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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 INSURANCE REFORM WITH CONSTRAINED AND UNCONSTRAINED MODELS'OF LABOUR SUPPLY by SHELLEY A. PHIPPS B.A.(Honours) , The Univers i ty of V i c t o r i a , 1981 M . A . , The Univers i ty of B r i t i s h Columbia, 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 th i s thes is as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA October 1987 © Shel ley A. Phipps, 1987 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of 6C0r>gYvvtcS The University of British Columbia 1956 Main Mall Vancouver, Canada V6T 1Y3 Date Q-f> ISS^ -DE-6f 3/811 ABSTRACT The goal of t h i s d i s s e r t a t i o n i s to i l l u s t r a t e the importance and f e a s i b i l i t y of conducting p o l i c y evaluations which pay a t tent ion to both e f f i c i e n c y and equi ty . Introducing an equity c r i t e r i o n necessar i ly involves introducing value judgements, but I suggest that o b j e c t i v i t y can be maintained through the adoption of an ' e t h i c a l l y f l e x i b l e ' approach. That i s , an analyst can avoid imposing his own p a r t i c u l a r values by e x p l i c i t l y conducting the evaluation from a number of d i f f e r e n t e t h i c a l p o s i t i o n s . This d i s s e r t a t i o n i l l u s t r a t e s the f e a s i b i l i t y of an e t h i c a l l y f l e x i b l e approach by carry ing out an evaluation of the proposals for the reform of the Canadian Unemployment Insurance (UI) programme made by the Macdonald and Forget Commissions. The evaluation proceeds in four stages: 1 . Behavioural models which take account of the existence of unemployment and UI are developed. 2 . The models are estimated using an appropriate Canadian data set . 3 . The estimated models are used to simulate behavioural responses to UI reform. 4 . Estimation and simulation resu l t s are used to carry out the e t h i c a l l y f l e x i b l e welfare eva luat ion . i i Two household labour-supply models are used. The f i r s t assumes that observed unemployment i s the outcome of u t i l i t y - m a x i m i z i n g choices . The second introduces the p o s s i b i l i t y that demand-side constraints may inter fere with supply-s ide choices . A form of switching regression with sample separation unknown is developed to allow estimation of 'constrained' labour-supply funct ions . Addi t iona l problems for estimation include a budget constra int which is non- l inear as a resu l t of the UI programme and a dependent v a r i a b l e , weeks of l e i sure (unemployment), which is l i m i t e d to values between zero and f i f ty - two . Both unconstrained and constrained models are estimated for s ingle men, s ingle women and couples, using l inear expenditure systems and data from the 1982 Survey of Consumer Finance. Estimation resul ts suggest that constrained labour-supply functions are less e l a s t i c than unconstrained funct ions , that there i s no observable d i f ference between the labour-supply behaviour of men and women in a constrained model, and that cross -e f fec t s are important in the determination of the labour-supply behaviour of couples. Estimated p r o b a b i l i t i e s of constraint take an average value of (approximately) 80 percent. The s imulat ion of behavioural responses to UI reform using the estimated unconstrained labour-supply functions suggests that large reductions in unemployment might be a n t i c i p a t e d . Simulation using the constrained labour-supply functions suggests that responses may be n e g l i g i b l e . Welfare evaluat ion measures are constructed for three e t h i c a l perspect ives: The f i r s t i s in the s p i r i t of U t i l i t a r i a n i s m ; the second is in the s p i r i t of John Rawls' theory of j u s t i c e ; the t h i r d i s in the s p i r i t of Robert Nozick's entitlement theory. The ' U t i l i t a r i a n ' measure is a mean of order r over the d i s t r i b u t i o n of i n d i v i d u a l u t i l i t i e s . ( E x p l i c i t interpersonal comparisons are required for these eva luat ions . ) The 'Rawlsian' measure i s a mean of order r over the d i s t r i b u t i o n of i n d i v i d u a l incomes, censored at the poverty l i n e to focus at tent ion on the worst-off group. The 'Enti t lement' measure is a measure of the distance between the d i s t r i b u t i o n of i n d i v i d u a l costs (premiums) and benefi ts derived from UI. Three factors are important in the- determination of the welfare-evaluat ion r e s u l t s . F i r s t , the e t h i c a l pos i t ion adopted matters. Both UI reform proposals appear welfare-reducing from a U t i l i t a r i a n perspective and welfare-improving from an Entit lement perspect ive . Second, for the Rawlsian and U t i l i t a r i a n evaluat ions , the assumed i v degree of inequal i ty aversion is important. F i n a l l y , assumptions made about the nature of unemployment are c r i t i c a l . This i s most c l e a r l y i l l u s t r a t e d by the Rawlsian r e s u l t s . If unemployment i s assumed to be the outcome of u t i l i t y - m a x i m i z i n g choices , then both reform proposals appear welfare-improving: poor people choose to work more and the ir incomes increase . If unemployment may be the resu l t of demand-side constra ints so that increases in employment are not poss ib le , then UI reform merely resu l t s in reductions in income for the worst-off group. These resu l t s i l l u s t r a t e the importance of both the equity and the e f f i c i e n c y dimensions of a po l i cy evaluat ion. This thes is demonstrates the f e a s i b i l i t y of conducting an object ive p o l i c y evaluation which pays at tent ion to both. v TABLE OF CONTENTS Abstract i i L i s t of Tables v i i i L i s t of Figures x i Acknowledgements x i i I . Introduction 1 I I . The Unconstrained Labour-Supply Model 15 1. The Basic Model of Household Behaviour . . . . 15 2. Incorporation of UI in Budget Constraints . 19 3. L i n e a r i z a t i o n of the Non-l inear Budget Constraint 22 4. Formal Model 27 5. Stochastic S p e c i f i c a t i o n of the Model 32 a. Share Formulation 33 b. Non-l inear Budget Constraint with Stochastic Model 35 c. Truncation due to Non-part ic ipat ion . . 38 d. Censoring due to F u l l - y e a r Workers . . . 42 e. Der ivat ion of the L ike l ihood Functions . . 43 I I I . The Constrained Labour-Supply Model 46 1. The Basic Model of Household Behaviour . . . . 46 2. Survey of Previous Studies of Constraints . 50 3. The Formal Model of Constrained Behaviour . 59 4. Der ivat ion of the L ike l ihood Function . . . . . 64 IV. Est imation Results 69 1 . Data 69 2. Model 1 Estimation Results 74 3. Model 2 Estimation Results 84 4. E l a s t i c i t y Estimates 88 5. Conclusions 98 V. Simulation Results 100 1. Previous Studies of UI 101 2. Po l i cy Changes Simulated 109 3. Simulation Methodology 113 4. Modell ing UI Reform 119 5. Predicted Labour-Supply Responses to UI Reform 124 6. Conclusions 132 V I . Welfare Evaluat ion 135 v i 1. Methodology for the U t i l i t a r i a n Evaluations . . 135 2. Methodology for the Rawlsian Evaluations . 146 3. Methodology for the Entitlement Evaluations . . 150 4. Welfare Evaluation Results 154 V I I . Conclusions 162 Bibl iography 172 Appendix 1 193 Appendix 2 195 Appendix 3 198 v i i L i s t of Tables Table 4.1: Basic Data Averages 199 Table 4.2: Occupational 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 .202 Table 4.5: Mean Var iab le Values . Single Women and Single Men . . .203 Table 4.6: Mean Var iab le Values . Couples 204 Table 4.7: Model 1 Parameter Estimates. Single Women. . . .205 Table 4.8: Model 1 Parameter Estimates. Single Men 206 Table 4.9: Model 1 Parameter Estimates. Couples 207 Table 4.10: Model 2 Parameter Estimates 208 Table 4.11: P r o b a b i l i t i e s of Constraint in Unemployment. Single Women 209 Table 4.12: P r o b a b i l i t i e s of Constraint in Unemployment. Single Men 210 Table 4.13: P r o b a b i l i t i e s of Constra int . Couples 211 Table 4.14: Model 1 Labour-Supply E l a s t i c i t i e s . Single Men. 212 Table 4.15: Model 1 Labour-Supply E l a s t i c i t i e s . Single Women 213 Table 4.16: Model 1 Labour-Supply E l a s t i c i t i e s . Married Men. Wives F u l l - t i m e Workers 214 Table 4.17: Model 1 Labour-Supply E l a s t i c i t i e s . Married Men. Wives Part-t ime Workers 215 Table 4.18: Model 1 Compensated E l a s t i c i t i e s . Married Men. Wives F u l l - t i m e Workers 216 Table 4.19: Model 1 Compensated E l a s t i c i t i e s . Married Men. Wives Part-t ime Workers 217 v i i i Table 4.20: Model 1 Labour-Supply E l a s t i c i t i e s . Married Women. Husbands Seasonal Workers 218 Table 4.21: Model 1 Labour-Supply E l a s t i c i t i e s . Married Women. Husbands C y c l i c a l Workers 219 Table 4.22: Model 1 Labour-Supply E l a s t i c i t i e s . Married Women. Husbands Neither 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 . Married Women. Husbands Seasonal Workers 221 Table 4.24: Model 1 Compensated E l a s t i c i t i e s . Married Women. Husbands C y c l i c a l Workers 222 Table 4.25: Model 1 Compensated E l a s t i c i t i e s . Married Women. Husbands Neither 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 224 Table 4.27: Model 2 Labour-Supply E l a s t i c i t i e s . Couples. Rationed and Unrationed .225 Table 5.1: Model 1. Labour-Supply Responses. Single Men. 226 Table 5.2: Model 1. Labour-Supply Responses. Single Men. Unemployed Population 227 Table 5.3: Model 1. Labour-Supply Responses. Single Women. 228 Table 5.4: Model 1. Labour-Supply Responses. Single Women. Unemployed Population 229 Table 5.5: Model 1. Labour-Supply Responses. Married Men. 230 Table 5.6: Model 1. Labour-Supply Responses. Married Men. Unemployed Population 231 Table 5.7: Model 1. Labour-Supply Responses. Married Women. 232 Table 5.8: Model 1. Labour-Supply Responses. Married Women. Unemployed Population 233 Table 5.9: Model 2. Labour-Supply Responses. Single Men. 234 Table 5.10: Model 2. Labour-Supply Responses. Single Men. Unemployed Population 235 Table 5.11: Model 2. Labour-Supply Responses. Single Women. 236 Table 5.12: Model 2. Labour-Supply Responses. Single Women. Unemployed population 237 Table 5.13: Model 2. Labour-Supply Responses. Married Men. 238 Table 5.14: Model 2. Labour-Supply Responses. Married Men. Unemployed Population 239 Table 5.15: Model 2. Labour-Supply Responses. Married Women. 240 Table 5.16: Model 2. Labour-Supply Responses. Married Women. Unemployed Population 241 Table 6.1a: Equivalence Scales Impl i c i t in Low-income Cut-of fs 242 Table 6.1b: Model 1 U t i l i t y Sca l ing Fac tors , s(A) 243 Table 6.1c: Model 2 U t i l i t y Scal ing Factors , s(A) 244 Table 6.2: U t i l i t a r i a n Welfare Evaluat ion Resul t s . Model 1. 245 Table 6.3: U t i l i t a r i a n Welfare Evaluat ion R e s u l t s / M o d e l 2. 246 Table 6.4: Rawlsian Welfare Evaluat ion Resul ts . Model 1. 247 Table 6.5: Rawlsian Welfare Evaluat ion Resul t s . Model 2. 248 Table 6.6: Entit lement Welfare Evaluat ion Results 249 x L i s t of Figures Figure 2 .1 . The Budget Constraint for Alberta 19 Figure 2.2. The Budget Constraint for Newfoundland 19 x i A C K N O W L E D G E M E N T S I would l i k e to thank my thes is committee, David Donaldson, Terry Wales and Steve Jones, for a l l of the ir advice and encouragement. Specia l thanks are also due Cra ig R i d d e l l , Lars Osberg, Jon Kesselman and the people in ' C wing for much patience and many he lp fu l comments. Above a l l , I want to thank my family and Darren for u n f a i l i n g support over many years . I. INTRODUCTION In th i s d i s s e r t a t i o n , I conduct an evaluation of proposed changes to the Canadian Unemployment-Insurance programme (Ul) which pays at tent ion to both the equity and the e f f i c i e n c y dimensions of these changes. Most economic studies focus on e f f i c i e n c y and avoid discuss ions of equity . However, evaluations based so le ly on an e f f i c i ency c r i t e r i o n such as the Pareto p r i n c i p l e can y i e l d incomplete rankings of a l t e r n a t i v e s . The p r i n c i p l e i s s i l e n t , for example, when one i n d i v i d u a l benefits at the expense of another, a dilemma few po l i cy changes can avo id . (The p o t e n t i a l Pareto improvement c r i t e r i o n , while complete, f a i l s to sa t i s fy basic r a t i o n a l i t y propert ies ( t r a n s i t i v i t y , asymmetry of s t r i c t preference) . ) f The introduct ion of an equity c r i t e r i o n , while reso lv ing the problem of incompleteness, requires the choice of a spec i f i c a t t i tude toward inequa l i ty . I suggest that th i s d i f f i c u l t y fA feas ib le a l t ernat ive A i s Pareto e f f i c i e n t i f there i s no other feas ib le a l t ernat ive A' such that everyone prefers A' to A (or such that everyone but i n d i v i d u a l X is ind i f f erent between A and A' and X prefers 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 preferred to a l t e r n a t i v e A' i f no-one i s worse off in A than in A' and at least one i n d i v i d u a l i s 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 i s s o c i a l l y preferred to a l t ernat ive A' i f ind iv idua l s who are better off in A can p o t e n t i a l l y compensate ind iv idua l s who are worse off and s t i l l prefer A to A ' . 1 Introduction / 2 can be overcome through the adoption of an "e th ica l ly f l e x i b l e " ! approach. That i s , while value judgements are , of course, required to assess the equity dimensions of a proposed p o l i c y change, an evaluation can nevertheless remain 'objec t ive ' by e x p l i c i t l y incorporat ing a range of d i s t r i b u t i o n a l judgements; by, e f f e c t i v e l y , conducting a s e n s i t i v i t y ana lys i s over a l t ernat ive e t h i c a l pos i t ions rather than just imposing one. My analys i s of proposed changes to Canadian UI po l i cy w i l l adopt an "e th i ca l ly f l ex ib le" approach. However, for reasons of f e a s i b i l i t y , at tent ion w i l l be r e s t r i c t e d to three e t h i c a l p o s i t i o n s : The f i r s t w i l l be in the s p i r i t of U t i l i t a r i a n i s m (a mean of order r defined over the d i s t r i b u t i o n of i n d i v i d u a l u t i l i t i e s ) ; the second w i l l be in the s p i r i t of John Rawls' "theory of jus t ice" (a mean of order r defined over the d i s t r i b u t i o n of i n d i v i d u a l incomes, censored at the poverty l ine to focus at tent ion on the ' w o r s t - o f f group); the t h i r d w i l l be in the s p i r i t of Robert Nozick's "entitlement theory" (a measure of the distance between the d i s t r i b u t i o n of i n d i v i d u a l benefits and the d i s t r i b u t i o n of i n d i v i d u a l costs associated with the UI fThe term "e th ica l ly f l ex ib l e" i s used in the l i t e r a t u r e on measures of poverty and inequa l i ty . An index i s said to be "e th ica l ly f l e x i b l e " i f i t is consistent with a var ie ty of s o c i a l welfare functions (Blackorby and Donaldson, 1980; Chakravarty, 1983). Introduction / 3 programme). U t i l i t a r i a n i s m and the Rawlsian approach are l o g i c a l choices because they are the two ph i losophica l approaches most frequently discussed by economists and because they take polar pos i t ions on the issue of equi ty . Nozick's outlook i s in teres t ing because, unl ike U t i l i t a r i a n i s m and Rawls' theory, i t i s procedural rather than end-state in nature. These e t h i c a l pos i t ions are very d i f f erent and require correspondingly d i f f eren t approaches to po l i cy evaluat ion. UI reform is a topic su i tably approached from an e t h i c a l l y f l e x i b l e perspect ive . The h i s tory of UI in Canada i s character ized by a s t i l l unsett led debate over whether the programme should be designed according to s o c i a l insurance p r i n c i p l e s or according to i n d i v i d u a l need. A basic e f f i c i e n c y / e q u i t y trade-of f i s c l e a r . Unemployment Insurance was f i r s t es tabl i shed in Canada in 1940. Record unemployment during the depression of the 1930s had convinced people that unemployment i s not synonymous with l az ines s . Recognition that the average worker, a man with a dependent family during th i s per iod , could , through no faul t of h is own, f ind himself without a job and consequently without means of providing for h i s family led to the implementation of a UI scheme designed to provide Introduction / 4 income protect ion for primary workers. The fundamental purpose of the UI Act of 1940 was "to promote economic and s o c i a l secur i ty of Canadians by supporting workers from one job to the next" (Dingledine, 1981). Chron ica l ly unemployed groups such as seasonal workers were not covered by the o r i g i n a l UI Act . UI was intended to be s t r i c t l y a s o c i a l insurance programme; workers were supposed to 'earn' the r ight to benef i ts by paying premiums. Thus, e l i g i b i l i t y condit ions were s t r ingent . Workers were required to have had a minimum of t h i r t y weeks of insurable employment in a 104-week q u a l i f y i n g period in order to be e l i g i b l e for any benef i t s , and only 42 percent of the labour force had jobs deemed ' i n s u r a b l e . ' Then, s a t i s f y i n g the minimum q u a l i f y i n g condit ions provided only a minimum of benef i t s . A worker was required to have been f u l l y employed for f ive years before he was e n t i t l e d to the maximum benefit duration of one year. F i n a l l y , income replacement was much less generous than is current ly the case. Workers without dependants received benefits equal to 34 percent of the i r previous insured income while workers with dependants received benefits equal to 40 percent of insured income. In 1949, the unemployment rate increased sharply and many of the unemployed were not e l i g i b l e to c o l l e c t UI benef i t s , given the r e s t r i c t i o n s of the 1940 Act . Hence, in 1950, an Introduction / 5 amendment was passed to provide 'supplementary benef i ts ' for exhaustees and for those not q u a l i f y i n g for regular UI but having made at least ninety d a i l y contr ibut ions during that f i s c a l year. Benefits were paid at 80 percent of the regular rate and financed p a r t i a l l y through increased premiums but p a r t i a l l y through general revenue. This amendment const i tuted a s i g n i f i c a n t step in the d i r e c t i o n of a 'needs-oriented' UI programme. Another step in the same d i r e c t i o n was taken when coverage was extended to include seasonally unemployed, self-employed fishermen. Need rather than earned r ight to benefits again motivated the change. Few changes were made to UI l e g i s l a t i o n during the 1960s, but growing d i s s a t i s f a c t i o n with the programme led to a ser ies of reviews culminating in the G i l l Report and eventual ly the White Paper, "UI in the 1970s," tabled June, 1970. These reports favoured a return to s t r i c t insurance p r i n c i p l e s on the grounds that a s ing le programme i s fundamentally unable to cope with a l l types of unemployment. It was recommended that UI" be l e f t a s o c i a l insurance programme designed to handle f r i c t i o n a l unemployment and that th i s be co-ordinated with a general assistance plan based on a needs test to deal 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 new UI Act was passed. Under the new act , benefits were made payable in three phases. During the f i r s t two phases, entitlement depended on work record as under the o ld ac t . In the t h i r d phase, however, the programme departed from s o c i a l insurance p r i n c i p l e s . Benefits were to be based on the reg ional unemployment rate and financed from general revenue. Hence, the 'supplementary benef i ts ' introduced with the 1950 amendment were made part of the regular programme. F i n a l l y , the prov i s ion of spec ia l s ickness , maternity and retirement benefits broadened the scope of UI from i t s i n i t i a l focus on primary workers. With the 1971 reform of the UI programme, coverage became nearly un iversa l (96 percent of the labour force was covered). This broader base for premium c o l l e c t i o n was intended to allow an increase in the income-replacement rate to 66 2/3 percent for those without dependants; an increase in benefit generosity was bel ieved necessary as a resu l t of a survey of non-deferrable expenses r e l a t i v e to income. For ind iv idua l s with dependants and with average insured earnings less than one- th ird of maximum insurable earnings, the benefit-replacement rate was increased to 75 percent for the extended-benefit phase. The idea of need again motivated these changes. At the same time, entrance requirements were lowered so that a minimum of eight weeks of insurable Introduction / 7 employment e n t i t l e d a worker to regular benef i t s . To o f f - se t the work d i s incent ive e f fec ts ant i c ipated as a resu l t of these changes, benefi ts were made taxable . And, to give r e l i e f to upper and middle-income groups covered by UI for the f i r s t time, contr ibut ions to UI were made tax deduct ib le . Increasingly higher rates of unemployment throughout the 1970s, in combination with the more generous provis ions of the 1971 Act , led the programme into unantic ipated f i n a n c i a l d i f f i c u l t i e s . From 1970 to 1975, the cost of UI climbed from $730 m i l l i o n to $3.3 b i l l i o n . The government's share of t o t a l programme cost rose from 22 to 51 percent over the same per iod . N a t u r a l l y , such huge expenditure increases led to concern about the generosity of UI and i t s impact on work incent ives . A ser ies of amendments during the 1970s tended toward retrenchment, thus moving in the d i r e c t i o n opposite to that taken during the 1950s. In 1976, the spec ia l 75 percent replacement rate for workers with dependants was e l iminated . In 1977, the basic entrance requirement was made var iab le - from eight to fourteen weeks, depending on the regional unemployment ra te . In 1979, repeat claimants and new entrants to the labour force were required to demonstrate twenty weeks of insurable employment Introduction / 8 in order to qua l i fy for benef i t s . Income-replacement rates were reduced to 60 percent for a l l c la imants . Of course, these changes have not resolved the debate. The 1981 White Paper, "UI in the 1980s," provided an assessment of the problems of UI: 1. The programme is too complex to understand and administer so that under- and over-payments are very common. 2. Costs are too high, but most attempted or suggested methods of cost reduction involve serious i n e q u i t i e s . Var iable entrance requirements, for example, mean that people in d i f ferent regions w i l l be treated d i f f e r e n t l y merely because they l i v e in regions with d i f f erent unemployment rates . 3. Work incentive problems continue to e x i s t . There i s general publ ic concern over programme abuse. Again, in 1986, the report of the Commission of Inquiry on Unemployment Insurance (the Forget Commission) maintained that Canadians strongly support Unemployment Insurance as a short-term income securi ty programme for those i n v o l u n t a r i l y out of work, but there i s considerable debate across the country about the meaning of ' shor t - t erm, ' 'income s e c u r i t y , ' ' i n v o l u n t a r i l y ' and 'out of work.' Major complaints were summarized (p.33) as: Introduction / 9 1. The program i s u n f a i r . 2. The program has the wrong incent ives . 3. I t ' s not an insurance programme anymore. 4. The government runs the show. 5. The program i s administered i n e f f i c i e n t l y and de l ivered i n s e n s i t i v e l y . C l e a r l y , the basic dilemma is unresolved. How can the goal of maintaining an insurance programme for workers with strong labour-force attachment be reconci led with the goal of providing r e l i e f to those in need? The issue is further complicated by continuing high rates of unemployment in Canada and programme costs which in 1986 have climbed above $12 b i l l i o n annual ly . In summary, therefore , an inves t igat ion of Canadian UI which takes account of both equity and e f f i c i e n c y seems appropriate for a number of reasons: 1. The h i s tory of UI in Canada i s marked by a ser ies of reforms tending sometimes in the d i r e c t i o n of a s t r i c t ' s o c i a l insurance' philosophy and at other times in the d i r e c t i o n of a 'needs-based' philosophy. 2. There ex i s t s general concern that the incentive ef fects generated by UI impede labour-market adjustment and d i s t o r t l abour- l e i sure choices . Introduction / 10 3 . High rates of unemployment have put a f i n a n c i a l s t r a i n on the programme and made i t a target for reform. 4 . High rates of unemployment mean high rates of dependency on UI so that reductions in programme spending w i l l a f fect large numbers of people. D i s t r i b u t i o n a l impl icat ions of a l t ernat ive cost-reducing proposals are s i g n i f i c a n t and thus of i n t e r e s t . The reports of the Royal Commission on the Economic Union and Development Prospects for Canada (the Macdonald Commission) and the Commission of Inquiry on Unemployment Insurance (the Forget Commission) have both made proposals for major reform of the Canadian UI system. These proposals const i tute the set of potent ia l reforms evaluated in th i s thes i s . Indiv idual proposals , or packages of proposals , are deemed welfare-improving according to a p a r t i c u l a r e t h i c a l pos i t ion i f they improve a measure of welfare consistent with that p o s i t i o n . Not ice , however, that the reverse impl icat ion need not hold: a government choosing a po l i cy change preferred according to a p a r t i c u l a r e t h i c a l pos i t ion is not to be interpreted as having s o c i a l preferences consistent with that p o s i t i o n . UI i s , after a l l , only one of a large number of p o l i c i e s a f f ec t ing the d i s t r i b u t i o n of income in Canada. A government may choose to change UI in a manner which appears consistent with one e t h i c a l pos i t ion Introduction / 11 while r e d i s t r i b u t i n g income through other tax / t rans fer p o l i c i e s in a manner consistent with an e n t i r e l y d i f f eren t p o s i t i o n . Soc ia l preferences could only be in ferred from an assessment of the o v e r a l l incidence of government p o l i c y . However, since i t i s not the intent ion of t h i s analys i s to make any assessment of the e t h i c a l p o s i t i o n of the government implied by i t s po l i cy choices , th i s i s not a problem. A v a l i d question to ask, on the other hand, i s whether there is any reason to be concerned about the d i s t r i b u t i o n a l impl icat ions of i n d i v i d u a l po l i cy changes. That i s , i s there any point in analysing UI in a manner consistent with a p a r t i c u l a r e t h i c a l pos i t ion i f a change which is inequitable according to th i s pos i t ion might be preferred ( p e r h a p s f o r e f f i c i ency reasons) i f i t could be implemented in combination with a change to some other po l i cy which compensated for the inequity? I would argue that there i s a need to determine the d i s t r i b u t i o n a l consequences of i n d i v i d u a l po l i cy changes. To assess whether a p a r t i c u l a r po l i cy change f i t s into the complete package of government p o l i c i e s in a manner which is consistent with s o c i a l preferences, i t s d i s t r i b u t i o n a l impact must be known. Even i f a government chooses an ' inequi tab le ' p o l i c y change, i t w i l l want to know s p e c i f i c a l l y which inequ i t i e s are being Introduction / 12 generated in order to make c o r r e c t i o n s . Moreover, in a second-best world, p o l i c y changes enacted to remedy inequi t i e s are u n l i k e l y to be without a d d i t i o n a l incentive e f fects themselves. Since i t i s not cos t less to remove i n e q u i t i e s , we might worry about introducing them. F i n a l l y , since i t i s poss ib le to generate equity measures ( e . g . , of progress iv i ty ) for i n d i v i d u a l p o l i c i e s which aggregate to give an o v e r a l l measure of the impact of a package of p o l i c i e s (Blackorby and Donaldson, 1984), i t may be possible to devise po l i cy evaluation measures which have a s imi lar property . An e t h i c a l l y f l e x i b l e analys i s of p o t e n t i a l changes to the Canadian UI system requires the development of a model of household behaviour which takes account of the existence of unemployment and unemployment insurance. E x i s t i n g studies of the impact of UI on behaviour t y p i c a l l y employ models of search (Ham and Rea, 1985) or models of labour supply ( F o r t i n , 1984) and assume that unemployment i s the resu l t of i n d i v i d u a l u t i l i t y - m a x i m i z i n g choices . However, i t seems l i k e l y that some part of observed unemployment i s not the resu l t of u t i l i t y - m a x i m i z i n g choices . P a r t i c u l a r l y during periods of recess ion, some i n d i v i d u a l s may be observed unemployed as a resu l t of demand-side constra ints rather than supply-s ide choices . This i s a very d i f f erent Introduction / 13 in terpre ta t ion of the basic nature of unemployment than that t r a d i t i o n a l l y used in studies of UI , and i t i s l i k e l y to y i e l d very d i f f erent predict ions about the impact of UI on labour-supply behaviour: i f i n d i v i d u a l s are not unemployed by choice , they are un l ike ly to be as responsive to changes in UI as t r a d i t i o n a l models have pred ic ted . Since basic assumptions about whether unemployment i s p r i m a r i l y generated from the demand side or the supply side of the labour market are c r i t i c a l for p r e d i c t i n g behavioural responses to UI, they are also c r i t i c a l for an evaluation of proposed UI reform. Thus, I consider two very d i f f erent models of labour supply: Model 1 i s a t r a d i t i o n a l model in the labour-supply t r a d i t i o n which assumes that a l l observed unemployment i s the resu l t of unconstrained u t i l i t y - m a x i m i z i n g choices; Model 2 i s a labour-supply model which departs from t r a d i t i o n by introducing the p o s s i b i l i t y that some observed unemployment i s the resu l t of demand-side c o n s t r a i n t s . Chapters Two and Three of the thes is develop, respec t ive ly , Model 1, the unconstrained model of labour supply, and Model 2, the constrained model of labour supply. Chapter Four presents estimation resul ts for the two models. Chapter Five discusses the Macdonald and Forget proposals for the reform of UI and the simulation of behavioural responses to these Introduct ion / 14 proposals using the estimated models. Chapter Six develops welfare evaluation measures consistent with U t i l i t a r i a n i s m , Rawls' theory of j u s t i c e and Nozick's entit lement theory and, f i n a l l y , uses estimation and simulation resu l t s to conduct the e t h i c a l l y f l e x i b l e evaluat ion . Chapter Seven provides a summary of the p r i n c i p a l f indings . I I . THE UNCONSTRAINED LABOUR-SUPPLY MODEL In th i s chapter, I develop a basic unconstrained model of household behaviour (Model 1) in the labour-supply t r a d i t i o n . I f i r s t out l ine how the parameters of the Canadian UI programme are incorporated in household budget constra ints in order to make behaviour responsive to UI and, thus, to make the basic labour-supply model useful for an evaluat ion of proposed UI reforms. Then, I discuss the empir ica l implementation of Model 1. This involves the choice of a funct iona l form for est imation, the incorporat ion of demographic 'taste* proxies within the chosen funct ional form and the choice of a s tochast ic s p e c i f i c a t i o n . I conclude Chapter Two with a discuss ion of est imation problems. 1. The B a s i c Model of Household Behaviour Labour-market behaviour depends upon a host of fac tors , many of which f a l l outside the t r a d i t i o n a l scope of economic ana lys i s ; even the set of purely 'economic' determinants i s mul t i -d imens ional . Yet , the proposed evaluation of changes to UI requires a model of behavioural response. To obtain such a model, a number of s impl i fy ing assumptions must be made; namely, that the world i s s t a t i c and c e r t a i n , that 15 The Unconstrained Labour-Supply Model / 16 ind iv idua l s have chosen region of residence, occupation, and s ize of family and that households choose weeks of l e i sure and consumption of a composite commodity in order to maximize u t i l i t y subject to a s ingle budget constra int which incorporates the parameters of the Canadian UI programme. Thus, members of a household are assumed to make jo in t decis ions about consumption of l e i sure and goods. I n t r a - f a m i l i a l a l l o c a t i o n i s ignored; a l l household members are assumed to experience the same l e v e l of welfare. However, the household behaves s e l f i s h l y with respect to outside i n d i v i d u a l s . Since choice of region of residence and occupation may be influenced by the a v a i l a b i l i t y of UI benef i t s , t rea t ing these choices as given ignores important channels through which UI can influence behaviour. P o s s i b i l i t i e s for varying hours worked each week are s i m i l a r l y ignored. The behavioural responses modelled here are r e s t r i c t e d to changes in weeks of labour supply. The unconstrained model of household behaviour (Model 1) assumes that observed weeks of both employment and unemployment r e f l e c t u t i l i t y -max imiz ing choices; that households form optimal plans and, on average, are able to carry them out (random 'errors in opt imizat ion' may cause The Unconstrained Labour-Supply Model / 17 deviat ions from des ired p lans ) . Given the existence of UI, i t i s assumed that households plan annual patterns of employment and unemployment for working members which enable them to earn entitlement to UI and then to stop working and c o l l e c t earned b e n e f i t s . f Of course, the notion of a f ree ly chosen optimal annual pattern of employment and unemployment i s h ighly u n r e a l i s t i c for a number of reasons. F i r s t , Model 1 assumes that i n d i v i d u a l s plan at a l l times e i ther to be employed or to be unemployed and rece iv ing UI benefi ts (except during the two-week waiting p e r i o d ) . This ignores the fact that people do not always f i l e claims for UI when faced with a s p e l l of unemployment (see Glenday and Alam, 1982). Second, workers face a period of d i s q u a l i f i c a t i o n from UI i f they v o l u n t a r i l y leave t h e i r jobs. T h i r d , given today's high rates of unemployment, people cannot r a t i o n a l l y expect to quit a job each year and f ind a new job or be r e - h i r e d at the des ired time and wage the fol lowing year. However, there are cases in which the model of annual plans seems to provide an appropriate descr ip t ion of labour-market behaviour. It is commonly a l l e g e d , for example, that the existence of UI allows fishermen or construct ion workers to tFor many people, an optimal annual pattern w i l l consis t of f i f ty - two weeks of employment with no weeks of unemployment. The Unconstrained Labour-Supply Model / 18 plan annual patterns of employment and unemployment. There is support for th i s idea in the study by Glenday and Alam (1982) which analyses a 10 percent sample of a l l ind iv idua l s who f i l e d a c laim for UI during the period 1974 to 1979. In the ir ana lys i s of t h i s l ong i tud ina l data set , Glenday and Alam f ind some evidence that ind iv idua l s using the UI system do follow patterns of employment and unemployment: 35 percent of the ir sample had average periods of employment (1974-1979) which were less than six months; 65 percent of the sample had average periods of unemployment which were less than six months. Thus, for ind iv idua l s who regu lar ly use UI, the idea of annual employment/unemployment patterns may have some v a l i d i t y . F i n a l l y , though, the choice of an annual framework for household planning can be j u s t i f i e d on pragmatic grounds. The assumption of an annual pattern of employment and unemployment i s a s i m p l i f i c a t i o n made in concession to the l i m i t a t i o n of a s ing le cross - sec t ion of data which gives no information concerning past work records. If ind iv idua l s are assumed to follow an annual pattern of employment and unemployment, then, other things equal , th is year's employment period w i l l match l a s t year's employment period and can be used to e s tab l i sh entitlement to UI . The Unconstrained Labour-Supply Model / 19 2. I n c o r p o r a t i o n of UI i n Budget C o n s t r a i n t s Within the framework of the equi l ibr ium p lan , UI has a major impact on budget constra ints and th i s impact var ies across regions. Figure 2.1 i l l u s t r a t e s the budget constra int facing a s ingle ind iv idua l l i v i n g in Alberta ( in 1981, the year in which the data were c o l l e c t e d ) ; Figure 2.2 i l l u s t r a t e s the equivalent budget constra int for an i n d i v i d u a l l i v i n g in Newfoundland. (Budget constra ints are i l l u s t r a t e d for these two provinces as examples of low and high unemployment areas. Both budget constra ints are drawn contingent on the annual r e p e t i t i o n assumption.) Indiv iduals are required (in 1981, as current ly ) to work a minimum number of weeks, l a b e l l e d MIN in Figures 2.1 and 2.2, to be e l i g i b l e for UI benef i t s . This var ies with the regional unemployment rate and with labour-force status new and re-entrants must have longer work records . (However, since new and re-entrants have not yet es tabl i shed patterns of employment, t h e i r behaviour is not captured by th i s model.) Those working fewer than the minimum required weeks are unaffected by the UI programme except to the extent that i t provides an incentive to increase labour supply in order to q u a l i f y (or to the extent that they must pay premiums). Net wage rates are thus given by the slope of the l i n e AB in The Unconstrained Labour-Supply Model / 20 Figure 2.1. The Budget Constraint for A l b e r t a . Those ind iv idua l s working more than the minimum q u a l i f y i n g weeks earn one week of UI entitlement for each week worked (for the f i r s t twenty-five weeks). Thus, UI e f f e c t i v e l y operates as a wage subsidy over a port ion of the budget constra int (see the segment 'Subsidy' in Figure 2.1); each week of employment is compensated with both a wage payment and an extra week of UI entit lement. Indiv iduals s a t i s f y i n g the minimum work requirement are also e l i g i b l e for weeks of The Unconstrained Labour-Supply Model / 21 Figure 2 . 2 . The Budget Constraint for Newfoundland, WEEKS OF LEISURE UI benefits based on the regional unemployment rate rather than on i n d i v i d u a l work records . Adding 'earned benef i t s ' to 'regional ly-extended benef i t s ' means that i n d i v i d u a l s can eventually accumulate enough benefit weeks to enable them to 'take the rest of the year o f f ' and c o l l e c t UI (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 the point at which th i s i s poss ib le ( l abe l l ed 'MAX' in Figure 2 . 1 ) means that po tent ia l weeks of UI are being given up. In a model where ind iv idua l s choose annual patterns of employment to gain e l i g i b i l i t y for UI followed by The Unconstrained Labour-Supply Model / 22 unemployment with UI compensation, the UI programme imposes an i m p l i c i t tax on wages for weeks of work beyond MAX (see the segment 'Tax' in Figures 2.1 and 2.2); each extra week of work i m p l i c i t l y 'costs ' one week of UI benef i t . Indiv iduals working more than f i f t y weeks are unaffected by UI since a two-week wait ing period is imposed before they are e l i g i b l e to receive benef i t s . The l i n e AB again represents net wage rates in such cases. (This sect ion follows Rea (1977)). 3. L i n e a r i z a t i o n of the Non-linear Budget C o n s t r a i n t It i s c l ear that the UI programme complicates household budget constra ints already complicated by a progressive income-tax system.f For s i m p l i c i t y , i t i s assumed that people face budget constra ints which are extensions of the l inear segments on which they are observed. There are two stages to t h i s l i n e a r i z a t i o n process . F i r s t , the budget constraint is piece-wise segmented as a resu l t of the progressive marginal tax brackets of the Canadian income-tax system. For est imat ion, the i n d i v i d u a l ' s basic net wage, represented by the l i n e AB in Figures 2.1 fMany features of the Canadian tax- transfer system are ignored. The Unconstrained Labour-Supply Model / 23 and 2.2, i s ca l cu la ted as the l inear extension of the marginal tax segment on which he i s observed to be located with non-labour income adjusted appropr ia te ly . To i l l u s t r a t e th i s process , the household budget constraint incorporat ing the income-tax system can be compared with the budget constra int operative in the absence of income taxation and UI, pX+w,L1+w2L2<w1T+w2T+NLINC1 +NLINC2 where: L ^ l e i s u r e demand, in weeks, head L 2 = l e i s u r e demand, in weeks, second earner X=commodity demand for the household (assuming a s ingle composite commodity) T=total time ava i lab l e (52 weeks) p=price of the composite good w^=weekly wage NLINCj=non-labour income. To incorporate income taxat ion , f i r s t define t o t a l incomes: YT=W , (T-L,)+NLINC1 Y1'=W2 ( T - L 2 )+NLINC2 r n m m Y =Y,+Y2 Next, define a tax funct ion: T i = T j + t j ( Y i ~ y j ) ' where: i=1,2 indexes husband and wife j indexes marginal tax brackets The Unconstrained Labour-Supply Model / 24 T • th Yj i s the smallest taxable income in the j tax bracket T T j i s the tax payable on Yj t j i s the marginal tax rate appl icable to the j bracket . Thus, with taxation the household budget constraint becomes: P X ^ Y T - T T + Y J - T 2 . Or, subst i tut ing and re-arranging: p X + d - t l J w ^ t + d - t ? ) w 2L 2<( l - t l ) w , T +d-t^)w 2 T+ (1-t l ) NLINC,+(1-t^)NLINC 2 - T l + t l Y T j -T^+t^Y T 3. Re-written, th i s becomes: pX+w!L!+w2L2^w1T+w2 T+NLINC,+NLINC 2 , where w^=(1-tj)w^, i=1,2 and the tax adjustments are incorporated in the non-labour income terms. E f f e c t i v e l y , the l i n e a r i z a t i o n process assigns ind iv idua l s the wage rate W j d - t j ) and adjusts non-labour income to take account of the fact that they have not paid taxes at the marginal rate , t j , on a l l earned income. The second stage of l i n e a r i z a t i o n takes account of the n o n - l i n e a r i t i e s introduced by the UI programme. Again, the budget constraint is taken to be a l inear extension of the segment on which the i n d i v i d u a l i s observed. Those ind iv idua l s located on segments one and four are simply assigned the net wage corresponding with the l i n e AB in Figures 2.1 and 2.2 (which is i t s e l f an extension of the The Unconstrained Labour-Supply Model / 25 appropriate tax bracket , as descr ibed) . Single ind iv idua l s located on the subsidy segment of the budget constraint receive t o t a l income of w(T-L)+Bwq(QA(T-L)+EXT)+NLINC ( i . e . , employment earnings + UI benefits + NLINC ) where: w i s now also net of UI premiums (Premiums are ca lcu la ted as 1.8 percent of the gross weekly wage, provided the gross wage is greater than 63 d o l l a r s and that the weekly premium does not exceed 5.67 d o l l a r s . ) B=the benefit replacement rate (=.60 in 1981) - w^  =the net replaceable wage rate (The maximum weekly (gross) replaceable wage i s 315 d o l l a r s . In a d d i t i o n , ind iv idua l s with gross weekly wages above 465 d o l l a r s are required to repay 60 percent of any UI benefits received.) QA=the rate at which weeks of employment earn weeks of UI benefit (=1, for the f i r s t 25 weeks (1981)) EXT=weeks of regional ly-extended benefits to which the i n d i v i d u a l i s e n t i t l e d . ( E l i g i b l e claimants receive two weeks of extended benefits for every hal f percentage point the l o c a l unemployment rate exceeds 4 percent . ) Tota l income i s composed of employment earnings , UI benefit rece ipts and non-labour income. Thus, the budget constraint The Unconstrained Labour-Supply Model / 26 can be re -wr i t ten as: (2.1) pX+Cw+Bw^jL^ {w+Bwq}T+ Bw^EXT+NLING. Indiv iduals located on the tax segment of the budget constraint receive t o t a l income of: w(T-L)+Bwq(MAXWK-(T-L)) +NLINC ( i . e . , employment earnings + UI benef i ts + NLINC) where MAXWK=maximum benefit duration (50 weeks in 1981). Hence, the budget constra int incorporat ing UI can be wri t ten: (2.2) pX+Cw-Bv^jL^w-Bw^T +BwqMAXWK+NLINC. The simple ' l i n e a r i z a t i o n ' treatment of the piece-wise l inear budget constraint e l iminates the fundamental endogeneity problem in the non-stochastic model by re -wr i t ing UI benefits (which depend on weeks of work) as an exogenous wage subsidy/tax in combination with a s h i f t in non-labour income. Notice that i f u t i l i t y functions are * assumed to be quasi-concave, then the choice of l e i s u r e , L , which maximizes u t i l i t y subject to the true (non-l inear) budget c o n s t r a i n t , w i l l a l so maximize u t i l i t y subject to the * l i n e a r i z e d constraint which passes through L ; the reverse i s not t r u e . Not ice , as w e l l , that the e f f ec t ive tax/subsidy is r e l a t i v e l y smaller for workers with incomes above maximum insurable earnings. The Unconstrained Labour-Supply Model / 27 4. F o r m a l M o d e l With th i s treatment of the non- l inear budget constra int in mind, the problem for couples in Model 1 can be represented more formally: Choose L 1 f L 2 , X in order to MAX u = U ( L , , L 2 , X ; A ) S .T . X+v iln+w2L2< V ^ T + W Z T + N L I N C T + N L I N C Z where: 1. p, the p r i c e of the composite commodity, X, has been normalized to equal 1 . 2. A i s a vector of demographic c h a r a c t e r i s t i c s . 3. wages and non-labour incomes take the appropriate values fol lowing the l i n e a r i z a t i o n procedure. The problem for s ingle i n d i v i d u a l s ! i s : Choose L , and X in order to MAX u=U(L,,X;A) S . T . X + w ^ ^ T + N L I N C , . It i s assumed that a l l households with the same demographic c h a r a c t e r i s t i c s have the same u t i l i t y funct ion . Household-specif ic di f ferences are incorporated only insofar fA household in which only one leisure-demand dec is ion i s made is termed ' s i n g l e , ' but a s ingle worker may have dependants. Households with non-working spouses are not ' s ing le ' households, since the decis ion not to work i s a leisure-demand d e c i s i o n . The Unconstrained Labour-Supply Model / 28 as the u t i l i t y functions are allowed to depend on demographic c h a r a c t e r i s t i c s . To empir ica l ly implement the model, i t i s assumed that household u t i l i t y functions for couples take the form u = B(X - 7 o ( A ) ) d - S i - ^ ) ( L , - 7 1 ( A ) ) * 1 ( L 2 - 7 2 ( A ) ) 0 2 . Maximizing u t i l i t y subject to the budget constra int X+w 1L 1+w 2L 2^w 1T+w 2T+NLINC 1+NLINC 2 gives the fol lowing l e i sure and commodity-demand equations for couples: w,L,=7, (A ) w 1+69 1 ( Y - 7 0 ( A ) - 7 , ( A ) w , - 7 2 ( A ) w2 ) w 2 L 2 = 7 2(A ) w 2+e 2 ( Y - 7 0(A ) - 7 1(A ) w 1 - 7 2(A ) w 2 ) X= 7O(A) + ( 1 - 0 1 - 6 9 2 ) ( Y - 7 0 ( A ) - 7 , ( A ) w ,-y 2 ( A ) w2 ) where Y is f u l l income (non-labour income+w^+WjT) . Making the normalization B » I/[ ( i - a , - ^ ) 0 " 0 1 ' * 2 * (e, ( 0 2 > * 2 ] , the i n d i r e c t u t i l i t y function becomes V ( w , , w 2 , Y ) = [ Y - 7 0 ( A ) - w l 7 l ( A ) - w 2 7 2 ( A ) ] / [ w / 1 w 2 e z ] . Since the household expenditure funct ion, e ( u , w 1 f w 2 ) = M I N{X+ w 1 L 1 + w 2 L 2 | U(X , L 2 , L 2 ;A ) > u } , w i l l equal f u l l income, Y, only i f V(w, ,w 2 ,Y)=u, 0 8 e ( U , w 1 , w 2 ) = 7 0(A ) + w 1 7 1(A ) + w 2 7 2(A ) + w 1 1 w 2 2 u . This is the expenditure function consistent with the l inear expenditure system (LES) which, despite l i m i t a t i o n s , seems the most su i table choice of funct ional form. The demand The Unconstrained Labour-Supply Model / 29 equations of the LES have the des irable property that they automatical ly sa t i s fy most of the r e s t r i c t i o n s required by the hypothesis of u t i l i t y maximization. ("Adding up," homogeneity, and symmetry are imposed; the remaining requirement of negative semi-definiteness of the Slutsky matrix i s easy to check: X>7 0,L^>7^ and O<0^ <1 i=1,2.) An add i t i ona l advantage is that the LES allows easy so lut ion for i n d i r e c t u t i l i t y functions as i s required for the welfare a n a l y s i s . One major disadvantage of the LES is that a l l goods are required to be subs t i tu tes . This i s not necessar i ly a problem when broad aggregates are modelled, but may be viewed as overly r e s t r i c t i v e with respect to the l e i sure time of husbands and wives (see Deaton and Muellbauer, 1980). A second major disadvantage is that Engel curves must be l i n e a r . C l e a r l y , the l inear expenditure system is h ighly r e s t r i c t i v e . However, i t s advantages in terms of ease of estimation and r e c o v e r a b i l i t y of the ind irec t u t i l i t y function make i t an appropriate choice for th i s a n a l y s i s . Demographic var iab les are incorporated in the l e i s u r e and commodity-demand equations by assuming that 7 .=£(7-0+7. . A . ) ; 1 <iM 1 1 J J i=0,1,2 indexes the gamma parameters; J=1,10 indexes 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 / 30 = 0 , i f not A2=WEST=1 i f residence is in the Western provinces; =0, i f not A3=CITY=1 i f residence is in a c i t y with population greater than 100,000; =0, i f not Aft=EFAM=number in the economic family (where economic family i s defined as a l l household members re lated to the head, inc luding the head) A5=YRSE1=years of education of head AG=YRSE2=years of education of wife A7=SEA1=1 i f husband works in a seasonal occupation ( f i s h i n g , hunting, fores try , cons truct ion) ; =0, i f notf A8=CYC1=1 i f husband works in a c y c l i c a l occupation (mining, product f a b r i c a t i o n , assembly and r e p a i r , transport equipment operat ion, materials handl ing); =0, i f not A9=PART2=1 i f wife works part time; =0, i f nott-A 1 0 = number of ch i ldren less than seven years of age. The analogous l e i sure and commodity-demand system for s ingle fFor s i m p l i c i t y , the spec ia l features of fishermen's benefits are ignored. t-To be e l i g i b l e for UI, part-t ime workers must work at least f i f t een hours per week for a gross wage of at least $63 (1981), 20 percent of maximum insurable earnings. Since the data do not provide information on hours worked, part-t ime workers are assumed e l i g i b l e for UI i f they pass the wage tes t . The Unconstrained Labour-Supply Model / 31 household heads i s WiLi=w , 7 i ( A ) + 0 , ( A ) ( Y - 7 o ( A ) - w l 7 l ( A ) ) X = 7 0 ( A ) + ( 1 - 0 , ( A ) ) ( Y - 7 o ( A ) - w l T l ( A ) ) where Y i s again f u l l income. The major di f ference between the demand system for s ingle i n d i v i d u a l s and the demand system for couples i s that demographic var iables are assumed to exert a l inear inf luence on both of the basic parameters of the u t i l i t y funct ion: n-!, (n°+?ijV'' * i 4 ( * i ° + * i j A j ) ; i=0,1 indexes the gamma parameters; j=1,8 indexes the demographic v a r i a b l e s , f For s ingle men, A,=ATLAN=1 i f residence is in the A t l a n t i c provinces; =0, i f not A2=WEST=1 i f residence is in the Western provinces; =0, i f not A3=CITY=1 i f residence is in a c i t y with population greater than 100,000; =0, i f not A„=EFAM=number in economic family (where economic family i s defined as a l l household members re lated to the head, inc luding the head) A5=YRSE=years of education of head A6=SEA=1 i f male head works in a seasonal occupation f i n order to keep the number of parameters to be estimated manageable in the case of couples, i t was not poss ib le to allow the theta parameters to depend on demographic c h a r a c t e r i s t i c s . The Unconstrained Labour-Supply Model / 32 ( f i s h i n g , fores try , cons truct ion) ; =0, i f not A7=CYC=1 i f male head works in a c y c l i c a l occupation (mining, product f a b r i c a t i o n , assembly and r e p a i r , transport equipment, materials handling); =0 i f not A 8= number of ch i ldren less than seven years . For s ingle women: A,=ATLAN=1 i f residence is in the A t l a n t i c provinces; =0, i f not A2=WEST=1 i f residence is in the Western provinces; =0, i f not A3=CITY=1 i f residence is in a c i t y with population greater than 100,000; =0, i f not Aa=EFAM=number in economic family (where economic family i s defined as a l l household members re la ted to the head, inc luding the head) A5=YRSE=years of education of head A6=PART=1 i f female head works part time; =0, i f not A 7= number of ch i ldren less than seven years . 5 . S t o c h a s t i c S p e c i f i c a t i o n o f t h e M o d e l In estimation form, the demand equations of the LES for couples are: (2.3) w ,L 1 /Y=7 1 (Ajv^ /Y+e, ( l-7 0 (A) /Y-7i (A)w 1 /Y~7 2 (A)w 2 /Y)+e , (2.4) w 2 L 2 / Y =7 2 ( A ) w 2 / Y +0 2 ( 1 - 7 o ( A ) / Y -7 , ( A ) w , / Y ~7 2 ( A ) w 2 / Y ) + e 2 The Unconstrained Labour-Supply Model / 33 (2.5) X/Y=7o(A) /Y+(1-0 , -0 2 ) (1 -7 0 (A) /Y-7 , (A)w, /Y-y 2 (A)w 2 /Y )+e 3 where the 7^ are l inear functions of demographic var iables as previously described, and the e^  have been added to represent 'random errors in o p t i m i z a t i o n . ' (Random events acc identa l i n j u r y , unexpected expenditures - may cause ind iv idua l s to deviate from the ir optimal employment/unemployment p lans . ) The e^  are assumed to follow a j o i n t l y normal d i s t r i b u t i o n with E(e^) = 0, i = 1,2,3, and covariance matrix Z 1 . The e^  are assumed independent and the covariance matrix i s assumed constant across observations (see Appendix 1 for d e t a i l s ) . For s ingle i n d i v i d u a l s , the demand equations of the LES in estimation form are: (2.6) w ,L, /Y=7, (A)w, /Y+0, (A) (1~7 0 (A) /Y- 7 , (A)w, /Y)+e , (2.7) X / Y = 7 0 ( A ) / Y + ( 1 - 0 , ( A ) ) ( 1 - 7 o ( A ) / Y - 7 , ( A ) w , / Y ) + e 2 where both 7^ and 0, are l inear functions of demographic var iables and the e^  follow a j o i n t l y normal d i s t r i b u t i o n with means of zero and covariance matrix Z 2 . a. Share Formulation Notice that the equations have been writ ten in share form ( i . e . , the value of leisure/consumption as a share of f u l l income, Y=w,T+w2T+NLINC,+NLINC2 for couples , or Y=w,T+NLINC, The Unconstrained Labour-Supply Model / 34 for s ingle household heads). Thus, when the s tochast ic terms are r e s t r i c t e d to ensure that i n d i v i d u a l budget constra ints are s a t i s f i e d , the assumption of a constant covariance matrix across households i s maintained. Suppose, instead, that the equations were not written in share form. Then, the error terms would be added to l e i s u r e and commodity demands d i r e c t l y , and s a t i s f a c t i o n of household budget constra ints would require that w, e ,+w 2e 2+e 3 = 0 . This has the further impl icat ion that w^var(e 1)+ w | v a r ( e 2 ) + v a r ( e 3 )=0 (taking the variance of both sides of the l inear r e s t r i c t i o n above). Given that wage rates d i f f e r , th i s is not consistent with the assumption of a constant covariance matrix for a l l households. This problem is avoided when the equations are written in share form s ince , in th i s case, the r e s t r i c t i o n on the disturbance terms i s just e ,+e 2 +e 3 =0. Writ ing the equations in expenditure form would also resolve th i s problem. An a d d i t i o n a l impl icat ion of the r e s t r i c t i o n on the error terms i s that one of the equations can be dropped without a f f ec t ing estimation r e s u l t s . Since the focus of th i s study is on l e i s u r e demand/labour supply, the commodity-demand equation is dropped. For households with a s ingle decision-maker, th i s leaves only one leisure-demand equation to estimate. The Unconstrained Labour-Supply Model / 35 b. Non-l inear Budget Constraint with Stochastic Model A f i r s t problem for estimation is that the simple ' l i n e a r i z a t i o n ' treatment of the piece-wise l inear budget constraint i s only v a l i d i f i t can be assumed that the errors are small enough to keep observed ( s ° = s ( w , 7 , 0 , A ) + e ) and optimal (s(w,7,0,A)) shares on the same segment of the budget cons tra in t . If th i s is not true , then using the wage rate which corresponds with the observed segment w i l l be incorrec t . Parameter estimates w i l l be biased and inconsistent as a resu l t of the c o r r e l a t i o n between wage rate and error term. A so lut ion to th i s problem, which involves a much more complicated approach to est imation, i s out l ined in Wales and Woodland (1979). The demand equations are , again, to be written in share form. But, for th i s procedure, l e i s u r e i s to be valued by the grossf (assumed exogenous) wage rate rather than by the wage rate corresponding with the observed budget segment. As before, the share formulation allows for the s a t i s f a c t i o n of household budget constraints without fThe 'gross' wage referred to here i s ac tua l ly net of tax, but gross of UI. That i s , since the focus of research is on UI, a t tent ion w i l l only be given to the proper treatment of th i s source of n o n - l i n e a r i t y . Proper treatment of n o n - l i n e a r i t i e s due to both the progressive Canadian income tax and the UI programme would become too complicated for th i s pro jec t . The Unconstrained Labour-Supply Model / 36 v i o l a t i n g the assumption of a constant covariance matrix across households. To solve the problem of endogeneity introduced by the s p e c i f i c a t i o n e r r o r , Wales and Woodland propose that for each i n d i v i d u a l and a vector of parameters, a check be made to see i f L ( W j ) i s located on segment j for each j . If there i s such a segment then e * = s ° - w L * ( w j ) / Y . If not, then a l l corners must be checked to f ind the one y i e l d i n g the highest u t i l i t y . This w i l l determine e = s ° - w L c / Y . The procedure must continue u n t i l the vector of parameters which maximizes the value of the l i k e l i h o o d function has been located. The one remaining complication in deal ing with a budget constra int which incorporates UI i s the existence of a small non-convex region. Wales and Woodland deal only with the case of piece-wise l i n e a r convex budget c o n s t r a i n t s . However, as pointed out by Hausman (1985), when there are non-convex regions in the budget c o n s t r a i n t , i t i s poss ible to have mult ip le tangencies. Thus, in the Wales and Woodland procedure described above, L^(w^) might be located on segment j for more than one j . Avoiding th i s problem involves checking which L j ( W j ) y i e l d s the highest u t i l i t y in cases of mult ip le 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 corner . The highest The Unconstrained Labour-Supply Model / 37 u t i l i t y determines L (w.j). A l l of t h i s , f i n a l l y , describes the correct approach to estimation when the budget constraint i s piece-wise l inear and contains a non-convex region and when the error term is intended to represent ' errors in o p t i m i z a t i o n . ' A number of papers (see, for example, Burt less and Hausman, 1978; K i l l i n g s w o r t h , 1983; M o f f i t t and Nicholson, 1982; Yatchew, 1985; Zabalza, 1983) have dealt with the correct approach to estimation when the budget constraint is piece-wise l i n e a r , but the stochast ic component i s interpreted as random v a r i a t i o n s in taste . As pointed out by Mof f i t t (1985) the in terpre ta t ion of the error term has a major impact on the model. The two cases described above are quite d i f f e r e n t . The ' errors in opt imizat ion' model says that ind iv idua l s with the same wage and demographic c h a r a c t e r i s t i c s make the same optimal choices , but we do not observe these choices as a resu l t of errors in carry ing them out. Thus, we do not necessar i ly observe u t i l i t y - m a x i m i z i n g segments. In the random tastes model, on the other hand, we do observe u t i l i t y - m a x i m i z i n g segments, but these choices , because they depend on stochast ic preferences, are endogenous. In the ' errors in opt imizat ion' model, any value of l e i sure may be observed. In the 'random tastes' model, c l u s t e r i n g at kink points i s expected i f the budget constra int is convex. If i t The Unconstrained Labour-Supply Model / 38 i s non-convex, and i f preferences are regu lar , cer ta in ranges for the value of l e i sure must be ruled out . The endogeneity problem in the 'random tastes ' model is not the same as the endogeneity problem in the ' errors in opt imizat ion' model, and must be treated in a d i f f erent way. The correct approach to estimation is a genera l i za t ion of models in which the d i screte and continuous choices of p a r t i c i p a t i o n and hours are modelled simultaneously (see M o f f i t t , 1985 for an exposit ion of appropriate techniques of estimation given d i f f erent interpretat ions of the stochast ic component). An ideal model would incorporate both sorts of errors (see J . L . Arrufa t and A. Zabalza (1986) for the estimation of such a model). However, th i s i s beyond the scope of th i s ana lys i s , which w i l l incorporate only one disturbance term, to be interpreted as errors in opt imizat ion . Var ia t ions in taste are handled d e t e r m i n i s t i c a l l y by al lowing the 7 and 6 parameters to depend on demographic c h a r a c t e r i s t i c s . c. Truncation due to Non-part ic ipat ion A second estimation problem is easier to t r e a t . Since Model 1 assumes that ind iv idua l s are fol lowing optimal The Unconstrained Labour-Supply Model / 39 employment/unemployment patterns , i t assumes that they are in a pos i t ion of ' equ i l ibr ium' with respect to the UI programme. That i s , Model 1 assumes that weeks of unemployment match weeks of e n t i t l e d benef i t . For estimation of Model 1, anyone not sa t i s fy ing th i s requirement must be excluded from the sample. In p a r t i c u l a r , th i s excludes anyone located on segment one of the budget constraint (see Figures 2.1 and 2.2) since such ind iv idua l s are unemployed for many weeks but are not e l i g i b l e for any weeks of benef i t . This cannot be a pos i t ion of ' equ i l ibr ium' in the sense that weeks of e n t i t l e d benefit match weeks of unemployment. Indiv iduals located on segment four of the budget constra int (see Figures 2.1 and 2.2) , on the other hand, can be in a pos i t ion of e q u i l i b r i u m . People employed for f i f ty - two weeks of the year are not ' e l i g i b l e ' for any benefits since the i r plans do not allow s u f f i c i e n t weeks of unemployment to f u l f i l l the two-week waiting period requirement. This can be a pos i t ion of equi l ibr ium with respect to UI since ind iv idua l s on segment four are neither unemployed nor e n t i t l e d to receive any benef i t s . (This conclusion is only v a l i d in the context of the optimal annual p l a n . Otherwise, an i n d i v i d u a l who worked f i f ty- two weeks la s t year would c e r t a i n l y be e l i g i b l e to receive benefits th i s year. Model 1 abstracts from long-term planning.) The Unconstrained Labour-Supply Model / 40 Since the exclusion of ' d i s e q u i l i b r i u m ' observations means that the sample i s truncated at the minimum weeks required to gain e l i g i b i l i t y to UI, a p o t e n t i a l sample s e l e c t i v i t y b ias , analogous to the bias caused by excluding non-part i c ipants , i s introduced. f For s ing le i n d i v i d u a l s , observations are only included in the sample i f s ? < s . M I N s ( w i , 7 , 0 , A ) + e i < S i M I N O R r e . ^ s ^ I N - s ( w i r 7 l f 9 r A ) where: 1. e^  follows a normal d i s t r i b u t i o n with mean zero and variance a2 2. s^ I N is the l e i s u r e share for an i n d i v i d u a l who works just enough weeks to gain e l i g i b i l i t y to UI . Est imating a model which ignores the truncat ion of the error d i s t r i b u t i o n w i l l y i e l d biased parameter estimates. Truncation means that the expectation of the error term is non-zero: E(e. ) = E ( e i l e i <s .^-s (w i , 7 , 0 , A) ) = f (*)/FU) t i n th i s model, the dec i s ion to p a r t i c i p a t e and the decis ion to work enough weeks to be e l i g i b l e for UI are treated as a s ingle d e c i s i o n . The Unconstrained Labour-Supply Model / 41 where \^=s^ I N-s i (w i , 7, 6, A) (see Johnson and Kotz , 1970, pp 81-87). For couples, the truncation problem is analogous. Households are only included in the sample i f both husband and wife work enough weeks to be e l i g i b l e for UI: B 0<c MIN , S t ^ s , . and - 0K_ MIN Or, e i ^ s , f N - s , (w.,7,e fA) and e 2 i ^ s 2 ^ I N - s 2 (w i, 7,e ,A) where e 1 f e 2 follow a b i v a r i a t e normal d i s t r i b u t i o n with E(ej)=0 (j=1,2) and covariance matrix Z 3 (see Appendix 1). Again, ignoring the truncat ion of the error d i s t r i b u t i o n s w i l l resu l t in biased parameter estimates since the expectations of the error terms w i l l no longer equal zero. The problem can be overcome through the app l i ca t ion of a technique proposed by Wales and Woodland (1980) in the context of female n o n - p a r t i c i p a t i o n . In the der ivat ion of the l i k e l i h o o d funct ion, household dens i t i e s can be written as condi t iona l on e^ < s ^ I N - s ( w . , 7 , 6 , A ) for s ingle i n d i v i d u a l s , or on both e 1^<s,^ I I N - s , (w^,7,0 ,A) and e 2 ^ < s 2 M I N - s 2 ( w ^ , 7 , 0 , A ) in the case of couples . f fAmemiya (1973) has demonstrated the asymptotic normality and e f f i c i ency of the maximum l i k e l i h o o d estimators for th i s The Unconstrained Labour-Supply Model / 42 d . Censoring due to F u l l - y e a r Workers The f i n a l major problem for the estimation of Model 1 ar i ses as a resu l t of speci fying l e i sure demand/labour supply in terms of annual weeks: weeks (of l e i sure or of labour) must be no less than zero and no greater than f i f t y - t w o . The r e s t r i c t i o n that weeks of l e i s u r e must not exceed f i f ty- two has already been avoided by excluding anyone i n e l i g i b l e for UI. However, the r e s t r i c t i o n that weeks of l e i sure be non-negative (weeks of work be no greater than 52) remains a problem. Most studies of labour supply avoid th i s d i f f i c u l t y by spec i fy ing the l a b o u r / l e i s u r e choice in terms of hours. However, in the context of a model of UI , t h i s i s not appropriate s ince working over-time hours in a week w i l l not af fect e l i g i b i l i t y for UI benef i t s . Thus, the leisure-demand choice must remain a choice of weeks and the l imi ted dependent var iab l e problem must be treated . Correc t ly s p e c i f i e d , the model becomes s ° = s ( w , 7 , 0 , A ) + e ; s ° > O , or , e>-s(w,7,6 ,A) . s°=0 ; s°<0, o r , e< - s (w i ,7 ,0 ,A) . Ignoring the r e s t r i c t i o n s on the error d i s t r i b u t i o n w i l l , again, lead to biased parameter estimates, p a r t i c u l a r l y s ince a large number of observations are located at s°=0 t (cont 'd) model Twith respect to included observat ions) . Thus, the covariance matrix for the parameters can be approximated by the inverse of the negative Hessian matrix. The Unconstrained Labour-Supply Model / 43 ( i . e . , at f i f ty- two weeks of work). The problem i s straightforward to t rea t , however, since i t i s of the c l a s s i c ' T o b i t ' var ie ty (see Tobin, l958 and Maddala, 1983). e. Derivat ion of the L ike l ihood Functions In summary, i n d i v i d u a l l e i s u r e demand/labour supply decis ions have three components: 1. the dec is ion to p a r t i c i p a t e 2. the dec is ion to work f u l l - y e a r 3. the choice of weeks of work/ le i sure Decisions (1) and (2) are ' threshold ' dec i s ions . That i s , an ind iv idua l must f i r s t decide whether or not to p a r t i c i p a t e in the labour force (which for Model 1, means he must work enough weeks to be e l i g i b l e for UI) . Then, he must decide 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 , i t i s only i f he decides to work just part of the year that an ind iv idua l must choose weeks of l e i s u r e (labour supply) . The three decis ions together determine leisure-demand ( labour-supply) , but i t is only in the event of a part-year choice that the t h i r d (conventional labour-supply) dec i s ion must be made. For a s ingle i n d i v i d u a l , the f i n a l form of the s tochast ic model i s : The Unconstrained Labour-Supply Model / 44 (2.8) s ° = 7 , ( A j w ^ Y + G , ( A ) ( 1 - 7 O ( A ) / Y - 7 i ( A ) w , / Y ) +e;0<RHS<1 (2.9) s°=0;RHS<0 (2.10) s ° = s M I N ; R H S > s M I N where s M I N =the l e i sure share for an ind iv idua l who works the minimum number of weeks required to qua l i fy for UI . The model i s estimated by maximum l i k e l i h o o d . For s ingle men and women, taking the truncat ion and censoring d i f f i c u l t i e s into account, the l i k e l i h o o d function becomes L = { n m ; " S ° f (e . )de . /P1 .} {n n f ( e - ) /P1 . } i=1 - « i i i i=m+1 1 1 where: s M I N - s ( ) P1-=J f(e-)de- ( i . e . , the p r o b a b i l i t y of working at least the minimum number of weeks to qua l i fy for UI) . the f i r s t m workers are' observed to work f i f ty- two weeks. For couples, the f i n a l form of the demand system i s : (2.11) S?=7i (Ajw^Y+e, ( 1-7o (A) /Y-7 , (A)w, /Y-7 2 (A) w 2 /Y) +e; 0<RHS< 1 (2.12) s?=0;RHS<0 (2.13) S ? = S M I N ; R H S > s M I N And, (2.14) S?=7 2 (A)w 2 /Y+0 2 (1-7 0 (A) /Y- 7 1 (A)w 1 /Y- 7 2 (A)W 2 /Y)+e;0<RHS<1 The Unconstrained Labour-Supply Model / 45 (2.15) s°=0:RHS<0 (2.16) S 2=S ;RHS>s This model i s a l so estimated by maximum l i k e l i h o o d . Here, the der ivat ion of the l i k e l i h o o d function is more complicated. Four household s i tuat ions are poss ib le : (1) Both i n d i v i d u a l s work f i f ty - two weeks ( i = 1 , . . . K ) : M- j " 3 ' 0 j " 5 1 0 f ( e | , e?)deMe ? / P 2 . X — co — oo X X X X X (2) Wife works f i f ty - two weeks, husband works less than f i f ty - two weeks ( i = K + 1 , . . . L ) : X? = ; " S 2 ° f (e | , e?)de?/P2. X —oo X X X X (3) Husband works f i f ty - two weeks, wife works less than f i f ty - two weeks (i=L+1,. . . M ) : Xf = ; " S l ( ) f ( e j , e ? ) d e | / P 2 . X — oo X X X X (4) Both i n d i v i d u a l s work less than f i f ty - two weeks (i=M+1,. . .N) : X? = f ( e J f e ? ) / P 2 . SMIN_ ( ) -MIN ( ) where P2.= J J" 1 f (e J , e ?) de Me?. 1 —OO —CD 1 1 1 1 The l i k e l i h o o d funct ion for couples (Model 1) i s thus: L=n xm x?n x?n x?t i i i li-.Kii l i ' M I 1 fSee Appendix 1 for a discuss ion of the s i m p l i f i c a t i o n of the double in tegra l s for est imation. I I I . THE CONSTRAINED LABOUR-SUPPLY MODEL In Chapter Three I develop the constrained model of household behaviour. The idea of 'constrained' labour supply i s motivated in sect ion 1 through references to t h e o r e t i c a l models; the empir ica l s ign i f i cance of the concept i s i l l u s t r a t e d in section 2 through a survey of the l i t e r a t u r e on ra t ion ing models. Section 3 derives rationed labour-supply functions for couples and sets out the estimating equations for both couples and s ingle household heads. Section 4 derives the l i k e l i h o o d functions for the estimation of the constrained models. 1. The Basic Model of Household Behaviour The unconstrained labour-supply model (Model 1) assumes that observed weeks of unemployment (employment) are the outcome of i n d i v i d u a l u t i l i t y -max imiz ing choices , given the existence of UI . However, i t can be argued that th is assumption i s u n r e a l i s t i c for periods of high unemployment when demand-side constra ints may inter fere with optimal household plans . Such constra ints may take quite d i f f erent forms: 1. A l a y - o f f may exceed an i n d i v i d u a l ' s desired quantity of unemployment, but he or she may nonetheless prefer to 46 The Constrained Labour-Supply Model / 47 wait for r e c a l l rather than to search for another job. 2. No job of fers may be forthcoming. Constraints of the f i r s t var i e ty may be explained by models in which unemployment i s the outcome of long-run, i m p l i c i t contracts between r i sk-averse workers and r i s k - n e u t r a l firms (Azar iad i s , 1975; B a i l y , 1977). In these models, optimal r i s k - s h a r i n g involves f ixed wage, var iab le employment contracts . Knowing the r i sk of unemployment at d i f f erent f irms, workers choose the contract o f f er ing the highest expected value. While the r i sk of unemployment is thus taken into account ex ante, th i s does not mean that workers are not constrained i f they f ind themselves l a i d - o f f , ex post . Yet, since the chosen contract gave the highest long-run expected u t i l i t y , the worker's optimal choice , given the cons tra in t , i s to wait for 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 d i f f e r e n t i a l s provide another explanation for the existence of 'constrained' unemployment. Workers choose occupations with a high r i s k of unemployment i f a compensating., wage means that the expected u t i l i t y from that occupation exceeds the expected u t i l i t y from a l l other occuptions. Again , though, i t i s only the r i sk of unemployment which is taken into account ex ante. Real ized unemployment can s t i l l be perceived as a cons tra in t , ex post . t The Constrained Labour-Supply Model / 48 These f i r s t two models refer p a r t i c u l a r l y to l a y - o f f unemployment. The 'eff ic iency-wage' hypothesis (Shapiro and S t i g l i t z , 1984) provides an explanation for the existence of 'constrained' unemployment which is not t i e d to the context of l a y - o f f s . In th i s model, poor monitoring c a p a b i l i t i e s mean that workers are paid a wage premium to ensure a high l e v e l of e f f o r t . Paying workers a wage higher than the ir marginal products means that employment i s r e s t r i c t e d . At the p r e v a i l i n g wage rate , some workers who would prefer to work remain unemployed. Again, though, th i s does not necessar i ly mean that employment opportunit ies at a lower wage are unavailable elsewhere. I f , for example, the efficiency-wage hypothesis i s most relevant for workers in the 'primary sector' (Doeringer and P iore , 1971) where e f for t may be d i f f i c u l t to monitor, then 'secondary-sector' jobs may be ava i lab le for unemployed primary workers (Jones, 1985). But, waiting for a primary-sector job may have a higher expected value than accepting a low-wage secondary-sector job. Moving out of the primary sector may make return more d i f f i c u l t i f , for example, a low wage in a worker's previous job is used as a screen for low fNo attempt is made to model such decision-making processes. These t h e o r e t i c a l models are discussed merely to point out poss ible explanations for the existence of cons tra in t s , which, i f v a l i d , have impl icat ions for est imation. The Constrained Labour-Supply Model / 49 product iv i ty (Weiss, 1980). Again, unemployment may in some sense be 'vo luntary , ' but the observed wage does not correspond with the u t i l i t y - m a x i m i z i n g choice of employment/unemployment. Constraints of the second var i e ty are quite d i f f e r e n t . An i n d i v i d u a l who receives no job of fers can more convincingly be termed ' i n v o l u n t a r i l y ' unemployed. And, such a scenario may not be u n r e a l i s t i c . Abraham (1983) estimates that there were f ive unemployed workers for every job vacancy in the United States in the late 1970s. In the Canadian context, the idea that job offers may be scarce seems p laus ib le at the regional i f not at the nat ional l e v e l . Since both Model 1 and Model 2 take region of residence as given, a regional shortage of job offers w i l l mean that ind iv idua l s face labour-market cons tra in t s . This view of unemployment as a constra int on labour supply i s consistent with the pos i t i on taken by many s o c i a l psycholog is t s . In a recent survey, Kelv in and J a r r e t t (1985) report how unemployment i s viewed as a process of psychological 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 react to unemployment with shock. Then, he or she w i l l o p t i m i s t i c a l l y begin act ive job search. If no job i s located , anxiety and pessimism w i l l fo l low. Eventual ly , the The Constrained Labour-Supply Model / 50 unemployed ind iv idua l w i l l become apathetic and resigned to h i s or her new s i t u a t i o n . Evidence (see Kelv in and J a r r e t t ) suggests that most unemployed ind iv idua l s eventual ly pass through a l l of these stages. Differences of personal i ty or circumstance ( e . g . , a l t ernat ive sources of income) w i l l a f fect only the speed of t r a n s i t i o n . From th i s perspect ive , unemployment i s not the outcome of i n d i v i d u a l choice . It i s something which happens t £ an i n d i v i d u a l with negative consequences for his perception of se l f and for his re la t ionsh ips with other people (see also Osberg, 1986). A constraint of the second type may be more binding than a constraint of the f i r s t type, but the basic problem for estimation is the same. If constra ints ex i s t , observed weeks of unemployment and observed weekly wage rate are not a u t i l i t y -max imiz ing combination; labour-supply functions s traightforwardly estimated using observed data w i l l be biased. 2 . S u r v e y o f P r e v i o u s S t u d i e s o f C o n s t r a i n t s Empir ica l work to date supports the idea that constra ints ex i s t in the labour market. The e a r l i e s t such evidence can be found in studies of labour supply such as Rea (1974), DaVanzo et a l . (1976) and Wales and Woodland (1976). Rea The Constrained Labour-Supply Model / 51 (1974) f inds very large negative res iduals for unemployed workers suggesting that des ired labour supply i s greater than observed ( i . e . , that unemployed workers are constrained) . Da Vanzo et a l . and Wales and Woodland f ind that parameters estimated from a f u l l sample of both employed and unemployed workers d i f f e r from parameters estimated from a sub-sample of employed workers only . Of course, these resul t s can be explained i f unemployed workers have tastes which d i f f e r systematical ly from the tastes of fully-employed workers. 'Tastes' would then account for the negative res iduals and for the biased parameter estimates s ince , under th i s assumption, e l iminat ing unemployed workers would generate a sample s e l e c t i v i t y problem. I f , however, ' tastes ' are not the f u l l explanation, then these studies are at least not inconsistent with the existence of constra ints in the labour market. Ashenfelter (1980) uses t ime-series data (1930-67) to estimate an aggregate labour-supply/commodity-demand system taking account of the poss ib le existence of constra ints on labour supply. Assuming that the preferences of both constrained and unconstrained workers can be represented by a common Stone-Geary u t i l i t y funct ion, he derives labour-supply and commodity-demand equations for the two groups. For the unemployed workers, the quanti ty constra int The Constrained Labour-Supply Model / 52 i s incorporated by treat ing i t as a ' r a t i o n ' on labour supply. For his estimating equations, Ashenfelter uses weighted averages of constrained and unconstrained equations, where the weights used are the appropriate p r o b a b i l i t i e s of being constrained or not constrained, proxied by the observed unemployment rate (and one minus the unemployment r a t e ) . While the model i s very simple and there are problems with using the observed unemployment rate as a proxy for the p r o b a b i l i t y of being constrained, the f inding that th i s s i g n i f i c a n t l y increases the value of the l i k e l i h o o d function for the system leads Ashenfelter to conclude that labour-supply constra ints may be empir i ca l ly important. Ham (1982) e x p l i c i t l y tests for the existence of labour-supply constra ints among prime-aged men by comparing ful l -sample estimates of a l i n e a r labour-supply equation with estimates based only on ful ly-employed workers, but corrected for poss ib le sample s e l e c t i v i t y bias using a general izat ion of the Heckman (1979) procedure. The two sets of estimates should be the same i f there are no labour-market cons tra in t s , but should d i f f e r in predictable ways i f such constra ints e x i s t . Ham finds evidence in support of the existence of constra ints and concludes that ignoring th i s p o s s i b i l i t y w i l l r e su l t in biased parameter The Constrained Labour-Supply Model / 53 estimates on, in p a r t i c u l a r , demographic var iab les such as race, education and number of ch i ldren which af fect the p r o b a b i l i t y of being unemployed. Blunde l l and Walker (1982) estimate a system of household l e i sure and commodity demands which allows for the p o s s i b i l i t y that a l l of the men but none of the women face i n s t i t u t i o n a l constra ints on labour supply. Unlike Ham, Blunde l l and Walker maintain a d i rec t l i n k between the theory of u t i l i t y maximization and t h e i r estimating equations by choosing a household expenditure function (a genera l izat ion of the Gorman polar form proposed by Muellbauer, 1981) and der iv ing the corresponding demand equations. As we l l , the ir model has the advantage of taking into account the interact ions among household l e i s u r e demand and consumption dec i s ions . The existence of a constraint on a husband's l e i s u r e , for example, might have s i g n i f i c a n t impl icat ions for his wife's l e i s u r e demand as well as for household consumption. The disadvantages of Blundel l and Walker's approach are that t h e i r model does not provide a test for the existence of constra ints and that the ir data (a sample of two-adult manual worker fami l ies from the U.K. Family Expenditure Survey of 1974) does not give sample separation information ( i . e . , information about which workers perceive themselves to be constra ined) . Hence, the The Constrained Labour-Supply Model / 54 demand system is f i r s t estimated assuming no rat ions are operat ive , then a corresponding demand system, derived from the same expenditure function but incorporat ing quanti ty constra ints (the technique used for th i s i s a t t r i b u t a b l e to Neary and Roberts, 1980) i s estimated assuming a l l men are constrained. In both cases, parameter estimates are p l a u s i b l e , but nothing can be sa id about which i s pre ferred . (On the other hand, nothing here suggests that the existence of constra ints i s implaus ib le . ) Ryan (1983) estimates a demand system using an approach s imi lar to that of B lunde l l and Walker and using the same Univers i ty of Michigan PSID data as was used by Ham. This gives Ryan the advantage of both sample separation information and a household model consistent with u t i l i t y maximization. Choosing a Stone-Geary form for the d i r e c t u t i l i t y funct ion , he derives l e i s u r e and commodity demand equations for both constrained and unconstrained households. The ent ire system i s then estimated by maximum l i k e l i h o o d using a genera l izat ion of the Tobit approach to truncated samples. (For rationed i n d i v i d u a l s , we know only that des ired hours are greater than observed hours; for these people the sample i s ' truncated' at observed hours.) With th i s approach, no information i s los t through the exclusion of constrained workers, although resul t s may be biased i f The Constrained Labour-Supply Model / 55 i n d i v i d u a l s l i e about whether or not they are constrained. In addi t ion to h i s f u l l model, Ryan estimates a model excluding rationed households and a model inc luding a l l observations but ignoring cons tra in t s . While estimated parameters c l e a r l y d i f f e r , no systematic pattern appears to indicate the nature of poss ible bias introduced by ignoring c o n s t r a i n t s . Moreover, the three cases are non-nested and the n o n - l i n e a r i t y of the equations and the truncation of the error d i s t r i b u t i o n make i t impossible to conduct non-nested tests of a l t e r n a t i v e models. So, Ryan i s unable to test the hypothesis that ra t ion ing e x i s t s . Again, though, h i s work suggests that empir i ca l re su l t s are sens i t ive to assumptions made about the existence of cons tra in t s . In a l l of the c r o s s - s e c t i o n a l studies discussed, i t i s poss ib le that observed di f ferences between fully-employed and unemployed workers are merely the resul t of d i f ferences in t a s t e . Ham (1984) reports an attempt (1980) to contro l for taste d i f ferences through the estimation of a f ixed-e f fec t s model, taking advantage of the long i tud ina l nature of the PSID data (1967-71). Incorporating f i x e d - e f f e c t s , labour-supply equations for fully-employed and constrained workers can be represented as (3.1) L S i J - P ' X . ^ a . + e ^ (3.2) L S . ° ^ ' X i t + v u i t + a . + e i t T h e C o n s t r a i n e d L a b o u r - S u p p l y M o d e l / 5 6 w h e r e r e p r e s e n t s a p e r m a n e n t t a s t e f a c t o r a f f e c t i n g i ' s d e s i r e d l a b o u r s u p p l y , X ^ t i s a v e c t o r o f e x o g e n o u s v a r i a b l e s i n c l u d i n g t h e w a g e r a t e , 0 i s a v e c t o r o f c o e f f i c i e n t s , u ^ f c r e p r e s e n t s u n e m p l o y m e n t w h i c h i s n o t a l a b o u r - s u p p l y c h o i c e a n d e^ f c i s a r a n d o m e r r o r t e r m . A n e x a m i n a t i o n o f t h e r e s i d u a l s f r o m t h e e s t i m a t i o n o f l a b o u r - s u p p l y f u n c t i o n s o f t h i s v a r i e t y r e v e a l s t h a t e v e n a f t e r c o n t r o l l i n g f o r p e r m a n e n t d i f f e r e n c e s i n t a s t e , t h e r e s i d u a l s f o r u n e m p l o y e d w o r k e r s a r e s i g n i f i c a n t l y n e g a t i v e . A g a i n , t h i s s u g g e s t s t h e e x i s t e n c e o f c o n s t r a i n t s . Ham ( 1 9 8 5 ) p o i n t s o u t t h a t s u c h e v i d e n c e i n f a v o u r o f c o n s t r a i n t s c a n s t i l l b e q u e s t i o n e d o n t h e g r o u n d s t h a t i n t e r t e m p o r a l f a c t o r s a n d u n c e r t a i n t y h a v e b e e n i g n o r e d a s w e l l a s o n t h e g r o u n d s t h a t u n e m p l o y e d w o r k e r s m a y h a v e h i g h t r a n s i t o r y t a s t e s f o r l e i s u r e i n y e a r s i n w h i c h t h e y e x p e r i e n c e u n e m p l o y m e n t . H e n c e , h e a t t e m p t s t o t a k e t h e s e t h r e e a d d i t i o n a l f a c t o r s i n t o a c c o u n t . U s i n g t h e f r a m e w o r k o f M a C u r d y ( 1 9 8 1 ) , Ham d e r i v e s t h e i n t e r t e m p o r a l e q u i v a l e n t s o f e q u a t i o n s ( 3 . 1 ) a n d ( 3 . 2 ) . I n f i r s t d i f f e r e n c e f o r m , t h e s e a r e ( 3 . 3 ) A L S i * = a + 5 A l n w i t + A e i t ( 3 . 4 ) A L S i ° = a + 6 A l n w i t + p A u i t + A e i t w h e r e : The Constrained Labour-Supply Model / 5 7 e f^c represents measurement error and t r a n s i t o r y taste di f ferences ' f ixed e f fec t s ' and demographic var iables disappear in the f i r s t di f ference form 5 can be interpreted as an ' intertemporal subs t i tu t ion ' e l a s t i c i t y . For est imation, Ham includes A u ^ t d i r e c t l y as a proxy for the large negative res iduals ant i c ipated i f a worker is constrained during periods of unemployment. If the c o e f f i c i e n t on A u ^ t is not s i g n i f i c a n t l y d i f f eren t from zero, the constraint hypothesis can be re jec ted . The var iab le Au^ f c i s approximated in two ways: 1 . the f i r s t d i f ference in a dummy var iable which is set equal to one i f an i n d i v i d u a l i s unemployed in year t , equal to zero, otherwise 2 . the f i r s t di f ference in the observed unemployment rate . In both cases, the A u ^ t proxies as well as Alnw^ f c are treated as endogenous through an instrumental var iables procedure (where the instruments are human c a p i t a l v a r i a b l e s , lagged f i r s t di f ferences in occupat ional , reg iona l , and i n d u s t r i a l unemployment rates and interact ions among them). To incorporate uncertainty in t h i s model, Ham follows the The Constrained Labour-Supply Model / 58 work of MaCurdy (1982, 1983), A l t o n j i (1984) and Browning, Deaton and I r i s h (1985). It i s now assumed that in each period labour supply and consumption are chosen to sa t i s fy the condi t ion X i t _ l = ( l + r ) / d + p ) E t _ 1 ( X u ) where: 1. X^ t=the marginal u t i l i t y of wealth in period t 2. r=the rea l interest rate 3. p=the rate of time preference 4. E t _ 1 (X^ f c )=the expectation of X ^ t given information a v a i l a b l e at t - 1 . This condi t ion is re -wri t ten as (3.5) X u = ( 1+p)/(l+r) X i t _ 1 ( l + u . t ) where u^ t= a forecast e r r o r . Ham assumes that expectations are formed r a t i o n a l l y so that u ^ t has a zero mean, condi t iona l on information ava i lab le at t - 1 . Taking logs: l n X i t = p - r + b + l n X i t _ 1 +v. t where 1. b=the population mean of l n ( l + u ^ ) 2. v^ t has zero mean condi t iona l on information ava i lab le at t - 1 . F i n a l l y , with the incorporat ion of uncerta inty , (3.4) becomes (3.6) A L S * t = a+6Alnw i t -*>Au i t +Ae i t +v i f c The Constrained Labour-Supply Model / 59 where a=p-r+b Notice that A u ^ t may be p o s i t i v e l y corre la ted with v^ t i f unemployment causes an increase in the marginal u t i l i t y of wealth. Ham estimates equation 3.6 by 2SLS using PSID data on 473 continuously-married prime-aged men from 1971 to 1979 and finds a small pos i t ive intertemporal subs t i tu t ion e l a s t i c i t y , but a lso f inds very s i g n i f i c a n t negative coe f f i c i en t s on the A u ^ t proxy v a r i a b l e s . Hence, even when accounting for l i f e - c y c l e labour-supply behaviour, uncerta inty , and the p o s s i b i l i t y of high t r a n s i t o r y tastes for l e i sure when unemployed, Ham finds evidence for the existence of labour-supply cons tra in t s . 3 . The Formal Model of Con s t r a i n e d Behaviour The constrained labour-supply model (Model 2) allows for the p o s s i b i l i t y that demand-side constra ints in ter fere with labour-supply choices . As in Model 1, households are assumed to choose annual weeks of employment/unemployment and consumption of a composite commodity in order to maximize u t i l i t y subject to a budget constraint which incorporates UI. However, constra ints may in ter fere with the r e a l i z a t i o n of these p lans . A worker may plan to be unemployed for ten The Constrained Labour-Supply Model / 60 -weeks each year, but may f ind himself or herse l f unemployed for twenty. To the extent that t h i s addi t iona l unemployment i s perceived as a cons tra in t , other household decis ions w i l l be a f fec ted . This creates spec ia l d i f f i c u l t i e s in the case of couples. Working from the dual side of the problem, the expenditure function for an unconstrained couple can be represented as: (3.7) e(u,w,,w 2)=MIN{w,L 1+ w 2 L 2 +X;U(L, ,L 2 ,X)>u} For a constrained couple (suppose, for example, that the husband is constrained) , the expenditure function i s : (3.8) e (u ,w, ,w 2 ,Z , )= MIN{w,Z 1 +w 2 L 2 +X;U(Z 1 ,L 2 ,X) >u} where Z^husband's constrained weeks of l e i sure ( L ^ Z , ) =w 1 Z,+MIN{w 2 L 2 +X;U(Z 1 ,L 2 ,X) >u} =w lZ,+)//(u,Z 1,w 2) (3.9) 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 the constrained and unconstrained expenditure funct ions , use can be made of the concept of a ' v i r t u a l ' wage (Rothbarth, 1941), the wage at which an unconstrained household w i l l choose Z, weeks of unemployment for worker one. Constrained and unconstrained expenditure functions are equivalent when evaluated at the * * * ~ * v i r t u a l wage, w : e (u, w , , w2) =w , Z , +uV(u, Z , , w2) =e (u, w , ,w 2 , Z , ) . Thus, using (3.9) , e (u ,w 1 ,w 2 )=w 1 Z,+e(u ,w 1 ,w 2 ,Z 1 ) -w 1 Z 1 The Constrained Labour-Supply Model / 61 Or, e (u ,w 1 ,w 2,Z 1 )=e (u ,w 1 ,w 2 )+ (w 1 -w 1)Z, (the des ired re la t i onsh ip between constrained and unconstrained expenditure funct ions) . This approach is taken from Deaton (1981). Analogously, i f the second worker is constrained ic ic e(u,w, ,w 2,Z 2 )=e(u, w,,w 2 )+(w 2 -w 2 ) Z 2 From these constrained expenditure funct ions , ' e f f e c t i v e ' / ' q u a n t i t y - c o n s t r a i n e d ' / ' r a t i o n e d ' f demand equations can be derived through an appl i ca t ion of H o t e l l i n g ' s lemma and a ser ies of subs t i tu t ions : If L ? = Z 1 ? w 2 n 2/Y= 7 2 w 2/Y+ 0 2 / O - 0 1 ) { i - 7 0 / y - w 1 z 1 / y - w 2 7 2 / y } . If L ? = Z 2 ; W,E,/Y= 7 1W 1/Y+ 0 1 / ( 1 - 0 2 ) { 1 - 7OA-W 2Z 2/Y-W 1 7 1 /Y} where Y= f u l l income as before. The important feature of these equations i s that they are u l t imate ly derived from the same expenditure ( u t i l i t y ) function as the unconstrained demand equations so that underlying preferences are the same for a l l households. The only di f ference between a constrained and an unconstrained household is the imposition of the exogenous quantity constra int on the constrained households. Thus, the constrained and unconstrained demand equations are sometimes referred to as a 'matched' system. fThe labour-supply function of a man or woman with a spouse who i s constrained w i l l be re ferred to as a ' rat ioned' labour-supply (leisure-demand) funct ion; a labour-supply (leisure-demand) function condi t iona l on a spouse's quantity cons tra in t . The Constrained Labour-Supply Model / 62 At es t imat ion, only one set of preference parameters w i l l be obtained. The Model 2 estimating equations for couples are given by 2.3, 2.4 and 3.10 and 3.11: (3.10) w i n i / Y = T l w l / Y + 0 1 / ( 1-0 2) ( l - T o A - w ^ / Y - w ^ / Y j + U ! (3.11) w 2 n 2 / Y = 7 2 w 2 / Y + 0 2 / ( 1-t?, ) { 1 - 7 o / Y - W 1 Z 1 / Y - W 2 7 2 / Y } + U 2 where e 1 , e 2 , u 1 , u 2 are j o i n t l y , normally d i s t r i b u t e d with E(e^)=0, E(u^)=0, i=1,2, and variance Z" (see Appendix 2) and where the gamma parameters are no longer assumed to be functions of demographic v a r i a b l e s . For s ing le i n d i v i d u a l s , the est imating equation i s the same as in the unconstrained model (2.6) except that the gamma and theta parameters are no longer assumed to be functions of the demographic v a r i a b l e s . Models 1 and 2 are intended to represent extreme views about the nature of unemployment. The strongest constrained model should ignore the poss ible influence of demographic c h a r a c t e r i s t i c s on labour supply by assuming that , given the choice , ind iv idua l s w i l l respond to wage rates in the same way. From th i s perspect ive , the demographic var iab les of Model 1 become important influences on the demand side of the labour market. A d d i t i o n a l years of education, for example, make a worker more a t t r a c t i v e to a firm making a The Constrained Labour-Supply Model / 63 h i r i n g dec is ion (rather than a f f ec t ing the worker's ' taste ' for unemployment). In r e a l i t y , demographic factors must influence both labour demand and labour supply. Even i f ind iv idua l s do face demand-side constra ints in the region/occupation in which they l ive /work, there i s presumably some element of taste in decis ions not to move/change occupations. Model 1 ignores the former, while Model 2 ignores the l a t t e r . However, the basic d i f ference between Models 1 and 2 i s that the estimation procedure for the constrained model takes account of the p o s s i b i l i t y that we do not always observe des ired l e i sure shares. For Model 2, an i n d i v i d u a l i s l a b e l l e d 'constrained' when given his or her observed wage, the i n d i v i d u a l would prefer to work more weeks (take fewer weeks of unemployment) than he or she i s observed to work. This does not necessar i ly mean that there i s no other job ava i lab le for him or her at a lower wage. It may be that unemployment is in some sense ' v o l u n t a r y . ' This does not af fect the basic point of Model 2: assoc ia t ing observed wage rates with observed unemployment can y i e l d biased parameter estimates i f at that wage observed unemployment i s not the u t i l i t y -max imiz ing choice . The Constrained Labour-Supply Model / 64 4. Derivat ion of the L ike l ihood Function Estimation of the constrained leisure-demand model involves a general izat ion of the ' T o b i t ' approach. For a s ingle i n d i v i d u a l observed to experience unemployment, there is some p r o b a b i l i t y , P c ^ , that he or she i s constrained: P c i = P R O B [ s ° > s ( 7 , 0 , w i ) + e i J = P R O B [ e i < s ° - s ( 7 , 0 , w i ) ] where, as before, s ° and s(7,0,w^) are observed and optimal l e i sure shares, s ° " s ( ) t C i i a . . . -co 1 1 And, there i s some p r o b a b i l i t y that an unemployed i n d i v i d u a l i s carry ing out an optimal p lan: P n c i = 1 - p c i ' If an i n d i v i d u a l i s constra ined, then, as in the basic Tobit model, a l l we know is that s?>s(7,6,w^)+e^ . If an i n d i v i d u a l i s carry ing out an optimal p lan , then there are no r e s t r i c t i o n s on the values the error term may take. For unemployed ind iv idua l s ( i=1 , . . .m) , the uncondit ional p r o b a b i l i t y of observing a p a r t i c u l a r data point i s XJ=(P c i)(P c i) / ( P c i ) • ( , - P c l ) f ( . 1 ) / ( , - P c l ) The Constrained Labour-Supply Model / 65 Or, taking account of the r e s t r i c t i o n that s ° £ 1 f X j = P c i / P 3 i + f ( e i ) / P 3 i 1-s() , x where P3-=/ f ( e - ) d e - . 1 —oo 1 1 Indiv iduals not observed to experience unemployment (i=m+1 .n) must work f i f ty - two weeks each year. As in Model 1, a l l we know about such ind iv idua l s i s that s ° ^ 0 (e^-s(7, 0,w)). For these i n d i v i d u a l s , -s() X?=/ f ( e . ) d e . . 1 —oo 1 1 Or, taking account of the r e s t r i c t i o n that s ° ^ 1 , -s() Xf = / f ( e . )de . / P 3 . . 1 — co 1 1 1 Thus, the l i k e l i h o o d function for s ingle i n d i v i d u a l s can be represented as: L=n XJ n x ? . i . I 1 i.rtf» 1 For couples, est imation of the constrained leisure-demand model i s more complicated. If one member of the household is constrained, th i s w i l l a f fec t the behaviour of the other. f i n the constrained model, households need not be in a pos i t ion 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 lans , but al lowing for the poss ib le existence of constra ints means that ind iv idua 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, ind iv idua l s may be located on segment one as a resu l t 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 is that s ° < 1 ; e^1-s(7, 0,w). The Constrained Labour-Supply Model / 6 6 Given that both members are labour-force p a r t i c i p a n t s ( i . e . , work one or more weeks), then, the fol lowing household conf igurat ions are poss ib le : Case 1: Neither husband nor wife experiences unemployment ( i = 1 , . . . K ) . For f u l l - y e a r workers, the only information ava i lab le i s that s ° ^0 and s 2 ^ 0 . For such a household, the relevant contr ibut ion to the l i k e l i h o o d function i s : X W " S 2 ° ; " ^ ^ ( e K e n d e J d e f / P ^ . X —oo — oo X X J. i . X 1_ s () 1_ s () where P 4 1 , = T 2 J 1 f ( e ! , e? )deMe? X — oo — oo 1 1 1 1 ( i . e . , the p r o b a b i l i t y that both husband and wife p a r t i c i p a t e ) . Case 2: One i n d i v i d u a l experiences unemployment while the other does not. Suppose, for example, that the wife experiences unemployment while the husband does not ( i = K + 1 , . . . L ) . Then, we know that the p r o b a b i l i t y the wife i s constrained i s : PROB[s?>s 2(7,0 ,X)+e 2 ;s?<O] s? - s ( ) ~ S 1 ( ) - J S f (u! ,e?)duMe? — 00 — co X I X X The Constrained Labour-Supply Model / 67 The p r o b a b i l i t y she i s experiencing her des ired l e v e l of unemployment i s then 1 - P c i ' Thus, the uncondit ional p r o b a b i l i t y of observing a household with the husband f u l l y employed and the wife unemployed i s : M = 0() f ( e i ^ ! ) d e J / P 4 2 i + P | . / P 4 2 . 1~S (\ ^ _ g ( ) where P4 2 .= / 2 / 1 f (u3,e?)duMe? 1 - co —co 1 1 1 1 (the p r o b a b i l i t y the wife's des ired l e i s u r e and the husband's e f f ec t ive l e i s u r e share are both less than 1). And, i f the husband experiences unemployment while the wife does not ( i=L+1 , . . .M) , the uncondit ional p r o b a b i l i t y of observing a p a r t i c u l a r data point i s : X i = 0° f ( e J , u ? ) d e ? / P 4 3 i + P ^ / P 4 3 i where P 3 . = / ~ S 2 ( ) / S l " s ( ) f ( e J , e ? ) deMe? C x —co —oo 1 1 1 1 and where P4 3 -= / / f ( e K u ? ) d e ? d u 2 • . 1 —oo —oo 1 1 1 1 Case 3: Both husband and wife experience unemployment ( i=M+1, . . .N) . In th i s s i t u a t i o n , four sub-cases must be considered: (i) Both ind iv idua l s are constrained in unemployment: The Constrained Labour-Supply Model / 68 1 r ' - * 9 ~ S < ) / . f " 5 0 ^ ) , e p d e j d e ? ^ , . . ( i i ) The husband i s unconstrained while the wife i s constrained: The husband must be located on his e f fec t ive leisure-demand function ( i . e . , his choice , while not i t s e l f constrained, i s condit ioned on his wife's quantity c o n s t r a i n t ) . 1?=/ S 2 _ S O / " S l ( ) f ( u ) , e ? ) d u ) d e ? / P 4 2 . . X —CO —CO X X X X X ( i i i ) The wife i s unconstrained while the husband i s constrained: l | = r " S 2 ( ) ; S ° " S ( ) f ( e ! , u ? ) d e j d u ? / P 4 3 . . X —oo —CO X X X X X ( iv) Neither is constrained; both are unemployed: l ? = f ( e j , e ? ) / P 4 , i . The uncondit ional p r o b a b i l i t y of observing both husband and wife unemployed is given by X? = 13+ 1?+ 1?+ 1?. F i n a l l y , the l i k e l i h o o d function for couples is L=fi x. 1n x?ri x?n x ? . ;=i 1(<MI l i ' L H li«<*n 1 IV. ESTIMATION RESULTS In Chapter Four I present est imation resu l t s for the unconstrained and constrained labour-supply models developed in Chapters Two and Three. I begin with a d iscuss ion of the data employed for the two sets of est imations . Then, I present parameter estimates for s ingle women, s ingle men and couples . I conclude the chapter with a comparison of estimated labour-supply e l a s t i c i t i e s for the two models. 1. Data The data set used for estimation i s the 1982 Survey of Consumer Finance (Incomes of Census Family Un i t s , 1981). In t o t a l , 40,308 households answered questions about demographic c h a r a c t e r i s t i c s , employment and income for the year preceding the survey (1981). However, not a l l of these observations are appropriate for inc lus ion in the es t imat ion . F i r s t , households not e l i g i b l e for UI must be excluded. Thus, households in which the head or wife was a student, farmer, permanently unable to work or more than s i x t y - f i v e years of age were dropped. Second, since the models assume that households make at most two leisure-demand dec i s ions , households with more than two income earners were e l iminated. S i m i l a r l y , since the model 69 Estimation Results / 70 assumes only one economic family per household, households with more than one economic family were e l iminated . T h i r d , s ince the "total earnings for head, for wife" var iables include m i l i t a r y earnings, earnings from boarders and earnings from self-employment, in addi t ion to wage earnings, households with earnings from any source but wages were e l iminated . This was necessary for the c a l c u l a t i o n of gross weekly wages. F i n a l l y , since wage rates cannot be ca l cu la ted for non-part ic ipants in the labour force , households with non-part ic ipants were excluded. A l l of th i s reduced the sample s ize from 40,308 to 11,019 households of which 6734 have two working heads, 1919 have a s ingle male working head and 2366 have a s ingle female working head. General features worth noting about the data are (see Tables 4.1 to 4 .3) , f i r s t , that 23.3 percent of the sample heads experienced some unemployment in 1981, the year in which the major recession of the 1980s began. A second d i s t i n c t i v e feature of the data i s revealed through an inves t igat ion of male/female d i f ferences: 24 percent of the women but only 3 percent of the men work part time. Part-t ime workers have a higher incidence of unemployment than f u l l - t i m e workers, yet women, o v e r a l l , are reported to have a lower incidence of unemployment than men. A s imi lar p e c u l i a r i t y , given the lower incidence of unemployment for women than for men, is Estimation Results / 71 that average weeks of employment are fewer for women, yet average weeks of unemployment are the same as for men. In fac t , for women, average weeks of employment plus average weeks of unemployment f a l l short of one year. This suggests that many women e i ther do not choose to c a l l themselves unemployed when not working or that they drop out of the labour force when they lose the ir jobs. (For est imat ion, any weeks not reported as weeks of employment are designated as weeks of ' l e i s u r e ' . ) Average incomes provide a t h i r d way to character ize the data . The average, net of tax, household income (1981) i s $22,202; the average, net of tax, per capi ta income (1981) i s $10,186. In t o t a l , 960 households are c l a s s i f i e d as 'poor' ( i . e . , the ir t o t a l incomes (1981) f a l l short of the S t a t i s t i c s Canada "Low-Income Cut -Of f s" ) . Of these 960 households, 260 are headed by a couple, 211 by a s ingle man and 489 by a s ingle woman. Table 4.2 presents average values by occupational group. Patterns here with respect to male/female d i s t r i b u t i o n and wage rates are much as might be expected. D i s t i n c t i v e features to note, however, are the very high rates of unemployment in occupations such as F o r e s t r y / F i s h i n g , Mining, and Construct ion . Table 4.3 provides average values by province . Again, basic expectations are f u l f i l l e d . Incomes are lowest and unemployment i s highest in the Estimation Results / 72 A t l a n t i c provinces . Incomes are highest in Ontar io , Alberta and B . C . The incidence of unemployment i s lowest in Ontario and in the P r a i r i e provinces; the recorded incidence of unemployment i s cons i s tent ly lower for women than for men. P r i o r to the estimation of Model 1, the data sets were further reduced by: 1. E l iminat ing households with heads report ing pos i t i ve weeks of work but no earned income. 2. E l iminat ing households with male part-t ime workers. 3. E l iminat ing households with heads out of ' equ i l ibr ium' with respect to the UI programme (see Chapter Two, Section 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 in Table 4.4 which compares numbers of workers on each budget segment before and af ter d i s q u a l i f i c a t i o n . The largest number of observations were el iminated from segment one (everyone was eliminated) and from segment two. Re la t ive ly few observations on segments three and four were found to be in ' d i s e q u i l i b r i u m . ' O v e r a l l , a s u r p r i s i n g l y large number of people s a t i s f i e d the condi t ion that weeks of unemployment match weeks of e n t i t l e d benef i t . For s ingle women and s ingle men, the f i n a l s izes of the Model 1 data sets were 2088 and 1677 observations Estimation Results / 73 r e s p e c t i v e l y . For couples , the basic version of Model 1 ( i . e . , the version without e i ther the correct ion for sample s e l e c t i v i t y or the Tobit correct ion) was estimated using the 5107 observations remaining in the data set at th i s po in t . However, for the more complicated versions of Model 1, th i s proved to be too large a sample, so 2500 observations were randomly selected from the 5 l07 . f For the estimation of Model 2, ' d i s e q u i l i b r i u m ' observations were returned to the data sets . Since , by the assumptions of Model 2, some part of observed unemployment does not r e f l e c t the u t i l i t y -max imiz ing choices of households, i t i s no longer necessary to require that each i n d i v i d u a l be in a pos i t ion of ' equ i l ibr ium' with respect to the UI programme. For s ingle women and s ingle men, d i s e q u i l i b r i u m observations were returned to the Model 1 data sets to create Model 2 data sets with 2297 and 1796 observations respec t ive ly . For couples, a l l d i s e q u i l i b r i u m observations were returned to the o r i g i n a l Model 1 data set of 5107 observations. Then, a random sample of 2000 observations was drawn for the estimation of Model 2. Differences in the mean c h a r a c t e r i s t i c s of the sample populations for Models 1 and 2 are reported in Tables 4.5 fTh i s was achieved using the subroutine RSEQ ava i lab le in the f i l e CPUrLIB at UBC. Estimation Results / 74 and 4.6. The most s i g n i f i c a n t feature to note is the increase in average weeks of unemployment observed in a l l Model 2 data sets . This i s to be expected, given that the majority of ' d i s e q u i l i b r i u m ' observations being returned to the sample are located on segments one and two ( i . e . , at the high-unemployment end of the budget c o n s t r a i n t ) . 2. Model 1 Estimation Results Model 1 parameter estimates are presented in Tables 4.7, 4.8 and 4.9. These estimates were obtained by maximum l i k e l i h o o d , using the numeric opt imizat ion routine FLETCH from the nonlinear function opt imizat ion package, UBC NLP. FLETCH uses a 'quasi-Newton' a lgori thm. Results from the three sets of estimations are discussed in t u r n . (a) MODEL 1: SINGLE WOMEN For s ingle women, as for s ingle men, correc t ing for possible bias introduced through the exclusion of a l l observations on segment one of the budget constra int had almost no impact on parameter estimates. Thus, to reduce the cost of computation, th i s procedure was omitted from a l l further est imation. A l l parameters reported for s ingle men and women have been obtained without using th i s c o r r e c t i o n . Estimation Results / 75 Table 4.7 presents Model 1 parameter estimates for s ingle women. 'Bas i c ' est imation of the unconstrained model ignores the censoring of the error d i s t r i b u t i o n which must ex is t as a resul t of the r e s t r i c t i o n that weeks of l e i s u r e cannot be observed to f a l l below zero. 'Tob i t ' estimation takes account of th i s r e s t r i c t i o n . The parameters 7 1 0 and 0 1 O are s t a t i s t i c a l l y s i g n i f i c a n t (at the 99 percent leve l ) in both models; in neither case is 7 0 0 s i g n i f i c a n t . With the exceptions of CITY and YRSE in the basic model and CITY in the tob i t model, a l l demographic var iables appear s i g n i f i c a n t l y at least once. Differences between the basic and tobi t parameter estimates show how ignoring the censoring of the error d i s t r i b u t i o n at f i f ty- two weeks of employment biases parameter estimates obtained in the basic Model 1 est imation. Estimated values for both 7 1 0 and 0 1 O increase enormously (in absolute terms) after the tob i t correc t ion i s made. The estimated value for the parameter 7 1 0 drops from -6.570 to -83.12; the estimated value for 0 1 O increases from .1047 to .4050. (700 is i n s i g n i f i c a n t in both cases and so w i l l not be discussed.) Such dramatic changes in estimated parameter values are not surpr i s ing given that 80 percent of the sample population are observed at the l i m i t ( i . e . , working f i f ty- two weeks). Estimation Results / 76 The estimated impact of demographic var iab les on the labour-supply parameters, y0, 7 l and 0, , i s a lso af fected by the tob i t c o r r e c t i o n . The estimated parameters for ATLAN, a dummy var iab le set equal to one for women l i v i n g in the A t l a n t i c region, follow the same pattern as 7 l 0 and 0 1 O : 7 M decreases from -6.249 in the basic model to -62.12 in the tob i t model; 0!, increases from .09333 in the basic model to .2659 in the tob i t model. (ATLAN also exerts a strong pos i t i ve influence on 7 o in both the basic and tob i t models.) WEST, the regional dummy var iab le set equal to one for women l i v i n g in the Western provinces , does not appear to influence e i ther 7 l or 0, in the basic model (WEST does influence 7 o p o s i t i v e l y ) , but does exert a strong influence on both parameters in the tobi t case. S i m i l a r l y , the estimated impact of EFAM, the number of ind iv idua l s in a woman's economic family , on 7 , and 0, i s s i g n i f i c a n t l y a l t ered when the tob i t correc t ion is made. The var iab le EFAM exerts a negative influence on 7 l and a pos i t i ve influence on 0, in the basic model. These signs reverse in the tobi t case. O v e r a l l , Model 1 resu l t s suggest that demographic v a r i a b l e s , as proxies for i n d i v i d u a l tas tes , influence the p a r t i c i p a t i o n / p a r t - y e a r / f u l l - y e a r choices made by s ingle women. This r e l a t i o n s h i p obscures the impact of demographic Estimation Results / 77 var iab le s on the actual choice of weeks of employment/unemployment i f a woman decides to work less than a f u l l year. There i s , for example, a connection between region of residence and the p r o b a b i l i t y that a woman w i l l choose to work f u l l - y e a r which obscures the r e l a t i o n s h i p between region of residence and choice of number of weeks of work for women who are choosing weeks. In p a r t i c u l a r , t h i s i s true for women l i v i n g in the Western provinces where average incidence and duration of unemployment are lower than in e i ther A t l a n t i c or Centra l Canada. In the context of Model 1, the low p r o b a b i l i t y that a woman l i v i n g in the West w i l l choose any unemployment hides the fact that the few women l i v i n g in the West who do choose unemployment have ' tas tes ' for l e i s u r e which are s i g n i f i c a n t l y d i f f erent from the '"tastes' of s imi lar women l i v i n g elsewhere in the country. S imi lar d i f f i c u l t i e s in in terpre t ing the impact of EFAM on a s ingle woman's labour-supply decis ion are overcome by c o r r e c t l y speci fying the model. The parameter estimates obta ined' using the correct ( tobi t ) s p e c i f i c a t i o n for Model 1 are consistent with the hypothesis of u t i l i t y - m a x i m i z i n g behaviour for a strong majority of observations: 2058/2088 observations (99 percent) sa t i s fy the r e g u l a r i t y condit ions for u t i l i t y maximization. (For t h i r t y women, 7 0 >X 0 . ) (b) MODEL 1: SINGLE MEN Est imation Results / 78 Table 4.8 presents Model 1 parameter estimates for s ingle men. As was true for s ingle women, the parameters 0 1 O and 7,o are s t a t i s t i c a l l y s i g n i f i c a n t (at the 99 percent leve l ) in both the basic and tob i t models. The parameter 7 0 0 i s s i g n i f i c a n t (with 95 percent confidence) in the basic model but not in the tob i t model. The pattern of change in 7 1 0 and 8i0 between the basic and tob i t models i s very s imi lar to that found for s ingle women: 7 1 0 changes from -8.856 to -140.0; 0 1 o changes from .1327 to .5873. Again, the absolute values of estimated parameters increase dramatical ly when the tobi t correc t ion is made. However, patterns of change in the coe f f i c i en t s on demographic var iab les are qui te d i f f eren t from those found for s ingle women. In the basic model, the impact of the regional var iab le s ATLAN and WEST, for example, i s s imi lar to the impact of these var iables on the labour-supply parameters and hence the labour supply of s ingle women. However, for s ingle men, the reg ional var iables are i n s i g n i f i c a n t a f ter the tob i t correc t ion i s made whereas, for s ingle women, the impact of ATLAN remains strong and the impact of WEST only becomes apparent af ter the tob i t c o r r e c t i o n . For s ingle men, region of residence has an Estimation Results / 79 important influence on the f u l l - y e a r / p a r t - y e a r choice . If t h i s choice i s not d is t inguished from the choice of weeks of work, ATLAN and WEST appear to exert an important influence on an i n d i v i d u a l ' s leisure-demand dec i s ion . If the tobi t correc t ion i s made, i t becomes c lear that region is not an important determinant of the number of weeks of employment/unemployment chosen. Rather, being a seasonal worker (presumably a majority of seasonal workers l i v e e i ther in the A t l a n t i c or the West), l i v i n g in a c i t y or having more education are the c r u c i a l taste factors inf luencing the actual choice of weeks (given that a part-year choice has already been made). A d i f ference in the modelling of male and female behaviour may be connected to th i s r e s u l t . Part-t ime workers are sometimes described as having d i f f erent ' tastes ' for l e i sure than f u l l - t i m e workers ( e . g . , Nakamura and Nakamura, 1983). Hence, a dummy var iab le set equal to one for part-t ime workers was included among the demographic ' taste ' proxies . However, since only 3 percent of the men in the sample work part - t ime , these men were excluded from the sample and the var iab le PART was only included in the set of demographic var iab les for women. S i m i l a r l y , workers who choose seasonal or c y c l i c a l occupations are sometimes viewed as having d i f f eren t tastes for l e i s u r e than workers choosing Estimation Results / 80 occupations with more stable employment patterns (Glenday and Alam, 1982). Hence, seasonal and c y c l i c a l dummy var iab le s were included for men, but not for women since only a very small f rac t ion of the sample of women was found in these occupations ( f i s h i n g , hunting, f o r e s t r y , cons truct ion , mining, materials handl ing) . However, women working in seasonal or c y c l i c a l occupations were retained in the sample. Perhaps without the seasonal dummy v a r i a b l e , the regional var iab les ATLAN and WEST would be more s i g n i f i c a n t determinants of the weeks of work chosen by s ingle men. Estimated parameter values for the tob i t model are again consistent with the hypothesis of u t i l i t y maximization for most observations: 1670 /1677 s ingle men (99.6 percent) sa t i s fy r e g u l a r i t y condi t ions . (c) MODEL 1: COUPLES Model 1 parameter estimates for couples are presented in Table 4.9. Results are reported for the basic uncorrected model, for the basic model corrected for poss ible sample s e l e c t i v i t y bias introduced by excluding non-part i c ipants , and for the tob i t model, again corrected for poss ible sample s e l e c t i v i t y b ias . (Since the sample s e l e c t i v i t y correc t ion had a s i g n i f i c a n t impact on parameter estimates obtained for couples, th is procedure is maintained in the estimation of Estimation Results / 81 a l l other models.) The basic pattern of re su l t s obtained for couples resembles the patterns obtained for both s ingle women and s ingle men (except that the correc t ion for sample-se lect iv i ty bias d id not s i g n i f i c a n t l y af fect parameter estimates obtained for e i ther s ingle men or s ingle women). The parameters 7 1 0 r 7 2 0 t 0,, 82 are s t a t i s t i c a l l y s i g n i f i c a n t (at the 95 percent leve l ) in a l l models and again increase subs tant ia l ly in absolute magnitude when the tobi t correct ion is made. In fact , the 9 parameters (marginal budget shares of l e i sure ) increase even more dramat ica l ly for married ind iv idua l s than for s ingle i n d i v i d u a l s . For couples, the only way that demographic var iab les (tastes) can af fect behaviour is through the ir impact on the gamma parameters, f As was a lso true for s ingle i n d i v i d u a l s , the estimated impact of the demographic var iables i s affected by the tob i t c o r r e c t i o n , suggesting that parameter estimates obtained in the basic model are biased. Compare the impact of demographic var iables on the y2 parameter in t 'Techno log i ca l ' r e s t r i c t i o n s made i t impossible to allow 0, and 82 to vary with demographic c h a r a c t e r i s t i c s for couples . This would have added twenty parameters to the t h i r t y - e i g h t already being estimated, causing d i f f i c u l t i e s for the optimization package. This di f ference between the models for s ingle household heads and for couples should be kept in mind. Estimation Results / 82 the basic model (with sample s e l e c t i v i t y correc t ion) with the impact of demographic var iab les on the y2 parameter in the tobi t model: the c o e f f i c i e n t on the Western dummy var iab le i s i n s i g n i f i c a n t in the basic model but increases in magnitude and becomes s i g n i f i c a n t in the t o b i t case; the coe f f i c i en t s on PART, a dummy var iable to indicate that the wife i s a part-t ime worker, and CLT7, the number of ch i ldren less than seven years of age in the household, are i n s i g n i f i c a n t in the basic model, but increase in magnitude and become s i g n i f i c a n t in the tobi t model. The tobi t correc t ion also af fects the estimated impact of demographic var iab les on 7 , . Some s i m i l a r i t i e s in patterns of change in the estimated taste coe f f i c i en t s for y^ and y2 can be noted. As was also true for y2, the coe f f i c i en t on the A t l a n t i c dummy i s i n s i g n i f i c a n t in both models while the coe f f i c i en t on the Western dummy is i n s i g n i f i c a n t in the basic model but increases in magnitude and becomes s i g n i f i c a n t in the tob i t model. Again, the coe f f i c i en t on CLT7, the number of ch i ldren less than seven years of age in the household, i s i n s i g n i f i c a n t in the basic model but becomes s i g n i f i c a n t in the tob i t model. This ends the l i s t of s i m i l a r i t i e s . Differences are , f i r s t , that the coe f f i c i en t on CITY, the dummy var iab le to indicate residence in a larger urban area, increases in absolute magnitude and becomes s i g n i f i c a n t in the tobi t model; second, that the coe f f i c i en t s on YRSE2, the Estimation Results / 83 years of education of the wife, and CYC, a dummy var iab le to indicate that the husband works in a c y c l i c a l occupation, follow the same pat tern; t h i r d , that the coe f f i c i en t on SEA, a dummy var iab le to indicate that the husband works in a seasonal occupation, while s i g n i f i c a n t in both models, increases in magnitude in the tob i t model. Thus, resu l t s again confirm that the estimated impact of demographic var iables on labour supply i s biased i f proper at tent ion is not given to the censoring of the error d i s t r i b u t i o n at f i f ty- two weeks of work. It would be in tere s t ing to compare Model 1 resu l t s for s ingle women with those obtained for married women and resul t s obtained for s ingle men with those for married men. However, since demographic var iab les can influence both the 7 and the 8 parameters for s ingle ind iv idua l s but only the 7 parameters for couples and since there are cross ef fects (the wife's l e v e l of education a f f ec t ing the husband's choice of l e i sure ) for couples which do not ex is t for s ingle household heads, observed patterns of changes are not d i r e c t l y comparable. Estimation Results / 84 3. Model 2 Estimation Results Model 2 parameter estimates are presented in Table 4.10. The model inc luding the tobi t correc t ion for the censoring of the error d i s t r i b u t i o n for f u l l - y e a r workers i s judged to be the appropriate s p e c i f i c a t i o n , and the consequences of not making th i s correc t ion have already been discussed in the context of Model 1. Therefore, a l l Model 2 resu l t s presented have been estimated using the tob i t c o r r e c t i o n . And, as for Model 1, a l l resu l t s presented for s ingle ind iv idua l s have been estimated without the correc t ion for poss ible sample s e l e c t i v i t y bias as a resu l t of the exclusion of non-part i c ipants , while a l l resu l t s presented for couples have been estimated with th 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 r observations on segment one of the budget constraint have been returned to the sample, ' p a r t i c i p a t i o n ' has the more normal in terpre ta t ion of 'working a pos i t i ve number of weeks.' (Model 1 treats anyone working less than the minimum 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 indicated in Table 4.10, the sh i f t parameters in the leisure-demand equations, 7 l and 7 2 , as well as the marginal budget share parameters, 0, and 0 2 , are in a l l cases s t a t i s t i c a l l y s i g n i f i c a n t (at the 95 percent l e v e l ) . For Estimation Results / 85 s ingle men, the s h i f t parameter in the commodity-demand equations, y0i i s a l so s i g n i f i c a n t . (Recall that demographic var iables are not included in Model 2.) Regulari ty condit ions 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 everywhere for a l l groups. Model 2 parameter estimates can be used to ca lcu la te ind iv idua l p r o b a b i l i t i e s of being constrained for ind iv idua l s observed to be unemployed in th i s 1981 data set ( P c i ) . Tables 4.11, 4.12 and 4.13 present sample ca l cu la t ions for s ingle women, s ingle men and couples that experience unemployment. O v e r a l l , estimated p r o b a b i l i t i e s of constraint are very h igh . The average p r o b a b i l i t y that a s ingle woman who is observed to be unemployed would prefer to work more weeks at her observed net wage and non-labour income i s 82.7 percent. Since net wages and non-labour incomes incorporate the e f fects of the UI programme, th i s means that even given the a v a i l a b i l i t y of UI, most unemployed women would optimally choose to work more weeks. (This resul t s says nothing about choices over jobs o f fer ing lower wages.) For s ingle unemployed men, the average p r o b a b i l i t y of constra int of 79.4 percent i s a lso s t r i k i n g l y h igh. For couples, the average p r o b a b i l i t y that a household in Estimation Results / 86 which the husband experiences unemployment but the wife does not i s 81.4 percent. This corresponds very c lo se ly with the values obtained for s ingle i n d i v i d u a l s . For couples in which the wife experiences unemployment but the husband does not, the average p r o b a b i l i t y that the household i s constrained is 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 prefer the wife to increase weeks of employment i s , on average, only 68.7 percent . This r e s u l t , providing some support for t r a d i t i o n a l views about the r e l a t i v e importance of the employment of husband and wife, i s p a r t i a l l y determined by the funct ional form chosen for estimation (husband's l e i sure and wife's l e i s u r e must be subst i tutes in a l inear expenditure system) and by the empir ica l fact that the average wage rate of married men i s much higher than the average wage rate of married women (see Table 4 .6) . F i n a l l y , couples in which both husband and wife experience unemployment are almost c e r t a i n l y constrained. On average, the estimated p r o b a b i l i t y that the household would prefer at least one person to work a d d i t i o n a l weeks is 97.5 percent. P r o b a b i l i t i e s of constra int in unemployment vary across regions. Unemployed s ingle women l i v i n g in the A t l a n t i c provinces are more l i k e l y to be facing demand-side constra ints (average p r o b a b i l i t y of constraint i s 85.6 percent) than are unemployed s ing le women l i v i n g in Centra l Estimation Results / 87 Canada (average p r o b a b i l i t y of constra int i s 80.4 percent) . Unemployed s ingle men are most l i k e l y to be constrained i f they l i v e in Western Canada (average p r o b a b i l i t y of cons tra int i s 83.5 percent) and, again, least l i k e l y to be constrained i f they l i v e in Central Canada (average p r o b a b i l i t y of constra int i s 74.8 percent) . Couples in which only the husband is unemployed are most l i k e l y to be constrained i f they l i v e in A t l a n t i c Canada (average p r o b a b i l i t y of constra int i s 84.9 percent) and least l i k e l y to be constrained i f they l i v e in Central Canada (average p r o b a b i l i t y of constra int i s 76.6 percent) . Couples in which only the wife i s unemployed are most l i k e l y to be constrained i f they l i v e in Western Canada (average p r o b a b i l i t y of constra int i s 70.1 percent) and least l i k e l y to be constrained i f they l i v e in A t l a n t i c Canada (average p r o b a b i l i t y of constra int is 67.3 percent) , f Such high estimated p r o b a b i l i t i e s of constraint for those observed to be unemployed lend support to a model of labour-market behaviour in which most people, having chosen to p a r t i c i p a t e , simply want to work f u l l - t i m e , a l l year; a model of labour-market behaviour in which most people simply want 'a j o b . ' f l f demographic var iab les are retained as taste proxies in Model 2, these p r o b a b i l i t i e s of constraint look quite d i f f e r e n t . 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 ince , in such a model, they have pronounced ' tastes ' for l e i s u r e . Estimation Results / 88 The constrained model of labour supply assumes, other things equal , that a l l ind iv idua l s respond to wage rates and non-labour incomes in the same way. Of two ind iv idua l s observed to experience the same number of weeks of unemployment, the i n d i v i d u a l with the lower wage rate w i l l have the lower p r o b a b i l i t y of cons tra in t . This expla ins , for example, why r e l a t i v e l y high-wage s ingle men l i v i n g in Western Canada have a r e l a t i v e l y high p r o b a b i l i t y of being constrained i f observed to be unemployed. However, th i s t r a d i t i o n a l supply-s ide approach to understanding the labour market ignores the p o s s i b i l i t y that opportunit ies may vary across wage / sk i l l l e v e l s . It a lso ignores the possible connection between absolute need and perception of constra int and how th i s might vary across income l e v e l s . A r e l a t i v e l y low-wage s ingle parent, for example, may prefer more than h i s or her observed quantity of employment i f present income seems i n s u f f i c i e n t to cover basic needs. More complicated aspects of the problem of labour-supply constra ints can c l e a r l y not be incorporated in th i s model. 4. E l a s t i c i t y E s t i m a t e s A l l of the d iscuss ion of resu l t s has so far focussed on the magnitude and s ign i f i cance of estimated parameter values . Of more in teres t are the associated labour-supply e l a s t i c i t i e s . Estimation Results / 89 For Model 1, the gross own-wage e l a s t i c i t i e s are ca lcu la ted as: O L S . / a w ^ (w. /LS. ) = [ (^/w?) ( Y - T o - T i W j - T j W j ) + ( 0 i / w i ) ( 7 . - 5 2 ) ] [w. /LSj] i = 1 r 2; j = 2,1 for couples, and as: O L S ^ B w , ) ( W l / L S / ) = [ (0 , /w 2 ) (Y-To-TiW,) + ( 0 ,/w , ) ( 7 l - 5 2 ) ] [w, /LS,] for s ingle men and s ingle women. Cross-wage e l a s t i c i t i e s for couples are given by: ( 3 L S . / 3 W j ) ( W j / L S . ) = [ ( 0 i / w i ) ( 7 j - 5 2 ) ] [w^/LS.] . E l a s t i c i t i e s of labour supply with respect to non-labour income are ca l cu la ted as: (3LS/3NLY)(NLY/LS)= [- (0/w)][NLY/LS]. Compensated own-wage e l a s t i c i t i e s are ca lcu lated as: [ 3 L S i / 9 w I-LS I (3LS^/3NLY)] [ W J / L S J ] i=1,2. For couples, compensated cross-wage e l a s t i c i t i e s are given by: [ B L S j / d w j - L S j ( 3 L S ^ / 3 N L Y ) ] [ W j / L S i ] . For Model 2, a l l e l a s t i c i t y formulas are as above except in the case of couples with one member constrained in unemployment so that the other member is operating on a rationed labour-supply funct ion . Then, gross own-wage e l a s t i c i t i e s are ca lcu la ted as: Estimation Results / 90 (3LS i (Zj ) /9w. ) ( w i / L S i ) = [ [ ^ ^ ( ( l - e j J w p i t Y - T o - w . Y . - W j Z j l + Ce . /t (1-0j)w.) ] [7 i - 5 2 ] ] [ w . / L S . ] i=1,2 j=2,1. Cross-wage e l a s t i c i t i e s for rationed households are given by: O L S ^ Z j J / B W j ) ( w j / L S i ) = [ c 7 i / ( ( l - 0 j ) w i ) ] [ Z i - 5 2 ] ] [ w j / L S i ] i = 1 ,2 j = 2 ,1 . F i n a l l y , e l a s t i c i t i e s with respect to non-labour income for rat ioned households are given by: (3LS i (Zj) /9NLY)(NLY/LS^) = [~8 ^/{(1-0jJwj)][NLY/LSj] i = 1 ,2 j = 2 ,1 . Compensated e l a s t i c i t i e s take the same form as for unrationed households, subs t i tu t ing the appropriate rat ioned d e r i v a t i v e s . Not ice , however, that the compensated cross-wage e l a s t i c i t y i s zero for rat ioned households since the gross cross-wage e l a s t i c i t y i s e f f e c t i v e l y just an e l a s t i c i t y of labour supply with respect to an income source which is f ixed from the perspective of the constrained household ( (52 -Z^w^ i = 1,2). The e l a s t i c i t y of rationed labour-supply functions with respect to the l eve l of constraint faced by the spouse, Z^, can a lso be ca l cu la ted: O L S . ( Z j ) / 9 Z j ) ( Z j / L S i ) = [ ( 0 . / ( ( l - 0 j ) w . ) W j ] [ Z j / L S . ] . Estimation Results / 91 Again, t h i s c lose ly resembles the formula for the e l a s t i c i t y of labour supply with respect to non-labour income except that the given element in th i s case i s the l e v e l of foregone employment earnings of the constrained spouse, ( W J Z J ; j=1,2) . Household income decreases as the l e v e l of constraint increases . Calculated e l a s t i c i t i e s are presented in Tables 4.14 through 4.26. Model 1 e l a s t i c i t i e s are evaluated at sample means (of wage rate , non-labour income, years of education, number of ch i ldren and number of i n d i v i d u a l s in the economic family) and at weeks of labour supply as predicted by the appropriate estimated labour-supply funct ion . Model 1 e l a s t i c i t i e s are ca l cu la ted for each major demographic group. Weeks are predicted at sample means to ensure that the e l a s t i c i t y i s evaluated at a point which i s ac tua l ly on the labour-supply funct ion . However, as should be expected, predicted weeks for the f u l l samples are in almost every case equal to f i f t y - t w o . Thus, e l a s t i c i t i e s are being evaluated at a corner and can only be interpreted as responsiveness to a drop in wage rate . For the unemployed samples, th i s i s not a problem. Hence, e l a s t i c i t i e s evaluated for these groups are most meaningful. (Both models are best interpreted as models of labour supply for unemployed i n d i v i d u a l s . ) Estimation Results / 92 Since a l l demographic var iables are excluded from Model 2 labour-supply funct ions , e l a s t i c i t i e s are simply evaluated at sample means for wage rates and non-labour incomes together with the weeks of labour supply predicted using the appropriate labour-supply funct ion. For constrained i n d i v i d u a l s , i t i s e spec ia l ly important to use predicted weeks s ince , by d e f i n i t i o n , observed weeks of work cannot correspond with a point on the ' t rue ' labour-supply funct ion . Weeks of constrained unemployment for rationed households are , of course, actual rather than predicted values. Table 4.14 reports Model 1 e l a s t i c i t i e s for s ingle men. Note, f i r s t of a l l , that e l a s t i c i t i e s are much larger when evaluated for the sub-sample who experience some unemployment than when evaluated for the f u l l sample of s ingle men (employed and unemployed). This is reasonable since t h i s i s the group able to respond to any wage change by adjust ing weeks of work. Second, e l a s t i c i t i e s are , in general , largest in the A t l a n t i c and smallest in the West. T h i r d , compensated own-wage e l a s t i c i t i e s are larger in r u r a l than urban areas. These resul t s are also reasonable in the context of a model which allows for regional v a r i a t i o n in ' tastes ' for unemployment. F i n a l l y , while there i s considerable v a r i a t i o n in ca lcu la ted e l a s t i c i t i e s across Estimation Results / 93 occupational groups, no c lear pattern is d i s c e r n i b l e . Model 1 e l a s t i c i t i e s for s ingle women are reported in Table 4.15. A nearly i d e n t i c a l pattern of resu l t s i s obtained. E l a s t i c i t i e s are larger for the unemployed sample than for the f u l l populat ion . E l a s t i c i t i e s are largest in the A t l a n t i c provinces and smallest in the Western provinces . And, while there is considerable v a r i a t i o n between e l a s t i c i t i e s ca lcu la ted for part-t ime workers and e l a s t i c i t i e s ca lcu la ted for f u l l - t i m e workers, no d e f i n i t e pattern emerges. Tables 4.16-4.19 report Model 1 e l a s t i c i t i e s for married men; Tables 4.20-4.25 report Model 1 e l a s t i c i t i e s for married women. Again, e l a s t i c i t i e s are larger when evaluated for the unemployed sub-sample than when evaluated for the ent ire populat ion. Gross own-wage e l a s t i c i t i e s for married men and married women are larger than the equivalent values for e i ther s ingle men or s ingle women. Compensated own-wage e l a s t i c i t i e s , on the other hand, are of s imi lar magnitudes for married men and s ingle i n d i v i d u a l s . This i s in contrast with the compensated own-wage e l a s t i c i t i e s evaluated for married women which are much larger than those for any other group. The labour-supply functions of s ingle women and men are, in general , p o s i t i v e l y - s l o p e d and i n e l a s t i c ; the Estimation Results / 94 labour-supply functions of married women are p o s i t i v e l y - s l o p e d and e l a s t i c . E l a s t i c i t i e s for married women who work part-t ime are highly e l a s t i c (the average gross own-wage e l a s t i c i t y for women who work part-t ime with husbands who work in seasonal occupations in A t l a n t i c Canada, for example, is 4.2886). This resul t provides further confirmation for the Nakamuras' (1983) f ind ing that i t i s women who work part- t ime who have labour-supply responses which are d i f f e r en t from those of the rest of the populat ion; that there i s l i t t l e d i f ference in behaviour between men and women who work f u l l - t i m e . Model 1 resul t s suggest, in p a r t i c u l a r , that there i s l i t t l e d i f ference between the labour-supply behaviour of s ingle working women and working men. E l a s t i c i t i e s with respect to non-labour income are much smaller than own-wage or cross-wage e l a s t i c i t i e s for married men and married women; e l a s t i c i t i e s with respect to non-labour income are larger than own-wage e l a s t i c i t i e s for s ingle men and s ingle women. For couples, labour-supply e l a s t i c i t i e s are largest in A t l a n t i c Canada and smallest in Western Canada. No c lear urban/rura l pattern i s evident . Occupation influences labour-supply e l a s t i c i t i e s of married men, but as was also Estimation Results / 95 the case for s ingle men, no c l ear pattern i s d i s c e r n i b l e . Within the model of j o i n t u t i l i t y maximization some in teres t ing cross ef fects on e l a s t i c i t y magnitudes emerge. Other things equal , the wife 's labour supply i s less e l a s t i c i f her husband works in a seasonal occupation; the husband's labour supply i s less e l a s t i c i f h i s wife i s a part-t ime worker. These re su l t s are p a r t l y determined by the l inear expenditure system in which husband's l e i sure must be a subst i tute for wi fe ' s . However, they are at least i n t u i t i v e l y p l a u s i b l e . If one member of a household experiences unsteady employment, i t i s reasonable that the couple w i l l j o i n t l y prefer the other member to follow a steady employment path and hence to be r e l a t i v e l y unresponsive to any i m p l i c i t tax generated by the UI system. The poss ib le consequences of such cross ef fects for household responses to labour-market po l i cy are often over- looked. Table 4.26 presents Model 2 e l a s t i c i t i e s for a l l groups. E l a s t i c i t i e s for couples presented in th i s table assume no rat ion ing occurs; the 'unemployed sample' of married men refers to couples in which the husband is unemployed, ignoring the status of h is wife . The 'unemployed sample' of married women refers to couples in which the wife i s Estimation Results / 96 unemployed, ignoring the status of her husband. Model 2 e l a s t i c i t i e s are , in general , smaller in absolute value than Model 1 e l a s t i c i t i e s . Introducing the p o s s i b i l i t y that , for some i n d i v i d u a l s , observed unemployment i s not a u t i l i t y - m a x i m i z i n g choice y i e lds a ' true ' labour-supply function which is less e l a s t i c than that which would otherwise be associated with observed behaviour. Within the framework of the constrained model, ind iv idua l s are less responsive to the i m p l i c i t 'UI-tax' than is suggested by the unconstrained model. Model 2 gross own-wage e l a s t i c i t i e s are larger for married men and married women than for s ingle i n d i v i d u a l s . Compensated own-wage e l a s t i c i t i e s are larger for s ingle ind iv idua l s than for married men and women. These d i f f erences , however, are smal l . A l l Model 2 labour-supply functions are p o s i t i v e l y - s l o p e d and i n e l a s t i c . And, in contrast with resu l t s obtained for Model 1 and resul t s reported elsewhere in the l i t e r a t u r e (see K i l l i n g s w o r t h , 1983), the own-wage responsiveness of married women is no greater than that of other groups. In fac t , the compensated own-wage e l a s t i c i t y for married women is a c t u a l l y the smallest value c a l c u l a t e d . For couples, introducing the p o s s i b i l i t y of constrained Estimation Results / 97 unemployment introduces , at the same time, the complication of rationed labour supply: i f a married man i s constrained, h is wife w i l l be operating on a rationed labour-supply funct ion; i f a married woman i s constrained, her husband w i l l be operating on a rat ioned labour-supply funct ion, f Table 4.27 compares unrationed e l a s t i c i t i e s evaluated for the f u l l sample with unrationed and rationed e l a s t i c i t i e s evaluated for the sub-samples of married men and women with unemployed spouses. E l a s t i c i t i e s are ca lcu la ted for married men with unemployed wives and for married women with unemployed husbands. Having a spouse who is unemployed by choice has l i t t l e impact on average own-wage e l a s t i c i t i e s , but having a spouse who i s unemployed as a resul t of demand-side constra ints reduces average own-wage e l a s t i c i t i e s . Average gross cross-wage e l a s t i c i t i e s for married men or women with unemployed (constrained or unconstrained) spouses are smaller than for the sample as a whole; average compensated cross-wage e l a s t i c i t i e s for married people with unemployed but unconstrained spouses are also smaller; compensated•cross-wage e l a s t i c i t i e s for those with unemployed and constrained spouses are zero. Gross cross-wage e l a s t i c i t i e s for e i ther men or women with fReca l l that the labour-supply function of a man or woman who i s constrained i s termed a ' rat ioned' labour-supply funct ion; a labour-supply function condi t iona l on a quantity c o n s t r a i n t . Estimation Results / 98 constrained unemployed spouses are small and negative; increasing the spouse's wage, for a given l eve l of cons tra in t , increases ' f ixed income' a t t r i b u t a b l e to t h i s source and decreases labour supply. E l a s t i c i t i e s with respect to the l e v e l of the spouse's constraint are small and p o s i t i v e ; increasing the l e v e l of the spouse's cons tra in t , for a given wage rate , decreases ' f ixed income' and thus increases labour supply. This r e s u l t , although p a r t i a l l y determined by the chosen funct ional form, t e l l s a story of husbands and wives working more i f the ir spouses are unable to work as much as the couple had planned. Notice that both husband and wife are sens i t ive to the constra ints faced by the other party . The poss ible responsiveness of a married man to his wife's unemployment i s often ignored. 5 . Conclusions Major estimation resu l t s are , f i r s t , that correc t ing the l imi ted dependent var iab le problem has, in a l l cases, a s i g n i f i c a n t impact on estimated parameters. Correct ing the sample s e l e c t i v i t y problem generated by the exclusion of 'non-part ic ipants ' i s important for couples but not for s ingle i n d i v i d u a l s . Second, Model 1 labour-supply functions are, with a few exceptions, p o s i t i v e l y - s l o p e d and i n e l a s t i c for s ingle men, s ingle women and married men. Model 1 Estimation Results / 99 labour-supply functions are p o s i t i v e l y sloped and e l a s t i c for married women who work f u l l - t i m e ; Model 1 labour-supply functions are p o s i t i v e l y - s l o p e d and very e l a s t i c for women who work part - t ime . T h i r d , in the context of Model 1, demographic var iables have a s i g n i f i c a n t impact on ca lcu la ted e l a s t i c i t i e s . For couples , spouse's demographic c h a r a c t e r i s t i c s also have an important influence on own-wage e l a s t i c i t i e s . Fourth, Model 2 labour supply functions are less e l a s t i c than Model 1 labour-supply funct ions . Estimated e l a s t i c i t i e s for married women are , in t h i s case, no larger than for any other group. A l l Model 2 labour-supply functions are p o s i t i v e l y - s l o p e d and i n e l a s t i c . F i f t h , married men and women are af fected by constra ints on the labour supply of the ir spouses: both married men and married women are found to respond ( i n e l a s t i c a l l y ) to an increase in spouse's constrained unemployment by increasing labour supply; labour-supply functions of married ind iv idua l s with spouses who are constrained are less e l a s t i c than labour-supply functions of married i n d i v i d u a l s with spouses who are not constrained. F i n a l l y , estimated p r o b a b i l i t i e s of constraint are very high, suggesting the potent ia l importance of the 'constrained' approach to modelling labour supply. V. SIMULATION RESULTS Chapter Five uses the estimated constrained and unconstrained models of labour supply and the 1982 Survey of Consumer Finance to predict behavioural responses to UI reform. Thus, the simulation resu l t s presented here are spec i f i c both to the estimated models and to the data set employed. For Model 2 s imulat ions , p r o b a b i l i t i e s of constraint are ca lcu la ted to correspond with 1981 labour-market condit ions (the year of the survey). In p r i n c i p l e , th i s i s not necessary. The estimated parameters for Model 2 are ' true ' estimates of the parameters of household u t i l i t y functions given the assumptions of the model and could be used to simulate behavioural responses for d i f f erent labour-market condi t ions . For a boom period or a more severe recess ion, for example, p r o b a b i l i t i e s of constra int cou ld , respec t ive ly , be reduced or increased and changes in behaviour predicted using Model 2. In th i s d i s s e r t a t i o n , a l l behavioural responses discussed in Chapter Five must be understood in the context of 1981 labour-market condi t ions . Section 1 of Chapter Five surveys other empir ica l studies of the impact of UI on the Canadian labour market. Section 2 provides d e t a i l s of the po l i cy changes simulated in th i s 100 Simulation Results / 101 a n a l y s i s . Sections 3 and 4 explain the s imulation process and the modelling of po l i cy changes. Section 5 discusses simulation r e s u l t s . Section 6 concludes. 1. Previous Studies of UI Much of the at tent ion UI has received from economists has focussed on i t s impact on labour-supply choices , ignoring the poss ible existence of constra ints on behaviour. It i s t r a d i t i o n a l l y agreed that UI generates a number of incent ive e f f ec t s . Most obviously , UI a f fects the behaviour of unemployed workers. Within a basic choice- theoret ic model, UI i s said to generate income and subs t i tu t ion e f f ec t s , both of which favour increased consumption of l e i s u r e (Rea, 1977; F o r t i n , 1984). The income of an unemployed worker is higher with a UI system than without (assuming he or she q u a l i f i e s ) so that i f l e i s u r e i s a normal good, the income ef fect suggests the worker w i l l prefer more l e i s u r e with UI than without. S i m i l a r l y , the subst i tut ion ef fect pred ic t s the choice of more l e i s u r e . With a UI system, the net benefit of returning to work is equal to the wage less the UI benefit rece ived. Without UI, the benefit i s the ent ire wage. The impact of UI on the behaviour of unemployed workers i s a l t e r n a t i v e l y analysed in the context of a search model of Simulation Results / 102 unemployment (Ham and Rea, 1985). Here, i t is assumed that unemployed workers perceive some frequency d i s t r i b u t i o n of jobs according to s k i l l requirements and wage l e v e l . However, workers are not aware of every job a v a i l a b l e . Rather, they must sample one job at a time u n t i l they f ind a job which is acceptable , where a c c e p t a b i l i t y depends on the worker's reservat ion wage. The reservat ion wage is t y p i c a l l y viewed as a function of a l t ernat ive sources of income, l e v e l of committed expenditures, previous wage and q u a l i f i c a t i o n s . UI is an a l t e r n a t i v e source of income which is predicted to increase the reservat ion wage and hence the probable duration of unemployment. Note that while both models predict that UI w i l l increase the duration of unemployment, th i s can be interpreted as i n e f f i c i e n t in the choice model whereas, to the extent workers f ind more su i table jobs, the increased duration of unemployment is interpreted as e f f i c i e n t in the search model. Note, as w e l l , that demand-side e f fects can be incorporated in search models through the a r r i v a l rate of job o f f e r s . The incentive ef fects of UI are not, however, confined to unemployed workers. A l l workers may be influenced by UI in t h e i r choices of region and occupation. I f , as in human Simulation Results / 103 c a p i t a l models, i t i s assumed that such long-run choices depend on the expected stream of returns over time, then the a v a i l a b i l i t y of UI may make a region or occupation character ized by high unemployment r e l a t i v e l y more a t t r a c t i v e (Plourde, 1982; Hey and Mavromaras, 1981). Yet another ef fect of UI may be to encourage the increased labour force p a r t i c i p a t i o n of marginal workers for whom the expected value of UI benefits may increase the expected returns to working enough to warrant p a r t i c i p a t i o n (Vanderkamp and Wilson, 1983). F i n a l l y , incentive ef fects of UI are recognized on the demand-side of the labour market. In an i m p l i c i t contract framework, i t i s assumed that firms must provide workers with a competitive expected l e v e l of u t i l i t y . The existence of UI decreases the ' cos t , ' in the form of reduced worker expected u t i l i t y , of l ay -o f f s to the f i rm. Thus, UI i s predicted to increase the frequency of unemployment as a resu l t of demand-side incentive e f fects (Topel , 1984; Marks, 1987). Empir ica l studies of UI in Canada have focussed on supply-s ide incentive e f f ec t s . Most early work takes advantage of major amendments to the UI programme which occurred in 1971 and 1979 to assess the impact of UI on the Simulation Results / 104 Canadian labour market. In 1971, replacement rates were increased to 66.6 percent (from a maximum of f i f t y percent) , qua l i fy ing weeks of employment were decreased to eight during the year preceding the unemployment s p e l l (from t h i r t y weeks during the two preceding years ) , coverage was extended to become nearly u n i v e r s a l , and spec ia l maternity, retirement and i l l n e s s benefits were introduced. At the same time, benefits were made taxable and the wait ing period was increased from one to two weeks. In 1979, the UI Act was again amended. This time, programme generosity was c u r t a i l e d . E l i g i b i l i t y requirements for new entrants , re-entrants and repeaters were t ightened, benefit rates were reduced to 60 percent, ind iv idua l s working less than twenty hours per week were removed from coverage, and high-income earners were required to repay a port ion of benefits received. Despite the complexity of these changes, many Canadian empir ica l studies of UI choose to model the programme very simply. Grubel , Maki and Sax (1975) and Green and Cousineau (1976), for example, use the average benefit to wage r a t i o and the proportion of claims ruled i n e l i g i b l e to model the impact of UI on aggregate unemployment. Lazar (1978) and Beach and K a l i s k i (1983) incorporate dummy var iab les to correspond with programme changes i n , r e spec t ive ly , the Simulation Results / 105 estimation of cont inuat ion and turnover rates and the estimation of the p r o b a b i l i t y of moving among a l t ernat ive labour-market s tates . (Beach and K a l i s k i take note of the timing of spec i f i c aspects of the 1979 amendments.) S iedule , et a l . (1975), R i d d e l l and Smith (1982) and Vanderkamp and Wilson (1983) construct "composite" UI var iables to measure the changing generosity of the programme. Glenday and Alam (1982) use the l o n g i t u d i n a l UI data base (1974-79) to estimate p r o b a b i l i t i e s of leaving unemployment for separate sub-samples of claimants and non-claimants of UI benef i t s . ( Individuals on temporary l a y - o f f are excluded from the sample to j u s t i f y the supply-s ide focus on the dec i s ion to return to employment.) The p r o b a b i l i t y of UI claimants leaving unemployment i s found to be s i g n i f i c a n t l y affected by benefit rates and by regional v a r i a t i o n in UI entit lements; the p r o b a b i l i t y of non-claimants leaving unemployment i s not s i g n i f i c a n t l y influenced by the UI programme. (Note, however, that a po tent ia l sample s e l e c t i v i t y problem is ignored.) In almost a l l cases , f empir ica l studies of the impact of UI on labour-supply behaviour f ind a pos i t ive r e l a t i o n s h i p between the generosity of the Canadian UI programme and fVanderkamp and Wilson (1983) f ind only a very small increase in women's p a r t i c i p a t i o n , and bel ieve th i s i s outweighed by the s t imulat ive impact of UI on employment and output (automatic s t a b i l i z a t i o n ) . Simulation Results / 106 aggregate unemployment (see Phipps, 1985 for a more de ta i l ed survey of these and other papers) . But note that th i s resu l t is not necessar i ly evidence for the existence of voluntary unemployment. The same pos i t ive assoc iat ion between UI and involuntary unemployment can be demonstrated in the context of an e f f i c i e n c y wage model (see Shapiro and S t i g l i t z , 1984; Jones, 1986). A recent study by Ham and Rea (1985) makes an attempt to incorporate demand-side elements in a search framework, although th i s i s not the focus of the work. Ham and Rea use a l o g i t model and the l ong i tud ina l UI data base (1975-80) to estimate the p r o b a b i l i t y of leaving unemployment condi t iona l on being unemployed ( i . e . , a 'hazard' funct ion) . Various measures of unemployment are included in the vector of exogenous var iab les in an attempt to capture the impact of demand-side condi t ions . Ham and Rea f ind that the U . S . (2 -d ig i t ) i n d u s t r i a l c l a s s i f i c a t i o n unemployment rates (assumed exogenous to the Canadian UI system) have a s i g n i f i c a n t negative influence on the p r o b a b i l i t y that men w i l l leave unemployment but not on the p r o b a b i l i t y that women w i l l leave unemployment. This d i f ference is a t t r i b u t e d to a poss ib le 'added-worker' e f fec t , although household decision-making is not e x p l i c i t l y modelled, nor i s a d i s t i n c t i o n made between married and s ingle women. Ham and Simulation Results / 107 Rea are unable to ident i fy a benef i t -rate e f f ec t , but they do f ind that UI entitlement has a very small but s i g n i f i c a n t impact on expected durat ion . A study of the 1971 changes to UI which uses a somewhat d i f f erent approach i s Rea (1977). Rea uses micro-data (1965-70) to estimate i n d i v i d u a l labour-supply funct ions . Using an i m p l i c i t contract model, he chooses to view a l l unemployment as ' vo luntary . ' Hence, having estimated labour-supply funct ions , he simulates changes in spec i f i c UI parameters by changing e f fec t ive wages and non-labour incomes (these values now incorporate UI ) , and finds that s p e c i f i c UI parameters are i n d i v i d u a l l y important in the determination of incentive e f f ec t s . Rea's work is a more care fu l study of i n d i v i d u a l d e t a i l s of the UI system than most other inves t iga t ions . However, there are s t i l l weaknesses. His labour-supply equations are not derived from u t i l i t y maximization. He does not deal with household (as opposed to ind iv idua l ) behaviour, which he admits to be s i g n i f i c a n t in the determination of labour supply. He depicts the budget constraint as piece-wise l i n e a r , given the existence of UI (see a lso F o r t i n , 1984; Glenday and Alam, 1982), but does not deal with th i s problem during est imation. F i n a l l y , he assumes a l l unemployment is ' v o l u n t a r y . ' Simulation Results / 108 The modell ing approach used in th i s study most c l o s e l y resembles the work of Rea (1977). Incorporation of the parameters of the present (1981) UI programme in the budget constra ints faced by households in both the constrained and unconstrained models enables the s imulation of behavioural responses to changes in the programme. Changing UI changes the l i n e a r i z e d 'net wage' and non-labour income with which each i n d i v i d u a l is faced. Given the estimated parameters of the le isure-demand/labour-supply funct ions , i t is poss ib le to pred ic t behavioural responses to these changes. Major d i f f erences , on the other hand, between t h i s study and the work of Rea are , f i r s t , the d i r e c t incorporat ion of the non- l inear budget constra int at estimation (although, unfortunate ly , convergence could not be obtained using the correct Wales/Woodland/Hausman procedure (see Chapter 2, sect ion 5(b)); second, the d i r e c t l i n k between the t h e o r e t i c a l model and the estimated labour-supply functions (allowing both e f f i c i e n c y and equity consequences of p o l i c y changes to be assessed); t h i r d , the allowance for poss ib le constra ints on labour-supply choices . Simulation Results / 109 2 . P o l i c y Changes Simulated The Royal Commission on the Economic Union and Development Prospects for Canada (The Macdonald Commission) and the Commission of Inquiry on Unemployment Insurance (The Forget Commission) have both recently recommended major reform of the Canadian UI programme. Based on hearings held across the country and on the ex i s t ing empir ica l economic l i t e r a t u r e , both Commissions propose s i g n i f i c a n t retrenchment in programme generosity in an attempt to minimize the adverse incentive ef fects bel ieved to be generated by UI and to return the programme to i t s o r i g i n a l s o c i a l insurance funct ion . No empir ica l evidence yet suggests the magnitude of behavioural responses to be ant i c ipated from ei ther the Macdonald or the Forget proposals: Models 1 and 2 provide a way of pred ic t ing these responses using two very d i f f erent models of labour supply. The Macdonald Commission released i t s report in 1985. Several recommendations for reform of the Canadian UI programme are g iven. UI should be experience-rated. That i s , premium contr ibut ions of firms should be l i n k e d , on a f i rm-by- f i rm bas i s , to i n d i v i d u a l records of l a y - o f f . This i s intended to el iminate the ' s u b s i d i z a t i o n ' of temporary l a y - o f f s . The benefit-replacement rate should be decreased Simulation Results / 110 from 60 to 50 percent of insurable earnings. Regionally-extended benef i ts should be e l iminated . Minimum q u a l i f y i n g weeks should be increased from the current var iab le entrance requirement of ten to fourteen weeks to a f ixed requirement of f i f t een (or poss ibly twenty) weeks. F i n a l l y , the entitlement per iod should be more c lo se ly l inked to work record by requir ing two (or three) weeks of employment for every week of UI benef i t . Together, i t i s hoped that these proposed changes in the structure of benefits w i l l decrease unemployment durations and discourage unstable patterns of employment and unemployment. Proposed changes are intended to be viewed as part of a larger package of s o c i a l securi ty reform to include the establishment of a 'Universa l Income Security Programme' (UISP) which would provide an a l t ernat ive source of support for low-income workers who suffer a loss as a resul t of benefit retrenchment and a T r a n s i t i o n a l Adjustment Assistance Plan (TAAP) to help workers (not necessar i ly low-income workers) f ind employment in more stable regions/occupations . These proposals const i tute the f i r s t package of potent ia l UI reforms to be invest igated using the labour-supply models developed in Chapters Two through Four. Note, however, the Simulation Results / 111 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 to be part of a larger package; second, since the model developed is a supply-side model, the impact of experience-rat ing UI cannot be assessed; t h i r d , since the model i s micro-economic, no attempt can be made to assess the consequences of UI reform for economic s t a b i l i t y . The report of the Forget Commission was released in November of 1986.t Like the Macdonald Commission, i t makes a number of recommendations for UI reform. Benefit entitlement should be based on cumulative hours rather than weeks worked. This change is proposed in an attempt to accomodate the needs of the growing number of part-t ime workers in the Canadian labour force . The recommended minimum hours of work necessary to gain e l i g i b i l i t y to UI is 350. This minimum is intended to apply to a l l workers applying for UI (new entrants , re -entrants , repeaters and appl icants for sickness or maternity benef i t s ) . A l l workers earning entitlement to UI should be e l i g i b l e to receive benefits for a standard f i f t y weeks. UI should be 'annual ized' so that workers do not a l l receive benefits paid at the same rate (current ly 60 percent of insurable earnings) . With annual i za t ion , the fBoth a majority report and a dissent ing minority report were issued. The Standing Committee on Labour, Employment and Immigration has since recommended abandoning the Forget proposals . Simulation Results / 112 replacement rate would vary according to weeks worked during the q u a l i f y i n g period (the f i f ty - two weeks preceding the unemployment s p e l l ) . Anyone fully-employed throughout the q u a l i f y i n g period would receive f u l l benef i t s . (The Forget Report recommends that th i s benefit replacement rate be increased to 66 2/3 percent of average insurable earnings as ca lcu la ted over the past f i f ty- two weeks, rather than over the past ten to twenty weeks, as i s current ly the case.) However, anyone working less than the f u l l f i f ty - two weeks would have earnings replaced at some frac t ion of 66 2/3 percent, where the appropriate f r a c t i o n i s ca lcu la ted as weeks worked div ided by f i f ty - two . Thus, annual izat ion would involve a major change in the time stream of UI benef i t s . Workers with less than a f u l l year of insurable employment would receive smaller weekly benef i ts for a longer period of time than they receive under the current system. With a f ixed entrance requirement and a f ixed period for receipt of benef i t s , the Forget Commission, l i k e the Macdonald Commission, recommends the e l iminat ion of a l l spec ia l provis ions for ind iv idua l s l i v i n g in high-unemployment regions. Funds saved through the e l iminat ion of regionally-extended benefits are to be used to develop an income supplementation programme and to encourage education and community development. These Simulation Results / 113 add i t i ona l new programmes are not discussed in d e t a i l in the Forget report , nor w i l l they be analysed here. However, as was also true for the Macdonald Commission proposals , major changes to UI should r e a l l y only be considered as part of the larger reform package. In addit ion to these proposals for the reform of the core UI programme, a number of minor recommendations are made in the Forget Report. One such proposal which is important from a modelling point of view is that high-income claimants should no longer be required to repay 40 percent of UI benef i ts rece ived. 3. Simulation Methodology The f i r s t step of the s imulat ion procedure, for both the unconstrained and constrained models, i s to generate the vector of i n d i v i d u a l error terms which, when added to weeks of l e i s u r e predicted by the estimated models, w i l l reproduce observed weeks. Po l icy- induced changes in behaviour can then be measured as deviat ions from observed weeks of l e i s u r e (unemployment). This procedure ensures that predicted changes in behaviour are ent ire ly , the resu l t of programme changes. Model 1 spec i f i e s that observed weeks of l e i s u r e can be no less than zero ( f i f ty - two weeks of employment) and no greater than f i f ty - two less the minimum number of weeks required to gain e l i g i b i l i t y to UI. Model 2 only requires Simulation Results / 114 observed weeks of l e i sure to remain within the obvious bounds of zero and f i f t y - t w o . Predicted weeks f a l l i n g outside these model-determined boundary values are set equal to the boundary values . Ind iv idua l errors are ca lcu la ted as the di f ference between actual and predicted weeks. For the unconstrained model, the second and f i n a l step of the simulation procedure i s to make the changes in 'net' wage rates and non-labour incomes implied by the proposed reforms of the UI programme and then to use the estimated leisure-demand equations to predic t behavioural responses. For the constrained model, s imulation of behavioural response to changes in UI is more complicated. For each i n d i v i d u a l , there i s some p r o b a b i l i t y he or she w i l l not be able to respond to a less generous UI programme by decreasing weeks of unemployment. The estimated parameters of Model 2 enable the c a l c u l a t i o n of i n d i v i d u a l p r o b a b i l i t i e s of c o n s t r a i n t . However, for each proposed reform of the UI programme there are two ways of c a l c u l a t i n g th i s p r o b a b i l i t y . If the p r o b a b i l i t y of constraint i s ca lcu la ted before the UI parameters are changed, a lower-bound estimate of the true p r o b a b i l i t y of constraint w i l l be obtained (assuming the programme is less generous after reform and given the pos i t ive estimated own-wage labour-supply e l a s t i c i t i e s ) . Ca lcu la t ing the p r o b a b i l i t y of Simulation Results / 115 constra int given the present system of UI assumes that , a f ter the programme i s made less generous and ind iv idua l s have revised t h e i r optimal employment/unemployment plans , anyone who was unconstrained before the programme change remains unconstrained after the change and is able to modify behaviour in accordance with the new p lan . This ignores the p o s s i b i l i t y that an i n d i v i d u a l may current ly be operating on the margin between being constrained and not being constrained; that when UI is made less generous and he or she decides an optimal employment/unemployment plan now involves more weeks of employment, he or she i s then unable to f ind the extra des ired weeks of work. Ca lcu la t ing the p r o b a b i l i t y of constra int af ter any programme change, on the other hand, represents an upper-bound estimate of the true p r o b a b i l i t y (assuming ind iv idua l s want to respond to a less-generous UI programme by increasing labour supply) . In th i s case, any ind iv idua l s not f u l l y able to carry out revised employment/unemployment plans w i l l be treated as constrained even i f , in the i n i t i a l s i t u a t i o n , he or she was not constrained and was thus p a r t i a l l y able to adjust to the revised programme. Simulations of behavioural responses for Model 2 are c a r r i e d out using both upper and lower-bound estimates of the p r o b a b i l i t y of c o n s t r a i n t . Simulation Results / 116 To incorporate the p r o b a b i l i t y of constra int without introducing the problem of uncertainty into the Model 2 s imulat ion procedure, a p r o b a b i l i t y of constra int (upper and lower-bound) i s ca lcu la ted for each s ingle i n d i v i d u a l in the sample. Then, each i n d i v i d u a l is replaced by ten ' r e p l i c a s ' of himself or h e r s e l f . A f r a c t i o n of these ten ind iv idua l s corresponding with the estimated p r o b a b i l i t y of constraint are assumed a c t u a l l y to be constrained. (If the estimated p r o b a b i l i t y of constraint for an i n d i v i d u a l i s 80 percent, then he or she is replaced by eight r e p l i c a s of himself or herse l f who are constrained and two rep l i cas of himself or herse l f who are not constrained. ) Constrained members of the enlarged population are assumed to be unable to respond to changes in the UI programme. Unconstrained members are assumed to behave as in Model 1: 'net' wages and non-labour incomes fol lowing UI reform are ca lcu la ted and the estimated parameters of the Model 2 leisure-demand equations are used to predic t behavioural responses. However, since Model 2 parameter estimates d i f f e r subs tant ia l l y from Model 1 estimates, predicted changes in unemployment re su l t ing from a given change in the UI programme w i l l a l so d i f f e r . (Model 2 parameter estimates suggest that ind iv idua l s are less responsive to var ia t ions in wages and non-labour incomes than i s true for Model 1 est imates.) Simulation Results / 117 For couples, the Model 2 s imulation procedure is more involved. To avoid introducing uncertainty , each household i s again replaced by ten r e p l i c a s of i t s e l f . A frac t ion of the rep l i ca ted households corresponding with the p r o b a b i l i t y that the household is constrained are assumed to be constrained. For households with only one working member unemployed, th i s p r o b a b i l i t y is ca lcu la ted as the appropriate i n t e g r a l over the marginal density funct ions , f , (e , ) or f , ( e 2 ) . f Constrained households with only one member unemployed are unable to respond to UI reform. By d e f i n i t i o n , the unemployed i n d i v i d u a l already experiences more unemployment than the household would choose. The spouse without unemployment i s unable to work more than the f i f ty - two weeks he or she already takes. Unconstrained households with only one member unemployed can adjust weeks of employment/unemployment taken by the unemployed i n d i v i d u a l . tExperiments were also conducted using condi t iona l p r o b a b i l i t i e s , f ( e 1 i u 2 ) and f ( e 2 l u 1 ) . However, from a behavioural point of view, i t makes l i t t l e sense to condi t ion 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 d i f ference between spouse's observed and quant i ty -constra ined leisure-demand share ( s ^ - s ^ z . ) ; i=1,2 and j=2,1) since the spouse w i l l only be operating on an e f f ec t ive function i f a constra int e x i s t s . Moreover, cond i t iona l p r o b a b i l i t i e s depend on estimated corre la t ions between error terms. This i s a problem for f ( e 2 l u 1 ) since the estimated c o r r e l a t i o n between u, and e 2 i s -.9994 and hence the cond i t iona l p r o b a b i l i t y of constra int for unemployed married women is c lose to 100 percent. Simulation Results / 118 It i s assumed that such responses are generated according to the estimated leisure-demand function for Model 2. If both household heads experience unemployment, each household i s replaced by ten r e p l i c a s , appropriate fract ions of which face ( i ) two constra ints ( i i ) one constraint ( i i i ) no cons tra in t s . P r o b a b i l i t i e s for these cases are ca lcu la ted as s?-s() s?-s() ( i ) P1=; 1 W ; 2 w f ( e , , e J ) d e 2 d e , — CO —00 ( i i ) (a)P2A=f_^1 S ( ) / g O _ s ( ) f ( e , , e 2 ) d e 2 d e i ( i i ) ( b ) P 2 B = J g O _ s ( ) J _ ^ 2 _ S ( ) f ( e , , e 2 ) d e 2 d e i ( i i i ) P3=1-P1-P2A-P2B (see Chapter 3, section 4) . If both household heads are constrained, no response to UI reform is poss ib l e . If only one household head is constrained, the behaviour of the unconstrained ind iv idua l can be adjusted according to the rationed (quantity-constrained) leisure-demand funct ion. If neither household head i s constrained, leisure-demand choices are free to respond to UI reform according to unrationed funct ions. 4 . M o d e l l i n g UI Reform Si m u l a t i o n R e s u l t s / 119 For the purposes of t h i s a n a l y s i s , the Macdonald Commission p r o p o s a l s are reduced t o : 1. d e c r e a s i n g the b e n e f i t - r e p l a c e m e n t r a t e to 50 percent (B=.50) 2. e l i m i n a t i n g r e g i o n a l l y - e x t e n d e d b e n e f i t s (EXT=0) 3. i n c r e a s i n g the minimum e l i g i b i l i t y requirement to 15(20) weeks (MIN=15; MIN=20) 4. r e q u i r i n g two weeks of employment for one week of UI b e n e f i t (QA=.5). f The Forget p r o p o s a l s are approximated by: 1. ' a n n u a l i z i n g ' the b e n e f i t - r e p l a c e m e n t r a t e 2. f i x 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 a t ten weeks of employment as an approximation of the proposed 350 hours 3. g r a n t i n g a f u l l f i f t y - w e e k b e n e f i t p e r i o d f o r anyone s a t i s f y 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 4. a b o l i s h i n g the b e n e f i t repayment requirement f o r high-income workers. Since the l a b o u r - s u p p l y models are formulated i n terms of weeks of employment/unemployment, the proposed switch to cumulative hours as a b a s i s f o r b e n e f i t e l i g i b i l i t y can only fThe assumption that i n d i v i d u a l s form annual plans (see Chapter 2, s e c t i o n s 1 and 2) means that no-one w i l l ever b u i l d a f i f t y - w e e k e n t i t l e m e n t p e r i o d . Thus, the f a c t that i t i s not p o s s i b l e to accumulate f i f t y weeks of b e n e f i t w i t h i n a one-year framework i s not a problem. Simulation Results / 120 be approximated by a ten-week entrance requirement. This i s p a r t i c u l a r l y inadequate for part- t ime workers. E i ther the Macdonald or the Forget proposals would resu l t in less money being spent on UI, and ant ic ipated uses for funds saved could influence household behaviour. Income taxes, for example, could be reduced to generate add i t i ona l incentives for increased supply of labour serv ices . Such secondary channels of influence from UI reform are, however, ignored. It i s assumed, in the s t a t i c and c e r t a i n model of labour-market behaviour employed here, that people pay no at tent ion to poss ible a l t ernat ive uses for funds saved by reforming UI. The analys i s which fo l lows, c l e a r l y , does not take a 'balanced-budget' approach. Changing the parameters of the UI programme can af fect household budget constraints by changing segment lengths or by changing net wages and non-labour incomes associated with p a r t i c u l a r segments. Decreasing the benefit-replacement rate (B=.50) does not affect segment lengths. However, slopes and intercepts are a f fec ted . Referring back to equations (2.1) and (2 .2) , i t i s obvious that lowering the benefit-replacement rate decreases both the rate of subsidy (and thus reduces the net wage rate) and the non-labour income associated with the subsidy segment. On the tax Simulation Results / 121 segment, a lower benefit-replacement rate reduces the i m p l i c i t UI tax (and thus increases the net wage rate) and decreases non-labour income. E l iminat ing regional ly-extended benefits (EXT=0) lengthens (creates) the subsidy segment of the budget constra int for workers in high-unemployment regions where such benefi ts are current ly a v a i l a b l e . (There i s , of course, no impact on the budget constra ints of workers for whom regional ly-extended benefi ts are current ly unavai lable . ) Net wage rates are unaffected, but non-labour income w i l l decrease on the subsidy segment and increase on the tax segment of the budget c o n s t r a i n t . Increasing the minimum number of weeks of work necessary to qua l i fy for UI again p r i m a r i l y af fects high-unemployment regions where minimum required weeks are current ly lower than elsewhere in the country. The impact of th i s p o l i c y change on i n d i v i d u a l budget constraints i s simply to shorten the subsidy segment. There i s no change in net wage rates or non-labor incomes. Requiring two weeks of e l i g i b l e employment to earn one week of UI benefit reduces the i m p l i c i t rate of subs id izat ion and hence reduces the net wage rate on the subsidy segment of Simulation Results / 122 the budget constraint but does not af fect non-labour income. The net wage rate on the tax segment i s not s i m i l a r l y affected since the i m p l i c i t 'UI tax' is only generated when add i t i ona l weeks of employment are taken at the expense of weeks of earned UI benef i t s . This can only occur on a one-for-one bas i s . However, since reducing the rate at which UI benefits can be earned w i l l increase the number of weeks which must be worked before the UI tax becomes operative (MAX), non-labour income increases . The Macdonald Commission package incorporates a l l of the above changes. (For s imulat ion, the option MIN=15 is a r b i t r a r i l y chosen.) The major components of the .Forget package are the e l iminat ion of regional ly-extended benefits and ' a n n u a l i z a t i o n . ' Under a system of annual i za t ion , there i s no subsidy segment in any province . Once the f ixed minimum entrance requirement of ten weeks of insurable employment has been reached, the f ixed entitlement per iod of f i f t y weeks means that every worker faces an i m p l i c i t UI tax. From ten to f i f t y weeks of employment, the UI tax rate increases as the benefit-replacement rate increases with a d d i t i o n a l weeks of work. Thus, between the end-points of ten and f i f t y the Forget budget constraint resembles the budget constra int for a piece-wise l inear progressive income tax. Simulation Results / 123 For s ingle i n d i v i d u a l s , the budget constra int i s changed as described above, new labour-supply choices are predicted and a check i s made to see i f the new choice of weeks of work i s consistent with the new wage rate and non-labour income (and poss ibly new budget segment). If not , then a second labour-supply pred ic t ion is made at the net wage and non-labour income which should apply at predicted weeks of work. This procedure i s used to avoid pred ic t ing weeks of work which would not be f e a s i b l e , given the new budget c o n s t r a i n t . In Figure 2.1, a point such as A could not be associated with the wage rate and non-labour income of the tax segment ( i . e . , C i s not f e a s i b l e ) . Idea l ly , the checking procedure should i t era te u n t i l predicted weeks are consistent with budget segment for each observation. However, i t is poss ible that convergence would never be reached since each net wage/non-labour income pair w i l l resu l t in one labour-supply p r e d i c t i o n . For s ingle household heads, therefore , reported wage rates and non-labour incomes are those of the second i t e r a t i o n . For couples (due to computational expense), reported values are for i n i t i a l changes. Fortunate ly , given that a majority of observations are o r i g i n a l l y located on the tax segment of the budget c o n s t r a i n t , given the general ly p o s i t i v e estimated own-wage e l a s t i c i t i e s and given the ' re trenching' nature of the po l i cy changes simulated, the case depicted in Figure 2.1 i s Simulation Results / 124 the most common error. As suggested by the diagram, the approximation involved through t h i s mis-association i s not l i k e l y to be excessive. Another weakness of the simulation approach employed i s that, for s i m p l i c i t y , increases in marginal income-tax rates which would occur as labour supply increases are ignored. Such increases could generate incentive e f f e c t s to p a r t i a l l y o f f - s e t the impact of UI reform. However, since the focus of thi s analysis i s on UI reform, the incentive e f f e c t s of the income-tax system are ignored (although the estimated model incorporates income taxes, as described in Chapter Two). F i n a l l y , non-participants continue to be excluded from t h i s analysis and from the welfare evaluation although, of course, changes in the UI programe may influence p a r t i c i p a t i o n decisions. 5 . Predicted Labour-Supply Responses to UI Reform Model 1 simulation results for single men and single women are presented in Tables 5.1-5.4; results for married men and married women are presented in Tables 5.5-5.8. In the context of a t r a d i t i o n a l model of unconstrained response, both the Macdonald and the Forget reform proposals s i g n i f i c a n t l y reduce average weeks of unemployment. For Simulation Results / 125 s ingle men, average weeks of unemployment for the f u l l sample f a l l from 4.92 to 2.75 under the Macdonald proposals and to 2.32 under the Forget proposals (Table 5 .1) . These numbers are the resul t of a drop in the t o t a l number of ind iv idua l s experiencing unemployment as well as of a drop in average weeks of unemployment experienced by the unemployed group. This i s c l ear from an examination of simulation re su l t s for the unemployed sample of s ingle men (Table 5.2) . Average weeks of unemployment f a l l from 19.12 to 16.19 under the Macdonald proposals and 14.17 under the Forget proposals . The incidence of unemployment drops from 27.13 percent to 18.55 percent under Macdonald (144 of the 455 workers unemployed in the i n i t i a l s i tua t ion 'choose' not to take any unemployment af ter the po l i cy change) and 18.07 percent under Forget (152/455 choose not to be unemployed). Of the i n d i v i d u a l components of the Macdonald package, reducing the benefit-replacement rate has by far the largest impact. Average weeks of unemployment experienced by the unemployed population of s ingle men drop from 19.12 to 16.44 while incidence drops from 27.13 percent to 22.72 percent. Other i n d i v i d u a l parameter changes also generate incentive e f fec t s , but the magnitudes are much smaller . Model 1 s imulat ion resu l t s for s ingle women are very s i m i l a r , although s ingle women experience less unemployment Simulation Results / 126 in the i n i t i a l s i t u a t i o n . For the population as a whole, average weeks of unemployment f a l l from 3.29 to 1.87 under the Macdonald proposals and to 1.74 under the Forget proposals (Table 5 .3) . For the unemployed sample of s ingle women, average weeks of unemployment f a l l from 19.03 to 15.71 under Macdonald and to 15.11 under Forget . Incidence of unemployment drops from 17.57 percent to 12.45 percent under Macdonald (107/367 i n i t i a l l y unemployed women choose to work a l l year) and to 12.02 percent under Forget (116/367 choose f u l l - y e a r employment; see Table 5 .4) . F i n a l l y , as was also the case for s ingle men, the s ingle most important component of the Macdonald package is the reduction in benefit-replacement ra te . Model 1 s imulation r e s u l t s for married men are very s imi lar to those obtained for s ingle men and s ingle women. Average weeks of unemployment f a l l from 3.41 to 2.19 weeks under the proposed Macdonald reform package and to 1.86 weeks under the proposed Forget package (Table 5.5) . For the unemployed sample, average weeks f a l l from 18.06 to 14.29 under Macdonald and to 15.65 under Forget . Average incidence of unemployment drops from 20.48 percent to 16.64 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) and to 13.20 percent under Forget (182/512 choose f u l l - y e a r employment; see Table 5.6) . Of the Simulation Results / 127 components of the Macdonald Commission package, reducing the benefit-replacement rate again has the largest impact. E l iminat ing regional ly-extended benefits generates s i g n i f i c a n t behavioural responses; other components of the package have very l i t t l e impact. Model 1 simulation resu l t s for married women again suggest that implementation of e i ther the Macdonald or the Forget proposals would subs tant ia l l y reduce observed unemployment. Average weeks of unemployment for married women drop from 5.60 to 3.72 under Macdonald and to 3.48 under Forget (Table 5.7) . For the unemployed sample of married women, average weeks f a l l from 20.51 to 15.37 under Macdonald and to 17.60 under Forget; incidence f a l l s from 38.52 percent to 34.04 percent under Macdonald (112 of 963 o r i g i n a l l y unemployed workers choose f u l l - y e a r employment) and to 29.60 percent under Forget (223/963 choose f u l l - y e a r employment; see Table 5.8) . Response to i n d i v i d u a l components of the Macdonald package, however, departs s i g n i f i c a n t l y from the pattern es tabl i shed by s ingle men, s ingle women and married men: the most important component of the proposed reform package is the e l iminat ion of regional ly-extended benefits rather than the reduction of the benefit-replacement ra te . (Average weeks of unemployment f a l l from 5.60 to 4.00 when regional ly-extended benefits are e l iminated. For the Simulation Results / 128 unemployed sample, average weeks f a l l from 20.51 to 16.60 weeks; incidence f a l l s from 38.52 percent to 35.04 percent . ) The second largest behavioural response i s generated by increasing the minimum e l i g i b i l i t y condit ion to twenty weeks (MIN=20); th i s i s followed by requir ing two weeks of work for every week of earned benefit (QA=.5). Decreasing the benefit-replacement rate has a much less important impact on the behaviour of married women than on the behaviour of any other group. This i s due both to i n i t i a l pos i t ions on budget constra ints and to r e l a t i v e e l a s t i c i t y magnitudes. More married women (673/2500) than married men (467/2500) are i n i t i a l l y located on the tax segment of the budget constraint (compare Tables 5.5 and 5.7) . And, the average duration of unemployment for married women located on the tax segment i s greater than for married men located on the tax segment. Thus, more women are affected by po l i cy changes such as e l iminat ing regional ly-extended benef i t s , increasing minimum entrance requirements and decreasing the rate at which weeks of employment earn weeks of UI benef i t . Twenty-nine married men are found on segment 1 after the entrance requirement i s increased to 20 weeks; f i f t y - e i g h t married women are found on segment 1. Given the large own-wage e l a s t i c i t i e s of labour supply for married women, i f a large number of women Simulation Results / 129 are af fected by changes at the lower end of the budget c o n s t r a i n t , a large increase in average observed labour supply can be expected. At the same time, these increases in a wife's wage and reductions in her non-labour income w i l l both, other things equal , serve to decrease her husband's labour supply. Since a r e l a t i v e l y small number of married men are d i r e c t l y affected by, for example, increasing minimum required weeks of work, such cross -e f fec t s reduce the average observed response for married men. Decreasing the benefit-replacement rate , on the other hand, a f fects a l l unemployed workers, regardless of the ir i n i t i a l pos i t ions on budget cons tra in t s . Thus, net wage rates and non-labour incomes w i l l change and behavioural responses can be ant i c ipa ted from a l l unemployed married men. Sixty-two of the 467 men i n i t i a l l y located on the tax segment increase weeks of work enough to reach e i ther segment 4 or f u l l - y e a r employment (see Table 5.5). Net wage rates and non-labour incomes of a l l married women must also change, but the lack of observed response in th i s case (only 2/673 women leave the tax segment) suggests an o f f - s e t t i n g influence on the ir labour-supply choices . Given the very large estimated cross-wage e l a s t i c i t i e s for married women, i f wage rates and non-labour incomes of married men change enough to generate s i g n i f i c a n t behavioural responses then s i g n i f i c a n t cross Simulation Results / 130 e f fec t s on the behaviour of the ir wives can also be expected. Simulation resu l t s suggest that such cross -e f fec t s are important: f ive women, i n i t i a l l y employed f u l l year, choose less than f u l l - y e a r employment fol lowing the po l i cy change. These women are part-t ime workers from the A t l a n t i c and West and have very large cross-wage e l a s t i c i t i e s . In general , the lack of movement off the tax segment of the budget cons tra in t , even though a l l women located on the tax segment experience an increase in net wage, suggests that cross-wage ef fects are o f f - s e t t i n g d i r e c t behavioural responses (compare the otherwise f a i r l y s imi lar responses of married women and s ingle men). The p o s s i b i l i t y of such i n d i r e c t consequences of labour-market p o l i c y changes are often over- looked, but resu l t s here suggest that they may be important and that more at tent ion should be paid to the modelling of the decision-making processes of households. The model used here i s very crude; i t might be worthwhile to develop more sophis t icated models of jo in t decision-making for the purposes of po l i cy a n a l y s i s . Incidence and 'dura t ion '* are subs tant ia l ly reduced by both the Macdonald and the Forget reform packages in a l l regions. However, the absolute magnitude of response is larger in fAverage weeks of unemployment i s only a very rough proxy for 'durat ion' of unemployment. Hasan and de Broucker (1982) discuss problems in accurately measuring durat ion . Simulation Results / 131 regions s t a r t i n g with higher unemployment rates . The Forget package a c t u a l l y resu l t s in a lower average duration of unemployment in A t l a n t i c than in Central Canada (although incidence remains h igher ) . As w e l l , e l iminat ing regional ly-extended benefits and increasing minimum e l i g i b i l i t y condit ions have a larger impact in A t l a n t i c Canada, where provis ions of the UI system are current ly more generous. It i s i n t e r e s t i n g , given the worry over the adverse incentive consequences of regional ly-extended benef i t s , that reducing the benefit-replacement rate has a much larger impact on workers in A t l a n t i c Canada than e l iminat ing regional ly-extended benef i t s . Simulation resu l t s for Model 1 suggest that behavioural responses to UI reform w i l l be very large . But, these resu l t s are based on the assumption that workers are able to respond to a cut in programme generosity by choosing a d d i t i o n a l weeks of employment. Model 2 s imulations qua l i fy these predic t ions by al lowing for poss ible constra ints on labour supply. Model 2 s imulation resu l t s (Tables 5.9-5.16) suggest that there may be almost no behavioural response to UI reform. Very high estimated p r o b a b i l i t i e s of constraint for a l l groups ensure th i s r e s u l t . Examining Model 2 s imulation output for the unemployed sub-sample of married men (Table 5.14) reveals that both incidence and average S i m u l a t i o n R e s u l t s / 132 weeks o f unemployment f a l l v e r y s l i g h t l y f o r b o t h t h e M a c d o n a l d a n d t h e F o r g e t r e f o r m p a c k a g e s . F o r s i n g l e men, s i n g l e women a n d m a r r i e d women ( T a b l e s 5.10, 5.12 a n d 5 . 1 6 ) , b o t h t h e M a c d o n a l d a n d t h e F o r g e t p r o p o s a l s r e s u l t i n an i n c r e a s e i n a v e r a g e weeks o f unemployment t o g e t h e r w i t h a s m a l l r e d u c t i o n i n i n c i d e n c e : a s m a l l number o f u n c o n s t r a i n e d ( a n d u n e m p l o y e d ) i n d i v i d u a l s e x p e r i e n c i n g o n l y a few weeks o f unemployment r e s p o n d t o t h e programme c h a n g e s by d e c i d i n g t o work a l l y e a r ; a m a j o r i t y o f c o n s t r a i n e d w o r k e r s , c u r r e n t l y e x p e r i e n c i n g l o n g p e r i o d s o f un e m p l o y m e n t , a r e u n a b l e t o r e s p o n d . 6. Conclusions The f i r s t m a j o r c o n c l u s i o n f r o m t h e p o l i c y s i m u l a t i o n s i s t h a t i f an u n c o n s t r a i n e d m o d e l o f l a b o u r s u p p l y i s v i e w e d a s t h e most a p p r o p r i a t e d e s c r i p t i o n o f r e a l i t y , m a j o r r e d u c t i o n s i n unemployment c a n be e x p e c t e d i f t h e C a n a d i a n UI s y s t e m i s r e f o r m e d a c c o r d i n g t o e i t h e r t h e M a c d o n a l d o r t h e F o r g e t p l a n s . C o m p a r i n g t h e two p r o p o s a l s i n t h e c o n t e x t o f M o d e l 1 s u g g e s t s t h a t b e h a v i o u r a l r e s p o n s e t o t h e F o r g e t p a c k a g e c o u l d be s l i g h t l y g r e a t e r : f o r s i n g l e i n d i v i d u a l s , b o t h i n c i d e n c e a n d a v e r a g e weeks o f unemployment ( f o r i n d i v i d u a l s c h o o s i n g u n e m p l o y m e n t ) w o u l d be l o w e r w i t h t h e F o r g e t scheme t h a n w i t h M a c d o n a l d ; f o r c o u p l e s , i n c i d e n c e Simulation Results / 133 would be lower, but average weeks of unemployment taken by the unemployed group would be s l i g h t l y higher under Forget . For e i ther reform package, the largest absolute reductions in weeks of unemployment are made by married women and s ingle men (the groups s t a r t i n g with the most unemployment). Post-reform, average weeks of unemployment taken by the unemployed are very s imi lar across demographic groups. For s ingle men, s ingle women, and married men, the most important component of the Macdonald package of reform proposals i s the reduction in benefit-replacement ra te . For married women, proposals such as e l iminat ing regionally-extended benef i t s , increasing minimum required weeks of work to e s tab l i sh e l i g i b i l i t y for UI, and requ ir ing two weeks of work to earn one week of UI benefit a l l have a larger impact on behaviour. These f indings i l l u s t r a t e the importance of jo int (household) responses to p o l i c y changes: large cross-wage e l a s t i c i t i e s o f f - se t the d i r e c t own-wage responses of married women to a reduction in benefit replacement rate . In a small number of cases, married women are a c t u a l l y induced to choose more unemployment fol lowing a reduction in benefit-replacement rate because th i s p o l i c y change simultaneously increases the ir husbands' wage rates . These re su l t s depend on a highly s i m p l i f i e d model of jo in t behaviour, but i l l u s t r a t e the potent ia l importance of Simulation Results / 134 developing more sophis t icated models for the analys is of labour-market p o l i c y . The second major conclusion obtained from the p o l i c y simulations i s that , i f a constrained model of labour supply is viewed as most r e a l i s t i c , nei ther the Macdonald nor the Forget proposals for the reform of the Canadian UI system w i l l have any s i g n i f i c a n t impact on unemployment. This resul t i s , of course, cond i t iona l on a model which takes occupation, region of residence and hours of work per week as given and ignores the poss ible influence of UI reform on the demand side of the labour market. V I . WELFARE EVALUATION Chapter Six develops welfare evaluation procedures consistent with U t i l i t a r i a n i s m , John Rawls' theory of jus t i ce and Robert Nozick's entitlement theory. Measures are then used, in conjunction with the resu l t s from the s imulation of behavioural responses described in Chapter F i v e , to conduct an e t h i c a l l y f l e x i b l e evaluation of UI reform proposals . Reported welfare evaluation r e s u l t s , l i k e reported simulation r e s u l t s , are thus dependent on the samples taken from the 1982 Survey of Consumer Finance; evaluations are conducted for a population of households character ized by having heads who are labour-force p a r t i c i p a n t s . The approach i s , again, more general than suggested by th i s a p p l i c a t i o n . 1. Methodology for the U t i l i t a r i a n Evaluations From a U t i l i t a r i a n point of view, s o c i a l welfare depends on i n d i v i d u a l l y perceived u t i l i t i e s . Since, for Model 1, i n d i v i d u a l perception of u t i l i t y depends on personal tas te , a U t i l i t a r i a n measure must f ind a means of comparing the u t i l i t i e s of ind iv idua l s with d i f f erent tas tes . And, since both leisure-demand models are formulated in terms of households, a U t i l i t a r i a n measure must f ind a means of 135 Welfare Evaluation / 136 d e r i v i n g i n d i v i d u a l from household u t i l i t y so that each member of the household ( inc luding ch i ldren and non-working economic family members) counts. Both requirements can be s a t i s f i e d by der iv ing 'normalized' per-person u t i l i t y functions: v*=V i (w i ,Y)= {V h (w i f Y)}{ l / s (A)} where: * 1. v^=mdividual normalized u t i l i t y (which i s the same for each i n d i v i d u a l in the household) 2. (w^,Y,)=the ind iv idua l i n d i r e c t u t i l i t y function 3. v h ^ w i ' Y ) = t h e household ind irec t u t i l i t y function 4. s(A)=a sca l ing funct ion, dependent on demographic c h a r a c t e r i s t i c s The sca l ing funct ion, s (A) , allows the comparison of the u t i l i t i e s of ind iv idua l s with d i f f erent tastes or the comparison of the u t i l i t i e s of ind iv idua l s from d i f f erent household conf igurat ions . The choice of s (A) , therefore, const i tutes an e x p l i c i t interpersonal comparison. That i s , * * i f v^ = V j where i and j are d i f f erent people (with d i f f erent tastes and/or household configurat ions) the judgement made is that i and j are equally well o f f . To derive the s(A) sca l ing factors for Model 1, where demographic var iables play a prominent r o l e , s tart with the Welfare Evaluat ion / 137 household expenditure funct ion: 9 9 e(u,w,A)=7o(A)+7 1(A)w 1+7 2(A)w 2 +w 1 1 w 2 2 u. From t h i s , define the i n d i v i d u a l 'normalized' expenditure function as (6.1) e*(u,w,A)=7 0(A)+7, (A)w 1+7 2(A)w 2+w? 1w 2 ? 2[s(A)u] for couples, or (6.2) e * ( u , w , A ) = 7 o ( A ) + 7 1 ( A j w ^ w ? 1 ( A ) [ s ( A ) u ] for s ingle i n d i v i d u a l s . Make the convenient normalization that s(A)=1 for some reference s ingle i n d i v i d u a l with no dependants. That i s , assume that the i n d i v i d u a l expenditure function equals the household expenditure function when the household consists of some reference s ingle i n d i v i d u a l with an a r b i t r a r i l y chosen set of demographic c h a r a c t e r i s t i c s , A . f Choose as reference wage, w , the weekly equivalent of the federal minimum wage for 1981 ($140). As reference earned income, choose the pover ty - l ine income appropriate for the POV R household, y (A ). Then, a so lut ion for a reference T> u t i l i t y l e v e l , u , can be obtained by equating the household expenditure function for the reference household with f u l l income for the reference household. The household fFor the implementation of Model 1, the reference household is a r b i t r a r i l y taken to be a representative s ingle man with no dependants, located in a r u r a l area in Central Canada who is neither 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 representative s ingle man with no dependants l i v i n g in a r u r a l area. For Model 2, being s ingle and male es tabl i shes the appropriate value for the gamma and theta parameters; the a d d i t i o n a l c h a r a c t e r i s t i c s merely determine a reference poverty-income l e v e l . Welfare Evaluat ion / 138 expenditure function equals the i n d i v i d u a l expenditure function for the reference household since s(A)=1. F u l l income is defined as 'poverty income + the value of l e i s u r e t ime, ' where l e i sure i s f ree ly chosen but evaluated at the reference wage. Thus, using the compensated leisure-demand function for the reference i n d i v i d u a l , L* = T 1 (A R)+0 (A R ) ( w R ) m ) " 1 [ s ( A ) u R ] , the reference measure of f u l l income can be constructed as VR POV/.R u r ,.R, .w.R, 0(A*)-1 Ri R Y =y (A ) + [ -y 1 (A )+8{A )w u ]w . Equating reference f u l l income with the i n d i v i d u a l expenditure function for the reference household, ,.R U ,,R\ R,, Rx0(A) R since s(A )=1, i t i s poss ible to solve for reference u t i l i t y : R uR = [ y P 0 V ( A R ) - 7 0 ( A R ) ] / [ ( l - 0 ( A R ) ) ( w R ) e ( A ) ] . This value for reference u t i l i t y can then be subst i tuted back into i n d i v i d u a l expenditure funct ions , 6.2 for s ingle i n d i v i d u a l s , and i n d i v i d u a l expenditure functions can be equated with f u l l incomes, y P 0 V ( A ) + [ 7 l ( A)+0 ( A ) w 0 ( A ) _ 1 u R s ( A ) ] w R for s ingle i n d i v i d u a l s , to solve for household-specif ic s(A) values . For households with a s ingle working head, interpersonal s ca l ing factors are thus Welfare E v a l u a t i o n / 139 s(A) = [y P O V(A>-7 o(A)]/[(l-0(A))(wV ( A )u R], where the poverty income and parameter values are a p p r o p r i a t e to household c h a r a c t e r i s t i c s . F o l l o w i n g the same procedure f o r couples y i e l d s s(A) = [yPOV(A)-7o(A)]/[(l-01-02)(wR)ei ( w V 2 u R . For Model 2, parameter val u e s vary only f o r s i n g l e men, s i n g l e women and cou p l e s . They are not f u n c t i o n s of demographic v a r i a b l e s . F i n a l l y , i n d i v i d u a l 'normalized' u t i l i t y can be represented as the now a p p r o p r i a t e l y - s c a l e d value of the i n d i r e c t u t i l i t y f u n c t i o n : V * = 1 / S ( A ) { [ ( T - L ) w + N L I N C - 7 o ( A ) ] / [ ( 1 - 6 ( A ) ) w 6 ( A ) ] } fo r i n d i v i d u a l s from households with a s i n g l e working head; V*=1/S(A){[(T-L,)w,+(T-L 2)w 2+NLINC 1+NLINC 2-7o(A)]/ d - ^ - e . j w ^ w f 2 } f o r i n d i v i d u a l s from households with two working heads. Table 6.1b presents r e p r e s e n t a t i v e values f o r Model 1 s c a l i n g f a c t o r s (assuming there are no c h i l d r e n l e s s than seven years of age i n the household and that re s i d e n c e i s i n C e n t r a l Canada). S u b s t a n t i a l v a r i a t i o n , p a r t i c u l a r l y , among s i n g l e men, s i n g l e women and coup l e s , r e f l e c t s v a r i a t i o n i n estimated Model 1 parameter v a l u e s . For example, four the estimated c o e f f i c i e n t f o r EFAM, the number of i n d i v i d u a l s i n the economic f a m i l y , i s negative f o r s i n g l e women and Welfare Evaluat ion / 140 pos i t ive for s ingle men (see Tables 4.7 and 4 .8) . Thus, as economic family s ize i s increased in Table 6.1b, 7 0 (A) i s reduced and s(A) i s increased for s ingle women while 7o(A) i s increased and s(A) i s reduced for s ingle men. Representative sca l ing factors are presented for comparison with Table 6.1a, but sca l ing factors a lso vary with demographic ' taste ' var iables for region of residence, occupation, number of ch i ldren less than seven, and years of education. Since Model 1 parameter estimates were obtained under the assumption that ' tastes ' for unemployment vary with demographic c h a r a c t e r i s t i c s , th is assumption now becomes an important determinant of interpersonal u t i l i t y comparisons. Model 2 ignores the possible influence of demographic var iables on ind iv idua l behaviour, so tastes are not important for interpersonal u t i l i t y comparisons except to the extent that estimated parameters d i f f e r for s ingle men, s ingle women and couples. Indiv idual u t i l i t i e s are scaled to r e f l e c t basic di f ferences among these groups and to r e f l e c t di f ferences in need as measured by the low-income-cut-offs . Model 2 sca l ing factors are very c lose ly t i e d to the interpersonal comparisons i m p l i c i t in the S t a t i s t i c s Canada Low-income cut -o f f s (compare Tables 1.a and 1.c) . Welfare Evaluat ion / 141 Scal ing factors e s tab l i sh the r e l a t i o n s h i p between the f u l l income necessary for an a r b i t r a r y household to achieve some reference u t i l i t y l e v e l and the f u l l income necessary for the reference household to achieve the same l e v e l , given the same reference wage rate and pover ty - l ine expenditure l e v e l but d i f f erent tastes and circumstances as re f l ec ted through d i f f erent values for the gamma and theta parameters. Estimated values for these parameters depend on the data set employed, the funct ional form chosen and the econometric s p e c i f i c a t i o n u t i l i z e d . They are also c r i t i c a l l y dependent on assumptions made about the nature of unemployment. (For Model 1, the assumption that demographic var iab les exert a l inear influence on gamma and theta parameters i s r e s t r i c t i v e and should be remembered.) This approach to interpersonal comparisons, while dependent on these l i m i t i n g fac tors , has at least the appeal of being e x p l i c i t and of being based on interpersonal comparisons which are commonly used elsewhere ( i . e . , whenever the Canadian poverty l ines are used) . f Jorgenson and Slesnick (1984, for example) develop an a l t e r n a t i v e econometric approach to making interpersonal comparisons. S tar t ing with a trans log i n d i r e c t u t i l i t y fGiven the a r b i t r a r y nature of the low-income-cut-offs , i t would be in teres t ing and perhaps important to to consider a l t e r n a t i v e s measures. Welfare Evaluat ion / 142 funct ion , they impose condit ions required for exact aggregation and for the i n t e g r a b i l i t y of demand funct ions . Then, fol lowing Barten (1964) they assume that d i f ferences in preferences across demographic groups appear only as d i f ferences in ' e f f ec t i ve ' quant i t i e s consumed ( i . e . , d i f ferences in quant i t i e s consumed div ided by commodity-specific household equivalence s ca l e s ) . This i s r e - in terpre ted as d i f ferences in ' e f f ec t i ve ' pr ices (pr ices m u l t i p l i e d by equivalence s ca l e s ) . The chosen funct ional form and the aggregation and i n t e g r a b i l i t y condit ions already imposed then determine 'commodity-specific trans log equivalence scales ' (p 76). F i n a l l y , a general household equivalence scale i s defined as the r a t i o of the expenditure function for an a r b i t r a r y household evaluated at a reference u t i l i t y l e v e l to the expenditure function for a reference household evaluated at the same u t i l i t y l e v e l . This equivalence sca le , dependent on demographic c h a r a c t e r i s t i c s and p r i c e s , const i tutes the basic interpersonal comparison made ( i m p l i c i t l y ) by Jorgenson and S lesn ick . Given the r e s t r i c t i o n s imposed,f Jorgenson and Slesnick can estimate aggregate expenditure shares and then recover i n d i v i d u a l expenditure shares and the parameters of the i n d i r e c t u t i l i t y funct ion . This procedure i l l s t r a t e s how a set of interpersonal comparisons can be based on observed behaviour fBlackorby and Donaldson (1987) show that exact aggregation i s stronger than required . Welfare Evaluation / 143 (as re f l ec ted in the data on expenditure shares) , on a chosen funct ional form, and on assumptions made about the way in which demographic c h a r a c t e r i s t i c s should be incorporated. The approach to interpersonal u t i l i t y comparisons employed in my work d i f f e r s from that of Jorgenson and Slesnick in a number of ways: F i r s t , the funct ional form is more r e s t r i c t i v e (although th i s has the advantage of y i e l d i n g a simpler expression for the interpersonal sca l ing f a c t o r ) ; second, demographic parameters are incorporated in a d i f f erent fashion (Model 1); t h i r d , observed behaviour is not assumed to r e f l e c t u t i l i t y - m a x i m i z i n g behaviour in a l l cases (Model 2); fourth , leisure/unemployment i s the p r i n c i p a l commodity consumed ( a l l other goods are aggregated into a composite commodity); f i n a l l y , a measure of need exogenous to the estimating data set , the low-income c u t - o f f s , const i tutes the base of the comparisons - taste di f ferences merely augment the pover ty - l ine u t i l i t y comparisons. * Given representations for i n d i v i d u a l u t i l i t i e s , v^, a welfare evalat ion measure in 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 i s U = { ( l / n ) Z ( v * ) r } l / r ;r/0,r<1 Welfare Evaluat ion / 144 * where v^ is the normalized i n d i v i d u a l u t i l i t y of the i t h i n d i v i d u a l and n i s the ent ire populat ion , inc luding dependants.f Each member of a mult i -person household i s assigned the same i n d i v i d u a l normalized u t i l i t y value and enters the U t i l i t a r i a n measure separately . This assumes a l l households members share the same l e v e l of u t i l i t y . The parameter r can be interpreted in two ways. F i r s t l y , fol lowing Atkinson (1970), r can be viewed as a means of introducing the diminishing marginal u t i l i t y required for a ' t rue ' U t i l i t a r i a n measure. Reca l l that with the Stone-Geary funct ional form, the marginal u t i l i t y of income must be constant. However, d iminishing marginal u t i l i t y of income can be achieved through the transformation v . = [ ( v * ) r / r ) ; r^O, r<1. (Raising v^ to the power r i s a monotonic transformation which introduces curvature; d i v i d i n g by r i s a normalization which ensures that the function v^ remains increasing in income when the parameter r i s negative.) Ca lcu la t ing an equal ly d i s t r i b u t e d equivalent income (Atkinson, 1970) consistent with a U t i l i t a r i a n s o c i a l welfare function y ie lds the measure U above: * fTh i s formulation cannot allow for negative u^ values . This created d i f f i c u l t i e s in the Model 1 evaluations for those s ingle men and women for whom regu lar i ty condit ions were not s a t i s f i e d . Reported welfare evaluation re su l t s exclude these observations. Welfare Evaluat ion / 145 Zv^=Z[ (v^) r / r ]=n(a r / r ) , where a i s equally d i s t r i b u t e d income. Then, a=U={ l / n ( Z ( u * ) r } 1 / / r , as above. A second in terpre ta t ion of the parameter r i s as a single-parameter indicator of the s o c i a l planner's l e v e l of inequal i ty avers ion . When r=1, no considerat ion i s given to d i s t r i b u t i o n in the assessment of s o c i a l welfare. When r approaches negative i n f i n i t y , the measure i s 'Maximin' and focusses on the welfare of the worst-off i n d i v i d u a l . At values between these extremes, trade-of f s are made between equity and e f f i c i e n c y . Under th i s i n t e r p r e t a t i o n , the ' U t i l i t a r i a n ' measure i s not s t r i c t l y U t i l i t a r i a n since the * chosen representations of u t i l i t y , v^, do not exhibit diminishing marginal u t i l i t y of income. In p r a c t i c e , the in terpre ta t ion given the parameter r w i l l not affect ca lcu la ted values for the U t i l i t a r i a n measure. To conduct the U t i l i t a r i a n a n a l y s i s , the measure U evaluated given the current UI system is compared with the measure U evaluated given proposed po l i cy changes. This i s done for a range of values for r . Welfare Evaluation / 146 2. Methodology for the Rawlsian Evaluations According to Rawls, economic and s o c i a l p o l i c y are to be governed by the 'second p r i n c i p l e of j u s t i c e ' (the di f ference p r i n c i p l e ) : Soc ia l and economic inequa l i t i e s are to be arranged so that they are to the greatest benefit of the least advantaged (Rawls, p.302). Rawls spec i f i e s that th i s p r i n c i p l e i s to be appl ied without reference to s p e c i f i c ind iv idua l s or the ir u t i l i t y funct ions . P o l i c i e s are to be chosen which maximize the wel l -being of the least we l l -o f f according to an index of 'primary s o c i a l goods' which Rawls says can be approximated by net income inc luding t r a n s f e r s . For the Rawlsian a n a l y s i s , therefore , welfare measurement must focus on the "worst-off group." The Rawlsian philosophy is usual ly expressed through a Maximin s o c i a l evaluation function which depends only on the welfare of the s ingle worst-off i n d i v i d u a l . However, i f , as suggested by A Theory  of Just i c e , th is i n d i v i d u a l i s interpreted as a representat ive , a broader measure is required . In Canada, people with incomes below some designated poverty l e v e l are l i k e l y candidates for members of th i s worst-off group. Welfare Evaluation / 147 To construct the Rawlsian measure, a "censored" income d i s t r i b u t i o n , in which incomes above the poverty l eve l are set equal to the poverty income l e v e l , is used ( i . e . , y = , POV POV x , POV . (y , . . . y ;y^, . . . y ) where y i s poverty income for a s ingle person with no dependants l i v i n g in a r u r a l area ($5949, using the S t a t i s t i c s Canada low-income c u t - o f f s ) ; y^, i = k , . . . n are actual household incomes for households with incomes below poverty l e v e l , d iv ided by the appropriate interpersonal sca l ing factor i m p l i c i t in the S t a t i s t i c s Canada low-income cut -o f f s (see Table 6.1a) and assigned to each member of the household so that a l l non-working household members are included in the welfare eva luat ion) . The sca l ing factors are ca lcu la ted as the relevant household poverty income divided by the poverty income for a s ingle person with no dependants l i v i n g in a r u r a l area . Indiv iduals from households with d i f f erent c h a r a c t e r i s t i c s rece iv ing the ir own appropriate poverty- l ine incomes are defined to be equally well o f f . If i t i s assumed that the same r e l a t i o n s h i p between incomes required for ind iv idua l s from d i f f erent households to be equal ly well off holds regardless of the l e v e l of well-being which is being compared, then the re la t i onsh ip between relevant poverty-income leve l s can be used as interpersonal sca l ing fac tors . Thus, the interpersonal comparisons used for the Rawlsian analys i s are based so le ly on di f ferences in Welfare Evaluation / 148 household need as measured by the Canadian poverty l i n e s . Ind iv idua l tastes do not enter the welfare evaluation as they do in the U t i l i t a r i a n case since parameters of the u t i l i t y function are not incorporated in the Rawlsian measure. (Number of household members and area of residence, the c h a r a c t e r i s t i c s for which poverty incomes vary, are given in th i s s t a t i c model so that tastes with respect to these v a r i a b l e s are also given.) The Rawlsian p o l i c y evaluation measure, R, is derived as the equally d i s t r i b u t e d income consistent with a mean of order r s o c i a l welfare function for the ent ire censored income * d i s t r i b u t i o n . Le t t ing e represent the e t h i c a l l y equivalent equally d i s t r i b u t e d income, i t must be true that { n R / n [ y P 0 V 3 r + l / n[g ( y i ) ] r } 1 / r = { l / n [ n ( e * ) r ] } 1 / r = e * ;r<1,r/0 where n i s the number of ' r i c h ' people (people with incomes above poverty l e v e l ) . f The second term can be re-wri t ten as gy- /n = n P / n [ [ l / n Pg y r ] 1 / r ] r = n P / n ( £ P ) r P P where n i s the number of 'poor' people; £ i s a mean of order r over people with incomes less than the poverty fAgain t h i s formulation cannot allow negative incomes (due, for example, to c a p i t a l los ses ) . However, th i s i s not a problem for the sample over which the evaluations are conducted since households with negative incomes are excluded p r i o r to est imation. Welfare Evaluat ion / 149 l e v e l . Thus, R=e*=[n R /n (y P 0 V + n P / n f ^ ) 1 ] 1 ^ . Using the mean of order r again allows for f l e x i b i l i t y in a t t i tude toward inequa l i ty , th i s time within a Rawlsian framework. Notice that the Rawlsian measure i s just y P < ^ V i f a l l incomes are above poverty l e v e l so that , in th i s case, the measure i s not sens i t ive to further income gains. Hence, R is only sensible i f some people have incomes below whatever value i s assigned to y P 0 V . If a l l incomes are below poverty l e v e l , R is just a mean of order r of i n d i v i d u a l scaled incomes. I f , as i s the case for t h i s sample, there are incomes both above and below the poverty l e v e l , then the value of R w i l l r e f l e c t a t t i tudes toward inequal i ty both between the poor and non-poor and among the poor. When r approaches negative i n f i n i t y , R approaches Maximin. In general , however, th i s Rawlsian measure implements the di f ference p r i n c i p l e in a manner which is more f l e x i b l e and, I be l i eve , more reasonable than 'Maximin' since i t i s sens i t ive to the welfare of the ent ire group of the poor rather than just to the welfare of the i n d i v i d u a l worst-off among them. Welfare E v a l u a t i o n / 150 3. Methodology f o r the E n t i t l e m e n t E v a l u a t i o n s Robert Nozick's e n t i t l e m e n t theory (1974) focusses on p r o c e d u r a l j u s t i c e . That i s , he views a given d i s t r i b u t i o n as j u s t " i f i t a r i s e s from another j u s t d i s t r i b u t i o n by j u s t means" (p.151). A d i s t r i b u t i o n i s j u s t only i f i t i s the h i s t o r i c a l r e s u l t of a c c e p t a b l e t r a n s a c t i o n s c a r r i e d out by p r o p e r t y h o l d e r s who have obtained t h e i r property j u s t l y . (Nozick f o l l o w s Locke i n h i s d e f i n i t i o n of r u l e s f o r e n t i t l e m e n t to p r o p e r t y . ) In c o n t r a s t to U t i l i t a r i a n i s m and Rawls' theory of j u s t i c e , Nozick argues that i n d i v i d u a l s are ends i n themselves; that t h e i r property should not be used as the means of a c h i e v i n g some conception of the common good. People should be f r e e to make t h e i r own d e c i s i o n s with respect to the d i s p o s a l of t h e i r p r o p e r t y . Hence, i t seems l i k e l y t h a t Nozick would disapprove of a UI programme such as the one which e x i s t s i n Canada today. However, he might be more fav o u r a b l y d i s p o s e d toward a UI programme i f i n d i v i d u a l b e n e f i t s more c l o s e l y matched i n d i v i d u a l c o s t s , f I d e a l l y , t h i s should be on an ex ante b a s i s ( i . e . , expected benefits=expected c o s t s ) . However, s i n c e the models developed do not e x p l a i n household behaviour under c o n d i t i o n s of u n c e r t a i n t y ( t h i s would be a worthwile f i t i s assumed that the ' r i g h t to UI' i s not p a r t of anyone's e n t i t l e m e n t . Welfare Evaluat ion / 151 extension), i t i s assumed that i t would be at least approximately consistent with the views of Nozick to choose a UI programme which more c lo se ly matched i n d i v i d u a l costs and benefits ex post . For Model 1, th i s i s reasonable since ind iv idua l s choose an annual pattern of employment and unemployment and hence both the premiums they pay and the benefits they rece ive . For Model 2, matching premiums ac tua l ly paid and benefits a c t u a l l y received i s much less reasonable for people who have not chosen to be unemployed. J u s t i f i c a t i o n for an ex post approach in t h i s case would have to appeal to a long time horizon (or, since I use cros s - sec t iona l data, to the idea that d i f f e r e n t ind iv idua l s within the data set current ly represent a f u l l range of unemployment experience) . This in terpre ta t ion of entitlement theory cannot, however, be pushed too far since a UI programme which exact ly matched i n d i v i d u a l costs and benefits ex post would have no insurance value; each par t i c ipant would e f f e c t i v e l y just be saving for periods of unemployment during periods of employment. However, as a means of assessing proposed reform of the ex i s t ing UI programme, the ex post matching of costs and benefits should y i e l d a ranking of p o l i c y options which would be approved by adherents of entitlement theory. Welfare Evaluation / 152 To evaluate proposed po l i cy changes in the s p i r i t of Nozick, then, i t seems appropriate to use some measure of the 'd is tance' between the d i s t r i b u t i o n of i n d i v i d u a l benefits in the form of UI benefits a c t u a l l y received and the d i s t r i b u t i o n of i n d i v i d u a l costs in the form of UI premiums ac tua l ly pa id . Several recent papers (Shorrocks, 1982; Chakravarty and Dutta, 1984) have looked at the issue of the measurement of the 'dis tance' between d i s t r i b u t i o n s of income. The idea underlying th i s l i t e r a t u r e is that both the l e v e l and the d i s t r i b u t i o n of income must be taken into account when comparing two d i s t r i b u t i o n s . The papers c i t ed above attempt to generate a more comprehensive technique of comparison than simply using an index of i n e q u a l i t y . They choose instead to make use of distance functions (metrics): A continuous function d: R n Rn=>RJ i s a distance function i f i t s a t i s f i e s the fol lowing propert i e s : 1. d(x,y)=0 i f f x=y; (Ref lex iv i ty ) 2. d(x ,y)=d(y,x); (Symmetry) 3. d(x,y)<d(x,z)+d(z,y); (Triangle R e l a t i o n ) . (Chakravarty and Dutta l i s t the a d d i t i o n a l property of 'population independence.' But, for my short-run,., c ros s - s ec t iona l app l i ca t ion the population w i l l be the same 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 Dutta argue that i f we want to compare Welfare Evaluation / 153 wel l -being in the two d i s t r i b u t i o n s , the distance function chosen must be "e th ica l ly coherent" with a spec i f i c s o c i a l evaluation funct ion . They construct a d ( x , y ) = f ( £ ( x ) , £ ( y ) ) where x and y are two d i s t r i b u t i o n s of income and i-(x) and £ ( y ) are the corresponding equivalent ly d i s t r i b u t e d incomes. £ ( x ) and £ ( y ) are , of course, dependent on the s o c i a l evaluation function chosen. My use of the concept of the distance between two d i s t r i b u t i o n s i s quite d i f f e r e n t . I want to use the idea of 'd is tance' to operat ional ize Nozick's entitlement theory. Let N=f(X,Y) be the p o l i c y assessment var iab le for the entitlement case, where N=f(X,Y) s a t i s f i e s the propert ies of a distance function as l i s t e d above; X is the d i s t r i b u t i o n of i n d i v i d u a l benef i ts ; Y is the d i s t r i b u t i o n of i n d i v i d u a l cos ts . A candidate for N i s N=Z | X . - Y . | . This function s a t i s f i e s the required propert ies (1 ,2 ,3 ) . It gives equal weight to each i n d i v i d u a l . And, the larger the discrepancy between cost and benefit for any i n d i v i d u a l , the larger the increase in N and the less l i k e l y a po l i cy w i l l be accepted by Nozick's s tandards . f Notice that th i s 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, contr ibut ions in the form of other taxes paid are ignored. As w e l l , no adjustments in programme costs accompany reform of programme benef i t s . This is a serious over-s ight from the entitlement perspect ive . Welfare Evaluation / 154 evaluation procedure need only account for members of the labour force , since other household members neither pay premiums nor receive benef i t s . Not ice , as we l l , that i t i s not necessary to incorporate a parameter to account for d i f ferent a t t i tudes toward i n e q u a l i t y . This i s i r re l evant from Nozick's point of view. Only the justness of i n d i v i d u a l transactions i s important. 4. Welfare Evaluat ion Results t The U t i l i t a r i a n welfare evaluation procedure for Model 1 ranks the ex i s t ing UI programme before both the Macdonald and the Forget reform proposals and ranks the Macdonald proposals before the Forget proposals (see Table 6 .2) . The same rankings are obtained as inequal i ty aversion is increased (except in the case of s ingle women, for whom ind iv idua l p o l i c i e s become indis t inguishable as r reaches -5 ) . For s ingle men and couples, reducing the benefit-replacement rate gains in rank r e l a t i v e to other components of the Macdonald package as inequal i ty aversion is increased. As less we l l -o f f groups become more important in the assessment of welfare, the income gains re su l t ing fResults are presented only for upper-bound p r o b a b i l i t y of constraint s imulat ions . Upper and lower-bound p r o b a b i l i t y models y i e l d the same rankings. Welfare Evaluat ion / 155 from increased employment out-weigh the loss of l e i s u r e time. In the context of Model 1, reducing the benefit replacement rate generated the largest 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 welfare evaluation procedure again ranks the ex i s t ing UI programme ahead of e i ther reform proposal (see Table 6 .3) . For s ing le women and couples, the Macdonald proposals dominate the Forget proposals; for s ingle men, the Macdonald proposals rank ahead of the Forget proposals for low leve l s of inequal i ty aversion (r=1,r=.5 ,r=- .5 ,r=-1) , but the ordering reverses as inequal i ty aversion increases (r=-5). This resu l t is re lated to the drop in rank for proposals to increase the minimum weeks of work necessary to gain e l i g i b i l i t y for UI benefits as inequal i ty aversion i s increased. For the unconstrained model, these proposals rank next to the ex i s t ing programme since working another few weeks to ensure UI entitlement involves only a minor change in behaviour. For the constrained model, increas ing minimum e l i g i b i l i t y condit ions can have serious consequences i f i t is impossible for some people to f ind the extra few weeks of work they need to e s tab l i sh e l i g i b i l i t y . Indiv iduals experiencing long periods of unemployment w i l l be the only ones af fected by th i s p o l i c y . Since these people have a high p r o b a b i l i t y of being Welfare Evaluat ion / 156 constrained and a high p r o b a b i l i t y of having low incomes, i t i s reasonable that increasing the minimum entrance requirement w i l l be less appealing from a U t i l i t a r i a n perspect ive as aversion to inequal i ty i s increased. Results indicate that th i s i s an important element of programme design since the Forget proposal , which suggests reducing rather than increasing the minimum entrance requirement, dominates the Macdonald proposal in the U t i l i t a r i a n evaluat ion for s ingle men as inequal i ty aversion increases . For couples, the Rawlsian welfare evaluation again ranks the e x i s t i n g programme ahead of e i ther reform package with the Macdonald reform package ranking ahead of the Forget package (see Table 6 .4) . For s ingle men and s ingle women, the Model 1 Rawlsian rankings are quite d i f f e r e n t . Both the Macdonald and the Forget proposals dominate the ex i s t ing programme at low l eve l s of inequal i ty avers ion , and Macdonald dominates Forget . While i t may, at f i r s t , appear c o u n t e r - i n t u i t i v e that an evaluation approach which focusses at tent ion on low-income groups should rank proposals which reduce ' the generosity of the UI programme as welfare-improving, th i s resu l t i s reasonable in 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 is made less generous, people choose to work more, and the i r incomes increase . Since loss of ' l e i s u r e ' Welfare Evaluat ion / 157 does not o f f - se t the welfare gain from higher incomes and since the group with high unemployment have r e l a t i v e l y low incomes, inducing these people to work more by making UI less generous must be welfare-improving from a Rawlsian perspect ive . Eventual ly , however, as inequal i ty aversion is increased, these rankings reverse; the cost of programme cut-backs to the poorest among the poor out-weighs the gains achieved through increased work e f f o r t . f There i s considerable v a r i a t i o n in the Rawlsian ranking of components of the Macdonald package as inequal i ty aversion is increased. Increasing minimum e l i g i b i l i t y condit ions climbs r e l a t i v e to reducing the benefit-replacement rate . E l iminat ing regionally-extended benefits i s cons i s tent ly ranked in f i r s t place for s ingle men and climbs to f i r s t place for s ingle women. These resu l t s suggest that the poorest ind iv idua l s in the sample make the largest increases in labour supply and hence income in response to increases in minimum e l i g i b i l i t y condit ions and to the e l iminat ion of regional ly-extended benef i ts ; that the poorest ind iv idua l s in the sample barely q u a l i f y for the e x i s t i n g programme and/or l i v e in high-unemployment regions where regional ly-extended benefits supplement 'earned' benef i t s . fThe 'poorest among the poor' are the poorest ind iv idua l s in the data set , a l l of whom are labour-force p a r t i c i p a n t s . The poorest ind iv idua l s in the Canadian population are not members of the labour force . Welfare Evaluation / 158 (It cannot be true that the poorest ind iv idua l s are simply not affected by these proposals , or the ex i s t ing programme would dominate.) The lack of correspondence between the Model 1 Rawlsian welfare evaluation resul t s obtained for s ingle men and women and the resu l t s obtained for couples again suggests the importance of modelling jo int responses to p o l i c y changes. For s ingle i n d i v i d u a l s , reforming UI appears to be welfare-improving as a resu l t of the large behavioural responses generated from the poor populat ion. For couples, behavioural responses on the part of a low-wage worker may not have any impact on the Rawlsian evaluation i f the low-wage worker has a spouse with a higher wage so that the household is not 'poor . ' For couples, requir ing two weeks of employment for each earned week of UI and reducing the benefit-replacement rate rank ahead of increasing minimum e l i g i b i l i t y condit ions or e l iminat ing regionally-extended benef i t s . This i s the opposite resu l t from that obtained for s ingle i n d i v i d u a l s . Low-income couples are not necessar i ly both located at the high-unemployment end of the budget c o n s t r a i n t . The somewhat surpr i s ing outcome of the Rawlsian welfare evaluations for Model 1 are very dependent on the assumption Welfare Evaluat ion / 159 of unconstrained labour supply. Rawlsian welfare evaluations look very d i f f erent for the constrained model (see Table 6 .5) . In th i s case, the ex i s t ing programme dominates e i ther reform proposal for a l l groups. For s ingle men, the Macdonald proposals dominate the Forget proposals at low l eve l s of inequal i ty aversion while the Forget proposals dominate at higher l eve l s ; for s ingle women and couples , the Macdonald proposals dominate throughout. This i l l u s t r a t e s the importance of assumptions made about the nature of unemployment. If ind iv idua l s are free to respond, the ir welfare increases as the i r labour supply and hence incomes increase (from the Rawlsian perspect ive) ; i f ind iv idua l s cannot respond, the only e f fect of UI retrenchment w i l l be to reduce incomes. Under the assumption of constrained labour supply, proposals to reduce the benefit-replacement rate rank ahead of proposals to increase minimum e l i g i b i l i t y requirements for s ingle men, s ingle women and couples. If workers are unable to obtain even a few a d d i t i o n a l weeks of employment, i t i s better to reduce the rate at which they receive weekly benefits than to stop benefit payment altogether by making e l i g i b i l i t y unatta inable . The Entit lement welfare evaluation ranks the Forget reform proposals f i r s t , the Macdonald proposals second and the Welfare Evaluat ion / 160 ex i s t ing programme l a s t (see Table 6 .6 ) . f The ex i s t ing programme ranks lower than any other version of UI. This resu l t holds for both constrained and unconstrained models and for a l l demographic groups. Perhaps not s u r p r i s i n g l y , the ranking obtained using the Entit lement approach is the opposite of that most commonly found for the U t i l i t a r i a n and Rawlsian approaches. (Varying inequal i ty aversion affects U t i l i t a r i a n and Rawlsian rankings; inequal i ty aversion i s not consistent with the ph i lo sophica l views of Nozick, so only one entitlement ranking is obtained for each model.) In the context of Model 1, reducing the benefit-replacement rate and e l iminat ing regional ly-extended benefi ts are the most welfare-improving components of the Macdonald package. In general , the p o l i c y changes which generate the largest behavioural responses are the p o l i c y changes which most improve welfare from the perspect ive of Nozick and in the context of Model 1. In the context of Model 2, increasing the minimum e l i g i b i l i t y requirement to twenty weeks of employment, requir ing two weeks of employment to earn one week of UI benefit and e l iminat ing regionally-extended benefits a l l dominate a reduction in benefit-replacement ra te . Since behavioural responses are small in Model 2, the only way to bring premium contr ibut ions and benefit receipts fThe ranking of Macdonald and Forget might reverse i f the experience-rat ing proposal were included as part of the Macdonald package. Welfare Evaluat ion / 161 into alignment i s to stop paying benefits to workers who are unemployed for long periods; workers who pay few premiums but c o l l e c t benefits for many weeks. In summary, three factors are c r i t i c a l in determining the resu l t s of welfare evaluat ion. F i r s t , and most obviously , re su l t s depend upon ph i losophica l judgements about what const i tutes 'we l fare . ' From the perspective of Entitlement theory, both reform proposals are welfare-improving r e l a t i v e to the e x i s t i n g UI system; from a U t i l i t a r i a n perspect ive , proposals for UI reform w i l l reduce welfare. Second, the U t i l i t a r i a n and Rawlsian rankings are sens i t ive to the degree of inequal i ty aversion assumed. T h i r d , welfare evaluat ion resu l t s for each of the three ph i lo sophica l pos i t ions considered are sens i t ive to assumptions made about the nature of unemployment. This is most dramat ica l ly i l l u s t r a t e d through the Rawlsian r e s u l t s . The assumption that unemployment i s the outcome of u t i l i t y - m a x i m i z i n g choices leads to the conclusion that UI reform w i l l increase the welfare of low-income workers; the assumption that some unemployment i s the resu l t of demand-side constra int leads to exact ly the opposite conclusion (at low leve l s of inequa l i ty avers ion) . V I I . CONCLUSIONS In this thes is I have conducted an evaluation of the Macdonald and Forget proposals for the reform of the Canadian UI system which takes e x p l i c i t account of both the e f f i c i ency and the equity dimensions of these proposals . Both reform proposals c a l l for a retrenchment in programme generosity in an attempt to reduce some of the adverse incentives generated by the e x i s t i n g programme. Thus, some ind iv idua l s must be 'worse -o f f af ter the p o l i c y change, and a pure assessment of the e f f i c i e n c y consequences of the proposals cannot produce a ranking of opt ions . Resolution of th i s problem involves introducing an equity c r i t e r i o n . To introduce d i s t r i b u t i o n a l considerat ions without imposing a spec i f i c set of value judgements, I have evaluated the welfare consequences of proposed p o l i c y changes using an ' e t h i c a l l y - f l e x i b l e ' approach. That i s , I have conducted the evaluation from three very d i f f e r e n t e t h i c a l points of view ( f e a s i b i l i t y l i m i t s the number of approaches which can be considered). The f i r s t approach i s in the s p i r i t of U t i l i t a r i a n i s m ; the second i s in the s p i r i t of Rawls' theory of j u s t i c e ; the t h i r d i s in the s p i r i t of Nozick's entitlement theory. Each of these welfare evaluat ions , however, depends 162 Conclusions / 163 fundamentally on an underlying model of household behaviour. One of the major f indings of t h i s thes is i s the degree to which welfare evaluations depend upon assumptions made about the nature of observed behaviour. For th i s a n a l y s i s , the c r u c i a l feature of the data to be explained is unemployment; the c r u c i a l question to ask is whether observed unemployment does or does not represent u t i l i t y -max imiz ing behaviour on the part of households. Since the answer to th i s question i s not obvious, I have estimated two separate sets of labour-supply equations (for s ingle men, s ingle women and couples) to r e f l e c t two d i f f erent views about the nature of unemployment. Model 1, the unconstrained model of labour supply, assumes that observed unemployment r e f l e c t s u t i l i t y -max imiz ing choices (up to a random error term); Model 2, the constrained model of labour supply, introduces the p o s s i b i l i t y that some part of observed unemployment i s the resul t of demand-side constra ints rather than supply-s ide choices . Chapter Two develops the unconstrained model of labour supply. Model 1 bui lds on a long t r a d i t i o n of ' labour-supply ' models of the impact of UI on household behaviour. Households, with one or two working heads, are assumed to choose weeks of unemployment and consumption of a Conclusions / 164 composite commodity to maximize u t i l i t y subject to budget constra ints which c a r e f u l l y incorporate the parameters of the Canadian UI system. U t i l i t y functions are assumed i d e n t i c a l for households with i d e n t i c a l demographic c h a r a c t e r i s t i c s . Since u t i l i t y functions depend on demographic v a r i a b l e s , ' tastes ' (as modelled through these var iables ) are assumed to influence choices . Incorporation of UI in household budget constra ints means that budget constra ints are piece-wise l i n e a r . The correct approach to est imating a model with a piece-wise l inear budget constra int is out l ined but not implemented (attempts to estimate th i s model were not success fu l ) . The piece-wise l inear budget constra int i s treated by l i n e a r i z i n g around the observed po in t . Thus, to the extent that observed and u t i l i t y - m a x i m i z i n g choices of l e i s u r e do not f a l l on the same segment of the budget c o n s t r a i n t , reported parameter estimates may be incons i s tent . The other major estimation problem for th i s model (as well as for Model 2) i s that observed weeks of l e i sure cannot f a l l outside obvious bounds, creat ing a l imi t ed dependent var iab le problem of the Tobit var i e ty which i s appropriate ly treated . Chapter Three develops the constrained model of labour supply. Model 2 s tar t s with the same basic assumptions as Model 1: households choose weeks of l e i sure and consumption Conclusions / 165 of a composite commodity in order to maximize u t i l i t y subject to budget constra ints which incorporate the parameters of the Canadian UI system. A f i r s t d i f ference between the two models i s that households with d i f f erent demographic c h a r a c t e r i s t i c s are no longer assumed to have d i f f erent ' tastes ' for unemployment. The second, and most s i g n i f i c a n t d i f ference between Models 1 and 2 i s that observed unemployment i s no longer assumed to correspond with the household's u t i l i t y - m a x i m i z i n g choices . The p o s s i b i l i t y of demand-side constra ints i s introduced, but no attempt is made to model how such constra ints may a r i s e . Incorporating the demand side of the labour market into an analys i s of the impact of UI on behaviour would c l e a r l y be an important extension. My model merely examines the consequences of the existence of constra ints for the estimation of labour-supply funct ions . For each unemployed i n d i v i d u a l , a p r o b a b i l i t y that observed unemployment i s greater than des ired unemployment plus a stochast ic error term is 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 the e r r o r . This p r o b a b i l i t y i s used to estimate a form of switching regression model with sample separation unknown where the two poss ible regimes are constrained and unconstrained unemployment. For the constrained regime, a l l that i s known is the p r o b a b i l i t y that observed unemployment i s greater than desired unemployment. Conclusions / 166 Both models of labour supply were estimated by maximum l i k e l i h o o d using a Stone-Geary funct ional form and the 1982 Survey of Consumer Finance. The Stone-Geary u t i l i t y function i s acknowledged to be a h ighly r e s t r i c t i v e funct ional form, but unfortunately , the basic econometric d i f f i c u l t i e s involved in estimating e i ther Model 1 or e spec ia l ly Model 2 do not, at present, allow the use of a more f l e x i b l e funct ional form. Est imation resu l t s for both models are reported in Chapter Four. Major f indings for Model 1 are, f i r s t , that c o r r e c t i n g the l i m i t e d dependent var iab le problem has a s i g n i f i c a n t impact on estimated parameters. Second, unconstrained labour-supply functions for s ingle men, s ingle women and married men are a l l p o s i t i v e l y - s l o p e d and i n e l a s t i c while unconstrained labour-supply functions for married women are p o s i t i v e l y - s l o p e d and e l a s t i c . Labour-supply functions of married women who work part-t ime are found to be p a r t i c u l a r l y e l a s t i c , confirming recent re su l t s (Nakamura and Nakamura, 1983) which suggest that the important d i f ference in labour-supply behaviour is to be found between part-t ime and f u l l - t i m e workers rather than between men and women. Model 1 re su l t s further suggest that a d i s t i n c t i o n might be made between the labour-supply behaviour of married women and s ingle women: there is no observable behavioural d i f ference between s ingle women and e i ther s ingle or married men. F i n a l l y , Model 1 estimation Conclusions / 167 resu l t s suggest that there are important in teract ions between own labour-supply behaviour and spouse's demographic c h a r a c t e r i s t i c s . Major resu l t s for Model 2 are , f i r s t of a l l , the very high estimated p r o b a b i l i t i e s of constra int for ind iv idua l s observed to experience unemployment. Such resu l t s suggest the v a l i d i t y of the assumption that some part of observed unemployment does not represent u t i l i t y - m a x i m i z i n g labour-supply choices . Another extension of the present work would be an attempt to determine whether Model 1 or Model 2 i s the preferred model, but th i s i s beyond the scope of the thes i s . A second estimation resu l t for Model 2 i s that labour-supply functions are less e l a s t i c than Model 1 labour-supply funct ions. T h i r d , there i s no di f ference between the Model 2 labour-supply functions of married women and those of any other group. F i n a l l y , important interdependencies are again evident for couples . Both married men and married women are found to respond, i n e l a s t i c a l l y , to increases in a spouse's constrained unemployment, and labour-supply functions of married men and women with a spouse who i s unemployed and constrained are less e l a s t i c than i f the spouse is unemployed by choice . These r e s u l t s , in conjunction with those obtained for Model 1 concerning the importance of a spouse's demographic Conclusions / 168 c h a r a c t e r i s t i c s for own-wage e l a s t i c i t e s , i l l u s t r a t e the importance of modelling jo in t behaviour and suggest that the development of more sophis t icated models would be an important area for future research. The estimated models of labour supply enable the simulation of behavioural responses to UI reform proposals under very d i f f erent assumptions about the nature of unemployment. The basic resu l t obtained using the estimated parameters of Model 1 is that e i ther the Macdonald or the Forget proposals would resu l t in a substant ia l reduction in observed unemployment. The basic f inding for Model 2 i s that neither the Macdonald nor the Forget proposals would have any s i g n i f i c a n t impact on observed unemployment. These c o n f l i c t i n g predic t ions of the l i k e l y behavioural consequences of proposed UI reform const i tute the ' e f f i c i e n c y ' dimension of the project eva luat ion . The other v i t a l dimension of a welfare evaluation of proposed UI reform i s , of course, the equity dimension. Chapter Six develops three a l t e r n a t i v e methods of assessing the impl icat ions of p o l i c y changes for s o c i a l welfare. The f i r s t approach developed is U t i l i t a r i a n ; well-being is measured by a 'mean of order r ' function of ind iv idua l normalized u t i l i t y values . The mean of order r allows for Conclusions / 169 varying a t t i tudes toward inequal i ty in the d i s t r i b u t i o n of i n d i v i d u a l u t i l i t y . Indiv idual u t i l i t i e s are scaled versions of the estimated Stone-Geary household ind irec t u t i l i t y funct ions . E x p l i c i t interpersonal comparisons, based on the interpersonal comparisons i m p l i c i t in the Canadian poverty l ines as wel l as on the estimated parameters of the labour-supply (and hence u t i l i t y ) funct ions, are required to obtain these i n d i v i d u a l normalized u t i l i t y values . Thus, assumptions made about the nature of unemployment (the nature of the observed data, more genera l ly ) , through the ir impact on estimated parameters, are c r i t i c a l both in pred ic t ing the amount of unemployment/leisure consumed after the po l i cy change ( u t i l i t y is an increasing function of unemployment/leisure) and in determining the value of the parameters of the u t i l i t y function i t s e l f and thus of the interpersonal comparisons of u t i l i t y which are made. The second approach to the assessment of s o c i a l welfare developed in Chapter Six is a measure which i s consistent with John Rawls' theory of j u s t i c e . The c r u c i a l features of th i s approach are that attent ion should be focussed on the ' w o r s t - o f f group in society and that personal tastes should not count in assessing wel l -be ing . Hence, the Rawlsian measure i s a mean of order r over an income (rather than a u t i l i t y ) d i s t r i b u t i o n censored at the poverty l i n e . Conclusions / 170 Differences in household need are incorporated according to the Canadian poverty l i n e s , but di f ferences in taste are ignored. Given the important ro le assigned to the S t a t i s t i c s Canada low-income c u t - o f f s , i t would be valuable to test the s e n s i t i v i t y of resu l t s obtained to a l t e r n a t i v e poverty measures. From the Rawlsian perspect ive , assumptions made about observed unemployment are p r i m a r i l y important in determining changes in labour supply and hence income. The f i n a l approach to the measurement of s o c i a l welfare developed in Chapter Six i s a measure which is consistent with Robert Nozick's entitlement theory. This measure defines s o c i a l welfare to be higher when the distance between the d i s t r i b u t i o n of benef i ts received from UI and the d i s t r i b u t i o n of contr ibut ions made to UI is smal ler . The entitlement measure pays no at tent ion to a t t i tudes toward inequal i ty nor does i t pay at tent ion to di f ferences in need. From the entitlement perspect ive , assumptions made about the nature of unemployment are p r i m a r i l y important for pred ic t ing the behavioural responses which determine UI benefits received and UI premiums pa id . Three factors appear to be c r i t i c a l in the determination of welfare evaluation r e s u l t s . F i r s t , resu l t s of course depend on the e t h i c a l pos i t ion adopted. From the perspect ive of Conclusions / 171 Noz ick 1 s entitlement theory, both the Macdonald and the Forget proposals for the reform of UI are welfare-improving r e l a t i v e to the ex i s t ing system. From a U t i l i t a r i a n perspect ive , e i ther proposal would reduce welfare i f implemented. A second important fac tor , in the context of the U t i l i t a r i a n and Rawlsian approaches, i s the assumed degree of inequa l i ty avers ion: rankings can change as inequal i ty aversion increases . F i n a l l y , as stressed e a r l i e r , welfare rankings of po l i cy proposals depend c r i t i c a l l y upon assumptions made about the nature of unemployment. This i s obviously important in the U t i l i t a r i a n case, since these assumptions af fect estimates of the parameters of the u t i l i t y funct ion . But, as i l l u s t r a t e d by the Rawlsian r e s u l t s , d i f ferences in underlying behavioural models can y i e l d opposite conclusions about the welfare consequences of po l i cy reform even according to a n o n - u t i l i t a r i a n measure; equity and e f f i c i e n c y are fundamentally interconnected elements of a p o l i c y eva luat ion . 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APPENDIX 1 The f u l l variance-covariance matrix for couples (Model 1) i s Z' = 0 2 a o e i e 2 e , e 3 a a 2 a e i e 2 e 2 e 2 e 3 a a a 2 e i e 3 e 2 e 3 e 3 Since the commodity-demand equation is dropped for est imation, i t i s necessary to make use of the fol lowing theorem (Anderson, 1958, p.24): If a vector of v a r i a b l e s , X, i s normally d i s t r i b u t e d with mean vector M and covariance matrix Z, the marginal d i s t r i b u t i o n of any set of components of X i s mul t ivar ia te normal with means, variances and covariances obtained by taking the proper components of n and Z , respec t ive ly . After the commodity-demand equation is dropped, the relevant covariance matrix i s thus: e 1 e 1 e 2 a a 2 e ,e 2 e 2 To s impl i fy the integrat ion required for the sample 193 / 194 s e l e c t i v i t y c o r r e c t i o n , the (now) b i - v a r i a t e normal dens i ty , f ( e 1 , e 2 ) can be re -wri t ten as the product of a marginal and a condi t iona l dens i ty: f(e T , e 2 ) = f , ( e , ) f 2 ( e 2 e,) where the marginal dens i ty , f ^ e , ) , is normal with mean zero and variance a 2 , and the cond i t iona l density f 2 ( e 2 e,) i s ^ 1 also normal, but with mean M_ =P (o /a ) e 1 ( and variance e 2 e , e 2 e 2 e , e 2 e 2 e , e 2 where p_ =a_ /(o-_ cr^  ) i s the c o r r e l a t i o n between e, and e 1 e 2 e 1 e 2 e 2 e 2 e 2 • F i n a l l y , the transformation of var iab les required to move from the d i s t r i b u t i o n in terms of the error terms to the d i s t r i b u t i o n in terms of observables i s s traightforward since the errors are merely addi t ive (and hence the Jacobian of the transformation is equal to one). APPENDIX 2 Dropping the commodity-demand equation, the system of e s t i m a t i n g equations f o r couples (Model 2) becomes (1) s?=st(w,7,0,A)+e 1 (2) s 2 = s*(w,7,0,A)+e 2 (3) s?=st(w,7,0,A,Z 2)+u 1 (4) s 2 = s 2 ( w , 7 , 0 , A , ) + u 2 The d i s t u r b a n c e terms are assumed to f o l l o w a j o i n t normal d i s t r i b u t i o n with means of zero and c o v a r i a n c e matrix Z 4 = a 2 a o a e, e,e 2 e,u, e,u 2 a a 2 a a e,e 2 e 2 e 2 u , e 2 u 2 a a a 2 a e , U i e 2 u , u, U , U 2 a a a a 2 t e,u 2 e 2 u 2 u,u 2 u 2 ' Again making use of Anderson (1958, p. 24), i t i s p o s s i b l e to break the c o v a r i a n c e matrix i n t o sub-matrices f o r e s t i m a t i o n . Consider the four p o s s i b l e s i t u a t i o n s i n which couples may be observed: (1) If n e i t h e r household member i s unemployed, the r e l e v a n t equations f o r e s t i m a t i o n are (1) and (2) with the a p p r o p r i a t e c o v a r i a n c e matrix f i t i s not p o s s i b l e to estimate every element of the f u l l v a r i a n c e - c o v a r i a n c e matrix. 195 / 196 (2) If only the wife i s unemployed, (a) the matrix for (1) is again appropriate i f she i s unconstrained, but (b) the matrix i s appropriate i f she i s constrained. (3) If only the husband is unemployed, the corresponding covariance matrices are given by (a) the matrix for s i t u a t i o n (1) and (b) the matrix (4) If both husband and wife are unemployed, four cases are poss ib le : (a) Neither husband nor wife may be constrained so that (1) w i l l be the appropriate sub-matrix. (b) only the wife may be constrained so that 2(b) w i l l again be appropriate . (c) only the husband may be constrained so that 3(b) w i l l again be appropriate . (d) both husband and wife may be constrained. In th i s case, a 2 a e 2U! / 197 the sub-matrix (1) w i l l be the relevant matrix for est imation. To s impl i fy in tegrat ion , the b i v a r i a t e density functions are again re-wri t ten as the product of marginal and condi t iona l d e n s i t i e s . A r b i t r a r i l y , i f both husband and wife are unemployed or i f neither i s unemployed, the marginal density i s written in terms of the error from the husband's labour-supply funct ion . If only one person i s unemployed, the marginal density i s written in terms of the error from his or her labour-supply funct ion . APPENDIX 3 198 Table 4.1.— Basic Data Averages. 199 NUMBER INCIDENCE OF UNEMPLOYMENT PERCENT FULL-TIME INCIDENCE: FULL-TIME WKRS INCIDENCE: PART-TIME WKRS AVERAGE WEEKS EMPLOYMENT AVERAGE WEEKS UNEMPLOYMENT AVERAGE GROSS WEEKLY WAGE MEN 8653 .24 .97 .23 .53 46.7 4.7 413. WOMEN 9100 .23 .76 .22 .25 41.9 4.8 238. TOTAL 17,753 .23 .86 .23 .28 44.2 4.75 323. Table 4.2.— Occupational Averages. Industry Mgt Sci/Prof Teaching C l e r i c a l Sales Services Mining Product Fab Construction # Men 865 834 368 492 881 823 Forestry/Fishing 329 976 1026 997 # Women Average Incidence  Wage Unemp Transportation 1059 543 1285 656 3143 823 1646 91 305 352 23 211 456 373 443 263 305 238 304 372 353 409 370 .08 .12 .13 .1.8 .17 .28 .63 .37 .25 .47 .31 200 Av Wks Av Wks Emp 50.02 47.64 45.65 44.26 45.44 40.36 32.11 42.16 46.03 41.26 44.25 Unemp 1.35 2.17 2.50 3.74 3.23 6.17 15.74 7.83 4.43 9.89 6.19 Table 4.3.— P r o v i n c i a l Averages. Province NFLD PEI NS NB QUE ONT MAN SASK ALTA BC # ObS 573 229 716 755 1767 2337 868 860 1578 1336 Per Capita Income 7379 7830 8005 8661 9980 10840 9770 10077 11314 12006 201 Incidence Incidence Incidence Of U  Men .43 .38 .35 .36 .27 .17 .20 .18 .18 .21 Of U  Women .34 .26 .24 .27 .20 .14 .13 .14 .13 .18 Of U  Both .38 .31 .29 .31 .23 .15 .16 .15 .15 .19 Table 4.4.— D i s t r i b u t i o n of Weeks Across Budget Segments. 202 Single Couples Men Before After Before After Single Women Segment 1 (Wks Lt Min) 423 37 71 Segment 2 (Wks Ge Min and Wks Le Max) 381 80 64 15 55 13 Segment 3 (Wks Gt Max and Wks Lt 50) 2686 2331 417 417 348 348 Segment 4 (Wks Lt 50) 8720 7572 1243 1229 1695 1670 Wage too Low 968 231 64 16 197 57 Notes: The numbers for couples include men and women i n d i v i d u a l l y . Part-time male workers have already been eliminated from the 'Before' numbers. The 'After' numbers exclude zero-income households as well as 'disequilibrium' households. Workers with weekly wages les s than $63 (1981), 20% of maximum insurable earnings, neither pay premiums nor receive UI bene f i t s i f unemployed. Corners are a r b i t r a r i l y assigned to Segments Two and Four as described above. 203 Table 4 .5.-- Mean Variable Values. Single Women and Single Men. Single Single Women Men Model I Model Model I Model II II F u l l U'd F u l l U'd F u l l U'd F u l l U'd At lan .19 .29 .19 .25 .17 .28 .17 .26 West .45 .38 .45 .41 .46 .36 .46 .39 C i t y .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 for ATLAN, WEST,CITY,PART ,SEA,and CYC i percentages. Other values are means. ' F u l l ' r e f e r s to the f u l l sample ; 'U'd' re f e r s to the sub--sample i n d i v i d u a l s who experience unemployment. 204 Table 4.6.— Mean Variable Values. Couples. Model I Model II F u l l W U'd H U'd F u l l W U'd H U'd At lan .24 .33 .38 .24 .28 .40 West .39 .37 .31 .39 .39 .30 C i t y .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 Yr s e l 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 values reported for Atlan,West,City,Part,Sea,and Cyc are percentages. Other values are means. ' F u l l ' r e f e r s to the f u l l sample of couples for the relevant model; 'W U'd' r e f e r s to the sub-sample i n which the wife i s unemployed; 'H U'd' refer s to the sub-sample i n which the husband i s unemployed. Table 4.7.— Model 1 Parameter Estimates. Single Women. 205 Basic Tobit Variable Coeff. T-Ratio Coeff. T-Ratio 700 -684.3 -1.350 7OO 22.12 .002431 701(Atlan) 979.3 3.149 701(Atlan) 2344. 2.699 702(West) 1188. 3.883 702(West) 4117. 5.606 7 0 3 ( C i t y ) 329.9 1.062 7 0 3 ( C i t y ) 742.2 1.227 704(Efam) -10.84 -.1404 704(Efam) -297.7 -1.751 705(Yrse) 4.079 .1190 705(Yrse) -108.1 -2.116 706(Part) -160.6 -.6887 706(Part) 1468. 2.817 707(Clt7) 901.9 3.758 7 0 7 ( C l t 7 ) 1517. 2.975 710 -6.570 -3.739 7IO -83.12 -5.445 7 l l ( A t l a n ) -6.249 .6964 7 l l ( A t l a n ) -62.12 -1.946 7l2(West) .5766 -.06839 712(West) -55.57 -2.357 7l3(City) .3705 .3589 7l3 ( C i t y ) -2.695 -.3233 7l4(Efam) -.7962 -2.108 714(Efam) 7.893 3.331 7l5(Yrse) -.02087 -.1830 715(Yrse) .1114 .1245 716(Part) 2.820 2.453 716(Part) 5.363 .3724 7l7(Clt7) -1.630 -1.365 717(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. 2088 OBS 2088 OBS Note: Reported T-Ratios are asymptotic. 206 Table 4.8.— Model 1 Parameter Estimates. Single Men. Basic Tobit Variable Coeff. T-Ratio Coeff. T-Ratic 7OO -1118. -2.027 700 873.4 .9486 -yOl(Atlan) 710.9 1.427 701(Atlan) -270.4 -.4646 702(West) 752.1 1.676 702(West) 775.3 1.333 703(City) 70.50 .1673 7 0 3 ( C i t y ) -886.4 -1.401 704(Efam) 144.7 1.672 704(Efam) 122.5 .9682 705(Yrse) 56.57 2.164 705(Yrse) 47.47 .9627 706(Sea) 1390. 3.278 706(Sea) 1029. 1.829 707(Cyc) 70.92 .1991 707(Cyc) 426.3 .8506 7 0 8 ( C l t 7 ) 378.8 .4288 708(Clt7) -386.1 -.2623 710 -8.856 -3.088 710 -140.0 -2.729 7 l l ( A t l a n ) -6.416 -2.542 7 l l ( A t l a n ) 30.70 .6964 712(West) -3.480 -1.967 712(West) -.8144 -.06835 7 1 3 ( C i t y ) 2.114 1.110 7 1 3 ( C i t y ) 70.58 1.561 7l4(Efam) . -.8694 -1.664 714(Efam) -1.090 -.3737 715(Yrse) .05111 .2885 715(Yrse) -2.080 -2.144 716(Sea) -2.741 -1.064 716(Sea) 29.52 2.324 7l7(Cyc) -2.180 -1.196 717(Cyc) 2.626 .2668 7 1 8 ( C l t 7 ) -1.705 -.3341 7 1 8 ( C l t 7 ) -44.13 -1.339 010 .1327 4.159 010 .5873 5.909 011(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 1677 OBS Note: Reported T-Ratios are asymptotic. 207 Table 4.9. —Model 1 Parameter Estimates. Couples. Basic 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 706(Yrse2) 475.4 2.728 647.2 2.877 138.0 .008490 707(Sea) -3353. -2.213 -3219., -1.652 1505. .9956 708(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 7IO -1.773 -2.060 -2.406. -2.137 -99.71. -7.660 7 l l ( A t l a n ) -1.203 -3.101 -.7368 -1.282 4.380 .7278 712(West) .1020 .3347 .2250 .5050 11.65 2.176 7 1 3 ( C i t y ) -.6442 -2.144 -.2527 -.5718 -14.49 -2.763 714(Efam) .1065 .7861 .1367 .7953 -.2468 -.001333 7 1 5 ( Y r s e l ) -.09444 -2.335 -.1478 -2.511 -1.059 -1.710 716(Yrse2) -.02970 -.6586 -.02954 -.4483 -2.343 -3.379 7l7(Sea) 2.849 7.031 3.685 6.079 57.30 8.596 718(Cyc) .04120 .1370 .5615 1.268 28.12 5.189 719(Part) 1.003 3.495 .5486 1.304 5.762 1.042 7110(Clt7) .1579 .7425 .1650 .5391 12.37 3.486 72 -2.392 -2.572 -5.499 -3.851 -108.0 -8.739 721(Atlan) -.8977 -2.137 -.4622 -.6718 5.071 .9523 722(West) .1935 .5892 .1427 .2600 9.769 2.100 7 2 3 ( C i t y ) -.8024 -2.457 -.3724 -.6803 -5.830 -1.272 724(Efam) .2100 1.474 .1374 .7026 -.9153 -.004971 725(Yrsel) -.05805 -1.328 -.1265 -1.693 -.6510 -.1107 726(Yrse2) .01216 .2423 .1657 1.964 1.729 2.485 727(Sea) .4876 1.169 .9047 1.290 5.321 .9774 728(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 .04669 14.88 .05208 11.00 .2832 17.97 62 .02941 18.71 .04072 15.39 .2101 12.99 LLF -16464. -10604. -529.6 5107 OBS 2500 OBS 2500 OBS Table 4.10.— Model 2 Parameter Estimates. 208 Single Men Single Women Variable Coeff T-Ratio Variable Coeff T-Ratio 7 0 7 l 691 -981.6 -45.84 .2963 -2.131 -9.627 10.84 70 61 -220.2 -36.09 .2227 -.9043 -11.30 13.21 LLF 1796 OBS -324.7 LLF 2297 OBS -293.1 Variable Married Men Coeff T-Ratio Variable Married Women Coeff T-Ratio 70 7 l 81 -9748. -46.70 .1061 -5.9449 -13.81 9.8545 70 72 62 -9748. -27.70 .06864 -5.9449 -17.85 15.11 LLF 2000 OBS 586.5 Note: Reported T-Ratios are asymptotic. Table 4.11.— P r o b a b i l i t i e s of Constraint i n Unemployment. Single Women. F u l l Sample Part-Time A t l a n t i c Western Central F r a c t i o n of Unemployed 570/2297 131/258 141/425 236/1034 193/838 (25%) (51%) (33%) (23%) (23%) # with Prob of 487/570 107/131 125/141 203/236 159/193 Constraint Ge 50% (85%) (81%) (89%) (86%) (82%) # With Prob of 439/570 104/131 113/141 186/236 140/193 Constraint Ge 66% (77%) (79%) (80%) (79%) (73%) # With Prob of 411/570 101/131 108/141 173/236 130/193 Constraint Ge 75% (72%) (77%) (77%) (73%) (67%) # With Prob of 393/570 96/131 103/141 164/236 126/193 Constraint Ge 80% (69%) (73%) (73%) (69%) (65%) Av Prob Of Constraint .8273 .8207 .8558 .8295 .8038 Table 4.12.— P r o b a b i l i t i e s of Constraint i n Unemployment. Single Men. 210 Fra c t i o n of U'd # With Prob of  Constraint Ge  50% # With Prob of  Constraint Ge  66% # With Prob of  Constraint Ge  75% # With Prob of  Constraint Ge  80% Av Prob of Constraint F u l l Sea Cyc Sample 551/1796 (31%) 447/551 (81%) 405/551 (74%) 378/551 (69%) 367/551 (67%) .7944 166/271 (61%) 140/166 (84%) 129/166 (78%) 121/166 (73%) 120/166 (72%) .8265 217/629 (34%) 178/217 (82%) 161/217 (74%) 156/217 (72%) 149/217 (69%) .8045 At lan 144/301 (48%) 116/144 (81%) 106/144 (74%) 102/144 (71%) 98/144 (68%) .7945 West 216/833 (26%) 185/216 (86%) 169/216 (78%) 158/216 (73%) 154/216 (71%) .8351 Cen 191/662 (29%) 146/191 (76%) 130/191 (68%) 118/191 (62%) 115/191 (60%) .7484 Table 4.13.— P r o b a b i l i t i e s of Constraint. Couples. 211 Av Prob of  Constraint Husband U'd; Wife Not A l l U'd Sea Cyc .8135 .8421 .8407 Neither Part .7376 F u l l Wife U'd; Husband Not .6873 .6728 .6989 Both U'd ' Av Prob of Constraint ,9745 .9759 .9738 .9737 A t l a n t i c Centre .9745 West .9746 Husband U'd; Wife Not ,8485 .7663 ,8307 Wife U'd; Husband Not .6726 .6803 .7007 Both U'd ,9883 .9479 .9773 Table 4.14.— Model 1 Labour-Supply E l a s t i c i t i e s . Single Men. F u l l Sample (Unemployed Sample) 212 Gross Own-Wage Seasonal C y c l i c a l Neither A t l a n t i c Rural .3061 (.8613) .1321 (.6208) .0468 (.4359) Centre Urban Rural .1582 (.4273) .2582 (.5537) .1246 (.3727) .1173 (.5909) .1200 (.4800) .1066 (.3818) West Urban Rural .0530 (.1364) -.0169 (.1839) .0277 (.3062) .0080 (.2430) .0252 (.3568) -.0074 (.2721) Non-labour Income Seasonal C y c l i c a l Neither A t l a n t i c Rural -.6452 (-1.4899) -.2792 (-.9262) -.1267 (-.5975) Centre Urban Rural .2517 (-.5649) .4524 (-.8793) .1748 (-.4544) .2435 (-.8282) ,1484 (-.5385) ,1970 (-.5439) West Urban Rural -.1441 (-.2392) -.1892 (-.4714) .1101 (-.4269) .1545 (-.4247) .0841 (-.4721) ,1153 (-.4595) Compensated  Own-Wage Seasonal C y c l i c a l Neither A t l a n t i c Rural .9582 (1.5134) .7896 (1.2753) .6743 (1.0664) Centre Urban Rural .6509 (.9166) .9206 (1.2138) .6222 (.8720) .7888 (1.2608) .5895 (.9426) ,7525 (1.0387) West Urban Rural .5869 (.6689) .6910 (.8940) .5632 (.8385) .7201 (.9550) .5304 (.8597) .6777 (.9587) 213 Table 4.15.— Model 1 Labour-Supply E l a s t i c i t i e s : Single Women. F u l l Sample (Unemployed Sample). Gross Own Wage Part-time Full-time A t l a n t i c Rural .1839 (.8701) .1029 (1.0131) Centre Urban Rural .1756 (.7037) .1997 (1.2121) .1288 (.4290) .1516 (.4657) West Urban Rural .2515 (.0917) .1836 (.1265) .0703 (.2608) .0178 (.4144) Non-labour Income Part-time Full-time A t l a n t i c Rural -.5159 (-1.4155) -.1484 (-1.2084) Centre Urban Rural -.2117 (-.8294) .2160 (-1.3266) -.0983 (-.3760) -.0999 (-.3780) West Urban Rural -.2892 (-.6503) -.3164 (-.7037) -.1167 (-.5888) -.1402 (-.6603) Compensated Own-Wage Part-time Full-time A t l a n t i c Rural .8084 (1.4760) .6727 (1.5757) Centre Urban Rural .5795 (1.1172) .5932 (1.6080) .4680 (.7654) .4675 (.7945) West Urban Rural .4420 (.7897) .4859 (.7892) .5483 (.8748) .5799 (1.0065) 214 Table 4.16.— Model 1 Labour-Supply E l a s t i c i t i e s . Married Men. Wives Full-time Workers. F u l l Sample (Unemployed Sample) Gross Own-Wage Seasonal C y c l i c a l Neither A t l a n t i c Rural 1.0185 (1.6674) .7309 (1.3806) .7338 (3.9412) Centre Urban Rural .7252 (.8053) .6182 (.6850) .7587 (2.0643) ,6665 (1.2865) .7957 (1.9215) .7261 (1.0899) West Urban Rural .6462 (1.5124) .6165 (2.1430) .5493 (.7436) .4966 (.7064) .6562 (1.2156) .5714 (.7945) Non-labour Income Seasonal C y c l i c a l Neither A t l a n t i c Rural -.2505 (-.5407) -.1324 (-.4218) .0940 (-1.0838) Centre Urban Rural -.1298 (-.2457) -.1904 (-.2776) ,1378 (-.5812) ,1692 (-.4948) .1375 (-.5223) .1646 (-.3262) West Urban Rural -.1212 (-.4146) -.1333 (-.7194) .0938 (-.2366) .1040 (-.2473) .0901 (-.3399) .0783 (-.2072) Gross Cross-Wage Seasonal C y c l i c a l Neither A t l a n t i c Rural .5808 (-.8205) -.4681 (-.7232) -.4857 (-2.0119) Centre Urban Rural -.5254 (-.4832) -.3995 (-.3837) ,5473 (-1.3101) -.4646 (-.7308) ,5610 (-1.1495) -.4944 (-.6610) West Urban Rural -.4944 (-1.0451) -.4945 (-1.4691) -.4262 (-.4596) -.3979 (-.4669) -.5036 (-.7568) -.4652 (-.5594) 215 Table 4.17.— Model 1 Labour-Supply E l a s t i c i t i e s . Married Men. Wives Part-time Workers. F u l l Sample (Unemployed Sample) Gross Own-Wage Seasonal C y c l i c a l Neither A t l a n t i c Rural .5000 (1.5441) .3957 (.6526) .3591 (1.0486) Centre Urban Rural .4802 (.2886) .3648 (.4980) .3117 (.6795) .3052 (.5793) .4534 (.5894) .3617 (1.4175) West Urban Rural .3021 (1.2089) .2878 (4.1786) .2337 (.2103) .1805 (.3439) .2635 (1.0617) .2786 (1.7566) Non-Labour Income Seasonal C y c l i c a l Neither A t l a n t i c Rural -.1980 (-.7465) -.1722 (-.3121) .0885(-.4512) Centre Urban Rural -.1279 (-.1702) -.1836 (-.2802) ,1010 (-.3335) .1357 (-.4528) .1233 (-.2255) .1359 (-.6359) West Urban Rural -.1690 (-.6637) -.1259 (-1.6364) .0944 (-.1517) .0672 (-.5025) .0800 (-.5213) .0719 (-.9790) Gross Cross-Wage Seasonal C y c l i c a l Neither A t l a n t i c Rural -.2699 (-.7299) -.1919 (-.3132) -.2079 (-.4125) Centre Urban Rural -.3764 (-.1166) -.2419 (-.2878) .2297 (-.3877) .2348 (-.2384) -.3121 (-.3285) -.2448 (-.8564) West Urban Rural -.1994 (-.7345) -.2733 (-3.2651) -.1865 (-.0924) -.1951 (-.5673) -.1893 (-.1589) -.2487 (-1.0443) Table 4.18.— Model 1 Compensated E l a s t i c i t i e s . Married Men. Wives Full-time Workers. F u l l Sample (Unemployed Sample) 216 Compensated  Own-Wage Seasonal A t l a n t i c Rural 1.3017 (1.9506) Centre Urban Rural 1.0084 (1.0885) .9014 (.9682) West Urban Rural .9294 (1.7956) .8997 (2.4262) Compensated  Cross-Wage Seasonal A t l a n t i c Rural -.3815 (-.5717) Centre Urban Rural -.3419 (-.3267) -.2709 (-.2847) West Urban Rural -.3089 (-.6487) -.2980 (-.8855) C y c l i c a l Neither 1.0141 (1.6638) 1.0170 (4.2244) 1.0417 (2.3475) .9497 (1.5697) 1.0789 (2.2047) 1.0093 (1.3731) .8325 (1.0268) .7798 (.9896) .9394 (1.4988) .8546 (1.0777) C y c l i c a l Neither -.3249 (-.4877) -.3658 (-.4756) .3552 (-.8483) .3177 (-.4625) .4031 (-.7534) .3669 (-.6949) .3028 (-.3396) .2712 (-.3143) .3624 (-.6002) .3256 (-.3684) 217 Table 4.19.— Model 1 Compensated Labour-Supply E l a s t i c i t i e s . Married Men. Wives Part-time Workers. F u l l Sample (Unemployed Sample) Compensated  Own-Wage Seasonal C y c l i c a l Neither A t l a n t i c Rural .7832 (1.8273) .6789 (.9358) .6423 (1.3318) Centre Urban Rural .7634 (.5718) .6480 (.7812) .5949 (.9627) .5884 (.8625) .7366 (.8726) .6449 (1.7007) West Urban Rural .5853 (1.4921) .5710 (4.4618) .5169 (.4935) .4637 (.6271) .5467 (1.3449) .5618 (2.0398) Compensated  Cross-Wage Seasonal C y c l i c a l Neither A t l a n t i c Rural -.2296 (-.5356) -.1759 (-.2864) -.1913 (-.3802) Centre Urban Rural -.2415 (-.1085) -.2107 (-.2359) .2085 (-.3232) .2126 (-.2154) .2845 (-.3008) .2229 (-.5190) West Urban Rural -.1765 (-.4373) -.1824 (-1.7942) -.1645 (-.0819) -.1667 (-.1382) -.1737 (-.4397) -.2202 (-.5979) Table 4.20.— Model 1 Labour-Supply E l a s t i c i t i e s . Married Women. Husbands Seasonal Workers. F u l l Sample (Unemployed Sample) 218 Gross Own-Wage Part-time Full-time. A t l a n t i c Rural 4.2886 (15.4811) 1.3022 (1.0757) Centre Urban Rural 1.2042 (30.7690) 5.1241 (15.7182) 1.0857 (20.7414) 1.4535 (9.1555) West Urban Rural 6.6930 (12.2176) 1.3740 (2.3367) .9745 (2.0967) .8139 (7.3864) Non-labour Income Part-time Full-time A t l a n t i c Rural -1.0321 (-5.2157) -.2641 (-3.0564) Centre Urban Rural -.1992 (-5.2299) -1.2364 (-4.2411) -.1486 (-3.5799) -.3110 (-2.3195) West Urban Rural -1.5482 (-2.5449) -.2910 (-.5657) -.1373 (-1.5412) -.1425 (-1.6914) Gross Cross-Wage Part-time Full-time A t l a n t i c Rural -3.0890 (-9.8412) -.8408 (-6.2569) Centre Urban Rural -1.0425 (-25.7950) -4.2963 (-12.4175) -.8571 (-15.8990) -1.0964 (-6.6064) West Urban Rural -5.7515(-10.6017) -1.3407 (-2.1674) -.8026 (-.5063) -.6835 (-5.7916) 219 Table 4.21.— Model 1 Labour-Supply E l a s t i c i t i e s . Married Women. Husbands C y c l i c a l Workers. F u l l Sample (Unemployed Sample) Gross Own-Wage Part-time Full-time A t l a n t i c Rural 12.6283 (17.2196) 1.5829 (11.0048) Centre Urban Rural 9.5136 (17.8084) 8.0167 (11.2029) 1.2283 (11.1187) 1.4981 (14.1320) West Urban Rural 8.3566 (13.1995) 6.8317 (11.0058) 1.7283 (10.1357) 1.4805 (8.3553) Non-labour Income Part-time Full-time A t l a n t i c Rural -2.2571 (-3.5978) -.1943 (-2.1772) Centre Urban Rural -1.0000 (-2.5697) -1.2850 (-2.7302) .1508 (-2.3702) .2420 (-3.3258) West Urban Rural .9045 (-1.8168) .6261 (-1.6393) .1596 (-1.7611) .1725 (-1.3002) Gross Cross-Wage Part-time Full-time A t l a n t i c Rural -9.9571 (-13.1108) -1.1970 (-7.4553) Centre Urban Rural -8.7010 (-15.7235) -7.3494 (-9.3251) -.9972 (-8.0951) -1.2094 (-10.4026) West Urban Rural -7.9041 (-11.9661) -6.9137 (-10.5512) -1.5188 (-8.1282) -1.3168 (-7.0963) 220 Table 4.22.— Model 1 Labour-Supply E l a s t i c i t i e s . Married Women. Husbands Neither Seasonal nor C y c l i c a l Workers. F u l l Sample (Unemployed Sample). Gross Own-Wage Part-time Ful l - t i m e A t l a n t i c Rural 14.2538 (22.1032) 2.1996 (18.9730) Centre Urban Rural 9.2992 (13.3731) 10.5466 (15.0533) 1.8070 (13.0551) 2.0632 (12.3440) West Urban Rural 10.6674 (15.2635) 7.0829 (11.1704) 1.8162 (11.3596) 1.6310 (13.0944) Non-labour Income Part-time Full-time A t l a n t i c Rural -1.1203 (-2.3122) .1647 (-2.4733) Centre Urban Rural -.9385 (-1.9632) -1.3008 (-2.1191) .1830 (-2.0213) .2713 (-2.2936) West Urban Rural ,7846 (-1.7461) .5311 (-1.1921) .1339 (-1.5594) .1178 (-1.7312) Gross Cross-Wage Part-time F u l l - t i m e A t l a n t i c Rural -12.3399 (-18.5173) -1.7650 (-14.1668) Centre Urban Rural -8.2238 (-11.2137) -9.4279 (-13.0923) -1.4947 (-10.1026) -1.6812 (-9.3863) West Urban Rural -9.9976 (-13.0923) -6.8616 (-10.3946) -1.5893 (-9.1886) -1.4713 (-11.0877) Table 4.23.— Model 1 Compensated E l a s t i c i t i e s . Married Women. Husbands Seasonal Workers. F u l l Sample (Unemployed Sample) 221 Compensated Own-Wage Part-time F u l l - t i m e A t l a n t i c Rural 4.4987 (15.6912) 1.5123 (11.2858) Centre Urban Rural 1.4143 (30.9791) 5.3342 (15.9283) 1.0084 (20.9515) 1.6636 (9.3656) West Urban Rural 6.9031 (12.4277) 1.5841 (2.5468) 1.1846 (2.3068) 1.0240 (7.5965) Compensated Cross-Wage Part-time Full - t i m e A t l a n t i c Rural -1.6129 (-5.0771) -.5422 (-3.9679) Centre Urban Rural -.6013 (-16.0464) -2.3889 (-6.8443) -.5329 (-9.6213) -.6338 (-3.5775) West Urban Rural -3.1568 (12.4277) -.6864 (-1.0778) -.4819 (-.8982) -.3807 (-3.2261) 222 Table 4.24.— Model 1 Compensated E l a s t i c i t i e s . Married Women. Husbands C y c l i c a l Workers. F u l l Sample (Unemployed Sample) Compensated Own-Wage Part-time Full-time A t l a n t i c Rural 12.8384 (17.4297) 1.7930 (11.2149) Centre Urban Rural 9.7237 (18.0185) 8.2268 (11.4130) 1.4384 (11.3288) 1.7082 (14.3421) West Urban Rural 8.5667 (13.4096) 7.0418 (11.2159) 1.9384 (10.3458) 1.6906 (8.5654) Compensated Cross-Wage Part-time Full - t i m e A t l a n t i c Rural -6.2450 (-8.1272) -.7814 (-4.7760) Centre Urban Rural -5.8960 (-10.5793) -4.6677 (-6.0154) -.6874 (-5.4968) -.8044 (-6.8602) West Urban Rural -5.1918 (-7.9855) -4.2765 (-6.4330) -1.0367 (-5.5160) -.8472 (-4.5330) 223 Table 4.25.— Model 1 Compensated E l a s t i c i t i e s . Married Women. Husbands Neither Seasonal nor C y c l i c a l Workers. F u l l Sample (Unemployed Sample). Compensated Own-Wage Part-time Ful l - t i m e A t l a n t i c Rural 14.4639 (22.3133) 2.4097 (19.1831) Centre Urban Rural 9.5093 (13.5832) 10.7567 (15.2634) 2.0171 (13.2652) 2.2733 (12.5541) West Urban Rural 10.8775 (15.4736) 7.2930 (11.3805) 2.0263 (11.5697) 1.8411 (13.3045) Compensated Cross-Wage Part-time F u l l - t i m e A t l a n t i c Rural -8.7554 (-13.1814) -1.2688 (-10.1169) Centre Urban Rural -6.0684 (-8.2795) -6.7166 (-9.3457) -1.1178 (-7.5249) -1.2144 (-6.7490) West Urban Rural -7.2209 (-9.9209) -4.7696 (-7.2444) -1.1680 (-6.7378) -1.0453 (-7.8655) Table 4.26.— Model 2 Labour-Supply E l a s t i c i t i e s F u l l Sample (Unemployed Sample) Single Men Single Women Gross Own-Wage .09815 ( .1848) .06335 ( .1541) Non-labour Income -.07393 (-.1543) -.05858 (-.1478) Compensated Own-Wage .3944 ( .4813) .2910 ( .3818) Married Men Married Women Gross Own Wage ,1283 ( .2121) ,1656 ( .2212) Gross Cross-Wage -.04674 (-.0608) -.0894 (-.1133) Non-labour Income -.02678 (-.0640) -.0249 (-.0408) Compensated Own-Wage .1941 ( .2780) .2011 ( .2567) Compensated Cross-Wage -.0087 (-.0113) -.0279 (-.0354) 225 Table 4.27.—Model 2 Labour-Supply E l a s t i c i t i e s . Couples. Rationed and Unrationed. F u l l Sample; Unrationed Gross Own-W Gross Cross-W Comp Own-W Comp Cross-W Constraint Married Men .1283 Married Women .1656 -.0467 -.0894 .1941 .2011 -.0087 -.0279 Spouse U'd Unrationed Married Men .1290 Married Women .1773 .0380 .0687 .1949 .2129 -.0080 -.0214 Spouse U'd; Rationed Married Men .0717 Married Women .1484 .0150 .03259 .1400 .1864 .01707 .0506 226 Table 5.1.— Model 1. Labour-Supply Responses. Single Men. BASE B=.5 EXT=0 MIN=15 MIN=20 QA=.5 MACD FORGET SEGMENT DIST'N SEGMENT 1 0 0 0 11 30 0 4 0 Corner 2 (Min) 2 4 8 0 8 7 0 1 SEGMENT 2(SUBSIDY)! 2 59 0 0 61 104 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 AV WEEKS U 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 1.45 227 Table 5.2.— Model 1. Labour-Supply Responses. Single Men. Unemployed Population. AV WKS U TOTAL ATLANTIC WEST CENTRE SEASONAL CYCLICAL NEITHER INCIDENCE TOTAL ATLANTIC WEST CENTRE SEASONAL CYCLCIAL NEITHER BASE B=.5 19.12 16.44 23.94 19.05 16.01 14.37 18.51 16.62 21.50 18.42 18.72 16.33 17.14 14.40 .2713 .2272 .4332 .3394 .2018 .1669 .2855 .2520 .5551 .4576 .3017 .2288 .1716 .1622 EXT=0 MIN=15 17.85 18.82 20.37 23.25 15.96 16.01 18.07 18.24 19.50 21.02 17.47 18.48 16.74 16.95 .2588 .2695 .3718 .4296 .2005 .2018 .2807 .2823 .5085 .5551 .2864 .2983 .1704 .1704 MIN=20 QA=.5 18.38 18.91 21.70 23.58 16.01 15.72 18.32 18.36 19.55 21.28 18.55 18.46 16.93 17.11 .2665 .2660 .4116 .4296 .2018 .1915 .2823 .2855 .5339 .5297 .2983 .2949 .1704 .1727 MACD FORGET 16.19 14.17 19.46 15.17 14.41 13.38 16.33 14.49 18.36 14.97 16.01 14.01 14.57 13.72 .1855 .1807 .2202 .2166 .1552 .1501 .2073 .2026 .3263 .3093 .2000 .1898 .1363 .1387 228 Table 5.3.— Model 1. Labour-Supply BASE B=.5 EXT=I SEGMENT DIST'N SEGMENT 1 0 0 0 CORNER 2 (MIN) 1 1 0 SEGMENT 2(SUBSIDY)7 8 71 CORNER 3 (MAX) 0 0 0 SEGMENT 3(TAX) 353 257 279 CORNER 4 (50) 0 0 0 SEGMENT 4 6 15 9 CORNER 5 (52) 1721 1807 1729 AV WEEKS U TOTAL 3.29 2.10 2.99 ATLANTIC 6.26 3.30 4.98 WEST 2.34 1.71 2.28 CENTRE 2.95 1.98 2.84 PART-TIME 7.35 5.04 6.15 FULL-TIME 2.88 1.81 2.67 onses. Single Women. MIN=15 MIN=20 QA=.5 MACD FORGET 12 35 0 3 0 0 0 5 0 0 7 3 57 95 0 0 0 0 0 0 340 320 291 140 228 0 0 0 0 0 6 6 9 22 23 1723 1724 1726 1828 1837 3.23 3.17 3.12 1.87 1.74 5.92 5.69 5.92 2.67 2.34 2.34 2.34 2.19 1.56 1.45 2.95 2.90 2.85 1.85 1.78 7.38 7.16 6.93 4.12 3.56 2.81 2.77 2.74 1.65 1.55 229 Table 5.4. Model 1. Labour-Supply Responses. Single Women. Unemployed Population. AV WKS U TOTAL ATLANTIC WEST CENTRE PART-TIME FULL-TIME INCIDENCE TOTAL ATLANTIC WEST CENTRE PART-TIME FULL-TIME BASE B=. 5 19.03 16.07 23.52 17.01 15.99 14.92 18.64 16.66 22.16 17.40 18.37 15.74 .1757 .1346 .2661 .1938 .1465 .1144 .1658 .1292 .3316 .2895 .1602 .1191 EXT=0 MIN=15 17.68 18.76 20.07 22.67 15.70 15.99 18.01 18.64 19.81 22.27 17.25 18.02 .1719 .1748 .2481 .2610 .1358 .1465 .1658 .1658 .3105 .3316 .1581 .1591 MIN=20 QA=.5 18.48 18.41 22.02 22.67 15.99 15.48 18.38 18.04 21.95 21.57 17.75 17.75 .1743 .1734 .2584 .2610 .1465 .1412 .1658 .1684 .3263 .3211 .1591 .1586 MACD FORGET 15.71 15.11 15.89 14.17 16.68 14.29 14.75 16.81 16.64 16.12 15.49 14.90 .1245 .1202 .1680 .1654 .1059 .1016 .1253 .1201 .2474 .2211 .1122 .1101 230 Table 5.5.—Model 1. Labour-Supply Responses. Married Men. BASE B=.5 EXT=0 MIN=15 MIN=20 0A=.5 MACD FORGI SEGMENT DIST'N SEGMENT 1 0 0 0 12 29 0 8 0 CORNER 2 (MIN) 3 3 8 0 0 10 0 3 SEGMENT 2(SUBSIDY)2 3 52 2 1 38 104 0 CORNER 3 (MAX) 0 0 0 0 0 0 0 0 SEGMENT 3(TAX) 467 404 392 458 436 412 258 281 CORNER 4 (50) 0 0 0 0 0 0 0 0 SEGMENT 4 40 53 43 39 39 40 46 46 CORNER 5 (52) 1988 2037 2005 1989 1995 2000 2084 2170 AV WEEKS U 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 Table 5.6.— Population. 231 Model 1. Labour-Supply Responses. Married Men. Unemployed AV WKS U TOTAL ATLANTIC WEST CENTRE SEASONAL CYCLICAL NEITHER INCIDENCE TOTAL ATLANTIC WEST CENTRE SEASONAL CYCLCIAL NEITHER BASE B=. 5 18.06 16.05 21.60 18.98 14.93 13.11 16.90 15.31 21.38 18.13 16.85 15.21 15.73 14.32 .2048 .1852 .3005 .2784 .1494 .1328 .2017 .1806 .4577 .4577 .2253 .1967 .1259 .1070 EXT=0 MIN=15 16.75 17.76 19.48 20.82 14.78 14.93 15.70 16.89 18.40 20.69 16.49 16.81 15.19 15.48 .1980 .2044 .2750 .3005 .1483 .1494 .2006 .2006 .4257 .4635 .1950 .2241 .1222 .1244 MIN=20 QA=.5 17.17 17.75 19.39 21.52 14.93 13.98 16.73 16.67 19.62 20.80 16.41 16.88 15.21 15.28 .2020 .2000 .2954 .3005 .1494 .1390 .1975 .1996 .4548 .4431 .2241 .2241 .1222 .1214 MACD FORGET 14.29 15.65 15.08 16.90 13.39 14.06 14.27 15.83 14.93 16.14 14.35 16.56 13.37 13.78 .1664 .1320 .2360 .1766 .1234 .0975 .1668 .1394 .3790 .3003 .1836 .1335 .1002 .0873 232 Table 5.7.— Model 1. Labour-Supply Responses. Married Women. BASE B=.5 EXT=0 MIN=15 MIN=20 QA=.5 MACD FORGET SEGMENT DIST'N SEGMENT 1 0 0 0 19 58 0 25 0 CORNER 2 (MIN) 4 5 8 0 0 16 0 6 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 AV WEEKS U 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 3.07 233 Table 5.8.— Model 1. Labour-Supply Responses. Married Women. Unemployed Population. AV WKS U TOTAL ATLANTIC WEST CENTRE PART-TIME FULL-TIME INCIDENCE TOTAL ATLANTIC WEST CENTRE PART-TIME FULL-TIME BASE B=.5 20.51 17.87 25.54 21.72 16.24 14.27 19.81 17.58 20.44 18.95 20.54 17.49 .3852 .3872 .3803 .4092 .2334 .2479 .5428 .5153 .3212 .3358 .4033 .4017 EXT=0 MIN=15 16.60 19.55 17.02 23.13 15.73 16.24 17.14 19.49 17.35 19.97 16.32 19.40 .3504 .3800 .3022 .3616 .2261 .2334 .5069 .5407 .2940 .3230 .3663 .3961 MIN=20 QA=.5 18.57 18.96 21.25 23.94 16.24 14.77 18.42 18.03 19.30 19.79 18.30 18.65 .3760 .3708 .3531 .3701 .2334 .2178 .5354 .5269 .3212 .3140 .3915 .3869 MACD FORGET 15.37 17.60 17.94 19.72 13.29 15.27 14.98 17.43 17.44 17.54 14.62 17.62 .3404 .2960 .3328 .3056 .2106 .1577 .4773 .4308 .2940 .2795 .3535 .3007 234 Table 5.9.— Model 2. Labour-Supply Responses. Single Men. UPPER-BOUND PROBBASE B=.5 EXT=0 MIN=15 MIN=20 QA=.5 MACD FORGET  OF CONSTRAINT AV WKS U 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 LOWER-BOUND PROB  OF CONSTRAINT AV WEEKS U 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 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. AV WKS U TOTAL ATLANTIC WEST CENTRE SEASONAL CYCLICAL NEITHER INCIDENCE TOTAL ATLANTIC WEST CENTRE SEASONAL CYCLCIAL NEITHER BASE B=.5 21.97 22.48 26.08 26.53 19.91 20.23 21.20 21.99 25.05 25.30 21.18 21.58 19.94 20.75 .3068 .2875 .4784 .4505 .2593 .2483 .2885 .2628 .6125 .5856 .3450 .3246 .1875 .1713 EXT=0 MIN=15 21.96 21.96 26.05 26.07 19.91 19.91 21.19 21.19 25.03 25.04 21.17 21.18 19.93 19.93 .3066 .3067 .4777 .4781 .2593 .2593 .2884 .2884 .6122 .6125 .3448 .3448 .1874 .1874 MIN=20 QA=.5 21.96 21.92 26.06 26.06 19.91 19.85 21.19 21.14 25.03 25.01 21.18 21.10 19.93 19.91 .3066 .3067 .4777 .4781 .2593 .2593 .2884 .2882 .6122 .6125 .3448 .3448 .1874 .1874 MACD FORGET 22.70 22.03 27.02 26.21 20.30 19.92 22.19 21.27 25.54 25.09 21.82 21.24 20.93 20.01 .2870 .3008 .4488 .4691 .2483 .2557 .2621 .2811 .5849 .6026 .3240 .3388 .1709 .1829 236 Table 5.11.— Model 2. Labour-Supply Responses. Single Women. UPPER-BOUND PROBBASE B=.5 EXT=0 MIN=15 MIN=20 QA=.5 MACD FORGET  OF CONSTRAINT AV WKS U TOTAL 5.91 5.75 5.90 5.91 5.90 5.89 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 LOWER-BOUND PROB  OF CONSTRAINT AV WEEKS U 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 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 Table 5.12.— Model 2. P o p u l a t i o n . 237 Labour-Supply Responses. S i n g l e Women. Unemployed AV WKS U TOTAL ATLANTIC WEST CENTRE PART-TIME FULL-TIME INCIDENCE TOTAL ATLANTIC WEST CENTRE PART-TIME FULL-TIME BASE B=.5 23.81 24.09 26.06 26.23 22.40 22.72 23.88 24.19 29.31 29.83 22.17 22.37 .2481 .2386 .3318 .3216 .2282 .2194 .2303 .2202 .5078 .4884 - .2153 .2070 EXT=0 MIN=15 23.78 23.80 26.00 26.02 22.39 22.40 23.86 23.88 29.27 29.31 22.15 22.15 .2481 .2481 .3315 .3318 .2282 .2282 .2303 .2303 .5078 .5078 .2153 .2153 MIN=20 QA=.5 23.79 23.75 26.01 26.00 22.40 22.34 23.86 23.84 29.29 29.24 22.15 22.11 .2481 .2481 .3318 .3318 .2282 .2280 .2303 .2303 .5078 .5078 .2153 .2153 MACD FORGET 24.20 23.84 26.36 26.00 22.80 22.43 24.32 23.97 29.95 29.41 22.48 22.18 .2381 .2447 .3214 .3287 .2188 .2250 .2198 .2264 .4876 .5008 .2066 .2123 238 Table 5.13.— Model 2. Labour-Supply Responses. Married Men. UPPER-BOUND PROBBASE B=.5 EXT=0 MIN=15 MIN=20 QA=.5 MACD FORGET  OF CONSTRAINT AV WKS U 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 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 LOWER-BOUND PROB  OF CONSTRAINT AV WEEKS U 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 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 Table 5.14.— Population. 239 Model 2. Labour-Supply Responses. Married Men. Unemployed AV WKS U TOTAL ATLANTIC WEST CENTRE SEASONAL CYCLICAL NEITHER INCIDENCE TOTAL ATLANTIC WEST CENTRE SEASONAL CYCLCIAL NEITHER BASE B=. 5 18.51 18.53 22.45 22.44 15.61 15.56 16.23 16.31 20.94 20.80 17.14 17.24 17.18 17.23 .2230 .2146 .3657 .3545 .1737 .1700 .1814 .1698 .5230 .5118 .2615 .2510 .1050 .9890 EXT=0 MIN=15 18.46 18.45 22.36 22.33 15.62 15.61 16.18 16.20 20.88 20.84 17.10 17.09 17.14 17.18 .2230 .2229 .3655 .3651 .1737 .1737 .1814 .1814 .5227 .5224 .2615 .2614 .1050 .1050 MIN=20 QA=.5 18.43 18.45 22.28 22.40 15.61 15.54 16.19 16.17 20.81 20.88 17.07 17.11 17.17 17.10 .2229 .2229 .3651 .3655 .1737 .1736 .1814 .1814 .5224 .5224 .2614 .2615 .1050 .1050 MACD FORGET 18.60 18.44 22.62 22.35 15.61 15.52 16.26 16.20 20.94 20.85 17.28 17.11 17.26 17.07 .2140 .2195 .3525 .3612 .1697 .1723 .1698 .1764 .5092 .5168 .2507 .2579 .0987 .1024 240 Table 5.15.— Model 2. Labour-Supply Responses. Married 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 LOWER-BOUND PROB  OF CONSTRAINT AV WEEKS U TOTAL 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 6.42 241 Table 5.16.— Model 2. Labour-Supply Responses. Married Women. Unemployed Population. AV WKS U TOTAL ATLANTIC WEST CENTRE PART-TIME FULL-TIME INCIDENCE TOTAL ATLANTIC WEST CENTRE PART-TIME FULL-TIME BASE B=.5 27.68 27.75 30.59 30.75 26.21 26.32 26.85 26.80 30.39 30.36 26.04 26.16 .3965 .3812 .4731 .4541 .3921 .3783 .3506 .3360 .5264 .5093 .3450 .3303 EXT=0 MIN=15 27.52 27.65 30.28 30.47 26.16 26.20 26.69 26.86 30.26 30.38 25.86 26.00 .3954 .3965 .4705 .4731 .3921 .3921 .3492 .3506 .5241 .5264 .3443 .3450 MIN=20 QA=.5 27.62 27.62 30.32 30.50 26.26 26.16 26.85 26.79 30.38 30.44 25.95 25.92 .3964 .3956 .4731 .4731 .3921 .3905 .3502 .3497 .5259 .5239 .3450 .3446 MACD FORGET 28.01 28.04 30.94 30.76 26.56 26.75 27.13 27.12 30.78 31.20 26.33 26.17 .3786 .3814 .4523 .4589 .3761 .3757 .3325 .3363 .5039 .4988 .3288 .3348 Table 6.1a.— Equivalence Scales Implicit in Low-income Cut-offs. City Size Gt 100,00 30,000-99,999 Lt 30,000 Rural Econ Family Size 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 Source: Statistics Canada, 1978. Table 6.1b.— Model 1 U t i l i t y Scaling Factors, s(A). Single Men Econ Family Size 1 2 3 4 5 6 7 or more C i t y Size  Gt 100,00 2.5289 3.2644 4.2855 4.8022 5.4245 5.7337 6.1459 30,000-99,999 1.2590 1.6960 2.3192 2.6621 3.0634 3.3010 3.6007 Lt 30,000 1.1374 1.5471 2.1300 2.4477 2.8248 3.0394 3.3163 Rural .9852 1.3390 1.8532 2.1338 2.4747 2.6676 2.9103 Single Women Econ Family Size 1 2 3 4 5 6 7 or more C i t y Size  Gt 100,00 4.7803 6.8052 9.7877 12.4327 15.8400 19.1041 22.4416 30,000-99,999 Lt 30,000 4.9685 7.0431 10.1475 12.9090 16.4306 19.8874 24.2580 4.6610 6.6200 9.5432 12.1384 15.4656 18.6960 22.8010 Rural 4.2761 6.0287 8.6587 11.0101 14.0497 17.0031 20.7201 Couples Econ Family Size 2 3 4 5 6 7 or more C i t y Size  Gt 100,00 4.9738 6.1330 6.8670 7.7355 8.3140 9.0259 30,000-99,999 Lt 30,000 4.1902 5.2820 5.9718 6.7735 7.3292 7.9968 3.9665 4.9919 5.6365 6.3933 6.9047 7.5277 Rural 3.6540 4.5674 5.1456 5.8353 6.3015 6.8578 Table 6.1c.— Model 2 U t i l i t y Scaling Factors, s(A). Single Men Econ Family Size 1 2 3 4 5 6 7 or more C i t y Size  Gt 100,00 1.2438 1.5948 2.0827 2.3848 2.7457 2.9799 6.1459 30,000-99,999 Lt 30,000 1.1756 1.4974 1.9557 2.2386 2.5703 2.7946 3.6007 1.0975 1.3997 1.8291 2.0922 2.4043 2.6093 3.3163 Rural .9998 1.2633 1.6437 1.8778 2.1606 2.3458 2.9103 Single Women Econ Family Size 1 2 3 4 5 6 7 or more C i t y Size  Gt 100,00 1.4502 1.8991 2.5230 2.9094 3.3710 3.6704 4.0446 30,000-99,999 1.3629 1.7745 2.3607 2.7225 3.1466 3.4335 3.7828 Lt 30,000 1.2631 1.6496 2.1987 2.5352 2.9343 3.1964 3.5208 Rural 1.1382 1.4751 1.9616 2.2610 2.6226 2.8595 3.1466 Couples Econ Family Size 2 3 4 5 6 7 or more C i t y Size  Gt 100,00 4.4457 5.2046 5.6740 6.2352 6.5992 7.0541 30,000-99,999 Lt 30,000 4.2943 5.0069 5.4468 5.9627 6.3112 6.7358 4.1425 4.8100 5.2191 5.7043 6.0230 6.4173 Rural 3.9303 4.5218 4.8858 5.3254 5.6134 5.9624 Table 6.2.— U t i l i t a r i a n Welfare Evaluation Results. Model 1. Single Men Base B=.5 Ext=0 Min=15 Min=20 Qa=.5 Macd Forget Single Women Base B=.5 Ext=0 Min=15 Min=20 Qa=.5 Macd Forget Couples Base B=.5 Ext=0 Min=15 Min=20 Qa=. 5 Macd Forget r = l . 656.0 634.1 650.3 656.2 654.6 653.2 619.1 599.4 r= l . 565.0 548.1 564.8 560.6 563.5 561.5 536.8 524.0 r= l . 885.3 865.6 870.0 881.7 876.9 876.0 838.0 811.5 r=.5 603.3 582.0 595.8 603.3 601.1 600.2 564.0 542.4 r=.5 526.5 510.0 526.2 521.2 524.7 522.6 496.6 483.2 r=.5 865.1 845.9 848.6 861.1 855.8 855.6 816.4 790.5 r=-.5 485.9 467.4 474.5 485.4 481.5 482.3 440.5 417.4 r=-.5 433.5 418.5 433.1 426.7 431.2 429.2 399.6 385.4 r=-.5 830.1 811.7 811.1 825.1 818.6 820.1 778.1 753.3 r=-l. 404.7 390.3 393.3 403.8 399.8 401.3 360.8 341.6 r=-l. 326.2 316.6 325.9 321.3 324.6 323.3 300.5 290.4 r=-l. 813.5 795.6 793.0 808.0 800.7 803.2 759.7 735.4 r=-5. 30.744484 30.744483 30.744790 30.744838 30.744795 30.744831 30.722080 30.721959 r=-5. ***** ***** ***** ***** ***** ***** ***** ***** r=-5. 565.9 562.1 554.8 563.1 556.4 562.4 541.8 534.1 Note: Reference utility=521.9. 246 Table 6.3.— U t i l i t a r i a n Welfare Evaluation Results. Model 2. Single Men Base B=.5 Ext=0 Min=15 Min=20 Qa=.5 Macd Forget Single Women Base B=.5 Ext=0 Min=15 Min=20 Qa=.5 Macd Forget Couples Base B=.5 Ext=0 Min=15 Min=20 Qa=.5 Macd Forget r = l . 2645. 2598. 2579. 2623. 2600. 2609. 2478. 2421. r = l . 2304. 2276. 2264. 2288. 2276. 2277. 2203. 2170. r= l . 3239. 3217. 3204. 3223. 3213. 3219. 3149. 3122. r=.5 2458. 2407. 2372. 2426. 2394. 2416. 2250. 2194. r=.5 2113. 2083. 2060. 2090. 2073. 2083. 1989. 1955. r=.5 3178. 3155. 3139. 3160. 3149. 3157. 3080. 3052. r=-.5 2075. 2020. 1942. 2005. 1955. 2024. 1785. 1742. r=-.5 1704. 1674. 1628. 1665. 1633. 1671. 1537. 1510. r=-.5 3104. 3079. 3056. 3080. 3066. 3081. 2987. 2956. r = - l . 1844. 1795. 1701. 1754. 1701. 1796. 1543. 1513. r= - l . 1434. 1409. 1361. 1392. 1358. 1406. 1274. 1254. r= - l . 3053. 3027. 3001. 3025. 3010. 3029. 2927. 2895. r=-5. 565.0 564.8 560.4 554.8 552.9 564.6 549.7 551.0 r=-5. 230.814 230.811 230.777 230.756 230.693 230.804 230.632 230.629 r=-5. 1695. 1676. 1674. 1653. 1632. 1673. 1566. 1546. Note: Reference utility=2278. Table 6.4.— Rawlsian Welfare Evaluation Results. Model 1. Single Men Base B=.5 Ext=0 Min=15 Min=20 Qa=.5 Macd Forget Single Women Base B=.5 Ext=0 Min=15 Min=20 Qa=.5 Macd Forget Couples Base B=.5 Ext=0 Min=15 Min=20 Qa=.5 Macd Forget r = l . 5813. 5821. 5822. 5815. 5816. 5813. 5821. 5817. r = l . 5609. 5624. 5620. 5614. 5607. 5619. 5618. 5611. r = l . 5924. 5921. 5918. 5921. 5915. 5921. 5909. 5907. r=.5 5784. 5793. 5794. 5787. 5788. 5784. 5792. 5787. r=.5 5552. 5567. 5563. 5556. 5549. 5561. 5560. 5550. r=.5 5921. 5918. 5914. 5917. 5910. 5919. 5903. 5901. r=-.5 5681. 5693. 5697. 5688. 5690. 5681. 5688. 5679. r=-.5 5358. 5373. 5371. 5362. 5354. 5366. 5359. 5345. r=-.5 5916. 5912. 5906. 5908. 5897. 5913. 5886. 5883. r = - l . 5596. 5612. 5618. 5609. 5609. 5596. 5602. 5590. r = - l . 5161. 5174. 5174. 5164. 5156. 5168. 5155. 5139. r = - l . 5907. 5902. 5894. 5895. 5881. 5903. 5867. 5862. r=-5. 3089. 30928 3102 3100 3100 3087 3027. 3011. r=-5. 710.6218 710.6195 710.6223 710.6221 710.6221 710.6214 710.6086 710.6031 r=-5. 5747. 5723. 5648. 5363. 5203. 5724. 5110. 5070. Table 6.5.— Rawlsian Welfare Evaluation Results. Model 2. Single 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 Single Women r= l . r=.5 r=-.5 r = - l . r=-5. 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 Welfare Evaluation Results. Model 1 Base B=.5 Ext=0 Min=15 Min=20 Qa=.5 Macd Forget Model 2 Base B=.5 Ext=0 Min=15 Min=20 Qa=.5 Macd Forget Single Men 983,319 680,135 779,354 949,058 876,023 848,964 455,752 399,723 Single Men 11,348,946 9,772,719 9,538,667 10,050,340 8,827,824 9,171,799 4,498,961 4,067,815 Single Women 929,355 695,348 783,652 900,723 856,560 808,397 490,911 445,502 Single Women 10,355,090 9,143,937 8,967,121 9,403,927 8,412,616 8,358,005 4,893,896 4,546,160 Couples 2,582,168 2,103,919 2,023,475 2,389,734 2,203,143 2,218,840 1,256,592 1,144,756 Couples 21,637,872 18,718,704 18,223,552 19,098,448 17,335,712 18,303,200 9,215,835 8,208,126 

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