The Causal Eect of Unemployment Duration on Wages: Evidence from Unemployment Insurance Extensions

The Causal Eect of Unemployment Duration on Wages: Evidence from Unemployment Insurance Extensions Johannes F. Schmieder Till von Wachter Stefan Bender Boston University UCLA, NBER, Institute for Employment NBER, and IZA CEPR, and IZA Research (IAB) October 2013 - PRELIMINARY Abstract Does the search subsidy provided by unemployment insurance (UI) help workers nd better jobs by or does the resulting increased time out of work lead to skill depreciation and lower reemployment wages? This paper investigates this question by exploiting strict age thresholds in the German UI system that determine workers' maximum potential UI benet duration. Using a regression discontinuity (RD) design we show that longer potential benet durations lead to sharp increases in nonemployment durations while lowering post-unemployment wages. We present a new theoretical result that shows how the average eect of UI extensions on reemployment wages can be decomposed into a reservation wage eect and an eect coming from changes in the wage oer distribution throughout the nonemployment spell. This decomposition can be implemented using information on how reemployment wages conditional on non-employment durations are aected by UI extensions. We show empirically that reemployment wages conditional on time out of work are not affected by increases in potential durations. Our theoretical result implies that in this case the negative eect of UI extensions on average wages is entirely due to changes in the wage oer distribution over time. Furthermore we can estimate the change in mean oered wages over time, by regressing reemployment wages on nonemployment durations and instrumenting for time out of work with the increase in potential UI durations at the age discontinuity. This IV estimate implies that each month out of work reduces wage oers (and reemployment wages) by 0.8 percent, pointing to high costs of long-term unemployment. We would like to thank David Card, Larry Katz, Kevin Lang, Claudia Olivetti, Daniele Paserman, Robert Shimer, Fabien Postel-Vinay, Albert Yung-Hsu Liu, as well as seminar participants at Princeton University, Northeastern University, the Atlanta FRB, the Minnesota FRB and the NBER Labor Studies meeting for helpful comments on this project. Johannes Schmieder gratefully acknowledges funding from the 2011 Scholars Program of the Department of Labor. All errors are our own. johannes@bu.edu tvwachter@econ.ucla.edu stefan.bender@iab.de

1 Introduction Do unemployment insurance (UI) benets help workers nd better jobs? While critics have long held that unemployment insurance creates a disincentive to nd work, proponents of more generous UI systems, apart from arguing for the benecial insurance eect of UI, often point out that taking more time to search for a suitable job may produce a positive eect on job match quality. Although these eects seem natural when UI benets are simply viewed as a subsidy to search eorts, another view holds that long periods of unemployment, possibly induced by generous UI benets, lead to lower reemployment wages and job quality, either due to skill depreciation (Ljungqvist and Sargent, 1998) or stigmatization (Blanchard and Diamond 1994). While estimates of the eect of UI extensions on job quality are important in their own right, they also oer an opportunity to disentangle the search subsidy eect from skill depreciation during non-employment. Estimates of the causal eect of time out of work on reemployment wages (through real or perceived decline of human capital) are important to gauge the long run eects of long-term unemployment. This paper sets out with a model that highlights how the eect of UI extensions on reemployment wages can be decomposed into an eect that comes through the slope and the shift of the reservation wage path and a second component that stems from wage oers declining throughout the spell of nonemployment. We provide a new theoretical result that shows that if the path of of reemployment wages conditional on the time of exiting nonemployment is not aected by UI extensions, then the average eect of UI extensions on reemployment wages is only due to changes in the wage oer distribution throughout the nonemployment spell. Furthermore, in this case, extensions in UI durations can be used as an instrument to estimate the change of the wage oer distribution with the duration of nonemployment using a 2SLS estimator. To identify a causal eect of maximum UI durations on reemployment wages we examine the system in Germany where the generosity of UI durations varies with the age at which an 1

individual claims UI benets. These rules lead to sharp increases in potential UI durations at several age thresholds where individuals of ages within a few days of each other face very dierent potential UI durations. We exploit this variation using a regression discontinuity design (RD) and a large administrative dataset covering unemployed workers in Germany. This design allows us to precisely estimate the eect of longer potential UI durations on various measures of job quality, such as the reemployment wage, whether an individual moved to a new location, switched industry or occupations, or the duration of the postunemployment job. We then go on to analyze how reemployment wages conditional on nonemployment duration vary with potential UI benet durations. While a substantial body of research has documented the disincentive eect of UI benets (for example, Solon 1979; Mott 1985; Katz and Meyer 1990; Meyer 1990; Hunt 1995), and the consumption smoothing eect of UI (for example, Gruber 1997), the evidence is weaker on how UI aects match quality. The early literature found mixed results based on research designs using observational studies (see Addison and Blackburn 2000 and Meyer 2002 for reviews of this literature). More recent studies by Lalive (2007) and Card, Chetty and Weber (2007)) used regression discontinuity designs to more clearly identify the eects and nd negative impact on wages. However, results are relatively imprecisely estimated and not statistically signicantly dierent from zero, while the condence intervals contain possible negative and postive values that are economically meaningful. We add to this literature in several ways: First, thanks to a large sample size and treatment variation, we obtain small condence intervals that allow for meaningful economic interpretation. Second, we are able to investigate a number of alternative measures of job and match quality, such as whether a job requires the employee to move to a new location, job stability, and industry or occupation mobility. Third, we investigate various long-term job outcomes such as wages and employment status ve years after the start of unemployment. Finally, we provide a careful analysis to ensure that our eects are not driven by selection eects or unobservables. 2

We nd strong eects of increased potential UI durations on job nding hazards. One month of additional potential UI benets increases nonemployment durations by about 0.15 months. Contrary to the view that this subsidy improves match quality, an additional month of potential UI duration decreases wages at the post-unemployment job by about 0.13 percent. This decrease is statistically signicant and robust to many alternative specications. Furthermore, match quality appears to be worse along many other measures of job quality, such as long term employment and wage outcomes or region, industry, and occupation mobility. This nding supports the view that long term unemployment may put the unemployed at a disadvantage by lowering their skills. Turning to our dynamic results, we show that reemployment wages conditional on time out of work do not change at the age discontinuity for most points of support. Together with evidence on how selection of individuals at dierent non-employment durations change at the age discontinuity, our theoretical results imply that increases in potential UI duration can serve as an instrument for the eect of nonemployment durations on reemployment wages. Our estimates imply that 1 month out of work lowers wages by about 0.8 percent. This implies that the wage of the average UI recipient in our sample declines by about 10 percent during the unemployment spell. The next section shows in a search model how the eect of UI extensions on reemployment wages is the sum of a reservation wage eect and an eect coming from changes in the wage oer distribution throughout the unemployment spell. In addition we derive conditions under which using UI extensions as an instrument for nonemployment durations provides valid estimates for the change in the wage oer distribution. Section 3 describes the institutional setting, the data, and the empirical methods used in this paper. In section 4 we present the main results of how potential UI durations aect average match quality, and we extensively verify the robustness of our ndings. Section 5 presents dynamic results of how reemployment wages and selection conditional on nonemployment duration vary with potential UI increases and implements the IV estimator. Section 6 discusses these results and concludes. 3

2 Theory We analyze a discrete time, non-stationary search model, based on Mortensen (1986) and van den Berg (1990). The model features endogenous search intensity in addition to the choice of accepting or rejecting job oers, thus allowing for UI extensions to aect nonemployment durations through changes in reservation wages as well as through changes in search eort. The distribution of wage oers may shift downward thoughout the unemployment spell, which may for example represent skill depreciation or stigmatization. The analysis will focus on three aspects: First, we show how the eect of UI extensions on reemployment wages can be decomposed into a reservation wage eect and changes in the wage oer distribution over the nonemployment spell. Second, we use the model to clarify how the eect of UI extensions on the reemployment wage path (i.e., reemployment wages conditional on the time of exiting unemployment) is informative about the response of reservation wages to UI extensions and with it about their eect on the reemployment wage path. Third, we show under what conditions it is possible to identify the change in the wage oer distribution over the nonemployment spell separately from the reservation wage eect using UI extensions as a form of exogenous variation. 2.1 Setup of Model The model describes the job search process of a single unemployed individual. We do not explicitly model heterogeneity, but we will discuss identication in the presence of heterogeneity in the methods section. 1 Unemployed individuals are risk neutral and maximize the present discounted value of income. Workers become unemployed in period t = 0 and immediately start looking for jobs. In each period t workers receive UI benets b t and choose search intensity λ t, which is normalized to be equal to the probability of receiving a job oer in that period. The cost of job search ψ(λ t ) is an increasing, convex and twice dierentiable 1 One can think of this model as allowing for heterogeneity if one allows individuals to have dierent parameters, so that all observed moments are integrated over these parameters. 4

function. Jobs oer a wage w and wage oers are drawn from a distribution with cumulative distribution function F t, which may vary with the duration of unemployment t. To simplify the exposition we assume that the distribution can be summarized by its mean in period t: µ t. 2 If a job is accepted, the worker starts working at the beginning of the next period and stays at that job forever. Optimal search behavior of the worker is described by a search eort path λ t and a reservation wage path φ t, so that all wage oers w φ t are accepted. In the appendix we provide details on the value functions and the rst order conditions as well as the derivations for the following results. 2.2 The Eect of Increasing Potential UI Durations on the Reemployment Wage The rst purpose of the model is to highlight the dierent channels how increasing maximum UI durations may aect the reemployment wage. We denote the reemployment wage as w (as opposed to a wage oer w ), the probability mass function of the distribution of nonemployment durations as g(t) and let E[w t] be the reemployment wage conditional on exiting unemployment at t. We can express the expected reemployment wage of an unemployed worker by integrating the reemployment wage conditional on exiting unemployment at t over the distribution of nonemployment durations: E[w] = 0 E[w t] g(t). An extension in potential UI durations P aects the expected reemployment wage through two components: de[w] = [ ] de[w t] g(t) + t=0 t=0 [ E[w t] dg(t) ] (1) µ t. The rst term is due to the shift in the reemployment wage path, while the second term 2 This is easily generalizable to more exible distribution functions characterized by a vector of parameters 5

is due to the shift in the distribution of nonemployment durations. To simplify notation we dene δ = [ ] de[w t] t=0 g(t), the average (weighted by the distribution of nonemployment durations) shift in the reemployment wage path. Furthermore we dene the slope of the reemployment wage E[w t + 1] E[w t] t E[w t]. We assume that over the part of the support of nonemployment durations where nonemployment durations are aect by an increase in P, E[w t] can be reasonably well approximated by a rst order taylor approximation E[w t] = ξ + π t, where π = t E[w t]. In the empirical part we show that this seems a reasonable approximation over the relevant interval. Furthermore in the appendix we show that π can also be interpreted as a weighted average of the slopes of the reemployment wage path, where the weights are shifts in the density of the duration distribution that is induced by the UI extension. We use the operator Ẽ to express this weighted average, so that π = Ẽ [ te[w t]]. In the empirical section we show that this has a natural interpretation as a local average treatment eect (LATE). In this case equation (1) can be written as: de[w] = δ + π dd (2) where dd duration D. 3 is the marginal eect of an increase in P on the expected non-employment This formula holds independently from our model and shows how in general the reemployment wage eect can be decomposed into shifts of the reemployment wage path and movement along the reemployment wage path due to increases in nonemployment durations. While the decomposition in equation (2) is mechanical, results from the search model provide key insights into the eect of changes in the outside option (in this case UI durations) on wages. In our model the shift in the reemployment wage path is due to a shift in the reservation wage: δ = t=0 3 Note that D = dd t=0 [t g(t)] and [ de[w t] dφ t ] dφ t g(t). Furthermore the slope of the reemployment = [ t=0 t dg(t) in the probability mass function have to sum up to 0, so that t=0 6 ]. Furthermore ξ cancels out because the changes dg(t) = 0.

wage path is a combination of two channels: changes in the reservation wage throughout the nonemployment spell and changes in the wage oer distribution throughout the nonemployment spell. Using again a rst order Taylor approximation we have that: t E[w t] de[w t] t φ t + de[w t] t µ t (3) dφ t dµ t The rst term of this equation captures that changes reservation wages over the nonemployment spell can aect observed reemployment wages. The second term of the equation represents the slope in reemployment wages relative to nonemployment durations that is due to shifts in the wage oer distribution over time. To simplify notation we denote this term θ t de[w t] dµ t t µ t, which will depend on how much the wage oer distribution changes over time t µ t as well as how much changes in that parameter aect actual reemployment wages de[w t] dµ t. Since this eect represents the change reemployment wages if we could exogenously increase unemployment durations by an extra period, while holding reservation wages constant throughout the nonemployment spell and not be aected by the increase in nonempoyment durations, we call θ t the causal eect of nonemployment durations on wages. Below we argue that under certain conditions that seem plausible in the light of our empirical results we have that de[w t] dµ t = 1. In that case θ t represents the change in mean wage oers over time or the change in the wage oer distribution over time. For simplicity, we will alternatively refer to θ t as the causal eect of nonemployment durations on wages or as the change in the wage oer distribution in the rest of the paper. Combining equations (2) and (3) it follows that the reemployment wage eect can then be written as a combination of the reservation wage eects and the change in the wage oer distribution over time: de[w] [ ] [ ] de[w t] = E dφ t de[w t] dd + dφ t Ẽ t φ t + θ t dφ t (4) Note that presence of the reservation wage response aects the reemployment wage in two 7

ways: through a shift in the reservation wage and through movements along the reservation wage path. A key implication of equation (4) is that in order to isolate the change in the wage oer distribution θ t throughout the unemployment spell it is necessary to isolate it from these two reservation wage eects. Another implication is that direct estimates of the eect of UI extensions (or other changes in the outside options) capture all three components. Hence, even absence a bias from selective reentry into the labor market, such estimates are hard to interpret. A closely related point of equation (4) is that estimators directly regressing wages on nonemployment durations are not only aected by selection, but again capture both eects from reservation wages and the wage oer distribution. A nal point of equation (4) is that the eect of extending UI benets on the reemployment wage is ambiguous, reecting the contrasting hypotheses about the eect of UI mentioned in the introduction: The rst component, shifting up the reservation wage, will tend to increase the reemployment wage, while the second component - longer nonemployment durations leading to more job oers drawn from a dierent wage oer distribution with lower reservation wages - will tend to decrease the reemployment wage. 2.3 The Eect of Reservation Wages on Reemployment Wages To obtain an estimate of the eect of nonemployment durations on the wage oer distribution, we thus need to infer about how reservation wages change with UI durations and over the nonemployment spells. The eect of the reservation wage on the reemployment wage conditional on exiting at time t is given as de[w t] dφ t, which enters in both the second and third terms of equation (4). The second key insight of the paper then is that an increase in potential UI durations aects the reemployment wage path and hence that this eect is indirectly informative about the reservation wage eect. This is captured in the following equation which highlights how changing P aects the value of unemployment at time t which in turn aects the optimal reservation wage and thus the reemployment wage. 8

de[w t] = de[w t] dφ t dφ t = de[w t] dφ t dvt u ρ, (5) Therefore the eect of the reservation wage on the reemployment wage can be expressed by the reemployment wage eect of UI extensions and the change in the value function: de[w t] dφ t = de[w t] / dv t u ρ as long as dv t u is not equal to 0, i.e. the UI extension does in fact aect the outside value. The latter iseasily testable, since if a change in P aects the hazard rate of exiting unemployment dht this implies that the outside option has in fact changed (see Appendix for a formal derivation). This yields the following result. Proposition 1. If de[w t] = 0 and dht < 0, then de[w t] dφ t = 0, i.e. Changes in the reservation wage do not aect reemployment wages. This proposition captures a simple but important insight: the eect of UI extensions on reemployment wages conditional on exiting unemployment at time t is informative about the eect of reservation wages on reemployment wages. This proposition thus indicates an simple test for whether or not reservation wages aect reemployment wages. If the exit hazard is changing and there is no eect of UI durations on reemployment wages, then changes in the reservation wage do not aect reemployment wages. 4 2.4 Identifying the Change in the Wage Oer Distribution throughout the Unemployment Spell If the reservation wage does not aect reemployment wages, then the rst two terms of equation (4) drop out. In other words, an increase in UI durations does neither aect reemployment wages through a shift in reservation wages (the rst term) nor through a rise 4 If the eect of UI durations on reemployment wages is not equal to zero, the equation (5) allows one to infer about the sign in the eect of reservation wages on accepted wages, which is equal to that the wage response. The magnitude depends on specic model parameters. 9

in nonemployment durations and hence a decline in reservation wages (the second term), since de[w t] dφ t t φ t = 0. Proposition 1 therefore suggests a way how the change in the wage oer distribution throughout the unemployment spell Ẽ [θ t ] can potentially be identied: Proposition 2. If the conditions for Proposition 1 hold, then the rst 2 components in equation (4) are zero and Ẽ [θ t] = de[w] dd Thus the (average) decline in the wage oer distribution is simply the eect of UI extensions on reemployment wages, divided by the eect on nonemployment durations. This is the same formula as the standard IV estimator and thus suggests that the change in the wage oer distribution - the causal eect of nonemployment durations on wages - can be estimated by regressing wages on nonemployment durations using two-stage least squares with UI extensions as an instrument. We will argue in the empirical section that the conditions for Proposition 1 do in fact seem to hold in practice. It is however also possible to isolate the change in the wage oer distribution in the more general case where this does not hold. Rearranging equation (4) yields: Ẽ [θ t ] = de[w] dd δ 1 dd Ẽ + Ẽ [ dv u t dt [ dv u t ] ] While the eects on the value function are not immediately observable, in the empirical section we will show how this formula can be used to derive bounds for the change in the wage oer distribution if the conditions for proposition 1 do not hold and δ is dierent from zero. Finally the following proposition formalizes under what condition E [θ t ] is infact the change in the mean of the entire wage oer distribution. Proposition 3. If the support of the wage oer distribution is convex (i.e., there are no wage ranges in which no oer is received) and de[w t] = 0, then 1 F t (φ t ) = 1, i.e. the 10

reservation wage is not binding. Furthermore θ t = t µ t = t E[w t], (6) i.e. the decline in the reemployment wage over time due to is the same as the change over time in the mean of the wage oer distribution. If the wage oer distribution is unimodal and continuous, such as a lognormal distribution, then the fact that shifts in reservation wages do not aect wages implies reservation wages indeed do not bind. However, if the wage oer distribution is for example bimodal, with a mode for very low wage jobs, and a mode for higher wage jobs, with little density in between. If the reservation wage lies in between the two modes as we will argue may be realistic in our empirical application of men with high labor force attachment then reservation wages bind, but small changes therein will not aect the mean of accepted wages. Hence, Proposition 3 has two important implications. First, if the wage distribution has a range in which workers do not receive wage oers and the reservation wage lies in that range, then E [θ t ] measures the eect of nonemployment duration over the eective wage oer distribution, i.e., that part of the distribution above the reservation wage, but not the entire distribution. Second, the fact that de[w t] = 0 does not necessarily imply that reservation wages are not binding vis-a-vis the entire wage oer distribution, just that for small changes they have no eect locally in the distribution. 2.5 Empirical Content of Model The key insights of our analysis are new with respect to the literature and hold beyond our particular modeling choices.. The key new insight of our analysis is to show that estimating whether reemployment wages conditional on unemployment durations are aected by changes in the UI benet path (or other factors aecting the value of nonemployment), 11

provides a test for the importance of the outside option of unemployed workers in the wage determination process. If reemployment wages conditional on unemployment duration do not respond to changes in the outside option, then the decline of reemployment wages over the unemployment spell can also not be due to changes in the outside option throughout the unemployment spell. Instead, it must be due to a decline of the wage oer distribution over the nonemployment spell. While we illustrated this insight in a model of wage posting, a symmetric intuition applies in wage bargaining models, where wages should in principle also be aected by the outside option of the unemployed worker. If they are not, then changes in the outside option throughout the unemployment spell should also not have an eect on reemployment wages and thus cannot explain the observed decline in reemployment wages. Furthermore a similar intuition would hold in a directed search model where workers choose to search for jobs in a segment of the labor market. In such a model wages are aected by the choice of the labor market and the reservation wage when searching in a market. If the wage conditional on unemployment duration does not respond to UI benet changes, then again workers are not responding to changes in the outside option and the outside option cannot explain the decline in wages over the unemployment spell. This insight allows for a straightforward test of the importance of the outside option for determining reemployment wages. However, for this test to be meaningful it is important to have a measure for how much the outside option is infact shifting and valued by workers. Such a measure can indeed be obtained by observing whether the hazard of exiting from unemployment changes throughout the unemployment spell. Such a change in the hazard could either occur because of a change in search eort or a change in reservation wages, but either way it indicates clearly that the outside option is changing for the unemployed individual. Showing that the exit hazard path changes thus shows that the outside option of remaining unemployed signicantly changes for an unemployed worker and thus if the reemployment wage does not change that the reemployment wage is not aected by the 12

outside option. This is the core intuition behind Propositions 1 and 2. Estimating the eect of UI extensions on average reemployment wages is relatively straightforward, as long as there is exogenous variation in potential UI durations. Yet, as the discussion in this section showed, it is dicult to decompose the eect de[w] into its components since neither wage oers nor the reservation wage are directly observed. Propositions 1 and 2, oer a way to identify the dierent components under some specic conditions. In order to see whether these conditions hold and to apply the decomposition if they do hold, it is crucial to obtain consistent estimates of de[w t], dh t, dd, and te[w t]. While these are relationships between observables, estimation of these moments is complicated by the presence of observed and unobserved heterogeneity. We will address these problems carefully when discussing our methods in Section 3.3. 3 Institutions, Data and Empirical Methods 3.1 Institutional Background After working for at least 12 months in the previous three years, workers losing a job through no fault of their own in Germany are eligible for UI benets that provide a xed replacement rate of 63 percent for an individual without children. 5 This paper focuses on the time period between 1987 and 1999, which is the longest period for which the UI system was stable, and during which the maximum duration of benets was tied to recipients' exact age when they began receiving UI benets and to their labor force history. Between July 1987 and March 1999, the maximum potential UI duration for workers who were younger than 42 years old was 12 months. 6 For workers age 42 to 43 maximum potential UI duration increased to 18 5 Sanctions for not taking suitable jobs exist but appear to be rarely enforced (Wilke 2005). For individuals with children the replacement rate is 68 percent. There is a cap on earnings insured, but it aects only a small number of recipients. Since they are derived based on net earnings, in Germany UI benets are not taxed themselves, but can push total income into a higher income tax bracket. 6 The age cutos were changed in 1999, a period we analyze in Schmieder, von Wachter, and Bender (2012a). The system was reformed substantially and most age cutos were abolished in 2004. For an investigation of the stepwise introduction of these age cutos between 1983 and 1987 see Hunt (1995). 13

months and for workers age 44 to 48, the maximum duration further rose to 22 months. 7 As we explain further below, to obtain precise measures of potential UI durations, we restrict ourselves to a sample of workers who were, based on their employment history, eligible to the maximum potential UI durations in their age group. Individuals who exhaust regular UI benets are eligible for means tested unemployment assistance benets (UA), which do not have a limited duration. The nominal replacement rate is 53%, but UA payments are reduced substantially by spousal earnings and other sources of income, which may explain why only about 50% of UI exhaustees take up UA benets. In Schmieder, von Wachter and Bender (2012a) we provide an in-depth assessment of the role of UA. 3.2 Data For this paper we have obtained access to the universe of social security records in Germany from 1975 to 2008. The data covers day-to-day information on every instance of employment covered by social security and every receipt of unemployment insurance benets, as well as corresponding wages and benet levels. We observe several demographic characteristics, namely gender, education, birth date, nationality, place of residence and work, as well as detailed job characteristics, such as average daily wage, occupation, industry, and characteristics of the employer. 8 For our analysis sample, we extracted all unemployment insurance spells where the claimant was between age 40 and age 46 on the claim date. For reasons discussed above, we 7 There are additional thresholds at older ages. For example, at age 49 potential UI durations increase to 26 months and at age 54 to 32 months. Since relatively few individuals reach these higher thresholds and the increases are smaller relative to the level of potential UI benets at the left side of these thresholds the match quality estimates are quite noisy and not very informative; therefore, we do not present results on them here. Furthermore at the age 54 threshold there is a more substantial eect on permanently leaving the labor force which makes the match quality estimates harder to interpret due to selection concerns. 8 Individual workers can be followed using a unique person identier. Since about 80 percent of all jobs are within the social security system (the main exceptions are self-employed, students, and government employees) this situation results in nearly complete work histories for most individuals. For additional description of the data see Bender, Haas and Klose (2000). Each employment record also has a unique establishment identier that can be used to merge establishment characteristics to individual observations. 14

consider unemployment spells starting any time between July 1987 and April 1999. For each UI spell we created variables about the previous work history (such as job tenure, experience, wage, industry and occupation at the previous job), the duration of UI benet receipt in days, the UI benet level, and information about the next job held after non-employment. Since we do not directly observe whether individuals are unemployed we follow the previous literature and, in addition to duration of UI benet receipt, we use length of nonemployment as a measure for unemployment durations (for example, Card, Chetty, and Weber 2007b). The duration of non-employment is measured as the time between the start of receiving UI benets and the date of the next registered period of employment. Our analysis period assures that we can follow individuals for at least 9 years after the start of the UI spell. The core part of our identication strategy is to use variation in potential UI durations at the age thresholds for any given UI claim spell. We calculate each individuals potential UI duration at the beginning of the UI spell, using information about the law together with information on exact birthdates and work histories. This method yields exact measures for workers who have been employed for a long continuous time and are eligible for the maximum potential benet durations for their age groups. However, the calculation is not as clear cut for workers with intermittent periods of unemployment because of complex carry-forward provisions in the law. We thus dene our core analysis sample to be all unemployment spells of workers who have been employed for at least 44 months of the last seven years and who did not receive unemployment insurance benets during that time period. 9 In our companion paper, we also show that the characteristics of our sample are comparable with those of UI recipients in the United States. 9 Individuals who have quit their jobs voluntarily are subject to a 12 weeks waiting period. To focus on individuals who lost their job involuntarily and minimize selection concerns due to quitting we restrict our sample to individuals who claimed UI benets within 12 weeks after their job ended. 15

3.3 Estimation The institutional structure and data allow us to estimate the causal eect of UI durations on wages, and once suitable conditions on the path of reemployment wages described in Section 2 are satised to obtain estimates of the causal eect of nonemployment duration on wages. Hence, our empirical strategy follows in three consecutive steps. Estimating the Causal Eect of UI Durations on Employment and Wages The institutional structure and data allow us to estimate the causal eect of large extensions in UI benet durations on non-employment duration, reemployment wages and other outcomes for workers with previously stable employment using a regression discontinuity design. We follow common practice and rst show smoothed gures to visually examine discontinuities at the eligibility thresholds (e.g., Lee and Lemieux 2010). To obtain estimates for the main causal eects, we follow standard regression discontinuity methodology and estimate variants of the following regression model: y i = β + γ P D ai a + f(a i) + ɛ i, (7) where y i is an outcome variable, such as non-employment duration (D) or reemployment wages (w), of an individual i of age a i. D ai a is a dummy variable that indicates that an individual is above the age threshold a. In the notation from Section 2, we obtain estimates for dd de[w] and. For our main estimates, we focus on the period from July 1987 - March 1999, and we use the sharp threshold at age 42. We estimate equation 7 locally around the two cutos and specify f(a i ) as a linear function while allowing dierent slopes on both sides of the cuto. We use a relatively small bandwidth of two years on each side of the cuto, and summarize our extensive sensitivity analysis belwo. In order to obtain additional power we also estimate a pooled regression model, where 16

we take the estimation samples for the age 42 and the age 44 cutos together. 10 For this procedure we normalize the age for all individuals within two years of the age 42 (44) threshold to the age relative to age 42 (44) (i.e. the rescaled age variable is set to 0 for someone who is exactly age 42 (44) at the time of claiming UI). We estimate the following model on the pooled sample: y i = β + γ P D ai a + f(a i) + ɛ i, where a i is the normalized age variable and P is the average change in potential UI durations at the age threshold. With this specication ˆγ is a direct estimate of the rescaled marginal eect, forcing it to be equal at the two cutos. Estimating the Shift in the Path of Reemployment Wages and Hazards The RD design provides estimates of the causal eect of UI duration of interesting in their own right. The main goal of the paper is to estimate the causal eect of nonemployment durations on wages. As derived in Section 2, the rst step in obtaining such an estimate is to assess whether the path of reemployment wages and the reemployment hazard shift in response to the UI extensions. If the probability of exiting nonemployment (the hazard rate) declines at each duration, this implies that individuals value future increases in UI durations. If the path of reemployment wages does not shift as well, this means the outside option does not bind, and we can use UI duration as an instrumental variable for nonemployment durations. To estimate the shift in the reemployment wage path, we follow two steps. In the rst step, we examine the changes in reemployment wages visually and estimate the dierence at each nonemployment duration. In a second step, we directly estimate the average shift in the reemployment wage path. For the rst step we estimate the following regression separately for each nonemployment 10 We also estimated all results at the age 44 cuto separately. The point estimates are very similar but lack precision. 17

exit month t: w i = δ t P i + f(a i ) + ɛ i t i = t, (8) where P i = P D ai a captures the eect of a change in UI durations for those reaching the age of eligibility. If cov(ɛ i, P i t i = t) = 0, then estimating equation (8) via OLS will yield ˆδ t as consistent estimates for the eect of UI durations on reemployment wages at each nonemployment duration t, de[w t]. However, while the identication assumptions of the RD design guarantee that individuals on both sides of the cuto are comparable on average (i.e., cov(ɛ i, P i ) = 0) in the total RD sample close to the age cuto, they do not imply that ɛ i and P i are uncorrelated conditional on the duration of unemployment t i. The time when people exit unemployment t i is aected by individual behavior and possibly by the treatment variable P i. We provide two alternative arguments that make cov(ɛ i, P i t i = t) = 0 plausible in our context. First, while we do not observe ɛ i, we can test whether observables are correlated with potential UI durations conditional on t. If cov(x i, P i t i = t) = 0 for all observables, then it seems plausible that: cov(ɛ i, P i t i = t) = 0 and that estimating equation (8) will yield consistent estimates of, de[w t], the eect of UI durations on the path of reemployment wages. Second, we can also make an argument based on the theoretical restriction that the reservation wage has to rise in response to an increase in P (i.e., de[w t] 0 for all t). If ɛ i is a person xed eect, then an estimate of ˆδ t = 0 for any given nonemployment duration t is only consistent with de[w t] > 0 if cov(ɛ i, P i t i = t) < 0. If we nd that ˆδ t = 0 at all nonemployment durations t, then it has to be the case that de[w t] = 0. This is because on average ɛ i is uncorrelated with P and therefore it cannot be that for all t: cov(ɛ i, P i t i = t) < 0. In other words, if it appears that reemployment wages are not aected by the UI extension at any duration, then there cannot be a bias driving from dierences in unobserved characteristics over the nonemployment spell.of course, while this is not often addressed in the literature, the same basic issues hold for estimating the eect on the hazard rate ( dht ). Similar arguments based on observables and theory can be made as for the 18

nonemployment eects conditional on t. 11 In the second step, we directly estimate the average shift in the reemployment wage path and test whether it is equal to zero. To do so, we estimate the following regression on the entire sample w i = δp i + T θ t + f(a i ) + ɛ i (9) t=1 where w i is the observed reemployment wage and θ t are time dummies for the duration of non-employment. The parameter δ captures the average shift in the reemployment wage ] path, such that δ = E. We are still estimating the regression in the RD setting and [ de[w t] hence control for age at the time of entering unemployment. Given the RD assumptions, the resulting estimate for δ is consistent; i.e., while individuals exiting at each nonemployment duration may be dierent in terms of unobservable characteristics in the high and low UI duration regimes, on average this must cancel out close to the cuto. In other words, dierential selection over the nonemployment spell cannot explain a shift in the entire reemployment wage path. Selection could, in principle, lead to a rotation of the observed reemployment wage paths. Yet, following the intuition outlined above we again use the prediction from the theory that de[w t] 0 since the reservation wage has to rise or stay constant. In this case, [ ] if δ = E de[w t] = 0, then it must be that de[w t] = 0 at all nonemployment durations t. Hence, if we cannot reject that the estimated ˆδ is equal to zero, we can conclude that the reemployment wage path and hence reservation wages have not shifted. 12 Estimating the Causal Eect of Nonemployment Durations on Reemployment Wages If the hazard rate declines ( dht < 0) and there is no change in reemployment wages ( de[w t] =0) then the relevant conditions hold, and the eect of UI durations on reemploy- ment wages are driven by higher nonemployment durations. The nal step then is to directly 11 Note that most of the literature presents estimates of the eect of UI durations on reemployment hazards without specically addressing this selection issue. 12 Below, we will use the condence interval for the estimate ˆδ to derive bounds for our causal estimates for small shifts in reservation wages. 19

estimate the causal eect of nonemployment duration on wages using an instrumental variables strategy. Recall that the goal is to etimate the change in the wage oer distribution ( t E[w t] in the notation of Section 2). If we assume linearity, we could estimate: w i = πt i + x i β + u i (10) If cov(u i, t i ) = 0, we have consistency of the OLS estimator ˆπ for t E[w t]. There are two key concerns with this approach. First, a long literature documents that individuals who nd a job within a very short time are dierent on average than individuals who are unemployed for a very long time, such that cov(u i, t i ) 0 and the OLS estimator is biased. The regression discontinuity does not change this problem, since this type of selection would be going on on either side of the threshold. Controlling for observables may alleviate the selection problem somewhat, but given that observables are correlated with t i, it seems likely that even after controlling for observables we still have that cov(u i, t i ) 0. Second, a key insight of Section 2 was that even absent a bias from selection, potential changes in reservation wages make OLS estimates of π hard to interpret. However, if reemployment wages do not respond (i.e., increase in nonemployment durations ( dht de[w t] = 0 at all t) despite an < 0 at all t), then Proposition 2 in Section 2 suggests an alternative way for estimating the change in the wage oer distribution E[θ t ] using the relationship: E[θ t ] = de[w] dd de[w] = dd Essentially this is an IV estimator, where we instrument nonemployment duration with potential UI durations. Both de[w] and dd can be estimated consistently using the RD design and E[θ t ] can then be calculated by dividing these two estimates or by directly estimating equation (10) using two stage least squares, whereby we instrument for D using the variation in P using the variation at the RD cuto. Below, we discuss further properties of the estimator, such as monotonicity and local average treatment eects, and derive bounds 20

for small eects of the outside options (Section 5.3). 3.4 Validity of RD Design A key aspect of all the three steps of our empirical strategy is the validity of the RD design. The regression discontinuity method only yields consistent results if factors apart from the treatment variable do not vary discontinuously at the threshold. If individuals have control over the forcing variable of the regression discontinuity estimator, in this case the age of claiming UI benets, then the estimates resulting from the RD can be biased. In our setting, both potential UI claimants and their employers face potential incentives to manipulate the age of claiming. We have examined this issue at length in our related paper (Schmieder, von Wachter, and Bender 2012a) and its Web Appendix, and conclude that sorting around the threshold is not a concern in this case. We only summarize the main ndings here and refer the interested reader to our precursor paper for a more detailed discussion. A standard test for sorting around the threshold is to investigate density plots to locate spikes near the threshold or permanent shifts of observations at the thresholds. Figure?? shows the number of unemployment spells in two-week age intervals around the cuto. The gure indicates that there is a small increase in the density right after the threshold. 13 Further investigation showed that this increase is not driven by individuals who postpone their claim until they are eligible for longer benets. Instead, if at all the incidence of lay o rises slightly at the eligibility age. The magnitude of this eect, however, is very small: only about 200 instances relative to about 500,000 observations in the sample close to the age cuto. A second standard test is to investigate whether predetermined characteristics of individuals in the sample vary discontinuously at the threshold. Table 1 presents results estimating equation (1) and (2) using two year bandwidths around the cutos. The rst panel shows the estimates for the age 42 threshold, where potential UI durations increase from 12 to 13 These increases in density are statistically signicant according to the McCrary (2008) test. 21

18 months; the second panel shows the estimates for pooling the age 42 and the age 44 cuto (where potential UI durations increase from 18 to 22 months. There is a statistically signicant change at the threshold is the fraction female in the age 42 model and the pooled model: The fraction of UI recepients who are female is estimated to increase by about 0.8 percentage points (or 0.5% in the pooled model). Furthermore there is a tiny dierence in the years of education variable at the rst threshold of about 0.03 years (or 10 days) of education. All other variables show essentially no (economically or statistically) meaningful dierence at the threshold. Both the increase in the density at the threshold as well as the increase in fraction of women are very small relative to the average density and the overall fraction of women. In smaller datasets, such minor discontinuities and density shifts would almost certainly not be detectable. While these ndings point to a small violation of the RD identication assumptions, these should have a relatively small impact on the overall results. In fact, neither trimming observations close to the eligibility thresholds nor directly controlling for observable characteristics aects our results. To ensure that our results are not aected by sorting around the threshold and by particular implementation choices of the RD estimator, we performed multiple robustness checks summarized in the sensitivity section (Section 6). 4 The Average Eect of UI extensions on Job Quality In our precursor paper we have shown that the UI extensions studied here lead to signicant increases in nonemployment duration (Schmieder, von Wachter, and Bender 2012a). Given the rise in nonemployment duration we found and that the related literature has documented and with it potential increase in the time to search for jobs or human capital depreciation it is important to assess whether there are responses in reemployment wages and other indicators of job quality to UI extensions as well. 22

4.1 The Eects of UI extensions on Nonemployment Durations As a benchmark, Table 2 and Figure 2 replicate the analysis of the eect of UI extensions on benet and nonemployment durations for the sample used in this paper, which diers slightly from the previous paper. Figure 2 (a) shows the eect of an increase in potential UI durations on the number of months of receiving UI benets. Each dot represents the average length of UI benet receipt for individuals who began collecting UI benets within a 2 month age window. Figure 2 shows that increasing potential UI durations from 12 to 18 months increases the actual time of receiving UI benets by 1.7 months. At the second threshold, the time of receiving UI benets increases by about 1 monthless than at the rst threshold but expected given the smaller increase in potential durations. This eect is partly mechanical, since individuals who would have exhausted their benets at 12 months or 18 months are now covered for up to 6 more months, and partly behavioral, since individuals may reduce their search eort and thus stay unemployed longer. Either way, the eect is quite large and clearly shows that the policy change is highly signicant for individuals. 14 To demonstrate the purely behavioral eect of an increase in potential UI durations, Figure 2 (b) shows the eect on nonemployment durations. At the rst age threshold the increase in potential UI durations leads to an increase of nonemployment durations of almost 0.9 months. At the second threshold, nonemployment durations increase by about two weeks. Increases in potential UI durations thus have a very clear eect on nonemployment durations and substantially change behavior of unemployed individuals. In Table 2, columns (1) and (2) conrm the visual impression. The eects on actual UI duration and nonemployment duration are very precisely estimated (for example, a t-statistic of larger than 10 for nonemployment durations in the joint model). The table also shows the marginal eect of an increase in potential UI durations by 1 month, i.e. the estimated RD 14 Another way to see this is that about 30 percent of recipients who are eligible for 12 months of UI exhaust their benets 23