Michael Pries University of Maryland

Richard Rogerson Arizona State University

We develop a matching model to account for the fact that worker turnover in Europe is much less than in the United States, whereas job turnover is roughly the same. The model assumes that the quality of worker-firm matches is both an inspection good and an experience good. Both parties have limited information at the time of meeting about the match’s quality, which is completely revealed only by engaging in production. Hiring practices play a key allocational role in this economy. We show how labor policies distort hiring practices and assess the consequences for labor market dynamics and welfare.

I.

Introduction

The idiosyncratic shocks, heterogeneities, and frictions that characterize modern labor markets suggest that efficient use of labor will involve two kinds of reallocation: the reallocation of jobs from less efficient establishments to more efficient ones (job turnover) and the reallocation of workers across existing jobs to obtain better matches between workers and jobs (worker turnover). Empirical work finds that the volume of We thank Nancy Stokey, Fernando Alvarez, Per Krusell, and three anonymous referees, as well as seminar participants at University of British Columbia, Simon Fraser, Princeton, Duke, Arizona State, Maryland, Wharton, Toronto, California at San Diego, Texas, and Rice for comments. Rogerson acknowledges support from the National Science Foundation. [ Journal of Political Economy, 2005, vol. 113, no. 4] 䉷 2005 by The University of Chicago. All rights reserved. 0022-3808/2005/11304-0005$10.00

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this reallocation is large. For example, Burgess, Lane, and Stevens (2000) report that roughly 13 percent of jobs in existence in the United States at any point in time will no longer exist one year later and that the annual volume of worker separations is roughly five times greater than this amount. The realization that many policies and regulations seem to directly inhibit this reallocation has generated much interest in developing models to assess the ways in which policies affect labor market flows, aggregate outcomes, and welfare (see, e.g., Bentolila and Bertola 1990; Hopenhayn and Rogerson 1993; Alvarez and Veracierto 2000). Given the differences between the United States and continental Europe in both policy regimes and labor market outcomes, much of this work has focused on comparisons of those economies, with a particular emphasis on job creation and destruction. However, cross-country empirical work (which we review below) has uncovered an important fact: while the levels of job creation and destruction in Europe and the United States are roughly similar, worker turnover is substantially greater in the U.S. economy. This suggests that a proper understanding of the role of policies on labor market outcomes must focus more on the role of worker turnover. In that spirit, this paper builds a general equilibrium model of both worker turnover and job turnover and uses it to assess the effects—both on labor market outcomes and on welfare—of the various policy differences that distinguish Europe from the United States. In the model that we develop, the degree of selectivity in firms’ hiring practices is a primary determinant of the level of worker turnover. If firms hire indiscriminately but keep only workers who turn out to be good matches, then turnover will be much higher than if they cautiously hire only those workers who appear up-front to be good matches. Our analysis therefore emphasizes worker turnover in the period immediately following the formation of a match. Two observations motivate this emphasis. First, in the United States, approximately 80 percent of all worker turnover is accounted for by separations that occur within the first two years of a match.1 Second, cross-country data show that separation rates in newly formed matches differ markedly across countries. Male workers aged 20–24 in France and Germany with tenure between zero and four years have a 46 percent and 43 percent chance, respectively, of being with the same employer five years later (OECD 1994, table 4.3). The corresponding figure for the United States is only 32 percent. For male workers aged 25–29 with five to nine years of tenure, however, the differences are much smaller: the probability of being with 1 This is based on the steady-state distribution implied by the tenure profile of separation rates in Pries (2004). Similar numbers are implied by the panel data estimates in Farber (1999).

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the same employer five years later is 61.1 percent in Germany, 70.1 percent in France, and 59.9 percent in the United States.2 Our model combines variants of two benchmark models from the literature: the Jovanovic (1979) learning model and the Pissarides (1985) matching model. Job flows are driven by idiosyncratic shocks to job productivity, and worker turnover (in excess of job turnover) is driven by the stochastic accumulation of information about match quality. We modify the Jovanovic model in one important way: we assume that match quality is both an inspection good and an experience good. Both parties to a match observe a signal about the match’s true quality prior to deciding whether to form a match, and matches form only if the signal about match quality exceeds a threshold value. True quality is revealed over time, but only if a match is formed. Labor market regulations affect worker turnover in the model by influencing hiring practices, that is, the level of the threshold signal. We examine four policies in our model—minimum wages, unemployment benefits, dismissal costs, and taxes—and then assess the quantitative impact of European-style policies on allocations and welfare in a calibrated version of the model. We find that minimum wages and dismissal costs both significantly affect worker turnover. Our analysis also shows that interactions between the various policies can be significant. For example, the effects of minimum wages on hiring practices are exacerbated by the presence of payroll taxes, even though payroll taxes by themselves have very little effect. We find that our model can account for almost half of the observed differences in worker turnover rates between the United States and continental Europe. We discuss plausible extensions that would amplify the model’s effects. The welfare costs of lowering worker turnover via changes in hiring practices are significant. The steady-state welfare cost of a policy that lowers worker turnover by 20 percent exceeds 2.4 percent of output. Although more stringent hiring practices increase the average match quality, they also necessitate that a greater fraction of output be devoted to recruiting. By way of comparison, Hopenhayn and Rogerson (1993) found that the steady-state welfare cost of lowering job turnover by 25 percent was 2.8 percent. Our explanation for lower worker turnover in Europe should be seen as complementary to that of Blanchard and Portugal (2001). They argue that policies that increase unemployment durations decrease quits to unemployment, thereby decreasing worker turnover. Our model of information and hiring practices is related to that of Kugler and Saint2 We calculated the numbers for the United States from tenure supplements of the Current Population Survey. Because of data availability, the values for the United States are four-year retention rates. The key point is that the ratios of the U.S. values to the European values are much lower at lower tenures.

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Paul (2004). While they examine hiring practices in a model with asymmetric information about worker quality, they focus on the issue of hiring from employment versus unemployment and do not analyze the effects of policy on worker turnover. II.

Job and Worker Turnover in the United States and Europe

This section summarizes empirical work on the relative magnitude of job and worker turnover in the United States and the countries of continental Europe with highly regulated labor markets. Briefly, job turnover measures the reallocation of employment positions across establishments between two points in time, whereas worker turnover measures the accumulated employment transitions experienced by workers over a given time interval. More formally, the job destruction (creation) rate between times t and t ⫺ 1 is the loss (gain) of employment positions at establishments that contracted (expanded) between periods t ⫺ 1 and t, expressed relative to average employment. Job turnover is the sum of the job creation and job destruction rates. Worker turnover is the sum of all hires and separations over a given time interval, divided by the average employment level. Worker turnover is necessarily larger than job turnover, since every instance of job turnover necessarily generates (at least) an equal amount of worker turnover. Table 2 in Davis and Haltiwanger (1999) reports economywide annual job turnover rates in the 20–25 percent range for Canada, France, Italy, and the United States; the figure for Germany is a bit smaller at 16.5 percent. Another data point is supplied by Blanchard and Portugal (2001), who find that annual job turnover is slightly higher in Portugal than in the United States.3 For our purposes, the key stylized fact, as noted earlier by Bertola and Rogerson (1997), is that there is no evidence that job turnover rates are substantially smaller in continental Europe than in the United States. Although evidence on cross-country differences in worker turnover is scarcer, the available evidence consistently suggests that worker turnover is substantially higher in the United States than in continental Europe. We mention a variety of data sources in order to give some sense of the magnitude of the differences. The most comprehensive measures of worker flows come from administrative records such as unemployment insurance or social security. On the basis of such records, Contini (2002) reports annual worker turnover rates in the 40–60 percent range for several countries in con3 The United States has a significantly higher job reallocation rate when measured quarterly. We believe that this is driven by the much higher use of temporary separations in the United States than in Europe. Because we focus on permanent separations, we believe that cross-country comparison of annual job flows is preferable.

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4

tinental Europe. If we assume a steady state, table 4 in Blanchard and Portugal (2001) implies an annual worker turnover measure of roughly 35 percent for Portugal. Burgess et al. (2000) provide estimates using unemployment insurance records for Maryland and find an annual worker turnover rate of roughly 125 percent. Recently available data from the Census Bureau for several other states covering a shorter time period indicate that the figures for Maryland are typical. These measures suggest that worker turnover in the United States is between two and three times larger than in Europe. There is tremendous heterogeneity in the nature of worker separations and accessions. They include student summer jobs, other seasonal jobs, part-time jobs, temporary separations, and instances of multiple job holding. A complete picture of differences in worker turnover across countries would decompose turnover into various types. Unfortunately, such measures are not currently available. However, at least for the United States, there are other measures of turnover based on less comprehensive data that implicitly filter out some high-frequency components of turnover. Blanchard and Diamond (1989) estimate a worker turnover rate of 76 percent. On the basis of very different information, Pries (2004) estimates a tenure profile for separation rates using the Current Population Survey tenure supplement, which also implies a steady-state worker turnover rate equal to 76 percent. Similar calculations for European countries would presumably also decrease their estimated worker turnover rates, though one might suspect that the adjustment might be smaller. In light of this evidence, we believe that the range of differences is probably somewhat smaller than the factor of two or three suggested by the previous sources. We think a conservative reading of the evidence suggests that worker flows in the United States exceed those in Europe by a factor of at least 1.5. The rate at which workers flow into unemployment can also provide some evidence on worker turnover. In fact, Blanchard and Portugal (2001) used this as a proxy for worker turnover when they extended their analysis beyond Portugal and the United States. While this proxy is available for many countries from publicly available data, it does not distinguish between a worker entering unemployment from employment and a worker entering unemployment from out of the labor force. It also abstracts from job-to-job transitions. With these caveats in mind, using data for 1985–2000, we divide the stock of unemployed workers who report being unemployed less than one month by the stock of employment to compute the monthly flow rate into unemployment. We find that the resulting flow rate is roughly four to five times higher in 4 The particular values for Belgium, France, Germany, and Italy are 41.7, 59.6, 43.8, and 61.7, respectively.

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the United States than in France, Germany, Italy, Spain, and Portugal. While the caveats are significant, these data also point to substantially larger worker flows in the United States than in Europe. We interpret the evidence reviewed above to support two conclusions. First, job turnover is very similar in the United States and continental Europe. Second, a variety of indicators suggest substantially higher worker turnover in the United States. A conservative estimate of the difference would appear to suggest that worker flows are 1.5 times larger in the United States, whereas a more liberal interpretation suggests a factor of perhaps 2.5. Although cross-country comparisons contain substantial noise, the marked differences in worker turnover between the United States and Europe seem too large to be dismissed as simply the result of mismeasurement. III.

Model

The model is a variant of the matching models studied by Diamond (1982), Pissarides (1985), and Mortensen and Pissarides (1994). In the spirit of these models, we make simplifying assumptions to permit analytic solutions. There is a continuum of identical workers, with total mass equal to one, with preferences defined by

冘 ⬁

bt(ct ⫺ an t),

(1)

tp1

where b is a discount factor, ct is consumption, n t 苸 {0, 1} is time spent working, and a measures the disutility associated with working. There is also a continuum of identical agents whom we refer to as entrepreneurs or firms, with preferences defined by

冘 ⬁

bt(ct ⫺ k vvt ⫺ k xx t),

tp1

where b and ct are as above, vt is the number of vacancies posted in period t, k v is the utility cost per vacancy posted, x t is the number of new (unfilled) employment positions created in period t, and k x is the fixed utility cost of creating an employment position. We discuss these costs in more detail below. The unit of production is a matched worker-entrepreneur pair. The observed output of a match at time t is given by yt p ¯y ⫹ et, where ¯y is true match quality and et is a mean-zero independently and identically distributed random variable. We assume that there are two types of matches: good matches (¯y p y g) and bad matches (¯y p y b ! y g). The role of the “noise” term et is to prevent workers and firms from perfectly inferring match quality immediately after first producing.

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Match quality is both an inspection good and an experience good.5 When a worker and entrepreneur meet, each receives the same signal p that corresponds to the probability that the match will be good if it is formed. The value of p is drawn from a distribution with the cumulative distribution function given by H(p) and is independent across matches. If a worker and firm decide to form a match, they attempt to infer its quality from the observed match outputs. As in Pries (2004), we assume that the noisy component of match output, e, is uniformly distributed, so that learning takes a simple “all-or-nothing” form. Specifically, if e is uniformly distributed on [⫺q, q], then whenever observed output is less than (greater than) y g ⫺ q, the match is revealed to be bad (good); whereas if observed output falls in the range [y g ⫺ q, y b ⫹ q], nothing is learned and the posterior probability that the match is good is equal to the prior probability, p. Let a p (y g ⫺ y b)/2q denote the probability that the match type is revealed. Consequently, a match of unknown type with prior probability p will be revealed as good with probability ap and will be revealed as bad with probability a(1 ⫺ p). Since all matches have the same probability of having their true type revealed, there is no selection effect on the distribution of match types. The quality of a match is persistent—a good match remains good and a bad match remains bad—as long as it remains intact; however, jobs may be hit by idiosyncratic shocks that render them unproductive. Specifically, any job that produces in period t becomes unproductive at the beginning of the next period with probability l. The unproductive state is absorbing.6 Entrepreneurs can create (unfilled) employment positions, at a onetime cost of k x. Posting a vacancy to find a worker imposes a per period disutility of k v on an entrepreneur. While it is standard in the literature to assume that k x p 0, assuming that k x 1 0 allows us to distinguish between worker flows and job flows. In particular, the model can distinguish between separations in which the entrepreneur ultimately hires a replacement worker and separations in which the job ceases to exist. We assume that unmatched workers can search costlessly, whereas matched workers cannot search; that is, there is no on-the-job search. We assume a constant returns to scale matching function m(v, u). A worker meets a vacant job with probability p p m/u, and a vacancy meets a searching worker with probability q p m/v. Constant returns to scale implies that p and q are functions only of the ratio v/u. We also assume two boundary conditions: as v/u r ⬁, p r 1 and q r 0, and as v/u r 0, p r 0 and q r 1. 5

Nagypal (2002) finds that learning about match quality is economically significant. We assume that an unfilled employment position never becomes unproductive. This is assumed only for analytic convenience: it implies that l does not enter the expression for the flow out of unemployment. 6

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Our assumptions about timing are standard. Matches that result from search in period t become productive in period t ⫹ 1. Matches of unknown quality at the beginning of period t will observe output at the end of the period and will update the information about match type accordingly. Matches that produce in period t find out at the beginning of period t ⫹ 1 whether the job will continue to be productive. If a match dissolves at the beginning of period t ⫹ 1, then the worker and entrepreneur are allowed to search in period t ⫹ 1. Whereas the above information is sufficient to formulate a social planner’s problem for the economy, in order to analyze a decentralized equilibrium we must also describe the process of wage determination. As is standard, we use a generalized Nash bargaining solution in which the worker’s threat point is the value of being unemployed, the entrepreneur’s threat point is the value of an unmatched employment position, and the worker’s share of the surplus is v.7 Period t wages are not contingent on period t output, and the wage received by a worker who is in a match that is known to be good with probability p will be denoted by w(p).

IV.

Equilibrium

In this section we define and characterize the steady-state equilibrium of the model.8 We are interested in equilibria in which employment positions are created and matches that are known to be bad are terminated. To guarantee that bad matches are terminated, it is sufficient to assume that y b ≤ a, since even with equality the match will be terminated if vacant positions have value. To guarantee that employment positions are created in equilibrium, it is sufficient, given the Inada conditions on the matching function, to ensure that there is a positive return to creating a position when the probability of meeting a worker is one. In what follows, we shall assume that these two conditions hold. Let Je(p) be the value to the entrepreneur of being in a match that with probability p is of high quality, and let Ju be the value to the entrepreneur of an unfilled employment position. These two values must satisfy Je(p) p max { Ju , py g ⫹ (1 ⫺ p)y b ⫺ w(p) ⫹ b(1 ⫺ l) # {a[pJe(1) ⫹ (1 ⫺ p)Ju] ⫹ (1 ⫺ a)Je(p)}}

7

(2)

See Kiyotaki and Lagos (2005) for an alternative wage-setting process. It is well known that in matching models like ours, the steady-state decision rules also characterize the dynamics out of the steady state. 8

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and

[冕

Ju p ⫺k v ⫹ b q

]

Je(p)dH(p) ⫹ (1 ⫺ q)Ju .

(3)

The interpretation of these expressions is quite straightforward. Consider the one for Je(p). The first three terms on the right-hand side are simply expected current-period profits, that is, expected output minus wages (recall that e has mean zero). The fourth term is expected future discounted profits: with probability 1 ⫺ l the match will remain productive, with probability a its type will be revealed, and with probability p it will be good, in which case the value of expected discounted profits will be equal to Je(1). If the match turns out to be bad, then the match will be dissolved and the entrepreneur gets Ju. When the match type is not revealed, the firm continues with the value Je(p). Finally, if the job exogenously becomes unproductive, then it will be terminated and future profits will be zero; that is, the capital value of the employment position is destroyed. Of course, the entrepreneur always has the option of simply not proceeding with the match, which has value Ju. Equation (3) is interpreted similarly. Note that these expressions implicitly assume that an entrepreneur with an unfilled employment position will necessarily post a vacancy, which must be true in a steady state with positive employment. Letting V(p) denote the value to the worker of being in a match that e is good with probability p and Vu be the value of being unemployed, we have V(p) p max {Vu , w(p) ⫺ a ⫹ b(lVu ⫹ (1 ⫺ l){a[pV(1) ⫹ (1 ⫺ p)Vu] e e ⫹ (1 ⫺ a)V(p)})} e

(4)

and

[冕

Vu p b p

]

V(p)dH(p) ⫹ (1 ⫺ p)Vu . e

(5)

These equations implicitly assume that both the worker and the firm make the decision about whether to form a match. As is well known, with Nash bargaining there will always be agreement about this decision, and hence there is no inconsistency. We denote the optimal decision rule for match formation by X(p), where X(p) p 1 indicates that they form the match and X(p) p 0 indicates that they not form the match. In equilibrium, optimal decisions will take the form of a reservation ¯ and do not form a match if p ! p ¯. rule: form a match if p 1 p This model has three aggregate state variables: the mass of matches

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known to be of good quality (eg), the mass of matches of unknown quality (en), and the mass of previously created but vacant employment positions (e v). In equilibrium, the distribution of p’s in matches of unknown ¯ 1], rescaled to integrate to one, quality will be proportional to H on [p, so there is no need to keep track of this distribution. We now define a steady-state equilibrium (of the form discussed above) for this model. Definition 1. A steady-state equilibrium is a list w(p), u, v, eg, en, e v, Je(p), V(p) , Vu, Ju, and X(p) such that the following conditions hold: e 1. 2. 3. 4.

Value functions: Given w(p), u, and v, J(p) , V(p) , Vu, and Ju satisfy e e equations (2)–(5). Match formation: Given w(p), u, and v, X (p) is an optimal decision rule. Free entry: Given w(p), the ratio v/u must be such that Ju p k x. Bargaining: The wage function w(p) is such that V(p) ⫺ Vu p v[ Je(p) ⫹ V(p) ⫺ Vu ⫺ Ju]. e e

5.

Steady state: The following four equations hold: leg p (1 ⫺ l)aen E[pFX(p) p 1], [l ⫹ (1 ⫺ l)a]en p m(v, u)E[X(p)], m(1, u/v)E[X(p)]e v p (1 ⫺ l)a{1 ⫺ E[pFX(p) p 1]}en ⫹ (v ⫺ e v){1 ⫺ m(1, u/v)E[X(p)]}, v ⫺ e v p l(eg ⫹ en).

One way to solve for the equilibrium is to find a wage function for which conditions 1–5 are satisfied. A simpler method is available, however: characterizing the equilibrium in terms of two values, the ratio ¯ . For this approach, it is useful to define v/u and the reservation value p the surplus function S(p) p Je(p) ⫹ V(p) ⫺ Vu ⫺ Ju. Substituting the value e functions into this expression gives S(p) p max {py g ⫹ (1 ⫺ p)y b ⫺ a ⫹ b(1 ⫺ l)[apS(1) ⫹ (1 ⫺ a)S(p)] ⫺ (1 ⫺ b)Vu ⫺ [1 ⫺ b(1 ⫺ l)]Ju , 0}. One can show that (1 ⫺ b)Vu p bpv

冕

S(p)dH(p) p

vv [(1 ⫺ b)k x ⫹ k v]. u(1 ⫺ v)

(6)

(7)

The first equality comes from using the definition for Vu plus the bargaining rule vS(p) p V(p) ⫺ Vu. The second equality comes from using e the bargaining rule (1 ⫺ v)S(p) p Je(p) ⫺ Ju and the free-entry condition

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Ju p k x in (3). Substituting into equation (6) yields

{

S(p) p max py g ⫹ (1 ⫺ p)y b ⫺ a ⫹ b(1 ⫺ l)[apS(1) ⫹ (1 ⫺ a)S(p)] ⫺

}

vv [(1 ⫺ b)k x ⫹ k v] ⫺ [1 ⫺ b(1 ⫺ l)]k x, 0 . u(1 ⫺ v) (8)

As the first argument of the max operator is monotonically increasing ¯ is unique. Moreover, it is easy to show in p, the reservation probability p ¯ . Differentiating and rearranging gives that S is linear for p 1 p S p

y g ⫺ y b ⫹ b(1 ⫺ l)aS(1) , 1 ⫺ b(1 ⫺ l)(1 ⫺ a)

(9)

¯ p 0, so we which is independent of p. Moreover, in equilibrium, S(p) ¯ for any p ≥ p ¯ . Substituting S(1) p (1 ⫺ can write S(p) p (p ⫺ p)S ¯ into equation (9) and rearranging implies that in equilibrium p)S S p

yg ⫺ yb ¯ { g(p). ¯ 1 ⫺ b(1 ⫺ l)(1 ⫺ ap)

(10)

The equilibrium can now be represented as the intersection of two ¯ -(v/u) space, one of which is upward-sloping and the other curves in p of which is downward-sloping. The upward-sloping curve describes op¯ p 0. Setting S(p) ¯ p 0 in (8), substituting timal match formation: S(p) ¯ ¯ , and rearranging gives S(1) p (1 ⫺ p)g(p) v v [(1 ⫺ b)k x ⫹ k v] ⫹ [1 ⫺ b(1 ⫺ l)]k x p u1 ⫺ v (y b ⫺ a) ⫹ [1 ⫺ b(1 ⫺ l)(1 ⫺ a)]g(p)p. ¯ ¯

(11)

¯ ¯ is increasing in p ¯ , this equation defines an upward-sloping Since g(p)p ¯ -(v/u) space. locus in p The downward-sloping curve corresponds to the free-entry condition expressed as (1 ⫺ b)k x ⫹ k v p bq(1 ⫺ v)

冕

¯ ¯ gives Substituting S(p) p g(p)(p ⫺ p)

S(p)dH(p).

冕

1

¯ (1 ⫺ b)k x ⫹ k v p bq(1 ⫺ v)g(p)

p ¯

¯ (p ⫺ p)dH(p).

(12)

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¯ is decreasing in p ¯ , this equation represents a negative reSince g(p) ¯. lationship between v/u and p The equilibrium is described by the intersection of these two curves. Given the conditions imposed earlier, there will indeed be an intersection of these two curves. The wage function can also be recovered. Note that (4) in conjunction with the bargaining rule implies w(p) p a ⫹ (1 ⫺ b)Vu ⫹ vS(p) ⫺ b(1 ⫺ l)v[apS(1) ⫹ (1 ⫺ a)S(p)].

(13)

Differentiation plus some algebra yields w (p) p [1 ⫺ b(1 ⫺ l)(1 ⫺ a) ⫺ b(1 ⫺ l)a(1 ⫺ p)]vg(p) ¯ ¯ p v(y g ⫺ y b),

(14)

¯ . To pin down the entire wage implying that w(p)is linear for p ≥ p ¯ p 0 implies that the endpoint w(p) ¯ can be schedule, note that S(p) determined as w(p) ¯ p a ⫹ (1 ⫺ b)Vu ⫺ b(1 ⫺ l)vap(1 ¯ ⫺ p)g(p). ¯ ¯

V.

(15)

Effects of Labor Market Policies: Analytic Results

Next we examine the effects of four types of labor market policies: unemployment benefits, taxes, employment protection, and restrictions on wage setting. These policies are the ones most commonly used to characterize the different institutional settings of European and U.S. labor markets. In this section, we characterize the effects of each of these policies analytically, and in the next section we carry out a quantitative analysis. A.

Unemployment Insurance

Differences in unemployment insurance systems across countries are substantial. We consider one dimension of unemployment insurance: the benefit b that all unemployed workers receive each period in which they are unemployed. To focus our analysis on the distortions induced by the payment of benefits, we assume that they are financed by a lumpsum tax that is levied on both employed and unemployed workers. It is straightforward to show that an increase in benefits is identical to an increase in the disutility of work, a (see, e.g., Mortensen and Pissarides 1999). In figure 1, the optimal match formation curve that represents equation (11) shifts to the right when a is increased. The free-entry curve is unaffected by a. We conclude that an increase in

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Fig. 1.—Determination of equilibrium values of p ¯ and v/u

unemployment benefits lowers the equilibrium v/u ratio and increases ¯. the cutoff value p B.

Taxes

Taxes also differ substantially between the United States and the countries of continental Europe. In a bargaining model such as ours, if taxes are the only distortion, then it is irrelevant whether taxes are levied on the firm or the worker—all that matters is the tax levied on the match. To this end, we consider a proportional tax on match output. When the previous analysis is repeated with such a tax, it is straightforward to show that raising the tax rate shifts both curves in figure 1 downward, ¯ is implying that v/u definitely decreases whereas the effect on p ambiguous. For future reference, we note that there is also a potential interaction between taxes and other policies such as the minimum wage. To see why this interaction may be important, it is necessary to note how bargaining adjusts wages to share the burden of the tax. If taxes are levied on the worker, then the firm will pay a higher (pretax) wage to the worker, as a way to share in paying the tax burden; if taxes are levied on the firm, then the worker will receive a lower wage as a way to share the burden. It follows that minimum wages may prevent a tax that is levied on the firm from being partly transferred to the worker via lower wages.

824 C.

journal of political economy Dismissal Costs

Next we analyze the impact of dismissal costs on the model’s equilibrium. It is useful to distinguish two different components of dismissal costs. One component is severance payments, which are simply cash transfers within a match. The second component is real resource costs, which include the costs associated with following whatever procedures are necessary in order to dismiss a worker.9 In contrast to transfers within a match, these costs represent transfers to a party outside the match. In the subsequent analysis, we assume that dismissal costs take the second form, since we think that these costs are most relevant for workers with short tenure. In particular, dismissal costs, denoted by d, are costs borne by the firm that are external to a match.10 One additional issue should also be noted. In reality, dismissal costs are not incurred in the case of voluntary separations, that is, in cases in which a worker quits. This suggests that in the real world any policy that attempts to impose penalties on employers for terminating employment positions must also effectively involve some restrictions or distortions to wage adjustments, since otherwise a firm could always avoid the penalty by reducing wages to a point at which the worker will quit. In what follows, we shall abstract from this aspect and assume that all separations in the model lead the entrepreneur to incur the cost d. In this sense, we are really analyzing a separation tax levied on employers rather than a dismissal cost per se. Dismissal costs levied on firms show up in two places in the conditions that characterize an equilibrium. First, they show up in the Bellman equation for a firm as payments that must be made in certain states. Second, they influence the threat points in the Nash bargaining. Specifically, the outside option of the firm in an ongoing match is now Ju ⫺ d instead of simply Ju, reflecting the fact that if a separation occurs, the firm must pay the cost d. However, note that if a firm and a worker have just met and are deciding whether to form a match, then the firm is not required to pay the dismissal cost in the event that the match is not formed, so that in this instance the outside option of the firm is still Ju. This asymmetry between new and ongoing matches implies that we must also index a matched firm-worker pair to indicate whether they are a newly matched pair or whether they are a pre-existing match. The resulting analysis is largely analogous to that done previously, so we simply sketch the details. 9 See, e.g., Emerson (1988) for a discussion of the various components in several countries. 10 Although we do not present the details, one can show that our assumptions about how dismissal costs affect bargaining imply that severance payments are neutral. However, if we also place lower bounds on wages, then severance payments have effects that look more like third-party costs.

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825

Let JI(p) denote the value to an entrepreneur of a match that has received a signal p, with the indicator I equal to zero for new matches and equal to one for continuing matches. Then JI(p) is defined by JI(p) p max { Ju ⫺ Id, py g ⫹ (1 ⫺ p)y b ⫺ wI(p) ⫺ bld ⫹ b(1 ⫺ l)[apJ 1(1) ⫹ a(1 ⫺ p)( Ju ⫺ d) ⫹ (1 ⫺ a)J 1(p)]},

(16)

where we again assume that matches discovered to be bad are terminated. Note that the negotiated wage for a match, wI(p), depends both on the signal p and on whether the match is new or old. The firm’s value from an unmatched vacancy, Ju, is defined by

[冕

Ju p ⫺k v ⫹ b q

]

J 0(p)dH(p) ⫹ (1 ⫺ q)Ju .

(17)

The analogous values for workers are defined by VI(p) p max {Vu , wI(p) ⫺ a ⫹ b(1 ⫺ l)[apV1(1) ⫹ a(1 ⫺ p)Vu ⫹ (1 ⫺ a)V1(p)] ⫹ blVu }

(18)

and Vu p b[pE HV0(p) ⫹ (1 ⫺ p)Vu].

(19)

The joint surplus of a match is given by SI(p) p JI(p) ⫹ VI(p) ⫺ ( Ju ⫺ Id) ⫺ Vu. Note that this expression assumes that the firm’s threat point is different in new and old matches. Following the same steps as earlier now leads to

{

SI(p) p max 0, py g ⫹ (1 ⫺ p)y b ⫺ a ⫹ b(1 ⫺ l)[apS 1(1) ⫹ (1 ⫺ a)S 1(p)] ⫺

}

vv [(1 ⫺ b)k x ⫹ k v] ⫺ [1 ⫺ b(1 ⫺ l)]k x ⫹ (I ⫺ b)d . u(1 ⫺ v) (20)

It is straightforward to show that when v/u is held constant, S 1(p) is increasing in d. Intuitively, higher dismissal costs lower the combined outside option of the worker and firm, thus raising the surplus. On the other hand, still holding v/u constant, one can show that S 0(p) is decreasing in the dismissal cost, d. Intuitively, when forming a new match, the worker and firm are assuming the obligation to pay the dismissal cost at some point in the future, and this future dismissal cost lowers the surplus relative to the alternative of not forming the match. It is also apparent from equation (20) that S 0(p) ≥ 0 implies S 1(p) 1

826

journal of political economy

0. It follows that any match quality that is acceptable at the time of meeting remains acceptable. Thus there is only one threshold value, and our analysis of equilibrium in the presence of dismissal costs entails ¯ and v/u that satisfy S 0(p) ¯ p 0 and the free-entry finding the values of p condition. In the interest of space, we do not repeat the derivations ¯ ¯ , but g(p) ¯ is now given here. It remains true that S 0(p) p (p ⫺ p)g(p) by ¯ { g(p)

y g ⫺ y b ⫹ b(1 ⫺ l)d . ¯ 1 ⫺ b(1 ⫺ l)(1 ⫺ ap)

(21)

Note that the slope is increasing in d. Intuitively, higher values of p are more valuable since they imply lower expected dismissal cost payments. When we proceed as before, the equivalent of equation (11) is v v [(1 ⫺ b)k x ⫹ k v] ⫹ [1 ⫺ b(1 ⫺ l)]k x p u1 ⫺ v (y b ⫺ a ⫺ bd) ⫹ [1 ⫺ b(1 ⫺ l)(1 ⫺ a)]g(p)p. ¯ ¯

(22)

For a given value of d, this describes an upward-sloping locus of points ¯ -(v/u) space. The free-entry condition is still given by equation (12) in p ¯ term that appears in it is now given by [21]) and is (though the g(p) ¯ -(v/u) space. still represented as a downward-sloping locus of points in p Next consider how an increase in d shifts these two curves. For a given value of the ratio v/u, one can show that increasing d shifts the optimal match formation curve down (the effect of d in the first term dominates ¯ ). Because g(p) ¯ is increasing in d, an increase in d the effect via g(p) also shifts the free-entry curve up. It follows that an increase in dismissal ¯ , whereas the impact costs necessarily raises the equilibrium value of p on v/u is not immediately apparent. Nevertheless, one can show that an increase in d lowers the equilibrium value of v/u. To see this, note that equation (20) defines a function S 0(p; v/u, d) that is decreasing in both v/u and d. Substituting this into the free-entry condition gives

冕 ( 1

(1 ⫺ b)k x ⫹ k v p b(1 ⫺ v)q

S 0 p;

0

)

v , d dH(p). u

(23)

Suppose that an increase in d led to an increase in the equilibrium v/u. The value of the integral term in (23) would decrease. This implies that q must increase, which contradicts the assumption that v/u rises. These results are intuitive. As it becomes more expensive to terminate matches, workers and firms require greater confidence that their match will be a good one and firms find it less profitable to open new vacancies. It is of interest to contrast the effects of increased unemployment insurance benefits with those of dismissal costs. Both policies lead to a shift in the optimal match formation curve in figure 1, but only dismissal

hiring policies

827

costs shift the free-entry curve as well. This latter effect tends to dampen ¯ . Hence, we expect the decrease in p and reinforce the increase in p ¯ relative to p will be larger in the case of employment that the change in p protection policies than for unemployment insurance. D.

Minimum Wages

We consider a simple restriction on wage setting—an exogenously specified minimum wage, denoted by w¯ .11 In the presence of a minimum wage, our definition of equilibrium must be modified along two dimensions. Previously we assumed that w(p) was consistent with surplus splitting for all values of p, with no side conditions on the function w(p). However, we now impose w(p) ≥ w¯ and require that V(p) ⫺ Vu ≥ e v[ Je(p) ⫹ V(p) ⫺ Ju ⫺ Vu], with equality for all p for which w(p) 1 w¯ . This e implies that workers always get at least a share v of the surplus, but possibly more if the minimum wage is binding. The second modification has to do with match formation. Previously there was never disagreement between workers and firms about match formation. However, it is now possible that a worker would like to form ¯ but the firm would not. As before, we assume a match and receive w that matches form only if both parties want to form them, which in this context is equivalent to assuming that the firm unilaterally chooses whether to form or continue the match. As a result, we modify the Bellman equations for the worker so that they take the firm’s decision rule X(p) as given. It follows that the worker’s Bellman equations no longer involve any maximization. The firm’s Bellman equations are unchanged. With a minimum wage, the approach in figure 1 cannot be used. Although the surplus function S(p) can be defined as before, it is no longer true that vS(p) and (1 ⫺ v)S(p) represent the surpluses for the worker and the firm. Consequently, it is necessary to solve explicitly for a wage function with the property that the five equilibrium conditions hold. As before, the firm’s optimal choice of a reservation value for match ¯ p Ju. In an equilibrium with a binding minimum quality satisfies Je(p) ¯ p w¯ . Hence p ¯ must satisfy wage, w(p) ¯ g ⫹ (1 ⫺ p)y ¯ b ⫺w¯ ⫹ b(1 ⫺ l)ap[ ¯ Je(1) ⫺ k x] ⫺ blk x p 0, py

(24)

where we have used the free-entry condition Ju p k x. ¯ This equation imposes a restriction on the equilibrium values for p 11 Empirical evidence (see Blau and Kahn 1999) suggests that wage distributions in Europe are compressed from below relative to the United States. Minimum wages are simply one mechanism that can produce this outcome.

828

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¯ has two effects. The first and Je(1), given w¯ . It shows that increasing w ¯. is a direct effect: when Je(1) is held constant, an increase in w¯ raises p That is, raising the minimum wage raises the minimal match quality. However, a change in w¯ also has an indirect effect via Je(1). Equation ¯ . If future (24) shows that an increase in Je(1), with w¯ fixed, reduces p returns are higher, a firm will accept a lower-productivity match today. We can show, however, that the first effect always dominates. To begin we shall show that if w¯ does not bind everywhere, then the value of an unemployed worker, Vu, is a sufficient statistic for the indirect effect. Suppose that w¯ does not bind at p p 1. Then Je(1) ⫺ Ju p (1 ⫺ v)S(1). Substituting into the expression defining S(1), using the equilibrium condition Ju p k x, and doing some algebra gives S(1) p

y g ⫺ a ⫺ (1 ⫺ b)Vu ⫺ [1 ⫺ b(1 ⫺ l)]k x . 1 ⫺ b(1 ⫺ l)

(25)

Hence, S(1) increases if and only if Vu decreases, and the same holds for Je(1) ⫺ Ju. It follows that if an increase in w¯ raises Vu, then the two effects on ¯ operate in the same direction and p ¯ necessarily increases. Hence, to p ¯ , it suffices to show that Vu cannot show that an increase in w¯ raises p decrease. The following lemma is useful in establishing this conclusion. ¯ , then both Lemma 1. If an increase in w¯ leads to a decrease in p ¯ V(p) ⫺ V and J (p) ⫺ J increase for all p ≥ p . e u e u ¯ decreases. We have already Proof. Let w¯ increase and suppose that p shown that Vu must decrease. To establish the claims, we consider separately values of p for which the minimum wage does and does not ¯ be the highest match quality for which w(p) p w¯ . bind. Let pˆ 1 p For p 1 pˆ , wages are determined by Nash bargaining with equality, so V(p) ⫺ Vu p vS(p) and Je(p) ⫺ Ju p (1 ⫺ v)S(p). Since Ju p k x and Vu e decreases, it follows from equation (6) that S(p) increases. Hence, V(p) ⫺ Vu and Je(p) ⫺ Ju also increase. e ˆ , the minimum wage binds, so Ve ⫺ Vu 1 0 (the worker ¯ p] For p 苸 [p, gets a positive surplus). Hence equation (4) implies V(p) ⫺ Vu p w¯ ⫺ a ⫹ b(1 ⫺ l){ap[V(1) ⫺ Vu] ⫹ (1 ⫺ a)[V(p) ⫺ Vu]} e e e p

w¯ ⫺ a ⫹ b(1 ⫺ l)ap ¯ [V(1) ⫺ Vu] e , 1 ⫺ b(1 ⫺ l)(1 ⫺ a)

(26)

so V(p) ⫺ Vu increases. Similarly, in this region, equation (2) implies e Je(p) ⫺ Ju p

py g ⫹ (1 ⫺ p)y b ⫺w¯ ⫹ b(1 ⫺ l)ap[ Je(1) ⫺ Ju] ⫺ blJu , 1 ⫺ b(1 ⫺ l)(1 ⫺ a)

so Je(p) ⫺ Ju also increases. QED

(27)

hiring policies

829

We then have the following result. ¯. Proposition 1. An increase in w¯ raises p Proof. The proof is by contradiction. Consider an increase in w¯ , and ¯ falls. As shown above, this implies that suppose to the contrary that p Vu has fallen. The Bellman equation for Vu implies that p satisfies

冕

1

(1 ⫺ b)Vu p bp

[V(p) ⫺ Vu]dH(p). e

(28)

p ¯

¯ decreases, the integral necFrom lemma 1 and the assumption that p essarily increases. Since Vu has fallen, it must be that p decreases. Similarly, the free-entry condition ( Ju p k x) implies (1 ⫺ b)k x p ⫺k v ⫹ bq

冕

[Je(p) ⫺ Ju]dH(p).

(29)

Lemma 1 implies that the integral increases, implying that q must decrease. But this contradicts the conclusion that p decreases. QED We are unable to sign analytically the effect of an increase in w¯ on p. If Vu increases, then p must decrease. To see this, note that if Vu increases, then Je(p) ⫺ Ju decreases for all p. The free-entry condition then implies that q increases, so p must decrease. However, we are unable to rule out the possibility that Vu decreases. In our quantitative work, we always find that p falls. VI.

Calibration

We calibrate the model by requiring that the steady-state equilibrium of the model with no policies match several salient features of the worker and job turnover data for the U.S. economy. We choose a period to be one month and set b to correspond to an annual discount rate of 4 percent. This implies b p 0.9966. Next, note that the equilibrium of the model is unchanged if the parameters y g, y b, a, k v, and k x are all multiplied by the same constant. As a normalization, we therefore set y b p 1. We also set a p 1, thus ensuring that bad matches are rejected in equilibrium. While this assignment is somewhat arbitrary, we found that the value of a had no effect on our findings given the remainder of the calibration procedure. We set y g p 1.9. This implies that the wage of a high-quality match is 25 percent higher than the wage of the match with the lowest acceptable value of p in equilibrium. Topel and Ward (1992) report that wages roughly double over the first 10 years of an individual’s labor market history and that cumulative wage increases associated with job changes over this period are around 33 percent. We think that this

830

journal of political economy

represents an upper bound on the importance of matching and hence choose 25 percent as the value for our benchmark calibration. We note that calibrating to a smaller value leads to larger effects of policies on both turnover and welfare, so calibrating to a relatively large value here corresponds to a conservative choice. The expected duration of an unemployment spell is given by ¯ . We target an unemployment duration of 3.33 months, 1/{p[1 ⫺ H(p)]} which is slightly higher than the number typically reported by the Bureau of Labor Statistics, for two reasons. First, in reality many unemployment spells end in labor force withdrawal rather than employment, creating a downward bias; second, our model abstracts from some labor force dynamics such as temporary layoffs, which are known to have shorter duration. We note, however, that the calibrated value of unemployment duration had little impact on how policies influence worker turnover. We have little direct evidence to guide the decomposition of the duration into the meeting (i.e., p) and matching (i.e., p ¯ ) components. In our benchmark specification, we assume that the probability that a match is formed conditional on a meeting is 0.5, implying that the equilibrium value of p is equal to 0.6. We choose l so that annual job destruction in our model is 11.3 percent, consistent with the value in Davis, Haltiwanger, and Schuh (1996). We match an annual rate rather than a quarterly rate because a significant fraction of quarterly destruction is accounted for by the process of temporary layoffs and our model abstracts from temporary separations.12 We measure job destruction in our model as it would be measured in the actual economy. In particular, if a match is terminated sometime between two survey dates because the match was bad, but the employment position is still not matched with a new worker at the time of the second survey date, we record it as job destruction. It follows that measured job destruction will be greater than the amount due to the value of l. In the equilibrium of our calibrated model, l is set at 0.0085; however, if the exogenous shock were the sole source of job destruction, the implied annual job destruction rate would be roughly 10 percent, indicating that about 10 percent of the measured job destruction in our model actually reflects unfilled vacancies for positions that have lost workers between survey dates. Conditional on a value of l, Pries (2004) estimated values of a and p g so as to match the empirical tenure profile of match separation rates in the United States. The implied values were a p 0.13 and E(p d p 1 ¯ p 0.4. We adopt both of these values in our calibration. As noted p) 12 The fact that job destruction measured annually is only about one-half of the annual rate that would be implied by the rate measured quarterly is strong evidence that a great deal of quarterly job destruction reflects temporary changes.

hiring policies

831

in Pries’s paper, these estimates are conservative, in the sense that they allow for the possibility that not all separations are due to learning about match quality. While there is little (if any) direct evidence to guide us in choosing a distribution for p, we can infer some of its properties in the context ¯ p 0.4 requires that there be relatively of our model. First, E(p d p 1 p) ¯ little mass in the right tail. Since this same condition imposes that p ¯ p 0.5, at least 50 cannot exceed 0.4 and our calibration target is H(p) percent of the mass lies below 0.4. Loosely speaking, this requires that the distribution H be somewhat skewed toward zero.13 On the basis of this, we choose a simple one-parameter family of distributions. Specifically, we take the density for a mean-zero normal distribution with standard deviation jp, restrict it to the interval [0, 1], and scale it proportionately so that it integrates to one. For each jp there is a unique ¯ such that H(p) ¯ p 0.5. However, there is only one value of value of p ¯ also yields E(p d p 1 p) ¯ p 0.4. That jp such that the implied value of p value of jp is 0.32. As is common in the literature, we adopt a Cobb-Douglas specification for the matching function, m(u, v) p Au hv 1⫺h, and set h p 0.5. (See the survey by Petrongolo and Pissarides [2001].) Given a value for h, the value of A determines the mapping between values of q and p. In our benchmark specification, we target a value of p p 0.6. If we also target a value of q, then this pins down the value of A. It turns out that this value has no effect on our findings; but to pin things down we target the value q p 0.6. One can show that the Hosios (1990) condition applies in our model. Though it is not important to our results, we choose the bargaining parameter so that the benchmark equilibrium allocation is efficient; that is, we set v p h p 0.5. There are two remaining parameters: k x and k v. The above discussion ¯ , but it rehas deduced targets for the two equilibrium values p and p ¯ are indeed equilibrium mains to ensure that the desired values of p and p values. We set k x and k v to accomplish exactly this. This implies k x p 2 and k v p 0.2125. This completes the calibration. Note that our calibration does not explicitly target either the unemployment rate or the rate at which workers leave jobs. In equilibrium, our calibration implies an unemployment rate of 6.0 percent and an annual worker turnover rate of approximately 46 percent.14 We calibrated our turnover process to the separation profile in Pries (2004), which implies an annual worker turn13

For example, this rules out a uniform distribution on [0, 1]. Here and subsequently we compute annual worker turnover as it is commonly done in empirical studies, by multiplying the monthly worker turnover rate by 12. In our calibrated equilibrium, the rate at which workers leave (and enter) employment is 1.93 percent each month, implying (gross) monthly turnover of 3.86 percent. 14

832

journal of political economy

over rate of 76 percent. On the basis of this, our model is capturing about 60 percent of worker turnover in the data. As noted at the beginning of this section, our model is not intended to capture all worker turnover; but as the 60 percent number indicates, we do capture a significant part.15

VII.

Effects of Labor Market Policies: Quantitative Results

We now turn to a quantitative evaluation of the various policies analyzed above. We examine policies that reflect the range of differences between the United States and the more highly regulated labor markets in continental Europe. For the case of minimum wages, we interpret the U.S. minimum wage to correspond to the lowest wage observed in the equilibrium of our calibrated benchmark model. On the basis of the evidence in Dolado et al. (1996), we consider a minimum wage that is 15 percent higher.16 For the case of dismissal costs we consider a cost that is three months’ worth of the lowest wage observed in the calibrated equilibrium.17 For unemployment insurance benefits, we consider an increase in benefits that corresponds to 20 percent of the lowest observed wage in the calibrated benchmark equilibrium.18 Finally, for the case of taxes, we shall be particularly interested in employer social security contributions because of the way in which they increase effective minimum wages. With this in mind, we believe that a tax of 3–4 percent on expected output reflects the relevant range of differences between 15 Another useful perspective on the flows generated by our model is provided by computing the ratio of worker flows to job flows, since one of the key stylized facts is that this ratio is much larger in the United States than in the labor markets of continental Europe. In our calibrated equilibrium, the annual rate at which workers leave employment is roughly twice the annual rate of job destruction. Davis and Haltiwanger (1999) estimate that in the U.S. economy this ratio is somewhere between three and four. By this metric, our model of learning about match quality accounts for between one-half and two-thirds of the excess turnover of workers. 16 Dolado et al. report Kaitz indices for legislated minimum wages relative to average wages for several countries. For the United States this value is 0.39, and for Belgium, France, Germany, Italy, and Spain, respectively, the values are 0.60, 0.50, 0.55, 0.71, and 0.32. They note that true minimum wages depend on many specifics, such as age, sector, and experience. 17 There are no quantitative estimates of nonseverance dismissal costs. Heckman and Pages (2000) estimate effective severance costs and find that European countries lie in the one- to four-month range. This range seems a natural one to investigate for the nonseverance costs as well. If wage restrictions rule out bonding, then severance payments act very much like third-party costs. 18 Dolado et al. (1996) report unemployment insurance replacement ratios across countries. The United States has a value of 0.5, and many of the countries from continental Europe lie in the interval [0.5, 0.7]. Our formulation of unemployment insurance abstracts from the duration of benefits, and differences along this dimension are also large.

hiring policies

833

TABLE 1 Effects of Individual Labor Market Policies Benchmark p p ¯ 1 ⫺ H(p ¯) E(pFp 1 p ¯) Unemployment duration Annual job destruction (%) Annual worker turnover (%) Separation rate at: 1 month 12 months 36 months Employment rate Output Welfare loss (%)

Minimum Wage

Dismissal Cost

Unemployment Insurance

Taxes

.60 .21 .50 .40

.47 .31 .34 .47

.56 .28 .38 .45

.46 .24 .45 .42

.47 .22 .48 .41

3.33

6.35

4.65

4.83

4.39

11.3

11.1

11.3

11.0

11.0

46.3

40.3

42.0

44.5

45.8

8.5 4.0 1.0 .94 1.71 0

7.6 3.4 1.0 .90 1.67 1.4

8.0 3.6 1.0 .93 1.70 .18

8.3 3.8 1.0 .92 1.68 .29

8.5 3.9 1.0 .92 1.69 .29

the United States and Europe.19 However, to illustrate the general effect of taxes alone, in this section we report the effects of a 15 percent tax on output. We note that, in general, the effects of these policies were fairly linear; that is, halving the policy change roughly halved the effects on the various statistics we consider. A.

Effect of Individual Policies

Table 1 shows the results of imposing these policies individually. The first two rows of the table indicate that in each case, we see a decrease ¯ , but note that the relative magnitudes of the in p and an increase in p changes in these two variables vary substantially: for unemployment insurance benefits and taxes, the change in p relative to the change in ¯ is much larger than for minimum wages and dismissal costs. The third p ¯. and fourth rows provide another way of interpreting the change in p ¯ —is Average unemployment duration—the reciprocal of p[1 ⫺ H(p)] shown in the fifth row. Next we consider the implications for job and worker flows. Changes in measured job destruction are very small, implying that virtually all of the policy-induced decrease in worker turnover reflects decreases in 19 The OECD (1994) reports that in 2001, employer social security contributions in the United States were 3.6 percent of gross domestic product, compared with 11.2, 7.2, and 8.5 percent in France, Germany, and Italy, respectively. Because contributions in the United States are capped, the aggregate figure may underreport the importance of these taxes in new matches. A figure of 5 percent may be more appropriate for the United States.

834

journal of political economy

worker turnover relative to job destruction. Minimum wages and dismissal costs have a significant effect on worker flows. In particular, a 15 percent increase in the minimum wage reduces worker turnover by roughly 13 percent, whereas the three-month dismissal cost reduces worker turnover by about 10 percent. This decrease in turnover occurs via a flattening of the tenure profile of separation rates. In all cases, the asymptotic value of the monthly separation rate is given by l p 0.0086, and this value is always attained by the end of four years. In the case of minimum wages and dismissal costs, we find that separation rates decrease substantially for new matches relative to the benchmark equilibrium. The evidence supports this important prediction that Europe has a less steeply sloped tenure profile of separation rates as opposed to simply a downward parallel shift. The Introduction reported some information for France and Germany based on household survey data. An additional source of information is the paper by Wolff (2004), who estimates the tenure profile of separation hazards from German panel data in the 1990s. His estimates imply a one-year survival rate of roughly 75 percent.20 Panel data estimates for the United States (see, e.g., Farber 1999) suggest a one-year survival rate of only about 50 percent. Wolff finds that while separation rates in Germany have a downward-sloping profile as in the United States, the profile is much flatter. The annual separation rate at four years of tenure in Germany has dropped by about one-third compared to its first-year value, whereas in the United States the hazard after four years has dropped by roughly 60 percent relative to its firstyear value.21 Table 1 also reports employment effects. The minimum wage policy has the largest impact on employment. We find that a 15 percent increase in the level of the minimum wage leads to a decrease in the employment rate of roughly four percentage points, which corresponds to roughly a 4.5 percent drop in the level of employment. It is important to note, however, that the decrease in employment in matches known to be good is roughly 2 percent, whereas the decrease in employment of matches not known to be good is almost 20 percent. There is mixed evidence (and considerable controversy) on the actual effect of mini20 We note that the German data also record changes in jobs within a firm as part of worker turnover, in contrast to all the studies cited for analysis of the United States. They report that slightly less than one-fifth of all separations are of this variety. 21 Additionally, we note that if the separation profile in Germany were simply one-half of the corresponding profile in the United States, then the overall turnover rate in Germany would be only one-fifth as large as it is in the United States. The effect is amplified because a change in separation rates influences the steady-state distribution of match tenure, and this distributional effect is large. Worker turnover in Germany is about onehalf of that in the United States, suggesting that the separation profile in Germany is disproportionately shifted down at low tenures relative to the United States.

hiring policies

835

mum wages on employment levels. However, in the context of France, using changes in the national minimum wage as natural experiments, Abowd et al. (2000) report an employment elasticity between ⫺1.5 and ⫺2 for workers in the vicinity of the minimum wage. Our implied change is similar for employment of workers in matches of unknown quality— the low-wage workers in our model. In contrast, the elasticity for highwage workers implied by our model is only ⫺0.15. We note that roughly 11 percent of workers earn the minimum wage in this policy experiment, which is in line with the estimates in Dolado et al. (1999). In our model, a dismissal cost of three months’ wages lowers the employment rate by 1 percent. This is about the same size of the effect found by Lazear (1990) but smaller than that found by Heckman and Pages (2000). Because the effects of unemployment insurance benefits and taxes work mainly through changes in meeting rates, the employment effects of these policies are very similar to those found elsewhere in quantitative analysis of matching models (see, e.g., Millard and Mortensen 1997). Finally, the last two rows of table 1 report the effects of each policy on steady-state output and a measure of the (steady-state) welfare loss associated with each policy.22 Our measure of the welfare loss is the percentage decrease in total output (expressed relative to the benchmark equilibrium output level) required in the no-policy equilibrium to make total utility the same as in the steady state with policies. The output effects mirror the effects on employment, though there is a small ¯ influence the composition of productivdifference since changes in p ities in the steady state. The welfare costs of the minimum wage are substantial, whereas the welfare costs associated with dismissal costs, unemployment insurance benefits, and taxes, taken by themselves, are found to be quite small.23 B.

Effects of Combined Policies

The above analysis focuses on how policies taken one at a time influence equilibrium allocations and welfare. This is obviously the best way to isolate the effects of individual policies. However, in reality, combinations of these policies are in place in most countries, and there may be important interactions between the policies. For example, one way in which workers and firms respond to dismissal costs is to have the worker accept lower wages in the initial period. A minimum wage diminishes this possibility, thereby exacerbating the effects of dismissal costs. A 22 Recruitment costs and the disutility of labor effort account for differences between the output and welfare measures. 23 Consistent with the notion that in reality third-party dismissal costs do accrue to someone, we assume that these costs are returned to consumers as lump-sum transfers.

836

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similar effect exists for taxes levied on firms. In fact, it is often argued that minimum wages are a greater problem in Europe precisely because of the large (payroll) taxes levied on employers, implying that the effective minimum cost of a worker is higher than the legislated minimum wage. We consider a combination of policies that are somewhat intermediate to those considered individually in table 1, since the representative country does not have extreme policies on all dimensions. In particular, we consider a minimum wage 7.5 percent greater than the lowest wage in the benchmark, a dismissal cost of 1.5 months of wages, and a tax of 3.5 percent. In this exercise, we set unemployment insurance benefits equal to zero since we found that this policy did not have any significant interaction with the other policies. The basic patterns are those found in the previous analysis, but of special note is the effect on worker turnover. We now have a drop in the worker turnover rate of roughly 21 percent. If we were to take the appropriate decreases implied by the individual policies in table 1 and sum them (as noted, the effects were roughly linear in the magnitudes of the policies), we would predict a decrease in the worker turnover rate of only 11 percent, implying that the interactions roughly double the impact. The welfare costs in this case exceed 2.4 percent of steadystate output. The policy settings just considered are rather moderate. Nonetheless, we find that they can account for a very sizable drop in worker turnover, with effectively no associated drop in the job destruction rate. As reviewed in Section II, the available evidence suggests that the economies of continental Europe have worker turnover rates that are about 50 percent less than those in the United States. In view of the above calculations, it seems that our model with moderate policy differences can account for roughly half of this difference. The essence of our model is that workers and firms want to create good matches but that the process of finding good matches takes time. Our analysis shows that several policies interact with the process of locating good matches by making it relatively more costly for firms to experiment with workers. In our model, a firm’s only alternative is to become more selective in whom it hires. However, in reality there are at least two additional margins that we think may be important. First, it may be possible for a firm to expend more resources during the recruiting stage in order to increase the chances of locating workers who will generate good matches (workers with higher p). A second alternative is that a firm may choose to train a worker and thereby make it more likely to create a high-quality match. Both of these alternatives would give the firm additional options and both would intuitively lead in the direction of lower worker turnover.

hiring policies VIII.

837

Conclusion

We build a model of job and worker flows in which worker turnover in excess of job turnover results from the desire to create high-quality matches in a world in which match quality is not perfectly observable ex ante. Hiring practices play an important role in the resource allocation process in this economy: firms and workers decide how much screening takes place prior to forming a match. We show analytically that equilibrium hiring practices are influenced by various labor market policies. These changes in hiring practices will influence observed labor market dynamics and in particular affect measures such as worker turnover and unemployment durations. Our quantitative assessment suggests that these elements can account for a sizable fraction of differences in worker turnover in the United States and continental Europe. We also show that the welfare costs of distorting the hiring process are substantial. Our model also suggests a novel perspective on the role of temporary contracts. While much work emphasizes the role that these contracts play in allowing firms to respond to temporary fluctuations, our model suggests that another key role is in facilitating the worker screening process. Recent work by Portugal and Vareja˜o (2003) using data from Portugal concludes that screening for permanent jobs is the single most important role played by temporary contracts. This paper suggests several areas for future work. On the empirical side, although the effects we have emphasized are consistent with observed patterns in aggregate cross-country data, it is also of interest to obtain cross-country micro data of high enough quality to allow a more detailed assessment of the mechanics stressed in this paper. On the theoretical side, there is also much to learn about the more proactive means—aside from simply being more selective—that firms can utilize in order to reduce costly worker turnover, such as job training or more resource-intensive recruiting techniques. References Abowd, John, Francis Kramarz, David Margolis, and Thomas Philippon. 2000. “The Tail of Two Countries: Minimum Wages and Employment in France and the United States.” Manuscript, School Indus. and Labor Relations, Cornell Univ. Alvarez, Fernando, and Marcelo Veracierto. 2000. “Labor Market Policies in an Equilibrium Search Model.” In NBER Macroeconomics Annual 1999, edited by Ben S. Bernanke and Julio J. Rotemberg. Cambridge, MA: MIT Press. Bentolila, Samuel, and Giuseppe Bertola. 1990. “Firing Costs and Labour Demand: How Bad Is Eurosclerosis?” Rev. Econ. Studies 57 (July): 381–402. Bertola, Giuseppe, and Richard Rogerson. 1997. “Institutions and Labor Reallocation.” European Econ. Rev. 41 (June): 1147–71.

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