Adverse Effect of Unemployment Insurance on Workers On-the-Job Effort and Labor Market Outcomes

Transcription

1 Adverse Effect of Unemployment Insurance on Workers On-the-Job Effort and Labor Market Outcomes Kunio Tsuyuhara May, 2015 Abstract Higher unemployment benefits lower the cost of losing one s job. Workers on-the-job effort may therefore decline and firms may respond by paying lower wages. Using a model of dynamic employment contracting in an economy with search frictions and firm commitment, I investigate the magnitude and macroeconomic consequences of this previously unexplored adverse effect of unemployment insurance in an equilibrium framework. The calibrated model shows that a moderate increase in unemployment benefits decreases the average wage, average employment duration, and aggregate output, and increases layoff rates, average unemployment duration, and unemployment rate. Keywords: Unemployment insurance, Work incentive, Moral hazard, Directed search Department of Economics, University of Calgary, 2500 University Dr. N.W. Calgary, Alberta, Canada ( kunio.tsuyuhara@ucalgary.ca). I thank Francisco Gonzarez, Toshihiko Mukoyama, Henry Siu, and Trevor Tombe for helpful comments. 1

2 1 Introduction Empirical studies regarding the generous unemployment insurance (UI) benefits impact on labor market outcomes often predict conflicting effects: beneficial but statistically very weak effects (e.g., Addison and Blackburn 2000; and van Ours and Vodopivec 2008) or adverse effects (e.g., Card, Chetty, and Webber 2007). However, equilibrium labor search models typically predict only beneficial effects on productivities (e.g., Acemoglu and Shimer 2000) and on wages (e.g., Krusell, Mukoyama, and Şahin 2010), as UI benefits increase job matching quality (the matching effect). These models generally abstract from employed workers response to UI. That is, higher UI benefits reduce the cost of losing one s job and discourage employed workers from exerting work effort on the job. I investigate the magnitude and macroeconomic consequences of this previously unexplored adverse effect of UI in a search and matching framework I study these behavioral responses (the behavioral effect) toward UI using a model of dynamic employment contracting in an economy with search frictions and firm commitment. I develop a framework based on Tsuyuhara (2014) in which a firm output depends on the unobservable effort of its worker. The job is destroyed and the match discontinues if the output is too low (layoff). Furthermore, I introduce into the model a government-run UI system that pays a constant benefit to unemployed workers, and is financed by a proportional income tax. In this model, the workers are arrowed to search on the job. The worker search is a directed process; that is, the firms offer a contract to attract workers, and the workers direct their search to a particular job offer. A higher UI benefit, therefore, enables searching workers to choose a higher wage offer at the expense of lower employment probability. As in the standard search and matching model, this would induce beneficial matching effects on wages at the expense of higher unemployment rate. However, in this model, employed workers decide how much effort to exert based on the disutility of effort and the cost of layoff. A higher benefit reduces the cost of layoff and, therefore, reduces incentive to exert effort on the job. Moreover, firms would respond to this behavioral change of their employees by offering lower wages (the contractual effect). A major objective of this paper is to quantitatively assess these opposing effects on labor market outcomes in a consistent equilibrium environment. The calibrated model shows that a 10% increase in UI benefits from its current U.S. level would increase average layoff rate by 0.1% point (from 2.2 to 2.3), which results in a decrease in average employment duration by one month (from 33.8 months to 32.8 months). If I increase the 2

3 benefits by 10% points, which is common in various empirical studies, 1 the average layoff rate increases by 0.2% (from 2.2 to 2.4) and the average employment duration decreases by almost three month (from 33.8 to 30.9). The increases in benefits in those policy experiments are still modest compared with the massive expansion of UI benefits in the U.S. after the great recession in 2008; however they would have potentially significant impacts not only on unemployment but also on employment. Several indirect empirical evidences support these results. Christofides and McKenna (1996) show that a significant number of jobs terminate when they meet a UI eligibility requirement, and Green and Sargent (1998) show that job hazard rate for seasonal jobs significantly increases after qualification for UI. 2 The model without workers effort decision on the job, which is similar to the model in Menzio and Shi (2010) (MS model hereafter), does not show those adverse effects. In addition to those direct impacts of lower worker effort, 10% increase in a UI benefit decreases the highest equilibrium wage and the average equilibrium wage. The reduced incentive due to a higher UI benefit makes worker effort more expensive. Firms then respond to it by demanding less effort, and therefore wages decrease. Moreover, a higher UI benefit shifts the distribution of employed worker toward jobs with lower wages. It generates the distributional effect of UI policy, which lowers the average wage. Furthermore, a higher UI benefit decreases the aggregate output more substantially (by 0.4% with 10% increase in UI benefits) in the current model than in the model without worker effort (by 0.1%). This is because decrease in aggregate output in the current model is caused by the higher unemployment and the lower productivities of employed workers, whereas the decrease in the model without worker effort is caused only by the higher unemployment. These novel findings suggest that incorporating employed workers incentive within a firm results in the effects of UI on macroeconomic outcomes that are significantly different from those in previous studies. Most of the existing studies on UI focus on unemployed workers job search behavior, and typically treat the behavior of employed workers and contracting problems between an employer and an employed worker in a parsimonious manner. In the optimal UI literature, the primal interest is the trade-off between providing insurance for consumption smoothing and the workers job search incentives. For example, Hopenhayn and Nicolini (1997) analyze a repeated moral 1 See Nakajima (2012) and references therein. 2 Lazear, Shaw, and Stanton (2013) also argue that worker effort serves as a more important role than the composition of the workforce (the matching effect) in explaining the firm s productivity change due to the UI policy. 3

4 hazard problem between the unemployed worker and the benevolent social planner who offers a long-term UI contract but cannot monitor the workers search effort. In this class of literature, Wang and Williamson (1996, 2002) are closest in spirit to the current paper in the sense that UI policy affects the employed worker job-retention effort. However, these studies abstract from how employment contracts responds to the change in UI policy. Acemoglu and Shimer (1999, 2000) respectively introduce firms ex-ante decision regarding capital investment and technology choice in a job search model where unemployed workers can direct their search toward a particular job. These models provide important implications for the effect of UI policy on the firm s decisions and resulting search behavior by the unemployed. Yet, these models disregard employed workers on-the-job behavior. The mechanism that generates the adverse effect is related to efficiency wage models (e.g., Shapiro and Stiglitz 1984); however, this paper extends the scope of study by incorporating equilibrium interaction between firm contracting decisions and labor market conditions. The potentially adverse effect of UI policy on on-the-job effort has been discussed in policy debates Hopenhayn (1996); however, the relevant incentive mechanism is absent in the previous search and matching models. In those models a higher benefit does not affect workers on-the-job effort and incentive contracting design. 3 This paper contributes to the literature by providing a tractable general equilibrium model for analyzing how UI policies affect both the workers search behavior and incentive contracting problems with in a firm. 2 Labour Market with Search Friction and Moral Hazard I consider a labor market with a continuum of infinitely lived workers with measure 1 and a continuum of firms whose measure is determined by competitive entry. All workers and firms are ex ante homogeneous. Time is discrete, continues forever, and is indexed by t. Each worker has a utility function u(w) where w is income in a period. Following the standard assumption in the literature, I assume that workers cannot save nor borrow against their future income. When employed, each worker exerts costly effort, e R +, for the project of the firm in each period. The worker s effort is unobservable to the employer. The cost of effort is given by c(e). Period utility of a worker is u(w) c(e), and each worker maximizes the expected lifetime sum 3 Previous models with endogenous job destruction typically discuss firms decision in terms of job shutdown caused by idiosyncratic productivity shock, and by design, UI policy changes do not affect their decision. 4

5 of utilities discounted at rate β (0, 1), considering the endogenous job-turnover. Each firm hires a single worker for a job. A job in each period results in one of two possible outcomes as a function of the worker s effort: y, called success, with probability r(e) and 0, failure, with probability 1 r(e). If the project succeeds, the job continues in the next period, whereas if the project fails, the job is destroyed due to the low productivity and the worker becomes unemployed (layoff). The expected period profit of a firm is r(e)y w. Each firm maximizes the expected sum of profits discounted at the rate β, considering the endogenous job destruction. I assume that firms commit to a wage-tenure contract. That is, an employment contract specifies a wage profile as a function of the worker s tenure in the firm conditional on survival of the employment relationship. Furthermore, because the workers effort levels are unobservable, the firm needs to determine how much effort to induce given the proposed wage offer. Therefore, a contract specifies a wage profile {w t } t 0 and a recommended effort profile {e t } t 0. In equilibrium, such wage and recommended effort profiles jointly deliver an expected lifetime utility to the worker that is referred to as the value of a contract and is denoted by x. There is a government-run UI system that is financed by a proportional income tax at a rate τ. I assume that all unemployed workers are eligible to receive constant UI benefit b and that benefits are of infinite duration. I model the workers job search as a directed process with respect to the value of job offers. In each period, there are two stages: search/matching stage and production stage. In the search/matching stage, firms post a vacancy at a flow cost k > 0 and offer a contract to recruit a worker. Firms offer contracts with different values to attract workers, and the labor market consists of a continuum of submarkets indexed by x X where X denotes the entire labor market. Let the value of contract x and the value of unemployment U represent the worker s employment state in some period, and G t denote the distribution of workers over X in period t. The fraction of unemployed workers in period t is identified by u t = G t (U). I denote the evolution of G t generically with an operator Ψ such that G t+1 = Ψ(G t ), where Ψ is endogenously determined according to workers job search and firm contracting decision. Both employed workers and unemployed workers have a chance to search for a job with probability λ e and λ u, respectively. Specifically, each worker chooses which submarket to enter to find a job. The ratio of vacant jobs to searching workers in submarket x is denoted by θ(x) and is referred to as the tightness of submarket x. I assume a standard constant returns to 5

6 scale matching technology such that job-finding probability in submarket x is given by p(θ(x)), a function of the market tightness. On the other hand, job-filling probability in submarket x is given by q(θ(x)). The matching technology satisfies that p(θ) = θq(θ). Workers who find a successful match after on-the-job search continue to the production stage with a new employer. In the production stage, unemployed workers consume the net UI benefit (1 τ)b. 4 An employed worker receives the current period net wage income (1 τ)w t as specified in the contract and exerts effort e t for the current period project. At the end of this stage, the project outcome is publicly realized. 3 Equilibrium Conditions 3.1 Competitive Firm Entry and Market Tightness Let J(x) denote a value of a job to the firm that offers a contract of value x to a worker. This is an endogenous value function that is determined in the optimal contracting problem below. During the search stage, a firm chooses what contract to offer to attract a searching worker. The firm s expected value of creating a vacancy in submarket x is given by q(θ(x))j(x). Given the market tightness function θ(x), if the cost k of creating a vacancy is strictly greater than the expected value, then firms do not create any vacancies in submarket x. If k is strictly smaller than the expected value, then firms create infinitely many vacancies in submarket x. Therefore, the competitive firm entry and zero-profit condition generate an equilibrium relationship between these two endogenous functions as follows: q(θ(x))j(x) k = 0. (1) 3.2 Job Search An employed worker evaluates the value of current contract for the remainder of life. it continuation value of contract. 5 I call Consider a worker whose continuation value of the current contract is W. If she receives an opportunity to search and chooses to visit submarket x, she 4 Following the current US system, I assume that the benefit b is considered as taxable income. Furthermore, I disregard home production in this study, and all the income for the unemployed comes from the UI. 5 It is important to note that this value not only reflects the value of the future wages of the current job, but also reflects future gains from on-the-job search as well as losses from job destruction. The derivation of this value will be provided later as a part of optimal contract problem. 6

7 gains net value of search x W with probability p(θ(x)). Therefore, a worker s optimal search problem is to choose which submarket to enter to maximize the expected net value of search. I denote the optimal net expected value of search given W as follows: D(W ) = max p(θ(x))(x W ). (2) x X I denote with m(w ) the worker s optimal search policy of this problem and define the composite function ˆp(W ) = p(θ(m(w ))). That is, ˆp(W ) is the probability that a worker with reservation value W successfully finds an employer in the optimally chosen submarket. Given the optimal search strategy, if an employed worker finds an opportunity to search with probability λ e, her gross expected value for the next period is W + D(W ); whereas if she does not find the opportunity to search with probability 1 λ e, she stay in the current job, which gives continuation value W. Therefore, the expected value from entering the next period with a continuation value W is λ e (W + D(W )) + (1 λ e )W = W + λ e D(W ). For unemployed workers, an appropriate continuation value in the above argument is the value of unemployment U that is determined as follows. First, if an unemployed worker has an opportunity to search a job with probability λ u, the expected net value of search is D(U) using U as a reservation value for the search decision. If she does not have an opportunity to search, she stays unemployed. The above argument for employed workers implies that the expected value from entering the next period as an unemployed worker is U +λ u D(U). A worker who is currently unemployed consumes the constant net UI benefit (1 τ)b, and the value of unemployment must satisfy the following recursive equation; 6 U = u((1 τ)b) + β ( U + λ u D(U) ). (3) 3.3 Optimal Contracting Problem I describe the optimal contracting problem following the recursive contracting approach developed in Spear and Srivastava (1987). The appropriate state variable is a continuation value of contract that the firm promised to deliver to the worker, denoted by V in the following. The choices of a firm in the recursive contracting problem are the current wage and recommended effort {w, e} and the continuation value W that the firm promises to deliver in the following 6 I assume that workers who lost the job due to failure in the previous period cannot search and stay unemployed for one period. This assumption is simply a matter of timing and is typical in the literature. 7

8 period. 7 Then, the maximized value of a job J(V ) is expressed recursively by subject to J(V ) = max r(e)y w + βr(e)(1 λ e ˆp(W ))J(W ), (4) ξ={w,e,w } V = u(w) c(e) + β[r(e)(w + λ e D(W )) + (1 r(e))u], (5) ( e arg max c(e) + β ( r(e)(w + λ e D(W )) + (1 r(e))u )), and (6) e R W {X : J(W ) 0}. (7) The terms r(e)y w in the right hand side of (4) is the firm s current period payoff. following term is its discounted expected value; the job continues with probability r(e) and then the worker will stay in the firm in the next period with probability 1 λ e ˆp(W ). If the job is still active in the next period, its value is J(W ). The firm s choice is subject to the following: (5) a promise-keeping constraint, which requires ξ to provide the worker with the lifetime utility V, (6) an incentive compatibility constraint, which requires the contract induces the worker to voluntarily exert the desired level of effort, and (7) an individual rationality constraint, which requires the firm does not choose a continuation value that leads to a negative profit (value). The solution to this contracting problem is a set of policy functions with respect V, denoted by ξ = {w (V ), e (V ), W (V )}. The 3.4 Government Budget Constraint In each period, the government-run UI system meets the following temporal budget constraint: τ w(x)g t (dx) = (1 τ)bu t. (8) 3.5 Block Recursive Equilibrium Definition 1. A Block Recursive Equilibrium (BRE) is a set of individual objects {D, m, U, J, ξ, θ } and the operator Ψ such that 7 To prove the existence of a recursive equilibrium that will be discussed below, I need to introduce a lottery and allow the firm to randomize over these choices. The purpose of introducing the lottery is to guarantee that the firm s optimal value function J is concave. However, computed examples shows that the firm s value function is concave without lottery for all the parameter configurations, which implies that lottery is not used at the optimal. Therefore, for expositional simplicity, I do not include the lottery in the model description. 8

9 1. the market tightness θ satisfies condition (1), 2. the value of job search D and the optimal search policy m satisfy equation (2), 3. the value of unemployment U satisfies equation (3), 4. the value of firm J and an optimal contract policy ξ satisfy equation (4), 5. Ψ is derived from the optimal policy functions, ξ and m, and 6. the government budget constraint (8) is satisfied. 4 Policy Experiments Existence of a BRE and the qualitative characterization of its optimal contract are discussed in detail in Tsuyuhara (2014). In this paper, I solve the model numerically and describe some of its key quantitative features. Then, using the calibrated model, I study how the generosity of UI affects employed workers effort and investigate its macroeconomic consequences. To highlight how this model differs from the models of previous studies, I compare the results with those from Menzio and Shi s (2010) version of the model (MS model, hereafter) in which there is no workers effort decision on the job. 4.1 Calibration One period is set to be one month. The production level of a successful project y is normalized to 1. I set the discount factor β equal to 0.996, so that the annual interest rate in the model is 5%. The worker s utility function is of the standard CRRA form u(w) = w1 σ 1 σ. I choose σ = 2, a common value in the literature. The worker s disutility of effort is of a quadratic form c(e) = 1 2 e2. The matching technology is summarized by the employment probability function p(θ) = θ(1 + θ γ ) 1/γ. Following Menzio and Shi (2010), I set γ = 0.5 so that the elasticity of substitution between vacancies and applicants is 2/3. I normalized λ u = 1. The above parameters are calibrated without solving the model and are common to the benchmark and MS model. Table 1 summarizes these parameters. 8 There are four parameters left to be calibrated, and these are chosen by solving the model. I set b = so that the value of unemployment benefit is 40% of the average wage, which is the upper end of the range of income replacement rates in the U.S. (Shimer, 2005). For this 8 To compute the model with exogenous, fixed productivity, I calibrate the model with the probability of success so that the involuntary job destruction probability matches the empirical moment. 9

10 level of UI, a balanced budget requires a 2.1% labor income tax rate. The probability of success is given by a function r(e) = exp( ρ e ). The productivity parameter ρ, vacancy creation cost k, and probability of search for the employed λ e are set at 0.008, 0.073, and 0.85, respectively so that the computed average rates of transition between employment and unemployment and across employers jointly match the empirical moments in the U.S. data. 9 Table 2 summarizes these parameters. Figure 1 plots the equilibrium value functions, J(x). As discussed above, the computed value functions are concave in all the parameter configurations and clearly so for the calibrated parameter values. Therefore, the optimal contract does not use lottery in equilibrium. Figure 2 plots the optimal continuation value and the optimal search strategy for each value of the current contract. As shown in Tsuyuhara (2014), the optimal continuation value increases with tenure, and this is shown as an increasing continuation value profile over the current value. When employed workers search for a job, they look for a job that offers a contract with higher value than the continuation value of the current job. Therefore, the optimal search strategy implies a larger value than the optimal continuation value until these lines cross once at Once the current contract value reaches this point, there is no vacancy offering a better contract and the employed workers stop searching. This point indicates the highest starting value of contract. However, the optimal continuation value keeps increasing past this point even without the form s retention motive. This is because the firm can increase the probability of success by promising higher value to the worker. The firm continues increasing the value until the cost of required higher wage outweighs the benefit of higher probability of success. The point where the cost and the benefit are equal determines the highest equilibrium value. This segment of the value of contract constitutes a monopsonistic labor market. These two lines, combined with the 45-degree line, characterize a discrete-time dynamical system that describes how the value of contract increases over time via either on-the-job search or promotion within a firm. Figure 3a displays six simulated sample paths of value dynamics over 20 years (240 months). For expositional purposes, the lowest value represents the value of unemployment. Notably, these paths show that it takes only a short time for the value of contract to reach the highest starting value, at ; however, it takes a substantially longer time to reach the highest equilibrium value afterward. In Figure 3b, the MS model does not show this feature, and the value reaches 9 The data used for computing these statistics are described in detail in Menzio and Shi (2011). 10

11 the highest equilibrium value relatively quickly after reemployment. This comparison implies that the lack of competition in the monopsonistic segment slows down the promotion and the wage growth. This feature may help explain why displaced workers experience long-lasting earning losses after unemployment. Figure 4 shows the optimal wage profile over the value of contract. I draw these profiles on the active submarkets to highlight the correspondence between the value dynamics and these profiles. It demonstrates that wage increases steadily until the current value reaches the highest starting value, but wage growth slows down substantially once the value of contract passes that point. This feature is consistent with the above discussion regarding the lack of competition as a reason of slow wage growth. Figure 5 shows the incentive compatible effort profile over the value of contract. Unlike the wage profile, the effort profile indicates that effort steadily increases over the whole domain. However, there is a very narrow range of values of effort, which translates into productivity over (0.9732, ). This result suggests that workers effort choice in the current model does not account for large productivity differences among homogenous workers. 4.2 Changes in Unemployment Benefit Table 3 summarizes the effects of an increase in the UI benefit b by 10% from the above benchmark calibration. The first two columns present the results from the current model (Baseline), and the remaining columns present the results from the MS model. I use a 10% increase to start for two reason. First, as this is a calibration exercise using few empirical moments to pin down model parameters, small deviations from the benchmark level of benefit would provide the most reliable results. Second, it allows me to compare my results with those in Acemoglu and Shimer (2000) that analyze a similar search model and use a 10% increase for their policy experiment. I computed the average job transition rates and other aggregate statistics using the steady state cross-sectional distribution of workers. Furthermore, I computed the average employment duration and average unemployment duration based on simulations of labor market transitions of 10,000 workers over 240 months. A balanced budget with a 10% increase in b requires a 2.4% labor income tax rate. The current model and the MS model share the standard effects of a higher UI benefit. In a directed search model, a higher UI benefit induces unemployed workers to search for a job with a higher initial wage at the expense of employment probability. Therefore, the average 11

12 job finding probability decreases (the lower job finding rate), and the average unemployment duration increases by 0.1 month (3 days) in the current model and by 0.06 month (1.5 days) in the MS model. As a result, the unemployment rate rises in both models. These figures are consistent with Atkinson and Micklewright s (1991) survey of empirical studies, though slightly smaller than Acemoglu and Shimer s (2000) result from their calibrated model, in which a 10 % increase in unemployment benefit raises the average unemployment duration by one week. As all unemployed workers search for a job with a higher initial wage, the lowest equilibrium wage increases in both models as a result of a higher UI benefit. The current model, however, shows a stark contrast to the MS model that is new in the literature and important for policy. First, a 10% increase in a UI benefit increases average layoff rate by 0.1% point and decreases the average employment duration by 1 month in the current model. The MS model does not generate these effects because the rate of job destruction is assumed to be constant. In the current model, however, an employed worker chooses how much effort to exert by comparing the benefit of staying employed with the cost of layoff. A higher benefit reduces the cost of layoff and thus discourages employed workers to exert effort. Therefore, a higher benefit increases the average rate of job destruction, which causes the higher layoff rate and thus decreases the average employment duration. In this sense, the higher unemployment rate due to a more generous UI benefit in this model is caused by the lower job finding rate and the higher layoff rate. In addition to those direct behavioral effects, a higher UI benefit causes the contractual and distributional effect. That is, a higher UI benefit makes the employed worker effort more expensive for the employer. Therefore, firms demand less effort, which results in lower wage offer. The adverse effect on contracts is clearly seen from the lower highest equilibrium wage by and lower average wage by in the current model. In contrast, in the MS model, UI policy does not affect employed workers behavior. Therefore, firms have no incentive to respond to the policy change and the highest equilibrium wage stays the same. Moreover, due to a higher average layoff rate, a higher UI benefit shifts the distribution of employed workers toward jobs with lower wages. This distributional effect of more generous UI policy decreases the average wage even with the higher lowest equilibrium wage. In the MS model, however, a higher UI benefit simply eliminates the low wage jobs without causing a significant change in employed worker distribution, and thus a more generous UI increases the average wage. Furthermore, 10% increase in a UI benefit decreases the aggregate output by 0.4% in the 12

13 current model, however, only by 0.1% in the MS model. This is because decrease in the current model is caused by the higher unemployment and the lower productivities of employed workers, whereas decrease in aggregate output in the MS model is caused only by the higher unemployment. This result implies that workers on-the-job effort has a strong amplification effect of the policy change. 4.3 Robustness To examine robustness of the above mentioned results, I consider the following two alternative cases. First, I increase the UI benefits by 10% point, which is equivalent to a 26% increase in benefits. This is because various empirical estimates are available that examine the effects of a 10% point increase in the replacement rate of UI benefits. Second, I raise the coefficient of risk aversion to σ = 4. This is because it crucially affects how workers evaluate the cost of layoff and thus how they respond to the UI policy change. Table 4 summarizes the results of a 10% point increase in UI benefits. The results indicate further magnified effects of the increase in UI benefits. The average unemployment duration increases by approximately a week in both models, which is consistent with existing estimates of the effects of a 10% point increase in UI benefits, summarized in Nakajima (2012). The average employment duration here decreases by approximately 3 months and aggregate output decreases by 2.5%. The aggregate output in the MS model decreases only by 0.4%, which indicates strong amplification effect of employed worker effort on labor productivity. As far as I know, there are no comparable estimates of the change in employment duration or in aggregate output caused by an increase in UI benefits in the literature. Nevertheless, these results indicate that adverse effects of generous UI policy can be quite substantial. Table 5 summarizes the results of higher risk aversion. Higher risk aversion makes the workers more willing to avoid unemployment. Therefore, an increase in UI benefits may not cause as much adverse effect as in the baseline case mentioned above. However, despite this potential mitigating mechanism, a higher UI benefit still has adverse effects on unemployment rate, average layoff rate, average employment duration, and aggregate output. The effect on the average wage is smaller here but still negative. The overall comparison between the current model and the MS model is robust to the change in the coefficient of risk aversion. Therefore, my main conclusion regarding adverse effect of UI benefits is not dependent on the low degree of risk aversion. 13

14 5 Conclusion This paper investigated the effect of UI on labor market allocation and resulting macroeconomic consequences. The model incorporated employed workers unobservable effort and firm contracting decision into a search and matching model. This paper has two main contributions to the literature. First, the paper proposed a tractable equilibrium model for analyzing how labor policies affect both the workers search behavior and incentive contracting problems with in a firm. Second, I quantitatively show that adverse effect of generous UI policies on work incentives would outweigh the positive effect on unemployed workers search behavior. The calibrated model shows that a moderate increase in unemployment benefits decreases the average wage, average employment duration, and aggregate output, and increases layoff rates, average unemployment duration, and thus unemployment rate. The model does not incorporate ex-ante heterogeneous productivity of the firms and matching effect through worker search, which have been extensively analyzed in the previous studies. Nevertheless, it added a novel aspect of endogenous heterogeneity of worker productivity through contracting and sheds new light on the behavioral effect of UI for considering its macroeconomic consequences. 14

15 0.7 Figure 1: Firm Value Function Value of Contract Figure 2: Search Strategy and Continuation Value Search Strategy 295 Value of Contract Continuation Value degree Value of Contract 15

16 Figure 3a: Sample paths of value dynamics: Baseline 16

17 Figure 3b: Sample paths of value dynamics: MS 17

18 Figure 4: Wage Profile Wage Value of Contract 0.32 Figure 5: Effort Profile Effort Value of Contract 18

19 Parameter y - Output level 1 β - Discount factor σ - CRRA 2 γ - Matching technology 0.5 λ u - Probability of search (unemployed) 1 δ - Exogenous job-destruction Table 1: Parameters calibrated without solving the model: The exogenous jobdestruction parameter, δ, is defined only in the model without employed worker effort decision. Parameter Baseline MS b - Unemployment benefit ρ - Worker productivity k - Vacancy creation cost λ e - Probability of search (employed) Table 2: Parameters calibrated by solving the model: Baseline is the model studied in this paper. Column MS shows the values for the MS model. 19

20 Variable Baseline MS Unemployment benefit b Tax rate τ Unemployment rate 5.3% 5.6% 5.5% 5.6% Average Job finding rate 45% 44% 45% 44% Average Layoff rate 2.5% 2.6% 2.6% 2.6% Average unemployment duration Average employment duration Aggregate output Average wage Highest equilibrium wage Lowest equilibrium wage Table 3: Effect of a 10% increase in b: Variable Baseline MS Unemployment benefit b Tax rate τ Unemployment rate 5.3% 6.3% 5.5% 5.9% Average Job finding rate 45% 42% 45% 41% Average Layoff rate 2.5% 2.8% 2.6% 2.6% Average unemployment duration Average employment duration Aggregate output Average wage Highest equilibrium wage Lowest equilibrium wage Table 4: Robustness: 10% points (26%) increase in b: 20

21 Variable Baseline MS Unemployment benefit b Tax rate τ Unemployment rate 5.2% 5.9% 5.5% 5.7% Average Job finding rate 45% 44% 45% 43% Average Layoff rate 2.5% 2.7% 2.6% 2.6% Average unemployment duration Average employment duration Aggregate Output Average wage Highest equilibrium wage Lowest equilibrium wage Table 5: Robustness: Higher risk aversion (σ = 4) 21

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