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4Прикладная эконометрика, 2018, т. 52, с. 91-109. Applied Econometrics, 2018, v. 52, pp. 91-109.
Z. Nazarov1
The effect of the unemployment insurance wage replacement rate on reemployment wages: A dynamic discrete time hazard model with unobserved heterogeneity
This study estimates the effect of the unemployment insurance wage replacement rate on reemployment wages in the U.S. using the sample of men in the 1996 and 2001 Surveys of Income and Program Participation. I model employment search behavior in a dynamic discrete time hazard setting with three possible outcomes: finding a full-time job, finding a part-time job, or staying unemployed (continuing the job search). Ifind that reemployment wages decrease with the unemployment insurance wage replacement rate. Furthermore, the wage replacement rate depresses the prospect offinding full-time work while increasing the prospect of finding part-time work.
Keywords: UI wage replacement rate; reservation wage; reemployment wage; duration of unemployment; part-time employment; dynamic discrete time hazard model. JEL classification: J31; J64; J65.
he disincentive effect of unemployment insurance (UI), represented by the duration of ben-
efits, the amount of weekly benefits, and the wage replacement rate, on the prospect of reem-
ployment is well documented in the literature (Meyer, 1990; Katz, Meyer, 1990; Bover et al., 2002). Surprisingly, little attention has been paid to the effect of UI on re-entry wages after the spell of unemployment. If UI benefits depress the chances of finding a job and if an increase in the generosity of the program consequently leads to prolonged unemployment, then one would expect firms to discriminate against workers based on the duration of unemployment (Vishwanath, 1989; van den Berg, van Ours, 1999). The stigma factors may include the belief that prolonged unemployment is a possible signal of a worker's low productivity or of human capital depreciation.
The existing empirical evidence, based on unemployment spells of U.S. workers, is inconclusive about the effect of UI on the direction and magnitude of the wage premium after the period of unemployment. For example, the results from the Addison and Blackburn's (2000) study are very sensitive to the sample size and set of covariates used in the model. Although for some specifications they find a negative association between UI and reemployment wages, the final conclusion of the study is that relationships between some UI characteristics and reemploy-ment wages are positive. Another, more recent study by McCall and Chi (2008) finds evidence
1 Nazarov Zafar — Purdue University Fort Wayne, Indiana, USA; nazarovz@ipfw.edu.
1. Introduction
of a positive association between weekly benefits and reemployment wages, though this effect dissipates after 34 weeks of unemployment, and as unemployment progresses further, the effect becomes negative.
The results of any study that explores reemployment wages of workers after a period of unemployment are tremendously sensitive to the accuracy of information about the duration of unemployment and first accepted wages. The above studies use the employment history of displaced workers from surveys in which workers are asked about possible sources of unemployment and the length of unemployment in the preceding 2-5 year period after the job loss2. Therefore, the results may be biased due to inaccurate recall of the exact duration of unemployment and level of reemployment wages3. In contrast, this study uses the unemployment history of workers from the Survey of Income and Program Participation (SIPP). One of the advantages of the SIPP is that it contains monthly information on workers' employment status, and a sample of SIPP participants is interviewed monthly for several years. The short period between interviews helps to calculate with greater precision the duration of unemployment and determine as accurate as possible post-unemployment wages at the start of the first job after the period of unemployment.
In the empirical model, the main characteristic of UI that I model is the simulated wage replacement rate for each worker. I also use state-level characteristics, such as the average duration of UI benefits and the average weekly benefits. The inclusion of state-level information allows for additional sources of variation across states and time. I recognize several problems with the state or individual level UI parameters in labor force participation models. First, the state-level information may have a very weak influence on the worker's decision-making process. For instance, in my case, for a substantial fraction of workers who quit their previous jobs and therefore are not eligible for UI benefits, any changes in the UI program might not have any effect on their job search strategies. Second, UI program parameters are endogenous to labor market conditions. State authorities occasionally change the rules and level of weekly benefits as mac-roeconomic conditions in the state change. This fact might lead to a spurious correlation between replacement rate and reemployment wages. To avoid the latter problem I include in my analysis two series which capture changes in economic and labor market conditions in a given state and time such as the gross domestic product per capita and unemployment rate.
The empirical model is based on the assumption that in addition to the direct effect, the wage replacement rate indirectly affects reemployment wages through the duration of unemployment and the type of employment. I hypothesize that the most recent unemployment spell may have a negative effect on reemployment wages due to the employer's belief that a worker loses some portion of transferable human capital during a prolonged unemployment spell (van den Berg, van Ours, 1999). An additional consideration is that the longer a worker stays unemployed, the higher the propensity to accept a part-time job due to a gradual decline in his or her reservation wage. Therefore, I expect that the empirical model should provide evidence of the existence of a full-time wage premium.
2 Addison and Blackburn (2000) use the Displaced Worker Surveys for 1988, 1990, and 1992, which identify workers who were displaced from their jobs in the preceding 5-year period. McCall and Chi (2008) use the National Longitudinal Surveys from 1979 to 2002. The time gap between waves of the survey is 2 years.
3 The reemployment wages in these studies are assumed to be equal to wages on the day of the interview.
There are several important differences comparing with other studies. First, I allow for dif- | ferent exit strategies from unemployment, such as part-time and full-time reemployment. Sec- § ond, I explicitly model the non-random selection of workers into unemployment. Third, along ® with the common identification strategies, which involves inclusion of non-earned income (Mroz, 1999), marital status and number of young kids in the participation equation and exclusion these individual characteristics from the wage equation, I also use state and time level exogenous variations in Earned Income Tax Credit (EITX). Though in general EITX is a federal program, quite a lot of states have EITXs as part of their state income tax system.
Using the sample of men in the 1996 and 2001 panels of the SIPP, I find a negative association between the wage replacement rate and post-unemployment wages. I also find that the wage replacement rate affects the prospects of part-time and full-time reemployment in different ways. In particular, the hazard rate of part-time reemployment increases with the wage replacement rate, while, in contrast, the hazard rate of full-time reemployment decreases with this characteristic of the UI program. The policy simulation results also show that the generosity of UI reduces workers' reemployment wages.
The remainder of this paper is organized as follows. Section 2 explains the empirical model and the method of estimation. Section 3 discusses the data source and construction of the wage replacement rate. Section 4 discusses the primary findings of the study, and Section 5 presents my conclusions.
2. Empirical model
The main purpose of this paper is to explore the direct and indirect effect of the UI program's wage replacement rate on reemployment wages. I expect that an increase in the wage replacement rate negatively affects the worker's reemployment wage. My expectation is based on a simple search model in which the worker's reservation wage is positively affected by the generosity of the UI program (Mortensen, 1977). An increase in the reservation wage, first, increases the duration of unemployment (Mortensen, 1977). Consequently, the negative association between the duration of unemployment and the reemployment wage (Vishwanath, 1989) leads to a negative association between the wage replacement rate and the reemployment wage.
A study of the direct effect of the generosity of the UI program on the duration of unemployment and the effect of the latter on wages would be incomplete without considering the possible types of reemployment that a typical worker faces during a spell of unemployment. First, the propensity to accept part-time versus full-time work may differ over time as general economic conditions (such as the UI program's eligibility criteria and the generosity of benefits) change. Second, part-time jobs may compensate substantially less than full-time jobs. Ignoring these facts in the analysis of the relationship between the UI policy characteristics and post-unemployment wages may lead to erroneous conclusions.
Figure 1 motivates my empirical model by presenting all possible employment states and transitions faced by a worker, according to most surveys. The first wave of a survey gives us the initial pool of workers in different employment states. The substantial fraction of workers in this pool might be employed in the first reference month of the survey, while the remainder might be unemployed or out of the labor force. For those who are unemployed, the exact durations of unemployment are not observable; these observations are referred to as left-censored. This
particular problem is represented in box «Selection 1» of Figure 1. Further, following the workers, who were employed in the first reference month of the survey, economists may observe that some workers experience at least one incidence of unemployment due to layoffs or voluntarily separations. «Selection 2» in Figure 1 represents the non-random selection of workers into unemployment. For some fraction of workers, information on reemployment wages and types of reemployment is complete, while for the rest of workers, information on reemployment wages and types of reemployment is incomplete, or right-censored. The issue of right-censoring arises because either the survey ends before workers find any jobs or workers voluntarily leave the sample. Finally, for some workers search outcomes can be part-time jobs while some workers may end up with full-time jobs. This possibility is given by box «Selection 3» in the Figure 1.
The above discussion highlights three econometric issues. The first is the issue of left-censoring due to the absence of any information on some workers' initial duration of unemployment. The second is the non-random transition of workers from employment to unemployment. The final issue is the non-random transition of workers from unemployment to part-time or full-time employment.
To address the first issue, I introduce a logit equation that controls for the worker's employment status at the first reference month of the survey, (qfl) where qfl =1 if the worker was employed at period t, and qa = 0 otherwise. The set of covariates in the logit equation includes age, race, education, the region of residency and state unemployment rate included in vector X, and an unobserved time-invariant worker characteristic noted by v:
ln[Pr(qfl = 1)/Pr(qfl = 0)] = Xubq + vqa .
С
о о
CD
lo m
Nj — Worked in wave 1
N2 — Non-employed in wave 1 (left-censoring)
N3 — Always worked
N4 — experienced
spell of unemployment
<N
с
_o
о
<D
"<5
m
N5 -
Right-Censored spell
N6 — Censored spell
N7 — Part-time job Ns — Full-time job
Selection 3
Fig. 1. Employment states and transitions of workers in longitudinal surveys
The second econometric issue is the non-random selection of workers into unemployment. | Some workers may avoid unemployment in order to escape a sudden income shock or may vol- § untarily separate from the previous employer in order to get a better productivity match with ® another employer. One of the ways to avoid this issue is to include in the sample only workers who were laid off by their employers. This is the most common approach in the literature, but it substantially decreases the sample size of unemployed workers and allows us to make inferences only for the laid-off segment of the unemployed population. To ensure that the sample of unemployed workers is as complete as possible, and to address the issue of the non-random selection of workers into unemployment, another logit equation is added to the empirical model. In this logit equation, it is assumed that the log of odds of worker z's employment decision at period t, eit, follows the following process:
ln[Pr(e, =1| e,t- =1)/Pr(eit = 0| e,w =1)] = Xitbe + Zitce + ve i.
The set of controls explaining the worker's employment decision includes the same set of variables given in vector X and the time-invariant unobserved factor v. Furthermore, the probability of being employed is a function of the UI program characteristics included in vector Z. By adding Z in the above equation, I can estimate the effect of the wage replacement rate on the worker's labor market participation.
In this study, the final econometric issue, the worker's transition from unemployment to employment, is represented by a discrete time hazard model similar to those in (Bover et al., 2002) and (McCall, Chi, 2008)4. According to a standard search model, in each period, the unemployed worker receives at least one wage offer and the worker accepts a wage offer if it is higher than his or her reservation wage. Therefore, the worker's unemployment decision is modeled in the dynamic hazard setting by allowing UI program characteristics to vary over time. Furthermore, this flexible specification of the worker's job search process allows search outcomes to be represented as competing risks. In particular, in my case, the log of odds that outcome d = 0,1,2 (0 — unemployed, 1 — part-time employment, and 2 — full-time employment) will occur at any given period t is given by
ln [Pr(dit = 11 dt,t-1 = 0)/Pr(dtf = 01 di,t-1 = 0)] = Xitbd + Zc + Dg + F,nd + vd ..
The vector of parameters bd in the above equation measures the effects of sociodemograph-ic variables on part-time and full-time probabilities. These effects are restricted to be constant over time but vary across outcomes. The vector of UI characteristics Z consists of time-varying exogenous variables, which have direct impacts on the reservation wages (Kiefer, Neumann, 1979), and vector c measures the effect of these variables on both hazards. To capture time dependency of reservation wages, an additive dummy variable (D) for each quarter of unemployment is added to the model, allowing us to identify the effect (g) of an additional quarter of unemployment on reemployment probabilities (Bover et al., 2002). Two variables in the transition-to-employment equation represent family characteristics, F. These variables identify the effect of the number of children younger than 18 years old in the worker's family and the effect of the worker's marital status. Finally, v is assumed to be a time-invariant worker characteristic, which affects worker reemployment opportunities.
4 Both studies assume only a single hazard: return to full-time reemployment.
The wage equation in this study consists of the worker's accepted wage as a dependent variable and the observed duration of unemployment and type of reemployment as covariates. Both are included in vector L. The worker's reemployment wage may also vary by his or her socio-demographic characteristics, included in X. Some worker's time-invariant unobserved characteristics may also affect the reemployment wage and, in the above specification, they are included in v. Finally, a mean zero and an identically independent error term, u, conclude the possible factors that determine the worker's reemployment wage:
ln Wlt = X tbw + Lltq + vWi + uwU.
Assuming that variables in the vector X are not correlated with the unobserved error terms v and u, and that the latter two terms do not correlate with each other, I expect two potential en-dogeneity problems in the above wage equation. The duration of unemployment and type of re-employment may correlate with unobserved factors. For instance, the more motivated worker may be more likely to find any type of job more quickly, or an employer may offer a higher wage to the more motivated worker even if he or she experienced a prolonged unemployment spell. I assume that the UI program characteristics affect the reemployment wage only through the duration of unemployment and type of reemployment. Therefore, UI program characteristics may serve as instruments to solve the above-discussed endogeneity problems.
I could simply use an IV approach to consistently estimate parameters of interest without estimating the more complicated model. However, such a simple solution has a substantial limitation. Several studies (Addison, Portugal, 1989; Seninger, 1997) model the first stage with a To-bit model. Such a model ignores the dynamic features of the UI program and does not allow for multiple exit strategies. The eligibility criteria and UI benefit levels change throughout the spell of unemployment, and the propensity of finding a part-time or full-time job varies with changes in UI program characteristics. This argument justifies the use of the model proposed by this study.
To estimate the mixed continuous discrete model represented by my equations with endogenous explanatory variables in the wage equation, I use the discrete factor method (Mroz, Guilkey, 1995; Mroz, 1999) in this study. Instead of imposing a parametric joint distribution for unobserved factors Vj, the study uses a step function with a finite number of points to approximate the distribution of the unobserved factors (Heckman, Singer, 1984). In the discrete factor method, the parameters determining the step function are estimated jointly with other parameters of the model. Furthermore, the flexible specification of the common unobserved worker heterogeneity component, vj in all equations, allows for correlation across the system of equations and correlation across competing risks. The derivation of the likelihood function can be found in Appendix of the paper.
2.1. Identification
Identification of the main parameters of the model, associated with the observed duration of unemployment and type of reemployment, in this model is secured by exclusion restrictions and the dynamic structure of the model. Along with the non-earned income, marital status and number of kids less than 18 years old, I include information about worker's eligibility and amount of EITX benefits in Z that allow for identification through theoretical exclusion restrictions. In calendar year 2003, state income tax systems of fourteen states and the District of Columbia in the US had EITXs as the part of their systems. Table 1 summarizes the param-
о
Table 1. State earned income tax credits
Type of credit Year adopted State % of Federal Credit
Refundable credits 1999 Colorado 10
2000 DC 25
1998 Kansas 10
1987 1997 Maryland Massachusetts 16 15
1991 Minnesota 33
2000 1994 New Jersey New York 15 25
1988 Vermont 32
1989 Wisconsin 4 (1), 14 (2), 43 (3)
Nonrefundable credits 2000 Illinois 5
1990 Iowa 6.5
2000 Maine 5
1997 1975 Oregon Rhode Island 5 25.5
Source: Hotz and Scholz (2003).
Table 2. Earned income tax credit parameters, 1996-2003 (in nominal dollars)
Year # of depend. Phase-in Phase-in Max rate % range ($) credit ($) Phaseout rate (%) Phaseout range ($)
1996 1 34 0-6330 2152 15.98 11610-25078
< 1 40 0-8890 3556 21.06 11610-28495
0 7.65 0-4220 323 7.65 5280-9500
1997 1 34 0-6500 2210 15.98 11930-25750
< 1 40 0-9140 3656 21.06 11930-29290
0 7.65 0-4340 332 7.65 5430-9770
1998 1 34 0-6680 2271 15.98 12260-26473
< 1 40 0-9390 3756 21.06 12260-30095
0 7.65 0-4460 341 7.65 5570-10030
1999 1 34 0-6800 2312 15.98 12460-26928
< 1 40 0-9540 3816 21.06 12460-30580
0 7.65 0-4530 347 7.65 5670-10200
2000 1 34 0-6920 2353 15.98 12690-27413
< 1 40 0-9720 3888 21.06 12690-31152
0 7.65 0-4610 353 7.65 5770-10380
eters of state credits. The main feature of Table 1 is that the EITX parameters vary by state and were adopted in different years. The latter fact should help to provide enough of exogenous variation in the replacement rate to identify the effect in the wage and participation equations. Table 2 summarizes the main parameters of the federal credits, which I used to construct the EITX eligibility and benefit amount for each worker.
End of the Table 2
Year # of depend. Phase-in Phase-in Max Phaseout Phaseout
rate % range ($) credit ($) rate (%) range ($)
2001 1 34 0-7140 2428 15.98 13090-28281
< 1 40 0-10020 4008 21.06 13090-32131
0 7.65 0-4760 364 7.65 5950-10708
2002 1 34 0-7360 2506 15.98 13490-39202
< 1 40 0-10320 4140 21.06 13490-33178
0 7.65 0-4910 376 7.65 6130-11060
2003 1 34 0-7580 2547 15.98 13890-29666
< 1 40 0-10620 4204 21.06 13890-33692
0 7.65 0-5060 382 7.65 6310-11230
Source: 1996-2001 parameters come from Hotz and Scholz (2003), 2002-2003 parameters come from Internal Revenue Service Publication 596.
The dynamic structure also secures the identification of this model (Mroz, Savage, 2006). For instance, the transition-to-employment equation represents the probability of finding a parttime or full-time job at period t, conditional on not finding any job at period t — 1. The non-wage income at period t — 1 has a direct impact on the worker's unemployment decision at period t — 1, but it does not directly affect the worker's decision to stay unemployed at period t. However, the none-wage income at period t — 1 indirectly affects the worker's employment decision at period t through his or her employment decision at period t — 1, which is why it can serve as the additional instrumental variable. The same argument holds for the other time-variant exogenous variables in this study, which implies multiple sources of identification through the dynamic structure of the model.
3. Data and the construction of the wage replacement rate
The data source for my study is the Survey of Income and Program Participation (SIPP). The SIPP contains detailed information on workers' demographic and job characteristics. Sample SIPP participants are interviewed monthly for several years. In the 1996 panel, respondents were interviewed over a period of 48 months5, while in the 2001 panel they were interviewed for only 36 months. As discussed earlier, one of the advantages of the SIPP over other surveys is that it contains monthly information on workers' employment status. This information helps us precisely calculate the duration of unemployment spells and determine wages and working hours at the first job after the period of unemployment.
Table 3 demonstrates that the sample consists of 36973 male workers6. In the sample, 5430 workers were unemployed at the first survey wave. Information about these workers is included only in the equation that controls for the left-censoring issue, and they are not followed after the first wave. In the remaining portion of the sample, 3007 workers were un-
5 In my study, I use only the first 36 months of the 1996 panel.
6 Anyone in the panels who was employed in agricultural or construction industries was dropped from the sample. Furthermore, self-employed workers are not included in the final sample.
employed at some point during the next three years. These numbers imply that almost 10% | of workers in the sample experienced at least one incidence of unemployment in the succeed- § ing months. Only 2309 workers who reported incidences of unemployment in the succeed- ® ing months had complete unemployment spells7. For 698 workers, the exact durations of unemployment are not observable due to the right-censoring problem8. Among those whose spells were complete, 533 workers ended up with part-time jobs. This number implies that the part-time reemployment rate is 23% for men in the SIPP, which is slightly higher than statistics in the Current Population Survey. The possible explanation can be the fact that the SIPP oversamples the low income segment of the population which has the higher prevalence of part-time employment.
Table 3. Employment states and transitions of male workers in SIPP 1996-2001
Description #
Number of respondents in wave 1 36973
Unemployed 5430
Employed 31543
Number of unemployment spells 3007
Number of censored spells 2309
Part-time jobs 533
Full-time jobs 1776
Notes. Contingent workers are excluded from the sample.
Workers employed in agricultural and construction industries are excluded from the sample. Workers who are non-employed due to retirement or full-time school enrollment are excluded from the sample.
The state identifier in the survey helps merge information about the monthly unemployment rate and the average duration and amount of UI benefits by state. These state-level time-variant variables are extracted from U.S. Department of Labor data. Data from the Bureau of Labor Statistics provides information on consumer price indices from December 1995 through December 2003. All variables are normalized to 1995 dollars.
One of the key predictors in this study is the predicted UI program wage replacement rate for which a worker is eligible. To calculate this predictor, I first simulate UI benefits for each worker as a function of the average monthly earnings in the past 8 months, plus some sociode-mographic characteristics of the worker and state-specific characteristics, such the unemployment rate, the average duration of UI benefits, and the average benefit amount9. The parameters used in the simulation of UI benefits come from the regression of the actual benefit amounts on the predictors, which define the level of benefits, controlling for the possible sample selection
7 Complete unemployment spells are spells for which reemployment is observable before the last month of the panels.
8 The right-censored observations are observations for which unemployed spells are not complete at the end of the panels.
9 Sociodemographic variables include whether a worker is married and the number of children less than 18 years old in the family. In some states, these worker-specific characteristics define the level of benefits.
of workers into the UI program. The latter is performed by simultaneously estimating both UI benefits and UI program participation specifications using only the sample of unemployed workers in the 1996 and 2001 panels10. The variables included in the UI program participation equation and the estimates from both equations are presented in the appendix (Table A.1).
4. Results
4.1. The effect of unemployment duration on reemployment wages
In the first three columns of Table 4, I report the results of the wage equation obtained using the maximum likelihood method, however, without accounting for worker's unobserved heterogeneity. The estimates of the wage equation are comparable with the estimates obtained using the more conventional method, Ordinary Least Square (OLS). The duration of unemployment in this specification enters in a linear form and I also allow for interaction of the duration of unemployment and replacement rate. Assuming the orthogonal relationship between the duration of unemployment and the error term, I find that the duration of unemployment parameter is -0.04 (p < 0.001). This estimate implies that a one-month increase in the duration of unemployment decreases men's average wages by 4.0% if the replacement rate is equal to 0. For the replacement rate around of 67%, the negative effect of duration of unemployment disappears. In addition, using the same method of estimation and assuming the orthogonal relationship between part-time employment and the error term, I find that the part-time reemployment parameter has a value of -0.13 (p < 0.001), which can be interpreted as a 13% full-time wage premium for those who find full-time jobs.
I should be careful, however, in making any inferences on the basis of the results obtained using the conventional method. Table 4 demonstrates that after controlling for unobserved worker heterogeneity (Model 2), the size of the duration effect and interaction with the replacement rate increases. The results of Model 2 imply that a one-month increase in the duration of unemployment decreases men's average wages by 5.0% if the replacement rate is equal to 0 and this negative effect disappears for the replacement rate around of 71%. Based on these findings I can speculate that UI insurance benefits serve as a cushion, especially, for the workers with low earnings and high replacement rates.
I also find that the size of the full-time wage premium substantially increases in magnitude in Model 2. The estimate of the full-time wage premium implies that, on average, full-time jobs pay 19% more than part-time jobs if the worker's motivation and ability are taken into account. The increase in magnitude of the part-time employment parameter may indicate that the more motivated and able worker's part-time wage is significantly higher than the part-time wage of the less able and motivated worker. Therefore, in the conventional method, the part-time employment parameter captures the positive effect of unobserved factors on wages.
10 According to Gruber (1997), only 60% of eligible workers actually receive UI benefits during unemployment.
Table 4. Wage equation
Model 1 Model 2 Model 3
Est. Error z-stat. Est. Error z-stat. Est. Error z-stat.
Constant 1.68 0.52 3.24 1.59 0.48 3.29 0.77 0.64 1.21
Part-time job -0.13 0.04 -3.20 -0.19 0.06 -3.44 -0.18 0.06 -2.97
Business cycle characteristics
State unemployment rate 0.01 0.02 0.64 0.01 0.01 0.63 0.01 0.02 0.27
State GDP per capita 0.01 0.00 2.95 0.01 0.00 3.35 0.01 0.00 3.03
UI characteristics
State average length of UI 0.00 0.00 0.62 0.01 0.00 1.57 0.01 0.00 1.58
State average UI benefits 0.14 0.10 1.47 0.15 0.10 1.53 0.14 0.10 1.34
UI replacement rate (UI RR) -0.01 0.00 - 10.32 -0.01 0.00 -9.23 0.00 0.00 -0.76
Length of the spell
Total -0.04 0.01 -4.15 -0.05 0.01 -3.09 — — —
1 to 4 months 0.76 0.20 3.85
5 to 8 months 0.49 0.21 2.39
9 to 12 months 0.29 0.38 0.77
13 to 16 months 0.11 0.26 0.41
Interaction terms
UI RR x Total x 100 0.06 0.00 2.58 0.07 0.00 2.78 — — —
UI RR x (1 to 4 months) x 100 -0.88 0.00 -2.34
UI RR x (5 to 8 months) x 100 -0.40 0.00 -0.97
UI RR x (9 to 12 months) x 100 -0.11 0.01 -0.21
UI RR x (13 to 16 months) x 100 0.17 0.00 0.38
Year
1997 0.04 0.05 0.78 0.04 0.07 0.57 0.04 0.08 0.44
1998 0.10 0.07 1.42 0.09 0.07 1.27 0.09 0.08 1.10
2001 0.14 0.05 2.96 0.12 0.07 1.88 0.12 0.07 1.67
2002 0.13 0.05 2.34 0.11 0.05 2.22 0.10 0.05 1.98
2003 0.17 0.06 2.65 0.14 0.07 2.09 0.15 0.06 2.55
Race
Black -0.15 0.04 -3.78 -0.13 0.04 -3.36 -0.13 0.04 -3.31
Asian 0.00 0.08 -0.03 -0.01 0.08 -0.13 -0.02 0.08 -0.21
Other -0.03 0.07 -0.49 -0.05 0.07 -0.75 -0.06 0.07 -0.77
Education
High school 0.11 0.04 2.47 0.07 0.04 1.98 0.08 0.04 2.17
Some college 0.17 0.05 3.83 0.18 0.04 4.62 0.19 0.04 4.73
College 0.30 0.05 5.60 0.30 0.08 3.77 0.30 0.07 4.49
Advanced degree 0.46 0.07 6.71 0.36 0.06 5.84 0.37 0.06 5.93
Age group
From 30 to 40 0.01 0.04 0.14 0.04 0.04 0.83 0.03 0.04 0.77
From 40 to 50 0.05 0.04 1.30 0.06 0.04 1.71 0.06 0.04 1.53
From 50 to 60 -0.03 0.05 -0.54 0.04 0.04 1.03 0.04 0.05 0.90
Above 60 0.28 0.11 2.51 0.33 0.23 1.42 0.33 0.31 1.06
Mass Point 1 (p = 0.385) 0 0 0 0 0 0 0 0 0
Mass Point 2 (p2 = 0.015) 0 0 0 1.84 0.20 9.03 1.81 0.22 8.33
Mass Point 3 (p3 = 0.600) 0 0 0 -3.74 1.38 2.70 -3.66 1.41 2.59
Log Likelihood -41590.22 -41272.05 -41265.03
Number of parameters 161 173 179
Notes. Sample of 36973 men using SIPP 1996-2001. Boldness of an estimate indicates onp < 0.1. Model 1 doesn't account for individual unobserved heterogeneity. Model 2 accounts for individual unobserved heterogeneity.
Model 3 accounts for individual unobserved heterogeneity and duration is presented in a more flexible way and interacted with the UI replacement rate.
In addition, the likelihood ratio test for the joint significance of the heterogeneity parameters provides additional evidence in favor of the more complicated model. The calculated statistic for the test is 636.34 (p-value < 0.001). The test confirms that the model with controls for the possible correlations between variables of interest and unobserved factors provides significant improvement in the value of the log likelihood function compared with the simpler model.
In the last three columns of Table 4, I report the results obtained using the more flexible specification of the duration of unemployment in the wage equation (Model 3). In particular, the duration of unemployment enters as a set of dummies and each dummy indicates on the specific duration of unemployment. In particular, I recognize five groups by duration of unemployment such as 1 to 4 months, 5 to 8 months, 9 to 12 months, 13 to 16 months and more than 16 months11. The latter group is used as a reference group in my analysis. Moreover, I also create interactions between the set of duration dummies and the simulated wage replacement rate in the wage equation. I use Model 3 to check whether the relationship between the duration of unemployment and wages can be non-linear.
The more flexible approach of modeling the duration of unemployment shows those workers who find jobs in first 8 months benefit from higher wages than workers with more prolonged unemployment spells. Within the former group, workers who find jobs in first 4 months receive even higher wage premiums from quicker reemployment. Though, the gain in wages from quicker return to work is depressed by the negative effect of the interaction term for the replacement rate and duration of unemployment. However, the latter is only true for workers with high replacement rates.
These results may suggest that the «true» relationship between duration of unemployment and wages is non-linear and there is no a significant difference in wages between workers with spells of unemployment 9 months and say 36 months, but there is a significant difference in wages for workers with spells 4 months and 9 months.
4.2. Selection into unemployment and back to employment12
The distinctive feature of my empirical model is that I control for the non-random selection of workers into unemployment. The first three columns of Table 5 provide a glimpse into the estimates for the transition-to-employment equation, and I would like to draw attention to two important facts. First, because of the statistical significance at the >10% level of the substantial number of the estimates in Table 5, I can conclude that the transition from employment to unemployment is not a random event. Second, based on the sign and magnitude of the wage replacement rate parameter, I can speculate that a worker with a high replacement rate has a higher likelihood of being displaced by an employer compared with a worker with a low replacement rate. This finding is somewhat similar to those of Baker and Rea (1998) and Jurajda (2002), who report the increasing hazard of unemployment among UI-eligible workers.
11 Instead of monthly duration dummies I use quarterly dummies due to some peculiarities of the data. Although the SIPP contains monthly information on workers' employment status, interviews are conducted monthly. As a result, one can observe discontinuities in reemployment probabilities for every 4 months.
12 The results from the logit equation, which controls for the left-censoring issue, are not presented in this paper but can be requested from the author.
The next six columns in Table 5 demonstrate the estimates from the transition-to-employ- | ment equation. I find that a higher average duration of UI benefits in a given state also decreas- § es the likelihood of any type of reemployment. This fact is compatible with the findings of the ® other studies (McCall and Chi, 2008; Bover et al., 2002) that the longer one receives UI benefits, the longer one would stay unemployed.
Table 5. Results from the model with unobserved heterogeneity
for the Employment-to-Unemployment and Unemployment-to-Employment equations
E-to-U transition U-to-E part-time work U-to-E full-time work
transition transition
Est. St.Err. z-stat. Est. St.Err. z-stat. Est. St.Err. z-stat.
Constant 5.82 1.08 5.39 -6.21 1.38 -4.51 -2.48 0.89 -2.78
Business cycle characteristics
State unemployment rate -0.11 0.02 -4.39 0.05 0.05 1.07 -0.06 0.03 -2.36
State GDP per capita 0.00 0.00 0.51 -0.02 0.01 -1.80 0.01 0.01 1.41
UI characteristics
State average length of UI -0.01 0.01 -2.24 -0.01 0.01 -0.70 -0.02 0.01 -2.20
State average UI benefits -0.07 0.20 -0.37 0.47 0.28 1.69 -0.05 0.17 -0.31
UI replacement rate -0.01 0.00 -13.29 0.003 0.00 1.45 -0.01 0.00 -7.43
Exclusion restrictions
Non-earned income -0.18 0.02 -9.78 -0.05 0.04 -1.20 -0.08 0.02 -3.08
Average non-earned income 0.12 0.02 4.65 0.09 0.05 1.91 0.10 0.03 3.72
Refundable EITX 0.05 0.03 1.64 -0.41 0.06 -6.70 -0.32 0.03 -10.17
Non-refundable EITX -2.42 0.81 -2.99 -1.18 1.70 -0.69 0.99 1.01 0.99
Eligible for refundable EITX -1.66 0.06 -25.56 1.93 0.14 14.16 1.61 0.07 22.06
Eligible for nonrefundable EITX 0.16 0.11 1.43 -0.13 0.24 -0.55 -0.33 0.14 -2.30
Number of kids less 18 years 0.09 0.02 3.82 0.04 0.05 0.75 0.01 0.03 0.50
Marital status 0.57 0.07 7.85 0.25 0.12 2.01 0.26 0.07 3.74
State dependency
From 1 to 4 months — — — 0.32 0.27 1.18 1.41 0.20 6.97
From 5 to 8 months — — — 0.38 0.27 1.37 1.28 0.21 6.15
From 9 to 12 months — — — 0.25 0.30 0.82 0.99 0.22 4.50
From 13 to 16 months — — — 0.09 0.36 0.27 0.71 0.26 2.76
Year
1997 0.06 0.07 0.90 -0.32 0.16 -1.98 -0.31 0.09 -3.34
1998 0.28 0.08 3.32 -0.25 0.18 -1.36 -0.35 0.10 -3.55
2001 -0.20 0.07 -2.94 -0.14 0.17 -0.82 -0.19 0.10 -2.04
2002 -0.25 0.07 -3.31 -0.40 0.17 -2.41 -0.31 0.09 -3.25
2003 -0.24 0.09 -2.60 -0.02 0.21 -0.08 0.22 0.12 1.93
Race
Black -0.38 0.08 -5.01 -0.01 0.14 -0.09 -0.28 0.08 -3.55
Asian -0.51 0.17 -2.95 -0.01 0.32 -0.04 -0.32 0.20 -1.56
Other -0.28 0.11 -2.59 -0.48 0.22 -2.23 -0.44 0.12 -3.60
Education
High school 0.39 0.10 3.86 -0.15 0.14 -1.07 0.20 0.08 2.66
Some college 0.38 0.11 3.41 0.26 0.14 1.90 0.29 0.08 3.73
College 0.37 0.13 2.75 0.30 0.16 1.85 0.31 0.09 3.53
Advanced degree 0.44 0.15 2.87 0.65 0.19 3.50 0.18 0.11 1.61
Age
From 30 to 40 0.01 0.07 0.16 -0.09 0.15 -0.62 -0.32 0.08 -3.85
From 40 to 50 0.14 0.07 1.93 -0.24 0.15 -1.58 -0.42 0.08 -4.97
End of the Table 5
E-to-U transition
U-to-E part-time work transition
U-to-E full-time work transition
Est. St.Err. z-stat. Est. St.Err. z-stat. Est. St.Err. z-stat.
From 50 to 60 0.23 0.10 2.38 -0.38 0.17 -2.18 -0.56 0.09 -5.95
Above 60 0.21 0.20 1.04 -0.35 0.33 -1.06 -1.02 0.23 -4.45
Mass Point 1 (p1 = 0.385) 0 0 0 0 0 0 0 0 0
Mass Point 2 (p2 = 0.015) 0.25 0.45 0.56 1.49 0.40 3.71 -0.20 0.37 0.54
Mass Point 3 (p3 = 0.600) 5.85 1.16 5.06 0.16 0.38 0.43 -0.43 1.29 0.33
Notes. Sample of 36973 men using SIPP 1996-2001. Boldness of an estimate indicates onp < 0.12. Model 3 accounts for individual unobserved heterogeneity and duration in the wage equation is presented in a more flexible way and interacted with the UI replacement rate.
I also find evidence that the wage replacement rate has a significant impact on the reemploy-ment hazards. First, an increase in the wage replacement rate increases the probability of parttime reemployment (although the estimate is not statistically significant at 0.1). At the same time, as expected, a higher wage replacement rate diminishes the prospect of finding a full-time job. The negative effect of the wage replacement rate on the full-time reemployment hazard can be explained by the fact that an increase in the replacement rate increases the worker's reservation wage, decreasing the number of acceptable full-time vacancies in the labor market and depressing the prospect of full-time reemployment.
I can explain the positive effect of the wage replacement rate on part-time reemployment by the eligibility rules of the UI program in the United States. The existing eligibility rules allow a worker receiving UI benefits to accept a part-time job without losing any benefits if his or her earnings from part-time employment do not exceed a certain amount13. A worker with a high replacement rate may be inclined to accept a part-time job as a temporary solution to his or her progressing unemployment14.
Table 5 provides evidence for non-stationary nature of the reservation wage (Kiefer, Neumann, 1979) in the job search process. The results show that the baseline hazard for full-time reemployment varies as unemployment progresses while the baseline hazard is almost constant. This fact can be seen from the estimates of the set of dummies identifying the number of quarters one has been unemployed already. The decreasing baseline hazard for full-time reemployment and non-changing one for part-time reemployment serve as support of the hypothesis that a discouraged worker who initially had a strong preference for full-time reemployment accepts a part-time job due to a gradual decline of his reservation wage.
4.3. Simulation
The main question of interest this study is the effect of the wage replacement rate on re-employment wages. To quantify the size of this effect, I simulate a 10% increase in the wage replacement rate. Along with the log of wages and duration of unemployment in months for workers, I compute the change in the fraction of unemployed workers who find part-time jobs
13 Also referred to as the «disregard level».
14 McCall (1996, 1997) finds that the UI program positively affects the worker's part-time reemployment probability.
and the percentage change in the part-time and full-time wage differential due to the policy | change. g
As expected, the proposed increase in the wage replacement rate decreases average reem- ® ployment wages. A simple comparison of the estimates for the mean of the log of wages and duration of unemployment in columns 2 and 4 of Table 6 reveals that the average wages decrease by 8.6% after a 10% increase in the wage replacement rate while the average duration of unemployment increases by 0.346 months. This implies that the wage elasticity with respect to the wage replacement rate is -0.86 and reemployment wages are sensitive to changes in the wage replacement rate.
These interesting results can be observed for the effects of the change in the wage replacement rate on part-time versus full-time reemployment wages and the fraction of part-time workers. A 10% increase in the wage replacement rate decreases average part-time wages by 6.1% and average full-time wages by only 8.6%. At the same time, the proposed policy increases the fraction of the workers who find part-time jobs. A 10% increase in the wage replacement rate increases the fraction of part-time workers by 2.1%.
Table 6. The effect of the wage replacement rate on wages and the proportion of part-time workers. Men
Variable Baseline +10% WRR
Mean St. Err Change St. Err.
Duration of unemployment (all workers) 7.065 0.0147 0.346 0.0043
Duration of unemployment (only part-time workers) 6.645 0.0275 0.187 0.0076
Duration of unemployment (only full-time workers) 5.485 0.0108 0.174 0.0032
Overall log of hourly wage rate 2.315 0.0024 -0.086 0.0004
Log of hourly part-time wage rate 2.093 0.0062 -0.061 0.0009
Log of hourly full-time wage rate 2.384 0.0021 -0.086 0.0004
Fraction of part-time workers 0.236 0.0011 0.021 0.0004
Full-time vs. part-time wage differential 0.291 0.0060 -0.025 0.0009
Notes. The sample consists of 23613 men from 1996 and 2002 panels of the SIPP. The estimates from Model 3 are used in simulation.
The total number of bootstraps is 251 including one without perturbing coefficients and 250 bootstraps with perturbing coefficients with random draws drawn from the multivariate distribution.
Using the results from the policy simulation, I can draw a conclusion that the UI program affects both part-time and full-time wages. A fraction of workers who are most affected by the increase in the wage replacement rate may transition more rapidly from unemployment to parttime employment after the policy change. Some of these workers would have found full-time jobs if the wage replacement rates were at the previous levels, and I suspect that these workers are less motivated and able workers. The movement of these workers from full-time employment to part-time employment positively affects the mean of full-time wages because these workers possess unobserved characteristics that negatively affect wages. However, I expect that the average duration of unemployment for full-time workers increases after the policy change (my findings support this expectation). The latter fact should have a negative impact on full-time wages. As a result, the combined effect of an increase in the wage replacement rate on full-time wages is negative, mostly because the duration effect compensates for the substitution effect.
The departure of some fraction of the less motivated and able workers with lower-than-average part-time wages to part-time employment decreases the mean of part-time wages. In the meantime, after the policy change, it takes also longer (on average) to find a part-time job. This fact also depresses the mean of part-time wages. As a result the combined effect is negative.
5. Conclusion
Using the 1996 and 2001 panels of the SIPP, I find evidence of the existence of a negative association between the wage replacement rate and post-unemployment wages. Moreover, my results show that workers with higher wage replacement rates are more likely end up with parttime jobs while at the same time they less likely find full-time jobs. I also find that part-time jobs compensate significantly less than full-time jobs.
One of the possible shortcomings of this study is that it ignores the other possible mechanisms of the effect of UI on reemployment wages. The generosity of UI may increase the resources devoted to the employment search that may lead to higher reemployment wages. I do not incorporate this possible mechanism in my empirical model because I cannot observe the monetary resources that a worker allocates to the job search during the period of unemployment. This would be important to tackle in future research.
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Received 22.10.2017; accepted 05.12.2018.
Appendix
Derivation of the likelihood function
The estimation strategy used in this paper assumes that there are M points of support to approximate distribution of v. Conditional on mass point vk = (vq,ve, vd,vw), individual i has the following contribution to the likelihood function:
Ak (vt ) = [ Pr (qfl =1|Vq )f [ Pr (qfl = 0|v„ J]-" Щ Pr (ea =1|v, )J" [ Pr = 0|v„J
T2 к
ХПП[ Pr (d = jjVd)]
1—
Х
Ti2 K
—------i4t [ wT -m
q-
i=Tj+i j=o V s
Vw
/
where
qi1 e {0 — unemployed, 1 — employed} — employment status at period 1;
eit e {0 — unemployed, 1 — employed} — employment status at period t;
T — the period when the worker transitions from employment to unemployment;
Ti2 — the period when the worker transitions from unemployment to employment;
dit e {0 — unemployed, 1 — part-time job, 2 — full-time job} — job search outcome at period t; wiT — reemployment wage rate at period T;
< — the probability density function of a random normal variable (wiT) with mean m and variance s.
The unconditional contribution for individual i is:
M
A =2pkA,
k=1
where pk — the probability for mass point vk with M — the number of assumed mass points. Finally, the likelihood function can now be written as follows:
I
L=n a,
i=1
where I is the number of individuals in the sample.
Table A.1. UI benefit
Participation in UI (first stage)
Benefit (second stage)
Est. Std. Error z-stat. Est. Std. Error z-stat.
Constant -5.44 0.42 -12.93 6.77 0.44 15.25
State unemployment rate 0.07 0.01 5.68 -0.09 0.01 -6.65
# kids under 18 -0.04 0.01 -3.93 0.07 0.01 5.49
Married 0.13 0.03 4.82 -0.10 0.03 -3.32
Race
Black -0.12 0.02 -4.70 — — —
Asian -0.19 0.06 -2.98 — — —
Other -0.12 0.04 -3.41 — — —
Education
High school 0.15 0.03 5.78 — — —
Some college 0.19 0.03 7.41 — — —
College 0.12 0.03 3.90 — — —
Professional degree 0.08 0.03 2.33 — — —
Age
From 30 to 40 0.03 0.03 0.94 — — —
From 40 to 50 0.11 0.03 3.73 — — —
From 50 to 60 0.16 0.03 4.95 — — —
Above 60 0.20 0.05 4.02 — — —
UI program
Average benefit duration 0.01 0.00 1.63 0.00 0.00 -1.02
Average benefit amount 0.46 0.08 6.00 0.15 0.08 1.93
State residency
Southeast -0.19 0.03 -6.58 -0.83 0.13 -6.63
Northeast -0.01 0.03 -0.51 -0.83 0.13 -6.55
Midwest -0.10 0.03 -3.57 -0.44 0.13 -3.30
Southwest -0.20 0.03 -6.29 -0.10 0.15 -0.63
End of the Table A.1 ^
- S
Participation in UI Benefit
(first stage) (second stage)
Est. Std. Error z-stat. Est. Std. Error z-stat.
State dependency
From 1 to 4 months 1.52 0.09 16.30 — — —
From 5 to 8 months 1.47 0.09 15.49 — — —
From 9 to 12 months 0.93 0.10 9.22 — — —
From 13 to 16 months 0.46 0.12 3.86 — — —
Year
1998 0.05 0.04 1.11 -0.03 0.05 -0.60
1999 0.02 0.05 0.49 -0.06 0.06 -1.01
2001 0.11 0.04 2.56 -0.08 0.05 -1.74
2002 0.25 0.04 5.73 -0.07 0.05 -1.52
2003 0.25 0.05 5.22 0.07 0.05 1.30
Rho -0.95 0.00 -281.96 — — —
Sigma 0.99 0.02 55.20 — — —
Lambda -0.94 0.02 -48.37 — — —
Notes. Sample consists of 16199 person/month observations using the SIPP 1996-2002. First stage dependent variable: amount of UI benefits in a given month.
Second stage dependent variable: whether participate in UI program in a given month conditional on being unemployed in that month.
