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Unemployment insurance’s labour market impacts Shen, Kailing 2006

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U N E M P L O Y M E N T INSURANCE'S LABOUR M A R K E T IMPACTS by Ka i l ing Shen . A . , The University of International Business and Economics, 1995 M . A . , The University of Br i t i sh Columbia, 1999 A T H E S I S S U B M I T T E D I N P A R T I A L F U L F I L L M E N T O F T H E R E Q U I R E M E N T S F O R T H E D E G R E E O F D O C T O R O F P H I L O S O P H Y in T H E F A C U L T Y O F G R A D U A T E S T U D I E S (Economics) The University of Br i t i sh Columbia September 2006 © Rai l ing Shen, 2006 11 Abstract This thesis examines Unemployment Insurance's (Ul) labour market impacts, focus-ing on the contingent, temporary natures of U l benefit. Using the Survey of Labour and Income Dynamics , the results suggest U l significantly affects both individuals ' employment/unemployment transitions and their job match quality. Chapter 2 presents a historical development of the U l program in Canada; a survey of related literature; and, finally, a theoretical analysis of how contingent, temporary U l benefit coverage could affect labour market dynamics. Chapter 3 empirically examines UI's impacts on individuals ' employment/ un-employment cycles. The two major findings are: 1) UI's minimum employment requirement is found to delay employment separation in the seasonal sector; and, 2) the availability of U l benefits is found to postpone reemployment in both the seasonal and non-seasonal sectors. Overall , simulation results suggest that without those de-lays, the national unemployment rate could be 16% lower (e.g. lowered from 7.6% to 6.6%) in the late 1990s. Simulation results also imply that, wi th the exception of the experience rating rules and the divisor rule, the 1996 Employment Insurance (EI) reform did not have a significant impacts on the national unemployment rate. Chapter 4 empirically examines UI's impacts on individuals ' reemployment wages. The random effect model it uses takes account of the endogeneity of both individ-uals' employment/unemployment durations and their ini t ial wages. Furthermore, the empirical specification allows U l benefits to have time-varying impacts. The re-sults suggest, overall, that U l coverage increases unemployed workers' reemployment wages by about 9.5%. i i i Contents Abst rac t ii Contents iii L is t of Tables v Lis t of Figures vii Lis ts of Symbols viii L is ts of Abbrevia t ions . . . . ix Acknowledgements x 1 In t roduct ion 1 2 U l and Labour Marke t : His tory , Li tera ture and Theory 5 2.1 Historical Development of Canadian U l Program and the EI Reform . 6 2.2 Literature Review 15 2.3 A Model of Labour Market Turnover with Contingent, Temporary U l 19 2.4 Figures 32 3 Contingent , Temporary U l and Employmen t /Unemploymen t C y -cles 39 Contents iv 3.1 Introduction 39 3.2 Theoretical Predictions 43 •3.3 Econometric Setup: Hazard Model with Heaping Effect 45 3.4 Data 49 3.5 Empirical Analysis 54 3.6 Conclusion 69 3.7 Tables and Figures 71 4 Temporary U I ' s T ime-vary ing Impacts on Reemployment Wages 93 4.1 Introduction 93 4.2 Theoretical Model . . 96 4.3 Literature 97 4.4 Data and Exploratory Analysis 99 4.5 Econometric Setup and Identification Issues . 102 4.6 Estimation Results 108 4.7 Conclusion. . I l l 4.8 Tables and Figures 112 5 Conclusions and Discussions 119 Bibl iography 124 A p p e n d i x A : Proofs 132 V List of Tables 2.1 Predicted Impacts of Contingent, Temporary U l Benefit 35 2.2 Predicted Impacts of Weekly U l Benefit Cu t 36 2.3 Predicted Impacts of Employment Requirement Week Cut 37 2.4 Predicted Impacts of Benefit Week Cut 38 3.1 Definitions of Time-varying U l Treatment Dummy Variables 78 3.2 Sample Description: Part 1. Unweighted Sample Counts 79 3.3 Sample Description: Part 2. Within-Observation-Window Spells' U n -weighted Distr ibution across Panel Years 80 3.4 Empi r ica l Hazard Rates 81 3.5 Summary Statistics of Unemployment Spells 82 3.6 Summary Statistics of Employment Spells 83 3.7 M a x i m u m Likelihood Estimates Using Pooled Pre-/Post-Reform U n -employment Spells 84 3.8 M a x i m u m Likel ihood Estimates Using Pooled Pre-/Post-Reform E m -ployment Spells 84 3.9 Illustration of UI 's Impacts on Hazard Rates: Based on Estimations Using Pooled Pre-/Post-Reform Spells 85 3.10 Estimated Heaping probabilities 86 List of Tables v i 3.11 Illustration of UI's Impacts on Hazard Rates: Based on Estimations Using Pre- and Post-reform Spells Separately 87 3.12 Illustration of UI's Impacts on Hazard Rates: Based on Alternative Estimations Using Pooled Pre-/Post-Reform Spells 88 3.13 Illustration of UI's Impacts on Hazard Rates: Based on Est imation Using Pooled Pre/Post-Reform Non-Seasonal Spells wi th Unobserved Heterogeneity Considered 89 3.14 M a x i m u m Likelihood Estimates Using Pooled Pre-/Post-Reform Non-Seasonal Spells wi th Unobserved Heterogeneity Considered 90 3.15 Simulated Density Functions 91 3.16 Summary Statistics from Simulations 92 4.1 Linear Regression Results of Reemployment Wages 114 4.2 Sample Composit ion by Individuals 114 4.3 Sample Composition by Durat ion and Wage Data Types 115 4.4 M a x i m u m Likelihood Estimation: No U l , No Wage Components . . . 115 4.5 M a x i m u m Likelihood Estimates: No U l 115 4.6 M a x i m u m Likelihood Estimates: U l Variables in Durat ion Parts . . . 116 4.7 M a x i m u m Likelihood Estimates: U l Variables in Durat ion Parts and Wage Parts 117 4.8 Illustration of UI's Impacts on Reemployment Process 118 v i i List of Figures 2.1 T iming of Workers 'Decis ion . . 32 .2.2 Value Function V(w,t) When t > Ne and t = Ne 33 2.3 Value Function V(w, t) When t > Ne, t = Ne and t = Ne - 1 34 3.1 Canadian Seasonally Adjusted Monthly Unemployment Rate . . . . . 71 3.2 Illustration of a Time-varying Variable 72 3.3 U l Benefit Schedule 73 3.4 Total Income 74 3.5 Predicted Hazard Rates wi th Contingent Temporary U l Coverage . . 75 3.6 Illustration of Empir ica l Hazard Heaping 76 3.7 A n Example of Week Sets by Calendar Properties 77 3.8 Illustration of Sample Spells Construction 77 4.1 Predicted Impact of Temporary U l Coverage on Unemployed Workers' Reservation Wages 113 4.2 Illustration of the Four Duration and Wage Parts of the Likel ihood Function 113 Lists of Symbols * significantly different from zero at 1% level; t significantly different from zero at 5% level; f significantly different from zero at 10% level ix Lists of Abbreviations UI Unemployment Insurance; EI Employment Insurance; SLID Survey of Labour and Income Dynamics; HMIN UI's minimum weeks of employment requirement; UMAX minimum employment weeks for maximum UI benefit coverage; HMAXYR minimum employment weeks for accumulating enough UI benefit coverage to the next year's job season; BEW UI benefit exhaustion week. Acknowledgements I would like to thank my advisor, David A . Green, for the most encouraging guid-ance during the 4 years of my research for this thesis. I also thank Craig W . Riddel l , Shinichi Sakata, Thomas Lemieux and Nicole Fort in for discussions and encourage-ment. Sincere thanks also go to Lee Grenon and James Croal wi th the Research Da ta Centre at the University of Br i t i sh Columbia, for answering many questions on the data and prompt processing of test results. Finally, I would like to thank Michel Bydard wi th the Human Resources and Development Canada for helping me to get unemployment insurance region definition files. 1 Chapter 1 Introduction This thesis is composed of three major chapters. The first main chapter (chapter 2) sets the overall policy, literature and theoretical background, while the two following chapters (chapter 3 and chapter 4) examine empirically how contingent, temporary Unemployment Insurance (UI) coverage affects labour market transitions and wage dynamics. For decades, UI has been an important policy tool in the labour market for most developed economies; while at the same time, the design of UI varies a lot over time and across countries. At the centre stage of this thesis is the 1996 Employment In-surance (EI) reform of Canadian UI program. This reform made a bundle of changes to the existing program parameters, as well as introduced several new instruments (such as experience-rating) to strengthen work incentives. The exogenous variation of UI treatment due to this policy change provides this thesis a new and novel source of identification. Chapter 2 serves as the foundation of this thesis. It has three parts. The first section reviews the historical development of the Canadian UI program and details of the main changes of the 1996 EI reform. The review discusses how the UI program has been assigned both an insurance role and an equalization role over time; how the EI reform is part of a bigger trend of social safety net reform in North American countries; as well as the economic implications of each major change of the EI reform. The second section reviews empirical studies of UI's labour market impacts since late Chapter 1. Introduction 2 1970s wi th emphasis on those using Canadian data. The focus here is the growing literature of using hazard model and duration data to study UI 's labour market impacts. The last section of chapter 2 outlines the theoretical foundation of the whole thesis. It theoretically explores how contingent, temporary U l benefit coverage af-fects individuals employment/unemployment cycles and reservation wages. A com-bination of analytical and numerical techniques is used here to solve workers' non-stationary dynamic programming problem. The results show how three main pa-rameters of an U l program (benefit duration, employment requirement and weekly benefit) interact wi th each other and how each affects work incentives differently. Moreover, the results also show how some U l parametric change could function like a double-edged sword on the labour market, providing both work incentives and disincentives at the same time. The empirical studies in this thesis use a common data source, a recently released Canadian micro panel data, the Survey of Labour and Income Dynamics (SLID). To match the panel nature of the data, an event-based sample selection procedure is used here to construct a set of multi-spell multi-state (employment and unemployment) sample spells. The main empirical work starts with chapter 3's study on how contingent, tem-porary U l coverage affects individuals ' employment/unemployment cycles. B y com-paring the estimated impacts using separate and pooled samples of spells from pre-and post-reform periods, this chapter confirms previous findings in a new context: 1) seasonal workers' probability of leaving employment is found to be lower before they satisfy UI's minimum employment requirement for benefit collection; and 2) availability of U l benefit is found to reduce both seasonal and non-seasonal workers' probability of leaving unemployment. Furthermore, the results of this chapter also Chapter 1. Introduction 3 reveal several new findings. In particular, it is suggested that U I program could have increased the overall unemployment rate of Canada in the late 1990s by about 14%. In other words, if all workers suddenly switch from respondingto U I incentives as estimated to ignoring those incentives and if all other things remain constant, the unemployment rate could drop from 7.6% to 6.6%. Chapter 3 also contributes to the literature by formulating a parsimonious econo-metric model for high-frequency duration data that greatly facilitates estimation of multi-cycle multi-state duration data while accommodating heaping in durations at low-frequency intervals. Specifically, this is a combination of a parametric base-line proportional hazard model with a measurement error type of model that takes account of calendar heaping spikes. Chapter 4 inherits many of the data and design features of chapter 3 and ex-tends the empirical analysis to examine contingent, temporary U I coverage's im-pacts on reemployment wages. The focus is on the non-seasonal sector only. The key contribution of this chapter is the introduction of simultaneous endogeneity of wages and employment/unemployment cycles, which is done by estimating a random-effect model wi th both employment/unemployment transition processes and wage processes. Also, UI 's impact on reemployment wages is allowed to be different de-pending on individuals ' remaining benefit durations at the reemployment weeks. The results suggest those who have at least 11 weeks of benefit left when reem-ployed receive about 12% to 14% higher reemployment wages than benefit exhaus-tees. Overall , the weighted average impact of U I coverage on the reemployment wages of Ul-covered unemployed workers is about 9.5% increase. In short, this thesis uses a new micro panel Canadian data set, explores a new source of treatment variation: exogenous policy change due to the Canadian E I reform, expands studies on the impacts of contingent, temporary U I coverage on Chapter 1. Introduction 4 employment/unemployment cycles and wage dynamics. It confirms previous find-ings about UIs impacts on labour market transitions in the new context while it also provides evidence of drops in reemployment wages as workers approach benefit exhaustion weeks. As of late 1990s in the Canadian labour market, the results sug-gest UI has not only had significant impacts on workers' employment/unemployment durations, but also has increased workers' reemployment wages significantly. 5 Chapter 2 Unemployment Insurance and Labour Market: History, Literature and Theory This chapter builds a foundation for later empirical works. The first section briefly reviews the history of Canadian unemployment insurance (Ul) program, in partic-ular, major changes made by the Employment Insurance (EI) reform in 1996. The second section reviews empirical studies of UI's labour market impacts, especially contributions of Canadian researchers. The last section studies contingent, tempo-rary U l coverage's impacts on employment/unemployment cycles and wage dynamics theoretically. Together, these three sections cover a broad range of materials relating to U l and its labour market impacts. Chapter 2. Ul and Labour Market: History, Literature and Theory 6 2.1 Historical Development of Canadian U l Program and the EI Reform 2.1.1 Canad ian U l P r o g r a m before the 1990s The Canadian U l program was officially established in 1940 1. The economic depres-sion of the 1930s played an important role in this historical event. Such view is expressed in Dingledine (1981) as, "with significant numbers of people unemployed, those out of work could no longer be categorized as lazy and of bad character." Consequently, it became politically necessary for public intervention to counter un-employment. In Canada, the rationale for establishing a public U l policy was mainly due to concerns about the sustainability of a private U l program. Though publicly managed, the Canadian U l program was carefully designed to mitigate two common problems in insurance market: adverse selection and moral hazard 2 . Only selected groups of the working population were covered by U L Among others, both workers who would certainly become unemployed (i.e. seasonal workers), and workers who would certainly not become unemployed (i.e. public servants), were excluded from U l coverage in the beginning. The insurance principle was also reflected in other dimensions of the program (such as eligibility requirements and maximum benefit 1 M o s t of the his tor ical informat ion presented in this section is based on Dingledine (1981) and Green and R i d d e l l (1993). 2 A d v e r s e selection refers to the increase of agents' incentive to purchase insurance as their risks, wh ich the insurer might not have full informat ion, increase. M o r a l hazard refers to the decrease of agents' r i sk-avoiding incentive once they are insured. B o t h of these problems are common i n the insurance market and cou ld damage the financial sus ta inabi l i ty of the relevant market. M o r e detai led discussion on these problems for the case of unemployment insurance could be found i n Gunderson and R i d d e l l (2000), Green and R i d d e l l (1993) among others. Chapter 2. UI and Labour Market: History, Literature and Theory 7 durations). Perhaps not too surprising, Canadian U I program had been financially healthy in earlier years. Since its establishment, the Canadian U I program was closely monitored and frequently adjusted. Over time, it was. assigned a second role: equalization. Many regard this addition as a consequence of the specific jurisdiction arrangement between the federal and provincial governments in Canada. Here, provincial governments are responsible for most social programs (e.g. welfare and education). The federal government only has a very small set of income redistribution instruments, among which U I is the most resourceful one. Gradually, changes were made to the U I program and it began to serve as an equalization program for the federal government as well. B y the 1990s, wi th annual expenditures in the range of $15-$20 bil l ion (Government of Canada, 1995), UI became the federal government's largest operating program. The incorporation of the equalization role into UI took off in 1971. Many features of the Canadian U I program today could be dated back to this event. Two changes made by the 1971 reform worth noting for our purpose are, First, extending UI coverage to nearly all paid workers. From this point on, UI began to cover seasonal workers, teachers and civi l servants. Only those marginal workers and people above 70 were excluded. Theoretically, such expansion of U I coverage created a channel for redistribution across industries, favouring industries wi th more transitory employment patterns. Second, linking benefit durations with regional labour market tightness through a 5-phase benefit structure. The 5 phases were, ini t ial benefit period, re-established ini t ial benefit period, labour force extended benefit period, national extended ben-efit period, and regional extended benefit period. To implement the 5th phase, 16 U I regions were established so that regional unemployment rates could be used to Chapter 2. Ul and Labour Market: History, Literature and Theory 8 measure the regional labour market tightness. Through this phase-based benefit structure, the federal government created another channel for equalization, favoring regions wi th higher unemployment rates. A s a result of the 1971 changes, U l became "an increasingly significant and integral part of the Canadian income protection system (Dingledine, 1981)", and the total U l benefit payment rose dramatically 3 . In the late 1970s, program misuse by both individual workers and governments at various levels became more and more of a concern of the public. There were also serious worries about this program's financial sustainability. As a response, the federal government made a sequence of amendments which somehow restored the U l program's emphasis on its insurance role. In the late 1980s, additional changes in the program made it even less generous and began to emphasize "active" labour market policies, such as training, rather than the traditional "passive" ones. Then, in 1996 the E I reform, the most important reform of the U l program in Canada, took place. 2.1.2 T h e Trend of Socia l Safety Ne t Reforms i n the 1990s The E I reform is indeed part of a bigger trend of social safety net reforms in the Nor th America in the 1990s. In Canada, the overall budget of social safety net experienced a series of big cuts in the earlier 1990s. It started in the year of 1990, when the fed-eral government set a 5% 'cap' on top of the growth rate of the cost-sharing transfer 4 to the three wealthiest provinces through the Canada Assistance P l an ( C A P ) . The 3 In nominal terms, the benefit paid in the first 9 years post-1971 was 5 times the amount paid in the 30 years pre-1971. Furthermore, according to Cansim II table 3840031, the national U l benefit payment more than doubled in 1972 from its level in 1971, that is increased from CAN$891 million to CANS1869 million. 4It mainly covered provincial welfare and social services funding. Chapter 2. UI and Labour Market: History, Literature and Theory 9 "cap on C A P lasted t i l l 1994/5. After that, the newly-elected Liberal government froze the overall welfare payment to provincial governments and cut U I expenditure even further. In the budget year of 1996/7, a new "block funding" mechanism re-placed both the C A P and old funding arrangement for medicare and post-secondary education. This new mechanism, called Canada Health and Social Transfer ( C H S T ) , allowed the federal government to cut its expenditure on the relevant areas (welfare, social services, medicare, and post-secondary education) by another 15% (from $17.4 bil l ion in 1994/5 to $14.9 in 1996/7, Government of Canada (1995, 1997)). Besides financial considerations, these sequential changes were also meant to encourage local initiatives in active labour market programs. Very similar policy changes also took place in the U.S . . Around the same period, the A i d to Fami-lies with Dependent Chi ldren was replaced by the Temporary Assistance for Needy Families with the passage of the Personal Responsibility and Work Opportunities Reconciliation Ac t . These changes of social safety net programs in these two Nor th American countries represent a common shift to the so-called 'pro-work philosophy. In this view, welfare should not be an "entitlement"; rather, welfare should only pro-vide temporary support in order to facilitate employable individuals ' stable labour market attachment. This 'pro-work' philosophy certainly promises an appealing re-sult. 2.1.3 T h e E I Re fo rm The main framework of the U I program in Canada is such that each workers' benefit durations are set individual ly 5 . Let the benefit coverage duration be df, weeks for a 5 T h i s is different from other developed economies. In the U . S . , the U I treatment is usual ly set at the state level rather than ind iv idua l level. Fur thermore , benefit coverage is set at 26 week for most states. O n the other hand, i n U . K . , U I coverage was set un i formly at 12 months i n 1990 and Chapter 2. Ul and Labour Market: History, Literature and Theory 10 paid worker who just lost his job. It is a function of two variables: 1) a measure of this worker's recent employment history, de (weeks); and, 2) the local unemployment rate at the beginning of his unemployment spell, ur%. In order to understand the changes made by the EI reform in 1996, it helps to present a reference point6. Specifically, according to the Ul program for the period from July 1994 to June 1996, 0 if de < 26 - w i db{de,ur) = I floor(de/2) + 2ur2 - 8 if de e [26 - uru40] (2.1) min{de + 2ur2 - 28, 50} if de > 40 Where ur\ = ceil{minmax{trunc(ur), 6 , 14}} and ur2 = ceil{minmax{trunc(ur), 6, Equation (2.1) shows that a worker could only collect Ul benefit if his/her pre-ceding employment weeks, de, is above the entrance requirement weeks, i.e. the minimum employment requirement (HMIN). The higher the local unemployment rate, the lower HMIN would be. Once passed week HMIN, a worker's benefit weeks would increase proportionally with local unemployment rate at the constant rate of 1 to 2, and increase with his/her preceding employment weeks, first at the rate of 2:1, and later at a higher rate of 1:1. The EI reform made at least 5 major changes on top of the above structure7: cut to 6 months from 1995 and the weekly payment is also uniform across workers. 6 T h e focus throughout this thesis is on the dura t ion of U l coverage. T h e other aspect, weekly U l payment is abstracted here. T h e U l pol icy in C a n a d a is such that there is essentially no direct variat ions across workers i n terms of their weekly U l benefit relat ive to their preceding weekly earnings. T h e benefit to earnings rat io , replacement ra t io , is always common to a l l workers. Indirect ly, there do exist some variat ions in the replacement ra t io due to the up l imi t of UI ' s insurable earnings. In that case, the var ia t ion is closely related w i t h workers ' earnings, mak ing it endogenous to workers ' other labour market experiences, such as employment /unemployment durat ions. 7 T h e informat ion of the E I reform here is most ly based on H u m a n Resources Development Chapter 2. UI and Labour Market: History, Literature and Theory 11 • Adoption of hour-based formula for employment weeks, de To understand this change, let's consider a very general case where individuals could have multiple jobs simultaneously as well as part-time jobs. Let hj>t be a worker's working hours on job j at week t. Then, for this worker, his employment weeks under pre-EI rules, dP™, is 2~2ti(2~2j I(hj,t) > 15) > 0] for all weeks within his current UI qualification period8. In other words, he needs to have at least one above (or equal)-15-hour job for a week to be counted as employed. Under this rule, two 12-hour jobs would not contribute to his de, while a 15-hour job is treated the same as 45-hour job for de purpose. The EI reform changed the formula to a hour-based one. Now, de = floor{2~2jt hjtt/35}, that is a worker's employment weeks equals the sum of total working hours within his qualification period divided by 35, the 'standard' weekly working hours. If the weekly working hours, hjtt, is taken exogenous, then this change of de formula obviously benefits all workers except those individuals who work on jobs of 15 to 34 weekly hours (Sweetman, 2000)9. • Cut of benefit weeks' up-limit The EI reform cut the maximum benefit weeks by 5 weeks, from 50 to 45. Not all workers are directly affected by this cut. According to (2.1), only those with de above 40 and ur above 10 are affected. But this cut of maximum benefit weeks does send a signal of less generous UI support. C a n a d a (1997-2002) and Rudner (1998). T h e discussion on the E I reform i n this thesis w i l l be focused on the regular benefit part of the C a n a d i a n U I program. Changes made on parental leave, sick leave and t ra in ing parts of the U I program, though are also part of the E I reform, are not incorporated i n the later empi r ica l examinat ion , thus are not the focus here. 8 Qual i f ica t ion per iod is defined as the shorter of 1) the 52 weeks per iod preceding the employment separation, and 2) the per iod from the beginning of last E I c l a i m to he employment separation. 9 I t is of course possible that this change could lead to profound impacts on the workplace arrangement, please refer to (Friesen, 2002) on research i n this respect. Chapter 2. UI and Labour Market: History, Literature and Theory 12 • Higher entrance requirement for new-entrants/re-entrants' (NEREs) Here, NEREs refer to workers whose UI employment and benefit collection du-rations in the 52 weeks preceding their current UI qualification period are less than 14 weeks pre-reform, or 490 hours post-reform. These are individuals with limited labour market attachment. The entrance requirements for them are set at a constant level independent of their local UI unemployment rates. The EI reform increased this universal entrance requirement from 20 weeks before the reform to 26 weeks after the reform. Obviously, this change created incentives for workers to keep more stable labour market attachment. • Introduction of worker side experience rating The worker side experience rating measures introduced by the EI reform affect the net amount of benefit workers' could enjoy. Before the reform, let yweek be a worker's average weekly earnings, then his weekly UI benefit amount was set at Q.55mm{ymeek, MIE/52}. Here MIE refers to maximum insurable earnings10, which sets an up-limit on both weekly UI benefit payment and UI payroll tax. Often, the 0.55 in the formula is refered as the replacement ratio of the UI program, linking benefit payment with worker's insurable earnings. The EI reform changed the formula for weekly benefit to (0.55 — 0.01eri)min{yweek, MIE/52}. Here erx is defined such that, starting from week 1, for each additional 20 weeks of UI benefit collection in the preceding 5 years, erx increases by 1 up to a maximum of 5. That is, workers replacement ratio are 55% if they collected less than 21 weeks of UI benefit in the preceding 5 years; 54% if they collected 21 to 40 weeks; 53% if they collected 41 to 60 weeks; and so on, till the minimum of 50% if they collected more than 100 weeks in the preceding 5 1 0 M I E is $42,380 before the reform and $39,000 afterward. Chapter 2. Ul and Labour Market: History, Literature and Theory 13 years. Obviously, er\ is where the worker-side experience rating came into play. This experience rating rule on replacement ratio is often referred as the 'intensity rule' of the EI reform. -The EI reform also introduced another experience rating rule, often called 'claw-back rule'. This is related to how high annual income workers are required to pay back some or all of their Ul benefit collection through the tax system. Before the reform, the Ul repayment at taxation time is set at minmax{0,0.3(yannual — 1.5MIE),0.3yUI}. Where yannual represents total taxable income of the year, and yUI is the total Ul payment received in the year. The EI reform changed the formula to minmax{0,0.3(yannual - (1.25 - 0.25er2)MIE), (0.3 + er3)yUI}. Here er2 takes 1 if the individual collected more than 20 weeks of Ul benefit within the preceding 5 taxation years11; 0, otherwise. If er2 is zero, then er3 is also zero. If er2 is one, then, starting from 0.1 and up to 0.7, er3 increases by 0.1 for each additional 20 weeks of Ul collection within the preceding 5 taxation years. The two major changes here are: 1) the upper limit for repayment is higher as the second term of minmax function shows. Thus, more people will need to repay their Ul benefit, which is consistent with the overall generosity cut of Ul program of this reform. 2) the formula incorporated worker-side experience rating through er2 and er3. This additional experience rating measure through taxation complements 'intensity rule' in the sense that 'intensity rule' mainly targets low income earners. It only affects individuals with annual earning below 1.1MIE12. The 'clawback rule' 1 1 There is a subtle different i n the definit ion of preceding 5 years between the ' intensi ty rule ' and 'c lawback rule ' . For the 'c lawback rule ' , i t refers to the preceding 5 t axa t ion years; whi le for the ' intensi ty rule ' , i t refers to the 5-year per iod preceding the start of current U l benefit c la im. 1 2 F o r workers who has annual earning above this amount, their effective replacement rat io is always below 0.5, the m i n i m u m amount that replacement rat io could get. Chapter 2. UI and Labour Market: History, Literature and Theory 14 mainly targets high income earners and only affects those with annual earnings above MIE 1 3 . These measures added two things to the unemployed workers' opportunity cost of UI collection: the expected drop in future benefit payment and the increased repayment. In extreme case, it might even be optimal for workers to stop collecting UI benefit while still unemployed14. • Discourage short employment by cutting weekly benefit using divisor rule As mentioned above, in Canada, workers' weekly UI benefit payment is a constant proportion of their average weekly earnings, yweek. The divisor rule introduced in the reform got its name from the new formula for yweek. Before the reform, yweek was ( S j t % , t ) / n - I n w o r ds , it equals the total earnings from all jobs within the benefit calculation period divided by the total number of working weeks within this period. The reform changed the denominator to mm{HMIN + 2,n}, thus setting a lower bound which is exactly two weeks above the entrance requirement on this term. The divisor rule does not affect benefit duration directly, but could affect weekly benefit payment depending on the number of actual weeks worked in the benefit calculation periods. Now that the entrance requirement of UI is based on total working hours, this week-based divisor rule effectively lowers workers weekly benefit if they achieved only minimal employment hours through intensive working weeks instead of having regular working weeks. In this sense, the divisor rule complements the new hourly system. 1 3 T h i s is due to the proper ty of minmax function. 1 4 T h e experience ra t ing rules in t roduced here only consider workers ' U I usage after the E I reform, that is from 1996 June onwards. T h u s these rules wou ld s t i l l i n their -phase-in per iod un t i l five years later. Surpr is ingly or not, the experience ra t ing rules were later cancelled i n M a y 2001, when the phase-in per iod was just about to end. Chapter 2. Ul and Labour Market: History, Literature and Theory 15 As described above, some of the changes made by the EI reform are straightfor-ward, while some are very subtle (i.e. institutional details that have hardly been considered in economic modelling). Together, these changes seem to shift the em-phasis of the program toward its insurance role, which is to discourage tailoring behaviours, and to encourage stronger labour market attachment. 2.2 Literature Review The theme of UI's labour market impacts has connections with a wide range of studies. It is far beyond this section to cover them all. The review here should focus more on empirical micro studies based on Canadian data. Earlier empirical works in this area are often based on aggregate or cross-sectional data. For example, to study changes of the Canadian Ul program in the late 1970s, Beach and Kaliski (1983a) use the aggregate transition probability matrix among the three major labour market status. Earlier studies also emphasize more on the classic labour-leisure model and the identification of labour demand versus labour supply. For example, Phipps (1991) and Phipps (1990) explore how the estimation of UI's impacts on labour supply is affected when demand-side constraints are considered. With micro-level longitudinal data sets become increasingly accessible, recent em-pirical Ul studies tend to emphasize the dynamic nature of labour market turnovers. The research interests are often to examine how Ul affects the entire distribution of unemployment spells, and occasionally, even that of employment spells. Clark and Summers (1979), an influential paper in this regard, demonstrates that although most unemployment spells are short, there are always a group of individuals with very long unemployment spells. Their study implies that labour market transi-tions across different states should not be modelled simply as Markov processes with Chapter 2. UI and Labour Market: History, Literature and Theory 16 constant transition rates, and therefore average unemployment duration or even un-employment rate could be misleading statistics for the labour market. A t the same time, their study also implies all workers are not the same in terms of labour market turnovers. Following Clark and Summers (1979), several Canadian studies start to examine issues related to the distribution of unemployment spells. Among them, Beach and Ka l i sk i (1983b) show how cross-sectional data sets tend to oversample long spells; Beach and Ka l i sk i (1987) explore how to estimate the distribution of unemployment spells using cross-sectional data sets. W i t h the availability of micro panel data in the late 1980s, most recent Canadian studies use duration models. Durat ion models not only could allow for more flexible distributions of labour market spells, but also could take account of unobserved heterogeneities across workers directly. Using administrative data on weekly U I collections of male workers from 1975 to 1980, H a m and Rea (1987) examine the impacts of remaining U I benefit length on workers' conditional reemployment probability (i.e. hazard rate). Being almost the first Canadian study to use duration model in this area, their study explores various specifications in order to examine the general pattern of duration dependency of the baseline hazard rates, as well as to examine the sensitivity of their main results. The results show unemployed workers hazard rate increases as the number of remaining UI benefit weeks decreases. The results are shown to be robust whether non-parametric or parametric baseline hazard specifications were used; or, whether spell-wise or individual-wise unobserved heterogeneity is considered. Overall , their results using Canadian data are quite consistent wi th those found using the U .S . data (Gri tz and MaCurdy , 1997; Lee, 2000; Meyer, 1990; Moffitt, 1985). UI not only could affect workers' unemployment duration, it could also affect Chapter 2. Ul and Labour Market: History, Literature and Theory 17 workers' employment spells. This point is highlighted by Green and Riddel l (1997) and Baker and Rea (1998) based on a natural experiment in Canada. Due to an unrelated dispute between the House of Commons and the Senate, U l entrance re-quirements of most regions were raised from 10 to 13 weeks to a uniform 14 weeks in the first 11 months of 1990. B o t h Green and Riddel l (1997) and Baker and Rea (1998) use this exogenous policy change as a rare opportunity to examine how U l entrance requirement could affect employment spells. Baker and Rea (1998) separately estimate duration models using samples of each province. The impacts of U l on employment spells are captured using four time-varying dummies for periods corresponding to four segments of the budget line. A s Baker and Rea (1998) use two alternative approaches to derive individuals' U l treatment, substantial emphasis of their study is to compare the estimated results from the two approaches and to discuss possible explanations of the differences. Al though using exactly the same episode of exogenous U l policy change, Green and Riddel l (1997) choose a very different research strategy. They restrict their sample to regions where the unemployment rate was at least 11.5% throughout 1989 and 1990. In these regions, the entrance requirement was uniformly 10 weeks in 1989 and 14 weeks in 1990. B y doing this, they not only achieve precision in the data used in the U l entrance requirement, but also highlight the impacts of U l on the distribution of employment spells in an extreme yet realistic setting. Al though Baker and Rea (1998) and Green and Riddel l (1997) approach the ques-tion differently, their results are quite consistent wi th each other. Both indicate the conditional employment separation probability (i.e. hazard rate) drops substantially prior to U l entrance requirement. Furthermore, Green and Riddel l (1997) show that much of the behavioural response in employment separation is observed as layoffs rather than quits, indicating certain cooperation between firms and workers. Chapter 2. UI and Labour Market: History, Literature and Theory 18 Besides UI's direct impact on unemployment or employment hazard rates, the empirical Canadian literature is also concerned with a wide variety of issues related to UI's labour market impacts, such as: - indirect impacts of U I on employment stabil-ity (Belzil , 2001); UI's differential impacts on seasonal versus non-seasonal workers (Green and Sargent, 1998); learning effect of UI collection experience (Corak, 1993; Lemieux and MacLeod , 2000); UI 's adverse selection problem among elder workers (Green and Ridded, 1993); sensitivity of the empirical results to consideration of in-stitutional details duration data derivation (Shannon and K i d d , 2000); UI's take-up rates (Storer and Audenrode, 1995). Regarding the 1996 E I reform, while Nakamura, Wong, and Diewart (2000) present the strategy designed for the reform, a series of studies are done to evaluate various aspects of labour market that this reform might have affected (Fortin, 2000; Friesen, 2002; Green and Riddel l , 2000; Human Resources Development Canada, 1997-2002, 2000, 2001a,b,c; Lacroix and Audenrode, 2000; Sweetman, 2000). More broadly, Gunderson and Riddel l (2000), Nakamura and Wong (2000), and Kesselman (2000) reviewed the lessons learned from Canada UI experiences from different angles; Welch (1977), Cousineau (1985), Atkinson and Micklewright (1991), and Holmlund (1998) provide survey of this empirical U I literature. Furthermore, there are a huge set of studies related to the current theme, such as theoretical studies on the issues of UI , unemployment, and labour market turnovers (Burdett, 1978; Ha l l , 2003; Jovanovic, 1979a,b, 1984; Milbourne, Purvis , and Scoones, 1991; Mortensen, 1978, 1982; Mortensen and Pissarides, 1994), empirical studies on labour market turnover only (Devine and Kiefer, 1991), studies on classifications of labour market states (Fl inn and Heckman, 1983; Jones and Riddel l , 1995), and so on. Chapter 2. Ul and Labour Market: History, Literature and Theory 19 2.3 A Model of Labour Market Turnover with Contingent, Temporary U l Although many theoretical works have examined UI's labour market impacts, most of them assume unconditional, infinite U l coverage 1 5. A s an exception, Green and Sargent (1998) show individuals ' employment spells theoretically should be affected by -UI benefit's minimum employment requirement, which is indeed supported by their empirical results. The model here extends Green and Sargent (1998)'s theoret-ical work by considering both the contingent and temporary nature of U l coverage. B y that, I relate to the fact that most countries' U l programs require some minimum labour market attachment for benefit eligibility and provide benefit for finite length of periods. U l benefit's temporariness critically relies on its contingency. Tempo-rary U l benefit coverage could only be effective with its contingent requirement on employment experiences, as Jovanovic (1984) pointed out, "[with temporary U l benefit coverage, if] Wi thout this requirement [minimum employment requirement], as the expiration date of his benefit approached, the unemployed worker could accept any job for an instant and then reenter unemployment immediately, thereby assuring himself of another maximum period of coverage." In a sense, the above remark signifies the relevancy to understand how U l pa-rameters, such as benefit duration and employment requirement, jointly affects the labour market transitions in both directions between employment and unemploy-1 5 S o m e studies that have considered uncondi t ional , finite U l coverage include Mor tensen (1977), V a n den B e r g (1990), Alb rech t and V r o m a n (2005), Coles and Mas te rs (2004). B u t none of them considered the contingency of U l coverage. Chapter 2. UI and Labour Market: History, Literature and Theory 20 ment states. Therefore, when examining UIs labour market impacts, we consider these two UI parameters together. The main contribution of this study is thus exploration of UI's labour market impacts where UI coverage is contingent and temporary by endogenizing both em-ployment and unemployment durations. By connecting workers' decisions while em-ployed and unemployed together in a single framework, the model here is able to allow workers' decision while employed to depend on his expected action while un-employed, which depends on his expected action if he became reemployed, and so on. In this way, workers labour market transitions are modelled to reflect a coherent set of underlying reaction functions to any possible situations in the long run. Many theoretical efforts have been made to endogenize the labour market tran-sitions in either directions between employment and unemployment states, while there have been only a few studies that endogenize the labour market transitions in both directions16, which are usually technically intense. Furthermore, the few joint-process types of models almost entirely rely on the stationarity of the prob-lem for analytical solutions. To consider the contingent, temporary UI coverage in these models will turn the problem into a non-stationary one, which is very difficult analytically. "It is, of course, desirable that theory should reflect the temporary duration of unemployment benefits, but my attempts to take account of it quickly led to an unexpected complexity in the analysis (Jovanovic (1984) page 115)." The strategy here is not to solve the non-stationary problem analytically alto-gether. Rather, I use a combination of numerical and analytical techniques to solve the problem and yet provide intuitive interpretations of the solution. 1 6 M o s t noticeably, Jovanovic (1984). Chapter 2. Ul and Labour Market: History, Literature and Theory 21 In particular, the results illustrate how key Ul parameters (benefit duration, employment requirement and weekly benefit) interact with each other and how each of them generates both work incentives and disincentives for workers, depending on the stages of their employment/unemployment cycles. 2.3.1 Setup The model here is about how an agent (the worker) makes labour market decisions. Intertemporal consumption allocation is simplified by assuming this agent to be risk neutral, thus wealth maximizing. The worker has discount rate, (3, for next week's income. The two kinds of decisions he makes are, whether to accept job offers when unemployed and whether to quit when employed. Each week, the probability for an unemployed worker to get an job offer is A, where the distribution of such job offer's wage rate w is F(w). Each week, the probability for an employed worker to get a redrawn for his wage at the current job is 77 (77 < A). The distribution of the new wage rate is also F(w). Such exogenous on-the-job wage movement creates a simple, transparent mechanism for employment separation. Figure 2.1 shows the sequence and timing of decisions and events for our model. As the figure shows, each week, an unemployed worker always search for job offers first. He could get at most one job offer each week. If he gets one offer, based on the offered wage rate, he then decides to accept it or not at the end of each week. On the other side, an employed worker always chooses, based on his current week wage rate, whether to quit or not at the beginning of each week. If quit, he will spend the rest of the week unemployed; otherwise, he will be working, and with some possibility, he could get wage redrawn at the end of the week. Chapter 2. UI and Labour Market: History, Literature and Theory 22 This particular timing design, rather than other possible alternatives, is cho-sen here mainly because it excludes the possibility of direct job to job transitions by making it impossible for a worker to quit and accept another offer within one period/week17. It also ensures a worker will stay at least one week on any job he accepted. This could be convenient for solving the worker's problem as it means that when solving the reservation wages through the indifference conditions we could use the value function of week 1 employment. In the literature on employment separation, there are more complicated ap-proaches, such as considering the wage-tenure relationship to be a reflection of how the exact productivity of each worker-firm match is revealed over time. The sim-ple approach taken here is adopted from Green and Sargent (1998), who use it in their theoretical analysis of the impacts of UI entrance requirement on employment separation18. The exogenous, wage movement approach here is used not only for its simplicity, but also because it is reasonable to believe employed workers are only par-tially isolated from overall productivity shock F(w). Commitment to the job match is still weak and not completely immune to outside opportunities at the initial stage of job match. A simple UI policy is assumed: a worker will be eligible for the benefit if he quits after completed at least Ne weeks of employment, that is, from the start of week 1 7 I n pr inciple , each employment spell could correspond to several job spells, wh ich could even have overlapping. A simple interpretat ion of the model setup here is that only the simplest sit-ua t ion is considered where each employment spell corresponds to only one job spell . B u t even in other si tuations, the exogenous wage dynamics is perhaps an easier approach to describe the corresponding wage processes. 1 8 T h e ma in difference of my s tudy and theirs is that they focus solely on employment separation process whi le here I extend their model to include reemployment process as wel l . A s a result, the coherency of the worker 's react ion function i n these two processes has become a cr i t ica l issue for the analysis here. Chapter 2. UI and Labour Market: History, Literature and Theory 2 3 Ne + 1 on. All qualified unemployed workers will be able to collect $B UI benefit per week for Nu weeks. 2.3.2 Character iza t ions of the Solu t ion The solution to this worker's optimization problem, assuming existence and well-behaved, is a set of reservation wages for the entire set of value functions for all situations. That's because: the worker has an infinite time horizon and his decisions regarding quitting or accepting job offers are interdependent. For example, an em-ployed worker's decision about quitting depends on the potential payoff he could get from starting a new unemployment spell. This depends on his subsequent decision about accepting job offers while unemployed, which in turn depends on his quitting decisions while he gets reemployed again, and so on. Let V(w,t) be the value function at the start of employment week t with wage w; W[t) refers to value function at the start of an unemployment week with t weeks of UI benefit remaining. Here is a set of representative value functions: Chapter 2. Ul and Labour Market: History, Literature and Theory 2 4 V(w,Ne + l) = m a x j W(Nu),w + Pv j V(x, Ne + 2)dF{x) + P(l - V)V(w,Ne + 2)^ V(w,Ne) = max !^W(0),w + pr) J V(x,Ne + l)dF(x) + P(l ~v)V(w, Ne + 1 ) | V(w,Ne-l) = max^W(0),w + Pvjv(x,Ne)dF{x) + p(l-'n)V(w,Ne)^ V(w,l) = m&x^W(0),w +(3r) J V(x,2)dF(x) +P(l-r])V(w,2)^ W{NU) = B + pxJmax{W{Nu-l),V(x,l)}dF(x) + p(l-X)W(Nu-l) ^ W(NU - 1) = B + pxJ m a x {W(NU - 2), V(x, 1)} dF{x) + 0(1 - X)W(NU - 2) W(l) = B + pxJm&x{W(0),V(x,l)}dF(x) + B(l-X)W(0) W(0) = pX Imax{W(0),V(x,l)}dF(x) + B(l - X)W(0) In words, the first value function V(w, Ne + 1) says that a worker who has been employed long enough to qualify for Ul benefit, maximizes his/her payoff by choosing whether to quit or not. If quit, his/her payoff will be the same as an unemployed worker with full Ul benefit, i.e. W(NU); if stay, he/she could get the current week's wage and would face potential wage adjustment. The other value functions for employed workers are written similarly, except that the payoff for quitting is now W(0), which is the same as an unemployed worker with no Ul benefit. Next, for an unemployed worker, his/her value functions at each week are com-posed of two parts: the current week benefit payoff if there is still Ul benefit left, and the discounted expected payoff next period, at which point he/she could choose to accept a job or not if a job offer arrives. The interdependence of the worker's problem while employed and unemployed is also captured in above value function set: value functions while employed, V(-), Chapter 2. UI and Labour Market: History, Literature and Theory 25 depend on {W(Nu),W(0)}; while value function while unemployed, W(-), depend on V(w, 1). To solve this set of value functions, a combination of analytical and numerical techniques are used. Assuming the existence and uniqueness of the solution, here are some important analytical properties of the solutions of the problem. The proofs of these propositions are in appendix A . P ropos i t ion 2.3.1 Vt > Ne + 1, workers value function at employment week t is given by f W(NU) + ifw> we*; V{w,t) = 1 K ' 1 - / 3 ( 1 - , 7 ) " (2.2) I W(NU) otherwise, where we* is implicitly given by (1 - P)W(NU) = we* + l _ p l \ _ n ) J' \* ~ ™ 61 d F ( x ) ( 2- 3) This proposition gives the analytical solution of the value function of a worker who ' has been employed long enough to qualify for UI benefit. Once qualified for U I ben-efit, the worker's problem becomes stationary. In other words, for weeks beyond Ne, the value functions and the corresponding reservation wages would remain constant. The intuit ion behind proposition 2.3.1 is illustrated by figure 2.2. A s shown in the figure, the option provided by UI of quitt ing created a bottomline of workers' value function. Given W(NU) at the optimal solution, the worker is indifferent between quitting and staying with wage we*. He wi l l quit if his wage is below we*, and his payoff wi l l be W(NU). He wi l l stay if his wage is above we*. The lower the probability that he wi l l face a redraw from the wage distribution, the steeper is the slope of his value function in this section, and in the extreme case where r\ = 0, the slope wi l l be — -u e 1-fi-ll! other words, the value function at weeks beyond Ne + 1 is composed of a horizontal segment and a straight up-sloping line. The position of the kink, we*, Chapter 2. UI and Labour Market: History, Literature and Theory 26 is related to the set of parameters of the problem, in particular, the distribution of wage offer, workers' discount rate, and offer arrival rate while employed. The other parameters are implicitly absorbed in the optimal value of W{NU). Propos i t ion 2.3.2 Assume W{Nu) > W(0), and Vz £ N s.t. 1 < i < Ne, V(we*,Ne + 1 — i) > W(0). Let w^* be workers reservation wage at employment week t. Then Vi e N s.t. 1 < i < Ne, V(we*,Ne + l-i) -W(0) Silo W " V)Y (2.4) dV{w, Ne + l-i) _ dw (1 - — 77))"1. if w>we* El=o(0(i - v ) Y ^ w e (2-5) 0 ifw < ^ e + i _ i jV(x,Ne + 2-i)dF(x) > JV(x,Ne + l-i)dF(x) (2.6) V{w, Ne + 2-i)> V{w, Ne + 1 - i) Vw (2.7) This second proposition implicitly defines the solution of the value function of an employed worker who still need to qualify for UI benefit, i.e. when his/her has been' employed for no more than Ne weeks. Equation 2.4 and 2.5 describe the overall shape of each week's value function, which is always composed of three straight line segments: a horizontal one when the wage is below current reservation wage, and two upward sloping ones for wages above current reservation wage. Equation 2.5 shows the later two segments intersect when the wage equals the reservation wage post Ne + 1, we*. The slopes of the first and third segments are independent of employment weeks, while the slope of the middle segment isnt. It is YfsllWi1 ~ v)Y- It decreases from 1 to l/Ef=o 1(^( 1 ~ v))3 as the worker moves back from only 1 week short of entrance requirement to the start of an employment spell. Chapter 2. UI and Labour Market: History, Literature and Theory 27 Inequalities of 2.6 and 2.7 help to establish the first two equations. Intuitively, inequality 2.6 says, overall, it is always strictly better to be closer to the entrance requriement week, JVe + 1; inequality 2.7 says, at any wage level, the payoff could not be lower if the worker is one week closer to Ne + 1. With the slope of each segment found, and with values of uie*, W(0), the knowl-edge that V(w,Ne + I — i) — W(0) if w < w^^^, and finally the fact that V(w, Ne + 1) = V(w, Ne) for w > we*, it becomes possible to backup all the value functions and reservation wages for employment week iVe, and then Ne — 1, and finally for the first week employed. The dynamics of the value functions are illustrated in figure 2.2 and figure 2.3. In particular, figure 2.2 shows, for week iVe, the value function looks like that of week Ne + 1 except for the lower part, which has a lower threshold of W(0) and the slope in the middle part is 1. The change could be proved straigntforward by comparing value functions at week Ne + 1 and Ne. If we move back one more week, figure 2.3 shows the value function for week Ne — 1 is shifted downward and with a steeper middle slope. As a matter of fact, the value functions will continue to be pushed downward and the middle section's slope will become steeper as the worker is farther away from Ne + 1. Propos i t ion 2.3.3 Assume > 0. Assume W(Nu)-W(0) > B > 0. Letwf* be the reservation wage when there are t weeks of UI benefit remaining at the start of an unemployed week. Define At = V(w%1} 1)-V(w?*, I), Vi e N, s.t. t e [1, Nu-1]. Then Wt e N, s.t. t e [1, Nu], V{w?*, 1) = W{t - 1) (2.8) B and wlf* > wx (2.9) \ft G N, s.t. t e [2,Nu - 1], A t < / ? A F « * ) A t _ ! and > v%* (2.10) Chapter 2. Ul and Labour Market: History, Literature and Theory 28 In this last proposition, the dynamics of reservation wage while unemployed is presented. Since (3\F(w™) < 1, this proposition shows how the reservation wage increases at an decreasing rate as workers have more weeks of U l benefit remaining. 2.3.3 N u m e r i c a l Search of the Solu t ion Above, under some assumptions, proposition 2.3.1 and proposition 2.3.2 present characterizations of workers' value functions while employed taking {W(NU), W(0)} as given, and proposition 2.3.3 presents characterizations of workers' value functions while unemployed taking V(w, 1) as given. The solution of the entire problem not only has to satisfy these propositions, the two parts of the solution (employed and unemployed ones) have to be consistent with each other. That is, the following two conditions have to be true for the solution. where G1^), G2(-) are implici t ly given in the propositions. Given the complexity of the solution as indicated in the propositions, it is very unlikely that the analytical solution wi l l be transparent or instructive. Therefore, numerical approach is used for the final solution. Specifically, the final numerical solution is based on a given set of parameters, the analytical propositions as well as the two consistency conditions. This is done by starting with some educated guess about {W(Nuy, Wfi)1}, and then calculating V1(w, 1) and {W(NU)2, W(0)2}, and so on, unti l {w{Nuy,w(oy} = {w{Nu)t+1,w{oy+1}. Specifically, the start value of {W(NU)1, jy(O) 1 } could be set around B/(l - p). Then we could get Vl(w, 1) by calculating wf and V(w, t) from £ = A r e + l t o £ = l V(w,l) = G1(W{Nu),W{0),w) {W(NU),W(0)} = G2(V(.,1)) (2.11) (2.12) Chapter 2. Ul and Labour Market: History, Literature and Theory 29 using previous analytical results. To get {W(NU)2, W(0)2} from V1(w,l), we can use the value function. These steps could be repeated unti l the results converge. Once the consistency conditions are satisfied, the full set of reservation wages and hazard rates are backed-out. 2.3.4 Economic Implicat ions The figures in table 2.1 illustrate the implications of preceding theoretical model for UI's impacts on individuals ' reservation wages and hazard rates. These figures show how each U l parameter generates both work incentives and disincentives on the labour market. For a given set of parameters (/?, n, A, F(-), Ne, Nu, B), workers' reservation wages are, relative to the case of no U l , lower in period EO (employed but before U l eligible) and period UO (unemployed with no U l benefit coverage), and higher in period E l (employed and eligible for U l ) and period U l (unemployed with some U l coverage). In period EO, individuals ' reservation wage decreases at an increasing rate as their prospects of getting U l coverage increases; in period UO, individuals ' reservation wage is constantly lower than the case of no U l , as the possibility of U l coverage after future job losses makes low-wage jobs more attractive. O n the other hand, in period E l , individuals ' reservation wage is constantly higher than the case of no U l as employed workers are able to collect U l if they quit; in period U l , individuals ' reservation wage decreases at an increasing rate as their prospects of exhausting U l coverage increases as time goes by. Similar to its impacts on the reservation wages, the implications of temporary contingent U l coverage on.hazard rates are such that, relative to the case of no U l , hazard rate is higher in periods EO and UO, and lower in periods E l and U l , with only one exception at the first week of satisfying U l employment requirement. Chapter 2. Ul and Labour Market: History, Literature and Theory 30 At that moment, the hazard rate of employed workers jumps to its unique peak. This dramatic movement is a result of reservation wage jump at that point, which means all job matches accumulated earlier with wages below the new high level of reservation wage will break suddenly. Now consider the impacts of adjusting the U l parameters. The figures of ta-ble 2.2 show the impacts of reducing weekly benefit payment, where the solid curves correspond to B = 20 and the dashed curves correspond to B = 19. The figures show the impacts of U l become weaker as B drops. For periods that reservation wage is pushed up, i.e. E l and U l , this benefit cut will lead to a weaker increase in the reservation wage; for periods where the reservation wage is pushed down, i.e. EO and UO , this cut will lead to a weaker decrease. The impacts of benefit cut on hazard rate tell very similar story. Next, for the other two U l parameters, benefit duration and minimum employ-ment requirement, the changes of U l impacts are mainly reflected as shifts of the curves to the new critical weeks. In particular, figures in table 2.3 show as number of minimum employment requirement weeks drops, the reservation wages and hazard rates for the employment spells are affected the most, almost as if the curves have been shifted to the left accordingly. With less weeks of employment required for U l coverage, theoretically, the U l program becomes more generous. Reemployment, therefore, becomes more attractive for unemployed workers, and their reservation wages should drop. But as the figures show, there is only a very slight drop of un-employed workers' reservation wages in this case. Similarly, figures in table 2.4 show as the number of U l benefit weeks drops, the reservation wages and hazard rates for the unemployment spells are affected the most. The expected weakening of U l im-pacts on the employment spells, though numerically consistent with the theoretical predictions, is hardly noticeable on the figures. Chapter 2. UI and Labour Market: History, Literature and Theory 31 Although the model presented above is simple, the implications for UI's labour market impacts discussed here should be able to capture most of those of a more 'realistic' UI program. After all, the discrete nature of eligibility of UI remains to be the most substantial change in workers payoff calculation. The results here confirm previous theoretical predictions in an extended context. For example, Green and Sargent (1998) highlight the entrance effect in period EO, while Meyer (1990) examined the benefit exhaustion effect in period U l . Here, these previous results are shown to be optimal in an unified framework where transitions in both directions of employment and unemployment are endogenized. In addition, these effects are found to coexist with UIs inducement effect of UI in period UO and its disincentive effect in period E l . Moreover, using a single theoretical framework, the findings here also highlight several intricacies of UI's labour market impacts. First, all these different aspects of UI's labour market impacts are interdependent on each other; second, while an UI program could be made more generous through different approaches (such as, shortening entrance requirement, lengthening benefit durations, or increasing weekly benefit payment), our theoretical model shows how each of the approach has different implications on the labour market turnovers. Finally, the kind of consistent patterns as illustrated in the figures of table 2.1 show how some UI parameters change could function like a double-edged sword on the labour market, providing both work incen-tives and disincentives. For example, if benefit duration becomes longer, unemployed workers with benefit coverage at any given week would have less work incentive and higher reservation wages, while short-tenured employed workers would have more work incentive and lower reservation wages. Given the populations of workers with different employment/unemployment du-rations have different compositions, both in terms of observables and unobservables, Chapter 2. Ul and Labour Market: History, Literature and Theory 32 various policy options could have quite different impacts in the labour market. There-fore, it is only sensible to have different Ul policy choices corresponding to changing policy priorities. As discussed in detail earlier, the EI reform increased employment requirement (divisor'rule), lowered benefit payment (experience rating) as well as benefit dura-tions, all on some conditional forms. When the overall generosity of the Ul program became less generous, it seems that, based on our theoretical model, UI's impacts,-both positive and negative, on the labour market would have been weakened. But as noted above, UI's impacts on the labour market could be rather intricate, EI reform's effects on those impacts could be less than uniform across heterogeneous workers. 2.4 Figures Figure 2.1: Timing of Workers' Decision an unemployed week y accept => exit • i ^ get an o f f e i \ r e j e c t = > s t a y job search<^ J • no offer => stay an employed week , get a redraw in wage , stay => work <T , „ ^ i-rT~~- same wage as before quit => exit Chapter 2. UI and Labour Market: History, Literature and Theory 33 Chapter 2. UI and Labour Market: History, Literature and Theory 34 Chapter 2. UI and Labour Market: History, Literature and Theory 35 Table 2.1: Predicted Impacts of Contingent, Temporary UI Benefit R e s e r v a t i o n wage H a z a r d ra te E m p l o y e d 10 15 20 25 30 35 40 45 50 weeks 10 c i \ E0 \ i i i i i i i i E l •V 10 15 20 25 30 35 40 45 50 weeks ! OQi I I I uo . Y ' U n e m p l o y e d 14, 10 15 20 25 30 35 40 45 weeks 50 Ul 10 15 20 25 30 35 40 45 50 weeks N o t e : T h e p a r a m e t e r set u s e d for n u m e r i c a l s i m u l a t i o n is : j3 — 0.8, r\ — 0 .1 , A — 0.2, NE = 20, NU = 30, B = 20, F(w) is a t r u n c a t e d n o r m a l d i s t r i b u t i o n i V ( 2 0 , 5 ) w i t h w > 0. I n t h i s case, t h e m i n i m u m e m p l o y m e n t r e q u i r e m e n t t h r e s h o l d week HMINQ equa l s NE + 1 = 21; a n d t h e benef i t e x h a u s t i o n t h r e s h o l d week BEWQ equa l s NU + 1 = 31 . A t t h e o p t i m a l , {W(NU), W(0)} equa l s t o {104 .9447 , 95} . Chapter 2. Ul and Labour Market: History, Literature and Theory 36 Table 2 .2 : Predicted Impacts of Weekly U l Benefit Cut R e s e r v a t i o n wage H a z a r d ra te E m p l o y e d c=- 101 -o 53 0 5 10 15 20 25 30 35 40 45 50 weeks HMINn i 1 HMINn HMINn E l t E0 \ 0 5 10 15 20 25 30 35 40 45 50 weeks 0: w 03i Ul U n e m p l o y e d U0 10 15 20 25 30 35 40 45 50 weeks 14 12 10 Q> 13 8 •o 1 6 X I 4 2 0 Ul 10 15 20 25 30 35 40 45 50 weeks N o t e : r e l a t i v e t o t h e p a r a m e t e r set i n f igure 2 .1 , the w e e k l y benef i t p a y m e n t is c u t f r o m $20 t o $19 p e r week . A t t h e n e w o p t i m a l , {W(NU), W(0)} equa l s t o { 1 0 1 . 1 4 6 6 , 9 5 } . T h e s o l i d l ines c o r r e s p o n d t o t h e o r i g i n a l p a r a m e t e r set, t h e g reen d a s h e d l ines c o r r e s p o n d t o t h e n e w set. Chapter 2. Ul and Labour Market: History, Literature and Theory 37 Table 2.3: Predicted Impacts of Employment Requirement Week Cut R e s e r v a t i o n wage H a z a r d ra te E m p l o y e d i i i =J ZJ .!. El EO 0 5 10 15 20 25 30 35 40 45 50 weeks Co- 10 2 8 -a | 6 J3 4 2 0 c i i i 3 1 1 1 1 El E 0 V \ 5 10 15 20 25 30 35 40 45 50 weeks Si Ul U n e m p l o y e d U0 10 15 20 25 30 35 40 45 50 weeks 1 4 r 12 10 ID t_ 8 • a | 6 JS 4 2 • i \ A w PQi Ul | U0 5 10 15 20 25 30 35 40 45 50 weeks N o t e : r e l a t i v e t o t h e p a r a m e t e r set i n f igure 2 .1 , e n t r a n c e r e q u i r e m e n t week Ne is c u t f r o m 20 t o 19 weeks . A t t h e n e w o p t i m a l , {W{NU), W(Q)} equa l s t o { 1 0 4 . 9 4 4 , 9 5 } . T h e s o l i d l ines c o r r e s p o n d t o t h e o r i g i n a l p a r a m e t e r set, t h e g reen d a s h e d l i nes c o r r e s p o n d t o t h e n e w set. Chapter 2. UI and Labour Market: History, Literature and Theory 38 Table 2.4: Predicted Impacts of Benefit Week Cut R e s e r v a t i o n wage H a z a r d ra te E m p l o y e d 10 15 20 25 30 35 40 45 50 weeks U n e m p l o y e d CS i c o t 25 20 15 101 5 0 ! CQi Ul | uo . Y C= 101 -o 10 15 20 25 30 35 40 45 50 weeks Ul 5 10 15 20 25 30 35 40 45 50 weeks N o t e : r e l a t i v e t o t h e p a r a m e t e r set i n f igure 2 .1 , benef i t week Nu is c u t f r o m 30 t o 25 weeks . A t t h e n e w o p t i m a l , {W(Nu),W(0)} equa l s t o { 1 0 4 . 9 4 2 , 9 5 } . T h e s o l i d l ines c o r r e s p o n d t o t h e o r i g i n a l p a r a m e t e r set, t h e g reen d a s h e d l ines c o r r e s p o n d t o t h e n e w set. 39 Chapter 3 Contingent, Temporary Unemployment Insurance Coverage and Employment /Unemployment Cycles 3.1 Introduction There is a trend of updating income support policies among industrial countries since the 1990s. Because of its coverage's employment requirement, Unemployment Insur-ance (UI) has a closer connection to the labour market relative to other programs. In the empirical literature, previous studies have examined how UI coverage's con-tingency affects employment spells (Baker and Rea, 1998; Green and Riddell, 1997), and how UI coverage's temporariness affects unemployment spells (Ham and Rea, 1987; Meyer, 1990; Moffitt, 1985). Though jointly these two sets of studies cover UI's impacts on both directions of employment/unemployment transitions, data sources and econometric setups often differ a lot across individual studies, making it difficult to form a synthesized view of the whole picture. Chapter 3. Contingent, Temporary Ul and Employment/Unemployment Cycles 40 This study re-examines contingent, temporary U l coverage's impacts on both directions of employment/unemployment cycles using a common Canadian data source, the Survey of Labour and Income Dynamics (SLID) . Besides the data set used, there are at least two other aspects of this study that reflect its Canadian origin: first, the seasonal sector, the often blamed UTabuser in Canada, is studied separately from the non-seasonal sector; and second, the 1996 Employment Insur-ance (EI) reform 1 of Canada is used here as a unique source of exogenous treatment variations. In theory, t iming is crit ical under contingent temporary U l program: the closer an employed worker is to his employment requirement week, the stronger the incentive is for h im to stay employed; the closer an unemployed worker is to his benefit exhaustion week, the stronger the incentive is for h im to leave unemployment. In short, UI 's impacts on work incentives are time-varying even in the 'steady state'. Such time-varying impacts of U l on the labour market are supported by several previous studies. In particular, both Moffitt (1985) and Meyer (1990) show the haz-ard (i.e. conditional probability) of leaving unemployment increases as unemployed workers approach their benefit exhaustion weeks using U .S . data. H a m and Rea (1987) also provide similar results using Canadian data. O n the employment side, both Green and Riddel l (1997) and Baker and Rea (1998) show the hazard of leaving employment decreases as workers approach their minimum employment requirement weeks. The identification of all of the above types of time-varying impacts critically relies on having exogenous variations of U l treatment (either employment requirement or benefit durations). For example, if all sample unemployment spells have the same l r T h e E I reform is the most influential change of the Canad i an U l p rogram i n recent history. Please refer to chapter 2 for a detailed review of this reform and its background. Chapter 3. Contingent, Temporary UI and Employment/Unemployment Cycles 41 number of initial UI benefit durations, then the impacts of UI would be indistin-guishable from the trend of baseline hazards. This is very close to the U.S. case. There workers' benefit durations are almost the same within each state. Different from that, workers' UI benefit durations depend positively on their pre-vious employment histories and their local unemployment rates in Canada. While such design does generate valuable treatment variations within Canadian data, the variations it generates could potentially be endogenous. Here the UI treatment is indirectly related to individuals' inherent work attitude through employment his-tories. While, to examine UI's impacts on labour market transitions, we need the variation of individuals' UI benefit durations to be exogenous to their inherent atti-tudes toward labour market attachment. To tackle this problem, this study uses the EI reform as a unique exogenous source of treatment variation. Although the usage of sample spells in two separate periods with different UI treatments could be good for identification, it also brings about a new problem for this study. That is how to account for across-period macroeconomic differences. This is a problem absent in previous studies. Figure 3.1 plots the Canadian unemployment rate in recent decades. Intervals A and B correspond to the pre- and post-reform sample periods of this study. The EI reform, as shown in the figure, happened in the middle of an economic recovery. Not surprisingly, evaluations of the EI reform constantly find substantial labour market improvement in post-reform years (Human Resources Development Canada, 1997-2002). Here, we could think of two types of impacts that the economic recovery might have on the employment/unemployment spells' baseline hazards: level-shifts and shape-changes. A post-reform dummy variable is used to account for level-shifts. To examine shape-changes, the analysis here compares the estimation results using pooled sample spells with those using sample spells from each individual period. The Chapter 3. Contingent, Temporary Ul and Employment/Unemployment Cycles 42 comparisons suggest the estimated Ul impacts based on pooled samples are hardly affected by this second type of macro impacts. We are not claiming that there are not many shape-changes in the baseline hazards of labour market turnovers across business cycles in general2; rather, what our results indicate is that it is possible for the estimated Ul impacts to be robust to macroeconomic recovery. It is also worth-noting that we consider such robustness is very likely to come from our usage of time-varying Ul dummy variables. How could the identification of the coefficients for time-varying Ul dummies not be affected by possible baseline hazards shape changes in this case? It might be explained using figure 3.2, which gives two examples of such variables. As shown here, this type of variable usually only takes value one at a subset of all the weeks covered by a spell. The set of value-one weeks vary across spells. For unemployment spells, it might depend on unemployment spells' initial Ul benefit durations; for employment spells, it might depend on weekly working hours and local unemployment rate. It is unlikely differences in the shapes of baseline hazards due to economic recovery across the two periods would match exactly all spells' sets of value-one weeks of a specifically defined time-varying variable at once. Using figure 3.2 as an example, the estimation of UI's impacts on unemployment hazards for workers with 11 to 20 weeks of benefit left could only possibly be affected by the macroeconomic recovery if such recovery only affects week 20 to 29 for the first spell and week 5 to 14 for the second one. That is indeed very unlikely. In terms of econometric setup, hazard models naturally allow for incomplete (censored) spells and time-varying variables. Various hazard models have become a common choice in this literature. For our study, since the Canadian Ul benefit is 2 A s a matter of fact, we do find some differences i n the patterns of baseline hazards across the two periods as w i l l be discussed i n detai l later. Chapter 3. Contingent, Temporary UI and Employment/Unemployment Cycles 43 denned in term of weeks, we need to examine the duration data by weeks as well. Bu t many of our sample spells ended at semi-monthly or monthly frequencies3. Tailored . to this particular feature of the sample spells, I thus extend the usual hazard model to allow for heaping effect. The results here confirm most of existing findings of the literature mentioned earlier in a new context, as well as uncover some new ones. In terms of aggregate impacts, the simulations here suggest that at the aggregate level, ceteris paribus, the overall unemployment rate of Canada in the late 1990s could drop by around 15% (e.g. from 7.6% to 6.6%) if there are no UI impacts. In terms of the E I reform, the results suggest there is a decline in the seasonality of the employment/unemployment cycles in the seasonal sector. Besides, simulation results also imply the E I reform, except for the experience rating rules and the divisor rule, has no significant impacts on the national unemployment rate. The rest of this paper is organized as follows: section 2 reviews theoretical im-plications of contingent temporary U I coverage. Section 3 explains the econometric formulation. Section 4 discusses the data construction. Section 5 presents empirical analysis. Section 6 concludes. 3.2 Theoretical implications According to the static labour and leisure model, UI's impacts on the labour market mainly work through its impacts on workers' budget lines. For the case of Canadian U I program setup, to be eligible for U I benefit coverage, a worker's employment weeks need to reach some minimum level, HMIN. After week HMIN, his benefit 3 I n fact, volat i le hazard rates are commonly found i n high-frequency labour market dura t ion data. Chapter 3. Contingent, Temporary UI and Employment/Unemployment Cycles 44 duration increases till week HMAX, at which point the worker reaches the upper bound of benefit duration available4. Figure 3.3.a and 3.4.a illustrate such a benefit schedule and its corresponding budget line. In this static model of labour and leisure choice, UIs impacts critically depend on the length of workers' planning horizon (Green and Sargent, 1998). Most sea-sonal workers in Canada are forced to have one-year planning horizon due to the weather and job season. Once their job season comes, they have to go back to work; otherwise, they will miss their whole employment season. As a result, the effective UI benefit weeks for workers in the seasonal sector is HYRMAX. Post the week of HYRMAX., one more week of work means one less week of benefit collection for seasonal workers. In terms of hazard rates, the static model thus predicts higher employment hazard rates for weeks between HMIN and HYRMAX, and a spike of unemployment hazard rate around the benefit exhaust week (BEW). The static model might be appropriate for seasonal workers but not for non-seasonal workers. They do not have as nearly a strong foresight on the timing and length of their upcoming employment spells as those in the seasonal sectors. It might be more reasonable to assume an infinite planning horizon with risky employment for non-seasonal workers. Therefore, we might want to consider a model as presented in chapter 2 for non-seasonal sector. This is a theoretical model for labour market turnover with contingent, tem-porary UI benefit as well as re-employment and job loss uncertainties. Figure 3.5 shows its implications for the entire pattern of UI's time-varying impacts on employ-ment/unemployment cycles. In summary, the model predicts: 1) entrance induction effect: a gradual drop of employment hazard rates before HMIN and an employ-4 H e r e , bo th HMIN and HMAX vary w i t h loca l unemployment rates. M o r e detailed informa-t ion about the schedule is presented i n section 2.1. Chapter 3. Contingent, Temporary Ul and Employment/Unemployment Cycles 45 merit hazard rates spike at HMIN; and, 2) benefit exhaustion effect: a gradual rise of unemployment hazard rates before BEW. Given the setup of Ul in Canada, work-ers' potential benefit weeks will continue to increase with their employment weeks up to a maximum, HMAX. Thus, they still have incentive to stay employed beyond week HMIN. For that, we expect a potential tailoring effect of Ul for workers after week HMIN but before week HMAX for non-seasonal workers (or HYRMAX for seasonal workers). Besides the above, two sets of new rules introduced by the EI reform are also considered in our specifications. First, the divisor rule. It discourages workers from short, unstable labour market attachment by cutting workers' weekly benefit pay-ment if the number of calendar weeks used to claim Ul benefit is less than HMIN+2. Second, worker-side experience rating rules. Simply speaking, workers would receive lower weekly payments and need to repay more of their received benefit through the tax system as their previous 5 years' Ul benefit collection weeks increase across each 20-week long interval. If the planning horizon is 53 weeks, considering the 2-week Ul waiting period, that means a worker has to work at least 31 weeks in a year to avoid those penalties. Therefore, we expect hazard rates for leaving employment to be lower before week 31, and those for leaving unemployment to be higher before week 19. 3.3 Econometric Setup: Hazard Model with Heaping Effect The model formulated here uses proportional hazard (PH) model as its starting point. Discrete time PH model has been widely used in the related literature (Green and Sargent, 1998; Meyer, 1990). The main advantage of discrete time PH model Chapter 3. Contingent, Temporary Ul and Employment/Unemployment Cycles 46 is that control variables could vary over the course of a single spell. It has close connection with continuous time PH model in that the probability of a spell to end at a discrete period is modeled as this spell hasn't survived the last period. Specifically, for spell j, let dj be its duration; 6j>t be its instantaneous hazard, that is 8jit — prob{dj = t\dj > t}; pjit be its discrete hazard at period t. Then Pjtt = 1 — exp(—6jtt). The way covariates are incorporated in these models is to set 9jt t = exp(at + flxj-t) (3.1) Then the log likelihood function of spell j with duration dj is Hfj4jtCj) = Cj ln{pj4j) + l n ( ! - Pj,s) s=l = Cj ln(l - exp(-exp(adj + P'xj>dj))) - ^ exp(as + P'xjtS) (3.2) s=l where Cj is a dummy variable which is 1 for complete spells and 0 for censored spells. This paper extends the above discrete time PH model by adding a heaping effect measurement error component. By heaping effect, I mean the tendency of labour market spells to end at certain low frequencies (e.g. monthly) while the frequency of analysis is high (e.g. weekly). As an illustration, figure 3.6 shows the pres-ence of heaping effect in our pre-reform seasonal employment sample spells. The dashed vertical lines in the figure represent weeks that could possibly contain cal-endar month ending dates in the sample. As shown in the figure, weekly empirical hazards fluctuate a lot and the hazard spikes match well with the dashed vertical lines. Furthermore, it can be shown most of the spikes between the vertical lines co-incide with weeks that have day 15 of calendar months of the period covered. These are our visual evidence of heaping effect. The irregular and frequent spikes of empirical hazard rates have been a common Chapter 3. Contingent, Temporary UI and Employment/Unemployment Cycles 47 feature in labour market duration data5. Here, to accommodate the vagueness of the observed spell ending, I use an idea similar to that used for relating a discrete time PH model with a continuous time PH model mentioned earlier. First, the calendar property of a spell j could be captured by 3 overlapping week subsets, {Hj, Hj, Hj}, where H® contains every week in spell j, Hj only has semi-monthly weeks, and Hj only has monthly weeks6. Figure 3.7 gives an example of such subsets of weeks. Define function h(t, Hlj) so that it gives the latest week in Hl- prior to week t. In particular, h(t, #j) = max{s|s < t, s e Hlj} (3.3) Let probabilities of reporting at each of the three frequencies (weekly, semi-monthly, and monthly) be {ao, a\,a2}, where {ao,ai,a2} 6 [0,1] and E;e{o,i,2} a ' = 1. Then the likelihood of spell j with heaping considered could be written as a weighted sum of the likelihood of this spell in each of the three frequencies, I f° f1 f2 \ X J j,dj ,Cj ' J j,dj ,Cji J j,dj ,Cj J ' '€{0,1,2} 5Baker (1992) refereed to such observation as digit preference, where he found respondents tend to "report the length of their current unemployment spell as an integer multiple of one month". To deal with digit preference, he used a formula to backup the underlying, smooth distribution of unemployment spells of Current Population Survey. Limited by data, his formula has to be abstract from variations of individual spells' calendar properties. Specifically, his formula assume every spell's week 4, 8, 12, etc, correspond to "integer multiple of one month", while not all calendar months have exactly 4 weeks in reality. Here, my formulation takes care of that calendar variations across spells as well as recognizes that not every spell starts at week 1 of a month. Torelli and Trivellato (1993) has raised similar concerns on the hazard spikes. The application of their method is substantially limited as they only gave formula for complete spells when it is common to have both complete and censored spells in duration data. 6Semi-monthly weeks are defined as those contain day 15 or last day of a month, while monthly weeks are defined as those contain last day of a month. Obviously, Vj , H? C Hj C H°. Chapter 3. Contingent, Temporary Ul and Employment/Unemployment Cycles 48 Finally, the likelihood with heaping at frequency I, fljidjtCj, is related to likelihood without heaping fj,djtcj a s follows f l = < J3,dj,Cj ^ 0 if dj £ H1- and Cj = 1 4M^j),o(l - ndsLh(djtHi)+ii1 ~ Pi,») if dj e H] and c3 = 1 (3-5) ^/j,min{Md,-+l,tfj),dj}>0 if Cj = 0 In other words, equation (3.5) says three things about observing spells at fre-quency i. first, it is impossible to observe spell-endings outside of the set of expected ending weeks, / / j ; second, ending at one of the expected ending weeks means the spell survived all observable intervals except the last one; third, observing an incomplete spell means it survived all observable intervals7. Although intuitive, the above heaping measurement model requires different like-lihood calculation for each individual spell depending on the set {Hj,Hj,H2} and whether the spell is complete or not. There are several ways to simplify this time-consuming procedure. First, we could derive each spell's calendar set {Hj,Hj,Hj} before running maximum likelihood estimation. Second, we could calculate the like-lihood of surviving till the last but one interval separately as a common component of all frequency specific likelihood. Finally, we could pre-program the mapping from phH and { / / J ^ 1 , / / * } to f'^.. There is an alternative nonparametric way to deal with the fluctuating hazard rates in the literature (Green and Sargent, 1998). That is to add time varying 7 H e r e , a l l under ly ing spells ' ending are pushed to their next heaping weeks. A more general setup would also al low the ending to be pushed to their previous heaping weeks. However, there is a prac t ica l difficulty i n such a general setup w i t h designating values for those t ime-varying variables at weeks when the observed spells have ended or have been censored. For example, w i t h no knowledge about the w o r k i n g hours in those weeks after the observed employment spells ended, i t becomes infeasible to impute the potential- E I benefit weeks associated w i t h those weeks. Chapter 3. Contingent, Temporary UI and Employment/Unemployment Cycles 49 dummy variable for end-of-month weeks on top of a non-parametric baseline. This alternative approach is both readily accessible and conceptually straightforward. But its ability to separately identify the baseline hazard and the coefficient for end-of-month dummy relies heavily on having rich variation across spells in their calendar properties89. It is.also worth-noting that, with heaping considered, the magnitude of the estimated coefficient for any UI time-varying dummy reflects the number of spell-endings at relevant intervals in all three frequencies (weekly, semi-monthly, and monthly); while without heaping consideration, that magnitude reflects endings only at weekly intervals. Finally, with heaping effect component taking care of the high frequency part of empirical hazards fluctuations, there is a weaker case for the 'expensive' non-parametric baseline specifications. That means parsimonious parametric baseline specifications become much sensible. Having tried polynomial of various orders as the baseline hazard trend, we choose to present our main results using a 2nd order polynomial and leave the results using 5th order polynomial for robustness check10. 3.4 Data The confidential SLID data is a recent Canadian micro panel data set. Currently, it has three panels: panel 1 for the years from 1993 to 1998, panel 2 for the years from 1995 to 2001, and the on-going panel 3 for the years from 1999 to 2002. Table 3.2 gives several basic sample counts of these panels. Like other survey data, SLID 8 t h a t is, the number of weeks/days i n each sequential month . A p p l i c a t i o n s of this nonparametr ic approach on our sample spells are not very satisfactory. T h e calendar spikes such as those shown i n figure 3.6 are absorbed most ly by baseline hazards. 1 0 I n s t e a d of direct p o l y n o m i a l to approximate the baseline, an ana ly t ica l ly equivalent approach, the Lagrang ian in terpola t ion p o l y n o m i a l me thod as discussed i n Cooper (1972), is used to mit igate the mul t ico l l inear i ty p rob lem i n numerica l computa t ion . Chapter 3. Contingent, Temporary UI and Employment/Unemployment Cycles 50 has a very rich set of demographical variables (e.g. age, gender, education). Besides these, S L I D also has detailed information about individuals ' job holdings (e.g. dates, wages, weekly working hours), making it possible to derive not only individuals employment/unemployment spells but a whole set of time-varying U I treatment variables according to the applicable UI legislation 1 1 . For the construction of employment/unemployment spells, S L I D does have a weekly labour force states variable readily available. Bu t its ' classification of the labour force states is not very useful for UI studies. For example, according to S L I D classification, self-employment is counted as employment. Bu t self-employment is not insurable employment according to UI . For another example, though individuals on temporary/seasonal layoff are regarded as employed in S L I D , they are eligible for UI benefit if they have enough preceding employment. To solve such discrepancies, the employment/unemployment sample spells used in this study are constructed from scratch based on job information. A s a result, it is worth-noting that the defin-itions for 'employment' and 'unemployment here do differ from textbook definitions considerably 1 2 : the 'employment spells'here are periods on paid jobs; 'unemployment spells' are periods in-between 'employment spells'. B y using these definitions, new entrants to the labour market, such as students who just graduate from universities, are excluded from our sample. Thus our study is mainly concerned wi th active paid n I t is of course better to use the exact, realized UI benefit collection durations than to use the derived ones whenever possible. But in general that kind of information is only available from administrative data sets, which usually have very limited information other than UI collections. Specifically, administrative data sets usually do not contain information on education, martial status, or individuals' labour market activities beyond benefit collection spells. 1 2 There is no search requirement imposed on the so-called "unemployment spells" as referred in this thesis. As a result, some might even find it more appealing to refer to these spells as non-employment spells. Chapter 3. Contingent, Temporary UI and Employment/Unemployment Cycles 51 labour market participants. In addition, with labour market spells custom-made, our estimation results should only be interpreted with our data construction procedure in mind. This is a special 'observation window' kind of procedure (see figure 3.8 for an illustration). It has three broad steps. First, raw employment/unemployment spells are created. Raw employment spells cover all the dates from the start to the end dates of paid jobs, except those on temporary layoffs. Since there is a two-week waiting period for UI benefit collection, two raw employment spells are merged with the intermediate dates added if they are separated by less than 14 days. After the raw employment spells are formed, those periods in-between are our raw unemployment spells. Next, obser-vation windows are created for each individual. These windows are periods of dates that we have no reason to believe a person is out of the labour force. In particu-lar, periods of schooling, disability, non-paid employment, outside the ten Canadian provinces, less than 20 or more than 50 years old are excluded from the entire set of dates of the panel period. In case of a problematic job ending, any dates afterward are also excluded13. Whatever dates left form the observation windows. For the two observation windows in figure 3.8, one possibility could be that the individual was attending school in the meanwhile. Finally, raw employment/unemployment spells and observation windows are considered jointly to establish the final sample spells. Only spells started within observation windows are selected. Furthermore, they would be cut at the end dates of their starting observation windows and flagged 1 3 H e r e , ' hav ing a problemat ic job ending ' refers to jobs whose endtyp9 variable is coded as 2 or 3, which means the job ended because of the job was denied by the respondent or because the survey d i d not receive informat ion about the job in subsequent collections. For these jobs, the per iod from the job end to the end of the panel is excluded from the corresponding ind iv idua l s ' observation window(s) . Chapter 3. Contingent, Temporary UI and Employment/Unemployment Cycles 52 as incomplete if they pass beyond those dates14. A key feature of the 'observation window' approach here is that it makes event-based sample spells selection rather than the usual person-based selection. As ta-ble 3.2 shows, less than half of the individuals would survive person-based selec-tion; that is, if we only select individuals who had no 'out of labour force' activities throughout their entire panel periods. Specifically, only 12,108 out 30,455 individuals have single panel-long observation windows in panel 1. In a longer panel, person-based selection could reduce the size of sample individuals even further. After all, being in the labour force is just one stage of the life cycle. By making the selection based on events, our 'event-based' approach mitigate panel data sets' sample size problem. From all the employment/unemployment spells created above, spells in two pe-riods are selected to represent pre- and post-reform sample spells. The pre-reform period is from July 4 1994 to December 31 1995. Here July 4 1994 is the day just after a previous major change in UI program. Although the EI reform's transition period started in mid 1996, December 31 1995 is chosen here to account for antic-ipation of the coming reform in early 1996. Since only panel 1 of SLID covers the pre-reform period, pre-reform sample spells naturally are those panel 1 spells started in this period. All spells are censored at June 30, 1996, if necessary. To match exactly the position and length of pre-reform period within the panel period of panel 1, the post-reform period is set from July 4, 1997 to December 31, 1998 and spells are chosen from panel 2 only. There are at least three considerations here. First, although panel 2 starts from January 1 1996, we need at least one year's 1 4 T h e jus t i f icat ion to exclude left-censored spells is based on concerns of dura t ion dependence wh ich means left-censored spells are expected to behave differently than fresh spells even after they have entered the observation windows. Chapter 3. Contingent, Temporary UI and Employment/Unemployment Cycles 53 labour market information to derive individuals' UI benefit weeks. Thus the earliest usable spells of panel 2 only start from January 1 1997. Second, since our pre-reform period starts in the middle of the year, it is also sensible to start our post-reform period at a similar time of the year to avoid seasonality differences. Finally, the third concern here is labour market sample spells' attrition over time due to the near absorption nature of employment states15: if we start with a sample of random individuals and observe them over time, more and more of them will be absorbed to stable long-term employment if they continue to stay on the labour market. As a result, the sample of individuals at the later part of each panel will not be random. Table 3.3 gives the unweighted sample distribution over the six panel years for each of the panel. The first part of this table shows the distribution of all spells, the second shows that of the seasonal ones, and the last one shows that of individual-wise first spells. A decreasing pattern is obvious across these three parts for all three panels. Moreover, the later a spell starts in the panel the more likely that individual has some earlier spells in the panel, that means, this individual is potentially more likely to be of a high turn over type in the labour market. Therefore, in order to have two sets of sample spells with comparable composition, the position and length of pre-,and post-reform periods within their respective panels are chosen to be the same. The final data issue here is the classification of seasonal and non-seasonal spells. As discussed earlier, we expect UI's impacts on seasonal and non-seasonal sectors to be different and our analysis study these two sectors separately. An option here 1 5 P r e v i o u s empi r ica l studies have examined sample a t t r i t ion in panel da ta set from another per-spective. V a n den B e r g and L i n d e b o o m (1998) tested the theoretical hypothesis that ind iv idua ls heterogeneous a t t i tude toward survey par t ic ipa t ion could make sample a t t r i t ion a potent ia l ly en-dogenous prob lem when s tudying labour market transit ions. B u t in the end, their results showed whether or not to take account of sample a t t r i t ion does not affect the results much. Chapter 3. Contingent, Temporary Ul and Employment/Unemployment Cycles 54 would be to define spells' seasonality according to characteristics of realized spell durations. But this will mean taking spell durations as exogenous and it will make our study of UI's impacts on the spell durations senseless. Therefore, I choose to define spells' seasonality using conditions at the start of each spell. Seasonal spells are defined according to job (or job absence) ending or job absence reasons of each spell's major job (assuming workers know whether their jobs would end for seasonal reason or not). For an employment spell, the major job is the longest job that started this employment spell. For an unemployment spell, the major job is the longest job among all jobs that ended the preceding employment spell. Specifically, a seasonal employment spell is one that started with a job ended (or job absence started) for seasonal reasons16; a seasonal unemployment spell is one that the preceding employment spell ended due to a job ended (or job absence started) for seasonal reasons. 3.5 Empirical Analysis Table 3.5 and 3.6 give the basic characteristics of the sample spells. Table 3.4 gives the empirical hazard rates of the sample spells. Here sample spells are divided into 8 groups according to their labour market states (unemployment/employment), seasonality (non-seasonal/seasonal), and periods (pre-/post-reform). In each case, the post-reform sample sizes are about 100 less than the pre-reform ones. The sample sizes of non-seasonal unemployment spells are about 2.5 times of those of seasonal unemployment spells; while the sample sizes of non-seasonal employment spells are 1 6 T h e approach here could be problemat ic for spells s tarted late in their panels. Because a l l spells on-going at the panel end wou ld be counted as non-seasonal. Fortunately, our sample periods are bo th three years pr ior to the end of panel and there should be l i t t le seasonal employment spells wh ich last more than 3 years continuously. Chapter 3. Contingent, Temporary Ul and Employment/Unemployment Cycles 55 at least 3 times of those of seasonal employment spells. Besides differences in sample sizes, non-seasonal and seasonal spells also differ in other dimensions. The seasonal spells have a higher proportion of married workers, male workers, non-immigrant workers and less educated workers. The average ages of workers with various seasonal spells are also slightly higher than those of workers with corresponding non-seasonal spells. Moreover, seasonality also interacts with the employment/unemployment spells' regional distributions. While non-seasonal employment/unemployment spells are more concentrated in Ontario and Quebec, seasonal employment/unemployment spells are more concentrated in Quebec and Atlantic provinces (that is, Newfoundland, Nova Scotia, New Brunswick, and Prince Edward Island). The last panel of table 3.5 gives the breakdown of reasons of unemployment and Ul coverage for unemployment spells. The first category is for those who left their preceding paid jobs voluntarily (such as family responsibility, or relocation). Accord-ing to the Canadian Ul rules, these workers are not eligible for Ul benefit coverage. So they have no Ul coverage for their 'unemployment' spells. The remaining four categories in this panel are for those who got unemployed involuntarily (such as firm shutdown or layoffs). As the table shows, the distributions across the five categories vary across the two periods and across non-seasonal and seasonal spells. For non-seasonal pre-reform unemployment spells, most (76%) unemployment spells are not qualified for Ul coverage from the beginning. Among the 76%, 34%, 37% and 5% are due to quit, permanent layoffs and temporary layoffs respectively. On the contrary, the majority (61%) of seasonal pre-reform unemployment spells are qualified for Ul coverage initially, with 4 1 % and 20% due to permanent layoffs and temporary layoffs Chapter 3. Contingent, Temporary UI and Employment/Unemployment Cycles 56 respectively17. For post-reform period, the basic pattern remains similar. In short, not only seasonal unemployment spells are more likely to be eligible for UI coverage initially relative to non-seasonal ones, these spells are also more likely to be due to temporary layoffs. Thus, before returning to their former employers in the near future, unemployed seasonal workers are more likely to wait, or 'enjoy leisure', rather than search for brand-new jobs. The critical" differences between seasonal and non-seasonal labour market turnovers are also evident in the figures of table 3.4. They present the basic patterns of hazard rates of seasonal and non-seasonal spells. Hazards for leaving unemployment and leaving employment in the seasonal sector are higher, more volatile than in the non-seasonal sector. In addition, the empirical hazard figures for the seasonal sector also show vague humps in the later half of the year, which are absent in figures for the non-seasonal sector. Having gone through the explorative analysis, I shall first explain the set of time-varying UI treatment dummy variables to be used before presenting the estimation results. This set of dummy variables, meant to catch the behavioural impacts of UI, is a quite special set of variables that have often been used in similar empirical studies (Green and Sargent, 1998). Unlike the usual case of time-constant variable, whose value remains the same for different weeks of a spell, the value of each time-varying variable is allowed to be different at different weeks of a spell. Accordingly, each 1 7Since seasonal unemployment spells are defined to be those due to layoffs of seasonal reasons. The proportion of seasonal unemployment spells due to quit is zero by construction. 1 8 One interesting difference is that there is a higher percentage of non-seasonal post-reform unemployment spells due to quitting than in the pre-reform ones. This change perhaps is due to improving macroeconomic situation. A simple story could be, as labour demand increases, workers are more likely to get better jobs, so more job separations are initiated by workers rather than firms. Chapter 3. Contingent, Temporary UI and Employment/Unemployment Cycles 57 time-varying variable of each spell takes a vector of values while each time-constant variable of each spell takes only a single value. Earlier on in the introduction section, an example of such time-varying variable is given. Here table 3.1 gives the full list of time-varying UI treatment dummy variables and their definitions. Here, the time-varying UI treatment dummy variables defined for unemployment spells are all related to the benefit exhaustion week (BEW) except the last one. For week t of an unemployment spell which has initially UI coverage of T weeks, there is max{T — t, 0} weeks of benefit left. Based on max{T — t, 0}, a group of dummy variables (BEW21+, BEWU-2o, BEW6.W, BEW2-5, BEWU BEWQ) is then created with thresholds of {20,10,6,1, 0}. As an example, suppose person i's unemployment spell j is covered for 30 weeks of UI benefit, then we have, (BEW2i+)ij = { 1 , 1 , 1 , 1 , 1 , 1 , 1 , 1 , 1 , 1 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , . . . , 0 } {BEWU-m)ij = { 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 1 , 1 , 1 , 1 , 1 , 1 , 1 , 1 , 1 , 1 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , . . . , 0} (BEW6.w)ij = { 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 1 , 1 , 1 , 1 , 1 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , . . . , 0} (BEW2-i)ij = { 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 1 , 1 , 1 , 1 , 0 , 0 , 0 , . . . , 0} (BEW^j = {0, 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 1 , 0 , 0 , . . . , 0} (BEW0)ij = { 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 1 , 0 , . . . , 0} The threshold weeks are set to be closer and closer as they approach the benefit exhaustion week. This is mainly motivated by theoretical predictions that the haz-ard rate of Ul-covered unemployed workers is increasing at an increasing rate prior to benefit exhaustion (figure 3.5). Depending on the number of initial UI benefit coverage weeks, these B£W-related time-varying variables would differ. The last UI variable WK19 is set to 1 for the 19th week of post-reform seasonal unemployment spells with initial UI coverage. It is mainly to recognize potential tailoring effect in Chapter 3. Contingent, Temporary Ul and Employment/Unemployment Cycles 58 the seasonal industry due to the experience rating rules . The estimated coefficients of hazard model from unemployment spells are given in table 3.7. To interpret, a coefficient J3 here means the hazard rate is proportionally increased by exp(/3). Thus, a negative coefficient means the conditional probability of reemployment is lower. In each estimation, pre- and post-reform sample spells are pooled together. The identification of Ul impacts here is thus from both within- and across-period Ul treatment differences. Given the setup of Canadian Ul program, the within-period Ul treatment differences are mainly due to variations of individuals' local unemployment rate movement across region and over time as well as their potentially endogenous employment history20, while the across-period Ul treatment variation should be exogenous. The estimated coefficients for B E W 2 1 + to BEW0 suggest that the more remaining Ul benefit weeks an unemployed worker has, the less likely his unemployment spell will end. In particular, for the non-seasonal spells, the coefficients increase from —1.51(s.e. 0.17) when there are at least 21 weeks of benefit to — 0.54(s.e. 0.34) when the worker just exhausted all his benefit. Seasonal workers are also shown to be responding to the experience rating rules by increasing their reemployment process just prior to the threshold week, week 20. In particular, the estimated coefficient for WK19 is shown to be 0.61(s.e. 0.29). The top two figures of table 3.9 illustrate the impact of temporary Ul benefit 1 9 O f course, these t ime-varying Ul t reatment variables are set to zeroes throughout for a l l un-employment spells w i t h no in i t i a l Ul coverage. 2 0 Jus t a caut ionary note, since a d u m m y for post-reform is inc luded i n the model , the identifica-t ion of the coefficient of unemployment rate is ma in ly based on w i t h i n per iod variat ions. Since bo th pre- and post-reform sample periods are only 18 months long. It is p robably more sensible to i n -terpret the coefficients of unemployment rate as shot-run impacts of loca l labour market condit ions on employment /unemployment cycles. Chapter 3. Contingent, Temporary Ul and Employment/Unemployment Cycles 59 coverage on unemployment hazard based on coefficients from table 3.721. Specifically, here I assume the worker has 28 weeks of Ul benefit coverage. Based on this, the solid lines give the hazard rates for him to leave unemployment at each of the first 50 weeks of being unemployed. As comparison, the dashed lines give his hazard rates in case of no Ul benefit exhaustion effects. The impacts illustrated here are very much consistent with theoretical predictions, especially for the non-seasonal part: with less and less weeks of Ul benefit left, the worker's hazard rate becomes closer and closer to the baseline rate. It is worth noting that there is an obvious difference in baseline hazard trend between non-seasonal and seasonal unemployment spells as shown in the figures. Non-seasonal unemployment spells' hazard is downward sloping, which means the longer a worker is unemployed, the less likely for him to get reemployed (i.e. neg-atively duration dependency). This finding is very similar to what was found in previous studies in this literature (such as Ham and Rea (1987)). On the other hand, seasonal unemployment spells' hazard is upward sloping, or positive duration dependent. An explanation for this could be based on the notion of 'seasonal', where workers are expected to end their unemployment spells within a year. Again, we find evidence suggesting important difference in the nature of labour market transitions between non-seasonal and seasonal sectors. The definitions of time-varying Ul treatment dummy variables used for employ-ment spells is in the second panel of table 3.1. In particular, the first four of them (HMIN6-W, HMIN2-5, HMINlt HMIN0) are defined relative to individuals' min-imum employment weeks (HMIN), also known as entrance requirement week. As discussed earlier, workers' benefit weeks increase up to a limit even beyond HMIN, 2 1 A l t h o u g h WK19 is included i n the es t imat ion for post-reform seasonal unemployment spells, the figure presented does not consider it as the focus here is not on the impacts of the E I reform. Chapter 3. Contingent, Temporary Ul and Employment/Unemployment Cycles 60 two additional Ul variables [HMINQ + 1 to HMAX0, HMIN0 + 1 to HYRMAXQ) are used here for non-seasonal and seasonal employment spells respectively to catch any possible tendency for workers to respond to the incentive of additional benefit weeks with extra employment weeks. The last two Ul related time-varying variables listed in the table are for post-reform seasonal employment spells only. They are meant to catch the impacts of divisor rule and experience rating rules introduced by the 1996 EI reform22. Depending on individuals working hours each week and on-going local unemployment rate, HMIN is recalculated in each week for each employment spells. So are HMAX, HYRMAX, HDIV. The estimated coefficients of hazard model from employment spells are given in table 3.8. The signs of the Ul-related coefficients for both non-seasonal and seasonal spells are all consistent with theoretical predictions except for HMIN2-5 for non-seasonal spells. Though theoretically this should be negative, it's coefficient is vaguely estimated to be slightly positive (0.06(s.e. 0.11)). In addition, most of the coefficients for seasonal spells are statistically significant while none of the coefficients for non-seasonal spells are statistically significant. To further appreciate the estimation results, the bottom two figures of table 3.9 illustrate the impact of Ul on employment hazard using coefficients from table 3.8. Here HMIN, HMAX and HYRMAX are set at 14, 40, 24 weeks respectively. The left figure for non-seasonal, spells shows that Ul incentives only have minimal impacts on the distribution of non-seasonal employment spells, while the right figure shows Ul has significant impacts on that of seasonal employment spells. The closer seasonal workers are to the minimum employment week HMIN, the stronger their 2 2 T h e r e are l i t t le impacts of these rules on non-seasonal spells based on al ternative estimations. Therefore, the discussion here focuses on tests that only consider divisor rule and experience ra t ing rules on seasonal employment /unemployment spells only. Chapter 3. Contingent, Temporary UI and Employment/Unemployment Cycles 61 tendency to postpone job-separation. Even after HMIN, these workers still tend to postpone job-separation before they accumulate enough benefit weeks for the rest of the year. Finally, table 3.10 summarizes the heaping probabilities estimated in our pre-ferred specifications. The numbers suggest heaping is indeed significant in our data. About 20% unemployment spells and 30% employment spells are "reported" in monthly terms, while the numbers drop to 10% and 20% for the semi-monthly cases. Overall, survey respondents get more precise about the dates of their reemployment than about the dates of their job separation. Given the weekly precision that our identification of UI impacts requires, vagueness of our data spells as measured here does indicate the importance to take account of it. 3.5.1 Robustness check Three sets of maximum likelihood estimation results are discussed here to as robust-ness checks of the preceding results23. First, we check how our results are affected by pooling spells of two periods together. In particular, our question is, if researchers only have pre- or post-reform period sample spells but not both, how would the esti-mation results differ from those based on pooled sample spells. Actually the two sets of estimation results suggest very similar UI impacts. In particular, the estimation results using the two periods of spells separately are illustrated as figures in table 3.11. These figures suggest both pre- and post-reform, non-seasonal and seasonal unemployment spells show considerable benefit exhaustion effect: the solid lines are much lower than their corresponding dashed lines before BEW in the relevant fig-ures. There are also considerable entrance effects found using both pre- and post-reform seasonal employments: the solid lines are much lower than the corresponding 2 3 M o r e specifications are tested but omi t t ed here. T h e y provide very s imi lar informat ion. Chapter 3. Contingent, Temporary UI and Employment/Unemployment Cycles 62 dashed lines prior to HMIN in the relevant figures. On a closer examination, a few things do surface from comparing figures based on separate period estimations and pooled periods estimations. The basic shapes of the baseline hazards for both seasonal employment and unemployment spells are different in pre- and post-reform figures. For seasonal unemployment spells, the baseline hazard is upward sloping in the pre-reform figure while close to flat in post-reform figure. It suggests, before the reform, most unemployed seasonal workers would get reemployed within a year and their chances of reemployment increase dramatically as their unemployment continues. It also suggests, after the reform, the flow of • unemployed seasonal workers back to employment is of relatively constant speed and there is no dramatic absorption of unemployed seasonal workers into employment state at the later period of the year-long time horizon. For seasonal employment spells, the inverse U shape of the baseline hazard as shown in the pre-reform figure becomes considerably flatter in the post-reform figure. This means ending of seasonal workers' employment spells is less concentrated in the middle part of a year-long time-horizon in the post-reform period. Together, the differences in the baseline hazards between estimates based on seasonal employment and unemployment spells suggest some critical change in the nature of seasonal labour market. This labour market seems to be making a movement away from cycling between employment and unemployment states annually. In short, seasonal labour market becomes less seasonal after the reform. Next, we check the sensitivity of our results to our model specification. As the top four figures of table 3.12 shows, the estimated UI impacts are not affected much if we assume no heaping effect. The bottom four figures of table 3.12 illustrate the estimated UI impacts when 5th order polynomials are used as our baseline hazard. Comparing this set of figures with our preferred set, it is easy to see with a more Chapter 3. Contingent, Temporary Ul and Employment/Unemployment Cycles 63 flexible setup, the baseline hazards at the end of the year are estimated to be declining instead of increasing as our preferred estimates suggest. Although it seems more intuitive to have a downward sloping hazard at the'later half of the year, given the much smaller sample sizes available at the later of the year, the estimation for this period is generally very imprecise. Finally, we check how our preferred estimation results are affected by considering individuals' unobserved heterogeneity. By that, I mean individuals' inherent ten-dency of labour market attachment. An important weakness of single spell hazard model often mentioned in the literature is it's lack of power to distinguish individu-als' unobserved heterogeneity from 'true' duration dependence of the baseline hazard rate (Heckman, 1991). Among others, Van den Berg (2000) and Lancaster (1990) both recommend multi-spell hazard models to tackle this problem. Intuitively, the advantage of multi-spell hazard models to single spell models is similar to that, of panel regressions to cross sectional regressions. By using multi-spell hazard model, researchers hope to know (implicitly) individuals' type (strong or weak labour mar-ket attachers) and use that information to adjust the composition of unobserved individual quality at different weeks of each type of spells. In the context of duration analysis, Lancaster (1990) argues that ignoring un-observed heterogeneity could lead to spurious negative duration dependency of the estimated baseline hazard. This is because it is more likely to have workers who consistently have long spells to have long spells. For example, in the case of unem-ployment spells, the later the week, the higher the proportion of individuals with consistently longer unemployment spells. Without considering the fact that these in-dividuals have longer unemployment spells repeatedly, the estimated baseline hazard rate will be biased down for later weeks. Or in other words, we would come to the wrong conclusion that the later the week in an unemployment spell, the harder for a Chapter 3. Contingent, Temporary UI and Employment/Unemployment Cycles 64 typical individual to get reemployed (i.e. negative duration dependence). Therefore, the slope of the baseline hazard estimated from multi-spell hazard model is expected to be higher than that of the baseline hazard from single spell model. If the impacts of these unobserved person-specific factors are important, then single-spell hazard models will produce un-reliable evidence. For our purpose, it is important to know whether our estimated UI impacts based on single spell hazard model are biased as a result of the potential existence of unobserved heterogeneity. To extend the previous single spell hazard model with heaping effect to the case of multi-spell multi-state, let {£1,62} be a random vector of standard joint normal distribution N(0,I). Without loss of generosity, we can rewrite equation (3.1) as follows to incorporate the unobserved heterogeneity, for an employment spell 9ejtt = exp(a« + (Fxis + a l i i e i ) (3.6) for an unemployment spell 9lt = e x p K + f3u'xjtt + a^er + a2,2e2) (3.7) Let the corresponding likelihood function of an employment and unemployment spell be fe and / e respectively. Then the likelihood function for individual i is, Since F() is the CDF for standard joint normal distribution, it is straightforward to use the method of Gaussian quadrature for numerical integration. The construc-tion here is quite similar to studies such as Ffedeker, Siddiqui, and Hu (2000) and Carneiro, Hansen, and Heckman (2003)24. 2 4 A often used alternative in the l i terature is to follow H e c k m a n and Singer (1984) and use Chapter 3. Contingent, Temporary Ul and Employment/Unemployment Cycles 65 Table 3.14 gives the estimated results using pooled pre- and post-reform non-seasonal spells25. Only non-seasonal spells are used here. That is both because we have more sample individuals in the non-seasonal sector and because the kind of unobserved heterogeneities that we are concerned about is mainly relevant in the non-seasonal sector. Our earlier evidence shows the length of seasonal workers' em-ployment/unemployment durations are heavily affected by the cycle of four seasons. The inherent seasonality makes the heterogeneity story less applicable. We are not expecting the relative length of these durations to be very informative for individuals' future durations. Table 3.14 shows that, overall, there are no dramatic differences between the multi-spell multi-state estimation results and the corresponding single spell estima-tion results as shown in table 3.7 and 3.8. Figures in table 3.13 also looks similar as their single-spell estimation counterparts. The similarity of the two sets of estimation results is comforting in the sense that for most researchers it is more cost-effective to use single spell hazard models than multi-spell multi-state hazard models. But on the other hand, table 3.14 suggests that unobserved heterogeneity is statistically significant for both employment and unemployment spells in our case. The coeffi-cient for ei in the employment spell part is 0.75 with s.e. 0.11; while the coefficient for e2 in the unemployment spell part is 0.65 with s.e. 0.10. non-parametr ic specification of the heterogeneity part . B u t as results of Bake r and M e l i n o (2000) indicates, the non-parametr ic approach could be sensitive i n certain cases i n their Mon te Ca r lo studies. 2 5 A s a prac t ica l note, to reach a reasonable d i s t r ibu t ion of the unobserved heterogeneity vector, I u t i l i zed an intermediate step rather than set a rb i t rary s tar t ing values of the covariance mat r ix . Specifically, I first est imated the mul t i -spel l mult i-state hazard mode l wi thou t U l variables, the result of which is presented pa r t ly i n table 4.4. T h e n , using that set of est imated coefficients as s tar t ing values, I est imated the model w i t h U l variables added. Chapter 3. Contingent, Temporary Ul and Employment/Unemployment Cycles 66 Also quite interesting is the change in the coefficients for Ul related variables in the unemployment spell part. Intuitively, we would imagine the estimated coeffi-cient for a dummy variable will increase if the average unobserved heterogeneity of the group of individuals covered by the dummy is negative; decrease if the average unobserved heterogeneity is positive. For unemployment spells, it means if a group of individuals tend to experience longer unemployment spells repeatedly, then the estimated coefficient of the dummy for this group will increase after unobserved het-erogeneity is considered. Applying such logic, a comparison between table 3.14 and 3.7 suggest that on average, individuals that on layoffs (both temporary and perma-nent) with initial Ul coverage tend to have long unemployment spells repeatedly. 3.5.2 P o l i c y impl ica t ions To examine policy implications, the distributions of average workers' employment/ unemployment spells are simulated under three scenarios: no Ul, with pre-reform Ul program, and with post-reform Ul program. All of these three simulations use post-reform sample spells and coefficients from single spell hazard model estimations using pooled samples (table 3.7 and 3.8). The simulated distributions are based on the average values for both time-constant variables and time-varying variables in each scenario. For pre-reform scenario, each spells Ul treatment variables are calculated based on pre-reform Ul rules; for post-reform scenario, post-reform Ul rules. For no Ul scenario, all Ul treatment variables are simply set to zeroes. Considering various economic and social impacts of the Ul program, the setup of no Ul scenario here could only be regarded as an extremely simplistic one. Its role here is merely to serve as a transparent benchmark to summarize the estimation results. The study here is not designed to evaluate policy changes as dramatic as to abandon Ul completely. Chapter 3. Contingent, Temporary UI and Employment/Unemployment Cycles 67 Therefore, results of the no UI scenario should only be treated cautiously. The simulated distributions are presented by figures in table 3.15. In each figure, the long dashed line corresponds to pre-reform UI treatment and short dashed line for post-reform UI treatment. In addition, to illustrate the impacts of experience rating rules and divisor rule, the corresponding coefficients are turned on for seasonal spells in the post-reform scenario. First, assuming all other things remain stable, the impacts of the EI reform as a result of changes in individuals' UI treatment are captured by the differences across long dashed lines and short dashed lines. As the figures show, in the non-seasonal sector, the pre- and post-reform curves overlap each other very well. Therefore, although it might be that the EI reform leads to various changes in individuals' UI treatment, our results suggest that the impacts of these changes might very well cancel out on average. In the two seasonal figures, the main differences between the dashed lines are due to the new experience-rating and the divisor rules introduced by the EI reform. Comparatively, the new experience-rating rules seem to have substantial impacts on the distribution of employment spells in the seasonal sector, while the divisor rule only have very transitory impacts. If we ignore those two rules, the two pairs of pre- and post- curves would overlap each other just as in the non-seasonal cases. Overall, the figures suggest the EI reform (except for the two sets of rules men-tioned above) did not affect much the UI treatment that workers received on average. But on the other hand, the experience rules and the divisor rule do have substantial impacts. Specifically, our results suggest these new rules are quite effective in en-couraging longer employment spells and shorter unemployment spells in the seasonal sector. Next, using the simulated distributions, we could study how workers' behavioural Chapter 3. Contingent, Temporary Ul and Employment/Unemployment Cycles 68 response to Ul incentives affects employment/ unemployment distributions. That is, the impacts of having Ul program versus no Ul program (or more precisely, the case where all other things remain the same except that workers no longer respond to Ul incentives). For the non-seasonal sector, the figures suggest Ul has little impact on the distribution of employment spells and relatively linear impact on the distribution of unemployment spells — there are less unemployment spells with shorter durations. For the seasonal sector, the figures suggest the distributions of both unemployment and employment spells are significantly affected by Ul: there are less short spells and more spells in the 20 to 35 week range in both employment and unemployment cases. Finally, it is interesting to understand our results' implications at the aggregate level. Using simulation results discussed above and assuming hazard rates for all weeks beyond 50 are the same as those at week 50, the upper panel of table 3.16 presents the estimated average durations under each of the three scenarios. The lower panel of it then gives the corresponding unemployment rates. Table 3.16 suggests Ul program increased the unemployment rate in the non-seasonal and seasonal sector by 15% and 18% respectively pre-reform, and 12% and 10% post-reform. If we assume a third of the labour force is in the seasonal sector, just as what our sample spells roughly show, then the overall impacts of Ul program on unemployment rate is 16% pre-reform and 11% post-reform. That means if the on-going unemployment rate with Ul is 7.6% and if suddenly workers are no longer responding to Ul incentives (as is loosely defined as the no Ul case), the unemployment rate would drop to 6.4% pre-reform and 6.8% post-reform. There are several reasons to consider the above 11% and 16% increases in un-employment rate to be an upper bound of the true values. First of all, this study defines unemployment and employment differently from the LFS does. Only paid Chapter 3. Contingent, Temporary UI and Employment/Unemployment Cycles 69 employment is considered in this study. Although some out of labour force peri-ods are excluded in the data used here, there is no searching requirement in the definition of unemployment here. Moreover, individuals who have no fresh employ-ment/unemployment spells are excluded from our sample. Many of these individuals could be those with very stable employment. 3.6 Conclusion This empirical work is related to the bigger question of income support program's labour market consequences.. It extends the literature by using a common data source and common econometric setups when investigating UI's impacts on both directions of employment/unemployment cycles. This study also pays attention to the different nature of seasonal and non-seasonal labour market by studying them separately. Most importantly, this study utilizes UI treatment variations due to the EI reform as an unique exogenous source of variation. The results confirm both findings of previous studies about UI's impacts on em-ployment (Baker and Rea, 1998; Green and Riddell, 1997) and those about UI's impacts on unemployment spells (Ham and Rea, 1987; Meyer, 1990; Moffitt, 1985). In particular, the empirical results presented above show, both non-seasonal and seasonal workers' reemployment probabilities are pushed down when they still have some UI benefit coverage left; and, seasonal workers' probabilities of employment separation are also pushed down before their entrance requirement weeks. More than just confirming previous findings in a new context where exogenous variation due to the EI reform is used, the results here also reveal new findings about the impacts of the EI reform and the aggregate impacts of UI. In particular, the results show, Chapter 3. Contingent, Temporary UI and Employment/Unemployment Cycles 70 (1) there is a decline in the seasonality of seasonal sector's employment/unemployment cycles after the reform due to the introduction of experience rating rules and divisor rule; (2) the EI reform (except for the experience rating rules and divisor rule) did not affected much the average UI treatment that workers received; and (3) UI program could have increased the overall unemployment rate by 16% pre-reform and 11% post-reform. In other words, if all workers suddenly switch from responding to UI incentives as estimated to ignoring those incentives, and all other things remain constant, the unemployment rate could drop from 7.6% to 6.4% pre-reform and 6.8% post-reform. Broad interpretations of our estimation results should take into account several choices made here. First, our sample spells are constructed using an event-based selection procedure; second, the definitions for 'employment' and 'unemployment' here are adapted to UI legislation; and last, the usual discrete-time hazard model is extended by a heaping effect component here. Interpretations of the results here also need to be clear about some limitations of the research. In particular, both seasonality and wages are taken as exogenous here. It would be interesting to explore how the size and composition of seasonal sector is affected by UI parameters. Knowing these, we could then have better understanding about the overall aggregate impacts of UI. Also since all the em-ployment/unemployment cycles should be coupled with wage or reservation wage dynamics, it would be interesting to know how robust our results would be if wages are endogenized. Chapter 3. Contingent, Temporary Ul and Employment/Unemployment Cycles 71 3.7 Tables and Figures Figure 3.1: Canadian Seasonally Adjusted Month ly Unemployment Rate 16 | : ; 1 1 1 j 15 [ 14 6 I . . . . . . . . J I I i I i . . I ^ 0 0 0 0 ( N ' d - v O O O O ( N T ) - ^ D O O O r S l ' ^ - ^ 0 r ~ - r ^ o o o o o o o o o o o > O N O \ O N O N O O O O C ^ O S O N O N O N ^ O N C ^ C > > O N O N C 3 N O O O O Year Note: A and B refer to pre- and post-reform periods respectively. Source: Statistics Canada C A N S I M I I table V2062815 Chapter 3. Contingent, Temporary Ul and Employment/Unemployment Cycles 72 Figure 3.2: Illustration of a Time-varying Variable 10 15 20 25 30 35 40 45 50 week 10 15 20 25 30 week 35 40 45 50 Note: Here the first time-varying dummy variable takes value 1 from week 20 to week 29 and value 0 for all other weeks; and the second one takes value 1 from week 5 to 14. In our study, both of these two variables could be capturing periods when the worker only has 11 to 20 weeks of Ul benefit left. Only in the first case, there are 40 weeks of initial Ul coverage, while in the second case, there are only 25 weeks of initial Ul coverage. Chapter 3. Contingent, Temporary UI and Employment/Unemployment Cycles 73 b: effective for seasonal Workers 36 o i • . . 1 . — i — . . . 1 0 5 10 15 20 25 30 35 40 45 50 weeks of employment Chapter 3. Contingent, Temporary Ul and Employment/Unemployment Cycles 74 Figure 3.4: Total Income a: actual 0 5 10 15 20 25 30 35 40 45 50 weeks of employment b: effective for seasonal workers 0 5 10 15 20 25 30 35 40 45 50 weeks of employment Note: Total income = wage income + U l benefit. Chapter 3. Contingent, Temporary UI and Employment/Unemployment Cycles 75 Figure 3.5: Predicted Hazard Rates with Contingent Temporary UI Coverage a: employment spells 14 12 10 W 13 8 T3 6 4 2 0 HMTWn i \ HMTWn !. E l EO \ i 5 10 15 20 25 30 35 40 45 50 weeks 14 12 10 13 8 T3 b: unemployment spells U l 10 15 20 25 30 35 40 45 50 weeks Chapter 3. Contingent, Temporary UI and Employment/Unemployment Cycles 76 Figure 3.6: Illustration of Empirical Hazard Heaping Note: There are 18 months in which spells could start in this case, from 1 July 1994 to 1 December 1995. Let there be 18 spells started on the first day of each of these 18 months. The set of dashed vertical lines in this figure covers all weeks that could possibly contain the last day of a month in these 18 spells. The thickness of these dashed lines is set to be proportional to the heaping possibilities. Chapter 3. Contingent, Temporary Ul and Employment/Unemployment Cycles 7 7 Figure 3 . 7 : A n Example of Week Sets by Calendar Properties H j 2 observable under monthly frequency IB • • H • a s H j 1 observable under semi-monthly frequency H H S Q E H B H • • • H El E Hj° observable under weekly frequency 10 15 20 25 . 30 week 35 40 45 50 Figure 3 . 8 : Illustration of Sample Spells Construction raw spells observation windows i i I = processed spells i complete spells nru employment spells l—1> censored spells — unemployment spells Chapter 3. Contingent, Temporary UI and Employment/Unemployment Cycles 7 8 Table 3.1: Definitions of Time-varying UI Treatment Dummy Variables variable def ini t ion for u n e m p l o y m e n t spells BEW21+ BEWn-m BEW6-10 BEW2-6 BEWi BEW0 WK19 when there are at least 21 weeks to the benefit exhaus t ion week (BEW) when there are 11 to 20 weeks to BEW when there are 6 to 10 weeks to BEW when there are 2 to 5 weeks to BEW when there is on ly 1 week to BEW the week of reaching BEW week 19 (just before experience r a t ing th reshold week) for employment spells HMINe-W HMIN2-5 HMIN! HMINQ HMIN0+1 to HMAXQ HMIN0+l to HYRMAXQ HMINQ+1 to HDIV HMIN0+1 to HEXP 6 to 10 weeks before m i n i m u m employment weeks (HMIN, also k n o w n as entrance requirement week) 2 to 5 weeks before HMIN 1 week before HMIN week of reaching HMIN after HMIN a n d t i l l week of achieving m a x i m u m benefit coverage (HMAX) after HMIN and t i l l week of achieving enough benefit coverage for the next j o b season (HYRMAX) after HMIN and t i l l the calendar week of HMIN + 2 (HDIV) after HMIN and t i l l the calendar week of 31 (HEXP) Chapter 3. Contingent, Temporary Ul and Employment/Unemployment Cycles 79 Table 3.2: Sample Description: Part 1. Unweighted Sample Counts p a n e l 1 2 3 t i m e p e r i o d covered 1993-1998 1996-2001 1 9 9 9 - 2 0 0 2 ° Individual-wise t o t a l w i t h obse rva t i on w i n d o w s w i t h a s ingle p a n e l - l o n g o b s e r v a t i o n w i n d o w 30,455 23,840 12,108 31,459 23,973 10,534 32,922 24,368 12,094 Spell-wise j obs p a i d j obs p a i d j o b e m p l o y m e n t spel ls t o t a l e m p l o y m e n t spel ls 44,550 39,055 41,596 32,880 50,599 44,013 46,092 34,816 39,095 34,212 35,287 27,358 spells started within observation windows e m p l o y m e n t i n t e r - e m p l o y m e n t / u n e m p l o y m e n t 8,784 10,133 6,835 7,664 4,119 4,840 ° T h e 3rd panel of S L I D is s t i l l on-going. Chapter 3. Contingent, Temporary UI and Employment/Unemployment Cycles 80 Table 3.3: Sample Description: Part 2. Within-Observation-Window Spells' Unweighted Distribution across Panel Years panel t ime pe r iod covered 1993-1998 1996-2001 1999-2002 e u e u e u t o t a l (as 100%) 10,133 8,784 7,664 6,835 ^4,840 4,119 panel year 1 19% 20% 2 1 % 22% 30% 3 1 % 2 20% 18% 20% 2 1 % 23% 23% 3 16% 18% 19% 18% 23% 24% 4 15% 16% 16% 14% 24% 23% 5 15% 14% 12% 10% ' - • -6 15% 15% 13% 13% - -to ta l seasonal(as 100%) 2,529 2,634 1,535 1,656 692 803 panel year 34% 1 24% 22% 22% 22% 33% 2 18% 18% 23% 22% 25% 2 1 % 3 16% 17% 2 1 % 2 1 % 23% 23% 4 14% 15% 16% 16% 20% 2 1 % 5 ' 14% 14% 9% 9% - -6 13% 14% 8% 10% - -t o t a l first spells ind iv idua l -wise (as 100%) 5,166 4,502 4,293 3,923 3,304 2,772 panel year 1 33% 34% 33% 35% 40% 4 1 % 2 23% 20% 20% 22% 2 1 % 22% 3 12% 15% 16% 15% 19% 20% 4 11% 11% 11% 10% 19% 17% 5 10% 10% 9% 8% - -6 11% 10% 11% 11% - -Note: e and u refer to employment and interemployment/unemployment spells re-spectively. Chapter 3. Contingent^ Temporary Ul and Employment/Unemployment Cycles 81 Table 3 .4 : Empirical Hazard Rates pre-reform post-reform Non-seasonal, unemployment spells 0 5 10 15 20 25 30 35 40 45 50 0 5 10 15 20 25 30 35 40 45 50 Seasonal, unemployment spells 0 5 10 15 20 25 30 35 40 45 50 0 5 10 15 20 25 30 35 40 45 50 Non-seasonal, employment spells 0 5 10 15 20 25 30 35 40 45 50 0 5 10 15 20 25 30 35 40 45 50 Seasonal, employment spells 0 5 10 15 20 25 30 35 40 45 50 0 5 10 . 15 20 25 30 35 40 45 50 Chapter 3. Contingent, Temporary Ul and Employment/Unemployment Cycles 82 Table 3.5: Summary Statistics of Unemployment Spells N o n - s e a s o n a l Seasona l p r e - E I p o s t - E I p r e - E I p o s t - E I s a m p l e size 1,649 1,458 793 613 weighted means s ingle (%) 37 37 35 34 female (%) 47 48 33 30 i m m i g r a n t ( % ) 14 12 8 9 age 34.8 35.9 36.0 36.4 l o g h o u r l y wage of los t j o b 2.4 2.4 2.4 2.4 i n i t i a l u n e m p l o y m e n t ra te 6.3 5.6 7.1 6.7 highest level of education(%) less t h a n h i g h schoo l 23 19 44 32 h i g h s c h o o l 30 34 23 36 pos t - s econda ry 34 35 24 27 u n i v e r s i t y or above 13 11 9 6 Region(%) O n t a r i o 26 32 20 22 A t l a n t i c 12 12 26 24 Q u e b e c 34 27 29 32 P a r i e r 17 17 13 10 B C 12 12 12 12 Reason of unemployment and Ul coverage(%) q u i t [so, no U l ] 34 41 0 0 p e r m a n e n t layoff, no U l 37 31 30 26 p e r m a n e n t layoff, w i t h U l 18 17 41 41 t e m p o r a r y layoff, no U l 5 6 9 14 t e m p o r a r y layoff, w i t h U l 6 5 20 19 Chapter 3. Contingent, Temporary Ul and Employment/Unemployment Cycles 83 Table 3.6: Summary Statistics of Employment Spells N o n - seasonal Seasona l p r e - E I p o s t - E I p r e - E I p o s t - E I s a m p l e size 1,725 1,613 547 435 w e i g h t e d m e a n s s ingle (%) 40 41 33 37 female (%) 51 53 40 34 i m m i g r a n t (%) 13 14 8 10 age 34.1 34.6 36.4 37.2 log h o u r l y wage of i n i t i a l j o b 2.3 2.4 2.4 2.5 i n i t i a l u n e m p l o y m e n t ra te 6.2 5.5 6.4 5.9 highest level of education(%) less t h a n h i g h s c h o o l 21 17 41 30 h i g h s c h o o l 30 33 25 36 pos t - s econda ry 36 36 25 28 u n i v e r s i t y or above 13 14 9 5 Region(%) O n t a r i o 31 32 21 23 A t l a n t i c 11 12 25 25 Q u e b e c 30 27 26 29 P a r i e r 16 17 13 11 B C 11 13 16 12 Chapter 3. Contingent, Temporary UI and Employment/Unemployment Cycles 84 Table 3.7: M a x i m u m Likelihood Estimates Using Pooled Pre-/Post-Reform Unemployment Spells non-seasonal seasonal sample size 3107 1406 post reform In of hourly wage unemployment rate 0.19 (0 .05)* - 0 . 0 0 (0.06) 0.02 (0.01) 0.29 (0 .07)* 0.20 0.09 $ - 0 . 0 6 (0 .02)* quit [so, no UI] permanent layoff, no U I permanent layoff, with U I (omitted group) temporary layoff, no U I temporary layoff, with U I - 1 . 8 6 (0 .17)* - 1 . 9 8 (0 .17)* - 0 . 3 7 ( 0 . 1 9 ) i 0.88 (0 .11)* - 2 . 1 3 (0 .14)* - 0 . 4 7 (0 .16)* 0.74 (0 .09)* time-varying UI treatment variables BEW21+ BEWn-20 BEW6.1Q BEW2-5 BEW! BEWQ WK19 - 1 . 5 1 (0 .17)* - 1 . 6 1 (0 .18)* - 1 . 2 1 (0 .22)* - 0 . 9 1 (0 .24)* - 1 . 2 4 0 .45)* - 0 . 5 4 (0.34) - 1 . 1 2 (0 .16)* - 1 . 2 0 (0 .15)* - 0 . 8 6 (0 .17)* - 0 . 6 6 0 .18)* - 0 . 3 3 0.33) 0.08 (0.30) 0.61 (0.29)1 Note: other control variables include gender, education dummies and regional dummies age, marit ial status, immigration status, Table 3.8: M a x i m u m Likelihood Estimates Using Pooled Pre-/Post-Reform Employment Spells non-seasonal seasonal sample size 3338 982 post reform In of hourly wage . unemployment rate - 0 . 1 8 (0.05)* - 0 . 1 9 0.07)* 0.03 (0.02)$ - 0 . 1 9 (0.10)t - 0 . 8 6 0.10 * - 0 . 0 5 (0.02)$ time-varying UI treatment variables HMIN6-W HMIN2_5 HMIN! HMINQ HMINQ + 1 to HMAXQ HMINo + 1 to HYRMAX0 HMIN0 + 1 to HDIV HMINo + 1 to HEXP - 0 . 1 4 (0.09) 0.06 0.11) - 0 . 0 8 0.25 - 0 . 1 2 0.24) - 0 . 0 7 (0.11) - 0 . 2 5 (0.14)t - 0 . 5 3 0.15)* - 0 . 4 5 0.27)f - 0 . 9 2 (0.37)1 - 0 . 2 3 (0 .12) | - 0 . 1 7 0.21) - 0 . 2 2 (0.15) Note: other control variables include gender, age, marit ial status, immigration status, education dummies and regional dummies Chapter 3. Contingent, Temporary Ul and Employment/Unemployment Cycles 8 5 Table 3 .9 : Illustration of UI's Impacts on Hazard Rates: Based on Estimations Using Pooled Pre-/Post-Reform Spells Chapter 3. Contingent, Temporary Ul and Employment/Unemployment Cycles 86 Table 3.10: Estimated Heaping probabilities u n e m p l o y m e n t e m p l o y e d p r o b a b i l i t y of re- non-seasona l seasonal non- -seasonal seasonal p o r t i n .. fre-q u e n c y s e m i - m o n t h l y 0.10 ( 0 . 0 2 ) * 0.10 (0 .03)* 0.16 (0 .03)* 0.20 (0 .03)* m o n t h l y 0.19 ( 0 . 0 2 ) * 0.18 ( 0 . 0 2 ) * 0.28 ( 0 . 0 2 ) * 0.30 ( 0 . 0 3 ) * Note: these estimates correspond to the maximum likelihood estimations of table 3.7 and 3.8. Chapter 3. Contingent, Temporary Ul and Employment/Unemployment Cycles 8 7 Table 3.11: Illustration of UI's Impacts on Hazard Rates: Based on Estimations Using Pre- and Post-reform Spells Separately non-seasonal seasonal pre-reform unemployment spells 32 r H i m; 0 5 10 15 20 25 30 35 40 45 50 0 5 10 15 20 25 30 35 40 45 50 pre-reform employment spells si / % 1—E; f Q-i SI >-Ml K 0 5 10 15 20 25 30 35 40 45 50 0 5 10 15 20 25 30 35 40 45 50 post-reform unemployment spells 32 r 0 5 10 15 20 25 30 35 40 45 50 0 5 10 15 20 25 30 35 40 45 50 post-reform employment spells 0 5 10 15 20 25 30 35 40 45 50 10 15 20 25 30 35 40 45 50 Chapter 3. Contingent, Temporary Ul and Employment/Unemployment Cycles 88 Table 3.12: Illustration of UI's Impacts on Hazard Rates: Based on Alternative Estimations Using Pooled Pre-/Post-Reform Spells non-seasonal seasonal unemployment spells, no heapin 0 5 10 15 20 25 30 35 40 45 50 0 5 10 15 20 25 30 35 40 45 50 employment spells, no heaping X! 0 5 10 15 20 25 30 35 40 45 50 0 5 10 15 20 25 30 35 40 45 50 unemployment spells, w i t h 5 th order po lynomia l s as baseline specif icat ion 0 5 10 15 20 25 30 35 40 45 50 0 5 10 15 20 25 30 35 40 45 50 employment spells, w i t h 5 th order po lynomia l s as baseline specif icat ion 0 5 10 15 20 25 30 35 40 45 50 0 5 10 15 20 25 30 35 40 45 50 Chapter 3. Contingent, Temporary Ul and Employment/Unemployment Cycles 89 Table 3.13: Illustration of UI's Impacts on Hazard Rates: Based on Estimation Using Pooled Pre/Post-Reform Non-Seasonal Spells with Unobserved Heterogeneity Considered Chapter 3. Contingent, Temporary UI and Employment/Unemployment Cycles 9 0 Table 3.14: Maximum Likelihood Estimates Using Pooled Pre-/Post-Reform Non-Seasonal Spells with Unobserved Heterogeneity Considered employment unemployment hazards hazards 0.75 ( 0 .11)* 0.02 ( 0.10) 0.65 ( 0 .10)* post r e f o r m - 0 . 1 8 ( 0 .06)* 0.23 ( 0 .06)* log of h o u r l y wage - 0 . 2 3 ( 0 .08)* - 0 . 0 2 ( 0.07) u n e m p l o y m e n t rate 0.03 ( 0.02)1 0.01 ( 0.02) time-varying UI treatment variables for employment spells HMINQ-W - 0 . 1 5 ( 0.10) — HMIN2-5 0.05 0.12) — HMIN - 0 . 1 0 ( 0.26) — HMINQ - 0 . 1 5 ( 0.10) — HMINo + 1 to HMAXo - 0 . 0 9 ( 0.11) — q u i t [so no UI] — - 2 . 0 6 ( 0 .20)* p e r m a n e n t layoff, n o U I — - 2 . 2 4 ( 0 .20)* t e m p o r a r y layoff, n o U I — - 0 . 4 1 0.22 f t e m p o r a r y layoff, w i t h U I — 1.05 ( 0 . 1 4 ) * time-varying UI treatment variables for unemployment spells BEW2i+ — - 1 . 7 9 ( 0 .20)* BEWn-20 — - 1 . 7 9 ( 0.20 * BEW6-10 — - 1 . 3 4 ( 0 .23)* BEW2-5 — - 1 . 0 2 ( 0 .25)* BEW! — - 1 . 3 3 ( 0 .45)* BEWo — - 0 . 6 3 ( 0 .37) f Note: the sample consists of 3796 individuals and the mean loglikelihood is -3.870. Other control variables included are gender, age, maritial status, immigration status, education dummies and regional dummies. Chapter 3. Contingent, Temporary Ul and Employment/Unemployment Cycles 91 Table 3.15: Simulated Density Functions non-seasona l seasonal unemployment spells 10 15 20 25 30 35 40 45 50 5 10 15 20 25 30 35 40 45 50 employment spells 10 15 20 25 30 35 40 45 50 10 15 20 25 30 35 40 45 50 Note: All of the simulations are based on average characteristics of post-reform spells and estimated coefficients using single spell hazard model. Solid line refers to case of no Ul treatment effect (setting the coefficients of Ul-related variables to zeros); long dashed line refers to Ul treatment according to post-reform rules; short dashed line refers to Ul treatment according to pre-reform rules. Chapter 3. Contingent, Temporary Ul and Employment/Unemployment Cycles 92 Table 3.16: Summary Statistics from Simulations no U l p re - re fo rm U l rules p o s t - r e fo rm U l rules average d u r a t i o n (weeks) non-seasona l u n e m p l o y m e n t spel ls 23.2 28.5 28.3 non-seasona l e m p l o y m e n t spel ls 116.8 124.2 121.2 seasonal u n e m p l o y m e n t spel ls 12.3 18.2 17.8 seasonal e m p l o y m e n t spel ls 30.0 34.9 37.9 u n e m p l o y m e n t ra te(%) non-seasona l sector 16.5 19.1 18.5 seasonal sector 29.1 34.3 31.9 o v e r a l l ( a s s u m i n g 1/3 of 20.7 24.1 23.0 the p o p u l a t i o n i n the sea-s o n a l sector) Note: All of the simulations are based on average characteristics of post-reform spells and estimated coefficients using single spell hazard model. 93 C h a p t e r 4 T e m p o r a r y U l C o v e r a g e ' s T i m e - v a r y i n g I m p a c t s o n R e e m p l o y m e n t W a g e s 4.1 Introduction A key rationale for Ul is its potential to improve job match qualities. It is a claim seen in most job search theories. There, the common logic is that workers would be able to have higher reservation wages thus better job matches with Ul subsidized searches. If it is indeed true, Ul could be beneficial in the long run, especially when there is active technology upgrading. It could then encourage individuals' to acquire new skills that are demanded by emerging, better paid but often unstable jobs. But as a matter of fact, in spite of the theoretical importance of the claim, whether or not Ul coverage actually improves unemployed workers' job match qualities is still an unsettled question empirically. Although some studies find UI's impact on reemployment wages to be positive, others find none (Addison and Blackburn, 2000; Burgess and Kingston, 1976; Classen, 1977; Ehrenberg and Oaxaca, 1976; Holen, 1977). One major problem with previous research is the lack of control for the endoge-nous correlation between unemployment durations and reemployment wages, which Chapter 4. Temporary UI's Time-varying Impacts on Reemployment Wages 94 should be two outcome variables of one single optimality strategy1. Theoretically, Ul-covered workers should have longer unemployment durations and higher reem-ployment wages at the same time. Besides, there is another important issue ignored previously: the possibility of Ul to have time-varying impacts on reemployment wages. Previous studies only differentiate unemployment spells according to ini-tial Ul benefit coverage. The timing of reemployment relative to benefit exhaustion weeks has not been considered. Theoretically, unemployed workers' reservation wage is closely related to the number of weeks of remaining benefit. The purpose of this study is thus to re-examine UI's impacts on reemployment wages with considerations of both the endogeneity of employment/unemployment cycles and the possibility of UI's impacts to be time-varying. The empirical study here uses the same data and historic event as the pre-ceding chapter. Specifically, this work uses a recent Canadian panel data set, the Survey of Labour and Income Dynamics (SLID) to examine sample employ-ment/unemployment spells in periods both before and after the Employment Insur-ance (EI) reform in 19962. There are both advantages and disadvantages in using Canadian data to study Ul effects relative to using U.S. data. In the U.S., variations of individuals' Ul benefit durations mainly exist at the state level, which lead to serious identification problem between state-fixed effects and Ul effects. While in x I t is wor th no t ing that most theoretical models make predict ions about U l in terms of hazard rates and reservation wages, not i n terms of reemployment wages. T h e reservation wage is indi rec t ly related to the realized reemployment wage through the d i s t r ibu t ion of wage offers—only those offers above the reservation wage could possibly be the realized reemployment wage. Lower reservation wage should cause higher unemployment hazard rates and a lower threshold of reemployment wages. T h e magni tude of U I ' s impacts c r i t i ca l ly depends on the shape of offering wages and posi t ion of s tar t ing reservation wages. B u t i n any case, the expected coincidence of UI ' s impacts on hazard rates and reemployment wages should be emphasized i n this s tudys identif icat ion of UI ' s impacts . 2 Please refer to chapter 2 for details about this reform. Chapter 4. Temporary UI's Time-varying Impacts on Reemployment Wages 95 Canada, the built-in dependency of UI benefit durations on preceding employment histories creates rich but very likely endogenous variations in individuals' UI benefit durations. In this sense, the identification of this study is strengthened by the usage of exogenous variation of UI benefit durations due to the EI reform. The main empirical analysis here is based on a full information maximum like-lihood model which endogenizes individuals' employment/unemployment durations, their wages at the start of each continuous sample period, and their reemployment wages. The two duration parts of the model inherit the hazard model with heaping effects used in the previous chapter. The wage parts of the model assume the wage distribution to be lognormal. Together, the four parts are linked through a vector of heterogeneity terms using a person-specific random effect setup. The preferred set of estimation result confirms that workers reemployed with remaining UI benefit coverage do have higher reemployment wage. Specifically, the wages would be 12% to 14% higher if a worker reemployed with at least 11 weeks of benefit left. On average, UI coverage increases Ul-covered workers' reemployment wages by about 9.5%. Furthermore, the evidence here shows there is a coincidence of reemployment wage decreases and unemployment hazard increases as workers approaching benefit exhaustion, which makes the evidence here even stronger in terms of supporting the job search subsidy role of UI. Besides, comparisons among estimation results of different specifications also suggest several important correlations in the micro labour market. In particular, we find longer employment durations and shorter unemployment durations are corre-lated mainly with persistent higher wages but not temporary wage shocks. We also find workers who get reemployed at precisely their benefit exhaustion weeks are also a group with persistently higher wages. The rest of this chapter is organized as follows: section 2 reviews theoretical Chapter 4. Temporary UI's Time-varying Impacts on Reemployment Wages 96 predictions on UI's impacts on reemployment wage; section 3 reviews the literature; section 4 discuss the data as well as some exploratory results; section 5 setups the econometric model and discusses the identification issues; section 6 discusses the main set of estimation results; and finally, section 7 concludes. 4.2 Theoretical Model By construction, UI has no impacts on wages in the standard textbook model of labour and leisure choice. There, individuals take wage rates as given and only make choices regarding time allocation. Instead, this study is motivated by the model of endogenous employment/unemployment cycles and contingent, temporary UI benefit explored in chapter 2. Figure 4.1 shows how the predicted pattern of unemployed workers' reservation wage looks like given the temporary UI benefit coverage. As the figure shows, during the period before exhausting all benefits, U l , the worker's reservation wage drops at an increasing rate. In the period after benefit exhaustion, UO, the workers reservation wage stays at a low level. The intuition of the dynamics of reservation wage here is that workers get to balance the cost of waiting one more period with the benefit of getting another draw of job offers at each period. At the benefit exhaustion period, the cost of waiting suddenly becomes higher, thus it is better for him to set reservation wage lower. For any period before exhaustion, the further away from the exhaustion period, the possibility of him having to actually wait till that period of exhaustion and the impact of benefit exhaustion on his reservation wage will be lower. Chapter 4. Temporary UI's Time-varying Impacts on Reemployment Wages 97 4.3 Literature Despite its importancy, there is only a small and quite old literature examining UI's impacts on reemployment wages. Most of the studies were done in late 1970s (Burgess and Kingston, 1976; Classen, 1977; Ehrenberg and Oaxaca, 1976; Holen, 1977), except for one recent study (Addison and Blackburn, 2000). All earlier studies use linear regressions. Due to data availability and variations in research questions, they differ in their measurement of Ul coverage and post-unemployment earnings, as well as their sample selection schemes. Burgess and Kingston (1976) use administrative data of a sample of workers from an experimental Ul service program (Service-to-Claimants Project) in the U.S. in late 1970s and find significant positive impacts of Ul on earnings in the one-year period post unemployment: a $1 rise of weekly benefit payment is estimated to increase post-unemployment earnings by $25; 1 additional week of potential benefit coverage is estimated to increase post-unemployment earnings by $69. Ehrenberg and Oaxaca (1976) use survey data (National Longitudinal Survey) and find it is mostly among older male job-changers that replacement ratio, i.e. the ratio of weekly Ul benefits to pre unemployment weekly wage, increase the post versus pre-unemployment wage ratio: a 0.1 increase of the replacement ratio is estimated to increase the wage ratio by 7%. Classen (1977) use administrative data (Continuous Wage and Benefit History File) and find weekly Ul benefit payment does not significantly affect the best-quarterly earnings in the post-unemployment year. Holen (1977) also use the ad-ministrative data from Service-to-Claimants Project and find an increase of $90 in the average quarterly earnings for the number of quarters with reported earnings post-unemployment for each $10 weekly Ul benefit. Chapter 4. Temporary UI's Time-varying Impacts on Reemployment Wages 98 Though the literature in the late 1970s is relatively small, serious questions and doubts are raised. Welch (1977) criticizes these studies on the ground of censoring biases, sample selection biases, simultaneity, etc. But more generally, it questions the validity of the results of these studies considering the tight connections between UI treatment, past earnings and post-employment earnings. The conclusion of Welch (1977) is that, "we have only very tentative evidence of post-wage effects and much remains to be done on this issue." The single recent study, Addison and Blackburn (2000), tries to settle the issue using a recent survey data (the Displaced Worker Surveys). Their measure of reem-ployment success is the log of the ratio of weekly earning at survey time over that of the lost job. Using linear regressions, they couldn't find much support for UI to improve post-unemployment wages either. In summary, the previous literature is relatively small; there are serious concerns about their data, approach; the results of different studies seem inconclusive. But, the sensitivity of the empirical results to sample selection and measurement choices at least eliminate the possibility of a strong, persistent and universal impact of UI coverage to reemployment wages. While at the same time, it makes one wonder whether it will be more productive to search for temporary impacts of UI, or for substantial impacts of UI among subgroups of workers. Contrary to the difficulty encountered among studies of UI's impacts on reem-ployment wages, studies of UI's impacts on unemployment durations have been quite successful in finding the predicted impacts of UI. This later literature find hazard for leaving unemployment increases as workers approach their benefit exhaustion weeks (Meyer, 1990). Furthermore, related literature also find hazard for leaving employment decreases as workers approach their minimum employment requirement weeks (Baker and Rea, 1998; Green and Riddell, 1997). In a new setting, which is Chapter 4. Temporary UI's Time-varying Impacts on Reemployment Wages 99 very similar as the current study, the study of the previous chapter confirms both of the these two findings, which then makes one wonder about the possibility of UI's impacts on reemployment wages to be time-varying as well. 4.4 Data and Exploratory Analysis This study inherits much of the data used in the study of the preceding chapter. To summarize, the data is in the form of sample employment/unemployment spells. These spells are constructed from a Canadian micro panel data set, the confidential version of SLID. The data construction is custom designed for our Ul studies. In particular, the 'employment spells' used here refer to periods of working on paid jobs; the 'unemployment spells' refer to periods in-between those 'employment spells'. Not in the paid labour market periods are excluded using an event-based 'observation window' approach, rather than the usual individual-based approach on the panel data. The final sample allows both multiple spells for each individual as well as incom-plete (right-censored) spells. The spells come from two periods of two panels: the pre-reform ones from panel l's 1994 July to 1995 December spells and the post re-form ones from panel 2s 1997 July to 1998 December spells. The set of time-varying Ul treatment dummy variables are exactly the same as in previous study, derived using SLID's information on individuals' job dates, weekly working hours as well as Ul unemployment rates and the applicable rules of Canadian Ul programs (please check table 3.1 for their definitions). The key dependent variable here, the wage, refers to the job-specific hourly wage at the end of relevant year. For employment spells, the hourly wage for the job started the spell is used, same as for the employment wages; for unemployment Chapter 4. Temporary UI's Time-varying Impacts on Reemployment Wages 100 spells, the hourly wage for the lost job is used; for reemployment wages, the hourly wage for the reemployment job is used. Table 4.1 gives linear regression results relating reemployment wages to UI in-centives using three different specifications. The samples used here are pooled pre-/post-reform reemployment wages of non-seasonal workers who either quit or are permanently laid-off and who got reemployed within 52 weeks without intermittent out of paid labour market activities. The estimated coefficients for Ul-related variables in column (1) of table 4.1 show the impact of UI benefit coverage on reemployment wages is very sensitive to the timing of reemployment relative to benefit exhaustion week. Reemployment wages of individuals who got re-employed with at least 11 weeks of benefit left are statisti-cally higher than those of individuals who got re-employed after benefit exhaustion. Specifically, earlier reemployment corresponds to about 20% (= exp(0.18)) higher wages. Within the group of individuals with initial UI benefit coverage, reemploy-ment wage is in general negatively correlative with remaining benefit weeks, with one salient exception: reemployment wages of those re-employed at the week of benefit exhaustion weeks are much higher than the trend would predict; they are indeed similar to those re-employed with at least 11 weeks of remaining benefit. One possible explanation of this exception could be the tailoring behaviour of some workers who prearrange the reemployment timing to take full advantage of their individual UI coverage. On the other hand, reemployment wages of workers without initial UI coverage at all are very similar to those of workers with UI coverage but re-employed with at least 11 weeks of remaining UI benefit. Overall, the estima-tion result confirms the theoretical prediction about the downward sloping of UI's impacts on reemployment wage as workers get closer to benefit exhaustion. To be comparable to previous literature, linear regression results of two additional Chapter 4. Temporary UI's Time-varying Impacts on Reemployment Wages 101 specifications are presented in table 4.1 as well. The differences are whether hourly-wage at preceding jobs and/or length of unemployment spells are included as control variables. Whether or not to include preceding wage in the regression really depends on the implicit assumptions about the wage dynamics econometrically. By excluding preceding wage from the control variable set, it is assumed that reemployment wages for an unemployed worker is a totally fresh redraw from the wage distribution once the observables, such as, gender, age, education, have been considered. On the other hand, including preceding wage allows the possibility of persistent wage differentials even after controlling for observables, The choice of whether or not to include log unemployment durations in the re-gression relates to both identification issues and theoretical assumptions. Generally speaking, the two outcomes of individuals' unemployment experiences, unemploy-ment durations and reemployment wages, are jointly determined. Therefore, un-employment duration is not an exogenous variable in the linear regression. The regression would suffer from the common endogeneity problem if unemployment du-ration is included in the control variables set and not instrumented. On the other hand, as workers stay unemployed longer, they will also get closer to benefit exhaus-tion week, mechanically. That means ignoring unemployment durations could lead to spurious Ul benefit exhaustion effect if there is truly just a downward trend of reservation wage. This dilemma will be solved later as both unemployment durations and reemployment wages are endogenized. The estimated regression coefficients when preceding wages and/or unemploy-ment durations are included are presented in column (2) and (3) of table 4.1, The results show the nature of the estimated coefficients on Ul-related variables remains very similar in this sample, although overall the inclusion of preceding wages seems Chapter 4. Temporary UI's Time-varying Impacts on Reemployment Wages 102 to lead to weaker impacts of Ul on reemployment wages. The differences here sug-gest that our earlier linear regression result in column (1) could have exaggerated UI's impacts on reemployment wages because of the endogeneity of unemployment durations and its correlation with individual-specific wage differentials. Finally, column (4) of table 4.1 gives the linear regression result when we assume quitters were eligible for UL Although the assumption is false in reality, the exercise here is to explore whether there is indeed a particular time pattern of reemployment wages due to Ul coverage. As the results suggest, reemployment wages of quitters, who thus are not eligible for Ul, do vaguely decline over time. The quitters who would otherwise have at least 11 weeks of remaining Ul benefit do not get higher wages than quitters who would have otherwise exhausted their benefits, which is strikingly different from the pattern found from laid-off workers. 4.5 Econometric Setup and Identification Issues For a more formal examination of the issue, a full information maximum likeli-hood model is used. Specifically, let individual i have N? employment spells, A f " unemployment spells, Nfw employment wages at the beginning of continuous em-ployment/unemployment periods, and N^w reemployment wages are chosen using the same set of requirements as in the linear regressions. Then, the four parts of the likelihood of person i are: {//}J=I,...,JV? for employment spells; {fk}k=i,...,N^ f ° r unem-ployment spells; {fi w}i=i,...,Nfw for initial employment wages; and, {f^}m=i,...,Niiw for reemployment wages. The overall likelihood function for this person is set as the product of all of the four parts, Chapter 4. Temporary UI's Time-varying Impacts on Reemployment Wages 103 / \lIf;I[Kl[fiWt[fZ0\ dF(^e2,e3) (4.1) Jelte2,e3 y j = l fe=1 , = 1 m = 1 J The first two parts here take account of employment/unemployment spells. The third initial employment wage part, /f™, controls for initial condition problem using the correlation between individuals' tendency of frequent labour market turnovers and wages. This is because our sample is not random. It only has individuals who started new employment or unemployment spells3. Together, individuals labour market activities are captured by the first three parts of the likelihood function. The fourth part for reemployment wage is then added to study the impacts of UI on reemployment wages. The four parts of likelihood function are connected through a person-specific random effect setup. Let { / L i e , u.u, Ltew, pLuw} be the extra term of each of these four parts in the model. Let { e i , e 2 , e 3 } be a 3-dimension random vector ~ N(0,1). Then, 3 Ano the r possible solut ion to deal w i t h in i t i a l condi t ion p rob lem i n s imi lar s i tuat ions is to al low a to ta l ly different employment dura t ion component for ind iv idua l s ' first spells. T h i s al ternative theoret ical ly should p lay s imi lar role as inc lud ing in i t i a l employment wages as done in this study, but i t w i l l cost a substant ial sample size i n this study. Ano the r p rac t ica l advantage of using employment wages is that it w i l l al low es t imat ion of the correlat ion ma t r i x of the unobserved heterogeneities in employment /unemployment durat ions and wages, wh ich could be then used to p in down the unobserved part of reemployment wages. Chapter 4. . Temporary UI's Time-varying Impacts on Reemployment Wages 104 (4.2) H = a i > 2 e i + a 2 ] 2 e 2 (4.3) ew = ai,3<u + a 2 , 3 e 2 + 03,3^3 (4.4) — a l , 4 e l + a 2 , 4 e 2 + a 3 , 4 e 3 (4.5) There is no extra dimension of randomness added for the last part of reem-ployment here. This is because the role of having {//, u,u, fiew} in this model is to capture the across-individual differences in employment stability, reemployment speed, as well as persistent wage differentials, in other words, the endogenous corre-lation between labour market transitions and wage dynamics. This is different from the role of the LIUW, which is present mainly because we need to control for unob-served heterogeneity while examining UI's impacts on reemployment wages. Since reemployment wages of unemployment spells should be employment wages of the fol-lowing employment spells, there are no particular interests and reason to entertain extra randomness in reemployment wages. Figure 4.2 gives an example.This worker only has one period of continuous em-ployment/unemployment cycles. Thus he has only one initial employment wage part in his overall likelihood function (/f™). This specific cycle starts with an em-ployment spell, ends with a second employment spell, and has one unemployment spell in-between. Thus he has three duration parts in his overall likelihood func-tion (/f, / " , / ! ) . Suppose his unemployment spell isn't due to temporary layoff and it lasted less than 50 weeks, then he would also have a reemployment wage part in his likelihood function (fiw). Overall, his likelihood function should be (fe' fu ' fe' few ' fuw) Chapter 4. Temporary UI's Time-varying Impacts on Reemployment Wages 105 The exact functional form for the employment and unemployment spells' parts is the discrete-time proportional hazard model with heaping effect as in the previous chapter. Specifically, let d be the duration of a spell; c be 1 if this spell is complete and 0 if not; a; be a vector of (potentially time-varying) control variable for this spell; \i be the individual and state-specific heterogeneity term of this spell; H° be the set of all weeks covered by this spell; Hj be the set of all semi-monthly weeks covered by this spell; and, H2 be the set of monthly weeks covered by this spell. Let d\ £ [0,1] be the probability of spells to heap at semi-monthly frequency; a2 € [0,1] be the probability of spells to heap at monthly frequency. Set ao = 1 — a\ — a2 € [0,1]. Let Q i , . . . , a 5o be the baseline hazard rates for week 1 to 50, which are transformed from 2-nd order polynomial; (3 the coefficient vector for control variable vector x, then the likelihood of this spell, is defined as follows, f(d,c,x,H°,Hl,H2,iJ,\a1)a2,aQ,a,j3) = ^ «(•/'(•) '£{0,1,2} (4.6) where nS f f V -p s ) ( i -nVi i1 -?-) ) nzni {h(d+l' Hl),d}(i-Ps(-)) if d £ Hl and c = 1 iideH1 and c = (4.7) if c = 0 and Chapter 4. Temporary UI's Time-varying Impacts on Reemployment Wages 106 ps(-) = l-ex.p(-ex.p(aa + Pxa + fj)) . (4.8) h{t, Hl) = max{t'|t' < t, t' e H1} (4.9) The exact functional form for the two wage parts, few and fuw, is based on lognormal distribution of wages with an individual-specific heterogeneity term for the given type of wage. That is, f[w = <£(ln(initial employment wage;) - pr°xf° - / /™6 e w ) , \/l e [1, N$L}\0) / r = 0(ln(reemployment wage j - 0™x™ - fj,uw, 5UW), Vm e [1, N^.ll) 1 v2 where, <f>(v, 5) = J-J= exp(- —) Since our model use person-specific random effect, the identification and control-ling of the unobserved heterogeneity relies on the composition of our sample. Out of the 3,796 individuals in our sample, the largest 4 categories of individuals in terms of number of each of the four possible types of events selected in the final sample are listed in table 4.2. The biggest group, 29%, is composed of those who have one valid employment spell and one valid initial employment wage information only; the second one, 18%, is composed of those with one unemployment spell only. Overall many individuals of our sample do have more than one type of events, which helps us to identify the correlation between heterogeneity terms of different parts. Fur-thermore, table 4.3 shows the total number of incidence in each of the four types of events and the proportion of no repetitions in each type. Table 4.3 shows the total number of incidence in each of the four types of events and the proportion of no repetitions in each type. It is shown that many of the sample individuals do have Chapter 4. Temporary UI's Time-varying Impacts on Reemployment Wages 107 multiple observations of any one of the four parts, which helps us to identify the variance of heterogeneity terms of each part of the likelihood. Besides functional form, the empirical identification of the four individual com-ponents of the model, {fwe,fe,fu,fwu}, also relies on the differences in the sets of control variables between duration parts and wage parts, i.e., exclusion restric-tions. The exclusion restrictions used in this study relate to using unemployment rates at different time in the duration parts and the wage parts: both fe and fu use on-going regional unemployment rate to proxy for local macro level labour market condition; while few and fuw use initial regional unemployment rate at the start of corresponding spell. The implicit assumptions here are: 1) both employment sep-aration and reemployment processes depends only on on-going unemployment rate once their initial conditions have been taken care of by the wage parts; 2) wages at the start of an employment spell depend only on the unemployment rate at that time; 3) reemployment wages potentially only depends on the unemployment rate as the unemployment spell start once the whole dynamics of unemployment rate have been taken into account of within the preceding employment and unemployment spells and initial employment wages components. If any of these assumptions are not valid, then the model proposed here will not be appropriate. Obviously, the above assumptions deviate from a standard spot market model of the labour market. Nonetheless, the idea here does share some of the features of the costless mobility contract model as argued by Beaudry and DiNardo (1991). Beaudry and DiNardo (1991) empirically shows that there is strong correlation between the wage we observe at a point of time and the best labour market condition since the job matches. Furthermore, they show such correlation is much stronger than the wage's correlation with the labour market condition at the job start or the on-going period. Although, they use annual national measures of the labour market, while Chapter 4. Temporary UI's Time-varying Impacts on Reemployment Wages 108 this study uses weekly regional unemployment rate, there is still reason to favor on-going rather than initial unemployment rate for the duration parts of our model given their strong results. In the future, it would be interesting to know whether other measures of unemployment rate or the change of unemployment rates is more powerful in explaining workers' employment/unemployment transitions. 4.6 Estimation Results The exploration of estimation results here is based on examination and comparison of a set of results, starting from the simplest setups. We first explore the differences on the estimation of duration parts of the model due to endogenization of wages. This is done by comparing two sets of estimated coefficients with no consideration of UI for a moment. Based on the template model, table 4.4 corresponds to a specification with the two duration parts only, and table 4.5 corresponds to another specification with both the two duration parts and the two wage parts. Comparison of the tables shows, besides coefficients on heterogeneity terms, the coefficients on log hourly wages are affected the most when the wage parts are added. In the employment duration part, the coefficient of log hourly wage increases from —0.22 (s.e. 0.08) when wages parts are omitted in table 4.4 to 0.03 (s.e. 0.13) when wage parts are added in table 4.5. At the same time, the positive coefficient for t\ in the employment hazards part drops significantly from 0.83 (s.e. 0.10) to 0.21 (s.e. 0.05) while the coefficient for t\ in the initial wages part is estimated to be significantly negative (—0.21 with s.e. 0.07). By adding the wage parts, we are effectively controlling for persistent wage differentials across individuals in the hazard parts. As a result, only transitory shocks of wages are used to identify the coefficient of wage in the duration parts. Therefore, the first estimated coefficient (—0.22) Chapter 4. Temporary UFs Time-varying Impacts on Reemployment Wages 109 corresponds to the joint impacts of persistent wage differentials and transitory wage shocks on the hazard of leaving employment, while the second one (0.03) corresponds to the impact of transitory wage shocks only. The differences of the estimated coefficient on wages and the major change in the coefficient on t\ thus suggests hazard of leaving employment is affected little by transitory wage shocks, rather it is correlated negatively with persistent higher wages. In other words, employment stability correlates mainly with individuals' persistent wage differentials; transitory wage shocks have little impact on it. Loosely speaking, the result here argues against the causal linkage from a temporary higher wage to a longer employment spell; instead, it argues for a stable correlation over time between higher wages and stable employment. Similarly, as to unemployment durations, the change of coefficient on log hourly wages for the preceding jobs from 0.15 (s.e. 0.08) in table 4.4 to 0.01 (s.e. 0.03) in table 4.5 indicates shorter unemployment duration correlates mainly with persistently higher wages and transitory wage shocks have little impact on it. As for short term impacts due to business cycle, the coefficients of unemployment rate in table 4.5 shows the most significant impact of unemployment volatility is on individuals' hazard of leaving employment, rather than individuals' hazard of leaving unemployment or their wages. Considering the empirical context here, it seems that a first sign of improvement/recovery of the economy is a slowdown of the entry to unemployment. On the other hand, the coefficients for reform flags suggest the long term impacts of business cycle are obvious in all of the three dimensions of labour market studied here: economic recovery in Canada in the late 1990s leads to significantly longer employment spells, significantly shorter unemployment spells and higher wages. Next, in table 4.6, Ul-related variables are added to the duration parts of the Chapter 4. Temporary UI's Time-varying Impacts on Reemployment Wages 110 specification of table 4.5. Comparing estimates of table 4.6 with table 4.5, we find one salient change in the estimation results due to adding UI variables in the duration parts— the coefficient on log hourly wage for unemployment duration part drops from 0.01 (s.e. 0.03) to —0.19 (s.e. 0.05). Using similar logic as before, this change indicates workers with positive wage shocks tend to be in the UTgroups where the corresponding coefficients are higher, such as the two groups of temporary layoffs and the omitted group of UI benefit exhaustees. Only when there is such correlation, would it be possible for us to find that there is little correlation between wages and unemployment durations when UI impacts are ignored, and that higher wages are correlated with longer unemployment spells when UI impacts are accounted for, at the same time. We could also compare estimates of table 4.6 with table 3.14 to check how en-dogenization of wages affects the estimation of the duration parts when UI impacts are considered. Similar to the comparison between table 4.4 with table 4.5, the com-parison here shows the coefficient on log hourly wage for unemployment hazard part increases and the coefficient on log hourly wage for employment hazard part drops. Furthermore, comparison of table 4.6 and 3.14 also shows, though endogenization of wages does not affect the magnitude of UI impacts much, but it does improve the precision of the estimated impacts substantially. Finally, table 4.7 presents our preferred set of estimation result where UI incen-tives are considered in the two duration parts and the reemployment wage part. By comparing the estimates of this model as presented in table 4.7 with previous linear regression results, it is easy to see much of the downward trend of reemployment wage towards UI benefit exhaustion week remains similar, except that the coefficient for BEWQ in the reemployment wages part is no longer statistically significant. This means reemployment wages of workers who have initial UI coverage and get reem-Chapter 4. Temporary UFs Time-varying Impacts on Reemployment Wages 111 ployed exactly at benefit exhaustion week are no longer significantly higher than the omitted group, those who get reemployed past benefit exhaustion weeks. This difference suggests workers reemployed at precisely the week of benefit exhaustion are also a group of workers with persistently higher wages. Furthermore, table 4.7 shows that the clearest and strongest evidence of UI's impacts on the labour market is its impacts on the hazards of leaving unemployment. At the same time, our results suggest UI coverage does affect workers' reemployment wages, it only leads to sta-tistically significant increases on reemployment wages for workers reemployed with at least 11 weeks of remaining benefit, in which case workers' reemployment wages are about 12% to 14% higher (exp(O.ll) = 1.12 and exp(0.13) = 1.14). Overall, the weighted average impact of UI coverage on the reemployment wages for UTcovered unemployed workers is about 9.5%. Figures of table 4.8 illustrate UI's impacts on unemployment hazards and reem-ployment wages as estimated here. As the figure shows, the timing of the drop of reemployment wages matches with the timing of the increase of unemployment haz-ards. The coincidence of UI's impacts on unemployment hazards and reemployment wages seems to support the notion that the availability of UI benefit does allow workers to set higher reservation wages. 4.7 Conclusion The study of this chapter examines an old, but open question in the empirical lit-erature. It inherits the data and econometric model of the previous chapter's work, then extends previous chapter's work by endogenizing individuals' wages and exam-ines the impacts of UI on reemployment wages using a full information maximum likelihood model. Specifically, the two features of this study are that both employ-Chapter 4. Temporary UI's Time-varying Impacts on Reemployment Wages 112 ment/unemployment cycles and wage dynamics are endogenized in the estimation; and that UI's impacts on reemployment wages are allowed to vary depending on the timing of reemployment relative to benefit exhaustion. The preferred set of estima-tion result suggests that reemployment wages of workers with Ul coverage indeed would be 12% to 14% higher than those of benefit exhaustees, but only if they got reemployed with at least 11 weeks of benefit left. Overall, the weighted average im-pact of Ul coverage on the reemployment wages for UTcovered unemployed workers is about 9.5%. Our evidence shows while Ul leads to longer unemployment spells, it does indeed help to improve workers' job match qualities. These two most prominent impacts of Ul are both statistically and economically significant. Moreover, comparisons among estimation results of different specifications sug-gest several important correlations in the micro labour market. Given only non-seasonal unemployment spells completed within 52 weeks due to permanent sepa-rations are studied here for reemployment wages, the impact of Ul on long term unemployed workers remains to be studied. 4.8 Tables and Figures Chapter 4. Temporary UI's Time-varying Impacts on Reemployment Wages 113 Figure 4.1: Predicted Impact of Temporary U l Coverage on Unemployed Workers' Reservation Wages 25 & 2°l .2 15 I | 101 PQi Ul UO _l_ 15 20 25 30 35 40 45 50 weeks Figure 4.2: Illustration of the Four Durat ion and Wage Parts of the Likelihood Function employed unemployed employed I ^ 'A ^ 'A ^ »J I'" ft ft and ft" ft Chapter 4. Temporary UFs Time-varying Impacts on Reemployment Wages 114 Table 4.1: Linear Regression Results of Reemployment Wages (1) (2) (3) (4) R2 0.26 0.47 0.47 0.28 p r ev ious wage (In) weeks of u n e m -p l o y m e n t (In) pos t r e fo rm u n e m p l o y m e n t ra te 0.04 (0.03) - 0 . 0 0 (0.01) 0.53 (0 .03)* 0.03 (0.02) 0.00 (0.01) 0.54 (0 .03)* - 0 . 0 1 (0.01) 0.03 (0.02) 0.00 (0.01)-0.03 (0.03) - 0 . 0 0 (0.00) q u i t [so, no UI] p e r m a n e n t l ay -off, no U I 0.20 (0.08)$ 0.18 (0.08)$ 0.17 (0 .06)* 0.12 (0.06)1 0.15 (0.06)$ 0.11 (0.06)$ 0.05 (0.10) 0.18 (0.08)$ time-varying UI treatment variables at the reemployment week (for permanent laid-off workers with UI coverage) BEW2i+ 0.18 (0.08 BEWn-20 0.19 BEWe-W 0.11 BEW2-5 0.11 BEW! - 0 . 0 5 BEW0 0.18 0.09 (0.10 0.10 0.14 0.09 $ 0.14 0.14 0.14 0.09 -0.04 0.17 0.07)$ '0 .07) t '0.08 $ '0.09) '0.15 '0.07)$ 0.11 0.13 0.14 0.08 -0.04 0.17 ' o .or '0.07) '0.08 '0.09 '0.15 '0.07 t 0.18 0.19 0.12 0.10 -0.05 0.17 0.08 0.09' 0 .10 0.10 0.14 0.09' if quitters are eligible for UI, their time-varying UI treatment variables at the reem-ployment week BEW21+ — — — 0.08 (0.08) BEWn-20 — — — 0.07 0.09 BEW&-W — — — - 0 . 1 3 0.10 -BEW2-5 • — — — - 0 . 2 0 0.24 BEWi — — — 0.31 0.11 * . BEW0 — — — 0.08 0.08 q u i t a n d no t e n o u g h e m p l o y m e n t weeks for U I — 0.19 (0 .07)* Note: The sample size is 1605. The independent variable is In of the reemploy-ment wage. Other control variables include constant, gender, age, maritial status, immigration status, education dummies and regional dummies. Table 4.2: Sample Composition by Individuals ca tegory b y coun t s o f y e jew ju juw n u m b e r of i n d i v i d u a l s percentage 1 1 0 0 1,107 2 9 % 0 0 1 0 700 18% 1 0 1 1 499 13% 1 1 1 0 301 8% a l l o the r pos s ib i l i t i e s 1,189 3 1 % t o t a l 3,796 100% Chapter 4. Temporary UFs Time-varying Impacts on Reemployment Wages 115 Table 4.3: Sample Composition by Duration and Wage Data Types c o m p o n e n t t y p e je jew ju juw t o t a l coun t s across i n d i v i d u a l s as 100% 3,338 1,874 3,107 1,605 coun ts a n d p r o p o r t i o n of i n d i v i d u a l s w h o have one inc idence o n l y 2,190 902 1,815 483 66% . 48% 58% 30% Table 4.4: Maximum Likelihood Estimation: No Ul, No Wage Components employment hazard unemployment hazard ei 0.83 0.10)* -0.36 ; o.o9)* €2 1.05 [ 0.09)* pos t r e fo rm -0.19 0.06)* 0.29 ; 0.07)* l o g o f h o u r l y -0.22 0.08)* 0.15 ; o.osit wage u n e m p l o y m e n t 0.03 0.02) 0.01 ( 0.02) ra te Note: the sample consists of 3796 individuals and the mean loglikelihood is -3.935. Other common control variables in the two parts include gender, age, maritial status, immigration status, education dummies and regional dummies. Table 4.5: Maximum Likelihood Estimates: No Ul employment hazards unemployment hazards in i t i a l wages reemployment wages (•2 e 3 0.21 ( 0.05)* -0.71 ( 0.17)* 0.79 ( 0.15)* -0.21 ( 0.07)* -0.17 ( 0.02)* 0.23 ( 0.10)+. -0.22 ( 0.05)* -0.10 0.06)+ 0.23 ( 0.09)1; pos t r e fo rm l o g o f h o u r l y wage u n e m p l o y m e n t ra te -0.19 ( 0.05)* 0.03 ( 0.13 0.03 ( 0 .02)f 0.29 ( 0.07)* 0.01 ( 0.03) 0.01 ( 0.08) 0.03 ( 0.10) 0.01 ( 0.13) 0.04 ( 0.01)* 0.00 ( 0.05) Note: the sample consists of 3796 individuals and the mean loglikelihood is -3.491. Other common control variables in the four parts include gender, age, maritial sta-tus, immigration status, education dummies and regional dummies. The two wage components also have constant terms. • Chapter 4. Temporary UI's Time-varying Impacts on Reemployment Wages 116 Table 4.6: Maximum Likelihood Estimates: UI Variables in Duration Parts employment unemployment in i t i a l reemployment hazards hazards wages wages 0.38 ( 0.19)1. 0.24 ( 0 . 1 3 U --0.19 ( 0.21) - 0 . 1 4 ( 0.06)$ £ 2 — 0.54 ( O . l l ) * 0.21 0.19) 0.21 ( 0 .06)* C3 — — 0.22 ( 0 .13)f 0.22 ( 0 .11)t pos t r e fo rm - 0 . 1 9 ( 0 .05)* 0.23 ( 0 .03)* 0.03 ( 0.09) 0.04 ( 0 .01)* l o g of h o u r l y wage 0.09 0.14) -- 0 . 1 9 ( 0 .05)* — u n e m p l o y m e n t ra te 0.03 ( 0.02)1 0.01 ( 0.08) 0.01 ( 0.11) 0.00 ( 0.05) time-varying UI treatment variables for employment spell sHMINQ_W - 0 . 1 4 ( 0.09) — — — HMIN2-5 0.06 ( 0.12) — — — HMIN! - 0 . 0 8 ( 0.26) — — — HMIN0 - 0 . 1 3 ( 0.25 — — — HMINo + 1 to - 0 . 0 8 ( 0.11) — — — HMAXQ q u i t [so, no UI] — - 2 . 0 2 ( 0 .00)* — — p e r m a n e n t layoff, no U I — - 2 . 1 9 ( 0 .02)* — — t e m p o r a r y layoff, no U I — - 0 . 3 7 ( 0 .03)* — — t e m p o r a r y layoff, w i t h — 1.04 ( 0 .03)* — — U I time-varying UI treatment variables for unemployment spells BEW21+ — - 1 . 7 3 ( 0 .06)* — — BEWn_2Q — - 1 . 7 4 ( 0 .01)* — — BEW6-w — - 1 . 3 0 0 .02)* — — BEW2-5 — - 0 . 9 8 ( 0 .04)* — — BEWi — - 1 . 2 9 ( 0 .03)* — — BEWp — - 0 . 5 9 ( 0 .03)* — — Note: the sample consists of 3796 individuals and the mean loglikelihood is -3.425. Other common control variables in the four parts include gender, age, maritial sta-tus, immigration status, education dummies and regional dummies. The two wage components also have constant terms. Chapter 4. Temporary UI's Time-varying Impacts on Reemployment Wages 117 Table 4.7: Maximum Likelihood Estimates: U l Variables in Duration Parts and Wage Parts employment unemployment in i t i a l reemployment hazards hazards wages wages 0.32 ( 0.19)t 0.33 ( 0.14)$ --0.18 ( 0.21) - 0 . 1 4 ( 0 .08)f — 0.45 ( 0 .14)* 0.21 0.19) 0.20 0 .08)* £3 . . — — 0.22 ( 0.13)1 0.22 ( o . n ) t pos t r e fo rm --0.19 ( 0 .05)* 0.22 ( 0 .03)* 0.03 ( 0.08) 0.03 ( 0 .01)* l o g of h o u r l y wage 0.04 0.14) - 0 . 1 1 0.06)$ — u n e m p l o y m e n t ra te 0.03 ( 0.02)$ 0.01 ( 0.10) 0.01 ( 0.11) 0.00 ( 0.04) time-varying Ul treatment variables for employment spells HMINQ-W -0.14 ( 0.10) — — — HMIN2-5 0.06 ( 0.12) — — — HMINX -0.08 ( 0.26) — — — HMINQ -0.13 ( 0.25) — — — HMIN0 + 1 to HMAX0 --0.08 ( 0.11) — — — q u i t [so, no U l ] — - 1 . 9 8 ( 0 .00)* — 0.14 ( ° - 2 1 ) p e r m a n e n t layoff, no U l — - 2 . 1 6 ( 0 .02)* — 0.11 ( 0.04)+. t e m p o r a r y layoff, no U l — - 0 . 3 5 0 .03)* — — t e m p o r a r y layoff, w i t h U l — 1.03 ( 0 .03)* — — time-varying Ul treatment variables for unemployment spells BEW21+ — - 1 . 6 9 ( 0 .07)* — 0.11 ( 0 .06)f BEWu-w — - 1 . 7 3 0 .01)* — 0.13 0.05 * BEW6.W — - 1 . 2 9 0 .02)* — 0.08 0.05 BEW2.6 — - 0 . 9 8 ( 0 .04)* — 0.07 ( 0.06) BEWi — - 1 . 3 0 ( 0 .03)* — 0.00 ( 0.09) BEW0 — - 0 . 5 9 ( 0 .03)* — 0.10 ( 0.12) Note: the sample consists of 3796 individuals and the mean loglikelihood is -3.423. Other common control variables in the four parts include gender, age, maritial sta-tus, immigration status, education dummies and regional dummies. The two wage components also have constant terms. 1 Chapter 4. Temporary UI's Time-varying Impacts on Reemployment Wages 118 Table 4.8: Illustration of UI's Impacts on Reemployment Process a: unemployment hazards 361 1 32 • I 2 8 \ I 0 5 10 15 20 25 30 35 40 45 50 b: reemployment wages i i / r / c \ A \ ' \l 0 5 10 15 20 25 30 35 40 45 50 119 C h a p t e r 5 Conc lus ions and Discuss ions This thesis's study on UI's labour market impacts belongs to a classical research area. Here, the focus is the contingent, temporary nature of Ul coverage; two as-pects of the labour market, employment/unemployment cycles and wage dynamics are examined. Some highlights of the thesis include: solving a non-stationary model of endogenous employment/unemployment cycles; formulating an event-based dura-tion data construction procedure; creating a parsimonious hazard model with heap-ing effect to account for volatile empirical hazards; utilizing the novel variations of Ul treatment due to the EI reform; estimating a 'super' model where both employ-ment/unemployment cycles and wage dynamics are endogenized; and allowing for Ul to have time-varying impacts on reemployment wages. Overall the approaches adopted here pay a lot of attention to details. As a result, the research here not only confirms previous findings in a new context but also suggests several new insights on the labour market and UL In chapter 2's theoretical modelling section, it is suggested that the three key parameters of a Ul program (benefit duration, employment requirement and weekly benefit) interact with each other and each generates both positive and negative impacts on individuals' work incentives, depending on the timing. In chapter 3, the analysis shows how the seasonal sector lost some of its seasonality after the EI reform; it is also able to show that the Ul program could have increased the overall unemployment rate of Canada in the late 1990s by about 15% (e.g. from 7.6% to 6.6%). In chapter 4, the Chapter 5. Conclusions and Discussions 120 analysis shows how important the persistent correlations among employment spells, unemployment spells and wages are in the labour market; it also shows that, while availability of UI significantly slows the reemployment process (from 23 weeks to 28 weeks of average non-seasonal unemployment durations, a 22% increase), it is also able to increase reemployment wages by 9.5% on average and 12%-14% for the group of very early unemployment-leavers, who have at least 11 weeks of benefit left at their reemployment weeks. The research here does suffer from several serious caveats: the definitions of employment and unemployment used here are different from the conventional ones in order to make them sensible for UTstudies; for computational reasons, all sample spells are censored at week 50 if they continue beyond that point. Furthermore, spells' seasonality is taken as exogenous and our set of control variables excludes all job-related information such as occupation, industry, and firm sizes. Given the huge differences of seasonal and non-seasonal labour market, it would be very useful for policy makers to know the factors that determine workers' seasonality choice. Although it is possible to get some aggregate measures of UI's impacts on the labour market, it would also be interesting to know how these impacts are realized at the workplace, whether it is realized through mobility across firms of different sizes and/or firms of different industries. Generally, UI is regarded as a sensible public policy in many developed countries because of both economic and political reasons. The focus of this thesis is entirely on the economic side, i.e., the insurance role of UI. From an economic point of view, most unemployed workers could not borrow against their human capital, thus facing liquidity constraints. Without UI coverage, many unemployed workers can't afford to search long enough for proper jobs. Subsidized by UI benefit, more patient search then becomes viable. But given the high cost to monitor workers job search activities, Chapter 5. Conclusions and Discussions 121 it is also possible for workers to take the Ul benefit as subsidy for leisure. Without strong evidence on UI's impact on reemployment success, it is hard to distinguish the job search subsidy story from the leisure subsidy one. Although job search theory has long been one of the major explanations for unemployment in the literature, people are still skeptical about the productive role of Ul through improved job matches. Instead, researchers have been very concerned about higher unemployment rate due to generous Ul program. But here, as shown in this thesis, although Ul coverage leads to longer unemployment spells, it also leads to better job matches at the same time — as implied by higher reemployment wages. These two most prominent impacts of Ul are both statistically and economically significant. Overall, the results here strongly suggest that Ul coverage does allow unemployed workers to continue working on high-quality jobs rather than having to accept low-wage jobs in a hurry. These results are rather encouraging as they suggest that the Ul program not only allows workers to smooth their consumption and maintain steady income streams, in addition, it also contributes to the overall human capital utilization of an economy. Together, the two empirical studies of this thesis suggest that longer unemployment spells or higher unemployment rates could be just the cost that we have to pay for better job matches. Therefore, it is only reasonable to evaluate the Ul program by considering its negative impact of higher unemployment rate and positive impact of better job matches together. Besides providing strong support to the general economic rational of Ul program, the results here also suggest ways to make the program more efficient. As shown repeatedly in this thesis, individuals' labour market turnovers are indeed sensitive to UI's contingent and temporary rules. Currently, the Ul program in Canada only takes into account individuals' employment histories within 2 years or so (1 year for Chapter 5. Conclusions and Discussions 122 benefit duration calculation, and 1 year for new entrants classification), except for the experience rating rules, which have a memory of 5 years and are shown to be very effective in promoting work incentives. As a result, workers who have been employed for 8 years are treated the same as those with 2 years of employment, while workers who repeatedly leave unemployment with many unused UI benefit weeks in the past are in general not rewarded with extra benefit weeks in their future unemployment spells. Our results suggest workers labour market attachment could be strengthened if additional experience-rating rules are implemented to reward workers with good UI usage histories. Given our results, it seems that the program could be more effective in promoting work incentives if UI benefit coverage calculation could take account of individuals' labour market and UI collection experiences for a longer period. In other words, if contingency works to promote work incentive, why not extend the basis of contin-gency. Doing it properly, a revised UI program might even be able to mitigate some of the current negative impacts of postponed reemployment. Although it is useful to compare the generosity of two UI programs, UI programs usually have multiple parameters. Modifying an existing UI program so that there is less incentive to abuse the system might be regarded as cutting down the generosity of the program as a whole, but it could actually mean more resources for the desired purposes, thus better welfare for most people. Finally, it is important to understand that the results here only suggest UI cover-age improves job match qualities in a particular developed country: Canada. Here, the whole system of UI, as well as other institutions has been almost constantly evaluated and modified for decades. Over time, many problems have been found, some fixed and others consciously compromised. Would such a custom-made UI program produce similar results in another developed economy? Maybe. Would it Chapter 5. Conclusions and Discussions 123 work similarly in a developing country such as China? I doubt. 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Industrial and Labor Relations Review 30 (4), 451-461. 132 Appendix A Proofs Proof (For Proposition 2.3.1) If Vi > Ne + 1, assume existence of unique reservation wage for each week, then the reservation wage for these different weeks will be the same because of the stationarity of the problem for this part. Without loss of generosity, set i = yVe + 1, then the value function could be writhen as in (A.l) V(w,Ne+l) = max jw (Ag,w + /?77 j V{x, Ne + l)dF(x) + p{l - rj)V(w, Ne + 1)| (A.l) Let the reservation wage be we*. Then, we have two equations that define we* as follows, V{we*,Ne + l) = w^ + pr] I V(x,Ne + l)dF(x) +P(l-n)V(we*,Ne + l) (A.2) V(we\Ne + l) = W(NU) (A.3) Substituting (A.3) to (A.2), we have W{NU) = we* + Pv Jv(x,Ne + l)dF{x)+P{l-V)W{Nu) (A.4) Rearranging terms in above equation, we then have Appendix A. Proofs 133 0n J V(x, Ne + l)dF(x) = -we* + (1 - 0(1 - n))W(Nu) (A.5) Substituting (A.5) to (A.l), we have V(w,Ne + l) = m&x{W(Nu),w-we* + (1 -0(1 - n))W(Nu) +0(l-rj)V(w,Ne + l)} (A.6) Rearranging terms in above equation, we then have (2.2). That means 0njv(x,Ne + l)dF(x) = 0nW(Nu) + 0rj J j 1 ™p(l-v) } d F ^ ^ Substituting (A.5) to (A.7), we then have (2.3). | Proof (For Proposition 2.3.2) This proposition can be proved by induction as follows: First, let's consider the case when i = 1, that is for week Ne. The value function at week NP_ is V(w, Ne) = max j W(0), w + 0n J V(x, Ne + l)dF(x) + 0(1 - rj)V(w, Ne + 1) (A.S) Assuming existence and uniqueness of the reservation wage at week Ne, w^^, we have, Appendix A. Proofs 134 • V(w%e,Ne) = wel + Pn Jv(x,Ne + l)dF(x) +0(l-n)V(w%e,Ne + l) (A.9) V(w%e,Ne) = W(0) (A.10) Obviously, we* > w^c. This could be shown by noticing V(we*,Ne) = W(NU) from (A.8), the assumption W(NU) > W(0), and (A.10). This inequality could then be used in the last term of (A.9) to calculate the exact value of Wft. Vw € [w^ _, we*], we have V(w, Ne) = w + 0V J V{x, Ne + l)dF(x) + 0(1 - n)V(w, Ne + 1) = w + pn Jv(x,Ne +l)dF(x)+0(1-n)W(Nu) (A.ll) Thus, Vw 6 [wexe,we*], £ > V ^ J V e ^ = 1. We then can backup w^e, considering this slope, V(we\Ne) = W(NU), and V(w%e,Ne) = W(0). This is illustrated at figure 2.2. And formally, w „ _ w e . _ W ( N u ) - W W = w , , _ V { w < - N , ) - W ( 0 ) Thus, we have proved (2.4) for i = 1. Also, dv{gwNe) = l,Vw e [w%e,we*}, as derived in (A.ll) proved the middle case of (2.5) for i = 1. Vw > w-, it is easy to see V(w, Ne) = V(w, Ne + 1) => = d V { w £ e + 1 ) = Appendix A. Proofs 135 (1 - p(l - 77))-1; while Vw < we*e, V{w, Ne) = W(0) = »  d v [ Q ^ e ) = 0. By these, (2.4)is proved for i = 1. Notice, Vw > we*, V{x,Ne + 1) = V ( : r , A g , and < we\ V(x,Ne + 1) = = V(we*,iVe) > V(x,Ne), thus JV(x,Ne + l)dF(x) > J V(x, Ne)dF(x). That means (??) as well as (2.7) are true for i = 1 and by this Proposition 2.3.2 is proved for i = 1. Second, let's consider the general case when i — k + 1, assuming Proposition 2.3.2 is true for all i, s.t. i < k, Vk > 1. The value functions when i = k + 1 and i = k are, V(w, Ne + 1 - k) = max j w ( 0 ) , w + /?77 y V(z, Ne + 2 - fc)dF(x) + 0(1 - n)V(w, Ne + 2 - fc)j (A.13) V > , i V e - f c ) = max j w ( 0 ) , w + /?77 y V(x, -/Ve + 1 - k)dF(x) + (3(1 - n)V(w, Ne + 1 - k) (A.14) I show wexe_k > W x e + 1 _ k by contradiction. The indifference conditions at these two weeks give us the following equality condition, Appendix A. Proofs 136 <e-fc + PvJ V(x, Ne + 1- k)dF(x) + (1 - 0(1 - vW(w%e_k, Ne + l~k) = W(0) = w%e+1_k + Pv I V(x, Ne + 2 - k)dF(x) +(l-P(l-v))V(wel+1_k,Ne + 2-k) If Wxe_k < w^e + 1_ f c, then V(w^e_k, Ne + 1 - k) = W(0), while we also know V(tw"e+1_fc, Ne+2-k) > W(0) by the setup of the value function. Thus, V(w%e_k, Ne+ 1 — k) < V (w'fi +l_k, Ne + 2 — k). Also, we have assumed Proposition 2.3.2 is true _ for i = k, thus J V(x, Ne + 1- k)dF(x) < J V(x, Ne + 2- k)dF(x). Therefore, we <e-k + PVJ V(x, Ne + 1- k)dF(x) + (1 - P(l - V))V(w%e_k, Ne + l-k) < <e+1_fc + Pr, f V(x, Ne + 2- k)dF(x) + (1 - 0(1 - vW(w%e+l_k, Ne + 2-which contradicts the equality condition above. Therefore we^e_k > we^e+l_k. By assumption, we also now voe^_k < we* since V(we*,Ne — k) > W(0) = should have V(w we can rewritten (A.14) as follows, +p(l-V)V(w,Ne + l-k) Appendix A. Proofs 137 where a ^ + i - k ) _ _,,)-. <7W Vw e K ; e _ f c , we*] C [w%e+1_k, we*}, V{w, Ne-k) = w + pn J V{x, Ne + 1- k)dF{x) +p{\-ri)V(w,Ne + l-k) s=0 -> d V ( w f ° ~ k ) - i > ( i - , » • s=0 Vw < <._ f c , l > , iVe - A:) = W(0) d V [ W d N w e ~ *° = 0 Therefore, (2.5) is true for i = k + 1. Based on the slopes given above, it is obvious that (2.4) is also true for i = k + 1. Now comparing (A.13) and (A.14) , since there exists w, for example we*, such that V(w,Ne + l-k) > W(0), also we know JV{x,Ne + 2-k)dF(x) > JV(x,Ne + 1 - k)dF{x) and V(x, Ne + 2-k)> V(x, Ne + l-k), therefore, (??) and (2.7) are also true for i = k + 1. Finally, the proof is complete by considering the above two steps jointly. | P r o o f (For Propos i t ion 2.3.3) First of all, V* € N, s.t. t G [1, Nu - l],'the value function at an unemployed week with t weeks of benefit remaining is, Appendix A. Proofs 138 W(t) = B + p\ / max {W(t - 1), V{x, 1)} dF(x) + P(l - X)W{t - 1) (A.15) It is then obvious that (2.8) is the just indifference condition of (A.15) which says the worker will get same payoff whether choosing to reject the offer or not at the reservation wage. (2.9) is true because: (2.8) => V(wlfk, 1) = W(l) = B + W(Q) = B + V{w?, 1) Ai = B. Since B > 0, thus > w%*. (2.10) is true because: Vi G N, s.t. t 6 [2, Nu - 1], (2.8) =>At =. v K . i j - y K M ) = W(t) -W(t-1) = pxJ{max{W{t-l),V{x,l)}-max{W(t-2),V(x,l)})dF{x) (A.16) (pX)-1At = (mex{W(t-l),V(x,l)}-max{W(t-2),V(x,l)})dF{x) (A.17) 0 < / (max{W(i - 1), V(x, 1)} - max{J¥(i - 2), V{x, l)})dF(x) < A t _ x F « * ) That is Now I should show (A.17) by induction. (A.18) first, we need to show the proposition is true for t — 2. Appendix A. Proofs 139 Notice f ( 0 ) F « ) + / V{x,l)dF(x)\ x>wf* max{W{2 - 1), V(x, l)}dF(x) - J max{W(l - 1), V(x, l)}dF(x) W(l)F(w%*)+ [ V(x,l)dF{x r*>T = W(l)F(w%*) - W{0)F(Wl) - / V{x, l)dF(x) since w%* > v%* from (2.9) = W(l)F(w%*)- j meix{W(0),V(x,l)}dF(x) Jx<w%* [W(l)-max{W{0),V{x,l)}}dF(x) J max{iy(2 - 1), V(x, l)}dF{x) - J max{W r(l - 1), V{x, l)}dF(x) > 0 < / [W(l)-W(0)]dF(x) = [W(l)-W(0)]F(w?) Thus 0 < A 2 < /?AF(w 2 J*)A 1 . Since A 2 > 0, we have w%* > w%*. Second, we need to prove if (A.17) is true V i £ N, s.t. 2 < i < k < Nu, then it is also true for t = k + 1 case . (A.17) is true when i = k w^x > wk*, similarly we have, Appendix A. Proofs 140 ( / 3 A ) _ 1 A f c + 1 max{W(k),V(x,l)}dF(x) - I m&x{W(k - 1), V(x, l)}dF{x) W(k)F(wr+1)+ / V(x,l)dF(x) W{k-l)F{w^)+ f V{x,l)dF{x) Jx>w]i* = w(k)F(wr+1)-w(k-i)F(wr) since u^+j > from above V{x, l)dF{x) = W(k)F{w%*+1) - / max{W(k-l),V(x,l)}dF{x) [W(k) - max{W(k - 1), V(x, 1)}] dF(z) n{W(k), V{x, l)}dF(x) - J max{W(k - 1), V{x, l)}dF(x) > 0 max < / [W{k) -W{k-l)}dF{x) = [ ^ - H / f f c - i U F K ; ) Thus 0 < A f c + i < / ? A F ( ^ ; i ) A f c . Since A f c + X > 0, we have w%*+2 > w^*+v Finally, the proof is complete by considering the above two steps jointly. | 

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