b:  Model 1 U t i l i t y  Scaling  Factors,  s(A)  243  Table 6.1c:  Model 2 U t i l i t y  Scaling  Factors,  s(A)  244  Table 6.2:  U t i l i t a r i a n Welfare  E v a l u a t i o n R e s u l t s . Model  1. 245  Table 6.3:  U t i l i t a r i a n Welfare  Evaluation Results/Model  2. 246  Table 6.4:  Rawlsian Welfare E v a l u a t i o n  R e s u l t s . Model 1.  247  Table 6.5:  Rawlsian Welfare  R e s u l t s . Model 2.  248  Table 6.6:  E n t i t l e m e n t Welfare  Evaluation  Evaluation Results  x  249  L i s t of  Figures  Figure 2.1.  The Budget C o n s t r a i n t for A l b e r t a  19  Figure 2.2.  The Budget C o n s t r a i n t for Newfoundland  19  xi  ACKNOWLEDGEMENTS  I would l i k e  to thank my t h e s i s committee,  T e r r y Wales and encouragement.  Steve Jones, S p e c i a l thanks  L a r s Osberg, Jon Kesselman  many  years.  family and  are a l s o  comments.  Darren for  Donaldson,  t h e i r advice due C r a i g  and the people  much p a t i e n c e and many h e l p f u l to thank my  for a l l of  David  Riddell,  i n ' C wing Above a l l ,  and  for  I  want  u n f a i l i n g support  over  I. INTRODUCTION  In t h i s d i s s e r t a t i o n , changes  to  the  I conduct an  Canadian  (Ul) which  pays  efficiency  dimensions  s t u d i e s focus on e f f i c i e n c y However, e v a l u a t i o n s such as the Pareto of a l t e r n a t i v e s .  policy  both  these  the  programme  equity  changes.  and  Most  the  economic  and a v o i d d i s c u s s i o n s  of  equity.  on an e f f i c i e n c y  criterion  p r i n c i p l e can y i e l d incomplete  rankings  The p r i n c i p l e i s  changes  silent,  for example,  at the expense of another,  can  improvement c r i t e r i o n , basic r a t i o n a l i t y  to  based s o l e l y  one i n d i v i d u a l b e n e f i t s few  proposed  Unemployment-Insurance  attention of  e v a l u a t i o n of  avoid.  while  (The  complete,  satisfy of  The i n t r o d u c t i o n of an e q u i t y c r i t e r i o n , while r e s o l v i n g  the  preference).)  problem of attitude  (transitivity,  to  Pareto  asymmetry  strict  properties  a dilemma  potential fails  when  f  incompleteness,  toward i n e q u a l i t y .  r e q u i r e s the choice of a I  suggest that t h i s  specific  difficulty  fA f e a s i b l e a l t e r n a t i v e A i s Pareto e f f i c i e n t i f there i s no other f e a s i b l e a l t e r n a t i v e A' such that everyone p r e f e r s A' to A (or such that everyone but i n d i v i d u a l X i s indifferent between A and A' and X p r e f e r s A to A ' ) . The Pareto p r i n c i p l e says that a l t e r n a t i v e A i s s o c i a l l y p r e f e r r e d to a l t e r n a t i v e A' i f no-one i s worse o f f i n A than i n A' and at l e a s t one individual is better o f f . The p o t e n t i a l Pareto improvement c r i t e r i o n says that a l t e r n a t i v e A is socially p r e f e r r e d to a l t e r n a t i v e A' i f i n d i v i d u a l s who are better o f f in A can p o t e n t i a l l y compensate i n d i v i d u a l s who are worse o f f and s t i l l p r e f e r A to A ' . 1  Introduction / 2 can be  overcome  through  the  adoption  of  an  "ethically  f l e x i b l e " ! approach. That i s ,  while value judgements  course,  the  proposed  required  to  policy  change,  remain ' o b j e c t i v e ' distributional sensitivity  by  analysis  equity  by,  over  feasibility,  alternative  flexible"  attention  will  first  be  mean  d i s t r i b u t i o n of  individual u t i l i t i e s ) ; John Rawls'  of  w i l l be order  in  r  a  positions  the  to  "entitlement  between the d i s t r i b u t i o n of  the d i s t r i b u t i o n of  three  spirit over  of the  (a mean  of  i n d i v i d u a l incomes,  be  theory"  reasons  to  focus a t t e n t i o n  third will  will  the second w i l l be i n  "theory of j u s t i c e "  poverty l i n e  group);  the  defined  order r d e f i n e d over the d i s t r i b u t i o n of  distance  ethical  restricted  (a  Robert N o z i c k ' s  of  conducting  approach. However, for  Utilitarianism  'worst-off  a range  to Canadian UI p o l i c y  The  the  a  nevertheless  incorporating  ethical positions:  censored at  can  effectively,  of proposed changes  the s p i r i t of  of  dimensions  evaluation  explicitly  of  imposing one.  adopt an " e t h i c a l l y of  an  judgements;  rather than j u s t  My a n a l y s i s  assess  are,  i n the (a  on  spirit  measure  of  the of the  i n d i v i d u a l b e n e f i t s and  individual costs associated  with the  UI  fThe term " e t h i c a l l y f l e x i b l e " i s used in the l i t e r a t u r e on measures of poverty and i n e q u a l i t y . An index i s s a i d to be "ethically flexible" i f i t is c o n s i s t e n t with a v a r i e t y of s o c i a l welfare functions (Blackorby and Donaldson, 1980; C h a k r a v a r t y , 1983).  Introduction / 3 programme). U t i l i t a r i a n i s m l o g i c a l choices approaches  because  most  they  frequently  because they take Nozick's  and  the Rawlsian are  the  discussed  p o l a r p o s i t i o n s on  outlook  is  by  interesting  suitably  perspective.  The  c h a r a c t e r i z e d by a s t i l l  unsettled  principles  or  according  efficiency/equity  Unemployment Insurance 1940.  was  Record unemployment  UI  individual  is  first  with l a z i n e s s .  Recognition  that the average  own,  consequently without to the  implementation  find  A  basic  is  of the  not  himself  worker, a  UI scheme  without for h i s  in  1930s  synonymous  this period, could,  means of p r o v i d i n g of a  the  in Canada  d u r i n g the d e p r e s s i o n  with a dependent f a m i l y d u r i n g  is  insurance  need.  established  unemployment  his  Canada  clear.  people that  of  in  debate over whether  had convinced  no f a u l t  ethically  a c c o r d i n g to s o c i a l  to  trade-off  of  very  approaches  approached from an  history  programme should be designed  equity.  p o s i t i o n s are  correspondingly d i f f e r e n t  UI reform i s a t o p i c flexible  i s s u e of  and  rather  These e t h i c a l  evaluation.  economists  is procedural  than e n d - s t a t e in n a t u r e .  to p o l i c y  philosophical  unlike  theory,  and r e q u i r e  are  because,  U t i l i t a r i a n i s m and Rawls'  different  two  the  it  approach  a  man  through job  and  family  led  designed to  provide  Introduction / 4 income  protection  for  primary  purpose of the UI Act of social  workers.  The  fundamental  1940 was "to promote economic  and  s e c u r i t y of Canadians by s u p p o r t i n g workers from  one  job to the next" groups such  (Dingledine,  as seasonal  o r i g i n a l UI A c t .  r i g h t to  workers were  UI was  insurance programme; benefits  workers were by paying  of  premiums.  of  and only 42 percent  to be e l i g i b l e  the minimum  benefits  equal  to  Workers 34  without  percent of  In 1949,  a any  jobs  qualifying  A worker was before  d u r a t i o n of one y e a r .  much l e s s generous dependants  their  income while workers with dependants to 40 percent of  for  employed for f i v e years  to the maximum b e n e f i t  case.  in  of the labour force had  income replacement was  c u r r e n t l y the  the  eligibility  i n s u r a b l e employment  satisfying  r e q u i r e d to have been f u l l y  Finally,  social  'earn'  Thus,  c o n d i t i o n s p r o v i d e d only a minimum of b e n e f i t s .  he was e n t i t l e d  the  Workers were r e q u i r e d to have had  t h i r t y weeks  deemed ' i n s u r a b l e . ' Then,  by  strictly a  supposed to  104-week q u a l i f y i n g p e r i o d i n order benefits,  unemployed  not covered  intended to be  c o n d i t i o n s were s t r i n g e n t . a minimum  1981). C h r o n i c a l l y  previous  than  is  received insured  received benefits  equal  i n s u r e d income.  the unemployment r a t e i n c r e a s e d s h a r p l y and many of  the unemployed  were not  given the r e s t r i c t i o n s  eligible  of the  to  collect  UI  benefits,  1940 A c t . Hence, i n 1950,  an  Introduction / 5 amendment was passed to p r o v i d e 'supplementary b e n e f i t s '  for  exhaustees and for those not  but  q u a l i f y i n g f o r r e g u l a r UI  having made at l e a s t ninety d a i l y c o n t r i b u t i o n s d u r i n g fiscal  year. Benefits  were p a i d at 80 percent of the r e g u l a r  rate and financed p a r t i a l l y partially  through  constituted  a  UI  d i r e c t i o n was taken seasonally  through i n c r e a s e d premiums  general  significant  'needs-oriented'  revenue. step  programme.  in  This  the  was  self-employed  in  extended  but growing series  of  eventually 1970.  dissatisfaction reviews  culminating  the in  on  the  favoured a r e t u r n grounds  that  recommended  programme designed that  this  that to  UI" be  a  Gill  left  with a  include rather  change.  1960s,  single  a  to  Report  to s t r i c t  a  same  1970s," t a b l e d  handle f r i c t i o n a l  be c o - o r d i n a t e d  to  d u r i n g the  fundamentally unable to cope with a l l types of It was  the  programme l e d the  the White Paper, "UI i n the  These r e p o r t s  principles  legislation with  of  fishermen. Need  than earned r i g h t to b e n e f i t s again motivated the  made to UI  but  amendment  direction  Another step  when coverage  unemployed,  Few changes were  that  a and  June,  insurance  programme  is  unemployment.  social  insurance  unemployment  general a s s i s t a n c e  and plan  based on a needs t e s t to d e a l with s t r u c t u r a l unemployment.  In 1971,  ignoring  most of the  recommendations of the  1970  Introduction / 6 White Paper, a benefits  new UI Act  was passed.  Under  were made payable i n three phases.  two phases, old act.  entitlement  act,  During the  first  depended on work r e c o r d as under the  In the t h i r d phase,  from s o c i a l  the new  however,  the programme departed  insurance p r i n c i p l e s . B e n e f i t s were to be  on the r e g i o n a l unemployment rate and financed from revenue. Hence, the the  'supplementary b e n e f i t s '  the p r o v i s i o n  retirement b e n e f i t s initial  broadened  the  sickness,  programme.  maternity  scope of  UI  from  and its  focus on primary workers.  With the nearly  of s p e c i a l  general  i n t r o d u c e d with  1950 amendment were made p a r t of the r e g u l a r  Finally,  based  1971  reform of the  universal  covered).  This  (96  UI programme, coverage  percent  broader  base  intended to allow an i n c r e a s e to 66 2/3 percent in b e n e f i t  of for  i n the  the  labour  force  was  collection  was  income-replacement  rate  premium  for those without dependants;  generosity  became  was b e l i e v e d necessary  an  increase  as a r e s u l t  a survey of n o n - d e f e r r a b l e expenses r e l a t i v e to income. individuals  with  dependants  and  with  average  earnings l e s s than o n e - t h i r d of maximum i n s u r a b l e the b e n e f i t - r e p l a c e m e n t the extended-benefit these changes. lowered so  a  earnings, for  The idea of need again motivated  At the same time,  that  For  insured  rate was i n c r e a s e d to 75 percent  phase.  of  minimum of  entrance requirements eight  weeks  of  were  insurable  Introduction / 7 employment e n t i t l e d a worker to r e g u l a r b e n e f i t s . the work  disincentive  these changes, relief the  effects  benefits  were  a n t i c i p a t e d as made  to upper and middle-income  first  time,  contributions  taxable.  To o f f - s e t  a result And,  of  to  give  groups covered by UI  for  to  tax  UI  were  made  deductible.  I n c r e a s i n g l y higher 1970s, the  rates  of unemployment  i n combination with the  throughout  the  more generous p r o v i s i o n s  of  1971 A c t , l e d the programme i n t o u n a n t i c i p a t e d f i n a n c i a l  difficulties.  From 1970 to  $730 m i l l i o n  to $3.3  t o t a l programme cost  1975,  the cost of UI climbed from  billion. rose  The government's  from  22 to 51  share  percent over  of the  same p e r i o d . N a t u r a l l y , such huge expenditure  increases  to concern about the g e n e r o s i t y  impact on work  incentives.  A s e r i e s of  toward retrenchment, to that  In 1976,  amendments d u r i n g the  thus moving  taken d u r i n g the  the  special  of UI and i t s  1970s  i n the d i r e c t i o n  led  tended opposite  1950s.  75 percent replacement  rate for workers  with dependants was e l i m i n a t e d . In 1977,  the b a s i c  entrance  requirement was  eight  fourteen  made  variable -  from  to  weeks, depending on the r e g i o n a l unemployment r a t e . repeat c l a i m a n t s and new e n t r a n t s r e q u i r e d to demonstrate  In  1979,  to the labour f o r c e  were  twenty weeks of  i n s u r a b l e employment  Introduction / 8 i n order to q u a l i f y  for b e n e f i t s .  were reduced to 60 percent  Of c o u r s e ,  for a l l  these changes have  1981 White Paper, "UI i n the of 1.  Income-replacement  rates  claimants.  not r e s o l v e d the debate. 1980s," p r o v i d e d an  The  assessment  the problems of U I : The  programme  a d m i n i s t e r so  is  too  that  complex  under-  to  understand  and over-payments  and  are  very  common. 2.  Costs are  too h i g h ,  methods of  cost r e d u c t i o n  V a r i a b l e entrance people  unemployment  most attempted  live  suggested  in  inequities.  for example,  regions w i l l  they  or  involve serious  requirements,  in different  merely because  3.  but  be t r e a t e d regions  mean  that  differently  with  different  rates.  Work i n c e n t i v e  problems  continue  to  exist.  There  is  Inquiry  on  general p u b l i c concern over programme abuse. Again,  in 1986,  the report  of the Commission of  Unemployment Insurance  (the Forget  Commission)  maintained  that Canadians s t r o n g l y  support Unemployment Insurance as  a  s h o r t - t e r m income s e c u r i t y programme for those i n v o l u n t a r i l y out of work, country  but there  about  security,'  the  is considerable meaning  'involuntarily'  of and  complaints were summarized (p.33)  debate a c r o s s  'short-term,' 'out as:  of  work.'  the  'income Major  Introduction / 9 1.  The program i s  unfair.  2.  The program has the wrong  3.  It's  4.  The government  5.  The program i s a d m i n i s t e r e d  incentives.  not an insurance programme anymore. runs the show. inefficiently  and  delivered  insensitively.  Clearly,  the b a s i c dilemma i s  of m a i n t a i n i n g  an  unresolved.  insurance  programme  strong l a b o u r - f o r c e attachment of p r o v i d i n g r e l i e f c o m p l i c a t e d by  to those  continuing  be  How can the for  goal  workers  with  r e c o n c i l e d with the  goal  in need? The i s s u e i s high r a t e s  of  further  unemployment  Canada and programme c o s t s which i n 1986 have climbed  in  above  $12 b i l l i o n a n n u a l l y .  In summary, t h e r e f o r e , takes  account  of  an i n v e s t i g a t i o n  both  equity  a p p r o p r i a t e for a number of 1.  The h i s t o r y of  and  UI in Canada  insurance'  i s marked by  distort  by  UI  impede  labour-leisure  a series  of  strict  times in  the  philosophy.  There e x i s t s general concern that generated  seems  d i r e c t i o n of a  philosophy and at other  d i r e c t i o n of a 'needs-based' 2.  efficiency  reasons:  reforms tending sometimes in the 'social  of Canadian UI which  the  incentive  labour-market  choices.  effects  adjustment  and  I n t r o d u c t i o n / 10 3.  High r a t e s of unemployment  have put a f i n a n c i a l  on the programme and made i t a target 4.  for  reform.  High r a t e s of unemployment mean high r a t e s on UI  so that  affect  large  reductions  of  i n programme  numbers  of  strain  dependency  spending  people.  will  Distributional  i m p l i c a t i o n s of a l t e r n a t i v e c o s t - r e d u c i n g p r o p o s a l s significant  The r e p o r t s of and  and thus of  Prospects  Commission) and the Insurance  interest.  the Royal Commission  Development  for  on the Economic  Canada  Commission of  (the Forget Commission)  (the  Inquiry on  thesis.  the set  of p o t e n t i a l  Individual proposals,  reforms  with  if  that  they  improve  position.  i m p l i c a t i o n need not  Unemployment proposals  These  proposals  evaluated  to a p a r t i c u l a r  a measure  Notice,  of welfare  to  consistent a large  be  however,  h o l d : a government  interpreted  as  having  with that p o s i t i o n . UI i s ,  number of  policies  this  that  the  choosing a  affecting  social  after  ethical  reverse policy position  preferences  a l l , only one of  the d i s t r i b u t i o n  income i n Canada. A government may choose to change UI i n manner which appears  consistent  with  are  consistent  change p r e f e r r e d a c c o r d i n g to a p a r t i c u l a r e t h i c a l i s not  in  or packages of p r o p o s a l s ,  deemed w e l f a r e - i m p r o v i n g a c c o r d i n g position  Union  Macdonald  have both made  for major reform of the Canadian UI system. constitute  are  one e t h i c a l  of a  position  Introduction / 11 while  redistributing  policies  through  i n a manner c o n s i s t e n t  position.  S o c i a l preferences  assessment of the However, s i n c e make  income  any  i s not  assessment  government  implied  of government  i n t e n t i o n of  the  by i t s  different  c o u l d only be i n f e r r e d from  the  of  tax/transfer  with an e n t i r e l y  o v e r a l l incidence  it  other  ethical  an  policy.  this analysis position  policy choices,  this  to  of is  the not  a  problem.  A v a l i d q u e s t i o n to ask, i s any  reason  to be  i m p l i c a t i o n s of any p o i n t  on the other hand, i s whether  concerned  about  i n d i v i d u a l p o l i c y changes.  in analysing  UI i n  particular ethical position  a manner  reasons)  combination  with  a  compensated for the need  to  determine  if  it  policies  in  preferences, if  a its  want to  to  some  the  be  i n t o the  manner  there  with  a  inequitable (perhapsfor  implemented  other  distributional To assess  is  consistent  policy  i n e q u i t y ? I would argue that  there  in which is  consequences  a of  whether a  particular  complete package of  government  which  is  consistent  d i s t r i b u t i o n a l impact  a government chooses  will  That i s ,  be p r e f e r r e d could  change  i n d i v i d u a l p o l i c y changes. p o l i c y change f i t s  distributional  i f a change which i s  a c c o r d i n g to t h i s p o s i t i o n might efficiency  the  there  social  must be known.  an ' i n e q u i t a b l e '  know s p e c i f i c a l l y which  with  Even  p o l i c y change,  inequities  are  it  being  Introduction / generated  in  second-best inequities effects  to make  world,  policy  are u n l i k e l y to  themselves.  inequities, since  order  it  Since  corrections. changes  enacted  to  be without a d d i t i o n a l it  i s not  progressivity)  for  to  generate  to  equity measures  give an  overall  policies  (Blackorby and Donaldson, 1984), policy  measure of  the  a  incentive  costless  individual policies  in  remedy  we might worry about i n t r o d u c i n g them.  is possible  to d e v i s e  Moreover,  12  remove Finally,  (e.g.,  of  which aggregate  to  impact of  a  package  i t may be  e v a l u a t i o n measures which  of  possible  have a  similar  property.  An e t h i c a l l y  flexible  Canadian UI system  analysis  of p o t e n t i a l changes  r e q u i r e s the development  to  the  of a model  of  household behaviour which takes account of the e x i s t e n c e  of  unemployment and unemployment i n s u r a n c e . E x i s t i n g s t u d i e s of the  impact of  search (Ham (Fortin,  UI on and  1984)  behaviour t y p i c a l l y  Rea,  1985)  r e s u l t of p e r i o d s of  some  of  choices.  p a r t of observed  labour  recession, a result  supply-side  some  of demand-side  choices.  This  the r e s u l t of  However,  it  Particularly  individuals  is  may  be  seems  very  the  during observed  constraints a  of  supply  unemployment i s not  utility-maximizing choices.  unemployed as than  models  and assume that unemployment i s  individual utility-maximizing l i k e l y that  or  employ models  rather  different  Introduction / interpretation  of the basic  t r a d i t i o n a l l y used in y i e l d very d i f f e r e n t  s t u d i e s of predictions  l a b o u r - s u p p l y behaviour: by c h o i c e , i n UI  if  U I , and i t about  the  than that  is l i k e l y  to  impact of UI  on  i n d i v i d u a l s are not  unemployed  they are u n l i k e l y to be as responsive to  as t r a d i t i o n a l  assumptions  about  generated from the labour  nature of unemployment  market  are  models  have p r e d i c t e d .  whether  unemployment  demand side critical  or the for  changes  Since is  supply  basic  primarily s i d e of  predicting  the  behavioural  responses to U I , they are a l s o c r i t i c a l for an e v a l u a t i o n proposed UI models of the  reform. Thus,  I  consider  labour supply: Model  two  very  is  the  1 i s a t r a d i t i o n a l model  result  of  of  different  l a b o u r - s u p p l y t r a d i t i o n which assumes that a l l  unemployment  13  in  observed  unconstrained  u t i l i t y - m a x i m i z i n g c h o i c e s ; Model 2 i s a l a b o u r - s u p p l y model which departs  from t r a d i t i o n by i n t r o d u c i n g the  that some observed unemployment  is  the  result  possibility  of  demand-side  constraints.  Chapters Two and Three of the t h e s i s develop, Model 2,  the  1,  the unconstrained model of c o n s t r a i n e d model  presents estimation  of  labour supply,  labour s u p p l y .  simulation  and Model  Chapter  r e s u l t s for the two models.  d i s c u s s e s the Macdonald and Forget p r o p o s a l s of UI and the  respectively,  Four  Chapter F i v e  for the  of b e h a v i o u r a l responses to  reform these  Introduction / p r o p o s a l s using the estimated welfare Rawls' and,  models.  Chapter Six  e v a l u a t i o n measures c o n s i s t e n t with theory  finally,  conduct the  of j u s t i c e uses  estimation  ethically  p r o v i d e s a summary of  and N o z i c k ' s  flexible  and  the p r i n c i p a l  develops  Utilitarianism,  entitlement  simulation  evaluation. findings.  14  theory  results  Chapter  to  Seven  II.  In  THE UNCONSTRAINED LABOUR-SUPPLY MODEL  this chapter,  household  I develop a  behaviour  tradition.  I  (Model  first  thus,  e v a l u a t i o n of  choice  parameters  labour-supply  proposed  UI  a  of  Model  1.  form  for  demographic form  and  This  'taste* the  analysis;  for  an the  involves  the the  within a  the  stochastic  with a d i s c u s s i o n  of  problems.  The B a s i c M o d e l o f H o u s e h o l d  which  to UI and,  discuss  proxies of  the  budget  estimation,  choice  I conclude Chapter Two  I  Behaviour  Labour-market behaviour depends upon a host of of  of  model u s e f u l  reforms. Then,  functional  functional  specification.  1.  the  of  labour-supply  i n c o r p o r a t e d i n household  implementation  of  estimation  the  the b a s i c  i n c o r p o r a t i o n of chosen  how  in  in order to make behaviour responsive  to make  empirical  1)  outline  Canadian UI programme are constraints  b a s i c unconstrained model  fall  outside  even the set  the  t r a d i t i o n a l scope  of p u r e l y 'economic'  m u l t i - d i m e n s i o n a l . Y e t , the to UI r e q u i r e s such a model, made; namely,  a model of a number of that  factors, of  economic  determinants  proposed e v a l u a t i o n of b e h a v i o u r a l response.  is 15  static  is  changes  To  s i m p l i f y i n g assumptions  the world  many  obtain  must  and c e r t a i n ,  be that  The U n c o n s t r a i n e d Labour-Supply Model / i n d i v i d u a l s have chosen  region of  residence,  o c c u p a t i o n , and  s i z e of f a m i l y and that  households  choose weeks of  and  composite  commodity  consumption  of  a  maximize u t i l i t y s u b j e c t  to a s i n g l e  i n c o r p o r a t e s the parameters Thus, members decisions  of  about  Intra-familial are  assumed  outside  in  Canadian UI  a household  are  assumed to  consumption  of  experience  r e g i o n of the  these c h o i c e s  programme. make  joint goods.  i g n o r e d ; a l l household  members  the  leisure  same  level  selfishly  of  with  as  residence  welfare.  respect  a v a i l a b i l i t y of given  ignores  and occupation may UI  benefits,  to  worked  behavioural  each  week  responses  are  similarly  modelled  here  are  be  treating  important channels  which UI can i n f l u e n c e b e h a v i o u r . P o s s i b i l i t i e s  for  through varying  ignored.  The  restricted  to  i n weeks of labour s u p p l y .  The unconstrained assumes  to  individuals.  i n f l u e n c e d by  changes  order  and  household behaves  Since c h o i c e of  hours  leisure  budget c o n s t r a i n t which  the  allocation is to  However, the  of  16  that  unemployment households  model of  observed reflect  household behaviour  weeks  of  utility-maximizing  form optimal plans and,  c a r r y them out  both  (random ' e r r o r s i n  (Model  1)  employment  and  choices;  that  on average,  are able  o p t i m i z a t i o n ' may  to  cause  The Unconstrained Labour-Supply Model / deviations it  is  from d e s i r e d p l a n s ) .  assumed  that  Given  households  the e x i s t e n c e of  plan  annual  17 UI,  patterns  of  employment and unemployment for working members which enable them to earn e n t i t l e m e n t collect  earned  Of c o u r s e ,  to UI and then to stop working  benefits.f  the n o t i o n  of a  f r e e l y chosen  p a t t e r n of employment and unemployment for a  number  of  reasons.  First,  i n d i v i d u a l s plan at a l l times e i t h e r unemployed and  receiving  unemployment face  a  file (see  period  Model  1  annual  unrealistic  assumes  that  to be employed or to be  UI b e n e f i t s  (except the  fact  during that  the  people  c l a i m s for UI when faced with a s p e l l Glenday and of  v o l u n t a r i l y leave  optimal  is highly  two-week w a i t i n g p e r i o d ) . T h i s ignores do not always  and  q u i t a job each year  1982). Second,  disqualification  their  r a t e s of unemployment,  Alam,  jobs.  Third,  people cannot and f i n d a new  the d e s i r e d time and wage the  of  workers  from  UI  if  given  today's  they high  r a t i o n a l l y expect  to  job or be r e - h i r e d  at  following  year.  However, there are cases in which the model of annual  plans  seems to provide an a p p r o p r i a t e d e s c r i p t i o n of labour-market behaviour.  It  i s commonly  e x i s t e n c e of UI allows  alleged,  for  example,  that  fishermen or c o n s t r u c t i o n workers  the to  tFor many p e o p l e , an optimal annual p a t t e r n w i l l c o n s i s t of f i f t y - t w o weeks of employment with no weeks of unemployment.  The Unconstrained Labour-Supply Model / plan annual p a t t e r n s  of  is  idea in the  support for t h i s  employment and unemployment. study  (1982) which a n a l y s e s a 10 percent  of  t h i s l o n g i t u d i n a l data  Alam f i n d some evidence that do  follow  percent  of  patterns their  of  employment  l e s s than s i x use U I , the  and  sample had average  average months.  In  Glenday  and  for  unemployment:  p e r i o d s of  s i x months;  p e r i o d s of Thus,  1979.  i n d i v i d u a l s using the UI system  (1974-1979) which were l e s s than the sample had  set,  Alam  individuals  who f i l e d a c l a i m for UI d u r i n g the p e r i o d 1974 to their analysis  There  by Glenday and  sample of a l l  18  35  employment  65 percent  unemployment which  of were  i n d i v i d u a l s who  regularly  idea of annual employment/unemployment  patterns  may have some v a l i d i t y .  Finally,  though,  the  choice  of an  household p l a n n i n g can  be j u s t i f i e d  The assumption  annual  unemployment  of  an  annual  on pragmatic  pattern  i s a s i m p l i f i c a t i o n made  l i m i t a t i o n of a s i n g l e c r o s s - s e c t i o n  of  follow  unemployment,  then,  an  annual other  employment p e r i o d w i l l match and can be used to e s t a b l i s h  grounds. and  in concession to  the  of data which g i v e s  pattern things  for  employment  i n f o r m a t i o n concerning past work r e c o r d s . assumed to  framework  If of  i n d i v i d u a l s are employment  equal,  l a s t year's  no  this  employment  e n t i t l e m e n t to U I .  and  year's period  The 2.  Incorporation  Unconstrained Labour-Supply Model /  o f UI i n Budget  Constraints  Within the framework of the e q u i l i b r i u m p l a n , impact on budget c o n s t r a i n t s and regions.  F i g u r e 2.1  illustrates  a single  individual  living  which the data were e q u i v a l e n t budget Newfoundland. two p r o v i n c e s areas.  UI has a major  impact v a r i e s  across  the budget c o n s t r a i n t  in Alberta  collected);  ( i n 1981,  F i g u r e 2.2  facing  the year  examples of  an i n d i v i d u a l  Both budget c o n s t r a i n t s  low  and  in  illustrates  high  the  living  (Budget c o n s t r a i n t s are i l l u s t r a t e d for  annual r e p e t i t i o n  in  these  unemployment  are drawn c o n t i n g e n t  on  the  assumption.)  I n d i v i d u a l s are r e q u i r e d minimum number of 2.2,  this  c o n s t r a i n t for  as  19  ( i n 1981,  as c u r r e n t l y ) to work  weeks, l a b e l l e d  to be e l i g i b l e  MIN in  for UI b e n e f i t s .  r e g i o n a l unemployment r a t e  and with  a  F i g u r e s 2.1  and  T h i s v a r i e s with  the  labour-force status  new and r e - e n t r a n t s must have longer work r e c o r d s .  (However,  s i n c e new and r e - e n t r a n t s have not yet e s t a b l i s h e d  patterns  of  by  employment,  model.) are  their  behaviour  i s not  captured  Those working fewer than the minimum r e q u i r e d  u n a f f e c t e d by the UI programme except to the extent  i t p r o v i d e s an i n c e n t i v e to i n c r e a s e labour supply i n to q u a l i f y  (or to the  extent that they must pay  this weeks that order  premiums).  Net wage rates are thus given by the slope of the l i n e AB i n  The Unconstrained Labour-Supply Model /  Figure 2.1.  The Budget C o n s t r a i n t for A l b e r t a .  Those i n d i v i d u a l s working more weeks earn one week of (for  the  first  operates as constraint  the  week of employment  than the minimum  UI e n t i t l e m e n t  twenty-five  a wage (see  20  weeks).  subsidy over  is  for each week Thus,  UI  a portion  segment ' S u b s i d y ' compensated  and an e x t r a week of UI e n t i t l e m e n t .  qualifying worked  effectively  of  the  budget  in F i g u r e 2 . 1 ) ;  with both a wage Individuals  the minimum work requirement are a l s o e l i g i b l e  each payment  satisfying  for weeks  of  The U n c o n s t r a i n e d Labour-Supply Model / 21  F i g u r e 2 . 2 . The Budget C o n s t r a i n t for Newfoundland,  WEEKS OF LEISURE  UI b e n e f i t s  based on the  r e g i o n a l unemployment r a t e  rather  than on i n d i v i d u a l work r e c o r d s . Adding 'earned b e n e f i t s ' 'regionally-extended benefits'  means that  e v e n t u a l l y accumulate enough b e n e f i t 'take the r e s t  of the  year o f f '  and  individuals  weeks to enable collect  UI  this  is possible  (labelled  can  them to  (assuming  they are not d i s q u a l i f i e d for q u i t t i n g ) . Working beyond point at which  to  'MAX' i n  the  Figure  2 . 1 ) means that p o t e n t i a l weeks of UI are being given up. In a  model  employment  where to  individuals gain  choose  eligibility  annual for  UI  patterns  of  followed  by  The  Unconstrained Labour-Supply Model /  unemployment with UI compensation, an  i m p l i c i t tax on wages for  work i m p l i c i t l y ' c o s t s '  2.1  and 2 . 2 ) ;  since a  are  represents  to  net  receive  wage  is  benefits.  rates  in  week  benefit.  weeks are u n a f f e c t e d  two-week w a i t i n g p e r i o d  eligible  (see  each e x t r a  one week of UI  I n d i v i d u a l s working more than f i f t y UI  imposes  weeks of work beyond MAX  the segment 'Tax' i n F i g u r e s of  the UI programme  22  such  imposed before The  line  cases.  AB  (This  by they  again section  follows Rea (1977)).  3.  Linearization  It  is  of the Non-linear  c l e a r that  budget c o n s t r a i n t s income-tax people  system.f  UI programme  already For  stages to t h i s  simplicity,  the  it  a  is  progressive assumed  that  which are e x t e n s i o n s of  which they are  constraint  progressive  Canadian income-tax system. b a s i c net wage, represented fMany f e a t u r e s ignored.  by  household  observed. There are  the two  l i n e a r i z a t i o n process.  the budget  r e s u l t of  Constraint  complicates  complicated  face budget c o n s t r a i n t s  l i n e a r segments on  First,  the  Budget  of  the  is piece-wise marginal tax  brackets  For e s t i m a t i o n , by the l i n e  Canadian  segmented as  the  of  the  individual's  AB i n F i g u r e s  tax-transfer  a  system  2.1 are  The U n c o n s t r a i n e d Labour-Supply Model / and 2 . 2 ,  is  calculated  marginal tax  as the  segment on which  linear  extension  of  he i s observed to be  23 the  located  with non-labour income a d j u s t e d a p p r o p r i a t e l y . To i l l u s t r a t e this process, the  the household budget c o n s t r a i n t  income-tax  system  constraint operative  can  be  compared  i n the absence  of  incorporating  with  the  budget  income t a x a t i o n  and  UI, pX+w,L +w L <w T+w T+NLINC 1  2  2  1  2  +NLINC  1  2  where: L^leisure  demand, i n weeks,  head  L = l e i s u r e demand, in weeks,  second earner  2  X=commodity demand for the household composite  single  commodity)  T = t o t a l time a v a i l a b l e p=price  (assuming a  of  (52 weeks)  the composite  good  w^=weekly wage NLINCj=non-labour  income.  To i n c o r p o r a t e income t a x a t i o n ,  first  YT=W,(T-L,)+NLINC1  Y1'=W  2  ( T - L )+NLINC 2  m  rn  2  m  Y =Y,+Y  2  Next, T  i  =  T  j  define +  t  j  (  Y  i=1,2  a tax  i~ j)' y  function:  where:  indexes husband and wife  j indexes marginal tax  brackets  define  total  incomes:  The Unconstrained Labour-Supply Model / T • Yj i s  the smallest  taxable  income i n the j  th  24  tax bracket  T T j i s the tax payable on Yj tj  is  the  marginal  tax r a t e  applicable  to  the  j  bracket. Thus, with t a x a t i o n the household budget c o n s t r a i n t PX^YT-TT+YJ  Or,  becomes:  -T . 2  s u b s t i t u t i n g and r e - a r r a n g i n g :  p X + d - t l J w ^ t + d - t ? ) w L <( l - t l ) w , T 2  ( 1 - t l ) NLINC,+(1-t^)NLINC Re-written,  this  +d-t^)w T+  2  2  -Tl+tlY j T  2  -T^+t^Y 3. T  becomes:  pX+w!L!+w L ^w1T+w T+NLINC,+NLINC , 2  where  2  2  2  w^=(1-tj)w^,  incorporated in  i=1,2  and  the  the non-labour  the l i n e a r i z a t i o n process  tax  adjustments  income terms.  are  Effectively,  a s s i g n s i n d i v i d u a l s the wage  non-labour income to  rate  Wjd-tj)  and a d j u s t s  the fact  that they have not p a i d taxes at the marginal r a t e ,  tj,  on a l l earned income.  The  second  stage  non-linearities  of  introduced by the  budget c o n s t r a i n t segment  on  is  which  individuals located assigned  the  F i g u r e s 2.1  linearization  taken to the  and  2.2  the  UI programme. A g a i n ,  the  one  is  itself  an  of  observed.  and four  c o r r e s p o n d i n g with is  of  of  individual  (which  account  be a l i n e a r extension  on segments  net wage  takes  take account  are  the l i n e extension  the Those  simply AB of  in the  The Unconstrained Labour-Supply Model / a p p r o p r i a t e tax b r a c k e t , as  Single individuals budget c o n s t r a i n t  described).  l o c a t e d on receive  25  the subsidy  total  segment of  the  income of  w(T-L)+Bw (QA(T-L)+EXT)+NLINC q  (i.e.,  employment earnings + UI b e n e f i t s  + NLINC )  where: w  is  now  also  c a l c u l a t e d as  net  1.8  of  UI  percent  premiums  of  p r o v i d e d the gross wage i s  (Premiums  the gross  weekly  -  w^ =the net (gross)  replacement r a t e r e p l a c e a b l e wage  r e p l a c e a b l e wage  is  (=.60 rate  315  in (The  weekly wages  are r e q u i r e d  60 percent  and  dollars.)  1981) maximum  d o l l a r s . In  i n d i v i d u a l s with gross to repay  wage,  g r e a t e r than 63 d o l l a r s  that the weekly premium does not exceed 5.67 B=the b e n e f i t  are  addition,  above 465 of any  weekly  UI  dollars benefits  received.) QA=the r a t e at which weeks UI b e n e f i t  (=1,  of employment earn weeks  for the f i r s t  25 weeks (1981))  EXT=weeks of r e g i o n a l l y - e x t e n d e d individual weeks of  is e n t i t l e d .  of  to which  the  ( E l i g i b l e claimants receive  two  extended b e n e f i t s  benefits  for every  half  percentage  p o i n t the l o c a l unemployment r a t e exceeds 4 p e r c e n t . ) Total  income i s composed of employment e a r n i n g s , UI  receipts  and non-labour income. Thus,  the budget  benefit  constraint  The Unconstrained Labour-Supply Model / can be r e - w r i t t e n (2.1)  26  as:  pX+Cw+Bw^jL^ {w+Bw }T+ Bw^EXT+NLING. q  Individuals constraint  located receive  on  total  the  tax  segment  of  the  budget  income o f :  w(T-L)+Bw (MAXWK-(T-L)) +NLINC q  (i.e.,  employment earnings + UI b e n e f i t s  where MAXWK=maximum b e n e f i t Hence,  the  budget  + NLINC)  d u r a t i o n (50 weeks i n 1981).  constraint  incorporating  UI  can  be  written: (2.2)  The  pX+Cw-Bv^jL^w-Bw^T +Bw MAXWK+NLINC. q  simple  linear  'linearization'  budget  endogeneity  treatment  constraint  problem  r e - w r i t i n g UI b e n e f i t s  in  eliminates the  of  the the  fundamental  non-stochastic  in combination with  non-labour  that  Notice  assumed to be q u a s i - c o n c a v e , which maximizes  model  by  (which depend on weeks of work) as an  exogenous wage s u b s i d y / t a x income.  piece-wise  if  utility  a shift  functions  then the choice of l e i s u r e ,  u t i l i t y subject  to the  true  in are * L ,  (non-linear)  budget c o n s t r a i n t , w i l l a l s o maximize u t i l i t y subject  to  the  * l i n e a r i z e d c o n s t r a i n t which passes i s not t r u e . N o t i c e , as w e l l ,  through L ; the  that the e f f e c t i v e  reverse  tax/subsidy  i s r e l a t i v e l y smaller for workers with incomes above maximum insurable  earnings.  The Unconstrained Labour-Supply Model / 4.  Formal  With t h i s  27  Model  treatment  of  the n o n - l i n e a r budget c o n s t r a i n t  mind, the problem for couples  i n Model 1 can be  in  represented  more f o r m a l l y : Choose L  1 f  L ,X  i n order to  2  MAX u = U ( L , , L , X ; A ) S . T . 2  X+v il +w L < n  2  2  V^T+WZT+NLINCT+NLINCZ  where: 1.  p, the p r i c e  of the  normalized to equal  composite  commodity,  X, has  1.  2.  A i s a v e c t o r of demographic  3.  wages and non-labour incomes take the a p p r o p r i a t e following  been  characteristics. values  the l i n e a r i z a t i o n procedure.  The problem for s i n g l e  individuals!  Choose L , and X in order  is:  to  MAX u=U(L,,X;A) S . T . X+w^^T+NLINC, .  It  i s assumed that a l l households  characteristics Household-specific  have  the  differences  with the same  same  utility  demographic function.  are i n c o r p o r a t e d only  insofar  fA household i n which only one leisure-demand d e c i s i o n is made i s termed 'single,' but a s i n g l e worker may have dependants. Households with non-working spouses are not ' s i n g l e ' households, since the d e c i s i o n not to work i s a leisure-demand d e c i s i o n .  The Unconstrained Labour-Supply Model / as  the  utility  demographic  functions  are  implement  household u t i l i t y  the model,  functions  u=B(X- (A)) d - S i - ^ ) ( L , 7 o  (A))*  7 1  g i v e s the for  2  1  2  depend  2  -  7  leisure  is  assumed  take the 2  ( A ) )  to the budget  1  following  ( L  1  X+w L +w L ^w T+w T+NLINC +NLINC 2  it  for couples  Maximizing u t i l i t y s u b j e c t 1  to  on  characteristics.  To e m p i r i c a l l y  1  allowed  28  0  2  that  form  .  constraint  2  and commodity-demand  equations  couples:  w,L,=7,  (A)w +69 1  (Y-7 (A)-7,  (A)  0  1  w  , -  7  2  w )  (A)  2  w L =7 (A)w +e (Y-7 (A)-7 (A)w -7 (A)w ) 2  2  2  2  2  0  (Y-7 (A)-7,  X=7O(A) + ( 1 - 0 - 6 9 ) 1  where Y i s  (A)  0  2  full  1  1  income  2  2  w ,-y  2  (A)  w ) 2  (non-labour income+w^+WjT) .  Making the n o r m a l i z a t i o n B»I/[  the  (i-a,-^) " 0  0 1  ' * * (e, 2  indirect u t i l i t y  2  2  f u n c t i o n becomes  V(w,,w ,Y)=[Y-7 (A)-w 2  (0 >* ],  0  l 7 l  (A)-w  Since the household expenditure  (A)]/[w/ w 1  2 7 2  e z 2  ].  function,  e(u,w w )=MIN{X+w L +w L |U(X,L ,L ;A)>u}, 1 f  will  2  1  equal f u l l  1  income,  2  2  2  2  Y, only i f V ( w , , w , Y ) = u , 2  0  8  e(U,w ,w )=7 (A)+w 7 (A)+w 7 (A)+w w u. 1  1  This  is  2  0  system  2  1  the expenditure  expenditure the most  1  2  1  2  2  function consistent  (LES)  suitable choice  which, d e s p i t e of  with the  limitations,  f u n c t i o n a l form.  The  linear seems demand  The U n c o n s t r a i n e d Labour-Supply Model / equations of the LES have automatically satisfy the  hypothesis  homogeneity,  of  and  the d e s i r a b l e p r o p e r t y that  most of  the  utility symmetry  maximization.  ("Adding  are  the  imposed;  negative  matrix i s easy  to check: X>7 ,L^>7^  for  indirect  utility  welfare a n a l y s i s . all  goods  are  necessarily but  as  a problem  to be  the  is  time  Muellbauer, curves must system i s terms of  of  husbands  and  for  This  (see  linear.  Clearly,  highly r e s t r i c t i v e . ease  of  indirect u t i l i t y  estimation  the  is  and  not  modelled,  is  linear  However, i t s  that  to  the  Deaton  1980). A second major disadvantage be  the  the LES i s  aggregates are  wives  An  solution  required  substitutes.  when broad  Slutsky  allows easy  One major disadvantage of  required  up,"  and O<0^<1 i = 1 , 2 . )  that the LES functions  of  by  remaining  may be viewed as o v e r l y r e s t r i c t i v e with respect  leisure  this  semi-definiteness 0  is  they  r e s t r i c t i o n s required  requirement of  a d d i t i o n a l advantage  29  and  that  Engel  expenditure  advantages  recoverability  in  of  the  f u n c t i o n make i t an a p p r o p r i a t e c h o i c e  for  analysis.  Demographic v a r i a b l e s are  i n c o r p o r a t e d in  the l e i s u r e  commodity-demand equations  by assuming that  7.=£(7-0+7. . A . ) ; 1  i=0,1,2 indexes  the gamma  <i  parameters; J=1,10  M  1  1  J  indexes  and J  the  demographic v a r i a b l e s : A,=ATLAN=1 i f  residence  is  in  the A t l a n t i c  provinces;  The Unconstrained Labour-Supply Model / =0,  if  not  A =WEST=1 i f 2  if  30  residence  is  i n the Western p r o v i n c e s ;  =0,  not  A =CITY=1 i f 3  greater  residence  is  than 100,000; =0,  in if  a city  the economic  family i s defined  as a l l household  the head,  i n c l u d i n g the  family  head  A =YRSE2=years of education of  wife  5  G  7  (fishing,  husband  hunting,  (where  economic  members r e l a t e d  to  head)  A =YRSE1=years of education of  A =SEA1=1 i f  population  not  A =EFAM=number i n ft  with  works i n forestry,  a  seasonal  occupation  construction);  =0,  if  notf A =CYC1=1 i f 8  (mining,  husband  product  works in  fabrication,  a  cyclical  assembly  occupation  and  repair,  t r a n s p o r t equipment o p e r a t i o n , m a t e r i a l s h a n d l i n g ) ; if  =0,  not  A =PART2=1 i f wife 9  works p a r t time; =0,  if  nott-  A = number of c h i l d r e n l e s s than seven years of 1 0  The analogous  l e i s u r e and commodity-demand system for  age.  single  fFor simplicity, the special features of fishermen's b e n e f i t s are i g n o r e d . t-To be e l i g i b l e for U I , p a r t - t i m e workers must work at l e a s t f i f t e e n hours per week for a gross wage of at l e a s t $63 (1981), 20 percent of maximum i n s u r a b l e e a r n i n g s . Since the data do not provide information on hours worked, part-time workers are assumed e l i g i b l e for UI i f they pass the wage test.  The Unconstrained Labour-Supply Model / household heads  is  WiLi=w,7i(A)+0,(A)(Y- (A)-w 7 o  X=7 (A)+(1-0,(A))(Y-7o(A)-w 0  (A))  l 7 l  l T l  (A))  where Y i s again f u l l  income.  The major d i f f e r e n c e  between the demand  i n d i v i d u a l s and  demand  demographic influence  31  the  variables  on both  of  are the  system  for  assumed  to  system  for  couples exert  basic parameters  of  single is  that  a  linear  the  utility  function:  n-!, n° ?ijV'' (  +  i=0,1  indexes  *i4 *i° *ij j (  the  gamma  demographic v a r i a b l e s , A,=ATLAN=1 i f =0,  if  +  A  ) ;  parameters;  f For s i n g l e  residence  is  in  j=1,8  indexes  the  men, the A t l a n t i c  provinces;  not  A =WEST=1 i f 2  residence  is  in the Western p r o v i n c e s ;  =0,  i f not A =CITY=1 3  greater  if  residence  is  than 100,000; =0,  A„=EFAM=number  in economic  in if  a city  with  population  not  f a m i l y (where  economic  family  i s d e f i n e d as a l l household members r e l a t e d to the head, i n c l u d i n g the  head)  A =YRSE=years of education of 5  A =SEA=1 i f 6  male head  head  works i n  a seasonal  occupation  f i n order to keep the number of parameters to be estimated manageable in the case of c o u p l e s , i t was not p o s s i b l e to allow the theta parameters to depend on demographic characteristics.  The Unconstrained Labour-Supply Model / 32 (fishing,  forestry,  A =CYC=1 i f  male head  7  (mining,  construction);  product  works i n  =0, i f  not  a cyclical  fabrication,  assembly  occupation  and  repair,  t r a n s p o r t equipment, m a t e r i a l s h a n d l i n g ) ; =0 i f  not  A = number of c h i l d r e n l e s s than seven y e a r s . 8  For s i n g l e  women:  A,=ATLAN=1 i f =0,  if  is  in  the A t l a n t i c  provinces;  not  A =WEST=1 i f 2  if  residence  residence  is  =0,  i n the Western p r o v i n c e s ;  not  A =CITY=1 i f 3  greater  residence  is  in  than 1 0 0 , 0 0 0 ; =0, i f  A =EFAM=number i n economic  a city  population  not  family  a  with  (where economic  family  i s d e f i n e d as a l l household members r e l a t e d to the i n c l u d i n g the  head)  A =YRSE=years of education of 5  A =PART=1 i f 6  head,  head  female head works part time;  =0, i f  not  A = number of c h i l d r e n l e s s than seven y e a r s . 7  5.  Stochastic  In e s t i m a t i o n couples  Specification  form,  the  of  the  Model  demand equations  of  the  LES  for  are:  (2.3)  w,L /Y=7 (Ajv^/Y+e,(l-7 (A)/Y-7i(A)w /Y~7 (A)w /Y)+e,  (2.4)  w L /Y=7 (A)w /Y+0 (1- (A)/Y-7,(A)w,/Y~7 (A)w /Y)+e  1  2  2  1  2  0  2  2  7 o  1  2  2  2  2  2  The Unconstrained Labour-Supply Model /  33  (2.5) X/Y=7o(A)/Y+(1-0,-0 )(1-7 (A)/Y-7,(A)w,/Y-y (A)w /Y)+e 2  0  where the 7^ are l i n e a r as p r e v i o u s l y represent  2  functions  described,  of demographic  and the  e^  injury,  individuals  unexpected  to  employment/unemployment a jointly  from  plans.)  added  -  may  their  cause optimal  The e^ are assumed to  normal d i s t r i b u t i o n  to  (Random events  expenditures  deviate  3  variables  have been  'random e r r o r s i n o p t i m i z a t i o n . '  accidental  2  with E(e^) = 0,  follow  i = 1,2,3,  and  c o v a r i a n c e matrix Z . The e^ are assumed independent and the 1  c o v a r i a n c e matrix (see  i s assumed  Appendix 1 for  constant  across  observations  details).  For s i n g l e  i n d i v i d u a l s , the demand  estimation  form a r e :  equations  of the LES  in  (2.6) w , L , / Y = 7 , ( A ) w , / Y + 0 , ( A ) ( 1 ~ 7 ( A ) / Y - , ( A ) w , / Y ) + e , 0  (2.7)  7  X/Y=7 (A)/Y+(1-0,(A))(1- (A)/Y- ,(A)w,/Y)+e 0  where both 7^  7 o  and 0,  v a r i a b l e s and the  7  are l i n e a r  e^ follow a  functions  of  j o i n t l y normal  2  demographic distribution  with means of zero and c o v a r i a n c e matrix Z . 2  a.  Share F o r m u l a t i o n  N o t i c e that (i.e.,  the  equations  the value of  have been  leisure/consumption  income, Y=w,T+w T+NLINC,+NLINC 2  written  2  in share  form  as a share of  full  for c o u p l e s ,  or Y=w,T+NLINC,  The U n c o n s t r a i n e d Labour-Supply Model / 3 4 for  s i n g l e household h e a d s ) .  Thus, when the s t o c h a s t i c  are r e s t r i c t e d to ensure that are s a t i s f i e d , matrix a c r o s s that  the  i n d i v i d u a l budget  assumption  households  is  of  a  constraints  constant  covariance  m a i n t a i n e d . Suppose,  instead,  the equations were not w r i t t e n i n share form.  Then,  e r r o r terms would be added to l e i s u r e and commodity directly,  and s a t i s f a c t i o n  would r e q u i r e  of household budget  w, e ,+w e +e = 0 .  that  2  1  both s i d e s  Given that wage the assumption households.  a  has  2  of the  rates d i f f e r , of  This  3  w|var(e )+var(e )=0  i m p l i c a t i o n that w^var(e )+ v a r i a n c e of  2  3  T h i s problem i s avoided  d i s t u r b a n c e terms  just  form  matrix  the  above). with  are  on the  expenditure  (taking  when the equations  in t h i s case,  in  further  all  in share form s i n c e ,  equations  the  for  written  is  constraints  i s not c o n s i s t e n t  constant c o v a r i a n c e  the  demands  linear restriction this  terms  the  restriction  e,+e +e =0. Writing 3  2  would  also  resolve  the this  problem.  An a d d i t i o n a l i m p l i c a t i o n terms i s t h a t one affecting i s on  is  decision-maker, to  of the equations  estimation r e s u l t s .  leisure  equation  of the r e s t r i c t i o n  estimate.  dropped. this  For  can be dropped  Since the  demand/labour s u p p l y ,  on the  focus of t h i s the  households  error without study  commodity-demand with  a  single  leaves only one leisure-demand equation  The Unconstrained Labour-Supply Model / b.  N o n - l i n e a r Budget C o n s t r a i n t with S t o c h a s t i c Model  A  first  problem  'linearization' constraint  is  for  estimation  treatment  of the  only v a l i d  if  is  that  piece-wise  i t can  to keep observed  and  shares on  optimal ( s ( w , 7 , 0 , A ) )  budget c o n s t r a i n t .  If  this  corresponds with  incorrect.  Parameter  inconsistent  as  of the  linear  budget  that  of  then using the  will  the  (s°=s(w,7,0,A)+e)  the observed  estimates  a result  simple  the same segment  i s not t r u e ,  rate which  the  be assumed  e r r o r s are small enough  35  segment be  the wage  will  be  biased  and  c o r r e l a t i o n between  wage  rate and e r r o r term.  A solution  to  t h i s problem,  which  complicated approach to e s t i m a t i o n , Woodland (1979).  The demand  involves a  much  more  i s o u t l i n e d in Wales and to  be  w r i t t e n in share form. But,  for t h i s procedure, l e i s u r e  is  to be valued  (assumed  by the  grossf  equations  are, again,  exogenous) wage  rate  rather than by the wage r a t e c o r r e s p o n d i n g with the observed budget segment. the s a t i s f a c t i o n  As b e f o r e , of  the share f o r m u l a t i o n allows  household budget  constraints  for  without  fThe ' g r o s s ' wage r e f e r r e d to here i s a c t u a l l y net of tax, but gross of U I . That i s , s i n c e the focus of r e s e a r c h i s on UI, a t t e n t i o n w i l l only be given to the proper treatment of this source of non-linearity. Proper treatment of n o n - l i n e a r i t i e s due to both the p r o g r e s s i v e Canadian income tax and the UI programme would become too c o m p l i c a t e d for this project.  The U n c o n s t r a i n e d Labour-Supply Model / violating across  the  assumption of  a constant  covariance  the  problem  specification  error,  of  endogeneity  Wales and  introduced  Woodland propose  each i n d i v i d u a l and a v e c t o r of parameters, to see  L ( W j ) is  if  such a  by  the  that  for  a check be  made  l o c a t e d on segment j for each j . If  there  segment then  e*=s°-wL*(wj)/Y.  If  not,  then  c o r n e r s must be checked to f i n d the one y i e l d i n g the utility.  This  w i l l determine  must continue the value of  The  one  e =s° -wL /Y.  u n t i l the v e c t o r the  l i k e l i h o o d f u n c t i o n has been  in  which i n c o r p o r a t e s UI i s  non-convex  region.  Wales and  piece-wise  However, as p o i n t e d non-convex  regions  convex  to have m u l t i p l e t a n g e n c i e s . Thus,  segment j  for  than  involves  more  checking which  Lj(Wj)  budget  only with  budget  the  constraints.  (1985), when there it  is  are  possible  i n the Wales and Woodland  L^(w^) one  a  the e x i s t e n c e of a s m a l l  in the budget c o n s t r a i n t ,  above,  procedure  d e a l i n g with  out by Hausman  described  highest  located.  Woodland d e a l  linear  procedure  all  of parameters which maximizes  remaining c o m p l i c a t i o n  of  The  c  constraint  case  matrix  households.  To s o l v e  is  36  j. yields  might  be  Avoiding  located this  on  problem  the h i g h e s t u t i l i t y  in  cases of m u l t i p l e tangencies and comparing u t i l i t y at Lj(w^) with the  u t i l i t y obtainable  at  each c o r n e r .  The  highest  The Unconstrained Labour-Supply Model /  37  u t i l i t y determines L (w.j).  All  of  this,  estimation  finally,  when the budget  and c o n t a i n s  a non-convex  intended to represent papers  describes  (see,  for  the c o r r e c t  constraint  approach  is piece-wise  to  linear  region and when the e r r o r term  is  ' e r r o r s in o p t i m i z a t i o n . ' A number  of  example,  Burtless  and  Hausman,  Killingsworth,  1983;  Moffitt  1985;  1983)  have d e a l t with the c o r r e c t approach to  Zabalza,  estimation but  the  and N i c h o l s o n ,  when the budget c o n s t r a i n t stochastic  variations  component  in taste.  is  model. The two The ' e r r o r s with the  of  necessarily  observe  random t a s t e s  model,  the  has a major impact on  the  are q u i t e that  but we do not observe them o u t .  utility-maximizing on  different. individuals  the other  stochastic  preferences,  make  Thus,  we do  segments.  hand,  the  these c h o i c e s as  we  u t i l i t y - m a x i m i z i n g segments, but these c h o i c e s , depend on  random  (1985)  model says  errors in c a r r y i n g  linear,  as  same wage and demographic c h a r a c t e r i s t i c s  same o p t i m a l c h o i c e s , a result  by M o f f i t t  cases d e s c r i b e d above  in optimization'  Yatchew,  is piece-wise interpreted  As pointed out  i n t e r p r e t a t i o n of the e r r o r term  1982;  1978;  do  not  In  the  observe  because  are endogenous.  they  In  the  ' e r r o r s i n o p t i m i z a t i o n ' model, any value of l e i s u r e may observed. points  In the  'random  i s expected  if  tastes'  model, c l u s t e r i n g at  the budget c o n s t r a i n t  i s convex.  be kink  If  it  The Unconstrained Labour-Supply Model / i s non-convex,  and  if  ranges for the value of  The endogeneity the same  as  optimization'  the  1985  estimation  problem  in  model, and must be t r e a t e d  which  regular,  'random t a s t e s '  endogeneity  to e s t i m a t i o n  the d i s c r e t e  p a r t i c i p a t i o n and Moffitt,  are  certain  l e i s u r e must be r u l e d o u t .  problem i n the  The c o r r e c t approach models i n  preferences  38  hours  and  the  not  'errors  in a d i f f e r e n t  in way.  a generalization  continuous  are modelled  for an e x p o s i t i o n  given d i f f e r e n t  is  model i s  of  choices  simultaneously  of (see  of a p p r o p r i a t e techniques  interpretations  of  the  of  stochastic  component).  An i d e a l model would i n c o r p o r a t e J.L.  A r r u f a t and  such a model). analysis,  A. Zabalza However, t h i s  both s o r t s of e r r o r s  (1986) for  the e s t i m a t i o n  i s beyond the  scope of  which w i l l i n c o r p o r a t e only one d i s t u r b a n c e  to be i n t e r p r e t e d as  (see of this term,  errors in o p t i m i z a t i o n . V a r i a t i o n s  t a s t e are handled d e t e r m i n i s t i c a l l y by a l l o w i n g the 7 and parameters to depend on demographic  c.  6  characteristics.  T r u n c a t i o n due to N o n - p a r t i c i p a t i o n  A second e s t i m a t i o n 1  in  assumes  that  problem i s e a s i e r individuals  are  to t r e a t .  Since  following  Model optimal  The Unconstrained Labour-Supply Model / employment/unemployment in a  position  programme.  of  That  patterns,  it  assumes that they  ' e q u i l i b r i u m ' with is,  Model  1  assumes  unemployment match weeks of e n t i t l e d of Model  1, anyone not  excluded from  the  satisfying  sample.  In  respect that  benefit.  this  to  are  the  weeks  for many benefit. sense  and 2.2)  weeks  but  that  weeks  of  For e s t i m a t i o n  requirement must  particular,  this  (see  hand, can be i n a fifty-two since  unemployment  weeks of  to  unemployed nor is  p o s i t i o n of  F i g u r e s 2.1  benefits  the  planning.)  weeks  match  and  2.2),  can be  the a  p o s i t i o n of  only  receive  v a l i d in  the  any  weeks  of  waiting  period  equilibrium  Model  context of  the  1  be  eligible  abstracts  from  with  neither  benefits.  i n d i v i d u a l who worked  would c e r t a i n l y year.  any  other  for  i n d i v i d u a l s on segment four are to  the  employed  'eligible'  two-week  of  of  on the  of the  weeks  segment four  year are not  fulfill  entitled  year this  any  ' e q u i l i b r i u m ' in  benefit  l o c a t e d on  annual p l a n . Otherwise, an weeks l a s t  for  (see  unemployed  t h e i r plans do not allow s u f f i c i e n t  to UI s i n c e  conclusion  not e l i g i b l e  be  excludes  p o s i t i o n of e q u i l i b r i u m . People  requirement. T h i s respect  such i n d i v i d u a l s are  entitled  Individuals  budget c o n s t r a i n t  benefits  are  T h i s cannot be a  unemployment.  for  since  UI of  anyone l o c a t e d on segment one of the budget c o n s t r a i n t F i g u r e s 2.1  39  (This optimal  fifty-two to  receive long-term  The Unconstrained Labour-Supply Model / Since the e x c l u s i o n that  the  sample  of  is  truncated  to gain e l i g i b i l i t y bias,  to is  s?<s.  bias  sample  caused  means  required  selectivity  by  excluding  introduced.f  observations  are  only  included  in  if  M I N  s(w , ,0,A)+e < i  the minimum weeks  potential  the  For s i n g l e i n d i v i d u a l s , the sample  at  to U I , a  analogous  non-participants,  ' d i s e q u i l i b r i u m ' observations  40  7  M  i  OR e.^s^ -s(w  S  I N  r  i r 7 l  I  N  i  f9 A) r  where: 1.  e^ f o l l o w s variance  2.  s^  IN  just  is  a normal  distribution  with mean  zero  and  a  2  the  leisure  share  for  an i n d i v i d u a l who  enough weeks to gain e l i g i b i l i t y  E s t i m a t i n g a model which ignores distribution  will  yield  T r u n c a t i o n means that  to U I .  the t r u n c a t i o n of  biased  the e x p e c t a t i o n  works  parameter  the e r r o r estimates.  of the e r r o r term  is  non-zero: E(e. ) = E ( l e e i  i  <s  .^-s  (w , , 0 , A) ) i  7  = f (*)/FU) t i n t h i s model, the d e c i s i o n to p a r t i c i p a t e and the d e c i s i o n to work enough weeks to be e l i g i b l e for UI are t r e a t e d as a single decision.  The Unconstrained Labour-Supply Model / where \^=s^ -s ( w , 7, 6, A)  (see  IN  i  i  Johnson and  Kotz,  41  1970,  pp  81-87).  For c o u p l e s ,  the t r u n c a t i o n problem i s analogous.  are only i n c l u d e d  in the  sample  work enough weeks to be e l i g i b l e  if  both  Households  husband and  wife  distribution  with  for U I :  0 MIN , St^s,. and  B  <c  -  MIN  0_ K  Or, - s , (w., ,e A) and  e i ^ s , f  N  e  I N  2 i  ^s ^  -s (w , ,e,A)  2  where e E(ej)=0 Again, will  f  7  2  1 f  e  i  7  follow  2  a bivariate  (j=1,2) and c o v a r i a n c e i g n o r i n g the  result  in  e x p e c t a t i o n s of  female  by  as  conditional  e2^<s  M I N 2  -  on on  s (w^,7,0,A) 2  In  since equal  (1980)  both  s^ -s(w.,7,6,A) I N  e ^<s,^ 1  in the case of  IIN  the  zero.  in  the d e r i v a t i o n  household d e n s i t i e s can be  e^<  1).  distributions  a p p l i c a t i o n of  Woodland  non-participation.  Appendix  estimates  through the  Wales and  likelihood function,  or  (see  the e r r o r  parameter  be overcome  the  individuals,  3  the e r r o r terms w i l l no longer  proposed  context of  matrix Z  t r u n c a t i o n of  biased  The problem can technique  normal  a the of  written  for  - s , (w^,7,0,A)  single and  couples.f  fAmemiya (1973) has demonstrated the asymptotic normality and e f f i c i e n c y of the maximum l i k e l i h o o d e s t i m a t o r s for t h i s  The Unconstrained Labour-Supply Model / d.  The  42  Censoring due to F u l l - y e a r Workers  f i n a l major problem for the e s t i m a t i o n  as a r e s u l t  of  specifying  leisure  terms of annual weeks: weeks (of be no  l e s s than  r e s t r i c t i o n that  zero and weeks of  of Model 1 a r i s e s  demand/labour supply  leisure  no greater  or of labour)  must  than f i f t y - t w o .  The  l e i s u r e must not exceed  fifty-two  has a l r e a d y been avoided by e x c l u d i n g anyone  ineligible  UI.  of  However,  non-negative  the  restriction  by s p e c i f y i n g in  weeks  (weeks of work be no greater  problem. Most s t u d i e s of  However,  that  the l a b o u r / l e i s u r e choice of  a model  than 52)  difficulty  UI, this  hours. is  not  a p p r o p r i a t e s i n c e working over-time hours i n a week w i l l affect  eligibility  c h o i c e must  for UI b e n e f i t s .  remain  a  choice  dependent  variable  specified,  the model becomes  s°=s(w,7,0,A)+e;s°>O, s°=0;s°<0,  or,  problem  or,  be  leisure-demand  and  treated.  the  limited Correctly  e>-s(w,7,6,A).  i  restrictions  again,  to  since a large  must  weeks  the  not  e<-s(w ,7,0,A).  I g n o r i n g the lead  of  Thus,  be  remains a  i n terms of of  for  leisure  labour supply a v o i d t h i s  the context  in  biased number of  on the parameter  error d i s t r i b u t i o n estimates,  observations  are  will,  particularly  l o c a t e d at  s°=0  t ( c o n t ' d ) model Twith respect to included observations). Thus, the covariance matrix for the parameters can be approximated by the inverse of the negative Hessian m a t r i x .  The Unconstrained Labour-Supply Model / (i.e.,  at  fifty-two  s t r a i g h t f o r w a r d to classic  e.  In  'Tobit'  weeks  treat,  of  work).  however,  v a r i e t y (see  The  since  problem  it  is  the  1983).  D e r i v a t i o n of the L i k e l i h o o d F u n c t i o n s  summary,  individual  d e c i s i o n s have three  leisure  demand/labour  the d e c i s i o n to p a r t i c i p a t e  2.  the d e c i s i o n to work f u l l - y e a r  3.  the c h o i c e of weeks of w o r k / l e i s u r e  Decisions  supply  components:  1.  (1) and (2)  are ' t h r e s h o l d ' d e c i s i o n s .  That i s ,  i n d i v i d u a l must f i r s t decide whether  or not to  i n the labour f o r c e  (which  1, means he must  enough weeks to be  eligible  for Model for UI) .  he  decides  to  work  just part  of  i n d i v i d u a l must choose weeks of l e i s u r e three  decisions  (labour-supply),  together but i t  c h o i c e that the t h i r d  the  an  participate  Then, he must  whether to work f u l l - y e a r or p a r t - y e a r . F i n a l l y , if  is  of  T o b i n , l 9 5 8 and Maddala,  43  it  year  work decide  is that  only an  (labour s u p p l y ) . The  determine  leisure-demand  i s only i n the event of a  (conventional labour-supply)  part-year decision  must be made.  For a s i n g l e model  is:  individual,  the f i n a l  form of the  stochastic  The U n c o n s t r a i n e d Labour-Supply Model / (2.8)  s°=7,(Ajw^Y+G,(A)(1-7O(A)/Y- (A)w,/Y)  (2.9)  s°=0;RHS<0 s°=s  where s  M I N  M I N  ;RHS>s  M I N  =the leisure  share  for an i n d i v i d u a l who works  minimum number of weeks r e q u i r e d to q u a l i f y  The model i s and  +e;0<RHS<1  7 i  (2.10)  i n t o account,  L={n ;" ° m  the  for U I .  estimated by maximum l i k e l i h o o d . For s i n g l e men  women, t a k i n g the  i=1  44  S  the  t r u n c a t i o n and c e n s o r i n g  l i k e l i h o o d f u n c t i o n becomes  f(e.)de./P1.} i i i  -«  difficulties  {n  f(e-)/P1.} i=m+1 n  1  1  where: s  M I N  -s()  P1-=J at the  f(e-)de-  (i.e.,  the p r o b a b i l i t y of working  l e a s t the minimum number of weeks to q u a l i f y first  m  workers  are' observed  to  work  for U I ) . fifty-two  weeks. For c o u p l e s ,  the  final  form of the demand system  is:  (2.11) S?=7i (Ajw^Y+e, ( 1-7o ( A ) / Y - 7 , ( A ) w , / Y - 7 (A) w / Y ) +e; 0<RHS< 1 2  (2.12)  s?=0;RHS<0  (2.13)  S?=S  M I N  ;RHS>s  2  M I N  And, (2.14) S?=7 (A)w /Y+0 (1-7 (A)/Y- (A)w /Y- (A)W /Y)+e;0<RHS<1 2  2  2  0  71  1  72  2  The Unconstrained Labour-Supply Model / (2.15)  s°=0:RHS<0  (2.16)  S =S  the  ;RHS>s  2  T h i s model  is  a l s o estimated  derivation  complicated. (1)  j "  X  '  3  the  maximum l i k e l i h o o d .  likelihood  Four household  j "  0  — co  (2)  Wife  X? = ; " X  (3)  S  2  weeks  Here,  is  more  possible: (i=1,...K):  f (e|,e?)deMe?/P2.  0  X  weeks  function  s i t u a t i o n s are  X  X  X  X  weeks,  husband works  less  than  less  than  (i=K+1,...L):  ° f (e|,e?)de?/P2.  —oo  X  Husband  works f i f t y - t w o  Xf = ; "  X  X  X  weeks,  wife works  weeks (i=L+1,. . . M ) :  S l ( )  f(ej,e?)de|/P2.  — oo  (4)  1  works f i f t y - t w o  fifty-two  X  5  — oo  fifty-two  .  of  by  Both i n d i v i d u a l s work f i f t y - t w o  M-  45  X  X  X  X  Both i n d i v i d u a l s work l e s s than f i f t y - t w o  weeks  (i=M+1,.  .N) :  X? =  f(eJ e?)/P2. f  J  -MIN J"  —OO  —CD  S  where P2.= 1  The  MIN_  (  )  l i k e l i h o o d function  ( 1  )  f (e J , e ?) de M e ? .  for couples  1  1  1  (Model 1)  1  is  thus:  L=n xm x?n x?n x?t iii  li-.Kii  li'MI  1  fSee Appendix 1 f o r a d i s c u s s i o n of the double i n t e g r a l s for e s t i m a t i o n .  the  simplification  of  III.  In  Chapter  THE CONSTRAINED LABOUR-SUPPLY MODEL  Three  I  develop  the  household b e h a v i o u r . The idea of i s motivated i n s e c t i o n models;  the  illustrated on  rationing  labour-supply  heads.  significance  functions  Section 4  of  model  Section for  3  to  theoretical  the  concept  for both  and  rationed  sets  out  couples and s i n g l e  d e r i v e s the l i k e l i h o o d  is  literature  derives  couples  of  labour supply  2 through a survey of the  models.  e s t i m a t i n g equations  'constrained'  1 through references  empirical in s e c t i o n  constrained  the  household  functions  for  the  e s t i m a t i o n of the c o n s t r a i n e d models.  1.  The B a s i c Model of Household Behaviour  The u n c o n s t r a i n e d l a b o u r - s u p p l y model (Model 1) assumes that observed weeks of unemployment of  individual  e x i s t e n c e of  (employment)  utility-maximizing UI .  However,  assumption i s u n r e a l i s t i c when demand-side household p l a n s .  it  for  can  are the  choices, be  argued  p e r i o d s of high  constraints  may  Such c o n s t r a i n t s  interfere  outcome  given  the  that  this  unemployment with  may take q u i t e  optimal different  forms: 1.  A l a y - o f f may exceed an i n d i v i d u a l ' s d e s i r e d q u a n t i t y of unemployment, but he  or she may 46  nonetheless p r e f e r  to  The C o n s t r a i n e d Labour-Supply Model / wait 2.  47  for r e c a l l r a t h e r than to search for another j o b .  No job o f f e r s  may be f o r t h c o m i n g .  C o n s t r a i n t s of the  f i r s t v a r i e t y may be e x p l a i n e d by  i n which unemployment i s  the outcome of l o n g - r u n ,  models implicit  c o n t r a c t s between r i s k - a v e r s e workers and r i s k - n e u t r a l firms (Azariadis,  1975;  risk-sharing contracts. firms,  Baily,  involves  Knowing  workers  1977).  fixed  the r i s k  choose  In these wage,  models,  variable  of unemployment  the c o n t r a c t  optimal  employment at  offering  different  the  highest  expected v a l u e . While the r i s k of unemployment i s thus i n t o account ex a n t e , not c o n s t r a i n e d i f Yet,  since  they  the chosen  expected u t i l i t y , constraint,  t h i s does not  the worker's  i s to wait  mean that workers  f i n d themselves l a i d - o f f , c o n t r a c t gave  for  taken  ex  the highest  optimal c h o i c e ,  are post.  long-run given  the  r e - c a l l (even though other  jobs  may be a v a i l a b l e ) .  Models of  compensating wage  differentials  e x p l a n a t i o n for the e x i s t e n c e of  provide  another  'constrained'  unemployment.  Workers choose o c c u p a t i o n s with a high r i s k of  unemployment  if  a compensating., wage means that  the expected  that occupation exceeds the expected occuptions.  Again,  unemployment which i s unemployment can  though,  it  taken i n t o  s t i l l be  is  utility only  utility  from a l l the  account ex a n t e .  perceived  as a  from other  risk  of  Realized  constraint,  ex  The C o n s t r a i n e d Labour-Supply Model /  48  post. t  These  first  two  models  refer  particularly  unemployment. The ' e f f i c i e n c y - w a g e ' Stiglitz,  1984)  to  hypothesis  provides an e x p l a n a t i o n  lay-off  (Shapiro  for the e x i s t e n c e of  'constrained'  unemployment which i s not t i e d to the  of l a y - o f f s .  In t h i s  model, poor  mean that workers are p a i d a l e v e l of e f f o r t .  that  the p r e v a i l i n g wage r a t e , work  remain  necessarily wage  are  mean that  the  'primary  effort  higher  sector'  secondary-sector  to  i s most  this  does  If,  for  relevant and  at a  j o b . Moving out  job  is  if,  the  1971)  job may  accepting  where  a  (Jones, have  a  a low wage i n screen  a  low-wage  of the primary s e c t o r  as  in  'secondary-sector'  for example,  used  lower  for workers  Piore,  a primary-sector than  not  example,  for unemployed primary workers  value  previous  though,  to monitor, then  make r e t u r n more d i f f i c u l t worker's  workers who would p r e f e r  (Doeringer  w a i t i n g for  expected  is  their At  elsewhere.  may be d i f f i c u l t  1985). But,  higher than  high  restricted.  Again,  hypothesis  jobs may be a v a i l a b l e  capabilities  employment o p p o r t u n i t i e s  unavailable  efficiency-wage  a wage  employment  some  unemployed.  monitoring  context  wage premium to ensure a  Paying workers  marginal products means  and  for  may a low  fNo attempt i s made to model such d e c i s i o n - m a k i n g p r o c e s s e s . These t h e o r e t i c a l models are d i s c u s s e d merely to p o i n t out possible explanations for the existence of constraints, which, i f v a l i d , have i m p l i c a t i o n s for e s t i m a t i o n .  The C o n s t r a i n e d Labour-Supply Model / productivity sense  be  (Weiss,  1980). A g a i n ,  'voluntary,'  correspond  with  but  the  unemployment may i n  the  observed  wage  utility-maximizing  49  some  does  not  choice  of  employment/unemployment.  C o n s t r a i n t s of the  second v a r i e t y are  i n d i v i d u a l who r e c e i v e s no job o f f e r s  quite different. can more  be termed ' i n v o l u n t a r i l y ' unemployed. may not be u n r e a l i s t i c . were f i v e  unemployed  United States in the  idea that  the  job  late  offers  1970s. may be  job  labour-market  offers  will  scarce  consistent  psychologists. report  how  context,  seems p l a u s i b l e Since both  as g i v e n ,  that  a  with  the  regional  individuals  unemployment  a constraint  position  In a recent  unemployment  optimistically located,  at  Model  face  survey, is  taken  on labour by  many  supply social  K e l v i n and J a r r e t t (1985)  viewed  as  a  process  p s y c h o l o g i c a l d e t e r i o r a t i o n . An i n d i v i d u a l w i l l f i r s t to  the  constraints.  T h i s view of unemployment as is  mean  there  job vacancy i n  In the Canadian  1 and Model 2 take region of r e s i d e n c e of  scenario  Abraham (1983) estimates that  the r e g i o n a l i f not at the n a t i o n a l l e v e l .  shortage  convincingly  And, such a  workers for every  An  with begin  shock. active  Then, job  he  search.  a n x i e t y and pessimism w i l l f o l l o w .  or If  of react  she no  will job  Eventually,  is the  The C o n s t r a i n e d Labour-Supply Model / unemployed i n d i v i d u a l w i l l h i s or her new s i t u a t i o n . suggests that  become a p a t h e t i c and r e s i g n e d Evidence (see  most unemployed  through a l l of these s t a g e s . circumstance affect  (e.g.,  to  Jarrett)  individuals eventually Differences  alternative  only the speed of  K e l v i n and  pass  of p e r s o n a l i t y  sources  of  50  or  income)  will  transition.  From t h i s p e r s p e c t i v e ,  unemployment i s not  the outcome  of  individual choice.  is  happens  t£  an  for h i s p e r c e p t i o n  of  It  i n d i v i d u a l with negative self  something  consequences  and for h i s r e l a t i o n s h i p s  Osberg,  with other people  1986). A c o n s t r a i n t of  b i n d i n g than a c o n s t r a i n t of problem for e s t i m a t i o n  is  which  (see  also  the second type may be the f i r s t  the same.  type,  more  but the  basic  If c o n s t r a i n t s  exist,  observed weeks of unemployment and observed weekly wage rate are  not  functions will  2.  a  utility-maximizing  straightforwardly  estimated  using  labour-supply observed  data  be b i a s e d .  Survey  of  Previous  E m p i r i c a l work to exist  combination;  i n the  be found i n  Studies  Constraints  date supports the  labour market. s t u d i e s of  DaVanzo et a l .  of  idea that  The e a r l i e s t  such evidence  labour supply such  (1976) and  Wales and  constraints  as Rea  can  (1974),  Woodland (1976).  Rea  The C o n s t r a i n e d Labour-Supply Model / (1974) f i n d s very  l a r g e negative  workers suggesting  that d e s i r e d  than  observed  constrained). that  (i.e.,  Da Vanzo  parameters  employed  and  estimated  from  course,  residuals  unemployed  unemployed  a l . and  estimated  from  Wales and Woodland  find  full  sample  differ  of employed  from  of  workers o n l y .  systematically  from the t a s t e s  would then account  negative r e s i d u a l s  for the  b i a s e d parameter  under t h i s assumption,  sample s e l e c t i v i t y  'tastes'  are not  the  are  least  at  constraints  Ashenfelter  not  for  problem. I f ,  explanation,  inconsistent  with  however,  then these  studies  the  existence  of  data  (1930-67)  to  in the labour market.  (1980)  t a k i n g account  uses  time-series  of the p o s s i b l e  supply.  Assuming  system  e x i s t e n c e of c o n s t r a i n t s  that  the  preferences  of  common  Stone-Geary  l a b o u r - s u p p l y and  utility  commodity-demand  groups. For the unemployed workers,  function, equations  he for  the q u a n t i t y  on both  c o n s t r a i n e d and unconstrained workers can be represented a  the  estimates  estimate an aggregate labour-supply/commodity-demand  labour  of  e l i m i n a t i n g unemployed workers  would generate a  full  Of  i f unemployed workers  'Tastes'  since,  both  parameters  f u l l y - e m p l o y e d workers. and  greater are  these r e s u l t s can be e x p l a i n e d  have t a s t e s which d i f f e r  is  workers  a  workers  a sub-sample  unemployed  labour supply  that et  for  51  by  derives the  two  constraint  The C o n s t r a i n e d Labour-Supply Model / is  incorporated  supply.  For  weighted  by  his  treating estimating  averages  equations,  where  probabilities  of  it  of the  as  a 'ration'  equations,  being  used  and are  constrained  rate).  uses  unconstrained the  or  not  p r o x i e d by the observed unemployment rate unemployment  labour  Ashenfelter  constrained weights  on  appropriate constrained,  (and one minus the  While the model i s very simple and there  are problems with using the observed unemployment rate as proxy for the p r o b a b i l i t y of being c o n s t r a i n e d , that  this  significantly  l i k e l i h o o d function conclude that  52  increases  for  the  labour-supply  the  system  leads  constraints  the  value  finding of  the  Ashenfelter  may be  a  to  empirically  important.  Ham  (1982)  explicitly  tests  labour-supply constraints full-sample estimates with estimates  for  the  existence  among prime-aged men by  of  a linear  based only  equation  workers,  possible  generalization  of the Heckman (1979) p r o c e d u r e . The two sets  of  should  be  labour-market c o n s t r a i n t s , ways i f  such  constraints  support of the e x i s t e n c e ignoring t h i s p o s s i b i l i t y  selectivity  the  same  if  but should d i f f e r exist.  Ham  of c o n s t r a i n t s will  result  bias  but  corrected for  estimates  sample  comparing  labour-supply  on f u l l y - e m p l o y e d  of  there in  finds  using  are  a  no  predictable evidence  and concludes in b i a s e d  in that  parameter  The C o n s t r a i n e d Labour-Supply Model / estimates on, race,  in p a r t i c u l a r ,  education  demographic v a r i a b l e s  and number  of  c h i l d r e n which  p r o b a b i l i t y of being  unemployed.  B l u n d e l l and Walker  (1982) estimate a  leisure  and  possibility  commodity  demands  that a l l of the  institutional  constraints  B l u n d e l l and  Walker  theory  of  equations  generalization Muellbauer, equations.  of  1981)  i n t o account the  face  labour  and  supply.  a direct  Gorman  the  their  form  the  estimating function proposed  corresponding  t h e i r model has the advantage  interactions  Ham,  between  expenditure polar  deriving  Unlike  link  and  a household  the  As w e l l ,  men but none of the women  maximization  by choosing  household the  on  allows  the  for  maintain  utility  among household  of  demand taking  l e i s u r e demand  The e x i s t e n c e of a c o n s t r a i n t  a husband's  leisure,  for  example,  implications  for h i s  wife's  Walker's approach are test  leisure  The that  might  disadvantages t h e i r model  for the e x i s t e n c e of c o n s t r a i n t s  sample of  two-adult  Family Expenditure separation  manual  workers p e r c e i v e  (i.e.,  themselves to  1974)  on  significant  as w e l l as  for  Blundell  and  of  does not provide  and that  worker f a m i l i e s  Survey of  information  have  demand  t h e i r data from the  does not  information  (a by  and consumption d e c i s i o n s .  household consumption.  as  affect  system of  which  such  53  a (a  U.K.  give  sample  about  which  be c o n s t r a i n e d ) .  Hence,  the  The C o n s t r a i n e d Labour-Supply Model / demand system operative, the same  is  first  estimated  assuming  no r a t i o n s  then a corresponding demand system, expenditure  constraints  (the  f u n c t i o n but  technique 1980)  is  constrained.  both  cases,  plausible,  estimated  parameter  Ryan (1983)  estimates a  demand  the  function,  equations The e n t i r e  an  approach  he  same  used by Ham.  This  derives  sample  separation  c o n s i s t e n t with  leisure  form for  system  is  then estimated  (For  of  rationed  individuals,  are g r e a t e r  the sample  is  the T o b i t  direct  and commodity  demand  t h i s approach, no i n f o r m a t i o n i s of c o n s t r a i n e d workers,  by maximum approach to we  than observed  'truncated'  at  utility  the  for both c o n s t r a i n e d and unconstrained  d e s i r e d hours people  both  a Stone-Geary  using a g e n e r a l i z a t i o n samples.  of  household model  m a x i m i z a t i o n . Choosing utility  existence  and u s i n g the  data as was  advantage  i n f o r m a t i o n and a  preferred.  the  system using  B l u n d e l l and Walker  U n i v e r s i t y of Michigan PSID Ryan  are  implausible.)  s i m i l a r to that of  gives  to are  estimates  (On the other hand, nothing here suggests that is  quantity  assuming a l l men  but nothing can be s a i d about which i s  of c o n s t r a i n t s  from  used for t h i s i s a t t r i b u t a b l e  Neary and R o b e r t s , In  are  derived  incorporating  54  know hours;  households. likelihood truncated only for  that these  observed h o u r s . )  l o s t through the  although r e s u l t s may  With  exclusion  be biased  if  The C o n s t r a i n e d Labour-Supply Model / individuals lie In a d d i t i o n  about whether or  to  his  excluding rationed observations  but  full  not they are  model,  households ignoring  parameters c l e a r l y d i f f e r ,  and a  model  no systematic  Moreover, the  constrained.  estimates  constraints.  i n d i c a t e the nature of p o s s i b l e constraints.  Ryan  a  model  including  While  b i a s i n t r o d u c e d by  are non-nested  impossible to conduct  t e s t s of a l t e r n a t i v e models. hypothesis  that  rationing  Again,  though, h i s  suggests that e m p i r i c a l r e s u l t s are s e n s i t i v e to made about the e x i s t e n c e of  In a l l  of  possible and  the  that  cross-sectional  studies  taste  (1984) r e p o r t s an  differences  fixed-effects  model,  nature  the  of  fixed-effects,  through  between  attempt the  t a k i n g advantage PSID  (3.2)  data  labour-supply  LSiJ-P'X.^a.+e^ LS.°^'X  i t +  vu  i t +  a. e +  work  (1967-71).  equations  for  i t  as  is  differences  estimation of the  it  fully-employed  (1980) to  and c o n s t r a i n e d workers can be represented (3.1)  the  assumptions  discussed,  unemployed workers are merely the r e s u l t of  for  the  constraints.  observed d i f f e r e n c e s  in t a s t e . Ham  and  non-nested  So, Ryan i s unable to t e s t  exists.  to  ignoring  the n o n - l i n e a r i t y of the equations and the t r u n c a t i o n of e r r o r d i s t r i b u t i o n make i t  all  estimated  p a t t e r n appears  three cases  55  control of  a  longitudinal Incorporating fully-employed  The where  represents  desired  labour  variables  a  supply,  coefficients,  u^  labour-supply  choice  Again,  Ham  for  this  (1985)  suggests  intertemporal well  as  on  the  transitory  out  s t i l l  factors  Using  the  ALS *=a+5Alnw  (3.4)  ALS °=a+6Alnw  where:  i  i  i t  i t  of  such  leisure Hence, into  these +Ae  i t  is  error  of  not  term.  An  estimation  reveals in  a  of  that  even  taste,  the  negative.  constraints.  on  in  the  have  favour  grounds  been  workers years  of  ignored  may  in  attempts  that  have  which  to  take  as high they  these  account.  (1981),  equations are  i t  +pAu  in he  MaCurdy of  which  evidence  unemployed  56 i's  vector  significantly  uncertainty  of  form,  are  /  exogenous  a  differences  existence  that  of  the  variety  and  factors  (3.3)  this  Model  affecting  is  random  from  workers  equivalents  difference  a  questioned  for  framework  intertemporal  0  is  fc  that  unemployment.  additional  rate,  be  grounds  three  vector  unemployment  permanent  the  tastes  experience  f i r s t  for  of  factor  a  residuals  unemployed  can  e^  Labour-Supply  taste  is  t  wage  and  functions  points  constraints  the  the  controlling  residuals  X^  represents  f c  of  labour-supply after  permanent  including  examination  Constrained  +Ae  i t  Ham  (3.1)  derives and  (3.2).  the In  The C o n s t r a i n e d Labour-Supply Model / 5 7 e^  fc  represents  measurement  error  and t r a n s i t o r y  taste  differences 'fixed effects' the f i r s t  and  demographic v a r i a b l e s disappear  difference  in  form  5 can be i n t e r p r e t e d as an ' i n t e r t e m p o r a l  substitution'  elasticity.  For e s t i m a t i o n , the l a r g e  Ham  includes A u ^ d i r e c t l y t  negative r e s i d u a l s  constrained  during  periods  coefficient  on  zero,  constraint  the  v a r i a b l e Au^ 1.  fc  the f i r s t  Au^  i s not  t  In both  procedure  regional,  be  is  If  the  different  from  rejected.  The  i n d i v i d u a l i s unemployed i n year  in the observed unemployment  the A u ^  (where lagged  v a r i a b l e which i s  set t,  otherwise  endogenous  variables,  can  i n a dummy  difference  cases,  t r e a t e d as  worker  unemployment.  significantly  hypothesis  difference  equal to z e r o , the f i r s t  of  if a  for  i s approximated in two ways:  equal to one i f an  2.  anticipated  as a proxy  t  proxies  through  the first  as w e l l  an  Alnw^  instrumental  instruments  are  differences  and i n d u s t r i a l unemployment  as  fc  are  variables  human in  rate.  capital  occupational,  r a t e s and  interactions  among them).  To i n c o r p o r a t e u n c e r t a i n t y  in t h i s model,  Ham f o l l o w s  the  The  C o n s t r a i n e d Labour-Supply Model /  work of MaCurdy (1982, Deaton and  1983),  I r i s h (1985).  Altonji  It  is  now assumed  p e r i o d labour supply and consumption the X  i t  (1984) and  58  Browning,  that  in  are chosen to  each  satisfy  condition _  =(l r)/d p)E _  l  +  +  t  (X )  1  u  where: 1.  X^ =the marginal u t i l i t y of wealth  2.  r=the r e a l i n t e r e s t  3.  p=the r a t e of time  4.  E _ (X^ )=the  in period t  t  t  1  This condition (3.5)  preference  expectation  fc  a v a i l a b l e at  rate  of  X^  t  given  information  t-1.  is  re-written  X = ( 1+p)/(l+r) u  where u^ = a f o r e c a s t t  as  X _ (l+u. ) i t  1  t  error.  Ham assumes that e x p e c t a t i o n s are formed r a t i o n a l l y so u^  t  that  has a zero mean, c o n d i t i o n a l on i n f o r m a t i o n a v a i l a b l e  t-1.  Taking  logs:  lnX =p-r b lnX _ i t  +  at  +  i t  1  +v.  t  where 1.  b=the p o p u l a t i o n mean of  2.  v^  t  at  has zero mean  ln(l+u^)  c o n d i t i o n a l on information  t-1.  Finally,  with  the  incorporation  of  becomes (3.6)  available  A L S * = a+6Alnw t  it  -*>Au +Ae it  it  +v  ifc  uncertainty,  (3.4)  The  C o n s t r a i n e d Labour-Supply Model /  59  where a=p-r+b N o t i c e that A u ^  t  may be p o s i t i v e l y  unemployment causes an increase  c o r r e l a t e d with v ^  in  t  if  the marginal u t i l i t y  of  wealth.  Ham estimates equation 3.6  by 2SLS using  c o n t i n u o u s l y - m a r r i e d prime-aged men finds  a  small  positive also  from 1971  to  intertemporal  elasticity,  but  coefficients  on the A u ^ proxy  finds  very  accounting  for  uncertainty,  and the p o s s i b i l i t y  for  when unemployed,  1979  life-cycle  significant  and  negative  labour-supply  when  behaviour,  of high t r a n s i t o r y  Ham  473  substitution  v a r i a b l e s . Hence, even  t  leisure  PSID data on  f i n d s evidence  tastes for  the  e x i s t e n c e of l a b o u r - s u p p l y c o n s t r a i n t s .  3.  The  The F o r m a l  Model o f C o n s t r a i n e d  c o n s t r a i n e d l a b o u r - s u p p l y model (Model 2) allows  possibility  that  demand-side  labour-supply choices. to  Behaviour  choose  annual  consumption of a utility  subject  As in Model  weeks  of  composite to  constraints  a budget  UI.  However, c o n s t r a i n t s  of  these p l a n s . A worker  for  interfere  1, households  constraint  may i n t e r f e r e  order to which  with the  with  are assumed  employment/unemployment  commodity i n  the  and  maximize  incorporates realization  may plan to be unemployed for  ten  The C o n s t r a i n e d Labour-Supply Model / weeks each y e a r , but may f i n d himself for twenty.  To the extent that t h i s  i s p e r c e i v e d as a c o n s t r a i n t , be  or h e r s e l f  additional  60 -  unemployed unemployment  other household d e c i s i o n s  will  affected.  This c r e a t e s s p e c i a l  difficulties  Working from the dual s i d e  in the  case of  of the problem, the  couples.  expenditure  f u n c t i o n f o r an unconstrained couple can be represented (3.7)  e(u,w,,w )=MIN{w,L +  For a  c o n s t r a i n e d couple  2  (3.8)  w L +X;U(L,,L ,X)>u}  1  husband i s c o n s t r a i n e d ) , e(u,w,,w ,Z,)= 2  2  2  2  (suppose,  for  the expenditure  example, function  MIN{w,Z +w L +X;U(Z ,L ,X) 1  2  2  1  2  where Z ^ h u s b a n d ' s c o n s t r a i n e d weeks of l e i s u r e =w Z,+MIN{w L +X;U(Z ,L ,X) 1  2  2  1  =w Z,+)//(u,Z ,w ) l  1  as:  that  the  is:  >u} (L^Z,)  >u}  2  (3.9)  2  where </ does not depend on w,. To e s t a b l i s h  a  r e l a t i o n s h i p between  unconstrained expenditure concept  of a ' v i r t u a l '  which an  functions,  wage  *  use can be made of  the  one. C o n s t r a i n e d and  *  Z, weeks  of  unconstrained  when evaluated at  *  at  ~  the  *  wage, w : e (u, w , , w ) =w , Z , +uV(u, Z , , w ) =e (u, w , , w , Z , ) . 2  Thus, u s i n g  2  (3.9),  e(u,w ,w )=w Z,+e(u,w ,w ,Z )-w Z 1  and  w i l l choose  expenditure f u n c t i o n s are e q u i v a l e n t virtual  constrained  (Rothbarth, 1941), the wage  unconstrained household  unemployment for worker  the  2  1  1  2  1  1  1  2  The C o n s t r a i n e d Labour-Supply Model /  61  Or, e(u,w ,w ,Z )=e(u,w ,w )+(w -w )Z, 1  (the  1  2  1  desired  2  1  relationship  unconstrained expenditure from Deaton  1  between  functions).  (1981). A n a l o g o u s l y ,  if  constrained  and  T h i s approach i s the  taken  second worker  is  constrained ic  e(u,w,,w ,Z )=e(u, 2  ic  w,,w )+(w -w ) Z  2  2  2  2  2  From these c o n s t r a i n e d  expenditure  'quantity-constrained'/  ' r a t i o n e d ' f demand equations  d e r i v e d through an  functions,  'effective'/  a p p l i c a t i o n of H o t e l l i n g ' s  can  lemma and  s e r i e s of  substitutions:  If  L?=Z  w n /Y=7 w /Y+0 /O-0 ){i-7 /y-w z /y-w 7 /y}.  If  L?=Z ;  2  1 ?  2  2  2  1  0  1  1  is  same expenditure demand equations all  1  1  income as  these equations  before.  that  the  exogenous  households. equations  2  2  2  Thus,  so that  The important  f u n c t i o n as  the  1  feature  of  unconstrained  underlying preferences The  only  are the same  difference  quantity constraint the  1  2  they are u l t i m a t e l y d e r i v e d from the  (utility)  households.  2  c o n s t r a i n e d and an u n c o n s t r a i n e d household of  1  a  W,E,/Y=7 W /Y+0 /(1-0 ){1-7OA-W Z /Y-W 7 /Y}  where Y = f u l l  for  2  2  be  on  is  between the  the  imposition constrained  c o n s t r a i n e d and u n c o n s t r a i n e d  are sometimes r e f e r r e d  a  to as a 'matched'  demand system.  fThe l a b o u r - s u p p l y f u n c t i o n of a man or woman with a spouse who i s constrained w i l l be referred to as a 'rationed' labour-supply (leisure-demand) function; a labour-supply (leisure-demand) f u n c t i o n c o n d i t i o n a l on a spouse's q u a n t i t y constraint.  The C o n s t r a i n e d Labour-Supply Model / At e s t i m a t i o n ,  only one set  of preference parameters w i l l  62 be  obtained.  The  Model 2  2.3,  2.4  e s t i m a t i n g equations  and 3.10  and  i  T l  l  1  2  7 2  where e , e , u , u 1  2  1  2  are  E(e^)=0, E(u^)=0, and  jointly,  i=1,2,  /Y-W Z /Y-W 7 /Y}+U 1  2  1  normally  2  (2.6)  longer  equation i s  the  2  distributed (see  2)  are no longer assumed to  be  same as  i n the  individuals, unconstrained  except that the  gamma and theta parameters  assumed  functions  to  be  with  Appendix  of demographic v a r i a b l e s . For s i n g l e  the e s t i m a t i n g model  7 o  and v a r i a n c e Z"  where the gamma parameters  functions  no  2  2  by  (l-ToA-w^/Y-w^/Yj+U!  2  (3.11) w n / Y = w / Y + 0 / ( 1-t?, ) { 1 2  couples are given  3.11:  (3.10) w n / Y = w / Y + 0 / ( 1-0 ) i  for  of  the  are  demographic  variables.  Models 1 and 2 are intended to represent extreme the nature of unemployment. The strongest should  ignore  the  possible  views about  constrained  influence  of  demographic  c h a r a c t e r i s t i c s on labour supply by assuming t h a t , choice,  individuals will  way. From Model the  this perspective,  1 become labour  example,  respond to  the demographic  important i n f l u e n c e s  market.  make a worker  wage r a t e s  Additional  on  years  more a t t r a c t i v e  model  given  in the  the same  variables  of  the demand side  of  of to  education, a firm making  for a  The C o n s t r a i n e d Labour-Supply Model / hiring decision  ( r a t h e r than a f f e c t i n g  for unemployment). influence  both  individuals  In  labour demand  do  face  region/occupation presumably  reality,  some  which  element  move/change o c c u p a t i o n s . Model 2 ignores the  of Model  the e s t i m a t i o n  procedure for  account of the  possibility  labelled  and  factors  labour s u p p l y .  live/work,  taste  in  in  is  not  the former,  if the  there  decisions  ignores  must  Even  constraints  they  1  'taste'  to  while  latter.  However, the basic d i f f e r e n c e  desired leisure  demographic  demand-side  in  the worker's  63  shares.  between Models 1 and 2 i s the c o n s t r a i n e d  that  For  we do  Model  model  not always  2,  an  that takes  observe  individual  ' c o n s t r a i n e d ' when given h i s or her observed  is  wage,  the i n d i v i d u a l would p r e f e r to  work more weeks (take  fewer  weeks of unemployment)  or she  work.  than he  T h i s does not n e c e s s a r i l y a v a i l a b l e for him unemployment i s affect  mean that there  or her at i n some  i s observed to  a lower wage.  i s no other It may be  sense ' v o l u n t a r y . '  the b a s i c p o i n t of Model 2: a s s o c i a t i n g  T h i s does  utility-maximizing  choice.  that not  observed wage  r a t e s with observed unemployment can y i e l d b i a s e d estimates i f at that wage  job  parameter  observed unemployment i s not  the  The C o n s t r a i n e d Labour-Supply Model / 4.  64  D e r i v a t i o n of the L i k e l i h o o d F u n c t i o n  E s t i m a t i o n of the c o n s t r a i n e d leisure-demand model a generalization  of  the  i n d i v i d u a l observed  to  'Tobit'  approach.  experience  involves  For  a  unemployment,  some p r o b a b i l i t y , P ^ , that he or she c  is  single  there  is  constrained:  P =PROB[s°>s(7,0,w )+e J c i  i  i  =PROB[e <s°-s(7,0,w ) ] i  where,  as b e f o r e ,  leisure s  i  °"  optimal  shares, s ( )  tCiia...  -co  And,  s ° and s(7,0,w^) are observed and  1  there  1  i s some p r o b a b i l i t y that an unemployed  individual  i s c a r r y i n g out an o p t i m a l p l a n : P  nci  If  = 1  - ci' p  an i n d i v i d u a l  is constrained,  model, a l l we know i s If  an i n d i v i d u a l  that  then,  unemployed  in the b a s i c  i s c a r r y i n g out an optimal p l a n ,  individuals  c i  c i  c i  )  •(,-P  (i=1,...m),  c l  then  there  the e r r o r term may t a k e .  the  unconditional  p r o b a b i l i t y of o b s e r v i n g a p a r t i c u l a r data p o i n t XJ=(P )(P ) /(P  Tobit  s?>s(7,6,w^)+e^ .  are no r e s t r i c t i o n s on the values  For  as  )f(. )/(,-P 1  c l  )  is  The C o n s t r a i n e d Labour-Supply Model / Or,  t a k i n g account  Xj=P  c i  /P3  i +  f(  P  s°£1f  x  1  1  observed  .n) must  (e^-s(7,  r e s t r i c t i o n that  , f(e-)de-.  not  Model 1, a l l  the  3 i  —oo  Individuals (i=m+1  )/  1-s()  where P3-=/ 1  e i  of  65  to  work f i f t y - t w o  we know  experience weeks  each y e a r .  about such i n d i v i d u a l s  0,w)). For these  unemployment  is  that  As  in  s°^0  individuals,  -s() X?=/ 1  Or,  f(e.)de.. 1  —oo  1  t a k i n g account  of  the  restriction  that s ° ^ 1 ,  -s() Xf = /  f(e.)de. — co  1  1  Thus, the  XJ  i. I  1  1  l i k e l i h o o d function  represented L=n  /P3..  1  for s i n g l e i n d i v i d u a l s can  be  as:  n x?. i.rtf»  1  For c o u p l e s ,  estimation  of  model i s more c o m p l i c a t e d . constrained,  this will  the c o n s t r a i n e d If one member of  affect  the behaviour  leisure-demand the household of  the  is  other.  f i n the constrained model, households need not be in a p o s i t i o n of ' e q u i l i b r i u m ' with respect to the UI programme. Optimal plans should be ' e q u i l i b r i u m ' p l a n s , but allowing for the possible existence of constraints means that i n d i v i d u a l s w i l l not a l l be observed in e q u i l i b r i u m . Thus, i n d i v i d u a l s may be l o c a t e d on segment one as a result of labour-market c o n s t r a i n t s . The only r e s t r i c t i o n which must be made i s that s ° < 1 ; e^1-s(7, 0,w).  The C o n s t r a i n e d Labour-Supply Model / 6 6 Given that work one  both members are l a b o u r - f o r c e p a r t i c i p a n t s or  more  configurations  are  Case 1: N e i t h e r  weeks),  then,  the  following  (i.e.,  household  possible:  husband nor  wife experiences  unemployment  (i=1,...K). For f u l l - y e a r s°^0  that  workers,  the  s ^ 0 . For  and  only i n f o r m a t i o n such  2  a household,  c o n t r i b u t i o n to the l i k e l i h o o d f u n c t i o n X W X  "  S  °  2  ;  —oo  X  1_ where P 4 , = T  ()  s 2  1  (i.e.,  the  is  relevant  is:  "^^(eKendeJdef/P^. — oo  the  X  1_  J.  i.  X  ()  s  J  — oo  X  available  1  f(e!,e?)deMe? 1  — oo  probability  that  1  1 1  both  husband  and  wife  participate).  Case 2: One  i n d i v i d u a l experiences  other  not.  does  experiences  unemployment  (i=K+1,...L). constrained  Suppose,  for while  Then, we know that is:  PROB[s?>s (7,0,X)+e ;s?<O] 2  2  -J  s?-s() — 00  S  ~S1() — co  f (u!,e?)duMe? X  I  X  X  unemployment while  example, the  that  husband  the  the wife  does  the p r o b a b i l i t y the wife  not is  The C o n s t r a i n e d Labour-Supply Model / The p r o b a b i l i t y unemployment  she  is  is  e x p e r i e n c i n g her  then  1 - P  ci'  Thus,  desired level the  f(ei^!)deJ/P4  M =0  ()  1~S  where P 4 . = 2  (the  1  /  /  -co  if  2  ()  f (u3,e?)duMe?  1  1 1  the  wife's  leisure  (i=L+1,...M),  i  0°  =  the  3  C x  ~  S  2  3  3:  )  /  —co  S  l  "  s  (  3 i +  e  1 1  1  Both  /  / —oo  probability  (i)  this  situation,  wife of  3 i  deMe? 1 1 2  1 1  and  wife  1  experience  1  unemployment  (i=M+1,...N).  In  1).  f(eKu?)de?du •. —oo  husband  the  is:  P^/P4  f( J,e?)  )  —oo  and where P 4 - =  Case  (  and  unemployment while the  unconditional  f(eJ,u?)de?/P4  where P . = /  leisure  share are both l e s s than  observing a p a r t i c u l a r data p o i n t X  1 1  desired  the husband experiences  does not  is:  —co  probability  fully  P|./P4 .  2 i +  ^ _g  (\ 2  husband's e f f e c t i v e  And,  unemployed  of  unconditional  p r o b a b i l i t y of observing a household with the husband employed and the wife  67  four sub-cases must be c o n s i d e r e d :  Both i n d i v i d u a l s are c o n s t r a i n e d in unemployment:  The C o n s t r a i n e d Labour-Supply Model / 1  r ' - * ~ 9  (ii)  S  <  / . f "  )  The  5  0  husband  ^ ) ,  is  68  epdejde?^,..  unconstrained  while  the  wife  is  constrained: The  husband must be l o c a t e d on h i s e f f e c t i v e  function  (i.e.,  his choice,  while not  c o n d i t i o n e d on h i s w i f e ' s q u a n t i t y 1?=/ X  S  2  _  S  /  O  —CO  (iii)  The  —CO  "  S l ( )  itself  leisure-demand constrained,  is  constraint).  f(u),e?)du)de?/P4 .. 2  X  wife  is  X  X  X  X  unconstrained  while  the  husband  is  constrained: l|=r"  S  2  —oo  X  (iv)  (  )  ;  S  °"  S  (  )  Neither  f(e!,u?)dejdu?/P4 .. 3  —CO  X  X  is constrained;  X  X  X  both are unemployed:  l?=f(ej,e?)/P4, . i  The  u n c o n d i t i o n a l p r o b a b i l i t y of observing both husband  wife unemployed i s  given by  X? = 13+ 1?+ 1?+ 1?. Finally,  the  l i k e l i h o o d function  L=fi x. n x?ri x ? n x ? . 1  ;=i  1(<MI  li'LH  li«<*n 1  for couples  is  and  IV. ESTIMATION RESULTS  In  Chapter  Four  I  present  estimation  results  for  u n c o n s t r a i n e d and c o n s t r a i n e d l a b o u r - s u p p l y models i n Chapters Two and T h r e e . data employed present  for  developed  I begin with a d i s c u s s i o n of  the two  sets  of e s t i m a t i o n s .  parameter estimates for s i n g l e conclude  the  couples.  I  the  chapter  estimated  labour-supply e l a s t i c i t i e s  Then,  women, s i n g l e  with  a  the I  men and  comparison  of  for the two models.  1. Data  The data  set  used  for  estimation  is  the  1982  Consumer Finance (Incomes of Census Family U n i t s , total,  40,308  households  answered  demographic c h a r a c t e r i s t i c s ,  employment  year p r e c e d i n g the survey observations estimation. excluded. student,  First,  farmer, years  appropriate households  assume  for  that  leisure-demand d e c i s i o n s ,  1981).  In  questions  about  and income for  inclusion  not e l i g i b l e  in which  permanently unable of age  of  (1981). However, not a l l of  Thus, households  sixty-five models  are  Survey  were  households  69  in  the head or wife to work  make  these the  UI must  at  with  more  Similarly,  since  be  was  or more  dropped. Second,  households  income e a r n e r s were e l i m i n a t e d .  for  the  a  than  since  the  most  two  than the  two model  Estimation Results / assumes only one economic  f a m i l y per household,  with more than one economic since  the  " t o t a l earnings  include  military  earnings  from self-employment,  households  with  eliminated.  earnings,  earnings  n o n - p a r t i c i p a n t s were  and 2366 have a s i n g l e  General f e a t u r e s 4.1  to 4 . 3 ) ,  experienced  feature  boarders  and  source but  wages  were  for the c a l c u l a t i o n of  labour  force,  A l l of  gross  households  this  11,019 households  1919 have a s i n g l e  with  reduced  the  of which  6734  male working head  female working head.  that  23.3  some unemployment of the  percent i n 1981,  1980s began.  differences:  24 percent  percent of the men work p a r t time.  (see  Tables  of the sample  heads  the year  in which the  A second  distinctive  of  unemployment than  3  P a r t - t i m e workers have  a  r e p o r t e d to have men.  A similar  i n c i d e n c e of unemployment for  of  the women but only  i n c i d e n c e of unemployment than f u l l - t i m e workers,  women, o v e r a l l , are  lower  variables  of the data i s r e v e a l e d through an i n v e s t i g a t i o n  male/female  higher  from  worth n o t i n g about the data are  first,  major r e c e s s i o n  any  excluded.  have two working heads,  wife"  wage r a t e s cannot be c a l c u l a t e d  the  sample s i z e from 40,308 to  for  Third,  in a d d i t i o n to wage e a r n i n g s ,  from  since  for n o n - p a r t i c i p a n t s i n  head,  earnings  T h i s was necessary  weekly wages. F i n a l l y ,  households  family were e l i m i n a t e d . for  70  a lower  incidence  peculiarity,  given  women than for men,  yet of the is  E s t i m a t i o n R e s u l t s / 71 that average weeks  of employment are  average weeks of unemployment fact,  for women,  that many  are the same  average weeks of  weeks of unemployment f a l l women e i t h e r  unemployed when not  fewer  for women,  yet  as for men.  In  employment p l u s  average  short of one y e a r . T h i s  do not  working or  choose  to  call  that they drop  labour f o r c e when they lose t h e i r j o b s .  suggests themselves  out of  the  (For e s t i m a t i o n ,  any  weeks not r e p o r t e d as weeks of employment are d e s i g n a t e d  as  weeks of  to  'leisure'.)  Average incomes p r o v i d e a t h i r d way  c h a r a c t e r i z e the d a t a . income (1981)  is  $22,202; the  c a p i t a income (1981) are c l a s s i f i e d as fall  The average,  is  'poor'  (i.e.,  of t a x ,  average,  $10,186. In  short of the S t a t i s t i c s  Of these 960 households,  net  household  net of  total,  their total  960  tax,  households  incomes  Canada "Low-Income  per  (1981)  Cut-Offs").  260 are headed by a c o u p l e ,  211  by  a s i n g l e man and 489 by a s i n g l e woman.  Table 4.2  p r e s e n t s average  values by  P a t t e r n s here with respect wage r a t e s features  are  to  unemployment Mining, by  much  as  occupational  to male/female d i s t r i b u t i o n might  note,  however,  in  occupations  be  are the such  expected. very as  Incomes are  Again, lowest  basic and  high  rates  of  Forestry/Fishing,  expectations  unemployment  and  Distinctive  and C o n s t r u c t i o n . Table 4.3 p r o v i d e s average  province.  group.  is  are highest  values  fulfilled. in  the  Estimation Results / A t l a n t i c p r o v i n c e s . Incomes are h i g h e s t  in Ontario,  and B . C . The i n c i d e n c e of unemployment i s and in  the P r a i r i e  provinces;  unemployment i s c o n s i s t e n t l y  P r i o r to further 1.  the e s t i m a t i o n  lowest i n  the recorded  72  Alberta Ontario  incidence  of  lower f o r women than for men.  of  Model  1,  the data  sets  were  reduced by:  E l i m i n a t i n g households  with  heads  reporting  positive  weeks of work but no earned income. 2.  E l i m i n a t i n g households with male p a r t - t i m e workers.  3.  E l i m i n a t i n g households with with respect Section  to  the UI  heads out of  programme  'equilibrium'  (see  Chapter  5(c)).  The d i s t r i b u t i o n of  excluded ' d i s e q u i l i b r i u m '  observations  i s presented i n Table 4.4 which compares numbers of on each budget The l a r g e s t  Two,  segment  and a f t e r  from  and from segment  two.  R e l a t i v e l y few o b s e r v a t i o n s on segments three and four  were  one  found to  of o b s e r v a t i o n s  disqualification. eliminated  segment  number  before  workers  (everyone was e l i m i n a t e d )  be i n  'disequilibrium.'  l a r g e number of people s a t i s f i e d  Overall,  Model  1  women and data  sets  surprisingly  benefit.  s i n g l e men,  the f i n a l  were  and  2088  a  the c o n d i t i o n that weeks of  unemployment match weeks of e n t i t l e d  For s i n g l e  were  1677  s i z e s of  the  observations  Estimation Results / respectively. (i.e.,  For  couples,  the  v e r s i o n of  Model  the v e r s i o n without e i t h e r the c o r r e c t i o n for  selectivity  However,  remaining in the  data set  this  a sample, so 2500 o b s e r v a t i o n s  were  5l07.f  For the e s t i m a t i o n of Model 2,  'disequilibrium'  were r e t u r n e d to the data s e t s .  observations  S i n c e , by the assumptions of  some p a r t of observed unemployment does not  the u t i l i t y - m a x i m i z i n g longer necessary  to  point. 1,  randomly s e l e c t e d from the  p o s i t i o n of  sample  at t h i s  for the more c o m p l i c a t e d v e r s i o n s of Model  proved to be too l a r g e  Model 2,  1  or the T o b i t c o r r e c t i o n ) was estimated using the  5107 o b s e r v a t i o n s  For  basic  73  choices  of  r e q u i r e that  'equilibrium'  households,  it  each i n d i v i d u a l  with r e s p e c t  to the UI  reflect is  no  be i n  a  programme.  s i n g l e women and s i n g l e men, d i s e q u i l i b r i u m o b s e r v a t i o n s  were r e t u r n e d to  the Model  1  data sets to  data sets with 2297 and 1796 o b s e r v a t i o n s couples,  all  random  sample  of  e s t i m a t i o n of Model  Differences  respectively.  d i s e q u i l i b r i u m observations  the o r i g i n a l Model 1 data set  in  the  2000  c r e a t e Model  were returned  of 5107 o b s e r v a t i o n s .  observations  was  drawn  Then, for  2 For to a the  2.  mean  p o p u l a t i o n s for Models 1  characteristics and 2 are  of  the  sample  r e p o r t e d i n Tables  f T h i s was achieved u s i n g the subroutine the f i l e CPUrLIB at UBC.  RSEQ a v a i l a b l e  4.5 in  Estimation Results / and  4.6.  The  increase  most  significant  i n average  Model 2 data s e t s . m a j o r i t y of  feature  to  weeks of unemployment T h i s i s to be  'disequilibrium'  is  the  observed i n  all  given that  the  expected,  note  74  o b s e r v a t i o n s being returned  the sample are l o c a t e d on segments one and two ( i . e . ,  to  at  the  Model 1 parameter estimates are presented i n Tables 4 . 7 ,  4.8  high-unemployment end of the budget c o n s t r a i n t ) .  2. Model 1 E s t i m a t i o n R e s u l t s  and  4.9.  likelihood,  These  estimates  using  the numeric  from the n o n l i n e a r f u n c t i o n FLETCH uses  a 'quasi-Newton'  three s e t s of e s t i m a t i o n s  were  obtained  by  maximum  optimization routine  FLETCH  o p t i m i z a t i o n package, UBC NLP. algorithm. Results  are d i s c u s s e d  from  the  in t u r n .  (a) MODEL 1: SINGLE WOMEN  For  single  women, as for s i n g l e men, c o r r e c t i n g for  possible  b i a s i n t r o d u c e d through the e x c l u s i o n of a l l o b s e r v a t i o n s on segment  one of the budget c o n s t r a i n t had almost no impact on  parameter  estimates.  computation, t h i s estimation.  Thus,  procedure was  to  reduce  the  omitted from  cost all  of  further  A l l parameters r e p o r t e d for s i n g l e men and women  have been o b t a i n e d without u s i n g t h i s c o r r e c t i o n .  Estimation Results / Table 4.7 p r e s e n t s women.  Model 1 parameter  'Basic' estimation  75  estimates for  single  of the u n c o n s t r a i n e d model  ignores  the c e n s o r i n g of the e r r o r d i s t r i b u t i o n which must e x i s t  as  a result  be  of the r e s t r i c t i o n that weeks of l e i s u r e cannot  observed  to  account of  fall  this  statistically models;  below  neither  tobit  case  model,  significantly  Differences  estimation  (at the 99 percent 7  is  exceptions of CITY and YRSE in the  'Tobit'  r e s t r i c t i o n . The parameters 7  significant  in  zero.  all  at l e a s t  1 0  and 0  level)  significant.  0 0  takes are  1 O  in  both  With  the  the b a s i c model and CITY  demographic  variables  in  appear  once.  between the b a s i c and t o b i t  parameter  estimates  show how i g n o r i n g the c e n s o r i n g of the e r r o r d i s t r i b u t i o n at fifty-two  weeks  of  employment b i a s e s  obtained i n the b a s i c Model for  both 7  after  and 0  1 0  the t o b i t  the parameter 7 value for  0  1 O  insignificant  1 estimation.  increase  1 O  parameter  enormously  estimates  Estimated ( i n absolute  c o r r e c t i o n i s made. The estimated 1 0  from  in both cases and  .1047 so w i l l  Such dramatic changes i n estimated s u r p r i s i n g given that are observed at the  (i.e.,  .4050.  not be  for  estimated (700  is  discussed.)  parameter values are  80 percent of  limit  to  terms)  value  drops from -6.570 to - 8 3 . 1 2 ; the  increases  values  the sample  working f i f t y - t w o  not  population weeks).  Estimation Results / The  estimated  impact  of  demographic  l a b o u r - s u p p l y parameters, y ,  variables  the  is also affected  by  the t o b i t c o r r e c t i o n . The estimated parameters for ATLAN,  a  0  dummy v a r i a b l e Atlantic  set  region,  equal  .2659 i n  the  l  to one  for women  follow the same p a t t e r n as  decreases from -6.249 in t o b i t model; 0!,  7  and 0 , ,  on  76  the b a s i c model  increases  tobit  l  (ATLAN  either  influence  positively),  on  both  estimated  7  o  parameters impact of  woman's economic  or  in  :  the  the  basic  a  strong  and  tobit  equal to  Western p r o v i n c e s , does not  to i n f l u e n c e  l  o  both  exerts  WEST, the r e g i o n a l dummy v a r i a b l e set  7  in  also  models.)  women l i v i n g i n the  7M  1 O  to -62.12 i n  influence  for  and 0  0  positive  7  the  from .09333 i n the basic model to  model. on  7  l i v i n g in  0,  the  tobit  EFAM, the  family,  appear  i n the b a s i c model (WEST  but does exert  on  7  a strong  case.  one  does  influence  Similarly,  the  number of  i n d i v i d u a l s in  ,  is  and  0,  a  significantly  a l t e r e d when the t o b i t c o r r e c t i o n i s made. The v a r i a b l e EFAM e x e r t s a negative on  0,  influence  in the b a s i c model.  on  7  l  and a p o s i t i v e  These s i g n s reverse  influence  in the  tobit  case.  Overall, as  Model 1 r e s u l t s  proxies  for  suggest that demographic v a r i a b l e s ,  individual  participation/part-year/full-year  tastes, choices  women. T h i s r e l a t i o n s h i p obscures the  influence made  impact of  by  the single  demographic  Estimation Results / variables  on  the  actual  employment/unemployment a full  year.  choose to  average  incidence  of  between  that a woman  which obscures  residence  for women  weeks  a connection  and the p r o b a b i l i t y  work for women who are i s true  for example,  work f u l l - y e a r  between region of  of  i f a woman decides to work l e s s than  There i s ,  r e g i o n of residence  choice  77  the  will  relationship  and c h o i c e of number of weeks of  choosing weeks. In p a r t i c u l a r ,  l i v i n g in  the Western  and d u r a t i o n  this  provinces  of unemployment  where  are  lower  than i n e i t h e r A t l a n t i c or C e n t r a l Canada. In the context of Model will  1, the low p r o b a b i l i t y that a woman l i v i n g i n the West choose any  unemployment h i d e s  women l i v i n g in 'tastes' the  the West  who do  the  fact  of  similar  women  country. Similar d i f f i c u l t i e s EFAM on a s i n g l e  the  choose unemployment  for l e i s u r e which are s i g n i f i c a n t l y  '"tastes'  that  living  have  different  elsewhere  i n i n t e r p r e t i n g the  woman's l a b o u r - s u p p l y d e c i s i o n  few  from  in  impact  the of  are  overcome  The parameter estimates o b t a i n e d ' using the c o r r e c t  (tobit)  by c o r r e c t l y s p e c i f y i n g  specification  for Model 1 are c o n s i s t e n t with the  of u t i l i t y - m a x i m i z i n g observations: the  2058/2088  regularity  t h i r t y women,  the model.  behaviour f o r observations  conditions 7 >X .) 0  0  a strong (99  for u t i l i t y  hypothesis  majority  percent) maximization.  of  satisfy (For  Estimation Results /  78  (b) MODEL 1: SINGLE MEN  Table 4.8 men. 7,o  presents  As was true  Model 1 parameter for s i n g l e  are s t a t i s t i c a l l y  in both the significant  women,  significant  b a s i c and  estimates for  single  the parameters 0  (at the 99 percent  t o b i t models. The  (with 95 percent confidence)  level)  parameter 7  model  not i n the t o b i t model. The p a t t e r n of change i n 7  8i  between  that  found  -140.0;  0  the b a s i c for s i n g l e  1 o  values of  changes  and t o b i t models women: 7  from .1327  to  estimated parameters  and  1 0  i s very s i m i l a r  changes  1 0  is  0 0  i n the b a s i c  but 0  and  1 O  from  .5873. A g a i n ,  -8.856 the  to to  absolute  increase dramatically  when  the t o b i t c o r r e c t i o n i s made.  However,  patterns  of  change  demographic v a r i a b l e s are q u i t e for  single  women. In  the b a s i c  r e g i o n a l v a r i a b l e s ATLAN and to the  impact  parameters and However,  for  of  these  insignificant after for  the  the  from those  model, the  the  on  the  supply of regional  tobit correction  on found  impact of  WEST, for example,  labour  men,  coefficients  different  variables  hence the single  in  is  the  similar  labour-supply single  women.  variables i s made  are  whereas,  s i n g l e women, the impact of ATLAN remains strong and the  impact  of  correction.  WEST For  only single  becomes  apparent  men, region  of  after  the  residence  tobit has  an  Estimation Results / important i n f l u e n c e t h i s choice  on the  full-year/part-year choice.  i s not d i s t i n g u i s h e d  i n d i v i d u a l ' s leisure-demand  correction  i s made, i t becomes  important  determinant  of  employment/unemployment worker (presumably either  i n the  having  more  influencing  a  the  of  are  the  choice  If  tobit  a  of  seasonal  workers  l i v i n g in  weeks  an  weeks  being  crucial of  the  of  seasonal  West),  influence  region i s not  number Rather,  majority  actual  decision.  the  chosen.  education  an important  c l e a r that  A t l a n t i c or the  If  from the c h o i c e of weeks of  work, ATLAN and WEST appear to exert on an  79  live  a city  or  taste  factors  (given  that  a  p a r t - y e a r c h o i c e has already been made).  A difference may be  i n the modelling  connected  to  this  of male and female  result.  Part-time  sometimes d e s c r i b e d as having d i f f e r e n t than f u l l - t i m e workers ( e . g . , Hence, a  dummy  v a r i a b l e set  part-time,  only 3 percent  variables  leisure  Nakamura and Nakamura,  1983).  equal  to one  different  for  'taste'  of the men in the  only i n c l u d e d i n  part-time proxies.  sample  occupations tastes  for  are  the set  sometimes  leisure  work  from the sample and of  than  viewed workers  the  demographic  for women. S i m i l a r l y , workers who choose  or c y c l i c a l  are  for  these men were excluded  v a r i a b l e PART was  workers  'tastes'  workers was i n c l u d e d among the demographic However, since  behaviour  seasonal as  having choosing  Estimation Results occupations  with  and  1982).  Alam,  more s t a b l e Hence,  v a r i a b l e s were i n c l u d e d  employment p a t t e r n s seasonal  for men,  only a very small f r a c t i o n of in  these  occupations  construction,  mining,  the  but not  Perhaps without  cyclical  found  hunting,  handling).  forestry,  However,  women  were r e t a i n e d  the seasonal dummy v a r i a b l e ,  of the weeks of work chosen  Estimated parameter  dummy  sample of women was  r e g i o n a l v a r i a b l e s ATLAN and WEST would be more determinants  (Glenday  since  working in seasonal or c y c l i c a l occupations the sample.  values for  the t o b i t  model are  again  most o b s e r v a t i o n s :  single  satisfy (c)  regularity  the  by s i n g l e men.  of u t i l i t y maximization  /1677  in  significant  c o n s i s t e n t with the h y p o t h e s i s 1670  80  for women  (fishing,  materials  and  /  men  (99.6  for  percent)  conditions.  MODEL 1: COUPLES  Model  1  parameter estimates  Table 4 . 9 . model,  for  Results  are reported for  the b a s i c  s e l e c t i v i t y bias  for couples  model c o r r e c t e d  introduced  are presented  the b a s i c  uncorrected  for p o s s i b l e  by e x c l u d i n g  sample  non-participants,  and for the t o b i t  model, again c o r r e c t e d for p o s s i b l e  selectivity bias.  (Since  had a s i g n i f i c a n t  impact on parameter estimates obtained  couples,  t h i s procedure i s  the  in  sample s e l e c t i v i t y  sample  correction  maintained in the e s t i m a t i o n  for of  Estimation Results / all  other  models.)  The b a s i c p a t t e r n of  results  obtained for couples  the p a t t e r n s  o b t a i n e d for both  (except that  the c o r r e c t i o n for s a m p l e - s e l e c t i v i t y  not s i g n i f i c a n t l y either 0,,  8  single  level)  in  absolute fact,  magnitude  did  estimates obtained  for  (at  increase  the  95  7  1  0  r  i s made.  budget shares  of  720t  percent  substantially  tobit correction  (marginal  men  bias  significant  when the  in In  leisure)  individuals.  the  only  ( t a s t e s ) can a f f e c t gamma parameters, estimated  way  that  demographic  behaviour i s through t h e i r  impact  by the t o b i t  of  the  demographic  variables  impact on the  f As was a l s o true for s i n g l e  estimates obtained i n the  women and s i n g l e  even more d r a m a t i c a l l y for married i n d i v i d u a l s than  couples,  affected  resembles  women). The parameters  and again  9 parameters  for s i n g l e  the  single  parameter  men or s i n g l e  a l l models  the  increase  For  affect  are s t a t i s t i c a l l y  2  81  individuals,  variables  c o r r e c t i o n , suggesting that the basic model  impact of demographic v a r i a b l e s  are b i a s e d .  on the y  2  is  parameter Compare  parameter  in  t ' T e c h n o l o g i c a l ' r e s t r i c t i o n s made i t impossible to allow 0, and 8 to vary with demographic c h a r a c t e r i s t i c s for c o u p l e s . T h i s would have added twenty parameters to the thirty-eight already being estimated, causing difficulties for the o p t i m i z a t i o n package. T h i s d i f f e r e n c e between the models for s i n g l e household heads and f o r couples should be kept in mind. 2  Estimation Results / the basic model the  (with sample  selectivity  impact of demographic v a r i a b l e s  the t o b i t variable  model: is  the  on the y  coefficient  insignificant  i n the  on  wife  dummy  increases the  on PART, a dummy v a r i a b l e to i n d i c a t e that  the  than  seven  become  years  i n the t o b i t  of  age  in  significant  in  the  tobit  the estimated  v a r i a b l e s on 7 , . Some s i m i l a r i t i e s the estimated t a s t e c o e f f i c i e n t s As was a l s o dummy i s  true for  y, 2  insignificant  model.  the  impact of  in patterns  for y^ and y  2  the c o e f f i c i e n t  insignificant  coefficient  c h i l d r e n l e s s than seven years insignificant tobit  are  magnitude The  tobit  demographic of change  in  can be noted.  on the  Atlantic coefficient  in the b a s i c model but  on  CLT7,  the  tobit  number  of is  i n the basic model but becomes s i g n i f i c a n t  in  are,  This  first,  of age  i n the  in the household,  model.  Differences  in  model.  in magnitude and becomes s i g n i f i c a n t  Again,  ends that  the  i n absolute magnitude  the t o b i t model; second,  that  list  of  the c o e f f i c i e n t  dummy v a r i a b l e to i n d i c a t e residence increases  household,  i n both models while the  the Western dummy i s  increases  the  i n the basic model, but increase  correction also affects  the  Western  case;  insignificant  on  the  in  i s a p a r t - t i m e worker, and CLT7, the number of c h i l d r e n  less  and  with  parameter  2  b a s i c model but  in magnitude and becomes s i g n i f i c a n t coefficients  correction)  82  similarities. on CITY,  the  i n a l a r g e r urban a r e a ,  and becomes s i g n i f i c a n t  the c o e f f i c i e n t s  on YRSE2,  in the  years of  education of the w i f e ,  indicate  that the  follow  to i n d i c a t e  seasonal  occupation,  increases  in  while  magnitude i n  again c o n f i r m  83  and CYC, a dummy v a r i a b l e  to  husband works i n  the same p a t t e r n ; t h i r d ,  a dummy v a r i a b l e  Estimation Results /  that  the  a cyclical  that that  the c o e f f i c i e n t the husband  significant the t o b i t  estimated  to the  c e n s o r i n g of  fifty-two  weeks of work.  It would  be  single  interesting  women  results  with  to  However, 7 and the  since  (the w i f e ' s  works in  model. Thus,  results  of  demographic  distribution  Model 1  for  results  married  level  choice of  leisure)  household  heads,  of  and  men with those for married  since  education  d i r e c t l y comparable.  at  and men.  both  the  i n d i v i d u a l s but only the 7 there  are c r o s s  affecting  the  for couples which do not e x i s t observed  is  for  women  demographic v a r i a b l e s can i n f l u e n c e  couples  a  models,  i f proper a t t e n t i o n  compare  8 parameters for s i n g l e  parameters for  on SEA,  both  the e r r o r  those obtained  obtained for s i n g l e  in  impact  v a r i a b l e s on labour supply i s b i a s e d not given  occupation,  patterns  of  changes  effects husband's  for  single  are  not  Estimation Results /  84  3. Model 2 E s t i m a t i o n R e s u l t s  Model 2 parameter estimates are presented i n Table 4.10. The model i n c l u d i n g the  t o b i t c o r r e c t i o n for  the c e n s o r i n g  the e r r o r d i s t r i b u t i o n for f u l l - y e a r workers i s the a p p r o p r i a t e s p e c i f i c a t i o n , and making t h i s c o r r e c t i o n context  of Model  1. T h e r e f o r e ,  judged to be  the consequences  have a l r e a d y been  of  not  discussed in  the  a l l Model 2 r e s u l t s  presented  have been estimated using the t o b i t c o r r e c t i o n . And, as Model  1, a l l r e s u l t s presented  for s i n g l e  been estimated without  the c o r r e c t i o n  selectivity  a  bias  as  non-participants,  while  result a l l results  for  individuals  for p o s s i b l e  of  of  the  have sample  exclusion  presented for  of  couples  have been estimated with t h i s c o r r e c t i o n . However, for Model 2, where ' d i s e q u i l i b r i u m budget  constraint  'participation'  r  have  has  o b s e r v a t i o n s on segment one of been  the  returned  more  normal  'working a p o s i t i v e number of weeks.' working l e s s than the minimum  to  the  the  sample,  interpretation  of  (Model 1 t r e a t s anyone  number of weeks necessary  to  gain e l i g i b i l i t y to UI as a ' n o n - p a r t i c i p a n t . ' )  As i n d i c a t e d  in Table  4.10,  leisure-demand e q u a t i o n s ,  7  the and  l  7  shift 2  parameters  in  the  , as w e l l as the marginal  budget share  parameters,  0,  and  0 ,  statistically  significant  (at  the  95 percent  2  are  in  all level).  cases For  Estimation Results / single  men,  the  shift  parameter  in  the  commodity-demand  equations,  yi  variables  are  conditions  for u t i l i t y - m a x i m i z a t i o n are s a t i s f i e d  for a l l  Model  is also significant.  0  not  included  in  ( R e c a l l that Model  2.)  2  parameter  estimates  probabilities  can  of  be  being  used  ).  Tables  calculations  4.11,  4.12  for s i n g l e  and  women,  unemployment. O v e r a l l ,  constraint  are  very h i g h .  woman who i s  income i s  means  82.7  percent.  even  to  given  data  present  lower  wages.)  net  wages  e f f e c t s of the  single  p r o b a b i l i t y of c o n s t r a i n t  sample  and  of  unemployed percent  men,  the  a  prefer  non-labour non-labour  UI programme,  availability  of 79.4  that  p r o b a b i l i t y that  says nothing about c h o i c e s over jobs For  set  estimated p r o b a b i l i t i e s of  this  UI,  unemployed women would o p t i m a l l y choose to work more (This r e s u l t s  for  to be unemployed would  Since  the  calculate  1981  her observed net wage and  i n c o r p o r a t e the that  4.13  The average  observed  to work more weeks at  incomes  everywhere  s i n g l e men and couples  experience  single  Regularity  constrained  i n d i v i d u a l s observed to be unemployed in t h i s c i  demographic  groups.  individual  (P  85  most weeks.  offering average  is also s t r i k i n g l y  high.  For c o u p l e s ,  the average  p r o b a b i l i t y that  a household  in  Estimation Results / which the husband experiences not i s 81.4  unemployment but the wife does  p e r c e n t . T h i s corresponds very c l o s e l y  values o b t a i n e d for s i n g l e the wife experiences  86  with  i n d i v i d u a l s . For couples  the  in which  unemployment but the husband does  not,  the average p r o b a b i l i t y that the household i s c o n s t r a i n e d much lower. The  average p r o b a b i l i t y that  the couple  would  j o i n t l y p r e f e r the wife to i n c r e a s e weeks of employment on average,  only 68.7  percent. This r e s u l t ,  providing  support for t r a d i t i o n a l views about the r e l a t i v e of  the  employment  determined by  the  of  husband  and  f u n c t i o n a l form  wife,  chosen  is  is, some  importance  is  partially  for  estimation  (husband's l e i s u r e and w i f e ' s l e i s u r e must be s u b s t i t u t e s a l i n e a r expenditure system) and by the e m p i r i c a l  fact  in that  the average wage r a t e of married men i s much higher than the average wage r a t e of married women (see couples  in  which  both  unemployment are almost  husband  Table 4 . 6 ) .  and  wife  Unemployed  provinces  are  constraints percent)  constraint  more  (average  single likely  average,  the household would p r e f e r at  l e a s t one person to work a d d i t i o n a l weeks i s  regions.  experience  c e r t a i n l y c o n s t r a i n e d . On  the estimated p r o b a b i l i t y that  P r o b a b i l i t i e s of  Finally,  in  97.5  unemployment  women l i v i n g to  probability  in  percent.  vary the  be  facing  of  constraint  than are unemployed s i n g l e women l i v i n g  across Atlantic  demand-side  in  is  85.6  Central  Estimation Results Canada  (average p r o b a b i l i t y of c o n s t r a i n t  Unemployed s i n g l e men are most they  live  in  constraint  is  constrained  Western 83.5  if  they  only the  husband  constrained  if  is they  if  the  wife  constrained  is  if  they  p r o b a b i l i t y of estimated  in  participate, model of want  'a  74.8  in  are  percent)  i s 76.6  percent).  constraint  are  in  i s 70.1 live is  lend which simply  support most want to  likely  Canada and l e a s t  work  labour-market behaviour  be  likely (average  Couples i n which  most  likely Canada  percent)  and l e a s t  percent),  to  be  (average  f  likely (average  Such  high  for those observed  model  people,  to  (average  i n A t l a n t i c Canada  to a  be  Couples i n which  Western  67.3  of  (average  in C e n t r a l Canada  unemployed  they  Canada  most  Atlantic  i s 84.9  live  probability  percent).  p r o b a b i l i t i e s of c o n s t r a i n t  be unemployed behaviour  if  is  if  l e a s t l i k e l y to  Central  they l i v e  p r o b a b i l i t y of c o n s t r a i n t to be c o n s t r a i n e d  in  live  p r o b a b i l i t y of c o n s t r a i n t only  again,  unemployed  p r o b a b i l i t y of c o n s t r a i n t to be c o n s t r a i n e d  and,  live  p r o b a b i l i t y of c o n s t r a i n t  (average  87  percent).  l i k e l y to be c o n s t r a i n e d  Canada  percent)  i s 80.4  /  of  having  full-time,  to  labour-market chosen all  year;  in which most people  to a  simply  job.'  f l f demographic v a r i a b l e s are r e t a i n e d as t a s t e p r o x i e s in Model 2, these p r o b a b i l i t i e s of constraint look quite different. Single men l i v i n g in A t l a n t i c Canada, for example, have a much lower p r o b a b i l i t y of being constrained s i n c e , in such a model, they have pronounced ' t a s t e s ' for leisure.  Estimation Results / The c o n s t r a i n e d model of labour supply assumes, equal,  that  all  individuals  non-labour incomes observed  to  in  the  experience  unemployment, the  respond  to  wage  same way.  Of  two  same  number  the  i n d i v i d u a l with  why  relatively  high-wage  Western Canada have a r e l a t i v e l y constrained i f traditional  observed  things  rates  individuals  of  weeks  This explains,  single  men  unemployed.  However,  this  s u p p l y - s i d e approach to understanding the labour  across w a g e / s k i l l  also  levels.  between  It  absolute  c o n s t r a i n t and how t h i s might r e l a t i v e l y low-wage  present  in  being  that o p p o r t u n i t i e s may  more than  for  living  market ignores the p o s s i b i l i t y  connection  of will  high p r o b a b i l i t y of  to be  and  the lower wage r a t e  have the lower p r o b a b i l i t y of c o n s t r a i n t . example,  other  88  h i s or  single  need  parent,  her observed  aspects  of  and  vary across  income seems i n s u f f i c i e n t  complicated  ignores  the  the  vary  possible  perception  of  income l e v e l s .  A  for example, may  q u a n t i t y of  prefer  employment  if  to cover b a s i c needs. More problem  of  labour-supply  c o n s t r a i n t s can c l e a r l y not be i n c o r p o r a t e d i n t h i s model.  4.  All  E l a s t i c i t y  Estimates  of the d i s c u s s i o n of r e s u l t s  magnitude and s i g n i f i c a n c e more i n t e r e s t  has so far focussed  on  the  of estimated parameter v a l u e s . Of  are the a s s o c i a t e d  labour-supply  elasticities.  E s t i m a t i o n R e s u l t s / 89 For Model  1, the gross own-wage e l a s t i c i t i e s are  calculated  as: O L S . / a w ^ (w./LS.) = [(^/w?)  (Y-To-TiWj-TjWj)  i = 1 2; j = 2,1 W l  i  for couples,  r  OLS^Bw, ) (  +(0 /w )( .-52)]  /LS/)=  i  7  [w./LSj]  and a s :  [(0,/w )  (Y-To-TiW,)  2  + ( 0 ,/w , ) ( - 5 2 ) ] 7 l  [w,/LS,] for  single  men and s i n g l e  Cross-wage e l a s t i c i t i e s (3LS./3Wj)(Wj/LS.)= E l a s t i c i t i e s of  women.  f o r couples  are given by:  [(0 /w )(7 -52)] i  i  [w^/LS.].  j  labour supply  with respect  to  non-labour  income are c a l c u l a t e d a s : (3LS/3NLY)(NLY/LS)= [ - ( 0 / w ) ] [ N L Y / L S ] . Compensated own-wage e l a s t i c i t i e s are c a l c u l a t e d a s : [3LS /9w -LS i  I  I  (3LS^/3NLY)]  [WJ/LSJ]  i=1,2. For c o u p l e s ,  compensated  cross-wage  e l a s t i c i t i e s are  given  by: [BLSj/dwj-LSj(3LS^/3NLY)][Wj/LS ]. i  For Model 2, a l l e l a s t i c i t y the  case  of  unemployment so rationed  couples that  formulas are as above except  with the  labour-supply  one  member  other member function.  e l a s t i c i t i e s are c a l c u l a t e d a s :  constrained  is operating  Then,  gross  in in  on  a  own-wage  Estimation Results /  90  (3LS (Zj)/9w.) (w /LS ) = i  i  i  [ [ ^ ^ ( ( l - e j J w p i t Y - T o - w . Y . - W j Z j l + Ce./t ( 1 - 0 j ) w . ) ] [7 -52]][w./LS.] i  i=1,2  j=2,1.  Cross-wage e l a s t i c i t i e s  for r a t i o n e d  households are  given  by: OLS^ZjJ/BWj) (w /LS ) = j  i = 1 ,2  [c7 /((l-0 )w )][Z -52]][w /LS ]  i  i  j  i  i  j  i  j = 2,1.  Finally,  elasticities  with respect  to non-labour income  for  r a t i o n e d households are given by: ( 3 L S ( Z j ) / 9 N L Y ) ( N L Y / L S ^ ) = [~8  ^/{(1-0jJwj)][NLY/LSj]  i  i = 1 ,2 j = 2 , 1 . Compensated  elasticities  u n r a t i o n e d households, derivatives.  take  the  same  Notice,  however,  that  elasticity  the gross  cross-wage  elasticity  of labour supply with respect fixed  elasticity  from the  respect  of  the  for  compensated  i s zero for r a t i o n e d households  household ( ( 5 2 - Z ^ w ^  The e l a s t i c i t y  as  s u b s t i t u t i n g the a p p r o p r i a t e r a t i o n e d  cross-wage  which i s  form  is  perspective  effectively  since  just  an  to an income source of  the  constrained  i = 1,2).  rationed  labour-supply  functions  to the l e v e l of c o n s t r a i n t faced by the spouse,  can a l s o be c a l c u l a t e d : OLS.(Zj)/9Zj)(Zj/LS )=[(0./((l-0j)w.)Wj][Zj/LS.]. i  with Z^,  Estimation Results / Again, of  t h i s c l o s e l y resembles the  labour supply  that  formula for the  with respect to  employment earnings . Household  of  level  the c o n s t r a i n e d spouse,  income decreases  as  elasticity  non-labour income  the given element in t h i s case i s the  the l e v e l  91  except  of  foregone j=1,2)  (WJZJ;  of  constraint  increases.  C a l c u l a t e d e l a s t i c i t i e s are presented 4.26.  non-labour income,  c h i l d r e n and number of at  weeks  appropriate  of  labour  are  as  predicted  labour-supply for  p r e d i c t e d at  number  i n the economic  supply  calculated  group. Weeks are the e l a s t i c i t y  years of e d u c a t i o n ,  individuals  estimated  elasticities  function.  each  sample  major  equal  evaluated  to  at  a  the  full  fifty-two. corner  responsiveness to a  the  Model  Thus, can  drop in wage not  only  be  that  rate.  For the  individuals.)  as  problem.  models  of  Hence,  labour  on  are  every being  interpreted  for these groups are most meaningful. interpreted  a  elasticities  1  expected,  in almost  evaluated  unemployed  is  and  samples are  this  best  by  means to ensure  samples,  are  family)  i s evaluated at a p o i n t which i s a c t u a l l y  p r e d i c t e d weeks for  of  demographic  the l a b o u r - s u p p l y f u n c t i o n . However, as should be  case  through  Model 1 e l a s t i c i t i e s are e v a l u a t e d at sample means (of  wage r a t e ,  and  in T a b l e s 4.14  as  unemployed elasticities (Both models supply  for  Estimation Results / Since a l l demographic  v a r i a b l e s are excluded  labour-supply functions, at sample  means  for  elasticities  wage  together with the weeks of appropriate  rates  it  is especially  weeks s i n c e ,  by  definition, a  and  For  incomes  point  on  the  use  predicted  of work  'true'  Weeks  of  c o n s t r a i n e d unemployment  households  are,  of  course,  rather  cannot  labour-supply  function.  actual  the  constrained  important to  observed weeks  2  evaluated  non-labour  function.  individuals,  with  are simply  labour supply p r e d i c t e d using  labour-supply  correspond  from Model  92  for than  rationed predicted  values.  Table 4.14  r e p o r t s Model  Note,  of a l l ,  first  evaluated  for  the  unemployment than single since  men this  Third,  single  men.  e l a s t i c i t i e s are much l a r g e r  when  when evaluated  weeks of  for  who for  experience the  unemployed).  i s the group able  largest  elasticities  sub-sample  (employed and  by a d j u s t i n g general,  that  1  full  This  is  sample  in the A t l a n t i c  change  e l a s t i c i t i e s are,  and s m a l l e s t  of  reasonable  to respond to any wage  work. Second,  some  i n the  in  West.  compensated own-wage e l a s t i c i t i e s are l a r g e r i n r u r a l  than urban a r e a s . context of a 'tastes'  for  These r e s u l t s  model which allows unemployment.  considerable v a r i a t i o n  in  are a l s o reasonable  in  for r e g i o n a l v a r i a t i o n Finally,  calculated  while  there  elasticities  the in is  across  Estimation Results o c c u p a t i o n a l groups,  no c l e a r p a t t e r n  Model 1 e l a s t i c i t i e s  for s i n g l e women are r e p o r t e d i n  4.15.  A  nearly i d e n t i c a l  Elasticities the  full  while  there  elasticities  is  e l a s t i c i t i e s calculated  in  are  for  for  obtained.  largest  the Western  considerable  calculated  Table  unemployed sample than  smallest  93  discernible.  results is  Elasticities  A t l a n t i c p r o v i n c e s and And,  p a t t e r n of  are l a r g e r for the  population.  is  /  in  the  provinces.  variation  part-time  for  between  workers  f u l l - t i m e workers, no  and  definite  p a t t e r n emerges.  Tables 4.16-4.19 men;  Tables  report Model  4.20-4.25  1 elasticities  report  Model  1  for  elasticities  married women. A g a i n , e l a s t i c i t i e s are l a r g e r when for the unemployed  sub-sample  e n t i r e p o p u l a t i o n . Gross  than when  married  evaluated  evaluated  own-wage e l a s t i c i t i e s  for  for  s i n g l e men or s i n g l e women. Compensated  elasticities,  on the other hand,  are of s i m i l a r  for married men and s i n g l e i n d i v i d u a l s . T h i s i s with the  compensated  own-wage e l a s t i c i t i e s  values own-wage  magnitudes in  contrast  evaluated  married women which are much l a r g e r than those for any group. The l a b o u r - s u p p l y f u n c t i o n s are,  in  general,  of  positively-sloped  the  married  men and married women are l a r g e r than the e q u i v a l e n t for e i t h e r  for  for other  s i n g l e women and  men  and  the  inelastic;  Estimation Results / labour-supply  functions  positively-sloped women who  and  work p a r t - t i m e  Canada,  who for  work  married  elastic.  in  example,  elastic  is  women  responses  who  seasonal is  between men and in  for  married  (the  average  occupations  4.2886).  part-time  which are d i f f e r e n t  p o p u l a t i o n ; that  suggest,  work  are  f o r women who work p a r t - t i m e  This  f u r t h e r c o n f i r m a t i o n for the Nakamuras' it  women  Elasticities  are h i g h l y  gross own-wage e l a s t i c i t y husbands  of  there i s  in  Atlantic  result  provides  have  that  labour-supply  from those of the r e s t of  l i t t l e difference  women who work  particular,  with  (1983) f i n d i n g  who  in  is  little  the  behaviour  f u l l - t i m e . Model 1  that there  94  results  difference  between the l a b o u r - s u p p l y behaviour of s i n g l e working  women  and working men.  E l a s t i c i t i e s with  respect  to non-labour  smaller than own-wage or cross-wage men  and  married  women;  income  elasticities  elasticities  with  are  much  f o r married respect  to  non-labour income are l a r g e r than own-wage e l a s t i c i t i e s  for  s i n g l e men and s i n g l e women.  For  couples,  A t l a n t i c Canada urban/rural  labour-supply  elasticities  and s m a l l e s t  in Western  pattern  is  labour-supply e l a s t i c i t i e s  evident. of married  are  largest  Canada. No  Occupation  in  clear  influences  men, but as was  also  Estimation Results / the case for s i n g l e men, no c l e a r p a t t e r n  Within  the  model  interesting  joint  cross effects  Other things if  of  equal,  maximization  on e l a s t i c i t y  the w i f e ' s  discernible.  magnitudes  labour supply i s  her husband works in a seasonal o c c u p a t i o n ;  labour supply i s  less e l a s t i c  worker. These r e s u l t s expenditure  system  substitute  for  intuitively  wife's.  plausible.  couple w i l l steady  However, If  one  employment,  employment  path  they member  it  is  the other and  hence  consequences  responses  to  of  such  labour-market  some emerge.  less the  elastic  husband's  is a  part-time  by the  linear  l e i s u r e must are of  be  at a  household that  member to  follow  to  be  the a  relatively  by the UI  cross  a  least  reasonable  to any i m p l i c i t tax generated  possible  household  husband's  j o i n t l y prefer  unresponsive  i f h i s wife  are p a r t l y determined  in which  experiences unsteady  The  utility  is  95  system.  effects  policy  are  for often  over-looked.  Table 4.26  presents Model  Elasticities  for couples presented  rationing occurs; refers  to  couples  i g n o r i n g the m a r r i e d women  2 elasticities  the in  'unemployed which  the  s t a t u s of h i s w i f e . refers  to  for a l l  in t h i s t a b l e sample'  of  husband  is  groups.  assume  married  in  which  men  unemployed,  The 'unemployed sample'  couples  no  the  wife  of is  Estimation Results unemployed,  ignoring  e l a s t i c i t i e s are,  the  in g e n e r a l ,  Model  1 elasticities.  some  individuals,  utility-maximizing function  which  status  of  smaller  unemployment  choice  yields  less  elastic  96  Model  2  in a b s o l u t e value  I n t r o d u c i n g the p o s s i b i l i t y observed  is  her husband.  /  a  than  that,  is  'true'  than for  not  labour-supply  that  which  would  otherwise be a s s o c i a t e d with observed behaviour. Within framework of responsive  the c o n s t r a i n e d  to the  implicit  model,  'UI-tax'  individuals  than i s  a  the  are  less  suggested by the  u n c o n s t r a i n e d model.  Model 2 gross own-wage men  and  married  women  Compensated own-wage than  differences,  however,  contrast  are with  for  in  than that  For c o u p l e s ,  larger and  for  single  women.  These  A l l Model 2 and  literature  labour-supply  inelastic.  for Model  1  (see  for  groups.  In f a c t ,  married  women  married  individuals.  And,  and  in  results  Killingsworth,  responsiveness of married  of other  elasticity  s m a l l e s t value  men  obtained the  single  are  married  are s m a l l .  results  1983), the own-wage  own-wage  for  positively-sloped  r e p o r t e d elsewhere  greater  than  elasticities  individuals  functions  e l a s t i c i t i e s are l a r g e r for  the is  women i s  no  compensated actually  the  calculated.  introducing  the  possibility  of  constrained  Estimation Results / unemployment i n t r o d u c e s , of  the  complication  r a t i o n e d labour s u p p l y : i f a married man i s  constrained,  h i s wife  will  function;  if  be  Table 4.27 the f u l l  a  woman i s  on a r a t i o n e d  compares u n r a t i o n e d  sample  evaluated  same time,  o p e r a t i n g on  a married  w i l l be o p e r a t i n g  at the  labour-supply  constrained,  her  husband  labour-supply function, e l a s t i c i t i e s evaluated  with u n r a t i o n e d  for the sub-samples  rationed  and r a t i o n e d  with  unemployed  wives  unemployed husbands. Having choice has l i t t l e but having  a  impact  spouse  demand-side  constraints  elasticities.  Average  married  men  or  unconstrained) whole;  average  women  for  married  a spouse who  on average  who  for  of married men and women  and  reduces  with  married  women  with  i s unemployed  own-wage  i s unemployed  as  f  elasticities  unemployed spouses. E l a s t i c i t i e s are c a l c u l a t e d for men  97  by  elasticities, a  result  average  of  own-wage  gross  cross-wage  elasticities  for  with  unemployed  (constrained  or  spouses are s m a l l e r than for the compensated  cross-wage  sample as  elasticities  a for  married people with unemployed but u n c o n s t r a i n e d spouses are a l s o s m a l l e r ; compensated•cross-wage  elasticities  for  those  with unemployed and c o n s t r a i n e d spouses are z e r o .  Gross cross-wage e l a s t i c i t i e s  for  e i t h e r men or women  with  f R e c a l l that the l a b o u r - s u p p l y f u n c t i o n of a man or woman who i s constrained i s termed a 'rationed' labour-supply f u n c t i o n ; a l a b o u r - s u p p l y f u n c t i o n c o n d i t i o n a l on a q u a n t i t y constraint.  Estimation Results / constrained  unemployed  increasing  the  constraint,  increases  source  and  respect  to the  and  constraint, and  thus  are  wage,  for  spouse's  'fixed  decreases  positive;  spouses  level  of the  negative;  given  level  the  Elasticities  with  level  of  decreases  labour s u p p l y .  This  are  the  more i f  'fixed  income' although  form,  tells  their  faced by the other p a r t y .  The p o s s i b l e  married man to h i s w i f e ' s unemployment  5.  l i m i t e d dependent significant  'non-participants' single  results  are,  first,  v a r i a b l e problem  impact on  sample s e l e c t i v i t y  for  constraints a  ignored.  Conclusions  Major e s t i m a t i o n  are,  Notice  responsiveness of i s often  a  spouses  are unable to work as much as the couple had p l a n n e d . that both husband and wife are s e n s i t i v e to the  small  spouse's  result,  functional  and wives working  of this  spouse's c o n s t r a i n t  p a r t i a l l y determined by the chosen s t o r y of husbands  and  a t t r i b u t a b l e to  supply.  for a given wage r a t e ,  increases  a  income'  labour  increasing  small  98  estimated  important  i n d i v i d u a l s . Second, Model  with a few e x c e p t i o n s , single  men,  single  has,  correcting in a l l  cases,  parameters. C o r r e c t i n g  problem generated is  that  by the  for couples  exclusion but  1 labour-supply  positively-sloped  women and  married  not  the a the of for  functions  and  inelastic  men.  Model  1  Estimation Results labour-supply functions  are p o s i t i v e l y  for m a r r i e d women who work f u l l - t i m e ; functions  are p o s i t i v e l y - s l o p e d  who work  part-time.  demographic calculated  Third, have  elasticities.  For  elasticities.  Model 1  a  context  2 labour  Model  spouse's  supply f u n c t i o n s  elasticities  for married women a r e ,  any  other  functions  are  positively-sloped  married men and  group.  women are  labour supply of t h e i r  All  in t h i s c a s e , Model and  affected  2  by  constrained  who  are  unemployment  are  Finally,  constraint  high,  importance of the supply.  labour-supply Fifth,  constraints  on  the  by  to an increase increasing  less  'constrained'  estimated  suggesting  with than  spouses  probabilities the  in  labour  elastic  of m a r r i e d i n d i v i d u a l s with  who are not c o n s t r a i n e d . very  larger  of married i n d i v i d u a l s  constrained  labour-supply functions  are  no  spouses: both married men and married  supply; l a b o u r - s u p p l y f u n c t i o n s spouses  are  Estimated  inelastic.  women are found to respond ( i n e l a s t i c a l l y ) spouse's  on  on own-wage  than Model 1 l a b o u r - s u p p l y f u n c t i o n s .  for  1,  demographic  less e l a s t i c  than  women  impact  a l s o have an important i n f l u e n c e  F o u r t h , Model  elastic  for  of  significant  couples,  99  labour-supply  very e l a s t i c  i n the  variables  characteristics  and  sloped and  /  of  potential  approach to modelling labour  V.  Chapter  Five  SIMULATION RESULTS  uses  the  estimated  constrained  unconstrained models of labour supply and the Consumer Finance reform.  Thus,  specific  to  the  For  constraint  are  this  for  2  calculated  i s not  are  household u t i l i t y model and c o u l d different  to  (the  necessary.  'true'  functions be used to  given  of  of  recession,  behaviour  to the data  set  probabilities  of  with  the  the  1981  survey).  In  parameters  parameters  the assumptions  simulate b e h a v i o u r a l  for  UI are  The estimated  estimates  constraint could, respectively,  dissertation,  year  to  here  correspond  labour-market c o n d i t i o n s .  severe  changes i n  presented  simulations,  conditions  principle, Model  2  1982 Survey of  responses  estimated models and  Model  labour-market  a more  simulation results  both to the  employed.  for  predict behavioural  and  of  of  the  responses  For a boom p e r i o d or  example,  probabilities  of  be reduced or i n c r e a s e d  predicted  using  Model  2.  a l l b e h a v i o u r a l responses d i s c u s s e d  F i v e must be understood i n the context of  1981  In  and this  i n Chapter  labour-market  conditions.  Section the  1 of Chapter F i v e surveys other e m p i r i c a l s t u d i e s of  impact of UI  provides d e t a i l s  on the Canadian of the  labour market. S e c t i o n  p o l i c y changes 100  simulated in  2  this  Simulation Results / analysis. and the  Sections  and 4 e x p l a i n  m o d e l l i n g of  simulation r e s u l t s .  1.  3  the s i m u l a t i o n  p o l i c y changes.  Section  Section  5  101  process discusses  6 concludes.  Previous S t u d i e s of UI  Much of the focussed  attention  on i t s  the p o s s i b l e  UI has  impact on  existence  r e c e i v e d from economists  labour-supply choices,  of c o n s t r a i n t s  on  ignoring  behaviour.  t r a d i t i o n a l l y agreed that UI generates a number of effects.  Most  obviously,  unemployed workers. Within UI i s  UI  affects  a basic  the  if  leisure  is  effects,  good,  the  qualifies)  income  effect  w i l l p r e f e r more  l e i s u r e with UI  without.  the  effect  c h o i c e of more l e i s u r e .  substitution  With a UI system,  r e t u r n i n g to work i s equal  The impact of UI on  the net b e n e f i t  i s the e n t i r e  the of  benefit  wage.  the behaviour of unemployed workers  a l t e r n a t i v e l y analysed i n the context  than  predicts  to the wage l e s s the UI  r e c e i v e d . Without U I , the b e n e f i t  1977; higher  suggests the worker Similarly,  both  (Rea,  (assuming he or she  a normal  of  model,  1984). The income of an unemployed worker i s  with a UI system than without  is  incentive  choice-theoretic  of which favour i n c r e a s e d consumption of l e i s u r e  so that  It  behaviour  s a i d to generate income and s u b s t i t u t i o n  Fortin,  has  of a search model  is of  Simulation Results / unemployment  (Ham and Rea,  1985).  unemployed workers p e r c e i v e jobs  according  to  However, workers  it  i s assumed  requirements  not  aware of  and  every  wage job  where a c c e p t a b i l i t y  available.  of committed e x p e n d i t u r e s , UI i s an a l t e r n a t i v e increase  the  d u r a t i o n of  typically  income,  level  source of  income which i s p r e d i c t e d  wage  and  hence  the  to  probable  unemployment.  the d u r a t i o n  both models p r e d i c t  of unemployment, in  the  unemployment model. Note,  is  jobs,  interpreted  as  this  c h o i c e model  workers f i n d more s u i t a b l e  well,  that  i n c o r p o r a t e d i n search job  of  the  p r e v i o u s wage and q u a l i f i c a t i o n s .  reservation  Note that while  inefficient  sources  find a  depends on  worker's r e s e r v a t i o n wage. The r e s e r v a t i o n wage i s viewed as a f u n c t i o n of a l t e r n a t i v e  of  level.  Rather, they must sample one job at a time u n t i l they job which i s a c c e p t a b l e ,  that  some frequency d i s t r i b u t i o n  skill  are  Here,  102  as  that UI w i l l can  be i n t e r p r e t e d  whereas, the  increase  to  the  extent  increased duration  efficient  in  as  the  of  search  demand-side  effects  can  be  models through the  arrival  rate  of  confined  to  be i n f l u e n c e d by UI  in  offers.  The i n c e n t i v e  effects  of UI are  not,  unemployed workers. A l l workers may t h e i r choices  of  region  however,  and o c c u p a t i o n .  If,  as  in  human  Simulation Results / c a p i t a l models,  it  is  assumed that  depend on the expected availability  of  characterized attractive  UI  may  by  (Plourde,  another e f f e c t  of  stream of  such l o n g - r u n  a  region  high  unemployment  1982;  Hey and  UI may  be  choices  r e t u r n s over time,  make  or  103  then  the  occupation  relatively  more  Mavromaras, 1981).  to encourage  the  Yet  increased  labour force p a r t i c i p a t i o n of marginal workers for whom expected  value  returns  to  of UI  benefits  working  enough  (Vanderkamp and W i l s o n ,  Finally,  incentive  demand-side of the framework,  it  effects  utility,  p r e d i c t e d to result  warrant  of UI  are  labour market. In that  expected  of UI decreases the expected  to  'cost,' of  increase  of demand-side  the  expected  participation  1983).  i s assumed  with a c o m p e t i t i v e  may i n c r e a s e  the  lay-offs the  to  workers existence  form of reduced the  firm.  frequency of  incentive  The  effects  the  contract  must provide  of u t i l i t y .  i n the  on  an i m p l i c i t  firms  level  recognized  Thus,  worker UI  unemployment as ( T o p e l , 1984;  is a  Marks,  1987).  Empirical  studies  supply-side advantage  of  of  incentive  UI  in  Canada  effects.  major amendments  Most to  have early  the UI  o c c u r r e d i n 1971 and 1979 to a s s e s s the  focussed work  programme  impact of UI on  on takes which the  Simulation Results / Canadian labour  market.  In 1971,  increased to 66.6  percent  q u a l i f y i n g weeks  of  during the  preceding  year  (from a maximum of  employment  t h i r t y weeks during the two extended  were  the  fifty  decreased  unemployment  preceding y e a r s ) ,  increased from one amended.  This  time,  curtailed.  Eligibility  re-entrants  and r e p e a t e r s  hours per week were earners  were  percent), to  eight  spell  (from  coverage  was  maternity,  and the w a i t i n g p e r i o d  to two weeks.  reduced to 60 p e r c e n t ,  were  b e n e f i t s were i n t r o d u c e d . At the same  b e n e f i t s were made taxable  again  rates  to become n e a r l y u n i v e r s a l , and s p e c i a l  retirement and i l l n e s s time,  replacement  104  In 1979,  the  programme  requirements  UI Act  was  generosity  for  were t i g h t e n e d ,  was  was  new  entrants,  benefit  r a t e s were  i n d i v i d u a l s working l e s s than  removed from coverage,  and  required  to  repay  a  complexity  of  these  changes,  twenty  high-income  portion  of  benefits  many  Canadian  received.  Despite  the  e m p i r i c a l s t u d i e s of UI choose  to model the programme  s i m p l y . G r u b e l , Maki and Sax (1975) and Green and (1976),  for example,  use the  and the p r o p o r t i o n of c l a i m s impact of  UI on  Beach and  Kaliski  correspond with  average  benefit  ruled i n e l i g i b l e  aggregate unemployment. (1983) i n c o r p o r a t e  programme  changes  in,  Cousineau  to wage  ratio  to model  Lazar  dummy  very  (1978)  variables  respectively,  the and to the  Simulation Results / estimation  of  estimation  continuation  of the  et a l .  turnover  p r o b a b i l i t y of  labour-market s t a t e s . timing of  and  specific  (Beach  (1975), R i d d e l l and  moving among  and K a l i s k i  a s p e c t s of the  rates  take  note of  1979 amendments.)  the changing g e n e r o s i t y  of  estimate p r o b a b i l i t i e s of sub-samples  temporary  sample to j u s t i f y r e t u r n to  the  is  by  and  rates  entitlements; unemployment  the is  not  selectivity  problem i s  between the  found  (1974-79) for  excluded  of  regional of  however,  that  to  separate benefits. from  UI  the to  claimants  to be s i g n i f i c a n t l y  by  Alam  focus on the d e c i s i o n  significantly  (Note,  In almost a l l c a s e s , f  are  probability  probability  programme.  on l a b o u r - s u p p l y  lay-off  The  l e a v i n g unemployment  base  non-claimants of UI  supply-side  employment.)  benefit  data  l e a v i n g unemployment  of c l a i m a n t s and  ( I n d i v i d u a l s on  UI  and  measure  the programme. Glenday and  longitudinal  the  Siedule,  Smith (1982) and Vanderkamp  "composite" UI v a r i a b l e s to  the  the  alternative  Wilson (1983) c o n s t r u c t  (1982) use  and  105  variation  affected in  UI  non-claimants  leaving  influenced  the  a  by  potential  UI  sample  ignored.)  e m p i r i c a l s t u d i e s of the  behaviour  generosity  of  find the  a  positive  Canadian UI  impact of  UI  relationship programme  and  fVanderkamp and Wilson (1983) find only a very small increase i n women's p a r t i c i p a t i o n , and b e l i e v e this is outweighed by the s t i m u l a t i v e impact of UI on employment and output (automatic s t a b i l i z a t i o n ) .  Simulation Results / aggregate unemployment  (see  Phipps,  survey of these and other p a p e r s ) . i s not n e c e s s a r i l y  evidence  1985 for a more d e t a i l e d But note that  association  i n v o l u n t a r y unemployment can be demonstrated of an e f f i c i e n c y Jones,  this  for the e x i s t e n c e of  unemployment. The same p o s i t i v e  wage model  (see  106  result  voluntary  between UI in the  and  context  Shapiro and S t i g l i t z ,  1984;  1986).  A recent  study  by Ham and  Rea (1985) makes  i n c o r p o r a t e demand-side  elements  although t h i s  focus  a logit  i s not the  model and the  in  a  an attempt  search  to  framework,  of the work. Ham and Rea  use  l o n g i t u d i n a l UI data base (1975-80)  to  estimate the p r o b a b i l i t y of l e a v i n g unemployment c o n d i t i o n a l on being measures  unemployed ( i . e . , of  unemployment  exogenous v a r i a b l e s  (assumed  industrial exogenous  Ham  the  significant  negative i n f l u e n c e  will  unemployment but  leave  women w i l l to a  leave unemployment.  possible  decision-making  'added-worker' is  and Rea  not  not  the  find  Various  vector  of  impact  of  that  the  U.S.  unemployment  Canadian on  in  to capture the  classification to  function).  are i n c l u d e d  in an attempt  demand-side c o n d i t i o n s . (2-digit)  a 'hazard'  UI  system)  rates have  the p r o b a b i l i t y that on the  probability  This difference effect,  explicitly  d i s t i n c t i o n made between married and  a men  that  is  attributed  although  household  modelled, single  nor  is  a  women. Ham  and  Simulation Results / Rea are unable to i d e n t i f y  a benefit-rate  effect,  do f i n d that UI e n t i t l e m e n t  has a very small but  107  but  they  significant  impact on expected d u r a t i o n .  A study of  the  different  1971  approach  (1965-70) to  changes to is  Rea  UI which  (1977).  estimate i n d i v i d u a l  Using an i m p l i c i t  c o n t r a c t model,  unemployment  'voluntary.'  as  labour-supply functions, parameters incomes  by  (these values  specific  UI  micro-data  labour-supply  functions.  he chooses  Hence,  effective  incentive  d e r i v e d from household admits to s u p p l y . He linear,  (as  Glenday and Alam, during estimation.  and f i n d s  investigations.  that  in  However,  equations  He does  the  in  the determination  budget  constraint  e x i s t e n c e of UI  (see  of  there  are  not  not d e a l  i n d i v i d u a l ) behaviour,  be s i g n i f i c a n t the  non-labour  individual details  His labour-supply  opposed to  given the  and  effects.  u t i l i t y maximization.  depicts  estimated  i n d i v i d u a l l y important  the UI system than most other weaknesses.  all  changes in s p e c i f i c UI wages  Rea's work i s a more c a r e f u l study of  are s t i l l  to view  having  now i n c o r p o r a t e U I ) ,  parameters are  d e t e r m i n a t i o n of  Rea  somewhat  uses  he simulates  changing  uses a  as  with  which of  he  labour  piece-wise  also Fortin,  1984;  1982), but does not d e a l with t h i s problem Finally,  he  assumes a l l unemployment  is  Simulation Results /  108  'voluntary.'  The m o d e l l i n g  approach  resembles  work  the  of Rea  parameters of the present constraints  used  in this (1977).  u n c o n s t r a i n e d models enables  the l i n e a r i z e d 'net each i n d i v i d u a l  is  i n the wage'  most  closely  Incorporation  of  (1981) UI programme i n the  faced by households  responses to changes  study  the s i m u l a t i o n of  programme. Changing UI  changes  and non-labour income with  changes.  non-linear  b e h a v i o u r a l responses on the other hand, first,  budget  unfortunately,  the  to these between t h i s  direct  constraint  at  section  direct  the  t h e o r e t i c a l model and the estimated  of  (see link  Chapter between  labour-supply  and e q u i t y consequences  changes  third,  the allowance  c o n s t r a i n t s on l a b o u r - s u p p l y c h o i c e s .  the the  (although,  ( a l l o w i n g both e f f i c i e n c y to be a s s e s s e d ) ;  Major  be obtained u s i n g  procedure  of  possible  study and  estimation  convergence c o u l d not  second,  is  incorporation  c o r r e c t Wales/Woodland/Hausman 5(b));  which  f a c e d . Given the estimated parameters  to p r e d i c t  Rea a r e ,  and  behavioural  it  work of  budget  in both the c o n s t r a i n e d  the l e i s u r e - d e m a n d / l a b o u r - s u p p l y f u n c t i o n s ,  differences,  the  for  the 2, the  functions of  policy possible  Simulation Results / 2.  Policy  Changes  Simulated  The Royal Commission on Prospects  for  109  Canada  the Economic Union and (The Macdonald  Commission)  Commission of I n q u i r y on Unemployment Insurance Commission) have both r e c e n t l y  Development and  (The  the  Forget  recommended major reform  of  the Canadian UI programme. Based on hearings h e l d a c r o s s  the  c o u n t r y and on the  existing  e m p i r i c a l economic  both  propose  significant  Commissions  programme g e n e r o s i t y incentive return  the  function. of  effects  in an attempt  b e l i e v e d to  programme  to  retrenchment  to minimize the  be generated  its  original  No e m p i r i c a l evidence  yet  b e h a v i o u r a l responses to be  literature, in  adverse  by UI  and  to  social  insurance  suggests the  magnitude  a n t i c i p a t e d from e i t h e r  the  Macdonald or the Forget p r o p o s a l s : Models 1 and 2 provide way of p r e d i c t i n g these responses models of  The  Commission  recommendations  programme are g i v e n .  firm-by-firm basis, intended to  lay-offs.  released for  reform  its of  report the  of  firms  to i n d i v i d u a l  eliminate  the  should  be  1985. UI  That  linked,  records of l a y - o f f .  'subsidization'  The b e n e f i t - r e p l a c e m e n t  in  Canadian  UI should be e x p e r i e n c e - r a t e d .  premium c o n t r i b u t i o n s  is  different  labour s u p p l y .  Macdonald  Several  using two very  a  is,  on  a  This  of  temporary  r a t e should be  decreased  Simulation Results / from  60  to  50  percent  Regionally-extended benefits qualifying  weeks  should  of  insurable  should  be  earnings.  be e l i m i n a t e d .  increased  from  Minimum  the  current  v a r i a b l e entrance requirement of ten to fourteen weeks to f i x e d requirement Finally,  the  of  fifteen  entitlement  period  l i n k e d to work r e c o r d by employment for every hoped that benefits  these  (or p o s s i b l y  twenty) be  more  r e q u i r i n g two (or three)  week of  proposed  w i l l decrease  should  UI b e n e f i t . changes  in  a  weeks. closely  weeks  Together, the  110  of  it  is  structure  of  unemployment d u r a t i o n s and discourage  unstable p a t t e r n s of employment and unemployment.  Proposed changes l a r g e r package establishment  are intended of s o c i a l  of  a  to be  security  viewed as reform to  ' U n i v e r s a l Income  for low-income benefit  retrenchment  A s s i s t a n c e Plan low-income  workers who  (TAAP)  workers)  suffer  and  a  to h e l p find  a  include  Security  (UISP) which would p r o v i d e an a l t e r n a t i v e  Transitional  employment  (not in  a the  Programme'  source of  l o s s as  workers  part of  support  a result  of  Adjustment necessarily more  stable  regions/occupations.  These p r o p o s a l s c o n s t i t u t e reforms to be  investigated  the f i r s t package of p o t e n t i a l UI using  developed i n Chapters Two through  the l a b o u r - s u p p l y Four. Note,  models  however,  the  Simulation R e s u l t s / many l i m i t a t i o n s : F i r s t ,  only the UI proposals are modelled,  although these are c l e a r l y intended package; model,  second, the  since  impact  assessed; t h i r d ,  to be p a r t of a  the model developed  of  is a  experience-rating  since  the  model  is  larger  supply-side  UI  cannot  of  1986.t L i k e the Macdonald  of  recommendations  reform  i n November  Commission, i t makes a  for UI reform. B e n e f i t  number  entitlement  should  be based on cumulative hours r a t h e r than weeks worked. i s proposed i n an attempt  the growing labour  number of  force.  necessary  entrants,  The  apply  to  or maternity b e n e f i t s ) .  fifty  eligible  weeks. UI  not a l l r e c e i v e percent of  workers in  recommended  re-entrants,  UI should be  to accomodate  part-time  to gain e l i g i b i l i t y  intended to  no  stability.  The report of the Forget Commission was r e l e a s e d  change  be  micro-economic,  attempt can be made to assess the consequences of UI for economic  111  minimum  to UI i s 350.  a l l workers repeaters All to  hours  Canadian of  for for  UI  for a  With  is (new  to  standard  so that workers  b e n e f i t s p a i d at the same rate earnings).  work  sickness  workers earning e n t i t l e m e n t benefits  of  T h i s minimum  applying  should be ' a n n u a l i z e d '  insurable  the needs the  and a p p l i c a n t s  receive  This  do  ( c u r r e n t l y 60  annualization,  the  fBoth a m a j o r i t y report and a d i s s e n t i n g m i n o r i t y report were i s s u e d . The Standing Committee on Labour, Employment and Immigration has since recommended abandoning the Forget proposals.  Simulation Results / replacement  rate would vary a c c o r d i n g to weeks worked d u r i n g  the q u a l i f y i n g  p e r i o d (the  unemployment s p e l l ) .  fifty-two  Report recommends  that  full  this benefit  c a l c u l a t e d over the past  fifty-two  the past  weeks, as  to twenty  would have  earnings  where  replaced  at  the a p p r o p r i a t e  i n v o l v e a major change  would r e c e i v e  full  Macdonald Commission, special  provisions  high-unemployment e l i m i n a t i o n of to  develop  encourage  an  for  regions.  income  education  insurable  2/3 as  fixed period  Commission, the  saved  benefits  for  like  elimination  individuals  community  employment  system.  and a  Funds  benefits.  for a longer p e r i o d of  supplementation and  66  calculated  stream of UI  Forget  regionally-extended  weeks  Thus, a n n u a l i z a t i o n would  year of  recommends  as  over  fifty-two  fraction is  requirement the  be  case.)  f r a c t i o n of  With a f i x e d  benefits,  r a t h e r than  full  under the c u r r e n t  of  Forget rate  the  time than they r e c e i v e  receipt  (The  c u r r e n t l y the  smaller weekly b e n e f i t s  entrance  the  is  i n the time  Workers with l e s s than a  throughout  i n s u r a b l e earnings  some  weeks worked d i v i d e d by f i f t y - t w o .  the  replacement  weeks,  However, anyone working l e s s than  preceding  benefits.  i n c r e a s e d to 66 2/3 percent of average  ten  weeks  Anyone f u l l y - e m p l o y e d  q u a l i f y i n g p e r i o d would r e c e i v e  percent,  112  the  of  all  living  in  through  the  are to be  used  programme development.  and  to  These  Simulation Results / a d d i t i o n a l new programmes are not d i s c u s s e d Forget r e p o r t , nor w i l l they  in d e t a i l  in  the  be analysed h e r e . However,  as  was a l s o true for the Macdonald Commission p r o p o s a l s , changes to UI should the  l a r g e r reform  for the  reform of the core  recommendations  are  p r o p o s a l which i s is  to these  the  important from  Forget R e p o r t . a modelling point  should no longer be  of UI b e n e f i t s  of  proposals  UI programme, a number of  that high-income c l a i m a n t s  minor  One  such  of  view  required  received.  S i m u l a t i o n Methodology  The f i r s t  step  of the  u n c o n s t r a i n e d and vector of  major  c o n s i d e r e d as part  In a d d i t i o n  made in  to repay 40 percent  3.  r e a l l y only be  package.  113  of  s i m u l a t i o n procedure,  c o n s t r a i n e d models,  is  to  for both  the  generate  the  i n d i v i d u a l e r r o r terms which, when added to  leisure  p r e d i c t e d by the estimated  models,  will  weeks  reproduce  observed weeks. P o l i c y - i n d u c e d changes i n behaviour can then be measured  as d e v i a t i o n s  (unemployment).  This  changes in behaviour changes. Model 1  procedure  specifies  than f i f t y - t w o  r e q u i r e d to gain  ensures  are e n t i r e l y , the  can be no l e s s than zero no g r e a t e r  from observed  weeks of that  result  that observed  of  leisure predicted programme  weeks of  leisure  ( f i f t y - t w o weeks of employment) less  eligibility  the minimum number of to U I .  Model 2 only  and  weeks  requires  Simulation Results observed weeks bounds  of  of  zero  leisure and  to remain  fifty-two.  o u t s i d e these model-determined to the boundary v a l u e s . the d i f f e r e n c e  the  s i m u l a t i o n procedure i s  the  UI  the  programme  able  to  decreasing of  there  is  respond  Model  2  and  final  step  to  use  the  simulation  probability.  calculated  before  a  less  generous  the  UI  constraint.  However,  after  reform  and  wage reforms  For  programme  If the  the UI  parameters  the  (assuming given  probability  the programme  each  positive  by  proposed  calculating  constraint  is  changed,  a  are  is  be  individual  true p r o b a b i l i t y of  the  labour-supply e l a s t i c i t i e s ) .  of  each  parameters  of  for  the  behavioural  The estimated  calculation  the  responses.  more c o m p l i c a t e d .  unemployment.  lower-bound estimate of w i l l be obtained  of  as  estimated  of  reform of the UI programme there are two ways of this  equal  changes in 'net'  to p r e d i c t b e h a v i o u r a l  UI i s  enable  p r o b a b i l i t i e s of  falling  some p r o b a b i l i t y he or she w i l l not  to  weeks of  then  model,  changes i n  individual,  weeks  i m p l i e d by the proposed  and  constrained  response to  obvious  and p r e d i c t e d weeks. For  to make the  leisure-demand equations  For  the  boundary values are set  second  r a t e s and non-labour incomes of  Predicted  114  I n d i v i d u a l e r r o r s are c a l c u l a t e d  between a c t u a l  unconstrained model,  within  /  constraint  less  generous  estimated  own-wage  C a l c u l a t i n g the p r o b a b i l i t y  of  Simulation Results / constraint after  given  the present  the programme  have r e v i s e d anyone who  system  i s made l e s s  t h e i r optimal  of UI  generous  assumes and  that,  individuals  employment/unemployment  was unconstrained  remains u n c o n s t r a i n e d a f t e r  before the  plans,  programme  change  the change and i s able to modify  behaviour i n accordance with the new p l a n . T h i s ignores possibility the  115  the  that an i n d i v i d u a l may c u r r e n t l y be o p e r a t i n g on  margin  between  being  c o n s t r a i n e d ; that when UI she decides  an  constrained  i s made l e s s  optimal  and  not  generous  and he  employment/unemployment  i n v o l v e s more weeks of employment,  he or she  is  being  plan  then  or now  unable  to f i n d the e x t r a d e s i r e d weeks of work.  Calculating programme  the  probability  change,  upper-bound  on  estimate  the of  of  constraint  other  the  hand,  represents  any an  probability  (assuming  i n d i v i d u a l s want to respond to a l e s s - g e n e r o u s UI  programme  by i n c r e a s i n g labour s u p p l y ) .  true  after  In t h i s c a s e , any  not f u l l y able to c a r r y out r e v i s e d  individuals  employment/unemployment  plans w i l l be t r e a t e d as c o n s t r a i n e d even i f ,  i n the  situation,  he  and  partially  able  or  she to  was not adjust  to  constrained the  revised  initial  was  thus  programme.  S i m u l a t i o n s of b e h a v i o u r a l responses for Model 2 are c a r r i e d out using  both  p r o b a b i l i t y of  upper  and  constraint.  lower-bound  estimates  of  the  Simulation Results / To  incorporate  the  i n t r o d u c i n g the  probability  problem of  of  constraint  uncertainty  lower-bound) sample.  i s c a l c u l a t e d for each s i n g l e  Then, each i n d i v i d u a l i s  of h i m s e l f  or h e r s e l f .  c o r r e s p o n d i n g with the are assumed a c t u a l l y  A  p r o b a b i l i t y of c o n s t r a i n t then he or she  is  for  replaced  herself  who are not c o n s t r a i n e d . )  p r o b a b i l i t y of  UI  programme.  assumed to behave as i n Model 1: incomes  (If  constraint  the  estimated percent,  or  C o n s t r a i n e d members of  the  be unable to respond  to  Unconstrained 'net'  members  wages and  parameters of the Model 2 leisure-demand equations b e h a v i o u r a l responses.  estimated are  However, since  estimates  estimates,  p r e d i c t e d changes i n unemployment r e s u l t i n g  2 parameter responsive than i s  from  Model  in the UI programme w i l l a l s o d i f f e r .  estimates to  substantially  suggest that  variations  true for Model  in  individuals  wages and  1 estimates.)  non-labour  used  Model  parameter  a given change  differ  are  non-labour  f o l l o w i n g UI reform are c a l c u l a t e d and the  to p r e d i c t  or  two r e p l i c a s of himself  e n l a r g e d p o p u l a t i o n are assumed to the  individuals  by e i g h t r e p l i c a s of himself  who are c o n s t r a i n e d and  changes i n  'replicas'  an i n d i v i d u a l i s 80  herself  2  i n d i v i d u a l i n the  f r a c t i o n of these ten  to be c o n s t r a i n e d .  Model  (upper and  r e p l a c e d by ten  estimated  without  i n t o the  s i m u l a t i o n p r o c e d u r e , a p r o b a b i l i t y of c o n s t r a i n t  116  2 1  from (Model  are  less  incomes  Simulation Results / For c o u p l e s ,  the  Model  i n v o l v e d . To a v o i d  2  simulation  procedure  introducing uncertainty,  is  each  more  household  i s again r e p l a c e d by ten  r e p l i c a s of  the  c o r r e s p o n d i n g with the p r o b a b i l i t y  r e p l i c a t e d households  that  the  household  constrained.  For  unemployed,  this  is  constrained  households  with  probability  appropriate i n t e g r a l  itself.  117  are  over the  assumed  only one is  A fraction  to  working  calculated  be  member as  marginal d e n s i t y  of  the  functions,  f , (e , ) or f , ( e ) . f 2  C o n s t r a i n e d households unable  to  respond  with only  to  UI  one member unemployed  reform.  By  definition,  unemployed i n d i v i d u a l a l r e a d y experiences more than  the  household  unemployment  would  choose.  The  member  the  unemployment  spouse  without  i s unable to work more than the f i f t y - t w o  he or she a l r e a d y t a k e s . Unconstrained households one  unemployed  employment/unemployment  can  adjust  are  with  weeks  taken by the unemployed  weeks only of  individual.  tExperiments were also conducted using conditional probabilities, f(e iu ) and f ( e l u ) . However, from a behavioural point of view, it makes little sense to c o n d i t i o n the c a l c u l a t i o n of the p r o b a b i l i t y of constraint on the difference between spouse's observed and q u a n t i t y - c o n s t r a i n e d leisure-demand share ( s ^ - s ^ z . ) ; i=1,2 and j=2,1) s i n c e the spouse w i l l only be o p e r a t i n g on an effective function if a constraint exists. Moreover, c o n d i t i o n a l p r o b a b i l i t i e s depend on estimated correlations between e r r o r terms. T h i s i s a problem for f ( e l u ) since the estimated c o r r e l a t i o n between u, and e i s -.9994 and hence the conditional probability of constraint for unemployed married women i s c l o s e to 100 p e r c e n t . 1  2  2  1  2  2  1  Simulation R e s u l t s / It  i s assumed that  the estimated  If  both  118  such responses are generated a c c o r d i n g to  leisure-demand f u n c t i o n for Model  household  heads  experience  2.  unemployment,  each  household i s r e p l a c e d by ten r e p l i c a s , a p p r o p r i a t e f r a c t i o n s of which face (i)  two  (ii)  constraints  one c o n s t r a i n t  (iii)  no c o n s t r a i n t s .  Probabilities (i)  P1=;  for these cases are c a l c u l a t e d as  s?-s() ; 1  s?-s() f (e,,e )de de,  W  — CO  ( i i ) (a)P2A=f_^  1  2  w  J  —00  S ( )  (ii) ( b ) P 2 B = J g O _  /gO_  s ( )  J_^  s ( )  f(e,,e )de d 2  2 _ S ( )  is  possible.  If  constrained,  the behaviour  can  adjusted  be  (quantity-constrained) household head free  to  funct i o n s .  to  2  only  section  one  4).  household  of the unconstrained  according  to  leisure-demand  UI  e i  c o n s t r a i n e d , no response  is constrained,  respond  e i  f(e,,e )de d  Chapter 3,  both household heads are  reform  2  2  ( i i i ) P3=1-P1-P2A-P2B (see If  2  reform  head  to  is  rationed If  neither  leisure-demand c h o i c e s according  UI  individual  the  function.  to  are  unrationed  Simulation 4.  For  Modelling  the  are  this  reduced  decreasing  /  119  Reform  p u r p o s e s of  proposals 1.  UI  Results  the  analysis,  the Macdonald  Commission  to:  benefit-replacement  rate  to  50  percent  (B=.50) 2.  eliminating  3.  increasing weeks  4.  regionally-extended the  r e q u i r i n g two  Forget  1.  'annualizing'  2.  fixing  weeks  proposals  the  employment granting  a  satisfying  are  the  approximated  to  15(20)  week of  UI  by: rate  as  of  an  full the  approximation fifty-week  benefit  labour-supply  benefit  models a r e  a basis  at  proposed period  for benefit  weeks 350  for  of  hours anyone  requirement  formulated the  ten  condition  repayment  employment/unemployment, h o u r s as  the  minimum e l i g i b i l i t y  workers.  cumulative  f o r one  condition  high-income  weeks of  employment  minimum e l i g i b i l i t y  the  the  of  benefit-replacement  abolishing  Since  requirement  (QA=.5). f  The  4.  minimum e l i g i b i l i t y  (EXT=0)  (MIN=15; MIN=20)  benefit  3.  benefits  proposed  for  i n terms  of  switch  to  eligibility  can  only  fThe assumption that i n d i v i d u a l s form annual plans (see C h a p t e r 2, s e c t i o n s 1 and 2) means t h a t no-one w i l l ever build a fifty-week entitlement period. Thus, the f a c t that it is not p o s s i b l e to accumulate f i f t y weeks of benefit w i t h i n a o n e - y e a r framework i s not a p r o b l e m .  be approximated by a ten-week particularly  Simulation Results /  120  entrance requirement. T h i s  is  inadequate for p a r t - t i m e workers.  E i t h e r the Macdonald or the Forget p r o p o s a l s would r e s u l t l e s s money being spent on U I , and a n t i c i p a t e d uses for  funds  saved c o u l d i n f l u e n c e household b e h a v i o u r . Income t a x e s , example, c o u l d be reduced to generate for  increased  channels of It  is  supply  of labour  influence  assumed,  additional  services.  the  static  labour-market behaviour employed a t t e n t i o n to p o s s i b l e  and  Such  here,  certain that  a l t e r n a t i v e uses for  reforming U I . The a n a l y s i s which f o l l o w s ,  for  incentives secondary  from UI reform a r e , however,  in  in  ignored. model  of  people pay  no  funds saved  by  c l e a r l y , does  not  take a 'balanced-budget' approach.  Changing the  parameters  of  the UI  programme  household budget c o n s t r a i n t s by changing segment  can  affect  lengths  or  by changing net wages and non-labour incomes a s s o c i a t e d  with  particular  rate  segments. Decreasing the b e n e f i t - r e p l a c e m e n t  (B=.50) does not a f f e c t i n t e r c e p t s are a f f e c t e d . and  (2.2),  it  benefit-replacement (and thus  is  lengths.  Referring  with  net wage  However, s l o p e s and  back to equations  obvious  r a t e decreases  reduces the  income a s s o c i a t e d  segment  that  lowering  both the r a t e of rate)  the subsidy  and  (2.1)  the  segment.  the subsidy  non-labour On  the  tax  S i m u l a t i o n R e s u l t s / 121 segment,  a  lower  i m p l i c i t UI tax  benefit-replacement  (and thus  increases  rate  reduces  the  the net wage r a t e )  and  decreases non-labour income.  Eliminating regionally-extended (creates)  benefits  the subsidy segment of  (EXT=0)  lengthens  the budget c o n s t r a i n t  for  workers i n high-unemployment regions where such b e n e f i t s  are  currently available.  the  budget c o n s t r a i n t s benefits  are  unaffected,  of  but  no impact on  regionally-extended  u n a v a i l a b l e . ) Net  non-labour and  of c o u r s e ,  workers for whom  currently  subsidy segment budget  (There i s ,  income  increase on  will the  wage  rates  are  decrease  on  the  tax segment  of  the  constraint.  I n c r e a s i n g the minimum number of weeks of work necessary qualify  for  regions where  UI  again p r i m a r i l y minimum r e q u i r e d  than elsewhere i n  the c o u n t r y .  affects weeks are The impact  to  high-unemployment currently  lower  of t h i s  policy  simply to  shorten  change on i n d i v i d u a l budget c o n s t r a i n t s  is  the subsidy segment. There i s no change  in net wage r a t e s or  non-labor  incomes.  R e q u i r i n g two weeks of e l i g i b l e of UI b e n e f i t hence  reduces  reduces the net  the  employment to earn one  week  i m p l i c i t rate of s u b s i d i z a t i o n and  wage rate on  the subsidy segment  of  Simulation Results /  122  the budget c o n s t r a i n t but does not a f f e c t  non-labour income.  The net  wage  rate on  is  affected  since  the i m p l i c i t 'UI tax'  the  tax segment  a d d i t i o n a l weeks of employment are weeks of  earned  UI b e n e f i t s .  one-for-one b a s i s . UI b e n e f i t s  can be earned w i l l  which must be  worked before  incorporates  all  can only  the UI  tax becomes  the  above  components of  'annualization.'  .Forget  regionally-extended Under a system  no subsidy segment  i n any  entrance requirement of has been  the  reached, the  operative  (For  chosen.)  package  are  and  of a n n u a l i z a t i o n , there  ten weeks  of  insurable  entitlement  period  as the  weeks of employment, the UI tax r a t e  benefit-replacement  rate  i n c r e a s e s with  is  minimum  employment of  weeks means that every worker faces an i m p l i c i t UI t a x . ten to f i f t y  the  benefits  p r o v i n c e . Once the f i x e d  fixed  a  weeks  changes.  The  elimination  on  The Macdonald Commission  the o p t i o n MIN=15 i s a r b i t r a r i l y  of  of  reducing the rate at which  simulation,  major  occur  i n c r e a s e the number of  of  when  taken at the expense  (MAX), non-labour income i n c r e a s e s . package  similarly  i s only generated  This  However, s i n c e  not  fifty From  increases additional  weeks of work. Thus, between the e n d - p o i n t s of ten and f i f t y the Forget budget c o n s t r a i n t resembles for a p i e c e - w i s e  linear progressive  the budget c o n s t r a i n t  income  tax.  Simulation Results / For s i n g l e  i n d i v i d u a l s , the budget c o n s t r a i n t  d e s c r i b e d above,  new l a b o u r - s u p p l y c h o i c e s  a check i s made to see consistent possibly  i s changed  are p r e d i c t e d and  i f the new c h o i c e of weeks of work  new  budget  segment).  prediction  is  work. T h i s procedure  is  would  not be  constraint.  In F i g u r e 2 . 1 ,  procedure  should  consistent  with  it  each  the  wage  given the  new  Ideally,  for  each  convergence  weeks  would  never  income  pair  therefore,  For couples  values  are  F o r t u n a t e l y , given that a m a j o r i t y of  are o r i g i n a l l y constraint, elasticities  l o c a t e d on  the tax  segment of  given the g e n e r a l l y p o s i t i v e and  p o l i c y changes  given  the  for  will  incomes (due  to  initial  observations the  estimated  'retrenching'  be  household  r e p o r t e d wage r a t e s and non-labour  reported  are  observation.  heads,  iteration.  the  the checking  predicted  net wage/non-labour  computational expense),  be  and non-labour income of  segment  the second  budget  A c o u l d not  in one l a b o u r - s u p p l y p r e d i c t i o n . For s i n g l e  of  and  of  result  are those  second  a v o i d p r e d i c t i n g weeks  until  that  a  net  a p o i n t such as  iterate budget  then  of  C i s not f e a s i b l e ) .  is possible  reached s i n c e  at  feasible,  with the wage rate  tax segment ( i . e . ,  not,  apply at p r e d i c t e d weeks  i s used to  work which  associated  If  made  non-labour income which should  changes.  as  with the new wage r a t e and non-labour income (and  labour-supply  However,  123  nature  budget own-wage of  s i m u l a t e d , the case d e p i c t e d in F i g u r e 2.1  the is  S i m u l a t i o n R e s u l t s / 124 the most  common e r r o r .  approximation  As suggested  i n v o l v e d through  by the diagram,  the  t h i s m i s - a s s o c i a t i o n i s not  l i k e l y t o be e x c e s s i v e .  Another weakness  of  the s i m u l a t i o n  that, for s i m p l i c i t y , which would occur  i n c r e a s e s i n marginal  as labour supply  Such i n c r e a s e s c o u l d generate o f f - s e t the impact  approach  employed  is  income-tax r a t e s  increases are  ignored.  incentive e f f e c t s to p a r t i a l l y  of UI reform. However, s i n c e the focus of  t h i s a n a l y s i s i s on UI reform, the i n c e n t i v e e f f e c t s of the income-tax system a r e ignored (although the estimated i n c o r p o r a t e s income Finally, analysis course,  taxes, as  d e s c r i b e d i n Chapter  n o n - p a r t i c i p a n t s continue t o be excluded and  from  changes  the w e l f a r e in  model  the UI  evaluation programe  Two).  from  this  although,  may  of  influence  participation decisions.  5.  P r e d i c t e d Labour-Supply  Model 1 s i m u l a t i o n r e s u l t s are presented married women context of a both  f o r s i n g l e men and s i n g l e  women  i n Tables 5.1-5.4; r e s u l t s f o r married men and a r e presented  i n Tables  t r a d i t i o n a l model  the Macdonald  significantly  Responses t o UI Reform  reduce  and  of u n c o n s t r a i n e d  the  average  5.5-5.8.  Forget  weeks  of  reform  In the response, proposals  unemployment. For  Simulation Results / single  men,  sample f a l l and to 2.32  average  weeks of  from 4.92  to 2.75  unemployment  r e s u l t of  proposals  a drop  i n the  average  weeks  of  unemployment  unemployed group.  This  simulation r e s u l t s  for the  (Table 5 . 2 ) . to  16.19  is clear  Average weeks of  under the Macdonald  percent to  of unemployment drops  initial  (152/455 choose not to be of  reducing the b e n e f i t - r e p l a c e m e n t impact. Average  weeks of  i n c i d e n c e drops from  Other i n d i v i d u a l parameter effects,  Model  1  similar,  the  of  'choose' and  Macdonald  men  the from the not 18.07  package,  rate has by far the  men drop from 19.12  27.13  of  unemployed).  unemployment experienced  unemployed p o p u l a t i o n of s i n g l e while  situation  the p o l i c y change)  components  the  19.12  under  under Macdonald (144  to take any unemployment a f t e r  individual  by  from  of  drop  examination  p r o p o s a l s and 14.17  455 workers unemployed in the  Of the  an  unemployment f a l l  18.55 percent  percent under Forget  as of a  unemployed sample of s i n g l e  Forget p r o p o s a l s . The i n c i d e n c e 27.13  These  t o t a l number  experienced  from  full  proposals  (Table 5 . 1 ) .  i n d i v i d u a l s e x p e r i e n c i n g unemployment as well in  the  under the Macdonald  under the Forget  numbers are the  for  125  percent to 22.72  changes a l s o generate  largest by to  the 16.44  percent. incentive  but the magnitudes are much s m a l l e r .  simulation  results  although s i n g l e  for  single  women experience  women less  are  very  unemployment  Simulation Results / in the  initial  situation.  For  the p o p u l a t i o n  average weeks of unemployment f a l l  from 3.29  the  1.74  Macdonald  proposals  proposals  (Table 5 . 3 ) .  women, average 15.71  and  For the  weeks of  12.02  choose f u l l - y e a r employment; case for  component of  fall  19.03  percent  to  see Table 5 . 4 ) .  Incidence  12.45  percent  is  choose (116/367  Finally,  the s i n g l e  most  the  to  as was  important  reduction  in  rate.  1 simulation r e s u l t s  for m a r r i e d men are very  to those obtained f o r s i n g l e  men and s i n g l e  weeks of unemployment f a l l  from 3.41  proposed Macdonald reform  package and to  the proposed Forget package sample,  from  under F o r g e t .  Macdonald package  benefit-replacement  Model  single  percent under Forget  s i n g l e men,  the  unemployed sample of  15.11  under  under  i n i t i a l l y unemployed women  to work a l l year) and to  a l s o the  1.87  Forget  from 17.57  under Macdonald (107/367  to  whole,  the  unemployment  under Macdonald and to  of unemployment drops  to  as a  126  average  weeks  Macdonald and to  15.65  to 2.19  (Table 5 . 5 ) .  fall  from  under F o r g e t .  women.  Average  weeks under the  1.86  weeks  For the  18.06  similar  to  under  unemployed 14.29  under  Average i n c i d e n c e  unemployment drops from 20.48 percent to  16.64  of  percent under  Macdonald (96 of 512 o r i g i n a l l y unemployed workers choose to work a l l year) choose  and to  full-year  13.20  employment;  percent under Forget see  Table  5.6).  (182/512 Of  the  Simulation Results / components of the Macdonald Commission package, benefit-replacement  rate  again  has  Eliminating  regionally-extended  significant  b e h a v i o u r a l responses;  package have very l i t t l e  Model that  5.60  to 3.72  weeks f a l l  benefits  either  the Macdonald  unemployed sample of to  generates  Forget  unemployment.  women drop  married women,  average  under Macdonald and to  under F o r g e t ; i n c i d e n c e  falls  from 38.52  percent under Macdonald  (112 of  workers choose f u l l - y e a r  17.60  percent to  963 o r i g i n a l l y  employment) and  34.04  unemployed  to 29.60  percent  under Forget (223/963 choose f u l l - y e a r employment; see to i n d i v i d u a l  package, however, established most  departs  components of  significantly  by s i n g l e men, s i n g l e  important component of  the  from  the r e d u c t i o n  the  of  unemployment  regionally-extended  benefit-replacement fall  benefits  Macdonald  the  pattern  the proposed reform package  regionally-extended benefits  weeks  Table  women and married men: the  the e l i m i n a t i o n of of  from  under Forget (Table  15.37  5.8) . Response  the  suggest  or the  reduce observed  unemployment f o r married  from 20.51  impact.  other components of  under Macdonald and to 3.48  5.7) . For the  largest  for married women again  p r o p o s a l s would s u b s t a n t i a l l y Average weeks of  reducing the  impact.  1 simulation r e s u l t s implementation of  the  127  from are  5.60  rather  rate. to  eliminated.  is than  (Average  4.00 For  when the  Simulation Results / unemployed sample, average weeks;  incidence f a l l s  The second  largest  weeks f a l l  from  20.51  to  128 16.60  from 38.52 percent to 35.04 p e r c e n t . )  b e h a v i o u r a l response  is  generated  by  i n c r e a s i n g the minimum e l i g i b i l i t y c o n d i t i o n to twenty weeks (MIN=20); t h i s  is  followed by r e q u i r i n g  for every week of earned b e n e f i t  Decreasing the  important impact on the behaviour  initial  positions  elasticity  5.7).  any other on  the budget  a  much  group.  This is  constraint  due  and  both  to  l o c a t e d on  (compare  affected  on by  the  tax  policy  requirements and  Thus,  changes  decreasing  such  increasing the  rate at  employment earn weeks of UI b e n e f i t . are found on  segment  1  a f t e r the  i n c r e a s e d to 20 weeks;  fifty-eight  on segment  the l a r g e  1.  Given  than tax  Tables 5.5  and  married  i s g r e a t e r than for married  segment.  regionally-extended benefits,  to  the  And, the average d u r a t i o n of unemployment for  men l o c a t e d  on  relative  women (673/2500)  initially  women l o c a t e d on the tax segment  less  of married women than  More married  (467/2500) are  of  r a t e has  budget c o n s t r a i n t s  magnitudes.  married men segment  of  work  (QA=.5).  benefit-replacement  the behaviour  two weeks of  more as  women  eliminating  minimum which  are  entrance weeks  of  Twenty-nine married men entrance requirement married women are  own-wage  found  elasticities  labour supply for married women, i f a l a r g e number of  is  of  women  Simulation Results / are a f f e c t e d constraint,  by changes a  large  at  the lower  increase  in  end of  average  129  the  budget  observed  labour  supply can be expected. At the same time, these i n c r e a s e s a wife's both,  wage and r e d u c t i o n s  other t h i n g s  e q u a l , serve to  labour s u p p l y . Since men  are  directly  i n her non-labour income decrease her  a r e l a t i v e l y small affected  minimum r e q u i r e d weeks  by,  of work,  for  will  husband's  number of example,  in  married  increasing  such c r o s s - e f f e c t s  reduce  the average observed response for married men.  Decreasing the b e n e f i t - r e p l a c e m e n t r a t e , on the other affects  a l l unemployed workers, r e g a r d l e s s of t h e i r  p o s i t i o n s on budget  c o n s t r a i n t s . Thus, net  hand, initial  wage r a t e s  and  non-labour incomes w i l l change and b e h a v i o u r a l responses can be a n t i c i p a t e d from a l l unemployed married men. S i x t y - t w o of the 467 men  initially  l o c a t e d on  the tax segment  weeks of work enough to reach e i t h e r segment employment  (see  Table  5.5).  Net wage  4 or  r a t e s and  increase full-year non-labour  incomes of a l l married women must a l s o change, but the of observed response the tax segment) labour-supply cross-wage  in t h i s case  (only 2/673 women  suggests an o f f - s e t t i n g  choices.  elasticities  Given  the  very  i n f l u e n c e on large  behavioural  leave their  estimated  for married women, i f wage r a t e s and  non-labour incomes of married men change enough to significant  lack  responses  then  generate  significant  cross  Simulation Results / effects  on  expected.  the  behaviour  Simulation r e s u l t s  are important:  five  women,  choose l e s s than f u l l - y e a r change.  of  their  wives  suggest that  can  such  also  full  general,  and have the lack  very l a r g e  year,  f o l l o w i n g the  These women are p a r t - t i m e workers from the  and West  be  cross-effects  i n i t i a l l y employed employment  130  policy Atlantic  cross-wage e l a s t i c i t i e s . segment of  the  budget c o n s t r a i n t ,  even though a l l women l o c a t e d on the  tax  segment experience  an  cross-wage  of movement  effects  off  increase are  i n net  and  single  i n d i r e c t consequences often  over-looked,  important and m o d e l l i n g of  wage, suggests  off-setting  responses (compare the otherwise m a r r i e d women  the tax  In  men).  direct  that more  behavioural  f a i r l y s i m i l a r responses of The  possibility  of labour-market  but r e s u l t s  that  of  such  p o l i c y changes  are  here suggest that they may be  attention  the d e c i s i o n - m a k i n g  should  be p a i d  processes of  to  the  households.  The model used here i s very crude; i t might be worthwhile develop more s o p h i s t i c a t e d for  the purposes of p o l i c y  Incidence  models of  joint  decision-making  analysis.  and ' d u r a t i o n ' * are s u b s t a n t i a l l y  reduced by  the Macdonald and the Forget reform packages However, the  absolute  to  magnitude  of  response  in a l l is  both  regions.  larger  in  fAverage weeks of unemployment i s only a very rough proxy for ' d u r a t i o n ' of unemployment. Hasan and de Broucker (1982) d i s c u s s problems in a c c u r a t e l y measuring d u r a t i o n .  Simulation Results / r e g i o n s s t a r t i n g with higher unemployment r a t e s . package a c t u a l l y  results  unemployment i n A t l a n t i c incidence  remains  in  a  lower average  than i n  As  benefits  e l i g i b i l i t y conditions  have  well,  and  of  (although eliminating  increasing  a larger  Forget  duration  C e n t r a l Canada  higher).  regionally-extended  The  131  impact  minimum  in  Atlantic  Canada, where p r o v i s i o n s of the UI system are c u r r e n t l y more generous. adverse  It  is  interesting,  incentive  benefits,  that  much l a r g e r  given  consequences  reducing the  impact  on  responses to  UI  of  worry  workers  in  over  the  regionally-extended  benefit-replacement  eliminating regionally-extended  Simulation r e s u l t s  the  Atlantic  r a t e has Canada  than  benefits.  for  Model  1  reform  will  be  suggest very  that  behavioural  large.  But,  these  r e s u l t s are based on the assumption that workers are able respond  to  a  cut  in  programme  generosity  by  allowing for  possible  labour s u p p l y . Model 2 s i m u l a t i o n r e s u l t s suggest that  for  all  qualify  constraints  (Tables  groups  estimated p r o b a b i l i t i e s of  ensure  this  result.  on  5.9-5.16)  there may be almost no b e h a v i o u r a l response  UI reform. Very high  to  choosing  a d d i t i o n a l weeks of employment. Model 2 s i m u l a t i o n s these p r e d i c t i o n s by  a  to  constraint  Examining  Model  2  s i m u l a t i o n output for the  unemployed sub-sample of  married  men (Table  that both  average  5.14)  reveals  i n c i d e n c e and  Simulation weeks  of  unemployment  fall  Macdonald and the Forget single both  women a n d m a r r i e d  t h eMacdonald  increase small  reduction  a  few weeks  by  deciding  workers,  women  weeks i n  proposals  a  t o work  respond  a l l year;  currently  result  together  men,  small  i n an with  a  number  of  experiencing  only  t o t h e programme  a majority  experiencing  the  5 . 1 0 , 5.12 a n d 5 . 1 6 ) ,  o f unemployment  o f unemployment  f o r both Forsingle  (and unemployed) i n d i v i d u a l s  first  major  of  long  changes  constrained  periods  of  simulations  i s  t o respond.  conclusion  that  i fan u n c o n s t r a i n e d  the  most  system  the  Forget Model  plans.  individuals Forget  that  and  choosing  scheme  according  be s l i g h t l y  incidence  c a n be  supply  of  expected  to either  than  behavioural greater:  average  weeks  i fthe  Canadian or  i n the context to the  f o rsingle of  major  t h eMacdonald  response  unemployment) would with Macdonald;  i s viewed as  reality,  Comparing t h e two p r o p o s a l s  1 suggests  package c o u l d both  description  i n unemployment i sreformed  from t h e p o l i c y  model o f l a b o u r  appropriate  reductions  of  (Tables  / 132  Conclusions  The  UI  packages.  incidence:  unemployment, a r e unable  6.  reform  slightly  and t h e Forget  i n average  unconstrained  very  Results  Forget  individuals,  unemployment ( f o r be l o w e r  f o rcouples,  with  the  incidence  would be lower,  but average  Simulation Results /  133  weeks of unemployment taken  by  the unemployed group would be s l i g h t l y higher under For e i t h e r in weeks  reform package, of  the  largest  unemployment are  made  absolute  Forget.  reductions  by married  women  and  s i n g l e men (the groups s t a r t i n g with the most  unemployment).  Post-reform,  taken  average  weeks  of unemployment  by  the  unemployed are very s i m i l a r a c r o s s demographic groups.  For s i n g l e  men, s i n g l e  important component proposals  is  married  women, and  of  the  married men,  Macdonald  package  women,  proposals benefits,  weeks of work to e s t a b l i s h  such  as  increasing  eligibility  impact on  importance of  joint  l a r g e cross-wage of  replacement  (household)  a  illustrate  the d i r e c t reduction  In a small number of c a s e s ,  benefit-replacement  change simultaneously These r e s u l t s  increases  depend on a  but  illustrate  rate  required  a l l have  responses to p o l i c y  to  For  for U I , and r e q u i r i n g  in  benefit women  following a  wage  policy rates.  h i g h l y s i m p l i f i e d model of the  potential  the  own-wage  because t h i s  t h e i r husbands'  a  changes:  married  induced to choose more unemployment  reduction in  behaviour,  women  reform  rate.  minimum  findings  e l a s t i c i t i e s off-set  married  rate.  are a c t u a l l y  b e h a v i o u r . These  most  eliminating  two weeks of work to earn one week of UI b e n e f i t  responses  of  the r e d u c t i o n i n b e n e f i t - r e p l a c e m e n t  regionally-extended  larger  the  importance  joint of  Simulation Results / developing more labour-market  The  second  simulations  sophisticated  major  conclusion  is that,  Forget p r o p o s a l s w i l l have  any  result  of  occupation,  for the  analysis  of  policy.  obtained  for  course,  region of  neither  the reform of  significant  the  policy  conditional residence  the  the Macdonald nor the Canadian UI  impact  on  unemployment.  on a  model which  and  as given and ignores the p o s s i b l e the demand s i d e of  from  i f a c o n s t r a i n e d model of labour supply  i s viewed as most r e a l i s t i c ,  is,  models  134  hours of work per  influence  labour market.  the  system This takes week  of UI reform  on  VI.  Chapter  Six  consistent justice then  develops  with  welfare  evaluation  Utilitarianism,  John  and Robert N o z i c k ' s e n t i t l e m e n t  used,  in  s i m u l a t i o n of Five,  WELFARE EVALUATION  to  conjunction behavioural  conduct an  with  taken  evaluations  results,  from the  are  flexible  thus  dependent  Survey of  Consumer  having  who  are  again,  more  participants.  The  heads  approach  in  is,  the  Chapter of  evaluation results,  are  1982  of  from  evaluation  a population  by  suggested by t h i s  results  conducted for  characterized  theory  t h e o r y . Measures are  the  reform p r o p o s a l s . Reported w e l f a r e  samples  Rawls'  responses d e s c r i b e d  ethically  reported simulation  procedures  of  UI like  on  the  Finance; households  labour-force general  than  application.  1. Methodology for the U t i l i t a r i a n E v a l u a t i o n s  From a U t i l i t a r i a n p o i n t of view, individually  perceived  s o c i a l welfare depends  utilities.  Since,  for  Model  i n d i v i d u a l p e r c e p t i o n of u t i l i t y depends on p e r s o n a l a U t i l i t a r i a n measure utilities both  of  i n d i v i d u a l s with  leisure-demand  households,  must f i n d  a  models  Utilitarian  a means  different are  formulated  measure must 135  1,  taste,  of comparing t a s t e s . And,  find  on  the since  in  terms  of  a  means  of  Welfare E v a l u a t i o n / deriving individual  from  member of the household economic  household u t i l i t y  i  each  non-working  counts.  Both requirements can be s a t i s f i e d  v*=V (w ,Y)=  that  ( i n c l u d i n g c h i l d r e n and  family members)  per-person u t i l i t y  so  136  by d e r i v i n g  'normalized'  functions:  {V (w Y)}{l/s(A)}  i  h  if  where: * 1.  v ^ = m d i v i d u a l normalized u t i l i t y each i n d i v i d u a l i n the  2. 3. 4.  (which i s the  h ^ i ' ) = t h e household w  Y  s(A)=a  scaling  for  household)  (w^,Y,)=the i n d i v i d u a l i n d i r e c t u t i l i t y v  same  indirect u t i l i t y  function,  function  function  dependent  on  demographic  characteristics The s c a l i n g utilities  function, of  s(A),  individuals  comparison of the  c o n s t i t u t e s an e x p l i c i t * * v^ = V j where  that  of  The  the  s(A)  tastes  i n d i v i d u a l s from choice  of  s(A),  or  people  configurations)  scaling  the  (with  the the  different therefore,  i n t e r p e r s o n a l comparison. That  i and j are e q u a l l y w e l l  To d e r i v e  comparison of  different  i and j are d i f f e r e n t  t a s t e s and/or household is  with  utilities  household c o n f i g u r a t i o n s .  if  a l l o w s the  is,  different  judgement  made  off.  factors  for  demographic v a r i a b l e s play a prominent r o l e ,  Model start  1, with  where the  Welfare E v a l u a t i o n / household expenditure  function: 9  e(u,w,A)=7o(A)+7 (A)w +7 (A)w 1  From t h i s , function (6.1) couples, (6.2)  1  define  the  2  9  +w w u. 1  2  2  1  individual  2  'normalized'  expenditure  as e*(u,w,A)=7 (A)+7, (A)w +7 (A)w +w? w [s(A)u] 1  0  1  2  for  ?2  2  2  or e*(u,w,A)= (A)+7 (Ajw^w? 7 o  some  reference  That i s ,  1 ( A )  1  i n d i v i d u a l s . Make the for  137  convenient  single  assume that  for  single  n o r m a l i z a t i o n that  i n d i v i d u a l with  dependants. function  equals the household expenditure f u n c t i o n when the  household  consists  with  some  a r b i t r a r i l y chosen  individual  no  s(A)=1  expenditure  of  the  [s(A)u]  reference set  Choose as r e f e r e n c e  single  for  the weekly e q u i v a l e n t  1981  ($140).  income, choose the p o v e r t y - l i n e POV household, utility  y  level,  expenditure  R (A ) .  T>  an  of demographic c h a r a c t e r i s t i c s , A . f  wage, w ,  f e d e r a l minimum wage  individual  Then,  a  As reference  solution  for  a  the  earned  income a p p r o p r i a t e for  u , can be obtained by equating the  f u n c t i o n for the  of  the  reference household  reference household with  full  income for the reference household. The household fFor the implementation of Model 1, the reference household i s a r b i t r a r i l y taken to be a r e p r e s e n t a t i v e s i n g l e man with no dependants, l o c a t e d i n a r u r a l area in C e n t r a l Canada who i s n e i t h e r a seasonal nor a c y c l i c a l worker. The reference household for Model 2 i s taken to be a r e p r e s e n t a t i v e s i n g l e man with no dependants l i v i n g in a r u r a l a r e a . For Model 2, being s i n g l e and male e s t a b l i s h e s the a p p r o p r i a t e value for the gamma and theta parameters; the additional c h a r a c t e r i s t i c s merely determine a r e f e r e n c e poverty-income level.  Welfare E v a l u a t i o n / expenditure function  function  for  the  equals  the  individual  r e f e r e n c e household  expenditure  since  s(A)=1.  income i s d e f i n e d as  ' p o v e r t y income + the value of  time,'  is  where l e i s u r e  Thus,  u s i n g the compensated leisure-demand f u n c t i o n for  the  wage.  individual,  (A )+0(A ) ( w ) R  R  T  1  R  m )  "  R  Y =y  POV/.R  [s(A)u ],  1  the reference measure of V  R  full  ,.R, .w.R,  income can be c o n s t r u c t e d as  0(A*)-1 R i R  (A ) + [ -y (A )+8{A )w u r  u ]w .  1  Equating  reference  expenditure ,.R  leisure the  reference L* =  Full  chosen but e v a l u a t e d at  reference  freely  138  income  f u n c t i o n for the  with  reference  the  individual  household,  ,,R\ R,, Rx0(A) R  U  since  full  s(A )=1,  it  is  possible  to  solve  for  reference  utility: R R u  =[y  P 0 V  (A )-7 (A )]/[(l-0(A ))(w ) R  R  R  R  T h i s value  for reference  u t i l i t y can  back i n t o i n d i v i d u a l expenditure individuals,  and  equated with f u l l y  P 0 V  individual  with a s i n g l e thus  then be  functions,  6.2  substituted for  functions  single can  be  incomes,  (A)+[ (A)+0(A)w 7 l  ].  expenditure  0 ( A ) _ 1  u s(A)]w R  to s o l v e for h o u s e h o l d - s p e c i f i c  are  e ( A )  0  working head,  R  for s i n g l e  s(A) v a l u e s .  For  individuals, households  interpersonal scaling  factors  Welfare  s(A) = [y where  POV  (A>-7 (A)]/[(l-0(A))(wV  the  poverty  appropriate procedure  income  t o household  f o r couples  and  R  2, p a r a m e t e r  demographic  and  individual  as  now  utility  F o l l o w i n g t h e same  (wV u .  ei  2  2  values vary  couples.  They  R  only f o r single are  not  'normalized'  utility  men,  functions  appropriately-scaled  c a n be  value  of  of  represented  the  indirect  function:  V*=1/S(A){[(T-L)w+NLINC- (A)]/[(1-6(A))w  6 ( A )  7 o  for  are  variables.  Finally, the  values  yields 1  women  R  characteristics.  POV  For Model  u ],  parameter  s(A) = [y (A)-7o(A)]/[(l-0 -0 )(w )  single  (A)  o  E v a l u a t i o n / 139  individuals  from  households  ]}  with a s i n g l e working  head;  V*=1/S(A){[(T-L,)w,+(T-L )w +NLINC +NLINC -7o(A)]/ 2  2  1  2  d-^-e.jw^wf } 2  for  individuals  Table  6.1b  scaling seven  presents  factors  years  from  households  with  representative  (assuming  C e n t r a l Canada). S u b s t a n t i a l  estimated  variation,  the economic  family,  f o r Model  children  less  particularly,  reflects  parameter v a l u e s . F o r  coefficient  heads.  and that r e s i d e n c e  s i n g l e men, s i n g l e women a n d c o u p l e s , 1  working  values  t h e r e a r e no  o f age i n t h e h o u s e h o l d  e s t i m a t e d Model  two  than is in among  variation  example,  four  1  in the  f o r EFAM, t h e number o f i n d i v i d u a l s i n is  negative  f o r single  women  and  Welfare E v a l u a t i o n / positive  for s i n g l e  economic  family size  reduced and s(A) is  increased  Table  is  scaling  Table 6.1b,  for s i n g l e  is  for  factors  variables  for  Thus,  as  7 (A)  is  0  women while  reduced  scaling  7o(A)  single for  also  region  men.  comparison vary  of  with  residence,  number of c h i l d r e n l e s s than seven, and years of  education.  Since Model  under the  assumption that  with  in  f a c t o r s are presented  but  'taste'  occupation,  increased  s(A)  6.1a,  demographic  is  T a b l e s 4.7 and 4 . 8 ) .  increased  and  Representative with  men (see  140  demographic  becomes an  1  parameter estimates were 'tastes'  for  characteristics,  important determinant  unemployment  vary  assumption  now  this of  obtained  interpersonal  utility  comparisons.  Model  2  ignores  variables  on  important f o r  the  possible  individual  influence  behaviour,  interpersonal u t i l i t y  so  of tastes  parameters d i f f e r  single  Individual u t i l i t i e s  reflect  basic differences  differences Model 2  factors  are  very  to men,  are s c a l e d  to  reflect  low-income-cut-offs. closely  tied  i n t e r p e r s o n a l comparisons i m p l i c i t i n the S t a t i s t i c s Low-income c u t - o f f s  not  for s i n g l e  among these groups and to  in need as measured by the  scaling  are  comparisons except  the extent that estimated women and c o u p l e s .  demographic  (compare Tables 1.a and  1.c).  to  the  Canada  Welfare E v a l u a t i o n / Scaling factors establish income necessary reference  the r e l a t i o n s h i p between the  full  for an a r b i t r a r y household to achieve  some  u t i l i t y level  and the f u l l  the r e f e r e n c e household to achieve  income necessary  the same l e v e l ,  different  t a s t e s and circumstances as r e f l e c t e d  values  Estimated values employed,  the  specification  for  the  gamma  f u n c t i o n a l form u t i l i z e d . They  level through  parameters.  influence  on  chosen and  set  econometric  are a l s o c r i t i c a l l y  dependent (For  demographic v a r i a b l e s exert  gamma  should  the  the nature of unemployment.  Model 1, the assumption that  r e s t r i c t i v e and  theta  the  for these parameters depend on the data  on assumptions made about  linear  and  for  given  same reference wage rate and p o v e r t y - l i n e expenditure but d i f f e r e n t  141  and  theta  be remembered.)  parameters This  a is  approach  to  i n t e r p e r s o n a l comparisons, while dependent on these l i m i t i n g factors,  has at l e a s t  the appeal of  being e x p l i c i t  being based on i n t e r p e r s o n a l comparisons which are used elsewhere ( i . e . , are  whenever the  and  of  commonly  Canadian poverty  lines  used).f  Jorgenson  and  alternative comparisons.  Slesnick  econometric Starting  (1984, approach with  a  for to  example) making  translog  develop  an  interpersonal  indirect  utility  fGiven the a r b i t r a r y nature of the l o w - i n c o m e - c u t - o f f s , it would be i n t e r e s t i n g and perhaps important to to consider a l t e r n a t i v e s measures.  Welfare E v a l u a t i o n / function,  they  impose  conditions  aggregation and for the Then,  f o l l o w i n g Barten  in preferences differences differences  (1964)  demographic groups  quantities  differences  appear  quantities consumed  r e - i n t e r p r e t e d as d i f f e r e n c e s  in ' e f f e c t i v e '  form  and  the  scales).  aggregation  and  already imposed then determine equivalence scales'  (p 76).  The  prices  a  utility  (prices  translog  general  household expenditure  f o r an a r b i t r a r y household evaluated at a r e f e r e n c e level  household  to  the expenditure f u n c t i o n  evaluated  equivalence s c a l e ,  at  made ( i m p l i c i t l y )  the  same  by  the b a s i c Jorgenson  r e s t r i c t i o n s imposed,f Jorgenson aggregate  expenditure  expenditure  shares  function.  for a  utility  dependent on demographic  and p r i c e s , c o n s t i t u t e s  utility  is  conditions  'commodity-specific Finally,  by  functional  integrability  e q u i v a l e n c e s c a l e i s d e f i n e d as the r a t i o of the function  This  chosen  as  (i.e.,  divided  equivalence s c a l e s ) .  equivalence  only  consumed  c o m m o d i t y - s p e c i f i c household  m u l t i p l i e d by  exact  functions.  they assume that  'effective' in  for  i n t e g r a b i l i t y of demand  across  in  required  142  shares and  the  level.  and  comparison  Slesnick.  Given  and S l e s n i c k can  parameters  This  characteristics  interpersonal  and then  T h i s procedure  reference  recover of  illstrates  estimate individual  the how  the  indirect a set  of  i n t e r p e r s o n a l comparisons can be based on observed behaviour f B l a c k o r b y and Donaldson (1987) show that exact i s s t r o n g e r than r e q u i r e d .  aggregation  Welfare E v a l u a t i o n / (as  reflected  chosen way  in  the data  f u n c t i o n a l form,  in  which  on  expenditure  shares),  and on assumptions  demographic  143  on  made about  characteristics  a the  should  be  incorporated.  The approach to  i n t e r p e r s o n a l u t i l i t y comparisons  employed  in my work d i f f e r s  from that of Jorgenson and S l e s n i c k  number  First,  of  ways:  restrictive  (although t h i s  simpler expression second,  fashion  (Model  has  the advantage  (Model  2);  form  1);  are  third,  composite  incorporated  in  a  observed behaviour  is  leisure/unemployment  exogenous cut-offs,  to  commodity);  the  c o n s t i t u t e s the  differences  finally,  estimating  merely  data  the  a measure  set,  base of the  augment  a  factor);  u t i l i t y - m a x i m i z i n g behaviour i n  fourth,  a  more  of y i e l d i n g  p r i n c i p a l commodity consumed ( a l l other goods are into a  is  interpersonal scaling  parameters  not assumed to r e f l e c t cases  functional  for the  demographic  different  the  in  the  is  the  aggregated of  need  low-income  comparisons poverty-line  all  taste utility  comparisons.  * Given welfare  representations  for  individual  utilities,  v^,  a  e v a l a t i o n measure i n the t r a d i t i o n of U t i l i t a r i a n i s m  is U={(l/n)Z(v*) } r  l / r  ;r/0,r<1  Welfare E v a l u a t i o n /  144  * where v^ i s  the normalized  individual  and  n  is  individual u t i l i t y  the  entire  population,  dependants.f  Each  member  assigned  same  i n d i v i d u a l normalized  the  of a  enters the U t i l i t a r i a n measure households  members share the  The parameter r  can be  multi-person  same l e v e l  r can  U t i l i t a r i a n measure.  functional constant.  form, However,  can be achieved  all  utility.  two ways.  be viewed as  v.=[(v*) /r);  utility  is  T h i s assumes  of  of  d i m i n i s h i n g marginal  through the  household  Firstly,  a means  r e q u i r e d for  R e c a l l that with the  the marginal  including  and  i n t r o d u c i n g the d i m i n i s h i n g marginal u t i l i t y 'true'  ith  u t i l i t y value  separately.  i n t e r p r e t e d in  f o l l o w i n g A t k i n s o n (1970),  of the  of a  Stone-Geary  income  must  u t i l i t y of  be  income  transformation  r^O, r<1.  r  ( R a i s i n g v^ to  the power  r is  a monotonic  transformation  which i n t r o d u c e s c u r v a t u r e ; d i v i d i n g by r i s a n o r m a l i z a t i o n which ensures income when equally  that  the  f u n c t i o n v^  the parameter  distributed  r is  equivalent  remains i n c r e a s i n g  negative.) income  Calculating  (Atkinson,  c o n s i s t e n t with a U t i l i t a r i a n s o c i a l welfare  in  function  an  1970) yields  the measure U above:  *  f T h i s f o r m u l a t i o n cannot allow for negative u^ v a l u e s . This c r e a t e d d i f f i c u l t i e s in the Model 1 e v a l u a t i o n s for those s i n g l e men and women for whom r e g u l a r i t y c o n d i t i o n s were not s a t i s f i e d . Reported welfare e v a l u a t i o n r e s u l t s exclude these observations.  Welfare E v a l u a t i o n / Zv^=Z[(v^) /r]=n(a /r), r  where  r  a  is  equally  145  distributed  income. Then, a=U={ l / n ( Z ( u * ) } r  A  second  ,  1 / / r  as  above.  interpretation  single-parameter  of  the  as  a  i n d i c a t o r of the s o c i a l p l a n n e r ' s l e v e l  of  i n e q u a l i t y a v e r s i o n . When r=1, distribution  in  focusses on  infinity,  the welfare  and  efficiency.  'Utilitarian'  is  welfare.  measure i s  the w o r s t - o f f  values between these extremes, equity  of s o c i a l  the  of  r  no c o n s i d e r a t i o n i s given  the assessment  approaches negative  parameter  trade-offs  Under  this  to  When  r  'Maximin'  and  individual.  At  are made  between  interpretation,  measure i s not s t r i c t l y U t i l i t a r i a n  the  since  the  * chosen  representations  d i m i n i s h i n g marginal interpretation  given  c a l c u l a t e d values  of  utility,  u t i l i t y of the  income.  parameter  for the U t i l i t a r i a n  To conduct the U t i l i t a r i a n a n a l y s i s , given the c u r r e n t UI system  v^,  r  for r .  In will  not  exhibit  practice, not  the  affect  measure. the measure U e v a l u a t e d  i s compared with the measure  e v a l u a t e d given proposed p o l i c y changes. range of v a l u e s  do  T h i s i s done for  U a  Welfare E v a l u a t i o n / 2. Methodology f o r the Rawlsian  According to Rawls, governed  by  Evaluations  economic and  the  'second  146  social policy  principle  of  are to  justice'  be (the  difference p r i n c i p l e ) : Social  and  economic  inequalities  are to be arranged so that they are to  the  greatest  l e a s t advantaged Rawls s p e c i f i e s  that  reference  to  specific  functions.  Policies  w e l l - b e i n g of the  For  the  p.302).  individuals  are to  be  or  their  chosen which  least well-off  according  utility  maximize to an index  which Rawls says can be  the of  approximated  income i n c l u d i n g t r a n s f e r s .  the  Rawlsian a n a l y s i s ,  must focus on the is usually  worst-off  therefore,  "worst-off  expressed  f u n c t i o n which depends  of  (Rawls,  of  t h i s p r i n c i p l e i s to be a p p l i e d without  'primary s o c i a l goods' by net  benefit  representative,  this  through  a Maximin  only on  social  the welfare  evaluation  of the  single  as suggested by A  Theory  is  interpreted  as  measure i s  r e q u i r e d . In  individual  a broader  measurement  group." The Rawlsian philosophy  i n d i v i d u a l . However, i f ,  Just i c e ,  welfare  Canada,  people with incomes below some designated poverty l e v e l l i k e l y candidates  for members of t h i s w o r s t - o f f  a  group.  are  Welfare E v a l u a t i o n / To c o n s t r u c t  the  distribution,  i n which incomes  set  equal to the  , POV (y  measure,  ,..  . y  . .  i s used  i s poverty  Statistics  i = k , . . . n are  y^,  households  with incomes below poverty l e v e l ,  Statistics  scaling  each  member  of  the  non-working household members evaluation).  The  scaling  r e l e v a n t household income for a s i n g l e rural  area.  poverty income  from  d i v i d e d by  the  household  are  so  in  the and  that  i n the  all  welfare  calculated  d i v i d e d by  person with no  Individuals  for  Table 6.1a)  are i n c l u d e d  factors  incomes  factor i m p l i c i t (see  rural  low-income  a c t u a l household  Canada low-income c u t - o f f s  assigned to  y =  income  in a  Canada  cut-offs);  appropriate interpersonal  are  (i.e.,  no dependants l i v i n g  the  income  POV .  ,  . y ) where y  person with using  "censored"  above the poverty l e v e l  x  ;y^,  ($5949,  a  poverty income l e v e l ,  POV  for a s i n g l e area  Rawlsian  147  as  the  the  poverty  dependants l i v i n g i n  households  with  a  different  c h a r a c t e r i s t i c s r e c e i v i n g t h e i r own a p p r o p r i a t e p o v e r t y - l i n e incomes are defined to be e q u a l l y w e l l o f f . that  the  same  r e l a t i o n s h i p between  i n d i v i d u a l s from d i f f e r e n t  households  holds r e g a r d l e s s of the l e v e l compared,  then  the  factors. Rawlsian  Thus,  the  analysis  incomes  based  is  assumed  required  between  used as i n t e r p e r s o n a l  solely  for  to be e q u a l l y well  i n t e r p e r s o n a l comparisons are  it  of w e l l - b e i n g which i s  relationship  poverty-income l e v e l s can be  If  on  off  being  relevant scaling  used for  the  differences  in  Welfare E v a l u a t i o n / household need as  measured by the  Individual tastes  do not  enter  Canadian poverty  the  U t i l i t a r i a n case  i n the  utility  function  measure.  (Number of household members and area of  are  the c h a r a c t e r i s t i c s given i n t h i s  not  for  static  s i n c e parameters  incorporated  which poverty  model so that  these v a r i a b l e s are a l s o  R  P 0 V  3  r  function *  for  Letting e  the  Rawlsian residence, vary,  are to  the  R, i s d e r i v e d as  with a mean of order r  entire  represent  the  censored  the e t h i c a l l y  i t must be true  income  equivalent  that  l/n[g( )] } / ={l/n[n(e*) ]} / =e* r  +  as  given.)  e q u a l l y d i s t r i b u t e d income, {n /n[y  the  of  t a s t e s with respect  e q u a l l y d i s t r i b u t e d income c o n s i s t e n t  distribution.  in  incomes  The Rawlsian p o l i c y e v a l u a t i o n measure,  s o c i a l welfare  lines.  welfare e v a l u a t i o n  they do  148  1  r  r  1  r  y i  ;r<1,r/0 where n  is  the number of  above poverty The  'rich'  people  (people with  level).f  second term can be r e - w r i t t e n  as  gy-/n = n / n [ [ l / n g y ] ] =n /n(£ ) P where n i s the number of 'poor' people; P  order r  P  over  incomes  r  1 / r  people with  r  P  incomes  P  r  P £  l e s s than  i s a mean the  of  poverty  fAgain t h i s f o r m u l a t i o n cannot allow negative incomes (due, for example, to c a p i t a l l o s s e s ) . However, this is not a problem f o r the sample over which the evaluations are conducted since households with negative incomes are excluded p r i o r to e s t i m a t i o n .  Welfare E v a l u a t i o n /  149  allows f o r f l e x i b i l i t y  in  level. Thus,  R=e*=[n /n(y V n  P  Using the mean of  order r again  R  P0  +  a t t i t u d e toward  /nf^) ] ^. 1  1  inequality,  this  time  within  framework. Notice that the Rawlsian measure i s all  incomes are above poverty  level  so t h a t ,  a  Rawlsian  just y ^ P<  in this  if  V  case,  the measure i s not s e n s i t i v e to f u r t h e r income g a i n s . Hence, R is  only  sensible  if  some  people  whatever value i s assigned to y poverty l e v e l ,  R  s c a l e d incomes.  is  If,  just a as  P 0 V  .  have  If a l l  mean of order  i s the case  incomes  incomes are below r of  for t h i s  individual  sample,  are incomes both above and below the poverty l e v e l , value of  R will  between the poor approaches general,  reflect  and non-poor  negative however,  difference I believe,  attitudes  this  R  Rawlsian  approaches measure  then  the both  poor. When  r  Maximin.  In  implements  the  p r i n c i p l e i n a manner which i s more f l e x i b l e and, more  reasonable  than  s e n s i t i v e to the  welfare of  the e n t i r e group  'Maximin'  since of the  rather than j u s t to the welfare of the i n d i v i d u a l among them.  there  toward i n e q u a l i t y  and among the  infinity,  below  it  is poor  worst-off  Welfare Evaluation 3.  Methodology f o r the  Robert  Nozick's  procedural as  just  means"  " i f i t arises (p.151). A  holders  (Nozick  follows  entitlement  of  who  respect  should  to the  as  one  more  individual  Ideally,  benefits=expected  conditions  their some  do of  on  an  costs). not  uncertainty  f i t i s assumed that anyone's e n t i t l e m e n t .  justly.  to U t i l i t a r i a n i s m  and  individuals  should  not  of  own  property.  the  a  matched  be  the  Hence,  common  it  (this 'right  t o UI'  seems  might  the  a  i s not  if  expected models  behaviour be  such  costs, f  (i.e.,  since  would  with  programme  individual  household  used  programme  UI  ante b a s i s  are  decisions  of a UI  However,  explain  by  for  toward  ex  the  out  i n Canada t o d a y . However, he  disposed  be  it is  of  conception  their  just  rules  property  b e n e f i t s more c l o s e l y  should  if  by  property  definition  f r e e t o make t h e i r  which e x i s t s  this  developed  his  their  on  distribution  transactions carried  would d i s a p p r o v e  favourably  only  Nozick argues that  d i s p o s a l of  that Nozick  the  be  focusses  distribution  just  In c o n t r a s t  achieving  likely  be  in  justice,  means of  just  have o b t a i n e d  Locke  (1974)  views a given  is  of a c c e p t a b l e  in themselves; that  good. P e o p l e  he  from a n o t h e r  to property.)  Rawls' t h e o r y  the  is,  150  Evaluations  theory  distribution  result  property  as  entitlement  j u s t i c e . That  historical  ends  Entitlement  /  under  worthwile part  of  Welfare E v a l u a t i o n / extension),  it  is  assumed  that  it  would  be  at  approximately c o n s i s t e n t with the views of Nozick to  151  least choose  a UI programme which  more c l o s e l y  matched i n d i v i d u a l  costs  and b e n e f i t s ex p o s t .  For Model 1,  this  since  i n d i v i d u a l s choose  an  annual  unemployment and hence benefits  they  reasonable  For  Model  2,  appeal to  w i t h i n the unemployment  employment  and  they pay and  the  matching  benefits actually received  for an  cross-sectional  reasonable  of  for people who have not chosen  Justification have to  pattern  both the premiums  receive.  a c t u a l l y p a i d and  is  ex post a long  time h o r i z o n  d a t a , to the  data set  approach i n  i s much  to be  unemployed.  since  idea that d i f f e r e n t  I  a full  entitlement  range  theory cannot,  costs  and  benefits  ex  post  would  insurance v a l u e ; each p a r t i c i p a n t would e f f e c t i v e l y for  use  individuals of  however,  be pushed too far since a UI programme which e x a c t l y  saving  would  experience).  T h i s i n t e r p r e t a t i o n of  individual  less  t h i s case (or,  c u r r e n t l y represent  premiums  periods  of  unemployment  during  matched  have  no  just  periods  be of  employment. However, as a means of a s s e s s i n g proposed reform of the e x i s t i n g and b e n e f i t s  UI programme, the ex post matching of  costs  should y i e l d a ranking of p o l i c y o p t i o n s  which  would be approved by adherents  of e n t i t l e m e n t  theory.  Welfare E v a l u a t i o n / To evaluate then,  it  i n the  proposed p o l i c y changes in the s p i r i t of N o z i c k ,  seems  'distance'  appropriate  between the  form  of  d i s t r i b u t i o n of actually  UI  benefits  Several  of  the  recent  1984)  papers  'distance'  account when comparing two  between  of  literature income  of  f u n c t i o n d: R  satisfies  of  i s that both the  d(x,y)=0 i f f  2.  d(x,y)=d(y,x);  3.  d(x,y)<d(x,z)+d(z,y); Dutta  x=y;  list  independence.'  cross-sectional  taken  cited  technique  inequality.  functions  of They  (metrics): function  (Reflexivity)  (Symmetry)  the  (Triangle Relation). additional  But,  for  my  property  for d i s t r i b u t i o n x and for d i s t r i b u t i o n  y.)  Chakravarty and  we want  argue that  if  of  short-run,.,  a p p l i c a t i o n the p o p u l a t i o n w i l l be the  Dutta  into  properties:  1.  'population  distributions  n  the f o l l o w i n g  (Chakravarty and  1982; the  R =>RJ i s a d i s t a n c e  n  the  premiums  d i s t r i b u t i o n s . The papers  choose i n s t e a d to make use of d i s t a n c e  it  and  issue of  must be  using an index  the  benefits  (Shorrocks,  to generate a more comprehensive  comparison than simply  if  of  received  have looked at the  the d i s t r i b u t i o n  A continuous  measure  individual  actually  income. The idea u n d e r l y i n g t h i s  above attempt  some  d i s t r i b u t i o n of  Chakravarty and D u t t a , measurement  to use  i n d i v i d u a l c o s t s in the form of UI  paid.  l e v e l and  152  to  same  compare  Welfare E v a l u a t i o n / well-being  in the two  distributions,  chosen must be " e t h i c a l l y coherent" evaluation  function.  the d i s t a n c e  where x and y are two  function  with a s p e c i f i c  They c o n s t r u c t  a  d i s t r i b u t i o n s of  income and i-(x)  are the corresponding e q u i v a l e n t l y d i s t r i b u t e d  £(x)  and  evaluation  My  use  function  of  the  distributions 'distance' Let  to  N=f(X,Y)  entitlement a distance of  are,  of c o u r s e ,  dependent  concept  of  operationalize  case,  the  the  Y is  This function s a t i s f i e s  social  between  I want to use the  Nozick's  idea  entitlement variable  above; X i s the the d i s t r i b u t i o n of  two of  theory. for  the  distribution individual  |X.-Y.|.  the r e q u i r e d p r o p e r t i e s  g i v e s equal weight to each  increase  i n N and  Nozick's  (1,2,3).  i n d i v i d u a l . And, the l a r g e r  d i s c r e p a n c y between c o s t and b e n e f i t  by  the  for N i s N=Z  accepted  distance  p o l i c y assessment  f u n c t i o n as l i s t e d  c o s t s . A candidate  be  incomes.  where N=f(X,Y) s a t i s f i e s the p r o p e r t i e s of  individual benefits;  l a r g e r the  on  and  chosen.  is quite d i f f e r e n t .  be  social  d(x,y)=f(£(x),£(y))  £(y)  £(y)  153  It the  for any i n d i v i d u a l , the  the l e s s l i k e l y a p o l i c y standards.f  Notice  that  will this  f T h i s assumes UI i s e n t i r e l y premium-financed. To the extent that UI i s financed from general revenue, c o n t r i b u t i o n s in the form of other taxes p a i d are i g n o r e d . As w e l l , no adjustments in programme c o s t s accompany reform of programme b e n e f i t s . T h i s i s a s e r i o u s o v e r - s i g h t from the entitlement perspective.  Welfare E v a l u a t i o n / e v a l u a t i o n procedure need labour f o r c e ,  since  other household  premiums nor r e c e i v e not necessary different  only account for  benefits.  to i n c o r p o r a t e  attitudes  is  the  neither  as w e l l ,  parameter to  toward i n e q u a l i t y .  from N o z i c k ' s point of view. transactions  a  members of  members  Notice,  154  that  pay  it  is  account  This is  Only the j u s t n e s s of  for  irrelevant individual  important.  4. Welfare E v a l u a t i o n R e s u l t s t  The U t i l i t a r i a n  welfare e v a l u a t i o n  ranks the e x i s t i n g and the  same  UI programme before  Forget reform  proposals before rankings  are  obtained i n the  individual policies For  proposals  men rate  and gains  women,  assessment of  couples, in  welfare,  for  income gains  The is whom  reaches  reducing  groups become more the  Macdonald  as r  rank r e l a t i v e  1  Macdonald  aversion  package as i n e q u a l i t y  i n c r e a s e d . As l e s s w e l l - o f f  in the  single  Model  Table 6 . 2 ) .  inequality  case of  components of the Macdonald is  as  (see  the  become i n d i s t i n g u i s h a b l e  single  benefit-replacement  both the  and ranks  the Forget p r o p o s a l s  increased (except  -5).  procedure for  to  the other  aversion important resulting  f R e s u l t s are presented only for upper-bound p r o b a b i l i t y of constraint simulations. Upper and lower-bound p r o b a b i l i t y models y i e l d the same r a n k i n g s .  Welfare E v a l u a t i o n / from i n c r e a s e d time.  In  employment  the  replacement  context  out-weigh the  of Model  1,  loss  reducing  rate generated the l a r g e s t  155  of  leisure  the  benefit  behavioural  response  for a l l groups except married women.  For Model 2,  the U t i l i t a r i a n  again ranks the e x i s t i n g proposal  (see  Macdonald  procedure  UI programme ahead of e i t h e r reform  Table 6 . 3 ) .  proposals  welfare e v a l u a t i o n  For s i n g l e  dominate  the  women and c o u p l e s ,  the  Forget  for  proposals;  s i n g l e men, the Macdonald p r o p o s a l s rank ahead of the Forget proposals  for  low  levels  (r=1,r=.5,r=-.5,r=-1),  but  another few a  reverses  (r=-5). This r e s u l t to i n c r e a s e  i n c r e a s e d . For the  model, these p r o p o s a l s rank  only  aversion  is  the  to gain e l i g i b i l i t y for UI  as i n e q u a l i t y a v e r s i o n i s  involves  ordering  rank f o r p r o p o s a l s  weeks of work necessary  s i n c e working  inequality  the  inequality aversion increases to the drop i n  of  minor  next  change  ensure UI  in  people to f i n d establish  eligibility.  of unemployment policy.  the e x t r a  will  if  it  few weeks  impossible  of work  benefits  entitlement  behaviour.  is  minimum  programme  c o n s t r a i n e d model, i n c r e a s i n g minimum e l i g i b i l i t y can have s e r i o u s consequences  related  unconstrained  to the e x i s t i n g  weeks to  as  For  the  conditions for  some  they need  to  I n d i v i d u a l s e x p e r i e n c i n g long p e r i o d s be the  only  ones a f f e c t e d  by  Since these people have a high p r o b a b i l i t y of  this being  Welfare E v a l u a t i o n /  156  c o n s t r a i n e d and a high p r o b a b i l i t y of having low incomes, is  reasonable  requirement  that  will  perspective  be  since  r a t h e r than  this the  is  minimum  appealing  an  from  increasing the  evaluation  for s i n g l e  For c o u p l e s ,  a  Utilitarian  of  proposal  entrance in  programme ahead of  reducing  requirement,  the  Utilitarian  men as i n e q u a l i t y a v e r s i o n  the Rawlsian welfare  Results programme  which suggests  the minimum  Macdonald  entrance  increased.  important element  Forget p r o p o s a l ,  dominates  existing  less  the  as a v e r s i o n to i n e q u a l i t y i s  i n d i c a t e that design  increasing  it  increases.  e v a l u a t i o n again ranks the  either  reform package with  the  Macdonald reform package ranking ahead of the Forget package (see  Table 6 . 4 ) .  For s i n g l e  men and s i n g l e  1 Rawlsian rankings are q u i t e d i f f e r e n t .  women, the  Both the  and the Forget proposals dominate the e x i s t i n g low l e v e l s of  inequality  F o r g e t . While that an  i t may,  evaluation  aversion, at f i r s t ,  approach which  low-income groups  should rank  generosity  UI programme  result  is  of the  reasonable  Macdonald  programme  and Macdonald appear  Model  at  dominates  counter-intuitive  focusses  attention  p r o p o s a l s which  on  reduce ' the  as w e l f a r e - i m p r o v i n g ,  this  i n the context of a model which assumes  i n d i v i d u a l s are free  to choose how  much unemployment  they  want. As UI  l e s s generous,  people  work  i s made  more, and t h e i r  incomes  increase.  Since  choose to  l o s s of  'leisure'  does not o f f - s e t  157  from higher  incomes  and  high unemployment have r e l a t i v e l y  low  the welfare  s i n c e the group with incomes,  Welfare E v a l u a t i o n /  i n d u c i n g these  l e s s generous perspective. increased, cut-backs  must  gain  people  to the poorest  There i s c o n s i d e r a b l e  Eliminating  place  for  poorest  single  minimum  for  women.  i n d i v i d u a l s i n the  regionally-extended in the and/or  live  in  regionally-extended  of  inequality  eligibility  benefits  These r e s u l t s  is  that  rate.  consistently  climbs to  first  that  largest  the  increases increases  and to the e l i m i n a t i o n the poorest  for the  high-unemployment supplement  of  individuals  existing regions 'earned'  of  conditions  income in response to  conditions  benefits  gains  aversion  suggest  sample make the  qualify  is  programme  the b e n e f i t - r e p l a c e m e n t  benefits;  sample b a r e l y  the c o s t  s i n g l e men and  in labour supply and hence i n minimum e l i g i b i l i t y  Rawlsian  inequality aversion  package as  to reducing  place  a  in the Rawlsian ranking  regionally-extended  ranked in f i r s t  from  UI  effort.f  variation  Increasing  climbs r e l a t i v e  by making  among the poor out-weighs the  of the Macdonald  increased.  as  rankings r e v e r s e ;  achieved through i n c r e a s e d work  is  work more  be w e l f a r e - i m p r o v i n g  E v e n t u a l l y , however,  these  components  to  programme where benefits.  fThe 'poorest among the poor' are the poorest i n d i v i d u a l s in the data s e t , a l l of whom are l a b o u r - f o r c e p a r t i c i p a n t s . The poorest i n d i v i d u a l s in the Canadian p o p u l a t i o n are not members of the labour f o r c e .  Welfare E v a l u a t i o n / (It  cannot be t r u e that  not a f f e c t e d  by these  the poorest proposals,  i n d i v i d u a l s are  or the e x i s t i n g  158  simply  programme  would dominate.)  The lack  of correspondence  between  the Model  1  Rawlsian  welfare e v a l u a t i o n r e s u l t s  obtained for s i n g l e men and women  and the  for  results  obtained  couples again  importance of m o d e l l i n g j o i n t For  single  individuals,  w e l f a r e - i m p r o v i n g as responses generated  a  responses to p o l i c y  reforming result  from the  of  low-wage  any  impact  large  on the  to  be  behavioural  of a low-wage  couples,  worker  the  ' p o o r . ' For c o u p l e s , each  benefit-replacement  earned week rate  e l i g i b i l i t y conditions  or  UI and of  eliminating  T h i s i s the opposite  i n d i v i d u a l s . Low-income at the  r e q u i r i n g two weeks of  of  rank ahead  evaluation  may  worker has a spouse with a higher wage so that  both l o c a t e d  Rawlsian  changes.  the  employment for  single  the  appears  the  if  household i s not  benefits.  UI  poor p o p u l a t i o n . For  b e h a v i o u r a l responses on the p a r t not have  suggests  result  reducing  increasing  the  minimum  regionally-extended  from that obtained for  couples are not  high-unemployment  end of  necessarily the  budget  constraint.  The somewhat evaluations  surprising  outcome of  the  Rawlsian  welfare  for Model 1 are very dependent on the assumption  Welfare E v a l u a t i o n / of u n c o n s t r a i n e d labour s u p p l y . Rawlsian welfare look very 6.5).  different  In t h i s c a s e ,  reform  proposal  for  the e x i s t i n g  for  Macdonald p r o p o s a l s l e v e l s of  the c o n s t r a i n e d  all  dominate the  inequality aversion  dominate at higher l e v e l s ; Macdonald p r o p o s a l s the  importance  unemployment. welfare  If  (from  single  made  incomes.  labour s u p p l y , p r o p o s a l s  the  at  low  proposals  This  about to  the  nature  respond,  if  the  illustrates  supply and hence  Rawlsian p e r s p e c t i v e ) ;  Under  the  women and c o u p l e s ,  are free  as t h e i r labour  the  men,  Forget  dominate throughout. assumptions  Table either  Forget p r o p o s a l s  while the  respond, the only e f f e c t  to reduce  model (see  For  for s i n g l e  individuals  increases  increase cannot  of  evaluations  programme dominates  groups.  to reduce the  of  of  their incomes  individuals  of UI retrenchment w i l l assumption  159  be  constrained  benefit-replacement  r a t e rank ahead of p r o p o s a l s to increase minimum e l i g i b i l i t y requirements  for s i n g l e  men, s i n g l e  women  and c o u p l e s .  workers are unable to o b t a i n even a few a d d i t i o n a l weeks employment, receive  it  is better  weekly  altogether  benefits  than  by making e l i g i b i l i t y  The E n t i t l e m e n t welfare proposals  to reduce the  first,  the  to  r a t e at which  stop  benefit  If of they  payment  unattainable.  evaluation  ranks the Forget  Macdonald p r o p o s a l s  second  reform and  the  Welfare E v a l u a t i o n / existing  programme  last  (see  Table  6.6).f  The  existing  programme ranks lower  than any  result  c o n s t r a i n e d and unconstrained  holds  and for a l l  for both  other v e r s i o n  demographic groups.  the ranking obtained using the  of U I .  Perhaps not  160  This models  surprisingly,  E n t i t l e m e n t approach i s  the  opposite of that most commonly found for the U t i l i t a r i a n and Rawlsian approaches. U t i l i t a r i a n and  (Varying i n e q u a l i t y  Rawlsian r a n k i n g s ;  not c o n s i s t e n t with  the p h i l o s o p h i c a l views  r a t e and  of Model  1,  eliminating  reducing  In g e n e r a l ,  the  b e h a v i o u r a l responses improve welfare context of Model  are  from 1.  employment,  r e q u i r i n g two  of  UI  benefits a l l rate.  benefit dominate  and  b e n e f i t s are  changes of  to  Nozick and in  a reduction  in  most the  increasing  twenty  weeks of employment  the  largest  which  of Model 2,  eliminating  In  package.  generate the  requirement  so  benefit-replacement  the p o l i c y  In the context  eligibility  of N o z i c k ,  of the Macdonald  the p e r s p e c t i v e  the minimum  week  the  p o l i c y changes which  is  for each model.)  regionally-extended  most w e l f a r e - i m p r o v i n g components  affects  inequality aversion  only one e n t i t l e m e n t ranking i s obtained the context  aversion  weeks  to earn  of one  regionally-extended benefit-replacement  Since b e h a v i o u r a l responses are small in Model 2,  the  only way to b r i n g premium c o n t r i b u t i o n s and b e n e f i t  receipts  fThe ranking of Macdonald and Forget might reverse experience-rating proposal were i n c l u d e d as part Macdonald package.  if of  the the  Welfare E v a l u a t i o n / i n t o alignment  i s to stop paying b e n e f i t s  to workers who are  unemployed for long  p e r i o d s ; workers who  but c o l l e c t  for many weeks.  benefits  In summary, three  f a c t o r s are c r i t i c a l  results  of welfare  results  depend  constitutes theory,  philosophical  'welfare.'  From  p r o p o s a l s for  UI reform  U t i l i t a r i a n and of  positions  inequality for  nature  of  will  reduce  rankings  aversion each  about  of  what  Entitlement  perspective,  welfare. are  the  Second,  sensitive  assumed.  of  unemployment.  unemployment  choices  obviously,  judgements  the p e r s p e c t i v e  the  to  Third,  three  leads  the welfare  the  welfare  philosophical  the is  This  is  most  Rawlsian r e s u l t s . the  outcome  of  dramatically  The  assumption  utility-maximizing  to the c o n c l u s i o n that UI reform w i l l  of  increase  low-income workers; the assumption that  unemployment i s the r e s u l t  of demand-side c o n s t r a i n t  to  conclusion  exactly  inequality  the  c o n s i d e r e d are s e n s i t i v e to assumptions made about  i l l u s t r a t e d through that  and most  from a U t i l i t a r i a n  Rawlsian  evaluation results  the  premiums  both reform p r o p o s a l s are w e l f a r e - i m p r o v i n g r e l a t i v e  to the e x i s t i n g UI system;  degree  pay few  i n determining  evaluation. F i r s t ,  upon  161  the  opposite  aversion).  (at  low  some leads  levels  of  VII.  In t h i s  thesis  of  the  of  the  Canadian UI system which takes e x p l i c i t account of both  the  Macdonald  I  and  efficiency  have  CONCLUSIONS  Forget  and  conducted proposals  the e q u i t y  in  attempt to  incentives  generated by the  the  reduce  reform  these  proposals.  the  some of  programme  the  adverse  e x i s t i n g programme. Thus,  i n d i v i d u a l s must be ' w o r s e - o f f assessment of  for  for a retrenchment i n  generosity  a pure  evaluation  dimensions of  Both reform p r o p o s a l s c a l l an  an  after  some  the p o l i c y change, and  efficiency  consequences  of  the  proposals cannot produce a ranking of o p t i o n s . R e s o l u t i o n of t h i s problem i n v o l v e s  i n t r o d u c i n g an  equity c r i t e r i o n .  introduce d i s t r i b u t i o n a l c o n s i d e r a t i o n s specific  set  of  value  welfare consequences 'ethically-flexible'  judgements,  of proposed  without  I  have  imposing  evaluated  p o l i c y changes  approach. That i s ,  using  considered).  l i m i t s the The  Utilitarianism; of  justice;  entitlement  Each  of  first  number of approaches approach  the second i s  the  third  is  a the an  I have conducted the  e v a l u a t i o n from three very d i f f e r e n t e t h i c a l p o i n t s of (feasibility  To  is  in  which can  the  spirit  view be of  i n the s p i r i t of Rawls' theory in  the  spirit  of  Nozick's  theory.  these  welfare  evaluations, 162  however,  depends  Conclusions /  163  fundamentally on an u n d e r l y i n g model of household behaviour. One of the major which welfare the nature crucial  f i n d i n g s of t h i s  evaluations  of observed  feature  of  the p a r t of  single  b e h a v i o u r . For  to ask i s whether  to t h i s  two separate single  question  sets of women  model  observed unemployment  labour s u p p l y , observed  constraints  Chapter Two supply.  the  unemployment;  observed  unemployment on  I  have  l a b o u r - s u p p l y equations  (for  and  of  i s not  is  'labour-supply'  1  the  the  models  on  of the  behaviour. Households, with  two  result  that of  1, that  choices  the c o n s t r a i n e d  model  some  part  demand-side  choices.  unconstrained  builds  assumes  utility-maximizing  r a t h e r than s u p p l y - s i d e  develops  reflect  supply,  i n t r o d u c e s the p o s s i b i l i t y  unemployment  Model  to  of unemployment. Model  labour  reflects  obvious,  couples)  (up to a random e r r o r term); Model 2,  of  this analysis,  u t i l i t y - m a x i m i z i n g behaviour  views about the nature  the u n c o n s t r a i n e d  of  to  households.  men,  different  the degree  depend upon assumptions made about  represent  Since the answer estimated  is  the data to be e x p l a i n e d i s  the c r u c i a l q u e s t i o n does or does not  thesis  a impact  one or two  model  long of UI  of  labour  tradition on  of  household  working heads,  are  assumed to choose weeks of unemployment and consumption of a  Conclusions / composite commodity to  maximize u t i l i t y  c o n s t r a i n t s which  c a r e f u l l y incorporate  the  system.  Canadian  identical  UI  for  households  characteristics.  Since  demographic v a r i a b l e s , variables) of UI  Utility  in household  a  constraint  is  estimate t h i s  utility  functions  depend  (as modelled through  same segment of  to the  the budget  of  problem f o r t h i s  model (as  weeks  of  leisure  (attempts The  do not  The  w e l l as cannot  bounds, c r e a t i n g a l i m i t e d dependent  for Model fall  to  piece-wise  fall  reported  other major  to  budget  around  extent that observed  constraint,  inconsistent.  budget  by l i n e a r i z i n g  leisure  estimates may be  observed  implemented  is treated  u t i l i t y - m a x i m i z i n g choices  that  linear  not s u c c e s s f u l ) .  Thus,  these  The c o r r e c t approach  piece-wise  but not  l i n e a r budget c o n s t r a i n t the observed p o i n t .  a  on  Incorporation  c o n s t r a i n t s means  with  model were  assumed  demographic  to i n f l u e n c e c h o i c e s .  outlined  are  of  identical  budget  model  budget  the parameters  functions  c o n s t r a i n t s are p i e c e - w i s e l i n e a r . estimating  to  with  'tastes'  are assumed  subject  164  on  and the  parameter estimation 2)  outside  is  that  obvious  v a r i a b l e problem of  the  T o b i t v a r i e t y which i s a p p r o p r i a t e l y t r e a t e d .  Chapter Three  develops  s u p p l y . Model 2  starts  the  constrained  with the  model  of  labour  same b a s i c assumptions  Model 1: households choose weeks of  l e i s u r e and  as  consumption  Conclusions / of a  composite  subject  to  commodity  budget  parameters of between the  in  order  constraints  the Canadian two models  i s that  'tastes'  significant  for  difference  the  i s no  household's  Models  i s made  an  important  impact of extension.  how such  is  that  2  to  correspond  choices.  The  i n t r o d u c e d , but no  c o n s t r a i n t s may  arise.  be  My  labour-supply  model  existence  probability  than d e s i r e d  most  UI on behaviour would c l e a r l y  e s t i m a t i o n of  greater  and  an  of  a  and  have  the labour market i n t o  consequences  individual,  the  1  longer assumed  I n c o r p o r a t i n g the demand s i d e of a n a l y s i s of the  assumed to  utility-maximizing  to model  different  second,  is  the  difference  households with  p o s s i b i l i t y of demand-side c o n s t r a i n t s attempt  A first  no longer  between  utility  incorporate  unemployment. The  observed unemployment with  maximize  which  UI system.  demographic c h a r a c t e r i s t i c s are different  to  of  merely  constraints  functions. that  examines for  For each  observed  unemployment plus  the the  unemployed  unemployment  a stochastic  This  probability  switching regression where  the  two  is  used to  model with  possible  estimate  a  sample s e p a r a t i o n  regimes  are  form  is  constrained  known i s the p r o b a b i l i t y that observed  i s g r e a t e r than d e s i r e d unemployment.  the of  unknown  u n c o n s t r a i n e d unemployment. For the c o n s t r a i n e d regime, that  is  error  term i s c a l c u l a t e d , based on the assumed d i s t r i b u t i o n of error.  165  and all  unemployment  Conclusions / Both models  of  labour supply  were  estimated  by  maximum  l i k e l i h o o d using a Stone-Geary f u n c t i o n a l form and the Survey of Consumer F i n a n c e . The Stone-Geary u t i l i t y i s acknowledged to be a h i g h l y r e s t r i c t i v e but  unfortunately,  the  basic  1982  function  functional  econometric  166  form,  difficulties  i n v o l v e d i n e s t i m a t i n g e i t h e r Model 1 or e s p e c i a l l y Model do n o t ,  at  functional  present, form.  allow  the use  of  Estimation  results  for  r e p o r t e d in Chapter first,  that  F o u r . Major f i n d i n g s  correcting  problem has a  significant  Second, u n c o n s t r a i n e d men, s i n g l e  married  results  impact  while u n c o n s t r a i n e d women  are  to  both  flexible  models  for Model  dependent  1  are are,  variable parameters.  functions  for  single  positively-sloped  labour-supply  positively-sloped  functions  and  elastic.  of married women who work  part-time  be p a r t i c u l a r l y  (Nakamura and Nakamura,  important d i f f e r e n c e  more  on estimated  labour-supply  Labour-supply f u n c t i o n s are found  limited  women and m a r r i e d men are a l l  and i n e l a s t i c for  the  a  2  elastic, 1983)  recent  which suggest that  in labour-supply  found between p a r t - t i m e  confirming  behaviour i s  to  the be  and f u l l - t i m e  workers r a t h e r  than  between men and women. Model 1 r e s u l t s  f u r t h e r suggest  that  a  distinction  might  behaviour of married  be  made  women and  observable b e h a v i o u r a l d i f f e r e n c e either  single  or  between single  the women:  labour-supply there  between s i n g l e  married men. F i n a l l y ,  Model  1  is  women  no and  estimation  Conclusions / results  suggest  that  there  are  important  167  interactions  between own l a b o u r - s u p p l y behaviour and spouse's demographic characteristics.  Major r e s u l t s estimated  for Model 2  probabilities  observed to  experience  the v a l i d i t y of unemployment  of  first  does  would be an attempt  constraint  unemployment.  not  second  for  functions  of the present work  labour-supply  functions.  for  less  Third,  Model 2  elastic there  those  of  any  other  interdependencies  are  married  married  men  and  inelastically,  to  again  increases  evident  for  in  are a  spouse's  women with a  spouse who i s than  if  the  to  Both  respond, constrained  of m a r r i e d men and  unemployed by  in c o n j u n c t i o n with those obtained for  1  the  importance  of  a  1  important  These r e s u l t s , concerning  that  difference  unemployed and c o n s t r a i n e d spouse i s  the  Model  couples.  found  and l a b o u r - s u p p l y f u n c t i o n s  2  of m a r r i e d women  Finally,  unemployment,  less elastic  no  group.  women  is  than  is  between the Model 2 l a b o u r - s u p p l y functions and  1 or Model  i s beyond the scope of  result  are  observed  utility-maximizing  to determine whether Model  labour-supply  suggest  some p a r t of  Another extension  estimation  high  individuals  Such r e s u l t s  represent  the p r e f e r r e d model, but t h i s  thesis. A  of a l l , the very  the assumption that  labour-supply choices.  is  are,  spouse's  are  choice. Model  demographic  Conclusions / characteristics  for  own-wage  elasticites,  illustrate  the  importance of modelling j o i n t behaviour and suggest that development  of  more  sophisticated  important area for future  The estimated models of  models  would  be  an  labour supply enable the  simulation  reform p r o p o s a l s under  very  d i f f e r e n t assumptions about the nature of unemployment. result  obtained  the  research.  of b e h a v i o u r a l responses to UI  basic  168  u s i n g the  estimated  The  parameters  of  Model 1 i s that e i t h e r  the Macdonald or the Forget proposals  would  substantial  result  in  a  unemployment. The b a s i c the Macdonald  nor  the  Forget  impact  conflicting  predictions  consequences  of  The  other  proposed UI  proposals  of  approach  likely  the UI  reform  of  a  course,  measured by  a  'mean of  normalized u t i l i t y v a l u e s .  is order  These  constitute  the  evaluation.  welfare the  evaluation  equity  function  assessing  The mean of  well-being of  of  dimension.  for s o c i a l w e l f a r e .  Utilitarian; r'  any  behavioural  three a l t e r n a t i v e methods of  developed  have  of  dimension  reform i s ,  would  neither  unemployment.  i m p l i c a t i o n s of p o l i c y changes  first  observed  observed  dimension of the p r o j e c t  Chapter Six develops the  on  proposed  vital  in  f i n d i n g for Model 2 i s that  significant  'efficiency'  reduction  The is  individual  order r allows  for  varying attitudes  toward i n e q u a l i t y  individual u t i l i t y . of the  estimated  functions.  Stone-Geary  Explicit  as  well  of  are s c a l e d  versions  indirect  utility  i n t e r p e r s o n a l comparisons,  as  on  implicit the  o b t a i n these  individual about  functions,  nature  of  on  estimated  parameters,  are  values.  change  (utility  unemployment/leisure) parameters of  the  is  and in  the  Thus,  unemployment through  critical  p r e d i c t i n g the amount of unemployment/leisure the p o l i c y  of  are r e q u i r e d to  nature of the observed d a t a , more g e n e r a l l y ) , impact  the  poverty  parameters  normalized u t i l i t y the  based on  in the Canadian  estimated  (and hence u t i l i t y )  made  in the d i s t r i b u t i o n  household  labour-supply  assumptions  169  Individual u t i l i t i e s  i n t e r p e r s o n a l comparisons lines  Conclusions /  their  both  consumed  an i n c r e a s i n g  determining the  u t i l i t y function i t s e l f  (the  in after  function  of  value of  the  and thus of  the  i n t e r p e r s o n a l comparisons of u t i l i t y which are made.  The second developed  approach to i n Chapter  the  Six  assessment of  is a  with John Rawls' theory of  measure which i s  justice.  t h i s approach are that a t t e n t i o n 'worst-off not count measure utility)  social  The c r u c i a l  welfare  consistent features  should be focussed  of  on  the  group in s o c i e t y and that p e r s o n a l t a s t e s should in  assessing  well-being.  i s a mean of order distribution  Hence,  r over an income  censored  at  the  the  Rawlsian  ( r a t h e r than poverty  a  line.  Conclusions / Differences  i n household need are i n c o r p o r a t e d a c c o r d i n g  the Canadian  poverty l i n e s ,  i g n o r e d . Given the  sensitivity  about  of  From  results  developed in Chapter  defines  the  are  measurement of  between the d i s t r i b u t i o n  to  be  of b e n e f i t s  measure pays  i n e q u a l i t y nor does i t pay a t t e n t i o n From the e n t i t l e m e n t nature  of  unemployment  p r e d i c t i n g the benefits  perspective, are  behavioural  consistent  the  distance  when  from UI  to a t t i t u d e s  to d i f f e r e n c e s  primarily  responses  toward i n need.  important  which  and  s m a l l e r . The  assumptions made about  the for  determine  UI  in the d e t e r m i n a t i o n  of  r e c e i v e d and UI premiums p a i d .  Three f a c t o r s appear to be c r i t i c a l welfare e v a l u a t i o n r e s u l t s . on the  welfare  measure  received  no a t t e n t i o n  in  This  the d i s t r i b u t i o n of c o n t r i b u t i o n s made to UI i s entitlement  made  income.  social  theory.  higher  the  important  measure which i s  entitlement  welfare  are  poverty  assumptions  primarily  to  Statistics  alternative  perspective,  Six i s a  Nozick's  social  to  i n labour supply and hence  approach to  Robert  obtained  unemployment  determining changes  with  in taste  i t would be v a l u a b l e to t e s t  the Rawlsian  observed  The f i n a l  but d i f f e r e n c e s  important r o l e assigned to the  Canada low-income c u t - o f f s ,  measures.  170  ethical position  First,  results  adopted. From  of course  depend  the p e r s p e c t i v e  of  Conclusions / Nozick s entitlement  theory,  1  both the  Macdonald  Forget p r o p o s a l s for the reform of UI are relative  to  the  perspective,  existing  either  proposal  implemented. A second the U t i l i t a r i a n degree  of  system.  and  aversion:  inequality aversion increases. welfare  in  Rawlsian approaches,  inequality  a  welfare  if  the context is  rankings  Finally,  the  Utilitarian  reduce  important f a c t o r ,  and  welfare-improving  From  would  the  can  change  as s t r e s s e d  i n the  assumptions  estimates  utility  function.  results,  differences  y i e l d opposite  But,  U t i l i t a r i a n case,  earlier,  as  of  the  parameters  illustrated  in u n d e r l y i n g  since  by  the  equity  fundamentally  efficiency  are  of  objective  policy  efficiency  into  that  evaluations account.  it  is possible  which take  the  Rawlsian can of  measure;  interconnected  elements of a p o l i c y e v a l u a t i o n . 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Economic  1  APPENDIX  The f u l l Z' =  0 a  v a r i a n c e - c o v a r i a n c e matrix for couples a  2  eie  2  a  eie  Since  a 3  2  a  2  e  2  e,e  3  e e  3  2  e e 2  the  a 3  2  e  3  commodity-demand  estimation,  it  is  p.24):  If  of  a  vector  make use  variables,  normally d i s t r i b u t e d  w i t h mean  M  matrix  and  covariance  marginal  d i s t r i b u t i o n of  components  obtained  by  components  of  taking n and Z ,  e1  e1e  a e,e  a 2  simplify  dropped  of the  X,  for  following  is  vector the  set  of  normal  covariances the  proper  respectively.  the commodity-demand equation  covariance matrix i s  any  v a r i a n c e s and  is  Z,  of X i s m u l t i v a r i a t e  with means,  To  equation  necessary to  theorem (Anderson, 1958,  After  is  o  eie  a  (Model 1)  i s dropped, the  relevant  thus:  2  2  e  2  the  integration 193  required  for  the  sample  / selectivity correction, f(e ,e ) 1  the  can be r e - w r i t t e n  2  a conditional  (now)  bi-variate  normal  194  density,  as the product of a marginal  and  density:  f(e T , e ) = f , ( e , ) f ( e 2  2  e,)  2  where the marginal d e n s i t y , a  and v a r i a n c e  2  ,  ^1  and the  f^e,),  i s normal with mean zero  conditional density f ( e 2  2  e,)  is  a l s o normal, but with mean M_ =P e  2  e2  e,e  e  (o 2  e  /a 2  e,e  2  where p_ e  1  e,  2  e  and v a r i a n c e  1 (  2  =a_ e  )e  1  /(o-_ e  2  e  cr^ ) i s 2  e  the c o r r e l a t i o n  between e,  and  2  e • 2  Finally,  the t r a n s f o r m a t i o n  from the d i s t r i b u t i o n distribution  in  of v a r i a b l e s  in terms  terms  of  of  of  the t r a n s f o r m a t i o n  is  the e r r o r  observables  s i n c e the e r r o r s are merely a d d i t i v e equal to  r e q u i r e d to  is  terms to  move the  straightforward  (and hence the Jacobian  one).  APPENDIX 2  Dropping  the  commodity-demand  estimating equations (1)  for couples  s?=st(w,7,0,A)+e 2  1  (4) s = s ( w , 7 , 0 , A , ) + u  2  The  2  2  d i s t u r b a n c e t e r m s a r e assumed  distribution Z = 4  a a a a  e,e  a 2  e,Ui e,u  o  e,e a  e  a  2  2  a  2  break  e u 2  the  a 2  be  for  a  2  U,U  a 2  covariance the  matrix  u  2  2  2  t '  2  2  (1958, p. matrix  four  24),  into  possible  i t is  possible  sub-matrices situations  in  for which  observed:  (1) I f n e i t h e r h o u s e h o l d equations  2  u,  u,u  e u  of Anderson  estimation. Consider c o u p l e s may  a  e u,  A g a i n making use to  e,u a  e u,  2  2  covariance  normal  a  e,u,  2  of  becomes  to follow a j o i n t  w i t h means of z e r o and  a  2  e,  2)  system  2  s?=st(w,7,0,A,Z )+u 2  (Model  the  1  (2) s = s*(w,7,0,A)+e (3)  equation,  member  estimation  appropriate covariance  f i t i s not p o s s i b l e variance-covariance  are  i s unemployed, (1)  and  the  (2)  relevant with  the  of t h e  full  matrix  to estimate every matrix. 195  element  (2)  If  only the wife  (a)  the  matrix  unconstrained, (b)  for  is  /  196  she  is  unemployed,  (1)  is  again a p p r o p r i a t e  if  but  the matrix a 2 a  e U! 2  is appropriate i f  she  (3)  husband i s  If  only the  covariance situation  (4)  If  matrices (1)  and (b)  is  constrained.  are  unemployed,  given  by  (a)  the  corresponding  the  matrix  for  the matrix  both husband and wife are unemployed,  four cases  are  N e i t h e r husband nor wife may be c o n s t r a i n e d so that  (1)  possible: (a) will (b)  be the a p p r o p r i a t e  sub-matrix.  only the wife may be c o n s t r a i n e d so that  2(b)  will  again  so that  3(b)  will  be a p p r o p r i a t e . (c)  only the husband  may be c o n s t r a i n e d  again be a p p r o p r i a t e . (d)  both husband and wife may be c o n s t r a i n e d .  In t h i s  case,  / the  sub-matrix  (1)  will  be  the  relevant  197  matrix  for  functions  are  est i m a t i o n .  To s i m p l i f y  integration,  the b i v a r i a t e d e n s i t y  again r e - w r i t t e n as the product of marginal and densities.  Arbitrarily,  unemployed or i f n e i t h e r is  written  in  terms  labour-supply function. the marginal d e n s i t y  if  both  i s unemployed, of  the  If  only one  is written  h i s or her l a b o u r - s u p p l y  husband  error  and  conditional wife  the marginal from  the  person i s  density  husband's unemployed,  in terms of the e r r o r  function.  are  from  APPENDIX 3  198  199 T a b l e 4 . 1 . — B a s i c Data Averages. MEN NUMBER  WOMEN  TOTAL  9100  17,753  .24  .23  .23  .97  .76  .86  .23  .22  .23  .53  .25  .28  41.9  44.2  4.8  4.75  8653  INCIDENCE OF UNEMPLOYMENT PERCENT FULL-TIME INCIDENCE: FULL-TIME WKRS INCIDENCE: PART-TIME WKRS AVERAGE WEEKS EMPLOYMENT  46.7  AVERAGE WEEKS UNEMPLOYMENT  4.7  AVERAGE GROSS WEEKLY WAGE  413.  238.  323.  200 T a b l e 4 . 2 . — O c c u p a t i o n a l Averages. Industry  # Men  # Women  Average  Incidence  Av Wks  Av Wks  Wage  Unemp  Emp  Unemp  Mgt  865  543  456  .08  50.02  1.35  Sci/Prof  834  1285  373  .12  47.64  2.17  Teaching  368  656  443  .13  45.65  2.50  Clerical  492  3143  263  .1.8  44.26  3.74  Sales  881  823  305  .17  45.44  3.23  Services  823  1646  238  .28  40.36  6.17  Forestry/Fishing  329  91  304  .63  32.11  15.74  Mining  976  305  372  .37  42.16  7.83  Product Fab  1026  352  353  .25  46.03  4.43  Construction  997  23  409  .47  41.26  9.89  Transportation  1059  211  370  .31  44.25  6.19  201 Table 4.3.— P r o v i n c i a l Province  # ObS  Averages. Per C a p i t a  Incidence  Income  Incidence  Incidence  Of U  Of U  Of U  Men  Women  Both  NFLD  573  7379  .43  .34  .38  PEI  229  7830  .38  .26  .31  NS  716  8005  .35  .24  .29  NB  755  8661  .36  .27  .31  QUE  1767  9980  .27  .20  .23  ONT  2337  10840  .17  .14  .15  MAN  868  9770  .20  .13  .16  SASK  860  10077  .18  .14  .15  ALTA  1578  11314  .18  .13  .15  BC  1336  12006  .21  .18  .19  202 T a b l e 4 . 4 . — D i s t r i b u t i o n of Weeks A c r o s s Budget Segments. Single  Single  Men  Women  Couples Before Segment 1  After  Before  423  After  37  71  (Wks L t Min) Segment 2  381  80  64  15  55  13  2686  2331  417  417  348  348  8720  7572  1243  1229  1695  1670  231  64  16  197  57  (Wks Ge Min and Wks Le Max) Segment 3 (Wks Gt Max and Wks L t 50) Segment 4 (Wks L t 50) Wage t o o Low  968  Notes: The numbers  f o r c o u p l e s i n c l u d e men and women i n d i v i d u a l l y .  male  a l r e a d y been  workers  'After'  have  numbers  households. insurable unemployed.  exclude  eliminated  zero-income  households  Workers w i t h weekly wages earnings, Corners  d e s c r i b e d above.  neither  pay  are a r b i t r a r i l y  from  less  as w e l l  than  premiums assigned  t h e 'Before'  as ' d i s e q u i l i b r i u m '  $63 (1981),  nor  Part-time  numbers. The  receive  t o Segments  20% o f maximum  UI  benefits i f  Two and Four as  203 T a b l e 4 .5.--  Mean V a r i a b l e V a l u e s . S i n g l e Women and S i n g l e Men. Single  Single  Women  Men  Model I  Model  Model I  Model  II  II  Full  U'd  Full  U'd  Full  U'd  Full  U'd  At l a n  .19  .29  .19  .25  .17  .28  .17  .26  West  .45  .38  .45  .41  .46  .36  .46  .39  City  .55  .44  .54  .45  .50  .37  .37  .37  Part2  .09  .17  .11  .23  —  -  —  -  Ef am  1.8  2.3  1.9  2.4  1.7  2.1  1.7  2.1  Yrse  12.0  11.0  11.8  10.7  11.2  9.4  11.1  9.4  Clt7  .10  .20  .20  .30  .00  .00  .00  .00  Sea  —  —  —  —  .14  .30  .15  .30  Cyc  —  —  —  —  .35  .41  .35  .39  Wnet  182.  96.9  183.  132.  227.  143.  232.  178.  Nlinc  2435.  5658.  2448.  4456.  3129.  5782.  3010.  4819.  Notes:  The  values  reported  p e r c e n t a g e s . Other v a l u e s 'Full'  refers  to  the  for  ATLAN, WEST,CITY,PART ,SEA,and  CYC  a r e means. full  i n d i v i d u a l s who e x p e r i e n c e  sample ; 'U'd' unemployment.  refers  to  the  sub--sample  i  204 T a b l e 4 . 6 . — Mean V a r i a b l e V a l u e s .  Couples.  Model I  Model I I  Full  W U'd  H U'd  Full  W U'd  H U'd .40  At l a n  .24  .33  .38  .24  .28  West  .39  .37  .31  .39  .39  .30  City  .41  .31  .30  .39  .32  .26  Part  .22  .26  .15  .28  .38  .21  Efam  3.2  3.4  3.2  3.3  3.5  3.3  Yrsel  11.3  10.8  9.73  11.3  11.0  9.6  Yrse2  11.8  11.2  10.7  11.6  11.1 "  10.6  Clt7  .45  .58  .53  .51  .69  .59  Sea  .14  .19  .33  .15  .21  .36  Cyc  .34  .38  .40  .35  .40  .41  Wnetl  254.  237.  146.  255.  247.  161  Wnet2  143.  71.  114.  147.  116.  121.  Nlinc  5484.  8499.  8967.  5409.  6763.  8085.  Notes:  The  percentages.  values  reported  for  Atlan,West,City,Part,Sea,and  Cyc  are  Other v a l u e s a r e means.  'Full'  refers  t o the f u l l  sample o f c o u p l e s  refers  t o t h e sub-sample i n which t h e w i f e  f o r t h e r e l e v a n t model; i s unemployed;  the sub-sample i n which t h e husband i s unemployed.  'W U'd'  'H U'd' r e f e r s t o  205 T a b l e 4.7.— Model 1 Parameter E s t i m a t e s . S i n g l e Women. Basic Variable  Tobit  Coeff.  T-Ratio  -684.3  -1.350  7OO  701(Atlan)  979.3  3.149  7  02(West)  1188.  3.883  702(West)  7  03(City)  329.9  1.062  7  7  04(Efam)  -10.84  -.1404  7  705(Yrse)  4.079  .1190  7  06(Part)  -160.6  7  07(Clt7)  901.9  710  -6.570  7ll(Atlan)  -6.249  .6964  7l2(West)  .5766  -.06839  7l3(City)  .3705  .3589  7l4(Efam)  -.7962  7l5(Yrse)  -.02087  7  7  00  Coeff.  T-Ratio  22.12  .002431  2344.  2.699  4117.  5.606  03(City)  742.2  1.227  04(Efam)  -297.7  -1.751  705(Yrse)  -108.1  -2.116  -.6887  706(Part)  1468.  2.817  3.758  7  07(Clt7)  1517.  2.975  -3.739  7IO  -83.12  -5.445  01(Atlan)  7  ll(Atlan)  -62.12  -1.946  7  12(West)  -55.57  -2.357  -2.695  -.3233  -2.108  7l3(City) 14(Efam)  7.893  3.331  -.1830  7  15(Yrse)  .1114  .1245  7  16(Part)  2.820  2.453  7  16(Part)  5.363  .3724  7l7(Clt7)  -1.630  -1.365  7  17(Clt7)  2.358  .3269  010  .1047  4.308  010  .4050  6.722  011(Atlan)  .09333  4.952  011(Atlan)  .2659  3.097  012(West)  .008581  .6405  012(West)  .2808  4.158  013(City)  -.001862  -.1407  013(City)  .02661  .8518  014(Efam)  .01086  2.203  014(Efam)  -.02724  -2.561  015(Yrse)  -.0001906 -.1190  015(Yrse)  -.004343  -1.401  016(Part)  -.01957  -1.366  016(Part)  .07137  1.558  017(Clt7)  .04585  3.054  017(Clt7)  .05605  1.889  LLF  -730.98  LLF  156.  7  2088 OBS  Note: Reported  2088 OBS  T-Ratios are asymptotic.  206 T a b l e 4.8.— Model 1 Parameter E s t i m a t e s .  S i n g l e Men.  Basic  Tobit  Variable  Coeff.  T-Ratio  7OO  -1118.  -2.027  7  -yOl(Atlan)  710.9  1.427  7  702(West)  752.1  1.676  702(West)  Coeff.  T-Ratic  00  873.4  .9486  01(Atlan)  -270.4  -.4646  775.3  1.333  703(City)  70.50  .1673  -886.4  -1.401  704(Efam)  144.7  1.672  704(Efam)  122.5  .9682  05(Yrse)  56.57  2.164  7  05(Yrse)  47.47  .9627  706(Sea)  1390.  3.278  7  06(Sea)  1029.  1.829  707(Cyc)  70.92  .1991  7  07(Cyc)  426.3  .8506  7  08(Clt7)  -386.1  -.2623  7  7  03(City)  7  08(Clt7)  378.8  .4288  7  10  -8.856  -3.088  7  10  -140.0  -2.729  7  ll(Atlan)  -6.416  -2.542  7  ll(Atlan)  30.70  .6964  7  12(West)  -3.480  -1.967  7  12(West)  -.8144  -.06835  7  13(City)  2.114  1.110  7  13(City)  70.58  1.561  -.8694  -1.664  7  14(Efam)  -1.090  -.3737  7l4(Efam)  .  7  15(Yrse)  .05111  .2885  7  15(Yrse)  -2.080  -2.144  7  16(Sea)  -2.741  -1.064  7  16(Sea)  29.52  2.324  7l7(Cyc)  -2.180  -1.196  7  17(Cyc)  2.626  .2668  18(Clt7)  -1.705  -.3341  7  18(Clt7)  -44.13  -1.339  010  .1327  4.159  010  .5873  5.909  7  011(Atlan)  .09613  3.431  e?ll(Atlan)  -.02106  -.2779  012(West)  .05621  2.624  012(West)  .03573  1.085  013(City)  -.02752  -1.242  013(City)  -.1790  -2.154  c?14(Efam)  .01486  2.495  014(Efam)  .01019  1.458  015(Yrse)  -.0008810 -.4640  015(Yrse)  .003621  1.396  016(Sea)  .1003  3.536  016(Part)  .03143  .9985  017(Cyc)  .03572  1.684  t?17(Clt7)  .03281  1.373  018(Clt7)  .003191  .006051  018(Clt7)  .01787  .5474  LLF  192.6  LLF  173.3  1677 OBS  Note: Reported T - R a t i o s a r e a s y m p t o t i c .  1677 OBS  207 T a b l e 4.9. — M o d e l 1 Parameter E s t i m a t e s . Basic  Couples.  Basic  Tobit  With SSC  With SSC  Variable  Coeff.  T-Ratio  Coeff.  T-Ratio  Coeff.  T-Ratio  700  -285.8  -.008339  -3954.  -1.042  -2520.  -.8524  701(Atlan)  -12.370  -8.081  -9154.  -4.793  -3833.  -2.643  <y02(West)  397.6  .3008  354.0  .2136  1653.  1.237  <y03(City)  -1652.  -1.271  -253.7  -.1542  -1697.  -1.280  704(Efam)  1107.  1.969  760.4  1.307  -127.5  -.002538  705(Yrsel)  -125.5  -.8051  -211.5  -1.060  -180.6  -.1062  475.4  2.728  647.2  2.877  138.0  .008490  707(Sea)  -3353.  -2.213  -3219.,  -1.652  1505.  .9956  7  06(Yrse2) 08(Cyc)  -2626.  -2.172  -1267.  -.8207  1551.  1.249  709(Part)  5392.  4.194  2920.  1.858  3810.  2.869  7010(Clt7)  -1931.  -2.164  -1470.  -1.335  894.8  .008709  -1.773  -2.060  -2.406.  -2.137  -99.71.  -7.660  -1.203  -3.101  -.7368  -1.282  4.380  .7278  7  7IO 7  ll(Atlan)  7  12(West)  .1020  .3347  .2250  .5050  11.65  2.176  7  13(City)  -.6442  -2.144  -.2527  -.5718  -14.49  -2.763  7  14(Efam)  .1065  .7861  .1367  .7953  -.2468  -.001333  7  15(Yrsel)  -.09444  -2.335  -.1478  -2.511  -1.059  -1.710  7  16(Yrse2)  -.02970  -.6586  -.02954  -.4483  -2.343  -3.379  2.849  7.031  3.685  6.079  57.30  8.596  7l7(Sea) 7  18(Cyc)  .04120  .1370  .5615  1.268  28.12  5.189  7  19(Part)  1.003  3.495  .5486  1.304  5.762  1.042  7  110(Clt7)  .1579  .7425  .1650  .5391  12.37  3.486  72 21(Atlan)  -2.392  -2.572  -5.499  -3.851  -108.0  -8.739  -.8977  -2.137  -.4622  -.6718  5.071  .9523  .2600  9.769  -.6803  -5.830  2.100 -1.272  7  7  22(West)  .1935  .5892  .1427  7  23(City)  -.8024  -2.457  -.3724  724(Efam)  .2100  1.474  .1374  .7026  -.9153  -.004971  725(Yrsel)  -.05805  -1.328  -.1265  -1.693  -.6510  -.1107  7  26(Yrse2)  .01216  .2423  .1657  1.964  1.729  2.485  7  27(Sea)  .4876  1.169  .9047  1.290  5.321  .9774  7  28(Cyc)  -.1095  -.3403  .5892  1.094  6.866  1.525  729(Part)  2.609  6.206  1.282  1.882  16.32  3.224  7210(Clt7)  .2955  1.170  .2624  .6465  6.343  1.970  ei 62  .04669  14.88  .05208  11.00  .2832  17.97  .02941  18.71  .04072  15.39  .2101  12.99  LLF  -16464.  -10604.  -529.6  5107 OBS  2500 OBS  2500 OBS  208 T a b l e 4.10.— Model 2 Parameter E s t i m a t e s . Single  Single  Men  Women  Coeff  T-Ratio  Variable  Coeff  T-Ratio  0  -981.6  -2.131  70  -220.2  -.9043  7l  -45.84  -9.627  691  .2963  10.84  LLF  -324.7  Variable  7  -36.09  -11.30  61  .2227  13.21  LLF  -293.1  2297 OBS  1796 OBS Married  Married  Men  Women  Variable  Coeff  T-Ratio  Variable  Coeff  T-Ratio  70  -9748.  -5.9449  70  -9748.  -5.9449  7l  -46.70  -13.81  72  -27.70  -17.85  81  .1061  9.8545  62  .06864  15.11  LLF  586.5  2000 OBS  Note: Reported T - R a t i o s a r e a s y m p t o t i c .  Table 4.11.—  P r o b a b i l i t i e s of Constraint  i n Unemployment. S i n g l e Women.  F u l l Sample Part-Time  Atlantic  Western  Central  570/2297  131/258  141/425  236/1034  193/838  (25%)  (51%)  (33%)  (23%)  (23%)  487/570  107/131  125/141  203/236  159/193  (81%)  (89%)  (86%)  (82%)  104/131  113/141  186/236  140/193  (79%)  (80%)  (79%)  (73%)  101/131  108/141  173/236  130/193  (77%)  (77%)  (73%)  (67%)  Fraction of Unemployed  # w i t h Prob o f Constraint  Ge 50% (85%)  # With Prob o f Constraint  Ge 66% (77%)  # With Prob o f Constraint  439/570  411/570  Ge 75% (72%)  96/131  103/141  164/236  126/193  Constraint  # With Prob o f  Ge 80% (69%)  (73%)  (73%)  (69%)  (65%)  Av Prob Of  .8273  .8207  .8558  .8295  .8038  Constraint  393/570  210 T a b l e 4.12.— P r o b a b i l i t i e s o f C o n s t r a i n t Full  i n Unemployment.  Single  Men.  Sea  Cyc  At l a n  West  Cen  551/1796  166/271  217/629  144/301  216/833  191/662  (31%)  (61%)  (34%)  (48%)  (26%)  (29%)  # With Prob o f  447/551  140/166  178/217  116/144  185/216  146/191  Constraint  (81%)  (84%)  (82%)  (81%)  (86%)  (76%)  # With Prob o f  405/551  129/166  161/217  106/144  169/216  130/191  Constraint  (74%)  (78%)  (74%)  (74%)  (78%)  (68%)  # With Prob o f  378/551  121/166  156/217  102/144  158/216  118/191  Constraint  (69%)  (73%)  (72%)  (71%)  (73%)  (62%)  # With Prob o f  367/551  120/166  149/217  98/144  154/216  115/191  Constraint  (67%)  (72%)  (69%)  (68%)  (71%)  (60%)  .7944  .8265  .8045  .7945  .8351  .7484  Sample Fraction of U'd  Ge  50% Ge  66% Ge  75% Ge  80% Av Prob o f Constraint  211 T a b l e 4.13.— P r o b a b i l i t i e s  of C o n s t r a i n t . Couples.  Av Prob o f Constraint  A l l U'd  Sea  Cyc  Neither  Husband U'd;  .8135  .8421  .8407  .7376  Part  Full  .6728  .6989  .9745  .9746  Wife Not Wife U'd;  .6873  Husband Not Both U'd '  ,9745  .9759  .9738  .9737  Av Prob o f Constraint Husband U'd;  Atlantic  Centre  West  ,8485  .7663  ,8307  .6726  .6803  .7007  ,9883  .9479  .9773  Wife Not Wife U'd; Husband Not Both U'd  212 T a b l e 4.14.— Model 1 Labour-Supply E l a s t i c i t i e s .  S i n g l e Men.  F u l l Sample (Unemployed Sample) Gross Own-Wage  Seasonal  Cyclical  Neither  Atlantic Rural  .3061  (.8613)  .1321  (.6208)  .0468 (.4359)  Urban  .1582 (.4273)  .1246  (.3727)  .1200  (.4800)  Rural  .2582 (.5537)  .1173  (.5909)  .1066  (.3818)  Urban  .0530 (.1364)  .0277 (.3062)  .0252 (.3568)  Rural  -.0169 (.1839)  .0080 (.2430)  -.0074 (.2721)  Non-labour Income  Seasonal  Centre  West  Cyclical  Neither  Atlantic Rural  -.6452 (-1.4899)  -.2792 (-.9262)  -.1267 (-.5975)  Centre Urban  .2517  Rural  .4524 (-.8793)  (-.5649)  .1748  (-.4544)  ,1484 (-.5385)  .2435 (-.8282)  ,1970  (-.5439)  West Urban  -.1441 (-.2392)  .1101  (-.4269)  .0841  (-.4721)  Rural  -.1892 (-.4714)  .1545  (-.4247)  ,1153  (-.4595)  Compensated  Seasonal  Cyclical  Neither  Own-Wage Atlantic Rural  .9582 (1.5134)  .7896 (1.2753)  .6743 (1.0664)  .6222 (.8720)  .5895 (.9426)  .7888 (1.2608)  ,7525 (1.0387)  Centre Urban  .6509 (.9166)  Rural  .9206 (1.2138)  West Urban  .5869 (.6689)  .5632 (.8385)  .5304 (.8597)  Rural  .6910  .7201  .6777 (.9587)  (.8940)  (.9550)  213 T a b l e 4 . 1 5 . — Model 1 Labour-Supply E l a s t i c i t i e s : F u l l Sample (Unemployed Gross Own Wage  S i n g l e Women.  Sample).  Part-time  Full-time  Atlantic Rural  .1839  (.8701)  .1756  (.7037)  .1288  (.4290)  (1.2121)  .1516  (.4657)  .1029  (1.0131)  Centre Urban Rural  .1997  West Urban  .2515  (.0917)  .0703 (.2608)  Rural  .1836  (.1265)  .0178  Non-labour Income  (.4144)  Part-time  Full-time  -.5159 (-1.4155)  -.1484 (-1.2084)  Urban  -.2117 (-.8294)  -.0983 (-.3760)  Rural  .2160  (-1.3266)  -.0999 (-.3780)  Urban  -.2892 (-.6503)  -.1167 (-.5888)  Rural  -.3164 (-.7037)  -.1402 (-.6603)  Part-time  Full-time  .8084 (1.4760)  .6727 (1.5757)  Urban  .5795 (1.1172)  .4680 (.7654)  Rural  .5932 (1.6080)  .4675 (.7945)  Atlantic Rural Centre  West  Compensated Own-Wage Atlantic Rural Centre  West Urban  .4420 (.7897)  .5483 (.8748)  Rural  .4859 (.7892)  .5799 (1.0065)  214 T a b l e 4.16.— Model 1 Labour-Supply E l a s t i c i t i e s . M a r r i e d Men. Wives F u l l - t i m e Workers. F u l l Sample (Unemployed Sample) G r o s s Own-Wage  Seasonal  Cyclical  Neither  Atlantic Rural  1.0185 (1.6674)  .7309 (1.3806)  .7338 (3.9412)  Urban  .7252 (.8053)  .7587 (2.0643)  .7957 (1.9215)  Rural  .6182 (.6850)  ,6665 (1.2865)  .7261  Centre (1.0899)  West Urban  .6462 (1.5124)  .5493 (.7436)  .6562 (1.2156)  Rural  .6165  .4966 (.7064)  .5714 (.7945)  Non-labour Income  Seasonal  (2.1430)  Cyclical  Neither  Atlantic Rural  -.2505 (-.5407)  -.1324 (-.4218)  .0940 (-1.0838)  Centre Urban  -.1298 (-.2457)  ,1378  (-.5812)  .1375  (-.5223)  Rural  -.1904 (-.2776)  ,1692 (-.4948)  .1646  (-.3262)  Urban  -.1212 (-.4146)  .0938 (-.2366)  .0901  (-.3399)  Rural  -.1333 (-.7194)  .1040  .0783 (-.2072)  Gross Cross-Wage  Seasonal  West (-.2473) Cyclical  Neither  Atlantic Rural  .5808 (-.8205)  -.4681 (-.7232)  Urban  -.5254 (-.4832)  ,5473 (-1.3101)  ,5610  Rural  -.3995 (-.3837)  -.4646 (-.7308)  -.4944 (-.6610)  -.4857 (-2.0119)  Centre (-1.1495)  West Urban  -.4944 (-1.0451)  -.4262 (-.4596)  -.5036 (-.7568)  Rural  -.4945 (-1.4691)  -.3979 (-.4669)  -.4652 (-.5594)  215 T a b l e 4 . 1 7 . — Model 1 Labour-Supply E l a s t i c i t i e s . M a r r i e d Men. Wives P a r t - t i m e Workers. F u l l Sample (Unemployed Sample) G r o s s Own-Wage  Seasonal  Cyclical  Neither  Atlantic .5000 (1.5441)  .3957 (.6526)  Urban  .4802 (.2886)  .3117  Rural  .3648 (.4980)  .3052 (.5793)  .3617  Urban  .3021  .2337 (.2103)  .2635 (1.0617)  Rural  .2878 (4.1786)  .1805  .2786 (1.7566)  Non-Labour Income  Seasonal  Rural  .3591  (1.0486)  Centre (.6795)  .4534 (.5894) (1.4175)  West (1.2089)  (.3439)  Neither  Cyclical  Atlantic Rural  -.1980 (-.7465)  -.1722 (-.3121)  .0885(-.4512)  Centre Urban  -.1279 (-.1702)  ,1010  (-.3335)  .1233  (-.2255)  Rural  -.1836 (-.2802)  .1357  (-.4528)  .1359  (-.6359)  West Urban  -.1690 (-.6637)  .0944 (-.1517)  .0800 (-.5213)  Rural  -.1259 (-1.6364)  .0672 (-.5025)  .0719  Gross Cross-Wage  Seasonal  Cyclical  (-.9790) Neither  Atlantic -.2699 (-.7299)  -.1919 (-.3132)  -.2079 (-.4125)  Urban  -.3764 (-.1166)  .2297 (-.3877)  -.3121 (-.3285)  Rural  -.2419 (-.2878)  .2348 (-.2384)  -.2448 (-.8564)  Urban  -.1994 (-.7345)  -.1865 (-.0924)  -.1951 (-.5673)  Rural  -.2733 (-3.2651)  -.1893 (-.1589)  -.2487 (-1.0443)  Rural Centre  West  216 T a b l e 4 . 1 8 . — Model 1 Compensated E l a s t i c i t i e s . Wives F u l l - t i m e Workers. F u l l Compensated  Sample  M a r r i e d Men. (Unemployed Sample)  Seasonal  Cyclical  Neither  Own-Wage Atlantic 1.3017 (1.9506)  1.0141 (1.6638)  1.0170 (4.2244)  Urban  1.0084 (1.0885)  1.0417 (2.3475)  1.0789 (2.2047)  Rural  .9014 (.9682)  .9497 (1.5697)  1.0093 (1.3731)  Urban  .9294 (1.7956)  .8325 (1.0268)  .9394 (1.4988)  Rural  .8997 (2.4262)  .7798 (.9896)  .8546 (1.0777)  Compensated  Seasonal  Rural Centre  West  Cyclical  Neither  Cross-Wage Atlantic Rural  -.3815 (-.5717)  -.3249  (-.4877)  -.3658 (-.4756)  Centre Urban  -.3419  (-.3267)  .3552 (-.8483)  .4031 (-.7534)  Rural  -.2709  (-.2847)  .3177  .3669  Urban  -.3089  (-.6487)  .3028 (-.3396)  .3624 (-.6002)  Rural  -.2980 (-.8855)  .2712 (-.3143)  .3256 (-.3684)  (-.4625)  (-.6949)  West  217 T a b l e 4 . 1 9 . — Model 1 Compensated Labour-Supply E l a s t i c i t i e s . Wives P a r t - t i m e Workers. F u l l Compensated  M a r r i e d Men.  Sample (Unemployed Sample)  Seasonal  Neither  Cyclical  Own-Wage Atlantic Rural  .7832 (1.8273)  .6789 (.9358)  Urban  .7634 (.5718)  .5949 (.9627)  .7366 (.8726)  Rural  .6480 (.7812)  .5884 (.8625)  .6449 (1.7007)  Urban  .5853 (1.4921)  .5169  .5467 (1.3449)  Rural  .5710  .4637 (.6271)  Compensated  Seasonal  .6423 (1.3318)  Centre  West (4.4618)  (.4935)  Cyclical  .5618  (2.0398) Neither  Cross-Wage Atlantic Rural  -.2296 (-.5356)  -.1759 (-.2864)  -.1913 (-.3802)  Urban  -.2415 (-.1085)  .2085 (-.3232)  .2845 (-.3008)  Rural  -.2107 (-.2359)  .2126  (-.2154)  .2229 (-.5190)  Centre  West Urban  -.1765 (-.4373)  -.1645 (-.0819)  -.1737 (-.4397)  Rural  -.1824 (-1.7942)  -.1667 (-.1382)  -.2202 (-.5979)  218 T a b l e 4 . 2 0 . — Model 1 Labour-Supply E l a s t i c i t i e s . Husbands Seasonal Workers. F u l l Gross Own-Wage  M a r r i e d Women.  Sample (Unemployed Sample) Part-time  Full-time.  4.2886 (15.4811)  1.3022 (1.0757)  Atlantic Rural Centre Urban  1.2042 (30.7690)  Rural  5.1241 (15.7182)  1.4535 (9.1555)  Urban  6.6930 (12.2176)  .9745 (2.0967)  Rural  1.3740 (2.3367)  1.0857  (20.7414)  West  Non-labour Income  .8139  (7.3864)  Part-time  Full-time  -1.0321 (-5.2157)  -.2641 (-3.0564)  Urban  -.1992 (-5.2299)  -.1486 (-3.5799)  Rural  -1.2364 (-4.2411)  -.3110 (-2.3195)  Urban  -1.5482 (-2.5449)  -.1373 (-1.5412)  Rural  -.2910 (-.5657)  Atlantic Rural Centre  West  Gross Cross-Wage  -.1425  (-1.6914)  Part-time  Full-time  -3.0890 (-9.8412)  -.8408 (-6.2569)  Urban  -1.0425 (-25.7950)  -.8571 (-15.8990)  Rural  -4.2963 (-12.4175)  -1.0964 (-6.6064)  Urban  -5.7515(-10.6017)  -.8026 (-.5063)  Rural  -1.3407 (-2.1674)  -.6835 (-5.7916)  Atlantic Rural Centre  West  219 T a b l e 4 . 2 1 . — Model 1 Labour-Supply E l a s t i c i t i e s . Husbands C y c l i c a l Workers. F u l l Gross Own-Wage  M a r r i e d Women.  Sample (Unemployed Sample) Part-time  Full-time  12.6283 (17.2196)  1.5829 (11.0048)  Urban  9.5136 (17.8084)  1.2283 (11.1187)  Rural  8.0167 (11.2029)  1.4981 (14.1320)  Urban  8.3566 (13.1995)  1.7283 (10.1357)  Rural  6.8317 (11.0058)  1.4805 (8.3553)  Part-time  Full-time  -2.2571 (-3.5978)  -.1943 (-2.1772)  Atlantic Rural Centre  West  Non-labour Income Atlantic Rural Centre Urban  -1.0000 (-2.5697)  .1508  Rural  -1.2850 (-2.7302)  .2420 (-3.3258)  (-2.3702)  West Urban  .9045 (-1.8168)  .1596  (-1.7611)  Rural  .6261  .1725  (-1.3002)  Gross Cross-Wage  (-1.6393) Part-time  Full-time  -9.9571 (-13.1108)  -1.1970 (-7.4553)  Atlantic Rural Centre Urban  -8.7010 (-15.7235)  -.9972 (-8.0951)  Rural  -7.3494 (-9.3251)  -1.2094 (-10.4026)  Urban  -7.9041 (-11.9661)  -1.5188 (-8.1282)  Rural  -6.9137 (-10.5512)  -1.3168 (-7.0963)  West  220 Table  4 . 2 2 . — Model 1 Labour-Supply E l a s t i c i t i e s .  M a r r i e d Women.  Husbands N e i t h e r Seasonal n o r C y c l i c a l Workers. Full  Sample (Unemployed  G r o s s Own-Wage  Sample).  Part-time  Full-time  Atlantic Rural  14.2538 (22.1032)  2.1996 (18.9730)  Centre Urban  9.2992 (13.3731)  1.8070 (13.0551)  Rural  10.5466 (15.0533)  2.0632 (12.3440)  Urban  10.6674 (15.2635)  1.8162 (11.3596)  Rural  7.0829 (11.1704)  1.6310 (13.0944)  West  Non-labour Income  Part-time  Full-time  Atlantic Rural  -1.1203 (-2.3122)  .1647 (-2.4733)  Urban  -.9385 (-1.9632)  .1830 (-2.0213)  Rural  -1.3008 (-2.1191)  .2713  (-2.2936)  Urban  ,7846 (-1.7461)  .1339  (-1.5594)  Rural  .5311  .1178 (-1.7312)  Centre  West  G r o s s Cross-Wage  (-1.1921) Part-time  Full-time  Atlantic Rural  -12.3399 (-18.5173)  -1.7650 (-14.1668)  Urban  -8.2238 (-11.2137)  -1.4947 (-10.1026)  Rural  -9.4279 (-13.0923)  -1.6812 (-9.3863)  Centre  West Urban  -9.9976 (-13.0923)  -1.5893 (-9.1886)  Rural  -6.8616 (-10.3946)  -1.4713 (-11.0877)  221 T a b l e 4.23.— Model 1 Compensated E l a s t i c i t i e s . Husbands Seasonal Workers. F u l l Compensated Own-Wage  Sample  M a r r i e d Women. (Unemployed  Sample)  Part-time  Full-time  4.4987 (15.6912)  1.5123 (11.2858)  Urban  1.4143 (30.9791)  1.0084 (20.9515)  Rural  5.3342 (15.9283)  1.6636 (9.3656)  Urban  6.9031 (12.4277)  1.1846 (2.3068)  Rural  1.5841 (2.5468)  1.0240 (7.5965)  Part-time  Full-time  (-5.0771)  -.5422 (-3.9679)  Atlantic Rural Centre  West  Compensated  Cross-Wage  Atlantic Rural  -1.6129  Centre Urban  -.6013 (-16.0464)  -.5329  Rural  -2.3889  -.6338 (-3.5775)  (-6.8443)  (-9.6213)  West Urban  -3.1568 (12.4277)  Rural  -.6864 (-1.0778)  -.4819  (-.8982)  -.3807 (-3.2261)  222 T a b l e 4.24.— Model 1 Compensated E l a s t i c i t i e s . Husbands C y c l i c a l Workers. F u l l Compensated Own-Wage  M a r r i e d Women.  Sample (Unemployed  Sample)  Part-time  Full-time  Atlantic Rural  12.8384 (17.4297)  1.7930  (11.2149)  Urban  9.7237 (18.0185)  1.4384  (11.3288)  Rural  8.2268  (11.4130)  1.7082  (14.3421)  Urban  8.5667  (13.4096)  1.9384  (10.3458)  Rural  7.0418  (11.2159)  Centre  West  Compensated  Cross-Wage  1.6906  (8.5654)  Part-time  Full-time  -6.2450 (-8.1272)  -.7814 (-4.7760)  Urban  -5.8960 (-10.5793)  -.6874 (-5.4968)  Rural  -4.6677 (-6.0154)  -.8044 (-6.8602)  Urban  -5.1918 (-7.9855)  -1.0367 (-5.5160)  Rural  -4.2765 (-6.4330)  -.8472 (-4.5330)  Atlantic Rural Centre  West  223 T a b l e 4 . 2 5 . — Model 1 Compensated E l a s t i c i t i e s .  M a r r i e d Women.  Husbands N e i t h e r Seasonal n o r C y c l i c a l Workers. Full  Sample  (Unemployed Sample).  Compensated Own-Wage  Part-time  Full-time  Atlantic 14.4639  (22.3133)  2.4097 (19.1831)  Urban  9.5093  (13.5832)  2.0171 (13.2652)  Rural  10.7567  (15.2634)  2.2733 (12.5541)  10.8775  (15.4736)  2.0263 (11.5697)  7.2930 (11.3805)  1.8411 (13.3045)  Rural Centre  West Urban Rural Compensated  Cross-Wage  Part-time  Full-time  Atlantic -8.7554 (-13.1814)  -1.2688 (-10.1169)  Urban  -6.0684 (-8.2795)  -1.1178 (-7.5249)  Rural  -6.7166 (-9.3457)  -1.2144 (-6.7490)  Urban  -7.2209  -1.1680 (-6.7378)  Rural  -4.7696 (-7.2444)  Rural Centre  West (-9.9209)  -1.0453  (-7.8655)  T a b l e 4.26.— Model 2 Labour-Supply Full  Elasticities  Sample (Unemployed Sample)  S i n g l e Men  S i n g l e Women  Gross Own-Wage  .09815 ( .1848)  .06335 ( .1541)  Non-labour  -.07393  -.05858  Income  Compensated Own-Wage  (-.1543)  .3944 ( .4813) M a r r i e d Men  (-.1478)  .2910 ( .3818) M a r r i e d Women  Gross Own Wage  ,1283 ( .2121)  ,1656 ( .2212)  Gross Cross-Wage  -.04674  (-.0608)  -.0894  Non-labour  -.02678  (-.0640)  -.0249 (-.0408)  Income  (-.1133)  Compensated Own-Wage  .1941 ( .2780)  .2011 ( .2567)  Compensated Cross-Wage  -.0087  -.0279 (-.0354)  (-.0113)  225 Table  4.27.—Model  2  Labour-Supply  Elasticities  . Couples.  Rationed and  Unrationed. Gross  Gross  Comp  Comp  Own-W  Cross-W  Own-W  Cross-W  Constraint  F u l l Sample; Unrationed M a r r i e d Men  .1283  -.0467  .1941  -.0087  M a r r i e d Women  .1656  -.0894  .2011  -.0279  M a r r i e d Men  .1290  .0380  .1949  -.0080  M a r r i e d Women  .1773  .0687  .2129  -.0214  M a r r i e d Men  .0717  .0150  .1400  .01707  M a r r i e d Women  .1484  .03259  .1864  .0506  Spouse U'd Unrationed  Spouse U'd; Rationed  226 T a b l e 5 . 1 . — Model 1. Labour-Supply Responses. S i n g l e Men. BASE  B=.5  EXT=0  MIN=15 MIN=20 QA=.5  SEGMENT 1  0  0  0  11  30  Corner 2 (Min)  2  4  8  0  8 0  MACD  FORGET  0  4  0  7  0  1  61  104  0  SEGMENT DIST'N  SEGMENT 2(SUBSIDY)!  2  59  0  CORNER 3 (Max)  10  10  4  10  4  1  1  0  SEGMENT 3(Tax)  419  320  338  408  382  352  168  262  CORNER 4 (50)  0  0  0  0  0  0  0  0  SEGMENT 4  23  27  25  23  23  25  34  40  CORNER 5 (52)  1222  1314  1243  1225  1230  1231  1366  1374  TOTAL  4.92  3.33  4.36  4.81  4.65  4.75  2.75  2.32  ATLANTIC  10.37  6.47  7.57  9.99  8.93  10.13  4.29  3.29  WEST  3.23  2.40  3.20  3.23  3.23  3.01  2.24  2.01  CENTRE  4.60  3.10  4.38  4.48  4.50  4.51  2.71  2.29  SEASONAL  11.94  8.43  9.92  11.67  10.44  11.27  5.99  4.63  CYCLICAL  5.65  3.74  5.00  5.51  5.53  5.44  3.20  2.66  NEITHER  2.48  1.64  2.38  2.43  2.43  2.45  1.54  1.45  AV WEEKS U  227 Table  5.2.—  Model  1.  Labour-Supply  Responses.  Single  Men.  Unemployed  Population. BASE  B=.5  EXT=0  MIN=15  MIN=20 QA=.5  MACD  TOTAL  19.12  16.44  17.85  18.82  18.38  18.91  16.19  14.17  ATLANTIC  23.94  19.05  20.37  23.25  21.70  23.58  19.46  15.17  WEST  16.01  14.37  15.96  16.01  16.01  15.72  14.41  13.38  CENTRE  18.51  16.62  18.07  18.24  18.32  18.36  16.33  14.49  FORGET  AV WKS U  SEASONAL  21.50  18.42  19.50  21.02  19.55  21.28  18.36  14.97  CYCLICAL  18.72  16.33  17.47  18.48  18.55  18.46  16.01  14.01  NEITHER  17.14  14.40  16.74  16.95  16.93  17.11  14.57  13.72  TOTAL  .2713  .2272  .2588  .2695  .2665  .2660  .1855  .1807  ATLANTIC  .4332  .3394  .3718  .4296  .4116  .4296  .2202  .2166  WEST  .2018  .1669  .2005  .2018  .2018  .1915  .1552  .1501  CENTRE  .2855  .2520  .2807  .2823  .2823  .2855  .2073  .2026  SEASONAL  .5551  .4576  .5085  .5551  .5339  .5297  .3263  .3093  CYCLCIAL  .3017  .2288  .2864  .2983  .2983  .2949  .2000  .1898  NEITHER  .1716  .1622  .1704  .1704  .1704  .1727  .1363  .1387  INCIDENCE  228 T a b l e 5 . 3 . — Model 1. Labour-Supply  onses. S i n g l e Women.  BASE  B=.5  EXT=I  MIN=15 MIN=20 QA=.5  MACD  FORGET  SEGMENT 1  0  0  0  12  35  0  3  0  CORNER 2 (MIN)  1  1  0  0  0  5  0  0  3  57  95  0  SEGMENT DIST'N  SEGMENT 2(SUBSIDY)7  8  71  7  CORNER 3 (MAX)  0  0  0  0  0  0  0  0  SEGMENT 3(TAX)  353  257  279  340  320  291  140  228  CORNER 4 (50)  0  0  0  0  0  0  0  0  SEGMENT 4  6  15  9  6  6  9  22  23  CORNER 5 (52)  1721  1807  1729  1723  1724  1726  1828  1837  TOTAL  3.29  2.10  2.99  3.23  3.17  3.12  1.87  1.74  ATLANTIC  6.26  3.30  4.98  5.92  5.69  5.92  2.67  2.34  WEST  2.34  1.71  2.28  2.34  2.34  2.19  1.56  1.45  CENTRE  2.95  1.98  2.84  2.95  2.90  2.85  1.85  1.78  PART-TIME  7.35  5.04  6.15  7.38  7.16  6.93  4.12  3.56  FULL-TIME  2.88  1.81  2.67  2.81  2.77  2.74  1.65  1.55  AV WEEKS U  229 Table  5.4.  Model  1.  Labour-Supply  Responses.  Single  Women.  Unemployed  Population. BASE  B=. 5  EXT=0  MIN=15 MIN=20 QA=.5  MACD  TOTAL  19.03  16.07  17.68  18.76  18.48  18.41  15.71  ATLANTIC  23.52  17.01  20.07  22.67  22.02  22.67  15.89  14.17  WEST  15.99  14.92  15.70  15.99  15.99  15.48  16.68  14.29  CENTRE  18.64  16.66  18.01  18.64  18.38  18.04  14.75  16.81  PART-TIME  22.16  17.40  19.81  22.27  21.95  21.57  16.64  16.12  FULL-TIME  18.37  15.74  17.25  18.02  17.75  17.75  15.49  14.90  TOTAL  .1757  .1346  .1719  .1748  .1743  .1734  .1245  .1202  ATLANTIC  .2661  .1938  .2481  .2610  .2584  .2610  .1680  .1654  WEST  .1465  .1144  .1358  .1465  .1465  .1412  .1059  .1016  CENTRE  .1658  .1292  .1658  .1658  .1658  .1684  .1253  .1201  PART-TIME  .3316  .2895  .3105  .3316  .3263  .3211  .2474  .2211  FULL-TIME  .1602  .1191  .1581  .1591  .1591  .1586  .1122  .1101  FORGET  AV WKS U 15.11  INCIDENCE  230 T a b l e 5 . 5 . — M o d e l 1. Labour-Supply Responses. M a r r i e d Men. BASE  B=.5  EXT=0  SEGMENT 1  0  0  CORNER 2 (MIN)  3  3  SEGMENT 2(SUBSIDY)2  3  CORNER 3 (MAX)  0  SEGMENT 3(TAX)  467  CORNER 4 (50) SEGMENT 4 CORNER 5 (52)  MIN=15 MIN=20 0A=.5  MACD  FORGI  0  12  29  0  8  0  8  0  0  10  0  3  52  2  1  38  104  0  0  0  0  0  0  0  0  404  392  458  436  412  258  281  0  0  0  0  0  0  0  0  40  53  43  39  39  40  46  46  1988  2037  2005  1989  1995  2000  2084  2170  TOTAL  3.41  2.76  3.06  3.35  3.21  3.27  2.19  1.86  ATLANTIC  6.49  5.28  5.36  6.26  5.73  6.47  3.56  2.99  WEST  2.23  1.74  2.19  2.23  2.23  1.94  1.65  1.37  CENTRE  2.69  2.23  2.52  2.69  2.63  2.64  1.88  1.65  SEASONAL  9.78  8.30  7.83  9.59  8.92  9.22  5.66  4.85  CYCLICAL  3.80  2.99  3.70  3.77  3.68  3.78  2.63  - 2.21  NEITHER  1.50  1.17  1.42  1.47  1.42  1.40  1.00  0.86  SEGMENT DIST'N  AV WEEKS U  231 Table  5.6.—  Model  1.  Labour-Supply  Responses.  Married  Men.  Unemployed  Population. BASE  B=. 5  EXT=0  MIN=15 MIN=20 QA=.5  MACD  FORGET  AV WKS U TOTAL  18.06  16.05  16.75  17.76  17.17  17.75  14.29  15.65  ATLANTIC  21.60  18.98  19.48  20.82  19.39  21.52  15.08  16.90  WEST  14.93  13.11  14.78  14.93  14.93  13.98  13.39  14.06  CENTRE  16.90  15.31  15.70  16.89  16.73  16.67  14.27  15.83  SEASONAL  21.38  18.13  18.40  20.69  19.62  20.80  14.93  16.14  CYCLICAL  16.85  15.21  16.49  16.81  16.41  16.88  14.35  16.56  NEITHER  15.73  14.32  15.19  15.48  15.21  15.28  13.37  13.78  TOTAL  .2048  .1852  .1980  .2044  .2020  .2000  .1664  .1320  ATLANTIC  .3005  .2784  .2750  .3005  .2954  .3005  .2360  .1766  WEST  .1494  .1328  .1483  .1494  .1494  .1390  .1234  .0975  CENTRE  .2017  .1806  .2006  .2006  .1975  .1996  .1668  .1394  INCIDENCE  SEASONAL  .4577  .4577  .4257  .4635  .4548  .4431  .3790  .3003  CYCLCIAL  .2253  .1967  .1950  .2241  .2241  .2241  .1836  .1335  NEITHER  .1259  .1070  .1222  .1244  .1222  .1214  .1002  .0873  232 T a b l e 5 . 7 . — Model 1. Labour-Supply Responses. M a r r i e d Women. BASE  B=.5  EXT=0  MIN=15 MIN=20 QA=.5  MACD  FORGET  SEGMENT 1  0  0  0  19  58  0  25  0  CORNER 2 (MIN)  4  5  8  0  0  16  0  6  SEGMENT DIST'N  SEGMENT 2(SUBSIDY)6  11  56  5  0  58  175  0  CORNER 3 (MAX)  0  0  0  0  0  0  0  0  SEGMENT 3(TAX)  673  671  535  646  601  571  374  465  CORNER 4 (52)  0  0  0  0  0  0  0  0  SEGMENT 4  280  281  277  280  281  282  277  270  CORNER 5 (50)  1537  1532  1624  1550  1560  1573  1649  1759  TOTAL  5.60  5.16  4.00  5.26  4.92  4.95  3.72  3.48  ATLANTIC  9.71  8.89  5.14  8.37  7.50  8.86  5.97  6.03  WEST  3.79  3.54  3.56  3.79  3.79  3.22  2.80  2.41  CENTRE  4.90  4.49  3.75  4.82  4.47  4.28  3.26  2.98  PART-TIME  6.57  6.36  5.10  6.45  6.20  6.21  5.13  4.90  FULL-TIME  5.33  4.82  3.69  4.92  4.56  4.59  3.32  3.07  AV WEEKS U  233 Table  5 . 8 . — Model  1.  Labour-Supply  Responses.  Married  Women.  Unemployed  Population. BASE  B=.5  EXT=0  MIN=15 MIN=20 QA=.5  MACD  TOTAL  20.51  17.87  16.60  19.55  18.57  18.96  15.37  17.60  ATLANTIC  25.54  21.72  17.02  23.13  21.25  23.94  17.94  19.72  WEST  16.24  14.27  15.73  16.24  16.24  14.77  13.29  15.27  CENTRE  19.81  17.58  17.14  19.49  18.42  18.03  14.98  17.43  PART-TIME  20.44  18.95  17.35  19.97  19.30  19.79  17.44  17.54  FULL-TIME  20.54  17.49  16.32  19.40  18.30  18.65  14.62  17.62  TOTAL  .3852  .3872  .3504  .3800  .3760  .3708  .3404  .2960  ATLANTIC  .3803  .4092  .3022  .3616  .3531  .3701  .3328  .3056  FORGET  AV WKS U  INCIDENCE  WEST  .2334  .2479  .2261  .2334  .2334  .2178  .2106  .1577  CENTRE  .5428  .5153  .5069  .5407  .5354  .5269  .4773  .4308  PART-TIME  .3212  .3358  .2940  .3230  .3212  .3140  .2940  .2795  FULL-TIME  .4033  .4017  .3663  .3961  .3915  .3869  .3535  .3007  234 T a b l e 5 . 9 . — Model 2. Labour-Supply Responses. S i n g l e Men. UPPER-BOUND  PROBBASE  B=.5  EXT=0  MIN=15 MIN=20 QA=.5  MACD  FORGET  TOTAL  6.74  6.46  6.73  6.74  6.73  6.72  6.51  6.63  ATLANTIC  12.48  11.95  12.45  12.46  12.45  12.46  12.11 12.29  WEST  5.16  5.02  5.16  5.16  5.16  5.15  5.04  5.09  CENTRE  6.12  5.78  6.11  6.11  6.11  6.10  5.81  5.98  SEASONAL  15.34  14.82  15.32  15.34  15.32  15.32  14.91  15.12  CYCLICAL  7.31  7.01  7.30  7.30  7.30  7.28  7.07  7.20  NEITHER  3.74  3.55  3.74  3.74  3.74  3.73  3.57  3.66  TOTAL  6.74  6.20  6.73  6.70  6.68  6.67  6.07  6.02  ATLANTIC  12.48  11.49  12.08  12.35  12.21  12.36  11.11  11.04  OF CONSTRAINT AV WKS U  LOWER-BOUND  PROB  OF CONSTRAINT AV WEEKS U  WEST  5.16  4.85  5.15  5.16  5.16  5.11  4.82  4.78  CENTRE  6.12  5.50  6.02  6.07  6.07  6.04  5.36  5.29  SEASONAL  15.34  14.33  15.09  15.32  15.18  15.28  14.04  13.93  CYCLICAL  7.31  6.74  7.17  7.26  7.25  7.21  6.60  6.55  NEITHER  3.74  3.37  3.70  3.70  3.70  3.69  3.29  3.25  235 Table  5.10.—  Model  2.  Labour-Supply  Responses.  Single  Men.  Unemployed  Population. BASE  B=.5  EXT=0  MIN=15  MIN=20 QA=.5  MACD  FORGET  TOTAL  21.97  22.48  21.96  21.96  21.96  21.92  22.70  22.03  ATLANTIC  26.08  26.53  26.05  26.07  26.06  26.06  27.02  26.21  WEST  19.91  20.23  19.91  19.91  19.91  19.85  20.30  19.92  CENTRE  21.20  21.99  21.19  21.19  21.19  21.14  22.19  21.27  SEASONAL  25.05  25.30  25.03  25.04  25.03  25.01  25.54  25.09  21.18  21.18  21.10  AV WKS U  CYCLICAL  21.18  21.58  21.17  21.82  21.24  NEITHER  19.94  20.75  19.93  19.93  19.93  19.91  20.93  20.01  TOTAL  .3068  .2875  .3066  .3067  .3066  .3067  .2870  .3008  ATLANTIC  .4784  .4505  .4777  .4781  .4777  .4781  .4488  .4691  WEST  .2593  .2483  .2593  .2593  .2593  .2593  .2483  .2557  CENTRE  .2885  .2628  .2884  .2884  .2884  .2882  .2621  .2811  SEASONAL  .6125  .5856  .6122  .6125  .6122  .6125  .5849  .6026  .3448  .3448  .3448  .3240  .3388  .1874  .1874  .1874  .1709  .1829  INCIDENCE  CYCLCIAL  .3450  .3246  .3448  NEITHER  .1875  .1713  .1874  236 T a b l e 5 . 1 1 . — Model 2. Labour-Supply Responses. S i n g l e Women. UPPER-BOUND  PROBBASE  B=.5  EXT=0  MIN=15 MIN=20 QA=.5  MACD  FORGET  TOTAL  5.91  5.75  5.90  5.91  5.76  5.83  ATLANTIC  8.64  8.44  8.62  8.63  8.63  8.62  8.47  8.55  WEST  5.11  4.98  5.11  5.11  5.11  5.09  4.99  5.05  CENTRE  5.50  5.33  5.50  5.50  5.50  5.49  5.34  5.43  PART-TIME  14.88  14.57  14.85  14.88  14.87  14.85  14.60 14.73  FULL-TIME  4.77  4.63  4.77  4.77  4.77  4.76  4.64  4.71  TOTAL  5.91  5.65  5.88  5.90  5.90  5.87  5.61  5.59  ATLANTIC  8.64  8.30  8.51  8.62  8.60  8.62  8.25  8.24  WEST  5.50  4.91  5.11  5.11  5.11  5.05  4.87  4.86  CENTRE  5.11  5.22  5.48  5.50  5.49  5.49  5.19  5.16  OF CONSTRAINT AV WKS U  LOWER-BOUND  5.90  5.89  PROB  OF CONSTRAINT AV WEEKS U  PART-TIME  14.88  14.42  14.75  14.88  14.86  14.82  14.33 14.31  FULL-TIME  4.77  4.54  4.75  4.77  4.76  4.74  4.51  4.49  237 Table  5.12.—  Model  2.  Labour-Supply  Responses.  Single  Women.  Unemployed  Population. BASE  B=.5  EXT=0  MIN=15  MIN=20 QA=.5  MACD  FORGET  TOTAL  23.81  24.09  23.78  23.80  23.79  23.75  24.20  23.84  ATLANTIC  26.06  26.23  26.00  26.02  26.01  26.00  26.36  26.00  WEST  22.40  22.72  22.39  22.40  22.40  22.34  22.80  22.43  CENTRE  23.88  24.19  23.86  23.88  23.86  23.84  24.32  23.97  PART-TIME  29.31  29.83  29.27  29.31  29.29  29.24  29.95  29.41  FULL-TIME  22.17  22.37  22.15  22.15  22.15  22.11  22.48  22.18  TOTAL  .2481  .2386  .2481  .2481  .2481  .2481  .2381  .2447  ATLANTIC  .3318  .3216  .3315  .3318  .3318  .3318  .3214  .3287  WEST  .2282  .2194  .2282  .2282  .2282  .2280  .2188  .2250  CENTRE  .2303  .2202  .2303  .2303  .2303  .2303  .2198  .2264  PART-TIME  .5078  .4884  .5078  .5078  .5078  .5078  .4876  .5008  .2153  .2070  .2153  .2153  .2153  .2153  .2066  .2123  AV WKS U  INCIDENCE  FULL-TIME  -  238 T a b l e 5 . 1 3 . — Model 2. Labour-Supply Responses. M a r r i e d Men. UPPER-BOUND  PROBBASE  B=.5  EXT=0  MIN=15 MIN=20 QA=.5  MACD  FORGET  TOTAL  4.13  3.98  4.12  4.11  4.11  4.11  3.98  4.05  ATLANTIC  8.21  7.95  8.17  8.15  8.13  8.19  7.97  8.07  OF CONSTRAINT AV WKS U  WEST  2.71  2.64  2.71  2.71  2.71  2.70  2.65  2.67  CENTRE  2.94  2.77  2.94  2.94  2.94  2.93  2.76  2.86  SEASONAL  10.95  10.64  10.91  10.89  10.87  10.91  10.66  10.78  CYCLICAL  4.48  4.33  4.47  4.47  4.46  4.47  4.33  4.41  NEITHER  1.80  1.70  1.80  1.80  1.80  1.80  1.70  1.75  TOTAL  4.13  3.57  3.96  4.09  4.05  4.01  3.37  3.31  ATLANTIC  8.21  7.13  7.70  8.08  7.93  8.06  6.60  6.55  WEST  2.71  2.44  2.71  2.71  2.70  2.60  2.37  2.33  CENTRE  2.94  2.43  2.80  2.93  2.92  2.85  2.30  2.21  LOWER-BOUND  PROB  OF CONSTRAINT AV WEEKS U  SEASONAL  10.95  9.68  10.35  10.87  10.74  10.60  9.07  8.98  CYCLICAL  4.48  3.91  4.38  4.44  4.37  4.43  3.78  3.70  NEITHER  1.80  1.48  1.72  1.78  1.79  1.72  1.34  1.31  239 Table  5.14.—  Model  2.  Labour-Supply  Responses.  Married  Men.  Unemployed  Population. BASE  B=. 5  EXT=0  MIN=15 MIN=20 QA=.5  MACD  FORGET  18.53  18.46  18.45  18.43  18.45  18.60  18.44  22.40  22.62  22.35  AV WKS U TOTAL  18.51  ATLANTIC  22.45  22.44  22.36  22.33  22.28  WEST  15.61  15.56  15.62  15.61  15.61  15.54  15.61  15.52  CENTRE  16.23  16.31  16.18  16.20  16.19  16.17  16.26  16.20  SEASONAL  20.94  20.80  20.88  20.84  20.81  20.88  20.94  20.85  CYCLICAL  17.14  17.24  17.10  17.09  17.07  17.11  17.28  17.11  NEITHER  17.18  17.23  17.14  17.18  17.17  17.10  17.26  17.07  TOTAL  .2230  .2146  .2230  .2229  .2229  .2229  .2140  .2195  ATLANTIC  .3657  .3545  .3655  .3651  .3651  .3655  .3525  .3612  WEST  .1737  .1700  .1737  .1737  .1737  .1736  .1697  .1723  CENTRE  .1814  .1698  .1814  .1814  .1814  .1814  .1698  .1764  SEASONAL  .5230  .5118  .5227  .5224  .5224  .5224  .5092  .5168  CYCLCIAL  .2615  .2510  .2615  .2614  .2614  .2615  .2507  .2579  NEITHER  .1050  .9890  .1050  .1050  .1050  .1050  .0987  .1024  INCIDENCE  240 T a b l e 5 . 1 5 . — Model 2. Labour-Supply Responses. M a r r i e d Women. UPPER-BOUND  PROBBASE  B=.5  EXT=0  MIN=15 MIN=20 QA=.5  MACD  FORGET  OF CONSTRAINT AV WKS U TOTAL  10.98  10.58  10.88  10.96  10.95  10.92  10.60 10.69  ATLANTIC  14.48  13.97  14.24  14.42  14.34  14.43  13.99  14.12  WEST  10.27  9.96  10.26  10.27  10.30  10.22  9.99  10.05  CENTRE  9.41  9.00  9.32  9.41  9.40  9.37  9.02  9.12  PART-TIME  16.00  15.46  15.86  15.99  15.98  15.95  15.51 15.56  FULL-TIME  8.98  8.64  8.90  8.97  8.95  8.93  8.66  8.76  10.98  9.78  9.70  10.78  10.58  10.40  8.61  8.41  ATLANTIC  14.48  12.56  11.35  13.67  12.83  13.91  10.24  10.26  WEST  10.27  9.39  10.07  10.27  10.38  9.60  8.90  8.59  CENTRE  9.41  8.32  8.23  9.41  9.31  8.93  7.22  7.00  PART-TIME  16.00  14.78  14.66  15.91  15.70  14.51  15.65  13.43  FULL-TIME  8.98  7.78  7.74  8.75  8.55  8.37  6.61  6.42  LOWER-BOUND  PROB  OF CONSTRAINT AV WEEKS U TOTAL  241 Table  5.16.—  Model  2.  Labour-Supply  Responses.  Married  Women.  BASE  B=.5  EXT=0  MIN=15 MIN=20 QA=.5  TOTAL  27.68  27.75  27.52  27.65  27.62  ATLANTIC  30.59  30.75  30.28  30.47  WEST  26.21  26.32  26.16  26.20  CENTRE  26.85  26.80  26.69  PART-TIME  30.39  30.36  FULL-TIME  26.04  TOTAL  Unemployed  Population. MACD  FORGET  27.62  28.01  28.04  30.32  30.50  30.94  30.76  26.26  26.16  26.56  26.75  26.86  26.85  26.79  27.13  27.12  30.26  30.38  30.38  30.44  30.78  31.20  26.16  25.86  26.00  25.95  25.92  26.33  26.17  .3965  .3812  .3954  .3965  .3964  .3956  .3786  .3814  ATLANTIC  .4731  .4541  .4705  .4731  .4731  .4731  .4523  .4589  WEST  .3921  .3783  .3921  .3921  .3921  .3905  .3761  .3757  CENTRE  .3506  .3360  .3506  .3502  .3497  .3325  .3363  AV WKS U  INCIDENCE  .3492  PART-TIME  .5264  .5093  .5241  .5264  .5259  .5239  .5039  .4988  FULL-TIME  .3450  .3303  .3443  .3450  .3450  .3446  .3288  .3348  Table 6.1a.— Equivalence Scales Implicit i n Low-income Cut-offs. C i t y Size Gt 100,00  30,000-99,999  Lt 30,000  Rural  1  1.2842  1.2047  1.1138  1.  2  1.6932  1.5798  1.4660  1.3069  3  2.2617  2.1138  1.9662  1.7502  4  2.6137  2.4434  2.2728  2.0230  5  3.0343  2.8299  2.6364  2.3525  6  3.3071  3.0913  2.8753  2.5683  7 or more  3.6480  3.4095  3.1708  2.8299  Econ Family Size  Source: S t a t i s t i c s Canada, 1978.  T a b l e 6.1b.— Model 1 U t i l i t y S c a l i n g F a c t o r s , s ( A ) . S i n g l e Men  City  Size  Gt 100,00  30,000-99,999  Lt 30,000  Rural  1  2.5289  1.2590  1.1374  .9852  2  3.2644  1.6960  1.5471  1.3390  3  4.2855  2.3192  2.1300  1.8532  4  4.8022  2.6621  2.4477  2.1338  5  5.4245  3.0634  2.8248  2.4747  6  5.7337  3.3010  3.0394  2.6676  7 o r more  6.1459  3.6007  3.3163  2.9103  Gt 100,00  30,000-99,999  Lt 30,000  Rural  1  4.7803  4.9685  4.6610  4.2761  2  6.8052  7.0431  6.6200  6.0287  3  9.7877  10.1475  9.5432  8.6587  4  12.4327  12.9090  12.1384  11.0101  5  15.8400  16.4306  15.4656  14.0497  6  19.1041  19.8874  18.6960  17.0031  7 or more  22.4416  24.2580  22.8010  20.7201  Couples  City  Gt 100,00  30,000-99,999  L t 30,000  Rural  2  4.9738  4.1902  3.9665  3.6540  3  6.1330  5.2820  4.9919  4.5674  Econ F a m i l y Size  S i n g l e Women  City  Size  Econ Family Size  Size  Econ Family Size  4  6.8670  5.9718  5.6365  5.1456  5  7.7355  6.7735  6.3933  5.8353  6  8.3140  7.3292  6.9047  6.3015  7 o r more  9.0259  7.9968  7.5277  6.8578  T a b l e 6 . 1 c . — Model 2 U t i l i t y S c a l i n g F a c t o r s , s ( A ) . S i n g l e Men  City  Size  Gt 100,00  30,000-99,999  L t 30,000  Rural  Econ F a m i l y Size 1  1.2438  1.1756  1.0975  .9998  2  1.5948  1.4974  1.3997  1.2633  3  2.0827  1.9557  1.8291  1.6437  4  2.3848  2.2386  2.0922  1.8778  5  2.7457  2.5703  2.4043  2.1606  6  2.9799  2.7946  2.6093  2.3458  7 or more  6.1459  3.6007  3.3163  2.9103  S i n g l e Women  City  Gt 100,00  30,000-99,999  Lt 30,000  Rural  1  1.4502  1.3629  1.2631  1.1382  2  1.8991  1.7745  1.6496  1.4751  3  2.5230  2.3607  2.1987  1.9616  4  2.9094  2.7225  2.5352  2.2610  Size  Econ Family Size  5  3.3710  3.1466  2.9343  2.6226  6  3.6704  3.4335  3.1964  2.8595  7 o r more  4.0446  3.7828  3.5208  3.1466  Couples  City  Gt 100,00  30,000-99,999  L t 30,000  Rural  4.4457  4.2943  4.1425  3.9303  3  5.2046  5.0069  4.8100  4.5218  4  5.6740  5.4468  5.2191  4.8858  Size  Econ F a m i l y Size 2  5  6.2352  5.9627  5.7043  5.3254  6  6.5992  6.3112  6.0230  5.6134  7 o r more  7.0541  6.7358  6.4173  5.9624  T a b l e 6.2.— U t i l i t a r i a n W e l f a r e E v a l u a t i o n R e s u l t s .  Model 1.  S i n g l e Men  r=l.  r=.5  r=-.5  r=-l.  r=-5.  Base  656.0  603.3  485.9  404.7  30.744484  B=.5  634.1  582.0  467.4  390.3  30.744483  Ext=0  650.3  595.8  474.5  393.3  30.744790  Min=15  656.2  603.3  485.4  403.8  30.744838  Min=20  654.6  601.1  481.5  399.8  30.744795  Qa=.5  653.2  600.2  482.3  401.3  30.744831  Macd  619.1  564.0  440.5  360.8  30.722080  Forget  599.4  542.4  417.4  341.6  30.721959  S i n g l e Women r = l .  r=.5  r=-.5  r=-l.  r=-5.  Base  565.0  526.5  433.5  326.2  *****  B=.5  548.1  510.0  418.5  316.6  *****  Ext=0  564.8  526.2  433.1  325.9  *****  Min=15  560.6  521.2  426.7  321.3  *****  Min=20  563.5  524.7  431.2  324.6  *****  Qa=.5  561.5  522.6  429.2  323.3  *****  Macd  536.8  496.6  399.6  300.5  *****  Forget  524.0  483.2  385.4  290.4  *****  Couples  r=l.  r=.5  r=-.5  r=-l.  r=-5.  Base  885.3  865.1  830.1  813.5  565.9  B=.5  865.6  845.9  811.7  795.6  562.1  Ext=0  870.0  848.6  811.1  793.0  554.8  Min=15  881.7  861.1  825.1  808.0  563.1  Min=20  876.9  855.8  818.6  800.7  556.4  Qa=. 5  876.0  855.6  820.1  803.2  562.4  Macd  838.0  816.4  778.1  759.7  541.8  Forget  811.5  790.5  753.3  735.4  534.1  Note: R e f e r e n c e  utility=521.9.  246 Table 6.3.— U t i l i t a r i a n Welfare Evaluation Results.  Model 2.  S i n g l e Men  r=l.  r=.5  r=-.5  r=-l.  r=-5.  Base  2645.  2458.  2075.  1844.  565.0  B=.5  2598.  2407.  2020.  1795.  564.8  Ext=0  2579.  2372.  1942.  1701.  560.4  Min=15  2623.  2426.  2005.  1754.  554.8  Min=20  2600.  2394.  1955.  1701.  552.9  Qa=.5  2609.  2416.  2024.  1796.  564.6  Macd  2478.  2250.  1785.  1543.  549.7  Forget  2421.  2194.  1742.  1513.  551.0  S i n g l e Women r = l .  r=.5  r=-.5  r=-l.  r=-5.  Base  2304.  2113.  1704.  1434.  230.814  B=.5  2276.  2083.  1674.  1409.  230.811  Ext=0  2264.  2060.  1628.  1361.  230.777  Min=15  2288.  2090.  1665.  1392.  230.756  Min=20  2276.  2073.  1633.  1358.  230.693  Qa=.5  2277.  2083.  1671.  1406.  230.804  Macd  2203.  1989.  1537.  1274.  230.632  Forget  2170.  1955.  1510.  1254.  230.629  Couples  r=l.  r=.5  r=-.5  r=-l.  r=-5.  Base  3239.  3178.  3104.  3053.  1695.  B=.5  3217.  3155.  3079.  3027.  1676.  Ext=0  3204.  3139.  3056.  3001.  1674.  Min=15  3223.  3160.  3080.  3025.  1653.  Min=20  3213.  3149.  3066.  3010.  1632.  Qa=.5  3219.  3157.  3081.  3029.  1673.  Macd  3149.  3080.  2987.  2927.  1566.  Forget  3122.  3052.  2956.  2895.  1546.  Note: R e f e r e n c e  utility=2278.  T a b l e 6.4.— R a w l s i a n W e l f a r e E v a l u a t i o n R e s u l t s . Model 1. S i n g l e Men  r=l.  r=.5  r=-.5  Base  5813.  5784.  B=.5  5821.  Ext=0  r=-l.  r=-5.  5681.  5596.  3089.  5793.  5693.  5612.  30928  5822.  5794.  5697.  5618.  3102  Min=15  5815.  5787.  5688.  5609.  3100  Min=20  5816.  5788.  5690.  5609.  3100  Qa=.5  5813.  5784.  5681.  5596.  3087  Macd  5821.  5792.  5688.  5602.  3027.  Forget  5817.  5787.  5679.  5590.  3011.  S i n g l e Women r = l .  r=.5  r=-.5  r=-l.  r=-5.  Base  5609.  5552.  5358.  5161.  710.6218  B=.5  5624.  5567.  5373.  5174.  710.6195  Ext=0  5620.  5563.  5371.  5174.  710.6223  Min=15  5614.  5556.  5362.  5164.  710.6221  Min=20  5607.  5549.  5354.  5156.  710.6221  Qa=.5  5619.  5561.  5366.  5168.  710.6214  Macd  5618.  5560.  5359.  5155.  710.6086  Forget  5611.  5550.  5345.  5139.  710.6031  Couples  r=l.  r=.5  r=-.5  r=-l.  r=-5.  Base  5924.  5921.  5916.  5907.  5747.  B=.5  5921.  5918.  5912.  5902.  5723.  Ext=0  5918.  5914.  5906.  5894.  5648.  Min=15  5921.  5917.  5908.  5895.  5363.  Min=20  5915.  5910.  5897.  5881.  5203.  Qa=.5  5921.  5919.  5913.  5903.  5724.  Macd  5909.  5903.  5886.  5867.  5110.  Forget  5907.  5901.  5883.  5862.  5070.  T a b l e 6 . 5 . — R a w l s i a n W e l f a r e E v a l u a t i o n R e s u l t s . Model 2. S i n g l e Men  r=l.  r=.5  r=-.5  r=-l.  r=-5.  Base  5721.  5653.  5314.  4160.  228.73306  B=.5  5712.  5643.  5296.  4737.  228.73304  Ext=0  5706.  5634.  5273.  4704.  228.73284  Min=15  5706.  5630.  5239.  4634.  228.73052  Min=20  5701.  5623.  5227.  4621.  228.73052  Qa=.5  5707.  5636.  5289.  4733.  228.73304  Macd  5770.  5585.  5157.  4531.  228.72802  Forget  5668.  5583.  5166.  4554.  228.72820  r=.5  r=-.5  r=-l.  r=-5.  S i n g l e Women r = l . Base  5382.  5251.  4677.  3826.  ****  B=.5  5367.  5236.  4659.  3811.  ****  Ext=0  5359.  5226.  4644.  3798.  ****  Min=15  5362.  5228.  4639.  3788.  ****  Min=20  5347.  5208.  4606.  3756.  ****  Qa=.5  5351.  5217.  4630.  3784.  ****  Macd  5301.  5153.  4533.  3694.  ****  Forget  5295.  5146.  4525.  3688.  ****  Couples  r=l.  r=.5  r=-.5  r=-l.  r=-5.  Base  5889.  5880.  5851.  5828.  4718.  B=.5  5885.  5875.  5846.  5821.  4659.  Ext=0  5881.  5870.  5838.  5810.  4468.  Min=15  5880.  5869.  5831.  5798.  3722.  Min=20  5877.  5865.  5826.  5791.  3712.  Qa=.5  5884.  5874.  5843.  5817.  4415.  Macd  5868.  5854.  5811.  5774.  3701.  Forget  5865.  5850.  5805.  5766.  3696.  Table 6.6.— Entitlement Model 1  Welfare Evaluation  S i n g l e Men  Results.  S i n g l e Women  Couples  Base  983,319  929,355  2,582,168  B=.5  680,135  695,348  2,103,919  Ext=0  779,354  783,652  2,023,475  Min=15  949,058  900,723  2,389,734  Min=20  876,023  856,560  2,203,143  Qa=.5  848,964  808,397  2,218,840  Macd  455,752  490,911  1,256,592  Forget  399,723  445,502  1,144,756  Model 2  S i n g l e Men  S i n g l e Women  Couples  Base  11,348,946  10,355,090  21,637,872  B=.5  9,772,719  9,143,937  18,718,704  Ext=0  9,538,667  8,967,121  18,223,552  Min=15  10,050,340  9,403,927  19,098,448  Min=20  8,827,824  8,412,616  17,335,712  Qa=.5  9,171,799  8,358,005  18,303,200  Macd  4,498,961  4,893,896  9,215,835  Forget  4,067,815  4,546,160  8,208,126  

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