sanctions in Boone et al (2002) involves choosing m optimally along with the other policy parameters. These features carry over to the present analysis, i.e., there exist interior solutions for m in both the time limits and the monitoring-cum-sanctions system. 7 However, it turns out that the optimalworkfare system with m chosen optimally along with b and p entails a positive but infinitesimally small value of m. To understand this result, note that a rise in m means that workers receiving UI are transferred to a less favorable state at a higher rate, thus implying a first-order negative welfare effect. Other effects, such as the induced effects on tightness, may conceivably offset the first-order effect. In our simulation results, however, the potentially offsetting indirect effects are not sufficiently strong to offset the first-order effect. It thus follows that although m must be strictly positive, is should be set as small as possible. Of course, a workfare system requires m>0, otherwise no screening would take place.
The computation of unemployment durations using the survey responses are described in Appendix C. It is helpful to have a sense of the mean unemployment exit hazards in the sample before analyzing the eﬀect of covariates on these hazards. 29 The solid line in Figure 2 shows the empirical hazards for the core sample. Though the hazard rate fluctuates throughout, there are sharp spikes at t = 17 and t = 35. These spikes reflect a reporting artefact known as the “seam eﬀect,” which is common in longitudinal panels such as the SIPP. To see how the seam eﬀect arises, recall that the SIPP data is collected by interviewing individuals every four months about their activities during the past four months, which is termed the “reference period.” Individuals tend to repeat answers about weekly job status. As a result, they under-report transitions in labor force status within reference periods and overreport transitions on the “seam” between reference periods. Hence, many spells of unemployment appear to last for exactly the length of one or two reference periods, which correspond to lengths of 17 and 35 weeks. The dashed hazard function plotted in Figure 2 shows the empirical hazards for spells that did not begin on a seam, and as one would expect, the two spikes no longer exist. 30 The potential for bias from the seam eﬀect is addressed below.
I have benefited from discussions with Joseph Altonji, Alan Auerbach, Olivier Blanchard, Richard Blundell, David Card, Liran Einav, Martin Feldstein, Amy Finkelstein, Jon Gruber, Jerry Hausman, Caroline Hoxby, Juan Jimeno, Kenneth Judd, Lawrence Katz, Patrick Kline, Bruce Meyer, Ariel Pakes, Luigi Pistaferri, Emmanuel Saez, Jesse Shapiro, Robert Shimer, Adam Szeidl, Ivan Werning, anonymous referees, and numerous seminar participants. Philippe Bouzaglou, Greg Bruich, David Lee, Ity Shurtz, Jim Sly, and Philippe Wingender provided excellent research assistance. I am very grateful to Julie Cullen and Jon Gruber for sharing their unemployment benefit calculator, and to Suzanne Simonetta and Loryn Lancaster at the Dept. of Labor for assistance with state UI laws. Funding from the National Science Foundation and NBER is gratefully acknowledged. The data and code used for the empirical analysis and numerical simulations are available on the author's website. The views expressed herein are those of the author(s) and do not necessarily reflect the views of the National Bureau of Economic Research.
In the insurance literature, there has been much interest towards using optimality considerations, including optimal stopping problems. From the standpoint of insurer seeking to maximize their expected returns, the optimal stopping time may be interpreted as the time to suspend the current trading if the situation is unfavorable, and to recalculate premiums; see, e.g., Jensen (1997); Karpowicz and Szajowski (2007); Muciek (2002); and further references therein. Insurance research has also focused on optimality from the individual’s perspective. One important direction relevant to the UI context was the investigation of the job seeking processes, especially when returning from the unemployed status (Boshuizen and Gouweleeuw 1995; McCall 1970; Wang and Wirjanto 2016). This was complemented by a more general research exploring ways to optimize and improve the efficacy of the UI systems (also in terms of reducing government expenditure), using incentives such as a decreasing benefit throughout the unemployment spell, in conjunction with sanctions and workfare; see Fredriksson and Holmlund (2006); Hairault et al. (2007); Hopenhayn and Nicolini (1997); Kolsrud et al. (2018); Landais et al. (2017), to cite but a few. A related strand of research is the study of optimal retirement strategies in the presence of involuntary unemployment risks and borrowing constraints (Choi and Shim 2006; De Angelis and Stabile 2019; Gerrard et al. 2012; Jang and Rhee 2013; Stabile 2006).
eﬃcient level of output by 2 percent, ˆ Y 0 ∗ = −2%, in the case of ¯ B = 1 and ρ A = ρ G = 0. In Figures 1-2, shocks are serially uncorrelated, ρ A = ρ G = 0, and diﬀerent degrees of risk sharing are considered: ¯ B = 0.5, 0.75, 1.0. Consistent with the theoretical results above, exact price stabiliza- tion is optimal in the case of perfect insurance ( ¯ B = 1), and the less risk sharing is (the lower ¯ B is), the more optimal policy diﬀers from the complete price stabilization. Consistent with Propo- sitions 3-4, less insurance makes optimal responses of output to the government-purchase shock (the productivity shock) larger (smaller). In Figures 3-4, ¯ B = 0.75 and ρ A , ρ G = 0, 0.5, 0.9. As the persistence of a shock becomes greater, the optimal responses to it involve larger ﬂuctuations in inﬂation and the output gap. Those ﬁgures show, however, that, regardless of the values of ¯ B, ρ A , and ρ G , deviations of optimal policy from the complete price stabilization is quantitatively very small (note that the inﬂation rate is expressed in percent per year). We thus conclude that, as far
Gruber concludes that unless risk aversion is very high (γ > 2), “the distortions of UI to search behavior are so large that the optimal benefit level is fairly low.” Unfortunately, estimates of γ are limited and are usually drawn from introspection about choices between gambles or experiments with small stakes that may not be informative about the risk pref- erences of unemployed agents. 17 The danger of using estimates based on introspection is underscored by the recent experimental work of Holt and Laury (2002), who show that sub- jects exhibit much higher degrees of risk aversion when playing with large real stakes than when introspecting about hypothetical gambles. Moreover, recent work on consumption of durables and liquidity constraints suggests that change in marginal utility induced by a tem- porary income shock may be very diﬀerent from the eﬀect of permanent shocks. Browning and Crossley (2003) show that the consumption of small durables such as clothes can reduce risk aversion with respect to temporary income shocks, because agents can reduce expen- ditures by postponing purchase of these durables without much of a welfare cost. On the other hand, Chetty (2004) and Chetty and Szeidl (2004) show that the consumption of large durables that involve transaction costs such as housing and vehicles amplify risk aversion with respect to temporary or moderate shocks, because they force agents to concentrate all their changes on a small share of their budget. These results point to the advantages of estimating γ directly from data on the behavior of unemployed agents.
In spite of its weaknesses, the model points to some interesting aspects of efficient contracts that real-world insurance systems lack. As argued by Hopenhayn and Nicolini (1997), unemployment insurances should create incentives not only by means of declining benefits during unemployment, but also through increased insurance contributions after a new job is found. Thereby the punishment for inappropriate actions by the agent is spread over several periods, which is more efficient if agents are risk-averse. However, this effect may be quite small in reality, because agents can self-insure against quickly declining replacement rates by saving. It remains to be seen if currently implemented insurance systems that do not use continuously declining replacement rates over time but often adopt two benefit levels (e.g. an unemploymentinsurance benefit paid for a certain time, social assistance thereafter), are reasonably good approximations of the optimal scheme.
There are two key mechanisms that yield the sign of (16): there is a taxation externality associated with search and there is an “entitlement eﬀect”. The taxation externality derives from the fact that, given that some insurance is optimal (b > 0), taxes are required to finance unem- ployment expenditure. Individuals, however, do not take into account that taxes can be lowered if search intensity (and hence employment) in- creases. Therefore, ∂W/∂s s > 0. Moreover, the so called entitlement eﬀect (c.f. Mortensen, 1977) will operate in this setting. Increasing the penalty will be conducive to search among those who are sanctioned since individ- uals will be eager to find a new job in order to qualify for (to be entitled to) UI benefit receipt. As a corollary to proposition 1, the optimal policy will involve an interior µ. In other words, the two tiered benefit structure, b > 0, p > 0, and µ ∈ (0, ∞ ), dominates the uniform benefit structure in welfare terms.
and Weiss (1979) analyzed the problem of optimal sequencing of bene…t payments over the spell of unemployment. The key result was that the bene…t level should decline monotonically over the unemployment spell, because such a pro…le involves stronger incentives to search. The recent paper by Hopenhayn and Nicolini (1997) has extended the analysis in Shavell and Weiss by considering a wage tax after reemployment in conjunction with the sequence of bene…t payments. The basic results are twofold: …rst, bene…ts should decrease over elapsed duration, as in Shavell and Weiss; second, the wage tax should increase with the length of the previous unemployment spell. These two papers o¤er a partial analysis in the sense that workers’ wages are given. A few recent contributions have also allowed for endogenous wage determination. Cahuc and Lehmann (2000) propose a model where …rms and unions bargain over wages and notice the possibility that a declining time pro…le may raise wage pressure by strengthening the power of “insiders” in the wage negotiations. This rise in wage pressure tends to o¤set the positive search incentives arising from a declining time pro…le. The paper by Fredriksson and Holmlund (2001) analyzes optimal bene…t sequencing in a model of search unemployment along the lines of Pissarides (1990). The model features endogenous search e¤ort, endogenous wage determination and free entry of new jobs. The analysis shows analytically that a declining time pro…le of bene…t payments is optimal, provided discounting is ignored. With discounting, numerical calibrations suggest that the wage pressure e¤ect is not strong enough to o¤set the favorable e¤ect on search incentives.
Pooling the eight panels yield a universe of 468,766 individuals from 149,286 households. 99,880 of these individuals experience at least one job separation (as de…ned below) during the sample period. Further restricting the sample to individuals between the ages of 18 and 65 who have at least three months of work history and have been included in the panel for at least three months leaves 78,168 individuals. Because of a problematic de…nition of unemployment status in the 1985 to 1987 versions of the SIPP, individuals sometimes report a job separation while also reporting unemployment duration equal to zero. Rede…ning unemployment status to only include those who report becoming unemployed and also a non-zero unemployment duration leaves 65,135 individuals. I drop observations from Maine, Vermont, Iowa, North Dakota, South Dakota, Alaska, Idaho, Montana, and Wyoming because the SIPP does not provide unique state identi…ers for individuals residing in these small states. This leaves me with a sample of 62,598 individuals and 86,921 unemployment spells. 33,149 of these spells are for women, whom I exclude. I also keep only those individuals who report actively searching for a job, as de…ned below, to eliminate those who have dropped out of the labor force. This leaves a sample of 16,784 individuals (3.6% of original sample) who experienced a total of 21,796 unemployment spells. Next, I drop temporarily layo¤s, since these individuals may not have been actively searching for a new job, leaving 21,107 spells. I then exclude individuals who never received UI bene…ts, leaving 7,015 spells. Finally, I further limit the sample to individuals who take up bene…ts within the …rst month after job loss because it is unclear how UI should a¤ect hazards for individuals who delay takeup. This last step produces a core sample consisting of 4,015 individuals (0.86% of the original sample) and 4,560 unemployment spells, of which 4,337 have asset and mortgage information.
To estimate the micro-elasticity of unemployment duration with respect to benefit levels, we use administrative data from the Continuous Wage and Benefit History (CWBH) that record em- ployment and unemployment history for all workers in 8 US states from 1976 to 1983. To identify the micro-elasticity, we estimate the effect of benefits using only within state×year variations in individual benefits. We fit a Cox proportional hazard model with state and year fixed effects in- teracted, and controlling for observable characteristics of the unemployed (age, education, marital status, ethnicity, number of dependents). We also introduce a series of non-parametric controls for previous wage and previous work experience. When adding this rich set of controls, the residual variation in benefits is likely to be exogenous, and comes primarily from non-linearities in the ben- efit schedule. We estimate this model for low- and high-unemployment regimes. 23 The Appendix provides all the details. Our main finding is that the elasticity of duration with respect to benefits is 0.34 (0.04) for low-unemployment regimes, and 0.32 (0.04) for high-unemployment regimes. 24 These estimates are very close, suggesting that the micro-elasticity is acyclical as in the simulation of our calibrated model presented in Figure 3 . These findings imply that the conventional Baily- Chetty formula would recommend a constant replacement rate over the business cycle, in sharp contrast with the optimal UI in our calibrated model, displayed in Figure 2 .
This paper studies the eﬀect of human capital depreciation and duration depen- dence on the design of an optimalunemploymentinsurance (UI) scheme. Our results partially confirm those obtained in most previous studies: benefits should decrease with unemployment duration. The optimal program also generates two main novel features, which are not present in stationary models. First, if human capital depreciates rapidly enough during unemployment, UI transfers are bounded below by a minimal “assis- tance” level that arises endogenously in the eﬃcient program. Second, we study the optimality of imposing a history contingent wage tax after reemployment. Our nu- merical simulations based on the Spanish and US economies show that the wage tax should decrease with the length of worker’s previous unemployment spell, and become a wage subsidy for long-term unemployed workers. As a by-product of our study, we de- velop a systematic approach suitable for studying recursively a wide range of dynamic moral-hazard problems, and other models with similar characteristics.
Another related literature is concerned with the “added worker eﬀect” and spousal labor supply as insurance. The paper by Burdett and Mortensen (1978) on labor supply under uncertainty studies job search by couples using a standard partial equilibrium search framework. When one family member becomes unemployed, part of the income loss can be oﬀset by increased spousal labor supply. 3 As shown by Cullen and Gruber (2000), this supply response may be substantially weakened by unemploymentinsurance. Our paper assumes exogenous search intensity and spousal job loss leads to wage adjustment but no change in search eﬀort. However, an extension of the basic model to incorporate endogenous search eﬀort would include mechanisms akin to the added worker eﬀect. An unemployed family member’s search eﬀort would respond to labor market outcomes of the spouse since those outcomes influence overall family income.
“Large” multiple-person families do feature in some realms of equilib- rium search and matching theory. A seminal contribution in this genre was oﬀered by Merz (1995) who studied an economy where each household was described as “a very large extended family”, where members could perfectly insure each other against fluctuations in labor income associated with tran- sitions between employment and unemployment. This approach has been adopted by others, including Hall and Milgrom (2008) in a recent paper. The “large family” approach has its virtues, but realism is not one of them. Modern industrialized economies are largely based on husband-wife families with at most two adult workers. Transfers across generations may occur so as to achieve some income smoothing but complete smoothing is utterly unrealistic. Empirical work has documented that consumption among U.S. workers falls substantially as unemployment strikes and that the presence of unemploymentinsurance markedly reduces the drop in consumption (Gru- ber, 1997). 1
The paper develops an equilibrium search and matching model where two-person families as well as singles participate in the labor market. We show that equilibrium entails wage dispersion among equally productive risk-averse workers. Marital status as well as spousal labor market status matter for wage outcomes. In general, employed members of two-person families receive higher wages than employed singles. The model is applied to a welfare analysis of alternative unemploymentinsurance systems, recognizing the role of spousal employment as a partial substitute for public insurance. The optimal system involves benefit differentiation based on marital status as well as spousal labor market status. Optimal differentiation yields small welfare gains but gives rise to large wage differentials.
The models in this study closely follow Hansen and Imrohoroglu (1992). The econ- omy consists of ex-ante identical heterogenous agents. They differ in their asset holdings and employment history. Each period they face stochastic employment offers. As agents are not able to borrow when they need to do so, they cannot sufficiently insure themselves against such idiosyncratic shocks. Therefore an unemploymentinsurance program can help them accommodating such shocks and increase the welfare in the economy. However, it is also possible for such an insurance scheme to introduce adverse incentives to the economy. When agents receive an employment offer, they are faced with a trade-off between work and leisure. If there is enough insurance payment when the agent is unemployed, then agents have an extra incentive not to work. They may want to live on insurance payments while enjoying extra leisure hours. If the agents are successful in defrauding the system this way the unemployment rate could rise significantly, creating serious welfare costs.
As the next step, it was asked whether a majority of the population would support switching from the current UI system with relatively high replacement ratios to the optimal policy. When voters can choose between the long-run equilibria associated with the current and the alternative policy, the majority votes for the regime change. In the closed economy case, the approval for the optimal policy is just above 50%, regardless of the level of risk-aversion assumed. There are basically two important demographic groups who oppose the policy change, namely old agents (retired individuals and older workers), who would suffer interest income losses under the optimal policy, and young agents with low resources, who might have difficulties maintaining an adequate consumption level in some states if the optimal system was imposed. In the open economy cases, almost the whole population supports the optimal UI system.
One of the classic empirical results in public finance is that social in- surance programs such as unemploymentinsurance (UI) reduce labor supply. For example, Moffitt (1985), Meyer (1990), and others have shown that a 10 percent increase in unemployment benefits raises av- erage unemployment durations by 4–8 percent in the United States. This finding has traditionally been interpreted as evidence of moral hazard caused by a substitution effect: UI distorts the relative price of leisure and consumption, reducing the marginal incentive to search for a job. For instance, Krueger and Meyer (2002, 2328) remark that be- havioral responses to UI and other social insurance programs are large because they “lead to short-run variation in wages with mostly a substi- tution effect.” Similarly, Gruber (2007, 395) notes that “UI has a sig- nificant moral hazard cost in terms of subsidizing unproductive leisure.” This paper questions whether the link between unemployment ben- efits and durations is purely due to moral hazard. The analysis is mo- tivated by evidence that many unemployed individuals have limited li- quidity and exhibit excess sensitivity of consumption to cash on hand (Gruber 1997; Browning and Crossley 2001; Bloemen and Stancanelli 2005). Indeed, nearly half of job losers in the United States report zero liquid wealth at the time of job loss, suggesting that many households may be unable to smooth transitory income shocks relative to permanent income.
payments roughly equal to 2/3 of the unemployment benefits. During the benefit period, the UI system would force the worker to accept brief employment spells or education offers. But the first of these ‘harassments’ was not forced on the worker until after more than two years of unemployment. The average unemployment spell in the data is 14 weeks. While there are restrictions on eligibility, they are generally quite easy to satisfy and the question of qualifying for benefits is not of great concern for the Danish worker. The system is voluntary and if the worker decides to participate he must pay an insurance premium. The system is heavily subsidized and the worker pays only about 1/3 of the actual premium. Thus, not surprisingly more than 80% of the labor force choose to participate in the system. Non-participants are generally very low wage workers and very high wage workers. For the very low wage workers, the welfare system will provide comparable insurance to the UI system. For the very high wage workers, the UI system provides very little insurance due to an upper bound on benefit payments. In effect, the upper bound on benefit payments is so restrictive that the Danish UI system can be characterized by a wage independent benefit scheme. In the data in this paper, everybody faces the same constant level of benefits except for the lowest 4 percent of the wage earners. The lowest 4 percent of wage earners receive benefits equal to 90% of their previous wage.