Does the effect of employment protection depend on the composition of unemployment?

Bastgen, Andreas Article Does the effect of employment protection depend on the composition of unemployment? Journal for Labour Market Research Provided in Cooperation with: Institute for Employment Research (IAB) Suggested Citation: Bastgen, Andreas (2024) : Does the effect of employment protection depend on the composition of unemployment?, Journal for Labour Market Research, ISSN 2510-5027, Springer, Heidelberg, Vol. 58, Iss. 1, pp. 1-28, https://doi.org/10.1186/s12651-024-00380-z This Version is available at: https://hdl.handle.net/10419/308515 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. 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Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http:// creat iveco mmons. org/ licen ses/ by/4. 0/. Journal for Labour Market Research Does theeffect ofemployment protection depend onthecomposition ofunemployment? Andreas Bastgen1* Abstract I develop an equilibrium-matching model with job rationing and endogenous layoffs in order to investigate whether the composition of unemployment (rationing versus frictional) influences the way firing costs affect employment. The model suggests that firing costs lead to a strong adverse employment effect if unemployment is mainly caused by job rationing, whereas in labor markets driven by search frictions firing costs have only a negligible impact on employment. The paper tests this hypothesis using data on the adoption of wrongful-dismissal laws adopted by U.S. state courts during the 1970s and 1980s. Results indicate that for two of the three wrongful-dismissal laws investigated, unemployment composition is crucial for the induced employment effects. Keywords Employment protection, Firing costs, Wrongful-dismissal-laws, Rationing unemployment, Search unemployment, Search-and-matching, Difference-in-difference JEL Classification J64, J65, O31, O38 1 Introduction Beginning in the 1970s, many countries have introduced employment protection laws (EPL). Policy makers typically consider EPL as a way to prevent unjust dismissals and to provide income security to workers (see Clark 2005). Scientists and policy makers are particularly interested in the employment effect of EPL. In standard search models with endogenous layoffs, EPL lowers turnover, while the sign of the employment effect remains ambiguous (see Pissarides 2000). The present paper contributes to the literature by exploring whether the effect of EPL is dependent on the cause of unemployment: search frictions or job rationing. I do so by leveraging on the job rationing model proposed by Michaillat (2012). In this model rationing unemployment occurs naturally due to diminishing marginal returns to labor and some sort of real wage rigidity. In such an environment, it is possible that the marginal product of the least productive worker falls short of the real wage, implying that firms would not extend employment beyond this point even in the absence of recruiting costs. Michaillat defines the unemployment level that prevails without search frictions as rationing unemployment.1 In the presence of wage rigidities, the marginal value of a worker is decreasing in firing costs.2 Frictionless employment is determined purely by comparing the wage to the marginal value of a worker. Hence, it decreases in firing costs, which directly implies that rationing unemployment has unambiguously to increase in firing *Correspondence: Andreas Bastgen [email protected] 1 Department of Economics, University of Applied Sciences Dortmund, Emil-Figge-Straße 44, 44227 Dortmund, Germany 1 The term rationing unemployment as defined by Michaillat (2012) should not be confused by mutually binding rationing constraints on the product and labor market as proposed by Keynesian disequilibrium models (see Barro and Grossman 1971). 2 I use the term “firing costs” and “EPL” interchangeably as the purpose of EPL is to make layoffs costly. 21 Page 2 of 28 A.Bastgen costs. However, an increase in rationing unemployment also increases total unemployment and thus leads to lower market tightness. Lower market tightness causes lower recruitment costs, which implies that the additional unemployment caused by search frictions has to be smaller. Michaillat 2012 discusses the pro-cyclical3 behavior of the search component. In the context of EPL, there is a second effect: EPL reduces job destruction rates. Thus, firms need to post fewer vacancies in order to maintain the same employment level over time. This second effect additionally lowers market tightness, recruiting costs and, finally, frictional unemployment. The theoretical model developed in the next section accordingly shows that frictional unemployment is monotonically decreasing in firing costs. The prediction of my theoretical model is simple: EPL will aggravate the situation, if EPL is introduced in a labor market characterized by heavy rationing. In contrast, if one introduces the same laws in a labor market driven by search frictions, aggregate employment will barely decrease or even increase. Other theoretical mechanism explaining the employment effect of EPL include for example Pissarides (2001). He gives a possible explanation why there is no clear detrimental effect of EPL on employment. If workers want employment protection as an insurance against income risk, firms do not oppose it, because offering it to their employees, enables firms to reduce the per-unit cost of labor. EPL legislation is needed to reach the optimal level of insurance, because perfect insurance markets cannot develop due to moral hazard. Boeri and Garibaldi (2007) show that in a dynamic labor market model under uncertainty, employment protection may cause a transitional job creating effect, which they call the “honeymoon” effect. There exists a large literature trying to investigate the effect empirically. Lazear (1990) uses European data to find that severance pay requirements reduce employment. International organizations found a negative impact on the participation rate, but a positive effect on the employment rate for prime age men (see OECD 1994). Several studies have supported the view that EPL can at least be associated with high youth unemployment rates.4 Despite this emerging consensus, recent studies [e.g. Noelke (2016)] challenge the conventional view. Using OECD data, he finds no robust evidence linking EPL to inferior youth labor market performance. He notes that although there is a strong positive correlation between regulations on temporary contracts and youth unemployment, country fixed effects completely wipe out this correlation. Cahuc et al. (2023) document that there exist judgespecific differences on granting compensation for wrongful dismissal. The paper assesses the impact of pro-worker judge bias on several key metrics like job creation, job destruction or employment. Interestingly, the employment effect depends on firm size. It is found to be negative for small and low-performing firms but not significant for the other firms. Several papers also emphasize the possibility that EPL may increase productivity and innovation by giving workers incentives to invest in firm-specific human capital5 or by inducing a structural shift in the economy.6 In order to minimize endogeneity problems, some empirical studies7 exploit a natural experiment, which has occurred in the United States during the 1970s and 1980s. As the U.S. has a long tradition of employment-at- will, EPL was almost non-existent until the mid-twenti- eth century. However, beginning in the late 1970s several U.S. state courts began to adopt wrongful-dismissal laws. The most prominent ones are the implied-contract, the public policy and the good-faith exception. Muhl (2001) provides detailed explanations of all three exceptions. The implied-contract exception states that even if there is no written contract, the employee may have a valid expectation of continued employment based on the supervisor’s statement, an established practice or description of termination processes in the employee handbook. Under the public policy exception, an employee is wrongfully discharged when the termination violates an explicit, well-established public policy of the state. For example, in most states an employer cannot terminate an employee for refusing to break the law at the request of the employer. The good-faith exception is the most significant departure from the traditional employment-at-will doctrine. This exception reads a covenant of good-faith and fair dealing into every employment relationship. Terminations are therefore subject to a “just cause” standard. Exploiting the variation happening in the 1970s and 1980s Macleod and Nakavachara (2007) argue that the effect of EPL differs between educational groups. They argue that the implied-contract and the good-faith exception raise employment of high skilled workers but have detrimental effects on employment of low skilled 3 Pro-cyclical here means being positively correlated with the business cycle. 4 See Esping-Andersen (2000), Heckman and Pages-Serra (2000), Bertola etal. (2007), Kahn (2007), Addison and Texeira (2003), Botero etal. (2004), Breen (2005), Allard and Lindert (2007), Cahuc etal. (2014). 5 See Ackerlof (1984), Soskice (1997), Zoega and Booth (2003), Belot etal. (2007), Pierre and Scarpetta (2013), Wasmer (2006), Acharya etal. (2014). 6 Bastgen and Holzner 2017 develop an equilibrium-matching model in which employment protection increases the willingness-to-pay for new ideas and thus shifts economic activity towards more innovation. 7 See Autor etal. (2006), Autor etal. (2007), Acharya et al. (2014) and Macleod and Nakavachara (2007). Page 3 of 28 21 Does theeffect ofemployment protection depend onthecomposition ofunemployment? workers. Autor et al. (2006) find significant negative employment effects only for the implied-contract exception, whereas the public policy and the good-faith exception do not significantly alter employment. Moreover, they find that the detrimental effect is more pronounced for production workers. As production workers have a lower level of formal education compared to non-pro- duction workers, these findings are in line with Macleod and Nakavachara (2007). Using the same natural experiment Autor etal. (2007) conclude that EPL reduces total factor productivity, while Acharya etal. (2014) note that EPL has the potential to raise innovation. I broadly follow the empirical approach of Autor etal. (2006) in order to validate my theoretical results. Unluckily, rationing und frictional unemployment are not directly observable. However, my theoretical model suggests that, given matching efficiency, high (low) total unemployment is associated with unemployment being driven by rationing (search frictions). Accordingly, when accepting my theoretical model and assuming that differences in matching efficiency are negligible,8 pre-treat- ment unemployment is a valid proxy for the composition of unemployment. This issue is discussed in more detail in chapter3.5. Empirical results suggest that the employment effects of the public policy and good-faith exception significantly depend on pre-treatment unemployment. In contrast, pre-treatment unemployment does not significantly influence the way the implied-contract exception impacts employment. A possible explanation for this result could be that firms quickly adapt to the implied-contract exception by updating their recruitment process.9 In this way, the implied-contract exception acts more as a law, which imposes additional recruiting costs. Correspondingly, the labor market effect of the implied-contract exception may not depend on the composition of unemployment. I structure the rest of the paper as follows: Section2 outlines the theoretical model and illustrates its main insights. Section3 provides some background information on wrongful-dismissal laws, describes the empirical model and discusses the results. Finally, section 4 concludes. 2 Theory 2.1 Framework The model is a variant of the classical search-and-match- ing model in the tradition of Mortensen and Pissarides (1994). It deviates from the basic textbook model by allowing for large firms, endogenous layoffs and real wage rigidities. The assumption of large firms with diminishing marginal returns combined with real wage rigidities opens up the possibility of rationing unemployment in the sense of Michaillat (2012), whereas endogenous layoffs allow studying the effects of firing costs. The model is set in continuous time and focuses on steady states.10 Therefore, the model has a medium-term focus. Although diminishing marginal returns are often associated with short-term models in which one production factor (capital) is fixed, there are several arguments why diminishing marginal returns may also translate into the medium run. These arguments include capital adjustments costs, barriers of entry and liquidity constraints. Diminishing marginal returns may also arise due to heterogeneous worker productivity. Agents are risk neutral and infinitely lived. Labor is the only factor of production. Households consume the entire production in each period. The model is populated by a unit mass of firms and workers. Each worker supplies one unit of labor. The discount factor is labeled β . Firms exhibit two different idiosyncratic states: A low productivity state L in which productivity equals γL and a high productivity state H in which productivity equals γH>γ L . I denote the mass of state H and state L firms as mH and mL , respectively. Firm i production reads γsNα i , where s={H,L} indicates the current state of firm i . As α<1 firms experience decreasing marginal returns. The transition probability from state H to state L is given by δ , whereas η denotes the probability of returning to state H . I call the optimal number of workers employed by firm i in the high state N H i , wherea s N L i denotes the optimal number of workers in the low state. Laying off workers causes firing costs f per worker. There is no exogenous rate of job destruction. In order to hire workers firms must post vacancies. If a firm posts a vacancy, it incurs per-period costs c. Unemployed workers and vacancies are matched using a standard constant returns to scale matching function (see Petrongolo and Pissarides 2001). Market tightness, defined as the ratio of vacant jobs and unemployed workers, is denoted as x , the worker-finding rate as m(x) , and the job-finding rate as xm(x) . 2.2 Profit functions andoptimality conditions The following equation governs employment in firm i over time t : 8 This assumption is discussed in detail in Section D in the Appendix. 9 Such an update may include a careful revision of new employment contracts and policy handbooks to rule out the danger that an implicit contract is established. 10 The steady state assumption implies that the model cannot be used to assess the economy’s behavior in the transition period between one steady state (e.g. low firing costs) and another (e.g. high firing costs). Due to the same reason, the model is not suited to investigate whether EPL amplifies or attenuates temporary shocks (e.g. aggregate technology shock) to the economy. 21 Page 4 of 28 A.Bastgen As there are no aggregate shocks, firm level employment remains constant as long as a firm stays in its productivity state. Moreover, note that there are no exogenous job separations. Together, these two assumptions imply that all firms, which remain in their current state neither post vacancies nor layoff workers. A firm experiencing an adverse transition (H⇒L) choses to layoff Li = NH i − NL i workers, whereas a firm facing a favorable transition (L⇒H) immediately hires NH i − NL i workers by posting V i= N H i−N L i m(x) vacancies. Firms in state L never have an incentive to post vacancies, whereas firms in state H never have an incentive to fire a worker. The following Bellmann equation characterizes the expected profit of firm i in state H with workforce NH i : Correspondingly, the expected profit of firm i in state L with workforce N L i reads: When determining N H i firms have to take into account that hiring requires posting vacancies. Posting a vacancy causes costs c per vacancy. Hiring an additional worker requires 1 m(x) vacancies [see Eq.(1)]. Correspondingly, the firm incurs recruiting costs c m(x) per worker. A firm entering state H choses NH i in order to equalize the marginal value of an additional worker with marginal hiring costs: When choosing NL i firms have to take into account that firing a worker causes firing costs f. Therefore, a firm entering state L choses NL i in order to equalize the marginal value of laying off an additional worker to marginal firing cost. 2.2.1 Closed form solutions forlabor demand To derive closed form solutions for NH i and NL i , I calculate the marginal value of an additional worker in both states by taking the partial derivative of eqs. (2) and (3) (1) dN i dt =m(x)Vi−L i (2) π H i NH i  =γH NH i α − WHNH i + β  δ  πL i  NH i + (1 − δ)πH i(NH i)  (3) π L i NL i )  =γ L NL iα −WLNL i +β  (1−η)πL i NL i +ηπH i (NL i] (4) ∂πH i  N H i  ∂NH i = c m(x ) (5) − ∂π L i  N L i  ∂NL i =f with respect to N H i and NL i respectively. Combining the marginal values with Eqs. (4) and (5) and rearranging yields: Equations(6) and (7) determine NH i and N L i for given market tightness and wages. 2.3 Wage Setting Michaillat 2012 shows that rationing unemployment arises, when diminishing returns are combined with rigid wages. I closely follow his approach by using the following simple wage schedule determining the wage in state s={H,L} . ω is a constant and µ is the wage elasticity with respect to changes in productivity. I assume µ<1 implying that the wage adjusts less than one-to-one to changes in productivity. Although, a simplistic wage schedule as posted above is only a rough approximation of reality, it captures empirical facts reasonable well. Empirically wages are linked to productivity, but experience a severe amount of rigidity. As long as wages are somewhat rigid, rationing unemployment may occur and the implications of the paper remain valid. This holds independent of the source of the rigidity (for example collective bargaining, minimum wage laws or efficiency wages). Further note that wages do not react to the introduction of employment protection itself (no pass through). However, in the presence of wage rigidity, I consider this an acceptable simplification. Even with flexible wage bargaining,11 rationing unemployment may arise, if the value of the outside option z is larger than the marginal product of labor evaluated at full employment.12 As many countries maintain generous unemployment benefit schemes, setting z to a high value compared to productivity is a realistic feature of many labor markets (see Hall 2005). Hence, my results are applicable even in a model with endogenous wages. (6) c m(x) =αγH  NH i  α−1 −WH+β  −δf+(1−δ) c m(x) (7) − f=γLα  NL i  α−1 −WL+β  −(1−η)f+ηc m(x) (8) WS =ωγ µ S 11 Large parts of the literature assume that wages satisfy the Nash bargaining solution with symmetric bargaining weights. In models with large firms the corresponding assumption is intra-firm wage bargaining as proposed by Stole and Zwiebel (1996), which is also known as generalized Nash Bargaining. 12 Hagedorn and Manovskii (2008) argue that a high outside option value is necessary to explain the large fluctuations in unemployment observed in the data. Page 5 of 28 21 Does theeffect ofemployment protection depend onthecomposition ofunemployment? Combining the wage-setting schedule with eqs. (6) as well as (7) and rearranging implies: It is useful to investigate the relationship between firm-level employment and market tightness implied by Eqs.(9) and (10). Market tightness enters the optimality conditions via recruiting costs. Intuitively, higher market tightness lowers the worker-finding rate and thus causes higher recruiting costs c m(x) . However, optimal firm-level employment in the two states depends very differently on recruiting costs. Firm-level employment in the high productivity state is decreasing in recruiting costs (and thus in market tightness) as higher recruiting costs require the marginal value of a worker to increase which can only be done by downward adjusting employment. In contrast, firm-level employment in the low productivity state is increasing in recruiting costs. Firms entering the low productivity state chose to layoff less workers if recruiting costs are high in order to save future hiring costs. Compared to a frictionless labor market in which firms hire (fire) workers until the marginal value of hiring (firing) equals zero, firms in state H employ less workers, while firms in state L employ more workers. 2.4 Rationing unemployment Rationing unemployment occurs if total labor demand in absence of recruiting costs falls short of labor supply (unity). This limiting case can easily be analyzed by letting matching efficiency go to infinity13 or setting vacancy posting costs to zero. By doing so, market tightness drops out of Eqs.(9) and (10). Solving both equations for firm-level employment yields firm-level labor demand schedules NH,R i and NL,R i occurring in a frictionless labor market: (9) N H i(x)=  αγH c m(x) (1−β(1−δ)) +ωγ µ H+βδf  1 1−α (10) N L i(x)=  αγL ωγ µ L −(1−β(1−η))f−ηβ c m(x) 1 1− α (11) N H,R i=  αγH ωγ µ H +βδf 1 1− α (12) N L,R i=  αγL ωγ µ L −(1−β(1−η))f 1 1− α N H,R i and NL,R i depend only on the labor elasticity of output α , the wage constant ω as well as on firing costs f . Note that NH,R i is decreasing in firing costs, while N L,R i is increasing. Firms entering the high productivity state hire less workers, because the marginal value of employing a worker is decreasing in firing costs, while firms entering the low productivity state keep more workers in order to save firing costs. To facilitate intuition, solve Eqs.(11) and (12) for the marginal product of labor: Equations (13) and (14) demonstrate that firing costs make it optimal for firms in the high productivity state to choose an employment level which guarantees that the marginal product of labor exceeds the real wage, whereas firms in the low productivity state choose an employment level which yields a marginal product of labor below the real wage. Firing costs reduce the gap between employment levels in both states and therefore reallocate workers to low productive firms. Note that it is total and not firm-level labor demand what matters for determining rationing unemployment. In the job-rationing model proposed by Michaillat (2012) rationing occurs when the marginal product of labor evaluated at full employment falls short of the real wage. It is not possible to make an analogous statement for the present model, as there is no marginal product of labor for the whole economy, but two different marginal products for each productivity state. Nevertheless, as in the standard model, rationing occurs if the wage compared to marginal productivity (corrected for firing costs) is high. To calculate rationing unemployment it is necessary to calculate aggregate labor demand, which is given by: where m H= η η+δ and m L= δ η+δ denote the share of firms in the high-, respectively, low productivity state. Rationing unemployment immediately follows as uR=1−NR . It depends not only on firm-level employment in both sectors but also on the (exogenous) distribution of firms across productivity states. Negative values of uR indicate that without recruiting costs labor demand would exceed labor supply, that is, there would be a shortage of labor. Allowing for negative values of uR is useful to highlight the crucial economic mechanism of the model. In that case, observable unemployment is caused entirely by search frictions. (13) αγH ( NH,R i ) α−1 =ωγ µ H +βδ f (14) αγL (N L,R i )α− 1 =ωγ µ L −[1−β(1−η)]f (15) NR =m H N H,R i +m L N L,R i 13 In this case, vacancies and workers are matched instantaneously. Correspondingly, the worker finding rate m(x) goes to infinity, which implies that recruiting cost go to zero. 21 Page 6 of 28 A.Bastgen 2.5 Equilibrium withfrictional labor market If search frictions are present, labor market flows have to be taken into account explicitly. As I restrict attention to stationary equilibria labor market flows must be balanced: where U=(1−(1−q)N) measures the pool of jobless individuals available for hiring. U is also referred to as beginning-of-period unemployment (see Blanchard and Gali 2010), that is, unemployment before hiring has taken place. In contrast, u measures within-period unemployment. Rearranging yields a Beveridge curve like expression: where NSS denotes the employment level consistent with balanced labor market flows as a function of the job-find- ing rate xm(x) and the job destruction rate q . In contrast, to the standard search and matching model, q is endogenous and given by: The second relationship between aggregate employment and market tightness is obtained using firm-level optimality conditions as well as the definition of aggregate employment. The latter reads: Equilibrium market tightness is determined by the intersection of Eqs.(17) and (19): Section A in the Appendix shows that two potential candidates for equilibrium market tightness x∗ and x∗∗ exist ( x∗∗ >x∗) . It also shows that in the high market tightness equilibrium, labor demand is increasing in recruiting costs, which contradicts empirical evidence. In addition, Section B in the Appendix shows that the high market tightness equilibrium is not stable, while the low market tightness equilibrium is. Thus, I focus on the low market tightness equilibrium x∗ . Given equilibrium market tightness x∗ , firm level employment is given by Eqs. (9) and (10). As N = mHNH i + mLNL i one can also calculate aggregate employment. Unemployment follows using u=1−N . The primary goal of the illustrative model is to shape intuition about how frictional and rationing unemployment react to changes in firing costs. First, rationing (16) qN =xm(x)U (17) N SS = xm(x) q+xm(x)(1−q) (18) q =δmH N H i(x)−N L i(x ) N (19) NFOC =m H N H i (x)+m L N L i (x ) (20) N SS (x)! =N FOC (x) unemployment increases in firing costs, if firing costs are reasonably low compared to the wage (see Appendix C for a proof)14: where  = �Aγ µ LγH−γLγ µ H �AγH( 1 −β( 1 −η))+γLβδ is an exogenous constant. Second, frictional unemployment decreases in firing costs if labor demand, for a given market tightness, is decreasing in firing costs (see Appendix C for a proof): This is a very weak assumption, as the only channel through which firing costs positively influence labor demand is via lowering market tightness (as less vacancies are needed for a given level of employment). Correspondingly, I formulate the following proposition: Proposition If Eqs. (21) and (22) are satisfied, an increase in firing costs causes an increase in rationing unemployment uR and a decrease in frictional unemployment u−uR . To facilitate intuition the models limiting behavior can be investigated. Assume that firing costs are raised to the highest level (denoted as f∗ ) consistent with the plausibility constraint NH i −N L i ≥ 0 . By definition, it holds that lim f → f ∗ (N H i−N L i)= 0 . Correspondingly, the job destruction rate q converges to zero as well. As labor market flows have to be balanced in steady state, the jobfinding rate also converges to zero. This is possible only if either market tightness or unemployment converge to zero. Thus, when restricting attention to equilibria with positive unemployment, market tightness converges to zero. Hence, lim f→f ∗ x∗ = 0 , implying lim f→f ∗  N−N R = 0 , that is, frictional unemployment vanishes when firing costs are raised to its maximum value. The remaining unemployment is due to job rationing. 2.6 Equilibrium characterization As the overall effect of a change in firing costs on employment is ambiguous, the next step is to numerically explore the models reaction to changes in firing costs in different economic regimes.15 Table1containsnumerical values for all exogenous variables of the model.Like in Michaillat (2012) the model is calibrated at a weekly (21) f <ω∗ � (22) ∂ N FOC (x,f) ∂f < 0 14 The reason why ∂ N R ∂f changes its sign at very high levels of f is rooted in the convex shape of NL,R . 15 A side effect of numerically calibrating the model is the possibility to graphically display the key results of the model, which vastly improves intuition. Page 7 of 28 21 Does theeffect ofemployment protection depend onthecomposition ofunemployment? frequency to fit U.S. data. I use a standard Cobb–Douglas specification of the matching function (see Pissarides and Petrongolo 2001), that is, M=τU�V1−� where τ denotes matching efficiency. Accordingly, the workerfinding rate reads m(x)=τx−� whereas the job-finding rate reads xm(x)=τx1−� . The baseline calibration consists of the following ten values for exogenous variables: matching efficiency is set to τ=0.233 . The discount rate is set to β=0.99 , vacanc y posting costs are set to c=0.214 and the output elasticity of labor is set to α=0.66 [all values correspond to Michaillat (2012)]). The matching elasticity with respect to unemployment is set to =0.7 (see Shimer 2005). Firing costs f are set to 0.27 reflecting that firing costs in the U.S. roughly equal one month of production (see Bartelsmann, etal. 2016). Finally, the wage elasticity µ is set 0.151 (see Shepotylo and Vakhitov 2020). All former variables are pinned down using direct empirical evidence, while the remaining variables are set to ensure that outcome variables match specific target values. First, the wage constant ω is set to 0.625 to target an unemployment rate of about 5.1 % . The transition probabilities between the high and low productivity state are set to δ=0.02 and η=0.08 targeting a job destruction rate of around 0.01 as well as a vacancy-filling rate of 0.325 (see Michaillat 201216). Finally, I target market tightness to equal 0.6, which is the average market tightness in the US during the 2001 to 2021 time period (see U.S. Bureau of Labor Statistics 2024). This pins down the productivity shifter to γ=0.5 . To illustrate different labor market responses, the model is simulated not only for the baseline value of firing costs, but instead for all f ∈( 0, 2) . This range covers the laissez-faire (f = 0) equilibrium, the baseline specification (f = 0.27) as well as European levels of firing costs (f = 1.89) .17 To investigate whether firing costs impact the labor market differently depending on the initial labor market state, the model is simulated using four different values ω∈[0.6125, 0.625, 0.64, 0.655] for the wage constant. As aggregate productivity remains constant, these differences translate into differences in the wage-to-produc- tivity ratio, hence representing four different states of the labor market. With a high real wage, the labor market is sluggish, which is reflected in severe job rationing, whereas search frictions do not play an important role. The opposite is true if the real wage is low: competition for workers is high, which makes search frictions the main driver of unemployment (see Michaillat 2012). Table2 shows total, frictional and rationing unemployment in percent for each wage regime either with very high ( f = 2.0 ), without ( f = 0 ) or with the baseline level of firing costs ( f = 0.27) . For a graphical illustration of all equilibria between f = 0 and f = 2 see Fig.7 in the Appendix. If the wage is low ( ω=0.6125 ), unemployment equals 2.47% before firing costs are introduced. Remarkably, rationing unemployment is highly negative, namely -7.21%. Hence, there would be a shortage of labor in the absence of search frictions. With search frictions, such a shortage never occurs, as market tightness and thus recruiting costs converge to infinity, if unemployment approaches zero. Even if the wage-to-productivity ratio is extremely low, there is always positive unemployment in an economy with search frictions. Correspondingly, search unemployment, measured as the drop in labor demand caused by recruiting cost, equals 9.68%.18 With increasing firing costs, the expected pattern materializes: Table 1 Numerical values Variable Value Source/Target Matching efficiency τ 0.233 Michaillat (2012) Discount factor β 0.999 Michaillat (2012) Matching elasticity  0.700 Shimer (2005) Vacancy posting costs: c 0.214 Michaillat (2012) Output elasticity α 0.666 Michaillat (2012) Firing costs f 0.270 Bartelsmann et al. (2016) Wage constant ω 0.625 5.1% Unemployment Prob. High ⇒ Low: δ 0.020 0.01 Job destruction rate Prob. Low ⇒ High: η 0.080 0.325 Vacancy filling rate Productivity high state γH 1 Normalization Productivity low state γL 0.5 0.6 Market tightness Wage elasticity µ 0.151 Shepotylo and Vakhitov (2020) 16 Michaillat (2012) estimates the job destruction and finding rates from the seasonally adjusted monthly series for total separations and hirings in all non-farm industries constructed by the Bureau of Labor Statistics (BLS) from the Job Openings and Labor Turnover Survey (JOLTS) for the December 2000 to June 2009 period. 17 Empirically firing costs range between one (U.S.) and seven months of production (see Bartelsmann etal. 2016). Taking purely mechanically, this translates into values for the firing cost parameter f ranging from f=3.6 to f=25.2 (weekly output in the model is roughly 0.9 ). However, taken into account the setup of the model this is not sensible. In the model, each separation involves paying firing costs. In reality, two thirds of job separations happen by mutual agreement (for job sorting, life cycle or personal reasons). In addition, half of the remaining separations are due to discontinuing temporary jobs. Only about 15% of all layoffs can be attributed to retrenchments (see D’Arcy etal. 2012). Retrenchments may be either a job closure or a dismissal. If firing costs have to be paid for 50% of all retrenchments (which seems to be a sensible approximation), this implies that only 7.5% of all dismissals are associated with paying firing costs. Considering this implies an empirically plausible range for f between 0.27 and 1.89 , which fits well into the range used in the simulation. 18 If, for example, NR =1.02 , it follows that uR=−0.02 . With a total unemployment rate of 4% the drop in labor demand (search unemployment) caused by search friction is 6%. 21 Page 8 of 28 A.Bastgen rationing unemployment picks up, as the cost of employing a worker rises, but remains negative up until about f=1 .1. Conversely, frictional unemployment monotonically decreases and becomes slightly negative for firing costs higher than f=1.85 . Total unemployment decreases slightly from 2.47% (at f=0 ) to 2.11% (at f=2 ). The near independence of total unemployment from firing costs hides that firing cost massively change the composition of unemployment from being entirely driven by search frictions to being entirely driven by job rationing. This heavily affects the effectiveness of other labor market policies. For example, if policy makers eliminate recruiting cost ( c=0 ) unemployment would completely vanish in the equilibrium without firing cost, while being not affected in the equilibrium with very high firing costs ( f=2 ). Despite the slight increase in employment, firing costs lower output from 0.914 to 0.90 (see Fig.9) as more workers are employed in low productive firms. From a welfare point of view, most relevant is net output defined as output minus sunk costs. Recruiting expenditures definitely belong to sunk costs. Firing costs are sunk, if they mainly consist of legal or bureaucracy costs. In contrast, if they consist mainly of a severance payment to workers, they do not belong to sunk costs. I measure net output using both interpretations of firing costs.19 If firing costs are interpreted as severance payment, net output decreases only marginally from 0.903 to 0.899 (0.4%), as lower gross output is compensated by lower recruiting expenditures. Naturally, the decrease in net output is somewhat larger if firing cost are considered sunk. In this case net output decreases from 0.903 to 0.889 (1.6%). Overall EPL performs remarkably well in a labor market with low wage-to-productivity ratio: aggregate employment increases, while all measures of output decrease only slightly. Apparently, in such an environment EPL provides benefits like higher job security and longer employment spells20 at low costs. Turning to the high wage labor market ( ω=0.655 ) reverses this impression. In this scenario, unemployment before introducing firing costs equals 13.03%. With increasing firing costs, unemployment heavily increases and reaches 20.16% at f = 2 . In this economy, search frictions do not matter much: even without firing costs, they cause only 0.73 percentage points of total unemployment. At f = 2 , frictional unemployment is roughly zero. However, as frictional unemployment is low in the first place, the decrease in frictional unemployment is small in total numbers. As rationing unemployment strongly increases (similarly as it does in the low wage setup), EPL has a strong adverse effect on aggregate employment, because due to low market tightness turnover costs are low and thus the marginal utility of reducing turnover is also low (see Fig.8 in the Appendix). The negative employment effect directly passes through on output: compared with the low wage equilibrium, gross output decreases far more steeply in firing costs (from 0.85 to 0.79), because lower aggregate employment reinforces the negative effect of decreasing average productivity. Net output defined as output minus recruiting costs very closely resembles the course of output as market tightness and, thus, recruiting expenditures are low for the whole range of firing costs. Correspondingly, savings in recruiting cost caused by lower turnover cannot even closely make up for the loss in gross output. Quantitatively, net output decreases by around 6.7%, when firing costs increase from f = 0 to f = 2 . If firing costs are sunk, the negative effect on net output increases to about 9.1%. If ω=0.625 and ω=0.64 outcomes range between the previously discussed results, ensuring that unemployment composition matters in a continuous way when assessing the effects of firing costs. The observed decrease in search unemployment is key for understanding why the composition of unemployment matters. This decrease occurs, because market Table 2 Calibration results The Table displays total, frictional and rationing unemployment in percent for four different wage regimes and three different levels of firing costs. Source: Own simulations Unemployment f = 0 f = 0.27 (Baseline) f = 2  ω=0.6125 Total 2.47 2.57 2.11 − 0.36 Frictional 9.68 7.68 − 0.39 − 10.07 Rationing − 7.21 − 5.11 2.44 9.65 ω=0.625 Total 4.65 5.13 8.12 3.47 Frictional 5.57 4.11 0.04 − 5.53 Rationing − 0.92 1.02 8.16 9.08 ω=0.64 Total 8.15 9.19 14.46 6.01 Frictional 2.14 1.43 0.02 − 2.12 Rationing 6.00 7.76 14.44 8.44 ω=0.655 Total 13.03 14.41 20.16 7.13 Frictional 0.733 0.50 0.02 − 0.713 Rationing 12,3 13.91 20.14 7.84 19 Note that the models equilibrium is unaffected by the specific type of firing costs, as wages follow a fixed schedule. 20 Note that, although important in reality, these benefits are not explicitly valued in the model. Page 15 of 28 21 Does theeffect ofemployment protection depend onthecomposition ofunemployment? low values and somewhat larger for high values of pretreatment unemployment. As standard errors go up when evaluating marginal effects off the mean, marginal effects become insignificant, when evaluated at a very low value of pre-treatment unemployment (four units below its mean). In contrast, if evaluated at a high pre-treatment unemployment rate, marginal effects are large enough to stay significant despite larger estimated standard errors. Turning to unemployment as dependent variable reveals that marginal effects are somewhat less significant. If pretreatment unemployment is evaluated at its mean, the marginal effect remains significant. However, as the coefficient on the interaction term is very small (compared to the main effect), larger standard errors lead to insignificance once marginal effects are evaluated at high or low values of pre-treatment unemployment. Public policy Exception Again the public policy exception reveals a rather different picture. Marginal effects are highly insignificant when evaluated at the mean of average pre-treatment unemployment. This corresponds to the result of Autor etal. (2006) who do not find any significant effect of the public policy exception. However, marginal effects become significant, when being evaluated at very low or very high values of the moderator. This holds true no matter whether the employment-to- population ratio or the unemployment rate is chosen as dependent variable.41 If average pre-treatment unemployment takes on a value two units below its mean, the employment-to-population ratio (the unemployment rate) significantly increases (decreases) after introduction of the public policy exception. This corresponds to the case in which the positive effect of a lower job destruction rate outweighs the negative effect of a lower jobfinding rate. Spoken differently, the decrease in frictional unemployment is larger than the increase in rationing unemployment. The story reverses, once the marginal effect is evaluated at a very high value of the moderator (two units above its mean). This case corresponds to a sluggish economy with rationing unemployment contributing the main part to total unemployment. Now, adopting the public policy exception has a detrimental effect on labor market performance. It lowers the employment- to-population ratio and increases the unemployment rate. Significance is somewhat lower compared to the case of a low moderator value, although p-values remain around 0.1, indicating at least weak significance. Note that in both cases estimated standard errors are large, because marginal effects are evaluated far off the mean of average pre-treatment unemployment. Marginal effects clearly reflect the large and significant interaction term coefficient, as discussed above. Table 4 Marginal effects Models are weighted by state’s share of national population aged 16-64 in each month using CPS sampling weights. All models include regional dummies. Standard errors in parentheses are computed using Huber-White standard errors, which allow for unrestricted error correlation within states ***, **, * indicate statistical significance at the 1%, 5% and 10% confidence level. Ui equals state i’s average unemployment rate in the 24month before the introduction of an exception to the employment-at-will doctrine Marginal Effect at Ui plus Dep. variable Variable −4 −2 0 2 4 Implied-contract-exception log(employment − to − population) posti,t − 1.063 − 1.318** − 1.573*** − 1.828*** − 2.083*** (0.897) (0.611) (0.449) (0.539) (0.799) log(unemploymentrate) posti,t 15.281 11.997* 8.714** 5.430 2.147 (9.497) (6.258) (3.836) (4.109) (6.754) Public policy-exception log(employment − to − population) posti,t 2.371** 1.166* − 0.039 − 1.243 − 2.448 (1.114) (0.644) (0.586) (1.015) (1.573) log(unemploymentrate) posti,t − 17.587* − 7.909 1.770 11.448 21.127 (10.087) (5.680) (4.795) (8.598) (13.604) Good-faith-exception log(employment − to − population) posti,t 8.108*** 3.579*** − 0.949 − 5.478*** − 10.007*** (2.693) (3.579) (0.893) (2.065) (3.492)( log(unemploymentrate) posti,t − 67.193*** − 29.615*** 7.961 45.538*** 83.116*** (19.213) (9.153) (0.274) (16.640) (27.484) 41 Again, significance levels are somewhat higher if the dependent variable is given by the employment-to-population ratio. 21 Page 16 of 28 A.Bastgen -3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 -4 -2 0 % -t nemyolpme egnah c- to- populaon rao pre-treatment unemployment rate relave to mean Implied-contract Excepon -8.0 -6.0 -4.0 -2.0 0.0 2.0 4.0 6.0 -4 -2 024 % -tnemyolpme egnahc-to- populaon rao pre-treatment unemployment rate relave to mean Public Policy Excepon Point Esmate 2,5 % Percenle 2,5 % Percenle -20.0 -15.0 -10.0 -5.0 0.0 5.0 10.0 15.0 -4 -2 024 % -tnemyolpme egnahc-to- populaon rao pre-treatment unemployment rate relave to mean Good-Faith Excepon Point Esmate 2,5 % Percenle 97,5% Percenle a Fig. 3 a Marginal Effects on the employment-to-population ratio. b: Marginal Effects on the unemployment rate Page 17 of 28 21 Does theeffect ofemployment protection depend onthecomposition ofunemployment? b -20.0 -10.0 0.0 10.0 20.0 30.0 40.0 -4 -2 024 % -change of the etartnemyolpmenu pre-treatment unemployment rate relave to mean Implied-contract Excepon Point Esmate 2,5 % Percenle 97,5% Percenle -60.0 -40.0 -20.0 0.0 20.0 40.0 60.0 -4 -2 024 % -change of the etartnemyolpmenu pre-treatment unemployment rate relave to mean Public Policy Excepon Point Esmate 2,5 % Percenle 97,5% Percenle -150.0 -100.0 -50.0 0.0 50.0 100.0 150.0 -4 -2 024 % -change of the etartnemyolpmenu Axis Title Good-Faith Excepon Point Esmate 2,5 % Percenle 97,5% Percenle Fig. 3 continued 21 Page 18 of 28 A.Bastgen Good-Faith Exception Marginal effects regarding the good-faith exception draw an even more pronounced pattern compared to the public policy exception. They are insignificant when evaluated at the mean of average pre-treatment unemployment, which again corresponds to the result of Autor etal. (2006). When marginal effects are evaluated at a very high or very low level of average pre-treatment unemployment, the large coefficient on the interaction term unfolds its impact: If the moderator is two units below its mean, adopting the public policy exception leads to a significant improvement of labor market conditions. The employment-to-population ratio increases by about 3.5%, whereas the unemployment rate drops by around 30%. In contrast, if average pre-treat- ment unemployment is two units above its mean, the public policy exception has a strong detrimental effect on both the employment-to-population ratio and the unemployment rate. The effect on the former is around 5.5%, while the effect on the latter is about 45%. Clearly, all coefficients are highly significant (at the 1% confidence level). For more extreme values of the moderator (four units above/below its mean) marginal effects become even larger while remaining strongly significant. 3.7 Interpretation Overall, results draw a mixed picture. Regarding the public policy and the good-faith exception, the analysis provides strong evidence in favor of the paper’s main hypothesis. The estimated coefficients on the interaction term are significant and have the expected sign. Correspondingly, marginal effects behave as expected: the insignificance results reported in Autor etal. (2006) vanish when marginal effects are evaluated at low or high values of average pre-treatment unemployment. The economic message behind these results is clear: although the public policy and the good-faith exception do not affect the employment-to-population ratio and the unemployment rate in a typical U.S. state, they do have strong effects when being introduced in a notably strong or weak labor market. Adopting the public policy or good-faith exception has positive labor markets effects in states with low unemployment, while adverse effects dominate in labor markets with high unemployment. This provides strong evidence for the mechanism proposed in the theory section: EPL lowers frictional unemployment, but increases rationing unemployment. Thus, it has adverse effects in markets driven by job rationing, but favorable effects in markets driven by search frictions. As rationing is likely to occur in sluggish labor markets, EPL widens the gap between strong and weak markets. Many states adopted wrongful-dismissal laws during the 1970s and 1980s. This may have contributed to the observed sharp rise in U.S. income inequality during the same period.42 The results for the public policy and good-faith exception do not translate to the implied-contract exception. Pre-treatment unemployment has no significant impact on the way the implied-contract exception influences the labor market. Instead, the implied-contract exception seems to have detrimental labor market effects in any case (although less significant in labor markets with low pre-treatment unemployment). There are two possible explanations for the observed pattern: first, the implied-contract exception could be structurally different from the other two wrongful-dismissal laws. This perception is supported by the fact that it is the only wrongful-dismissal law for which Autor etal. (2006) find significant effects on labor market performance. Firms may adapt quickly to the implied-contract exception by updating their recruitment process including a careful revision of new employment contracts and policy handbooks. The complication of the recruitment process may not be limited to the initial adoption, as continuous effort is needed to safely prevent the formation of implicit contracts. In this way, the implied-contract exception actually imposes additional recruiting costs instead of additional firing costs. An increase in recruiting costs unambiguously leads to lower employment/higher unemployment independent of the composition of unemployment. If this mechanism is true, obtained results are well in line with theoretical predictions. Alternatively, insignificance may result from a downward bias caused by omitting differences in matching efficiency (see section D in the Appendix). 4 Conclusion This paper studies the effects of EPL on labor market performance taking into account the composition of unemployment. The paper outlines a stylized equilibrium-matching model, which features diminishing marginal returns to labor and real wage rigidities. The model suggests that EPL unambiguously increases rationing unemployment while having a favorable effect on frictional unemployment. The first effect arises due to a lower marginal value of employing a worker (net of firing costs), while the second effect is caused by lower recruiting costs, which arise due to lower labor market tightness. Calibrating the model reveals that the overall effect of EPL crucially depends on initial unemployment composition. If search frictions mainly drive unemployment, the positive channel via lower recruiting costs is strong 42 The Gini-Index for the U.S. rose from about 39 at the beginning of the 1970s to about 45 at the beginning of the 1990s. Page 19 of 28 21 Does theeffect ofemployment protection depend onthecomposition ofunemployment? enough to offset the negative effect caused by a lower marginal value of employing a worker. In contrast, if rationing unemployment is the main contributor to overall unemployment, the reduction in recruiting costs is only negligible, causing EPL to unfold strong adverse labor market effects. The empirical part of the paper tests this theoretical prediction using data on the adoption of wrongfuldismissal laws by U.S. state courts. As discussed, I use average pre-treatment unemployment as proxy for the composition of unemployment. I have emphasized that this interpretation requires, amongst others, differences in matching efficiency across states to be negligible. Results confirm theoretical predictions for the public policy and the good-faith exception. In contrast, results regarding the implied-contract exception indicate that unemployment composition does not play a significant role in moderating labor market effects. A possible explanation is that firms adapt to the implied-contract exception, which complicates the recruiting process without actually affecting firing costs. Overall, theoretical and empirical results indicate that taking into account the composition of unemployment is crucial, when assessing aggregate labor market effects of EPL. Moreover, EPL is likely to act as an amplifier of regional differences in labor market performance. Appendix A. Equilibrium existence Equilibrium market tightness is determined by the intersection of Eqs.(16) and (19) that is where First, consider NSS . Higher market tightness implies a higher job-finding rate xm(x) and, given q , a higher value for NSS . The job destruction rate reads q =δm H N H i(x)−N L i(x ) N . As NH i (x ) is decreasing and N L i (x ) is increasing in market tightness [see Eqs.(9) and (10)], the job destruction rate is decreasing in market tightness. As NSS is decreasing in the job destruction rate, the positive effect of a higher market tightness on NSS is reinforced because of the indirect effect via the change of the job destruction rate. Intuitively, for a given level of employment higher market tightness leads to higher flows out of and lower flows (24) NSS (x)=NFOC (x) (25) N SS = xm(x) q+xm(x)(1−q)= 1 q xm(x) +(1−q ) into unemployment. In order to obtain balanced labor market flows higher market tightness requires higher aggregate employment. Correspondingly, the number of unemployed workers has to be low if market tightness is high. The sign of the slope of NFOC is ambiguous, as ∂ N H i(x) ∂x < 0 and ∂ N L i(x) ∂x > 0 . A necessary and sufficient condition for ∂ N FOC (x) ∂x < 0 is given by where � B=  γL γH(1−β(1−δ)) δβ  1−α 2−α < 1 . Thus, for a given set of exogenous variables, there exist a x , so that for each x smaller (larger) x it holds that ∂ N FOC (x ) ∂x is negative (positive). Moreover, the denominator of Eq.(10) goes to zero if x becomes large, implying that the slope of NFOC (x) goes to infinity. Thus, there exist two intersections of the NFOC (x) curve and the NSS (x) curve in (N,x) -space, reflecting two potential candidates for equilibrium market tightness, which I denote as x∗ (low market tightness equilibrium) and x∗∗ (high market tightness equilibrium). Let me first consider the second equilibrium candidate. As x∗∗ >x it holds that ∂ N FOC (x) ∂x   x=x ∗∗ > 0 . Note that ∂ N FOC (x ) ∂x has always the same sign as ∂ N FOC (x ) ∂c m(x) , be cause market tightness only matters for labor demand via recruiting costs. Correspondingly, labor demand in this equilibrium is increasing in recruiting costs, implying that an increase in search frictions (measured by c ) reduces unemployment. Clearly, such an equilibrium is not compatible with empirical evidence. Requiring labor demand to be decreasing in recruiting costs is equivalent to imposing an equilibrium refinement condition43 (26) f [γLβδ +�BγH( 1 −β( 1 −η))] +c m(x)[γL(1−β(1−δ)) +�BγHηβ ] <  � B γ H γµ L −γ L γµ H ω 43 The refinement condition is closely related to excluding the case of negative search unemployment. However, it is somewhat stronger as there exist equilibria, which do not satisfy the refinement condition but still exhibit positive search unemployment (NR − N> 0 ) . The intuition behind that goes as follows: search unemployment is being computed as difference in labor demand between an equilibrium with c=0 and c>0 , where c is not infinitesimally small. Thus, the difference between the two equilibria involves a discrete jump (!) in recruiting costs. As the derivative of labor demand with respect to recruiting costs itself depends positively (!) on recruiting costs, a positive derivative does not imply that search unemployment is negative. However, if the derivative is negative one can conclude that search unemployment is positive. Correspondingly, all equilibria satisfying the refinement condition (20) exhibit positive search unemployment. 21 Page 20 of 28 A.Bastgen This also implies that labor demand has to be decreasing in recruiting cost. This allows me to rule out the second equilibrium candidate. Correspondingly, the unique market tightness, which satisfies Eq.(20) and the refinement condition (27), is given by x∗ .44 B. Equilibrium stability The models steady equilibrium is determined by equating NSS (x) and NFOC (x) [see Eq.(20)]. Equation(20) is satisfied by two distinct values of x , denoted as x∗ and x∗∗ . The equilibrium characterized by x∗∗ is ruled out in the main text, as it requires unemployment to be locally decreasing in recruiting costs. In this section, I augment this argument by showing that the equilibrium associated with x∗∗ is not stable, while the equilibrium associated with x∗ is. As a full-blown out of steady-state analysis under rational expectations is not feasible, I use a simplified, yet intuitive, graphical analysis, which relies on the assumption that firms behave according to (8) and (9) even if market tightness is off its steady state value. Put differently, I assume that firms expect market tightness to remain constant at any given point in time. Figure4 shows the adjustment process resulting from a (small) deviation from the low market tightness equilibrium denoted by x∗ in the main text. First, note that the NFOC curve is downward sloping (in an environment around x∗ ) as ∂ N FOC (x) ∂x   x=x ∗ < 0. If x=x′<x∗ and N is below the NFOC -line, firms find it optimal to hire workers until N=NFOC (x′) . However, the new employment level can only be sustained, if firms continuously hire many workers from a small pool of unemployed. Correspondingly the NSS -line indicates a high level of market tightness x′′ >x∗ . Firms react to the increase in market tightness by reducing employment to N=NFOC (x′′) , which again leads to a decrease in steady state market tightness. However, as long as the negative slope of the NFOC -line is smaller in absolute value than the positive slope of the NSS -line this decrease does not fully offset the initial increase in market tightness. Hence, after one adjustment step market tightness is in between x0 and x∗ . The same process repeats itself until x∗ is reached, that is, the low market tightness equilibrium x∗ is stable. If the slope of NFOC evaluated at x=x∗ is larger in absolute (27) ∂ NFOC (x) ∂c m(x)     x=x Equilibrium ,c>0 < 0 value than the slope of NSS evaluated at x=x∗ , the adjustment process would not fully converge. In this case, the economy oscillates around x=x∗ . However, as NFOC becomes flatter (and eventually upward sloping) when x increases the magnitude of the oscillation process is bounded. Hence, a divergent behavior is not possible. Consequentially, analyzing the equilibrium associated with x∗ is meaningful in any case. In contrast, Fig.5 shows that the high market tightness equilibrium x∗∗ is not stable (knife-edge equilibrium). If market tightness is slightly below x∗∗ (for example at x0 , see point A) firms will downward adjust employment to NFOC (x′). To maintain the lower level of employment firms continuously hire less workers from a larger pool of unemployed, leading to lower market tightness as indicated by the NSS -line. As NFOC (x) is upward sloping around x=x′′ , firms react to lower market tightness by reducing employment, leading to an even lower market tightness. The economy diverges away from x∗∗. Analogous arguments hold true, if market tightness is slightly above x∗∗ . In fact, the high market tightness equilibrium turns out to be a modeling artifact and is not of any economic importance. Neglecting it does not harm the generality of my analysis. C. Proof ofthemain proposition (i) Condition for rationing unemployment being increasing in firing costs Labor demand in absence of search frictions in state H and L is given by: Note that total labor demand (without search frictions) equals Plugging the expressions for NH,R i and N L,R i into Eq.(30) and taking the derivative with respect to f yields: (28) N H,R i=  αγH ωγ µ H +βδ f1 1−α =  ωγ µ H+βδf αγ H 1 α− 1 (29) NL,R i=αγL ωγ µ L−(1−β(1−η))f 1 1− α =  ωγ µ L−(1−β(1−η))f αγL 1 α− 1 (30) N R,FOC =mHNH,R i+mLNL,R i= η η+δ NH,R i+ δ η+δ NL, R i 44 Even if one does not require Eq.(27) to be satisfied it can be shown numerically that (for reasonable parameter values) x∗∗ violates the plausibility constraint NH i ≥ NL i independent of the level of firing cost or the wage regime. Page 21 of 28 21 Does theeffect ofemployment protection depend onthecomposition ofunemployment? Therefore ∂ N R,FOC ∂f < 0 is equivalent to where � A=  ηβ γL γH 1−β(1−η)  1−α 2− α . Simply rearranging terms yields Eq. (21). (ii) Condition for frictional unemployment being decreasing in firing costs The frictional component measures the drop in labor demand caused by recruiting cost i.e. NR −N . Under the refinement condition [see Eq. (27)]) the frictional component is always positive and increases in recruiting costs and therefore in market tightness. Hence, showing that higher firing costs lead to lower frictional unemployment boils down to showing that higher firing costs lead to lower market tightness. To do so rewrite Eq. (24) as: The implicit function theorem implies that dx ∗ df =− ∂G ( x,f ) ∂f ∂G(x,f) ∂x , that is, market tightness is decreasing in firing costs if Gx and Gf have the same sign. Correspondingly, the next step is to compute the partial derivatives. It holds that: (31) ∂ NR,FOC ∂f=1 α−1  �ωγ µ H+βδf αγH� 2 −α α−1ηβδ αγH −�ωγ µ L−(1−β(1−η))f αγL� 2−α α−1f(1−β(1−η)) αγL   (32) ωγ µ H+βδf γH −ωγ µ L−(1−β(1−η))f γL �A< 0 (33) G x,f  =xm(x)−N FOC  x,f  ∗(q  x,f  +xm(x)(1−q  x,f ) G x=(xm(x))′  1−NFOC x,f  −∂NFOC x,f ∂xqx,f+xm(x)1−qx,f  −NFOC (x,f)[(1−xm(x))∂qx,f ∂x −(xm(x))′q  x,f  ] (34) = (xm(x))′  1−NFOC x,f  −(1−xm(x))δmH ∂NH ix,f ∂x−∂NL ix,f ∂x +NFOC  x,f  (xm(x))′q  x,f  −∂NFOC ∂x xm(x ) Given the refinement condition [see Eq. (27)], Gx is always positive.45 Thus, market tightness is decreasing in firing costs, if Gf>0 , which is the case if ∂ N FOC (x,f) ∂f < 0 . Therefore assuming ∂ N FOC (x,f) ∂f < 0 [Eq. (22)] is enough to guarantee that frictional unemployment decreases in firing costs.46 D. The role ofmatching efficiency In the main text average pre-treatment unemployment proxies the steady state composition of unemployment before treatment. Relatively high unemployment is associated with a large (small) share of rationing (search) unemployment, if matching efficiency is constant across observations. As no data on matching efficiency is available, it is necessary to assume that matching efficiency does not vary across states. This section analyzes how a violation of this assumption might change results. If matching efficiency in reality varies across states, estimation potentially suffers from an omitted variable bias. Luckily, it is possible to determine the sign of the resulting bias. Once matching efficiency is available, one can compute average pre-treatment matching efficiency τi for every state and append Eq.(23) by an additional interaction term τi∗posti,t . If matching efficiency is high, the share of frictional unemployment is low for a given unemployment rate. Correspondingly, the theoretical model (35) G f=− ∂N FOC x,f ∂fqx,f+xm(x)1−qx,f −(1−m(x))NFOC x,f∂qx,f ∂f =− ∂NFOC x,f ∂fxm(x) −(1−xm(x))δmH  ∂NH i  x,f  ∂f−∂NL i  x,f  ∂f  45 Note that ∂ N H i(x,f) ∂f − ∂N L i(x,f) ∂f < 0 . 46 ∂ N FOC (x,f) ∂f < 0 is equivalent to: f γLβδ +�AγH(1−β(1−η))  + c m ( x )  γL(1−β(1−δ)) +�AγHηβ  <  �Aγ µ L γH−γLγ µ Hω . where A is already known from equation Fehler! Verweisquelle konnte nicht gefunden werden.. The condition looks very similar to Eq.26, which I already have assumed to be satisfied (refinement condition). However, as �A<� B the condition is somewhat harder to satisfy than Eq.(26). Thus, the refinement condition does not automatically imply Gf>0. Note that the difference between ∂ N FOC (x,f) ∂f < 0 and the refinement condition ( 26 ) is quantitatively negligible. The difference is entirely due to the difference between A and B . Independent of any other parameter values, A=B if the discount factor β is set to unity. For reasonable values of β (for example β=0.999 ) A is only marginally smaller than B . Correspondingly, assuming ∂ N FOC (x,f) ∂f < 0 is only a very small additional assumption once the refinement condition (see Eq.(27)) is accepted (see Fig.6). 21 Page 22 of 28 A.Bastgen implies that in this case the employment effect of EPL should be more adverse. Put differently, the expected sign of the coefficient on τi∗posti,t is negative.47 Remember also, that theory implies that the coefficient on Ui ∗ posti,t should be negative as well. At the same time, observations with high pre-treatment average matching efficiency, on average, should have low levels of pre-treatment unemployment. Hence τi∗posti,t , and Ui ∗ posti,t are likely to be negatively correlated. Consider an observation with high pre-treatment unemployment rate. This observation is likely to have low pre-treatment matching efficiency. The latter causes the employment effect of EPL to be rather favorable. Correspondingly, omitting τi∗posti,t causes the coefficient on Ui ∗ posti,t to be less negative compared to a model that includes τi∗posti,t . Hence, differences in matching efficiency bias the estimated coefficient on Ui ∗ posti,t towards zero. Therefore, differences in matching efficiency cannot cause false significance. Accordingly, including matching efficiency is very unlikely to change conclusions in case of the public policy and good-faith exception. In contrast, taking into account differences in matching efficiency is likely to strengthen the presented empirical evidence. In addition, the bias may provide an alternative explanation for the lack of significance when evaluating the implied-contract exception.48 See Tables5, 6, 7 Table 5 Implied-contract exception Models are weighted by state’s share of national population aged 16-64 in each month using CPS sampling weights. Standard errors in parentheses are computed using Huber-White standard errors, which allow for unrestricted error correlation within states ***, **, * indicate statistical significance at the 1%, 5% and 10% confidence level. Ui equals state i’s average unemployment rate in the 24month before the introduction of the implied-contract exception Marginal effect at Ui plus Dep. variable Variable Coefficient −4 −2 0 2 4 Region log(employment − to − population) posti,t − 1.573*** − 1.063 − 1.318** − 1.573*** − 1.828*** − 2.083*** Yes (0.449) (0.897) (0.611) (0.449) (0.539) (0.799) posti,t ∗ Ui − 0.128 (0.180) log(employment − to − population) posti,t − 1.639*** 0.066 − 0.787 − 1.639*** − 2.492*** − 3.344** No (0.565) (1.200) (0.746) (0.565) (0.852) (1.333) posti,t ∗ Ui − 0.426 (0.284) log(unemploymentrate) posti,t 8.714** 15.281 11.997* 8.714** 5.430 2.147 Yes (3.839) (9.497) (6.258) (3.836) (4.109) (6.754) posti,t ∗ Ui − 1.642 (1.823) log(unemploymentrate) posti,t 10.303* 6.452 8.377 10.303* 12.229 14.155 No (6.077) (16.008) (10.131) (6.077) (7.690) (13.011) posti,t ∗U i 0.963 (3.315) 47 The argumentation reverses if the unemployment rate is used as dependent variable. 48 In main text the lack of significance is explained by structural differences between the implied-contract exception and the other two wrongful-dis- missal laws. Page 23 of 28 21 Does theeffect ofemployment protection depend onthecomposition ofunemployment? Table 6 Public policy exception Models are weighted by state’s share of national population aged 16-64 in each month using CPS sampling weights. Standard errors in parentheses are computed using Huber-White standard errors, which allow for unrestricted error correlation within states ***, **, * indicate statistical significance at the 1%, 5% and 10% confidence level. Ui equals state i’s average unemployment rate in the 24month before the introduction of the public policy exception Marginal effect at Ui plus Dep. variable Variable Coefficient −4 −2 0 2 4 Region log(employment − to − population) posti,t − 0.039 2.371** 1.166* − 0.039 − 1.243 − 2.448 Yes (0.586) (1.114) (0.644) (0.586) (1.015) (1.573) posti,t ∗ Ui − 0.602** (0.308) log(employment − to − population) posti,t − 0.160 3.172** 1.506* − 0.160 − 1.825 − 3.491* No (0.770) (1.396) (0.788) (0.770) (1.365) (2.106) posti,t ∗ Ui − 0.833** (0.403) log(unemploymentrate) posti,t 1.770 − 17.587* − 7.909 1.770 11.448 21.127 Yes (4.795) (10.087) (5.680) (4.795) (8.598) (13.604) posti,t ∗ Ui 4.839* (2.743) log (unemploymentrate) posti,t 2.878 − 25.289** -11.205* 2.878 16.961 31.045* No (6.705) (12.158) (6.670) (6.705) (12.215) (18.901) posti,t ∗ Ui 7.042* (3.602) Table 7 Good-faith-exception Models are weighted by state’s share of national population aged 16-64 in each month using CPS sampling weights. Standard errors in parentheses are computed using Huber-White standard errors, which allow for unrestricted error correlation within states ***, **, * indicate statistical significance at the 1%, 5% and 10% confidence level. Ui equals state i’s average unemployment rate in the 24month before the introduction of the good-faith exception Marginal effect at Ui plus Dep. variable Variable Coefficient −4 −2 0 2 4 Region log(employment − to − population) posti,t − 0.949 8.108*** 3.579*** − 0.949 − 5.478*** − 10.007*** Yes (0.893) (2.693) (3.579) (0.893) (2.065) (3.492)( posti,t ∗ Ui − 2.264*** (0.747) log(employment − to − population) posti,t − 0.551 7.554** 3.501** − 0.551 − 4.603** − 8.656** No (0.629) (3.106) (1.553) (0.629) (1.898) (3.468) posti,t ∗ Ui − 2.026** (0.808) log (unemploymentrate) posti,t 7.961 − 67.193*** − 29.615*** 7.961 45.538*** 83.116*** Yes (7.291) (19.213) (9.153) (0.274) (0.006) (0.002) posti,t ∗ Ui 18.789*** (5.642) log (unemploymentrate) posti,t 4.196 − 84.772*** − 40.288*** 4.196 48.680*** 93.164*** No (6.291) (28.054) (13.566) (6.291) (18.807) (33.562) post i,t ∗U i 22.242*** (7.571) 21 Page 24 of 28 A.Bastgen See Figures4, 5, 6, 7, 8, 9 Fig. 4 The figure shows the adjustment process resulting from a small deviation from the low market tightness equilibrium. Source: Own Simulations Fig. 5 The figure shows the adjustment process resulting from a small deviation from the high market tightness equilibrium. Source: Own Simulations