PENALTY VS. INSURANCE: A REASSESSMENT OF THE ROLE OF SEVERANCE PAYMENTS IN AN ECONOMY WITH FRICTIONS

Transcription

1 PENALTY VS. INSURANCE: A REASSESSMENT OF THE ROLE OF SEVERANCE PAYMENTS IN AN ECONOMY WITH FRICTIONS Etienne Lalé Discussion Paper 15 / November 2015 Department of Economics University of Bristol 8 Woodland Road Bristol BS8 1TN United Kingdom

2 PENALTY VS. INSURANCE: A REASSESSMENT OF THE ROLE OF SEVERANCE PAYMENTS IN AN ECONOMY WITH FRICTIONS ETIENNE LALÉ University of Bristol ABSTRACT. We analyze the effects of severance payments in an economy with labor-market frictions and incomplete insurance against idiosyncratic shocks. Workers and employers are paired together, they make decisions about continuing the employment relationship and they bargain on wages. As a result, in this setup, wage contracts that would neutralize mandatory severance payments are endogenous and potentially costly to implement. This mitigates the need for layoff penalties and insurance: in contrast to previous studies that precluded such wage contracts, we find that severance payments have limited effects on equilibrium allocations and that they entail significant welfare losses. High severance payments for incumbent workers are undone by a steeper wage profile, which is detrimental to newly-hired workers who are younger and have fewer savings. We find, meanwhile, that small lump sum payments of severance compensations combined with low unemployment benefits improve welfare. Severance compensations allow workers to maintain about the same level of consumption-smoothing but they have less negative spillovers onto firms job creation decisions. Therefore this component of severance payments could be part of an optimal unemployment insurance package. Keywords: Severance Payments, Precautionary Savings, Labor-Market Frictions, Welfare Effect JEL Codes: E21, I38, J63, J65 Current version: November This article is a substantially revised version of a paper previously circulated under the title: Matching Frictions, Self-Insurance and Severance Payments. I am grateful to Régis Barnichon, Pierre Cahuc, Christian Haefke, Grégory Jolivet, Dirk Krueger, Iourii Manovskii, Ander Perez, Fabien Postel-Vinay, Jean-Marc Robin, Eric Smith, Hélène Turon and Etienne Wasmer for helpful discussions. I also thank seminar participants at Penn Macro lunch seminar, the 27th congress of the EEA, the University of Bristol, Universitat Pompeu Fabra, the ADRES doctoral conference, University of St Gallen, the SaM annual conference in Mainz and the first African SaM workshop for their comments and suggestions. All errors are my own. Address: Department of Economics, University of Bristol, 8 Woodland Road, Bristol BS8 1TN, United Kingdom Phone: +44(0) etienne.lale@bristol.ac.uk. 1

3 1. INTRODUCTION The effects of government-mandated severance payments on equilibrium allocations and welfare is a topic of keen interest, at least since Hopenhayn and Rogerson (1993). The literature usefully distinguishes between the firing tax paid by the employer and the transfer to the dismissed worker, which subsume, respectively, the penalty and insurance roles of severance payments. Alvarez and Veracierto (2001) provided an early assessment of those two roles in the context of a frictional economy. They found that the firing tax improves welfare as it prevents workers from being sent to unemployment too often, whereas the transfer component plays a nonexistent, or even negative, insurance role. For tractability, and also for lack of an alternative wage-setting rule, their analysis assumed rigid wage contracts. 1 Our goal in this paper is to re-evaluate the role of severance payments without a priori restrictions on the flexibility of wage contracts. While this opens a potentially important role for Lazear (1990) s bonding critique, i.e. that mandatory severance payments can be undone by perfect wage contracts, 2 we consider an economy that suffers from incompleteness along other dimensions. The key implication for this economy is that wage contracts that would neutralize mandatory severance payments are endogenous and potentially costly to implement. Our analysis takes advantage of recent advances combining frictional labor market and incomplete market models. Krusell, Mukoyama and Şahin (2010) provide a unified treatment, showing how to maintain bilateral bargaining between the employer and the worker while allowing for asset accumulation. Bils, Chang and Kim (2011) further develop a version with bilateral bargaining and endogenous separations. We extend this model in a number of directions. The first ingredients we add are two-tiered employment relationships, consistent with the view that severance payments affect differently new hires and incumbent workers. We also include a realistically-calibrated unemployment insurance system to allow for an alternative insurance vehicle. Finally, we cast the model in a life-cyle setting to capture the link between age, tenure and accumulated assets. The first set of results concerns the neutrality of mandatory severance payments in a world with flexible wage bargaining. We find that, under incomplete insurance markets and a borrowing limit, 1 Alvarez and Veracierto (2001) write, The extreme form of rigid labor contracts we assume not only precludes insurance arrangements and makes the analysis tractable, but it also serves as a natural benchmark in the absence of an obvious intermediate case. (p.482). In this paper, we build a similarly rich economic model wherein Nash bargaining is the natural candidate solution for the wage-setting rule. 2 The resulting wage contract implements a different timing of payments between agents. There is an entry fee in that the wage is initially lower to compensate for the expected present value of the future transfer to the worker (Lazear, 1990). This is referred to as the bonding critique because the entry fee is akin to a bond issued by the newly-hired employee. 2

4 workers and firms can undo a large part of the effects of a mandatory severance transfer on equilibrium allocations. This entails a steeper wage profile, i.e. neutralizing the future transfer implies a hiring fee, as dictated by the bonding critique. Thus, while employment decisions remain unchanged, the new wage contract is less favorable to newly-hired workers. Welfare is lower because these workers are more likely to be younger and have fewer savings. A mandatory severance transfer of 6 monthly wages, for instance, creates a welfare loss between 0.8 and 1.2 percent of lifetime consumption. It is useful to contrast this result with the effect of a pure firing tax. In the model considered, a firing tax is a distortion of privately-efficient separation decisions, which results in a deadweight loss that is incurred jointly by workers and firms. Since firms carry part of the burden of the penalty, the welfare effects from workers perspective are of lower magnitude. The transfer component, on the other hand, shifts the bargaining power to workers at longer tenure, and therefore new hires need to bite the bullet in order to get into employment. In a second set of experiments, we analyze the insurance role of severance payments. As a first pass, we search for the optimal provision of unemployment insurance benefits and show that workers would prefer lower unemployment compensations. This is unsurprising because workers can selfinsure by accumulating assets and they receive insurance by bargaining on wages with risk-neutral employers. Therefore the question we ask is whether the transfer component of severance payments could improve the provision of insurance for a given tax level, e.g. the tax level required to finance an unemployment insurance system without severance compensations. The answer is positive. In the benchmark model calibrated to U.S. data and policies, a lump sum payment of 1.5 months of wages upon job loss combined with a replacement ratio of unemployment benefits around 20 percent increases lifetime consumption by 1 percent. Thus, the experiment indicates that severance compensations could be part of an optimal unemployment insurance package. As mentioned above, this paper is closely related to the study by Alvarez and Veracierto (2001). The purpose of that study was to assess the role of severance payments in a version of Hopenhayn and Rogerson (1993) s model wherein adding frictions opens a role for government-mandated policies. Our results show that rigid wage contracts is the most important of all frictions considered. Absent this assumption, the class of wage contracts is large enough to mitigate the effects of mandatory severance payments on resource allocations. This conclusion is reinforced by the fact that, since Ljungqvist (2002), it is known that establishment-level dynamics as in Alvarez and Veracierto (2001) 3

5 or a one-worker-one-firm structure are not essential to the effects of mandatory layoff payments on employment. 3 Our results also show that the adverse effects of severance payments on newly-hired workers generate significant welfare losses within a life-cycle setting. The life-cycle component establishes a useful connection to Rogerson and Schindler (2002) and, more recently, Cozzi and Fella (2015). These papers discuss the insurance role of severance payments when individuals face a risk of being displaced from their job late in the working life. We view our work as complementary. They abstract from the penalty role of severance payments as they consider exogenous separations only; conversely, we abstract from the effects of separation on subsequent earnings through, e.g., the loss of specific human capital. These two dimensions raise a further question, namely whether severance payments could foster investments in specific human capital by lowering the probability of job separation. 4 This, however, is beyond the scope of our analysis. This paper also contributes to a vast literature on the employment effects of mandatory severance payments. Bentolila and Bertola (1990) provided an early analysis showing how this policy simultaneously deters firing and hiring. Burda (1992), Hopenhayn and Rogerson (1993) and Millard and Mortensen (1997) analyzed the implications of such distortions in a general equilibrium context. More recently, the literature has shed light on the interaction between severance payments, wage-setting mechanisms and labor market institutions. Garibaldi and Violante (2005) study the implications of exogenous and endogenous wage rigidities. Fella and Tyson (2013) and Postel-Vinay and Turon (2014) consider endogenous private severance payments in response to government-mandated ones. Boeri, Garibaldi and Moen (2014) establish a relationship between mandatory severance pay and the efficiency of legal procedures. While these papers all provide elegant solutions to characterize the effects of severance payments, they often assume linear utility and thereby they preclude insurance issues (Bertola, 2004). 5 On the other hand, the questions we address are quantitative in nature and analytical solutions are beyond reach. Therefore we rely on numerical experiments. 3 Ljungqvist (2002) analyzes layoff taxes in a model with search efforts, a model with a matching function and a model with employment lotteries. Ljungqvist explains that, in the third model that stands similar to Hopenhayn and Rogerson (1993) and Alvarez and Veracierto (2001), the important assumption is to have layoff payments handed back lump sum to households. Thus, we attribute differences between Alvarez and Veracierto (2001) and the present paper to bilateral bargaining and efficient separations, and not to the one worker one firm structure of our model. 4 Intuition suggests that if workers value a smooth consumption profile, they should invest in general human capital since specific human capital increases earnings only at the current employer. Absent this motive, and if severance payments lengthen the duration of the employment spell, then workers may have higher returns from investing in specific human capital; see e.g. Wasmer (2006). 5 Perhaps the most significant exception in this respect is the study by Fella and Tyson (2013). They develop a searchand-matching model with risk-averse workers and market incompleteness, but they rule out wealth effects (they use a constant absolute risk aversion utility function) to obtain tractability. 4

6 Finally, the quantitative exercise combining severance compensations and unemployment benefits establishes a link to the literature on optimal unemployment insurance. Coles and Masters (2006) demonstrate that a decreasing time-path of benefits is desirable in a matching equilibrium with strategic wage bargaining. Coles (2008) shows that this time-path is also beneficial under Nash bargaining when search efforts are inputs of the matching function. Coles gives a further insight into optimal unemployment benefits, namely that they should deliver full insurance upon job loss. This dovetails with our findings providing support for paying lump sum severance compensations in the period when workers are separated from their jobs. The quantitative exercise is also relevant for a literature analyzing the joint design of employment protection and unemployment insurance, following Blanchard and Tirole (2008). This body of research has the potential of explaining why mandatory severance payments are not a universal feature, and why many countries implement not only one but several programs to help workers cope with joblessness; see e.g. Boeri, Conde-Ruiz and Galasso (2012) for a summary of the empirical evidence. The rest of the paper is organized as follows. Section 2 presents the model. Section 3 carries out the calibration and characterizes the steady-state equilibrium. Section 4 analyzes the effects of the penalty and transfer components of severance payments. Section 5 discusses the substitutability between severance compensations and unemployment benefits. Section 6 concludes. An appendix provides computational details about our model. 2. THE ECONOMY The model combines an incomplete market environment and a labor market subject to matching frictions. The main ingredients to capture the employment effects of severance payments are endogenous separations and two-tiered employment relationships. The ingredients for the quantitative exercise include a realistic unemployment insurance system and a life-cycle setting Environment. Demographics, preferences and objectives. Time is discrete and runs forever. One side of the market is populated by overlapping generations of individuals who work, retire and die. The duration of the working life and retirement phase are exogenous and fixed, respectively, to N w and N r periods. A retired agent who dies is replaced by a new entrant to the labor market to maintain the measure of the population at a constant unit level. Newborns are homogeneous and individuals are indifferent to 5

7 their offspring. 6 In every period, they derive utility from consumption c t > 0 according to a constant relative risk aversion function: u(c t ) = c1 σ t 1 1 σ σ > 0 is the coefficient of relative risk-aversion. They discount the future using a factor β that satisfies: β = (1 + r) 1, where r > 0 is the real interest rate. Finally, their maximization problem is subjected to a sequence of intertemporal budget constraints: c t + a t+1 (1 + r)a t + x d t where a is a risk-free asset which individuals can save but that they cannot borrow, i.e. a t 0. xt d is disposable income at time t, which will be determined below for those in the labor force. Retirees do not have access to retirement plans; this implies that xt d = 0 after retirement. On the other side of the market, there is a continuum of risk-neutral entrepreneurs. They maximize the expected value of the sum of profit streams, which they discount using the interest rate. The interest rate is exogenously given. 7 Production technology. The unit of production is a matched worker-firm pair. Labor is the only input and the flow of output that the worker-firm pair produces is y, which we refer to as match productivity. y is match-specific and evolves over time according to a first-order autoregressive process: y t+1 = (1 ρ) µ y + ρy t + ε t+1 µ y is the unconditional mean of the process, ρ (0,1) is the persistence and ε N ( 0,σε 2 ) is the innovation term. Hereafter G(. y) denotes the transition function for y, i.e. G(y y) = Pr{y t+1 < y y t = y}. Finally, we assume that a worker-firm pair is exogenously destroyed with per period probability δ. This assumption is inessential but it helps discipline the volatility of match productivity. 6 To be precise, there is no ex ante heterogeneity and, given a deterministic life-cycle and no bequest motive, newborn workers do not receive any assets from retired agents who die. These features make the lifetime utility of a newborn agent a natural welfare statistics to compare steady-state equilibria. Also, observe that this criterion does not aggregate welfare across newborn agents using a distribution of inherited wealth. 7 There are several motivations for keeping the interest rate exogenous, which are discussed in detail in Subsection 4.3 of the paper. For the purpose of presenting the model, it suffices to note that since assets are not passed from one generation to the next, one can focus on the lifetime utility of a newborn worker with a given initial asset level. Thus, the question we address is: how does the worker fare in economies that pay the same return to the risk-free asset while implying different earnings and labor market trajectories? 6

8 Timing of events. The timing of meeting and production is in three steps: (1) Unmatched workers search for an employer with a vacant job and vice versa. An employer pays a cost η > 0 per period to keep a vacant job open. The number of contacts per unit of time is given by a standard Cobb-Douglas matching function: m(u t,v t ) = Mu α t v 1 α t where u t is the number of unemployed and v t is the measure of vacancies. Letting θ t = v t/u t denote labor market tightness, the probability of a meeting is q(θ t ) = Mθ α t employer and θ t q(θ t ) = Mθ 1 α t for a prospective worker. for a prospective (2) Upon meeting, the potential worker-firm pair draws a productivity level from the distribution G 0 (y) = G(y µ y ). Agents observe y and decide whether to form a match or to walk away. (3) If they choose to stay together, the worker-firm pair starts producing. For parsimony, we keep track of two levels of tenure only: in employment, i = 0 indicates a short tenure and i = 1 an incumbent worker (longer tenure). Index i evolves stochastically according to p e p e i, j = 1 pe 0 1 with i, j {0,1}. 1/p e is the expected duration before switching from short to longer tenure. The labor market implications of this timing are as follows. First, since upon meeting, the employer and the worker can walk away at no cost or gain for either party, the timing ensures that if a firm does not hire, it does not have to fire (Ljungqvist and Sargent, 2007). 8 Second, the decision to dissolve the match can depend on tenure, among other variables. Hereafter we refer to the rule at i = 0 as the entry decision and the rule at i = 1 as the continuation decision. The match continuation decision will differ from the entry decision if, for instance, mandatory severance payments change the outside option of incumbent workers and employers. 8 One difference with the textbook model by Mortensen and Pissarides (1999) is that they assume that initial productivity is homogeneous (i.e. that G 0 (.) is degenerate) and that the value of being matched always dominates the value of continued search. In our setup, heterogeneity in initial match productivity is motivated by the following observation. Suppose that workers effectively need to buy the job from the employer due to, e.g., future severance payments. Since workers run down their assets during unemployment, the poorest could become unable to regain employment if all jobs were ex ante identical. The distribution G 0 avoids this problem by making luck (high productivity draw) a substitute to wealth to find a way out of unemployment. The other difference regarding match-productivity y is that we select a first-order autoregressive process to make connections to the data. Mortensen and Pissarides (1999) assume independent draws conditional on resampling y. 7

9 Government-mandated policies. The government runs two labor market programs. The first program is mandatory severance payments: there is a firing tax F paid by employers for each job that is terminated (penalty component), and a lump sum transfer T to the dismissed worker (insurance component). This policy is said to be self-financed when F = T. In this case, one cannot distinguish whether T is paid directly by the employer to the worker or whether it is transferred by the government upon collecting F from the employer. Consistent with observation, it is assumed that mandatory severance payments apply only to incumbent workers. 9 Finally, we also assume that severance payments are waived when the worker retires from the labor force or when the job is destroyed exogenously by the δ shock. Since our focus is on bilateral bargaining, we are only interested in the interaction between severance payments and shocks that can be contracted upon. The second program is an unemployment insurance system that stands similar to the current U.S. system. It pays a constant amount of benefits b 1 for a definite period of time; after unemployment benefits have expired, individuals move on to social assistance which provides significantly lower benefits b 0 for an indefinite period of time. Just like tenure accumulation, the exhaustion of unemployment benefits is governed by a two-state Markov process: p u i, j = 1 0 p u 1 p u with i, j {0,1}. p u is the per-period probability of exhausting benefits b 1. The individual then remains ineligible for b 1 as long as she does not work. The government finances unemployment insurance and social assistance benefits by means of a payroll contribution tax κ on wages Bellman equations. To formulate workers decision problems, denote by R, U, W the value of, respectively, retirement, unemployment and employment. For employers, denote by J the value of having a filled job. We formulate these decisions problems in recursive form, and therefore we omit the subscript for calendar time in the remainder of this section. Hereafter, τ denotes the age of a worker and a prime ( ) indicates the one-period ahead value of a variable. We have: τ = τ + 1. Beginning with retired workers, their asset value solves the equation: (1) R(a,τ) = max c,a { u(c) + βr ( a,τ )} 9 See, for instance, OECD (2004) and Figure 1 in Boeri, Garibaldi and Moen (2014): statutory severance payments are typically increasing in tenure, and the gradient of the increase varies considerably across countries. 8

10 subject to c + a (1 + r)a a 0 for every N w + 1 τ N w + N r, and where R(a,N w + N r + 1) = 0 for every a. For unemployed workers, there are two asset values indexed by their eligibility to unemployment benefits i {0,1}. These asset values are the solution to: U i (a,τ) = max c,a (2) { u(c) + β p u i, j j=0,1 ( (1 θq(θ))uj ( a,τ ) ˆ +θq(θ) max { W 0 ( y,a,τ ),U j ( a,τ )} dg 0 ( y ))} subject to c + a (1 + r)a + b i a 0 for every 1 τ N w, and where U i (a,n w + 1) = R(a,N w + 1) for every a. For employed workers, the asset values are indexed by their tenure at the current employer i {0,1} and they depend on match productivity, among other variables. These asset values are given by: { ( ( W i (y,a,τ) = max u(c) + β δu 1 a,τ ) c,a ˆ (3) + (1 δ) p e i, j j=0,1 subject to max { W j ( y,a,τ ),U 1 ( a + T j,τ )} dg ( y y ))} c + a (1 + r)a + w i (y,a,τ) a 0 for every 1 τ N w, and where W i (y,a,n w + 1) = R(a,N w + 1) for every y and a. Here we use T j as a short notation for T 1{ j = 1}, i.e. T depends on the tenure of the worker. In the budget constraint, w i (y,a,τ) is the wage of the worker, which is determined endogenously below. 9

11 Associated with equation (1) is a decision rule for asset holdings a R (a,τ). Similarly, associated with equations (2) and (3) are a set of decisions rules for asset holdings a U 0 (a,τ), au 1 (a,τ), and a W 0 (y,a,τ), aw 1 (y,a,τ), respectively. For employers, we assume that they operate under free entry, which dictates that the value of a vacant job is always zero. As in equation (3), if we use F j as a short notation for F 1{ j = 1}, then the asset values of matched employers indexed by the subscript i {0,1} solve: (4) J i (y,a,τ) = y (1 + κ)w i (y,a,τ) + 1 δ ˆ 1 + r p e i, j j=0,1 max { J j ( y,a,τ ), F j } dg ( y y ) for every 1 τ N w, and where J i (y,a,n w + 1) = 0 for every y and a. Moreover a = a W i (y,a,τ), i.e. an employer recognizes that the worker s next period asset decision is given by the policy function a W i (y,a,τ) Wage setting. Wages are set via Nash-bargaining, which has the potential of undoing the effects of mandatory transfers on employment decisions. The bargaining power of the worker is parametrized by φ (0,1). The wage schedule w i (.) indexed by i {0,1} is given by (5) w 0 (y,a,τ) = argmax {(W } 0 (y,a,τ; w) U 1 (a,τ)) φ J 0 (y,a,τ; w) 1 φ w for short tenures and (6) w 1 (y,a,τ) = argmax {(W } 1 (y,a,τ; w) U 1 (a + T,τ)) φ (J 1 (y,a,τ; w) + F) 1 φ w for longer tenures, for all (y,a,τ). Observe that, in equations (5) and (6), the outside option of the worker is given by insured unemployment, i.e. by the asset value U 1 (.). Consider first a currently unemployed worker. Upon meeting an employer, her outside option could be given by her current eligibility to unemployment benefits. However after just one period of employment, one needs to take a stand on whether the outside option is insured or uninsured unemployment. We use the first option because of our interest in comparing severance compensations and unemployment benefits: this requires the transfer F to enter the asset value of insured unemployment Another motivation for this choice is that the higher outside option is the relevant value for wage bargaining when quits and layoffs cannot be told apart, which occurs typically in search-and-matching models; see e.g. Hagedorn et al. (2015) and the discussion therein. 10

12 2.4. Match entry and continuation. Match entry decisions are based on the comparison between the value of being matched and the value of continued search. Similarly, match continuation decisions follow from comparing the value of continuing the match with that of dissolving the match. Therefore there are two threshold functions y 0 (a,τ) and y 1 (a,τ) that satisfy: (7) (8) J 0 (y 0 (a,τ),a,τ) = 0 J 1 (y 1 (a,τ),a,τ) = F for all (a,τ) Equilibrium conditions. Free entry. As previously noted, the model assumes free-entry for firms: employers exhaust the present discounted value of job creation net of the vacancy-posting cost. At the time of posting a vacancy, they observe the distribution of unemployed workers across asset levels and age. By the time of meeting these workers, this distribution has evolved according to the law of motion of the economy. Therefore the free-entry condition is: (9) η q(θ) = 1 N w r τ=1 i=0,1 ˆ ( J j a U i (a),τ ) p u i, j j=0,1 A µ i U (a,τ) da u Nw 1 µ U i (a,τ) denotes the beginning-of-period population of unemployed with asset level a, age τ and eligibility to unemployment benefits i. The conditional distribution used to form expectations is obtained by scaling µ U i (.) with the size of the unemployment pool u Nw 1, and the subscript indicates agents of age less than N w 1 periods. Balanced budget condition. Finally, the expenditures of the government are financed by the payroll tax. This condition gives: (10) κ N w τ=1 i=0,1 ˆ Y,A w i (y,a,τ)dµ W i (y,a,τ) = N w τ=1 i=0,1 b i ˆ A dµ U i (a,τ) with µ W i (y,a,τ) the population of employed worker with match productivity y, asset level a, age τ and tenure i Equilibrium. With the two conditions just described, we can define a stationary equilibrium of the model in a standard manner. A stationary equilibrium is a list of asset values (R(a,τ), U 0 (a,τ), 11

13 U 1 (a,τ), W 0 (y,a,τ), W 1 (y,a,τ), J 0 (y,a,τ), J 1 (y,a,τ)), a list of decisions rules for asset holdings ( a R (a,τ), a U 0 (a,τ), au 1 (a,τ), aw 0 (y,a,τ), aw 1 (y,a,τ)), a list of match entry and continuation rules (y 0 (a,τ), y 1 (a,τ)), a list of wage functions (w 0 (y,a,τ), w 1 (y,a,τ)), a population distribution across labor market status, match productivity, assets and age ( µ R (a,τ), µ 0 U (a,τ), µu 1 (a,τ), µw 0 (y,a,τ), µ 1 W (y,a,τ)), a value of labor market tightness θ and a payroll tax rate κ such that: (1) Optimal asset holding decisions: The asset holding decision a R (a,τ) solves the inner maximization problem in equations (1). Given tightness θ, and the wage schedules w 0 (y,a,τ), w 1 (y,a,τ), the asset holding decisions a U 0 (a,τ), au 1 (a,τ), aw 0 (y,a,τ), aw 1 (y,a,τ) solve the inner maximization problem in the equations (2) and (3). (2) Firms optimize: Given κ, the wage schedules w 0 (y,a,τ), w 1 (y,a,τ) and the asset holding decisions a W 0 (y,a,τ), aw 1 (y,a,τ), the asset values J 0 (y,a,τ), J 1 (y,a,τ) satisfy equation (4). (3) Optimal match entry and continuation decisions: Given the asset values J 0 (y,a,τ) and J 1 (y,a,τ), the match entry and match continuation rules y 0 (a,τ), y 1 (a,τ) are the solution to equations (7) and (8). (4) Two-tier Nash bargaining: Given the asset values U 0 (a,τ), U 1 (a,τ), W 0 (y,a,τ), W 1 (y,a,τ), J 0 (y,a,τ), J 1 (y,a,τ), the wage functions w 0 (y,a,τ), w 1 (y,a,τ) are the solution to (5) and (6). (5) Free-entry condition: Given the asset value J 0 (y,a,τ), the asset holding decisions a U 0 (a,τ), a U 1 (a,τ) and the population distribution µu 0 (a,τ), µu 1 (a,τ), labor market tightness θ is pinned down by equation (9). (6) Balanced budget condition: Given the wage schedules w 0 (y,a,τ), w 1 (y,a,τ) and the population distributions µ U 0 (a,τ), µu 1 (a,τ), µw 0 (y,a,τ), µw 1 (y,a,τ), the payroll tax rate κ satisfies equation (10). (7) Equilibrium distribution : ( µ R (a,τ), µ 0 U (a,τ), µu 1 (a,τ), µw 0 (y,a,τ), µw 1 (y,a,τ)) satisfies equilibrium stock-flow equations implied by the set of decision rules ( a R (a,τ), a U 0 (a,τ), a U 1 (a,τ), aw 0 (y,a,τ), aw 1 (y,a,τ)) and (y 0 (a,τ), y 1 (a,τ)), and by equilibrium tightness θ. The stock-flow equations across the different states of the economy (condition 7 in the above definition) can be deduced from the Bellman equations (1), (2), (3) and the free-entry condition (9). Notice that the latter is written from the perspective of the beginning of period after newborn workers have entered the economy. We assume that newborns are initially unemployed, with no unemployment insurance benefits (i = 0) and no assets (a = 0). 12

14 3. CALIBRATION AND STEADY-STATE ANALYSIS This section calibrates the model with no severance payments (F = T = 0). We use U.S. data for the calibration to accord with the unemployment insurance system embedded in the model. Moreover, mandatory severance payments are virtually non-existent in many U.S. states. This suggests that labor market dynamics as readily observed in U.S. data can be used for the calibration, without making assumptions on how these would be affected by the policy. Before we move on to the numerical results, we describe some properties of the steady-state without severance payments Parameters set externally. The model period is chosen to be one quarter, as a compromise between computational costs and the fast dynamics of the U.S. labor market which informs the model. We interpret the working life as a 40 years period and the retirement phase as 15 years, which gives N w = 160 and N r = 60. We choose the interest rate to be 4 percent on an annual basis, and thus β = The coefficient of relative risk-aversion σ is 2.0, a standard value in the literature. We normalize the unconditional mean of match productivity, µ y, to 1.0. The choice of the volatility of productivity shocks, σ ε, is discussed below. The persistence of this process is exogenously set to ρ = At an annual frequency, this implies a persistence of 0.75, which is in the lower range of the auto-correlation of wages typically observed in the data. 11 Of course, there are conceivably other reasons for these high auto-correlations, such as infrequent renegotiation of wage contracts. We ground the choice of ρ in the empirical auto-correlation of wages because a lower value for ρ implies a higher σ ε ; this leaves the results unchanged qualitatively but it also implies a wage dynamics in the model that does not square with the data (wages become too volatile). Following much of the literature, we invoke the Hosios-Pissarides rule to equate the unemploymentelasticity of the matching function, α, and the bargaining power of workers, φ. We choose α = φ = 0.5. The elasticity of 0.5 is within the range of values reported by Petrongolo and Pissarides (2001). The remaining parameters which we set exogenously are p e and p u, the transition probabilities that relate to tenure and the duration of benefits. We interpret short tenure as a period of less than 2 years, and thus we set p e = We use p u = 0.5 to make unemployment benefits expire after 2 quarters. 11 See, for instance, Chang and Kim (2006): the authors use wage data from the PSID to infer the parameters of a similar productivity process, which they estimate by controlling for selection into employment. They find an annual persistence of for men and for women (Table 1 in Chang and Kim, 2006). 12 p e is only relevant when we introduce severance payments later on in the analysis. The value we choose is motivated by the fact that, in labor markets with high levels of employment protection for high-tenure workers, temporary jobs are often not subject to dismissal costs. Temporary contracts usually run for less than 2 years. 13

15 Table 1. Parameter values (one model period is one quarter) Parameters set externally Subjective discount factor β Risk aversion σ 2.0 Periods in the labor force N w 160 Periods in retirement N r 60 Mean of match productivity µ y 1.0 Persistence of match productivity ρ Elasticity of the matching function α 0.50 Bargaining power of workers φ 0.50 Probability of switching to long tenure p e Probability of exhausting benefits p u 0.50 Parameters set internally Benchmark Low volatility High volatility Social assistance benefits b Unemployment insurance benefits b Efficiency of the matching function M Volatility of match productivity σ ε Probability of exogenous destruction δ Vacancy posting cost η Calibrated parameters. The remaining parameters are b 0, b 1, M, σ ε, δ and η. We calibrate these parameters jointly to match a set of targets which we discuss momentarily. We follow a standard practice for the vacancy posting cost η: we normalize market tightness θ to 1.0 and use the free-entry condition (equation (9)) to pin down a value for η. Our calibration targets are the following: (i) a 5 percent replacement ratio for social assistance, (ii) a 45 percent replacement ratio for unemployment insurance benefits, (iii) a monthly job-finding rate of 45 percent, (iv) a monthly separation rate of 3.5 percent. (i) and (ii) are based on institutional features of the U.S. labor market (OECD, 2010). (iii) is the monthly target used by Shimer (2005) and Krusell, Mukoyama and Şahin (2010), and (iv) is close to the monthly figure of 3.4 percent which they use Finally, we need an additional moment condition. Here, our strategy is to consider three specifications that differ with respect to the importance of endogenous separations, governed by the parameter σ ε. In the benchmark specification, our target is to have productivity shocks account for 50 percent of all separations. In the alternative, we consider a low volatility (resp. high volatility) economy where productivity shocks explain 25 percent (resp. 75 percent) of all separations. 13 In the model the job-finding and separation rates we compute are for workers aged strictly less than Nw periods, i.e. those are the moments conditional on staying in the labor force. 14 Observe that the job-finding rate of the model is not Mθ 1 α. There is a non-zero probability that, after meeting and observing the initial draw of match productivity, the worker and the employer choose to walk away. 14

16 3.3. Steady-state analysis. Table 1 summarizes the parameter values for the benchmark and the low and high volatility economies. To gain understanding of the workings of the model, in Table 2 we reported a set of statistics for each calibration. Beginning with outcomes in the aggregate vs. within each age group, we see that the model generates little differences in labor market turnover over the life-cycle. Younger workers are willing to take on any job to start accumulating assets, which explains why job-finding rates are higher in this group. Older workers have little chances of finding a job before retiring, and therefore they stay on the job longer and have lower separation rates. These patterns are qualitatively in line with the ingredients of the model. Of course, quantitatively they fall short of matching the empirical behavior of worker flows over the life-cycle (e.g. Choi, Janiak and Villena-Roldán, 2014). The age variable in the model does not carry a productivity component that would help rationalize these facts. The patterns of turnover just described explain why, in each economy, productivity and wages are slightly hump-shaped over the life-cycle: the productivity thresholds y 0 (a,τ) and y 1 (a,τ) are lower Table 2. Steady-state characteristics of economies without severance payments All years years years Benchmark economy Separation rate Job-finding rate Average productivity Average wage Average assets Low-volatility economy Separation rate Job-finding rate Average productivity Average wage Average assets High-volatility economy Separation rate Job-finding rate Average productivity Average wage Average assets NOTES: The first column reports a set of statistics for workers in the labor force. Therefore average assets do not include the assets of agents who have retired. The columns labeled 20-24, 25-54, report statistics for the corresponding age group. The separation rate and the job-finding rate are the moments conditional on staying in the age group. These rates are expressed in percentage points and converted to monthly values. 15

17 12 10 Benchmark Low volatility High volatility AGE Figure 1. Average savings over the life-cycle NOTES: This plot shows average savings within each age group, where savings are expressed as a function of average annual labor earnings. Solid line: benchmark economy; Dashed line: low-volatility economy; Dashed-dotted line: high-volatility economy. at both ends of the life-cycle, which results in difference with the group of workers aged 25 to 54. Finally, workers accumulate assets over the life-cycle. In the first age group, savings amount to only about 1.5 quarterly wage whereas those aged 55 to 59 have accumulated more than 8 years of wages. We comment further on the savings behavior of agents below. Turning to differences across calibrations, we observe that increasing the volatility of match productivity increases average productivity and wages. This is because the distribution of productivity among active matches is truncated below due to endogenous separations. Higher levels of earnings imply higher asset levels, as shown in the table. However, if we express savings in terms of average labor earnings in each economy, the savings behavior of agents appears very similar across calibrations. This point is illustrated in Figure 1. We observe that, in the three economies, agents accumulate up to 10.5 years of annual earnings labor on average. Then during the retirement phase, they run down their assets until they leave the economy. 16

18 4. QUANTITATIVE RESULTS: TRANSFER TO THE WORKER VS. A FIRING TAX In this section, we discuss the effects of mandatory severance payments on equilibrium allocations and welfare. For illustrative purposes we consider two polar cases: (i) a pure transfer from the firm to the worker and (ii) a pure tax on the worker-firm pair. Case (i) assumes that the transfer is the only component of severance compensations; in reality, they account for large share, but not all, of the payments (see Garibaldi and Violante, 2005). Case (ii) is what Bertola and Rogerson (1997) describe as the standard view, i.e. it focuses attention on the sunk portion of severance payments A transfer to the worker. Table 3 reports the effects of mandatory severance transfers on several economic outcomes. The first column ( base ) is the benchmark economy with no severance payments. The other columns characterize steady-states with increasing levels of severance payments. Table 4 in this section and Tables B1 and B2 in Appendix B follow this practice. The first remarks concern the labor market implications of severance payments. There are two forces shaping the effects on the separation rate: the payment of the transfer deters employers from dissolving the match, while receiving the transfer gives incentives to workers to separate. In the benchmark calibration, the second effect dominates: a transfer to the worker raises the separation rate. This also occurs in the low-volatility economy, but not in the high-volatility economy; see Table B1. More importantly, we find that severance payments have almost no effect on the hiring margin. Inspection of the separation and unemployment rates indeed shows that the job-finding rate remains almost constant across columns. Since severance payments have limited impact on separations and job-finding, their effect on unemployment is quantitatively small. In particular, it is an order of magnitude lower than what previous studies tabulated. Alvarez and Veracierto (2001) for instance find that a transfer amounting to 6 months of wages changes unemployment by 1.50 percentage points, whereas we find a change of only 0.25 percentage points. The second part of the table sheds light on these results. A mandatory transfer to the worker lowers the average wage because employers and workers internalize it into wage payments. The insights of Lazear (1990) s bonding critique carry over to a large extent in this environment. At the entry level, workers receive lower wages to compensate for the expected payment of the future transfer. The wages of incumbent workers actually increase because severance payments strengthen their bargaining position, but the drop in entry wages is larger and account for the lower average wage. Although the model contains only two tenure levels, the new wage schedule can be described 17

19 Table 3. Quantitative effects of severance payments: Benchmark economy Base F = T > 0 (in months of average wage) Equilibrium tax rate Separation rate Unemployment rate Average wage, overall Average wage, entry level Output Assets Welfare NOTES: F and T are measured in months of the average wage of the corresponding column. All rates are expressed in percentage points. Separation rates are converted to monthly values. Statistics without meaningful units of measurement are normalized to in the base column. Welfare effects are percentage point changes in lifetime consumption. as a steeper wage profile. 15 Finally, the decrease in the average wage and the slight increase in the number of unemployed account for the higher tax rates in the columns on the right of the table. 16 In order to gauge the effects of severance payments on other aggregate quantities, in Table 3 we report changes in gross output and assets. Output increases initially because workers with lower match productivity are separated from their jobs. The decrease in employment is the effect that dominates at high (F, T ) and this results in lower output. Quantitatively, these changes are plausibly small and the same result holds in other calibrations (Table B1). Finally, assets follow a slightly humpshaped pattern which mirrors the reduction in labor earnings on the one hand, and the fact that higher severance payments contribute to accumulating assets over the life-cycle. The last row of Table 3 shows the effects of mandatory severance payments on welfare. The welfare criterion is based on the lifetime utility of a newborn worker, which we use to compute percentage point changes in lifetime consumption. 17 As the table shows, severance payments produce negative welfare effects. This follows from the previous discussion: mandatory transfers have limited effects 15 If the tenure variable could take more values, severance payments would be introduced as a gradually increasing function of tenure, consistent with observation. The wage profile would inherit part of the tenure profile of severance payments, as in Dolado, Lalé and Siassi (2015). 16 As noted in Section 2, a pure transfer from the firm to the worker implies that the policy is self-financed. Therefore it affects the equilibrium tax rate κ only through equilibrium effects on wages and employment. 17 To be precise, if we denote with a tilde ( ) the lifetime utility of a newborn in an economy with severance payments, and given a lifetime utility of U 0 (0,1) in the base economy, the welfare criterion is ϑ = ( Ũ0 (0,1) + B U 0 (0,1) + B ) 1 1 σ 1 18

20 on equilibrium allocations because they can be undone by a steeper wage profile which, in turn, is detrimental to newly-hired workers. Since these workers are on average younger and have fewer savings, severance payments deteriorate welfare. In this regard, the life-cycle structure is key to capture the link between the wage-shifting effects of severance payments and the lack of accumulated assets. In this calibration wherein 50 percent of job separations are subject to severance payments, we find a 1.2 percent welfare loss when the mandatory transfer amounts to 6 months of the average wage. The corresponding figures in the low-volatility and high-volatility economies are 0.8 and 0.9 percent, respectively. 18 These figures are similar to the welfare loss computed by Hopenhayn and Rogerson (1993) in a frictionless environment, and they stand in contrast with the positive welfare effects in Alvarez and Veracierto (2001) A tax on the worker-firm pair. Next, we remove the transfer component, i.e. we set T = 0. We study the effects of varying the level of F > 0 and use the proceeds from the firing tax to finance unemployment insurance. That is, while F plays an overtly negative role by creating a deadweight loss for every worker-firm pair, the distortion will be mitigated by lowering the payroll tax κ. Table 4 shows the effects of introducing a firing tax in the benchmark economy. First, the firing tax lowers the separation rate: this is the penalty role of severance payments. The penalty component also reduces the surplus of every job. This has a negative impact on job creation, but in all three calibrations we find that the effect on worker flows into unemployment dominates the effect on outflows. As a result, the unemployment rate decreases. Second, the lower number of unemployed and the proceeds from F explain why the payroll tax used to finance unemployment insurance plummets. In fact, Table B2 in the appendix shows that, in the high-volatility economy, the effect is so large that the proceeds of the tax are eventually rebated as a wage subsidy. Turning to the effects on wages, Table 4 shows that the firing tax lowers the average wage. The mechanism is different from the wage-shifting effect analyzed in the previous section. A tax on worker-firm pairs reduces the size of the job surplus, and therefore both the profits of employers and 1 β Nw+Nr with B = 1 σ 1 1 β. ϑ measures the change in lifetime consumption relative to the base economy. Throughout the number we report for ϑ is expressed in percentage points. 18 Intuition would suggest that the benchmark economy predicts results that stand in between the figures based on the low-volatility and high-volatility economies. However, this does not seem to hold in this set of experiments and our conjecture is as follows. If severance payments are increased and if more separations are subject to severance payments, then the wage-shifting effect becomes larger and generates larger welfare losses. On the other hand, more separations are subject to severance payments in economies with more volatility in match productivity, where the penalty role of severance payments could be welfare-improving. This second argument explains why the welfare losses are not larger in the high-volatility economy. 19

21 Table 4. Quantitative effects of a firing tax: Benchmark economy Base T = 0, F > 0 (in months of average wage) Equilibrium tax rate Separation rate Unemployment rate Average wage, overall Average wage, entry level Output Assets Welfare NOTES: F is measured in months of the average wage of the corresponding column. All rates are expressed in percentage points. Separation rates are converted to monthly values. Statistics without meaningful units of measurement are normalized to in the base column. Welfare effects are percentage point changes in lifetime consumption. the wages of workers become lower. In particular, wages decrease for new-hires as well as incumbent workers, unlike in the previous section. This effect explains the large drop in assets reported in Table 4. The decline in output stems from the fact that firms have to retain their workers more often, which reduces productivity per worker. It dovetails with the idea that firing taxes lead to a less efficient allocation of labor resources. The experiments in Table 4 suggest that the penalty role of severance payments deteriorate welfare. Meanwhile, the mechanisms just discussed indicate that the welfare effect should be ambiguously signed. On the one hand, wages are reduced because of lower rents from employment. But the tax pressure from unemployment insurance is also lower, which could result in a welfare improvement. We find that the second effect prevails in the high volatility economy: a firing tax that amounts to 6 months of the average wage raises lifetime consumption by 0.7 percent; see Table B2. The benchmark economy predicts a welfare loss of 0.2 percent, and the low-volatility economy a loss of 0.6 percent. This is because separations that are subject to the firing tax represent a small fraction of all separations and therefore they generate little revenues for unemployment insurance. The case for a firing tax is different from Alvarez and Veracierto (2001): in our model the positive effect is mainly through an externality on the government budget, whereas in their model the firing tax improves job stability. Finally, in the three economies, and since we measure welfare from a worker s perspective, a tax on the worker-firm pair is less detrimental than a mandatory transfer from the firm to the worker. 20