Unemployment Insurance and Labor Supply*

Transcription

1 Unemployment Insurance and Labor Supply* Chantal Cases** Is unemployment insurance a disincentive to work? The question is almost as old as unemployment insurance itself. The fear of such effects as much as the macroeconomic nature of the risk seems to be one of the factors that has deterred private insurers from entering the field. Some analysts argue that the disincentive effects stem from the rise in unemployment. The effects would also partly explain the unemployment-insurance funds refusal to provide unlimited coverage, in an effort to avoid fostering dependency on the system. These arguments carry limited weight. To begin with, the prime cause of unemployment is the existence of a macroeconomic imbalance between labor supply and demand, which cannot be attributed solely to a wait-and-see attitude on the part of job-seekers. If that were so, the rise in unemployment would have been matched by a parallel growth in unfilled job offers but no such phenomenon has been observed. Second, the ever-greater restrictions introduced in the compensation system are primarily dictated by the need to contain overall system expenditure; it would be wrong to interpret the tightening purely as a response to a rising moral hazard. If the system does have disincentive effects, the only way to test them is to examine individual behaviors. Panel data the focus of this study allow such an exploration. The analysis does not refute the existence of the apparent disincentive effects of unemployment benefits, but suggests that their interpretation is more complex than expected. Their estimation is complicated by the interaction between eligibility for benefits and personal characteristics, as well as by the fact that the benefits cannot be fully measured. Also, it should be remembered that one of the purposes of unemployment insurance is to allow a longer job search so as to improve the match between the labor force and jobs available. *Originally published as "Assurance-chômage et offre de travail," Économie et statistique, no , /2. Names and dates in parentheses refer to the bibliography at the end of the article. ** At the time of writing, the author was working with INSEE s House Hold Income and assets division. I n the 1980s, most countries reformed their national unemployment-insurance systems, generally by cutting benefit levels or duration, or by restricting entitlements (Lefèvre 1996). Although the driving force behind these reforms was financial, their theoretical justification rests on the notion of moral hazard linked to unemployment insurance. In the unemployment sphere, the generally accepted concept of moral hazard refers to the potential disincentive effects of benefits on the search for, and acceptance of, a new job. Our study seeks to provide an empirical illustration of this specific mechanism. In fact, the term "moral hazard" could applied with equal appropriateness to the risk of INSEE STUDIES no. 5, october

2 entering unemployment as much as to the danger of remaining there in other words, to the behavior of firms as much as to that of workers. Layoffs could be interpreted, in that sense, as free-rider behavior on the part of employers. By cutting its workforce, a company can hope to boost its profits while distributing the cost of compensation among all the firms that finance the system. Empirical studies: from initial certainties to the challenging of results The measurement of a possible effect of the unemployment-benefit level (or "replacement ratio," i.e., the benefit divided by the last wage) on unemployment spells has been the focus of widespread debate since the 1960s. The initial estimates were made directly on unemployment spells or on the instantaneous escape rate from unemployment; in most cases, the estimates postulated a distinctive parameter specification. The typical study of the late 1970s thus examined the effect of the replacement ratio on the unemployment duration (Lancaster 1979; Nickell 1979). This type of analysis gradually gave way to a structural approach that explicitly modeled individual behavior using job-search models (Fishe 1982; Lancaster and Chesher 1983; Atkinson et al. 1984; Lancaster 1985; Narendranathan and Nickell 1985; Van der Berg 1990). By the early 1980s, a series of studies on unemployment spells in the United States was creating a consensus that benefits prolonged unemployment duration by raising the "reservation wage" the minimum wage accepted by the jobless for leaving unemployment (Lancaster and Nickell 1985; Danziger et al. 1981). The effect was estimated to add between half a week and a whole week to the unemployment spell for a 10-point increase in the replacement ratio. In 1984, Atkinson et al. powerfully challenged these findings. Their critique focused on the estimates lack of robustness and the choice of unemployment-benefit indicator. The authors suggested four alternative and economically justifiable measures for the replacement ratio. They showed that the elasticity of the unemployment spell to the ratio could vary from 0 to 0.6 according to the indicator chosen. Atkinson and his colleagues also examined the partially endogenous character of the benefit level, concentrating on the individual s career record (tenure in last job held, previous unemployment experience, etc.). Other critics (Hills 1981) showed the sensitivity of earlier results to the definition of unemployment used, in particular the inclusion of non-compensated jobless. Other weaknesses of the results are linked to the estimation method. For instance, the inclusion of an unobserved heterogeneity among individuals can modify the elasticity values (Lancaster 1990). The most recent studies, based on administrative records tabulating benefits actually paid, find a far narrower range of values. Narendranathan, Nickell, and Stern (1985), examining Britain, find the replacement-ratio elasticity of the unemployment spell is significant, but they put its value at only 0.3 (the studies mentioned above had estimated it at 1 or so). Moffitt (1985) obtained 0.4 for the United States. Only Meyer (1990) reports higher values, with a 1.5-week spell extension for a 10-point increase in the replacement ratio. The disincentive effect: empirical results vary from one country to another Moreover, the intensity of the effects varies considerably according to the country studied. While the results are fairly similar in Britain and the United States, the same does not hold for other European or OECD countries. In Germany, Wurzel (1988) finds a non-significant effect of unemployment benefits on the unemployment spell. The same has been found for Canada (Ham and Rea 1987). In Australia, a significant but weak negative effect is estimated by Trivedi and Kapuchinski (1985). In France, a multi-study compilation by Florens, Fougère, and Werquin (1990) finds the results to be "very ambiguous and highly sensitive both to the model used and to the data examined." Gérard-Varet et al. (1990) observe a lengthening of the unemployment spell with the rise in benefits, but only on a register of actual recipients. Among all the factors relating to compensation and benefits, however, benefit rates are not the only potential determinant 2 INSEE STUDIES no. 5, october 1997

3 of unemployment spells. Another factor is the change in the benefit-payment system. Several studies on U.S. data suggest a major change in the hazard rate as benefit recipients reach the end of their entitlement period. Moffitt and Nicholson (1982), for instance, estimate that an extra week of entitlement adds 0.1 weeks to the unemployment spell; Katz and Meyer (1990) put the lengthening at about 0.2 weeks. In France, Florence and Fougère (1989) show a significant effect of the exhaustion of entitlement on the hazard; Bonnal and Fougère (1990) find that the compensation duration has a positive effect on unemployment spells when unemployment leavers not only start a new job but are removed from the rolls of the state employment agency (Agence Nationale Pour l Emploi: ANPE). This result points to a dual disincentive effect. Lastly, the effects of compensation vary according to gender, age, and unemployment spell duration. Narendranathan, Nickell, and Stern (1985) find that the effect diminishes with age and becomes non-significant for the long-term jobless in Britain, where entitlement is in principle unlimited. In most studies, the population is stratified according to the criteria listed above, and the estimates are done separately for each category. Likewise, the empirical study that follows has been conducted separately for men and women. A fuller analysis of the compensation effect should include other factors besides unemployment duration. The benefit rate naturally influences the unemployment-exit wages. The theory holds that, by extending a productive job-search, unemployment benefits also allow job-seekers to receive offers at more attractive wages and thus, in theory, to secure more productive jobs. Moreover, compensation is just one of the factors likely to influence unemployment spells. Generally speaking, it is also important to measure the effect of the measured or unmeasured characteristics of the individual and the market on unemployment duration. This is done in the estimate that follows. Box 1 DATA DESCRIPTION The Unemployed Persons Monitoring Survey was conducted by INSEE. Initially, a sample of 8,238 job-seekers was selected from unemployed persons registered with the state employment agency (Agence Nationale Pour l Emploi: ANPE) in August 1986 (date E0). The persons chosen were interviewed on four successive occasions: in November 1986 (E1), May 1987 (E2), November 1987 (E3) and May 1988 (E4). The data set thus covers a combined period of 21 months. A total of 7,450 persons responded to the survey, which was supplemented by personal information. At E1, respondents were asked to report any status changes since E0 and to indicate the unemployment spell duration as of E0. At the dates E2, E3, and E4, they were asked to reconstruct the monthly calendar of their employment or unemployment status since the previous survey. It should be noted that the survey does not examine unemployment in the ILO sense but the status as reported by the respondents themselves. The end result is a time record of activity status for each individual, from the start of the unemployment spell still under way at E0, to the status at E4. This record may contain several unemployment spells. If an unemployment spell is in progress at the date E4, the duration data will be right-censored. In all, 10,345 unemployment spells were observed, of which 7,450 were under way in August The study will deal here with a sub-sample of the balanced panel, comprising job-seekers aged whose unemployment spell duration at E0 is known, making a total of 7,935 spells. Women represent a majority of the sample, with 4,255 unemployment spells versus 3,680 for men. The sample studied includes a fairly large proportion of censored periods (14% for men, 22% for women). The percentage rises steeply with age, exceeding 55% after age 50. Before age 40, the most common outcome is a fixed-term employment contract. This reflects the high occurrence of brief, repeated unemployment spells in the survey sample. Some respondents experienced seven different unemployment spells over the 18-month period studied, and one-third of the sample reported at least two. Most of the people in the sample had little or no educational qualifications: 32% have no diploma whatever, and 21% have no more than a Certificat d Études Primaires (the now discontinued primary-school-leaving diploma) or a Brevet d Études du Premier Cycle (a ninth-grade diploma). While confined to persons aged 20 and over, the sample also comprises a high proportion of young people: 28.8% are aged under 25. INSEE STUDIES no. 5, october

4 A study on French data We illustrate the effect of compensation on hazard rates by estimating a model on panel data compiled by Insee between 1986 and 1988 (see box 1). Like most empirical studies on unemployment spells, our model is based on theoretical job-search models derived from the specifications put forward by Lippman and McCall (1976). According to this theory, the decision to accept a job offered and the wage that characterizes it rests on an inter-temporal arbitrage. For each offer, the job-seeker compares the income expectations in two situations: (1) accepting the job or (2) staying unemployed in the hope of a better offer. The model identifies a "reservation wage" above which the offers will be accepted. The reservation wage rises when there is an increase in the mean value of the offered-wages distribution, the benefit rate, or the likelihood of being offered a job. In the model s simplest version, the structural parameters (rate of job offers received, offered-wages distribution, incomes) do not vary in time. In these conditions, the reservation wage is constant, as is the conditional probability of escape from unemployment, called the hazard rate. The latter is defined as the product of the probability of being offered a job and the probability of the offer s acceptance, that is, the odds that the offered wage will exceed the reservation wage. This theoretical model has been the focus of several criticisms and improvements. The main enhancements center on the development of non-stationary models (Van den Berg 1990). Under certain hypotheses, these models show the reservation wage and hazard to be non-constant. The two functions are decreasing if the model parameters (income received in the early part of the unemployment spell; mean of offered wages) decrease over time. In its reduced form, the hazard rate therefore depends, in principle, on a set of exogenous variables describing the characteristics of the individuals, the labor-market segment to which they belong or would like to belong, and the income they receive or expect to receive in different states of unemployment, employment, or inactivity. The variables we will introduce into the empirical model capture the theoretical model. It should be emphasized that the behaviors illustrated in those models are purely individual. If we wanted to assess the effect of a given variable on the overall unemployment rate, we would need to find an efficient way to aggregate individual behaviors. Also, the model is estimated for a specific period when the French economy was recovering and labor-market pressures were easing. As far as one can tell, the effects of the economic cycle on unemployment duration are probably not negligible. We begin with two separate regressions for men and women, to allow for the greater incidence of inactivity among women (Lollivier 1993). To address the main subject of our study the effect of benefits on the hazard rate we use two different approaches. The jobless monitoring survey allows a month-by-month tracking of benefit payments over the 18-month observation period as well as the pre-survey period. A dummy variable for benefit payment during the unemployment spell will be used to compare the hazard rates for non-recipients and recipients. To measure the impact of benefits more precisely, we also introduce a time-varying variable that tags the benefit termination date hence the duration of benefit payments. This will allow a comparison between recipients statuses before and after they stop being paid benefits. The cutoff point is simply the benefit termination date recorded in the survey, not the entitlement termination date expected by the unemployed respondent, since the survey does not contain any question about the latter date. We preferred this solution to an imputed date for entitlement termination: the accurate implementation of benefit regulations requires exhaustive information on the final job spells prior to unemployment, including complete earnings and past entitlements. That information is not fully documented in the survey. We also introduce age and the individual s wage level (when known) before the unemployment spell. Both variables play a multiple role in the model. The older the person and the higher the previous wage, the greater the expected future wage. The last wage also influences the benefit rate, while age influences the benefit duration (see above). These factors drive up the reservation wage and decrease the probability of accepting an offer. The values 4 INSEE STUDIES no. 5, october 1997

5 Table Estimation of model coefficients Variable Men Women Without heterogeneity With heterogeneity Without heterogeneity With heterogeneity α 0.88 (0.02)* 0.91 (0.02)* 0.85 (0.02)* 0.94 (0.02)* Constant (0.10)* (0.10)* (0.09)* (0.10)* Previous wage Under FF3,500 Reference Reference Reference Reference FF3,500-under FF4, (0.07)* 0.17 (0.08)* 0.17 (0.06)* 0.19 (0.07)* FF4,000-under FF4, (0.07)* 0.43 (0.08)* 0.16 (0.06)* 0.18 (0.08)* FF4,500-under FF6, (0.07)* 0.44 (0.07)* 0.29 (0.06)* 0.36 (0.07)* FF6,000 and over 0.59 (0.08)* 0.63 (0.08)* 0.54 (0.08)* 0.65 (0.09)* No wage or unreported 0.19 (0.17)* 0.21 (0.07)* (0.05) (0.06) Age (years) Reference Reference Reference Reference (0.06)* (0.07)* (0.05)* (0.07)* (0.07)* (0.08)* (0.06)* (0.07)* (0.08)* (0.08)* (0.07)* (0.08)* (0.09)* (0.09)* (0.07)* (0.09)* (0.09)* (0.10)* (0.09)* (0.10)* (0.10)* (0.10)* (0.11)* (0.11)* (0.11)* (0.10)* (0.11)* (0.12)* Cause of unemployment End of contingent job Reference Reference Reference Reference Layoff (0.06)* (0.06)* (0.06)* (0.07)* Voluntary separation or other (0.07)* (0.07)* (0.06)* (0.06)* Unspecified 0.60 (0.05)* 0.64 (0.05)* 0.57 (0.05)* 0.69 (0.06)* Benefit status No benefits Reference Reference Reference Reference Eligible for benefits 0.52 (0.06)* 0.52 (0.06)* 0.06 (0.05) 0.07 (0.06) Receiving benefits (0.02)* (0.06)* (0.05)* (0.06)* Households savings Under FF5,000 Reference Reference Reference Reference FF5,000 and over 0.23 (0.05)* 0.24 (0.05)* 0.09 (0.04)* 0.10 (0.05) Unspecified 0.02 (0.05) 0.03 (0.06) 0.09 (0.05) 0.10 (0.06)* Status in household Spouse of economically active person Reference Reference Reference Reference Spouse of unemployed person 0.12 (0.08) 0.11 (0.09) (0.08) (0.09) Single person (0.05) (0.06) 0.24 (0.05)* 0.28 (0.05)* Dependent child (0.06)* (0.06)* 0.19 (0.06)* 0.20 (0.07)* Other (0.14) (0.14) 0.29 (0.12)* 0.38 (0.17)* Log likewood η Standards errors are shown in parentheses. * Significant coefficient at the 5 % limit. INSEE STUDIES no. 5, october

6 1 Age is introduced in the model in the form of dummy varaiables for each five-year age group. Previous wages are also proxied by dummies. of these variables may also affect the probability of receiving job offers. This is due to the fact that the information channels of older or better-paid workers may be different, as may the signal given to employers. In the final analysis, the effect of age and the previous wage on the hazard rate is a combination of these sometimes conflicting factors 1. The benefit rate is determined not only by the earlier wage, but also by the circumstances of job separation. Workers who resign are ineligible for benefits, except in a very few specific cases where the departure is involuntary (a minor whose parents move, for example). Employees who have completed a fixed-term contract are entitled to benefits under the same conditions as workers laid off during an open-ended contract. However, the entitlement of workers on fixed-term contracts depends on the duration of their earlier contributions, which, in their case, may often be shorter. The cause of unemployment may also send a different signal to potential employers, promoting or inhibiting firm job offers. The actual payment of unemployment benefits will be captured by the specific variables described above. As a result, the effect of the unemployment cause will be more easily related, in the model, to the probability of receiving a job offer. The causes of unemployment have been grouped together into three categories: end of fixed-term contract; end of temporary or seasonal job; end of paid training program 2. Unemployed persons are also classified according to their 2. Paid training programs are equated here with contingent work contracts a consistent choice for an adult population (aged 20 and over). Some studies (Bonnal, Fougère, and Sarandon 1994) have examined these different categories in specific detail. The aim of these analyses was to assess the impact of employment policies, layoff procedures, resignations, and other reasons (such as early retirement, military service, end of schooling, and voluntary quitting for personal reasons). Box 2 THE ROLE OF INDIVIDUAL CHARACTERISTICS IN UNEMPLOYMENT EXIT Faster exits have been observed: a. for the young The effects of individual characteristics other than unemployment compensation are conventional and very similar in the two models estimated. Age effects, clearly visible even in the raw data, are very pronounced. First, the younger the job-seeker, the shorter his or her unemployment spells all other things being equal. Mean durations lengthen fairly steadily with age among men (see table). For women, the durations are stable between ages 25 and 45, rise steeply until age 55, and decline between ages 55 and 60. In the latter age group, where the most common exit is toward inactivity, the data indicate women decide more quickly than men to quit the labor force (Cases and Lollivier 1994a). b. for unemployment spells after contingent jobs The only clearly identified effect relating to the causes of unemployment is the differential between unemployment spells following a fixed-term job contract and other unemployment spells: the former are significantly shorter. Using a multiple-exit model, one can show that unemployment following a fixed-term job contract is far more likely to lead to another contingent job (Cases and Lollivier 1994a). The model thus captures the recurrence of unemployment spells alternating with contingent jobs which seems to be one of the more notable features of the sample used. By contrast, we find no significant difference in impact between voluntary and involuntary separations all other things being equal. c. for the unemployed with the highest earlier earnings The wage bracket of job-seekers before their unemployment spell has a significant downward influence on the spell s duration. Here, the existence of a probably greater number of job offers is a more powerful factor than the rise in the reservation wage. The variable has a comparable effect on men and women. Likewise, household savings have a positive effect on the hazard rate: the greater a job-seeker s savings, the shorter the unemployment spell. These results appear to confirm the assumptions behind the job-search-intensity models unless the job-seekers in our sample are simply able to access the market segments that offer the most jobs. Lastly, the job-seeker s status in the household has little impact all other things being equal on the hazard rate. The pattern for spouses of economically active persons does not differ significantly from that of spouses of unemployed persons (perhaps because the sample contains few of the latter). Female heads of household (with or without children) experience slightly shorter unemployment spells than the reference category, i.e., the spouses of economically active persons. Men in the same situation do not diverge from the reference. Dependent children are a case apart. Young men living with their parents escape from unemployment more slowly than the reference category, while young women in the same situation exit more rapidly. To describe this effect more fully, one should, no doubt, incorporate data on the military-service spell, which is the most common exit toward an economically inactive status for young males. 6 INSEE STUDIES no. 5, october 1997

7 status in the household, reflecting the fact that their status is often determined by the existence of other income sources than their own activity. We thus distinguish between jobless spouses of persons in employment, single heads of household (with or without children), and children living with their parents. Furthermore, we identify the persons who, at the start of the survey, reported a stock of more than FF5,000 in household assets. This figure is based on a concept of "initial wealth" that does not appear in the basic model. Danforth (1979) has shown a positive correlation between reservation wages and value of assets for the risk-averse unemployed. Under this hypothesis, people with a greater stock of assets are slower to escape from unemployment. One can also argue the opposite, within the framework of a model with an endogenized job-search intensity namely, a greater stock of assets allows an unemployed person to spend more money on the job search, and, if these outlays have increasing returns, the job-seeker will escape from unemployment all the sooner (Ben-Horim and Zuckerman 1987). Lastly, our model does not distinguish between different exit states (Cases and Lollivier 1993b and 1994a). The hazard rate will therefore aggregate the probabilities of the various possible destinations, such as regular job, contingent job, or inactivity. This simplification has a modest effect on the trend in the variation of the hazard rate, but the basic results on the impact of benefits are unaffected. However, we introduce an unmeasured individual heterogeneity factor to capture those differences between individuals that are not reflected in the variables described above (see appendix). A slight decrease in the hazard rate with unemployment duration All the models estimated, with or without heterogeneity, point to a slight decrease in hazard rates with the unemployment spell duration (see table). The values of the a coefficient that indicate the trend in the variation do not differ significantly for men or women in a given model (see appendix). The inclusion of measured heterogeneity (in exogenous variables) or unmeasured heterogeneity (random individual effect) is important for the analysis of duration dependency, as it allows the elimination of a bias due to what is known as the "mover-stayer" phenomenon. This effect is clearly visible in the following simple example: if the observed population is composed of sub-groups of homogeneous individuals with constant but different hazards, the structure of the population that stays unemployed will change in every period. Over time, it will include a relatively larger share of individuals belonging to the sub-groups with the lowest hazard rates. Total hazard will therefore seem to be decreasing, whereas the decline is simply due to the aggregation of different sub-populations. That is why the estimations of the models show a less steeply declining hazard when individual heterogeneity is included than when it is not. In the final analysis, when all factors are taken into account, we find a very weak decrease in hazard (a = 0.91 for men and a = 0.94 for women). When one distinguishes between exits to employment and exits to inactivity, the rate of exit to the various types of employment actually becomes constant (Cases and Lollivier 1993b). A likelihood-ratio test shows the introduction of a heterogeneity factor is significant for both sexes. Unobserved heterogeneity is greater among women than among men, and also produces a more sizable change in the form of hazard among women. The standard deviation of the heterogeneity factor α = 1 η is 0.53 for women and 0.30 for men. Unemployment compensation: an apparently minor impact The model distinguishes between three types of spell: (1) wholly uncompensated unemployment spells, and, for compensated spells, (2) the compensated portion of the unemployment spell and (3) the period subsequent to the exhaustion of benefit entitlement. The reference situation is (1) (see table) 3. 3 The compensation effect during unemployment spells is calculated as follows: (1) if the spell is fully compensated, the effect is equal to the sum of two coefficients: the "eligible for benefits" coefficient and the "receiving benefits" coefficient; (2) if the spell is not fully compensated, the effect is equal to the sum of the two coefficients payments for the compensated portion of the spell, and to the "eligible for benefits" coefficient for the uncompensated portion. INSEE STUDIES no. 5, october

8 For all job-seekers receiving benefits during their unemployment spell, we performed separate analyses of the sub-period in which the benefits were actually paid and the period following termination of payment, if one occurred. We find far lower hazard rates when benefit payments are in progress than after the payments have ceased, especially among men. Eligible job-seekers are therefore less likely to leave unemployment when they are still receiving benefits than when their entitlement is exhausted. A multi-destination model (Cases and Lollivier 1993b) shows that the exit rates for recipients are much slower not only toward inactivity but also toward employment. All the evidence here suggests that compensation prevents the discouraged-worker phenomenon and allowed job-seekers a broader choice among the positions offered. This is consistent with the theoretical job-search model described earlier. The finding cannot be interpreted exclusively as a moral-hazard behavior. Uncompensated male jobless occupy an intermediate status with respect to these two positions. They leave unemployment more quickly than persons still receiving benefits but more slowly than persons who have stopped receiving them. By contrast, we find no difference between the situation of women whose entitlement is exhausted and that of non-recipients. These results are consistent with other studies on French data. An entitlement-exhaustion effect has already been reported on data from a register of benefit recipients (Florens, Fougère, and Werquin 1990), as well as from a local register of an ANPE office (Bonnal and Fougère 1990). In the aggregate, male recipients do not escape from unemployment more rapidly than non-recipients, owing to the mean-effect on the unemployment spell duration suggested by the coefficient values (Cases and Lollivier 1993b). In contrast, for all female recipients, the mean of the two sub-periods is negative, and they appear to experience longer spells than non-recipients. In fact, the interpretation of this "entitlement-exhaustion effect" in our survey is ambiguous. Some unemployed persons report small benefits paid for very long periods (well over two years). These may be socially marginalized groups, who have little chance of finding work again, and who are long-term recipients of benefits that are more accurately described as welfare support. On this assumption, the payments are qualified by their recipients as unemployment benefits because of their perceived link to a joblessness status. If that is so, the measured effect is not a behavior effect but rather a selection effect that discriminates between the unemployed according to the number of job offers they receive. This interpretation is corroborated by a structural model on the same data, which we used to make separate estimates of the probability of being offered a job and the reservation wage. The model revealed practically no significant effect of benefit rates on either of these variables, and hence on individual behavior in regard to job offers (Cases and Lollivier 1994b). In sum, the models fail to support the claim that unemployment benefits had a disincentive effect in France during the period of study. The main determinants of the hazard rate are the individual characteristics of the unemployed (see box 2). 8 INSEE STUDIES no. 5, october 1997

9 REFERENCES Atkinson, A. B., Gomulka, J., and Micklewright, J. (1984), "Unemployment Benefits, Duration and Incentives in Britain: How Robust is the Evidence?" Journal of Public Economics, vol. 23, pp Ben-Horim, M. and Zuckerman, D. (1987), "The Effect of Unemployment Insurance on Unemployment Duration," Journal of Labor Economics, vol. 5, no. 3, July, pp Bonnal, L., and Fougère, D. (1990), "Les déterminants individuels de la durée de chômage," Économie et Prévision, no. 96, pp Bonnal, L. and Fougère, D. (1994), "L impact des dispositifs d emploi sur le devenir des jeunes chômeurs: une évaluation économétrique sur données longitudinales," Économie et Prévision, no. 115, pp Cases, C. and Lolllivier, S. (1993a), "Estimation de la durée du chômage en France en 1986," Crest working paper no Cases, C. and Lolllivier, S. (1993b), "Individual Heterogeneity in Duration Models with Segmentation," Crest working paper no Cases, C. and Lolllivier, S. (1994a), "Estimation d un modèle de sortie de chômage à destinations multiples," Économie et Prévision, no , pp Cases, C. and Lolllivier, S. (1994b), "A Structural Model of Unemployment with Multiple Destinations," Crest working paper no Danforth, J. P. (1979), "On the Role of Consumption and Decreasing Absolute Risk Aversion in the Theory of Job Search," in Studies in the Economics of Search, S.A. Lippman and J.J. McCall, eds., North-Holland. Danzinger, S., Haveman R., and Plotnick, R. (1981), "How Income and Transfer Programs Affect Work, Savings and the Income Distribution: A Critical Review," Journal of Economic Literature, vol. 19, September, pp Fishe, R. P. H. (1982), "Unemployment Insurance and the Reservation Wage of the Unemployed," Review of Economics and Statistics, vol. 64, pp , February. Florens, J. P. and Fougère, D. (1989), "Non Causality in Continuous Time: Applications to Counting Processes," Cahier Gremaq, no. 8912, Université des Sciences Sociales, Toulouse-I. Florens, J. P., Fougère, D. and Werquin, P. (1990), "Durées de chômage et transitions sur le marché du travail," Greqe working paper no. 90B07, June. Gerard-Varand, L. A., Joutard, X., Teissiere, G., and Werquin, P. (1990), "Durée du chômage et trajectoires individuelles vis-à-vis des marchés du travail. Deux études sur données micro-économiques," Rapport pour le comité Pirrtem-CNRS, Greqe-Ehess-Marseille. Ham, J. C. and Rea, A. (1987), "Unemployment Insurance and Male Unemployment Duration in Canada," Journal of Labor Economics, no. 5, July, pp Hills, S. M. (1981), "Estimating the Relationship Between Unemployment Compensation and the Duration of Unemployment: The Problem of Eligible Nonfilers," Journal of Human Resources, vol. 17, no. 3, Summer, pp Katz, F. and Meyer, B. D. (1990), "The Impact of the Potential Duration of Unemployment on the Duration of Unemployment," Journal of Public Economics, vol. 41, no. 1, February, pp Lancaster, T. (1979), "Econometric Methods for the Duration of Unemployment," Econometrica, vol. 47, pp Lancaster, T. (1985), "Simultaneous Equation Models in Applied Search Theory," Journal of Econometrics, vol. 28, pp Lancaster, T. and Chesher, A. (1983), "An Econometric Analysis of Reservation Wages," Econometrica, vol. 51, no. 6, November, pp Lancaster, T. and Nickell, S. (1980), "The Analysis of Re-unemployment Probabilities for the Unemployed," Journal of the Royal Statistical Society, A Series, vol. 143, no. 2, pp Lefèvre, C. (1996), "Couverture du risque de chômage : éléments de comparaisons internationales," Économie et Statistique, no , pp Lippman, S.A. and McCall, J.J. (1976), "The Economics of Job Search: A Survey," Economic Inquiry, vol. 14, pp Lollivier, S. (1993), "Le comportement d activité des femmes: quelques résultats sur données de panel," Crest working paper no Meyer, B. D. (1990), "Unemployment Insurance and Unemployment Spells," Econometrica, vol. 58, no. 4, July, pp Moffitt, R. (1985), "Unemployment Insurance and the Distribution of Unemployment Spells," Journal of Econometrics, vol. 28, no. 1, April, pp INSEE STUDIES no. 5, october

10 Moffitt, R. and Nickolson, W.(1982), "The Effect of Unemployment Insurance on Unemployment: The Case of Federal Supplemental Benefits," Review of Economics and Statistics, vol. 64, no. 1, February, pp Narendranathan, W. and Nickell, S. (1985), "Modelling the Process of Job Search," Journal of Econometrics, vol. 28, pp Narendranathan, W., Nickell, S. and Stern, J. (1985), "Unemployment Benefits Revisited," Economic Journal, vol. 95, pp Nickell, S. (1989), "Estimating the Probability of Leaving Unemployment," Econometrica, vol. 47, September, pp Trivedi, P.K. and Kapuchinski, C. (1985), "Determinants of Inflow into Unemployment and the Probability of Leaving Unemployment: A Disaggregated Analysis," in P.A. Volcker, ed., The Structure and Duration of Unemployment in Australia, Bureau of Labour Market Research, Monographs Series, no. 6, Canberra, Australian Publishing Service, pp Van den Berg, G. (1990), "Non stationarity in Job Search Theory," Review of Economics Studies, vol. 57, pp Wurzel, E. (1988), "Unemployment Duration in West Germany: An Analysis of Grouped Data," Bonn University, Institut für Stabilisierungs und Strukturpolitik, working paper no. 88/2. 10 INSEE STUDIES no. 5, october 1997

11 APPENDIX ESTIMATED MODEL Notations and definitions The hazard, or exit rate, is defined as the probability of escaping from unemployment at the end of a period t, on the assumption that the unemployed person has not exited previously. The probability is formulated as: P ( t T < t + d t T t ) θ ( t ) = lim. d t 0 d t It is therefore a conditional probability, and θ ( t ) = f ( t ) S ( t ), with S ( t ) = P ( T t ) = f ( u ) d u t as the "survivor function" in u. This hazard rate is estimated here on the assumption that it possesses a particular parametric form determined by the individual characteristics of the unemployed. Hazard-rate specification An earlier model based on the same data showed that the hazard could be estimated with a Weibull law (Cases and Lollivier 1993a). This specification assumes a monotonic hazard rate : θ ( t ) = α µ t α 1, α captures the trend in the variation of the hazard rate. If α < 1, the hazard decreases when the unemployment spell lengthens; if α > 1, the hazard increases (Lancaster 1990). If α = 1, the hazard is constant. The parameter µ is accordingly written as a function of several explanatory variables. Most of these describe the individual s characteristics at the start of the unemployment spell. The are noted x k, k = 1,, K. We also use a time-varying exogenous variable, x k + 1 ( t ) to characterize the benefit-payment period. We shall refer to it later on as the "dynamic variable." Its functional form will actually be very simple, since it consists in a dummy variable x k + 1 ( t ) = 1 ( τ t ), where τ is the observed benefit payment termination date. The parameter µ is ultimately written: Endogenous selection and conditional likelihood The estimation of the model is hampered by a specific difficulty here, namely, the unemployment spells reported in the sample are not fully representative of all possible unemployment spells. In other words, the sample is a stock sample subjected to an endogenous selection. The precise nature of this phenomenon may be understood if one thinks in terms of cohorts entering unemployment. The starting point is the date E0 at which the sample is drawn. Of the group of the individuals entering unemployment at the date -e, the only ones left at the date E0 are the unemployed with spells of T > e. The shortest periods are thus excluded from the sampling frame for each cohort of entrants, and this will inevitably bias the estimate of the duration distribution. Endogenous selection also makes it harder to estimate the non-parametric forms. One way of correcting the bias caused by endogenous selection would be to restrict the study to periods ranking above unity, which are not specifically subject to this selection (Lancaster 1990). This solution would, however, have the unacceptable consequence of eliminating almost three-quarters of the sample. The alternative we have chosen here is to maximize a conditional likelihood at the date of entrance into unemployment. For this, we assume ( X i, E i, T i ) can be treated as a vector of independent random variables between i different individuals with an identical distribution. We also assume the total unemployment spell T is independent of the unemployment entry date, subject to the exogenous variables xi. It should be noted that this assumption rules out any estimate of a date effect or economic-cycle effect in the model. The probability of a duration t conditional upon the unemployment entry date is thus written (Gouriéroux and Monfort 1991): λ ( t ) = θ ( t ) S ( t ) S ( e ) The likelihood of the sample is the product of the hazard rates at date t (for uncensored spells) and of the survival at the end of the survey (for censored spells). Let d be a variable with a value of 0 in the event of censoring and 1 otherwise. The likelihood is written: µ ( t ) = exp k x k β k + γ 1 ( τ t ). N S ( t i L = ) 1 d i θ ( t i ) S ( t i ) d i i = 1 S ( e i ) S ( e i ) INSEE STUDIES no. 5, october

12 APPENDIX After simplification, the log likelihood is written: N log (L) = i = 1 t i θ (u) du + d i log θ (t i ) (1) e i Without the dynamic variable, the log likelihood of equation (1) is written: N l ( d, t, e, µ, α ) = i = 1 [ d i ( log α + k x k β k + ( α 1 ) log t i ) x k β k ( t α e α ) ] k With the dynamic variable, the integrated hazard t i θ k ( u ) d u included in the likelihood has the e i value: exp ( x k β k ) ( t α i e α i ) k if τ i e i exp ( x k β k + γ ) ( τ α i e α i ) k + exp ( x k β k ) ( t α i τ α i ) k if e i τ i t i exp ( x k β k + γ ) ( t α i e α i ) k if t i τ i t i The appropriate terms for θ ( u ) d u and e i log θ ( t ) are included in the likelihood in accordance with the individual positions τi relative to ei and ti. Treatment of unobserved individual heterogeneity One of the distinctive features of the data base studied is that a substantial number of persons in the sample have experienced multiple unemployment spells. This recurrent pattern mainly concerns people reporting very brief spells, since the labor-market situations are observed for only 18 months. To capture this specific characteristic, we introduced an individual heterogeneity characteristic into the model. This effect proxies an unmeasured personal characteristic that will remain identical for all of the worker s successive unemployment spells. The introduction of a random individual effect is a method commonly used in estimating models on panel data. A standard parametric method for introducing a heterogeneity factor into Weibull-hazard duration models is to estimate a mixed hazard form of the type: θ ( t i j x i j, α, β, ν i j ) = ν i α µ t α 1 i j (2) where i is the index of the individual and j the index of the unemployment spell of individual i. Let ν i j = ν i. We assume the ν i values to be independent and identically distributed among individuals (according to the law (γ ( 1, η ) ). The log likelihood is written: L ( α, β, η ) = i where L i ( α, β, η ) = E ν i j L i ( α, β, η ) L i j ( α, β, η ) with L i j ( α, β, η ) the likelihood defined as in (1), with the form (2) for θ. One could integrate the expression in accordance with the vi distribution, but this would require fairly complex calculations. We prefer to use a simulated maximum likelihood method. This consists in sampling H occurrences of a γ ( 1, η ) variable and maximizing the simulated likelihood: s L i j H = 1 H h = 1 j L i j ( α, β, η ν i h ) The estimate of η will be obtained by iteration. This method has good convergence properties for n H 0 when the sample size n + and H + (Laroque and Salanié 1989; Gouriéroux and Monfort 1991b). Here, the number of draws H has been set at INSEE STUDIES no. 5, october 1997