Economic Dynamics Newsletter

Robert Shimer on Labor Market Frictions and Business Cycles

I would like to use this opportunity to discuss some of my recent research on the business cycle implications of labor market frictions. For reasons that I will discuss more below, I will frame my discussion in terms of the Mortensen-Pissarides matching model (Pissarides 1985, Mortensen and Pissarides 1994, and Pissarides 2000). This model has been used extensively for policy analysis, for example to examine the role that unemployment insurance and mandatory firing costs play in generating highunemployment rates in Europe (Pissarides 1999). With some exceptions (notably Merz 1995 and Andolfatto 1996), however, there has been little exploration of the model’s ability to match a standard set of business cycle facts. In a recent working paper (Shimer 2002a), I argue that the Mortensen-Pissarides model is quantitatively incapable of generating significant employment fluctuations in response to empirically plausible productivity shocks. That is, the model has almost no amplification mechanism. Despite this, the structure of the model allows us to think about other types of shocks that look to be a much more promising explanation for business cycle fluctuations.

The Mortensen-Pissarides Matching Model

I begin by describing the simplest version of the Mortensen-Pissarides matching model. There are two types of agents, workers and firms, both risk-neutral and infinitely-lived with a common discount rate. Workers may be either employed or unemployed. Employed workers earn an endogenous wage w but may not search for another job. Unemployed workers get a fixed payment b and may find a job. Firms have access to a production technology with constant returns to scale in labor. That is, each employed worker yields a fixed revenue p and must be paid the wage w. To hire new workers, firms must create a vacancy at a per-period cost of c. In other words, a firm’s per-period profits are n(p-w) – c v, where n is the number of employees and v is the number of vacancies. Free entry drives the discounted profits from creating a vacancy to zero.Rather than modelling the search process explicitly, the Mortensen-Pissarides model reduces it to a black-box “matching function”. Let U denote the fraction of workers who are unemployed and V denote the number of vacancies in the economy. Then the number of matches is a function M(U,V), increasing in both arguments. The standard assumption is that this function has constant returns to scale, which implies that each unemployed worker finds a job with probability M(U,V)/U and each vacancy is filled with probability M(U,V)/V, both functions only of the vacancy-unemployment ratio V/U. The vacancy-unemployment ratio, and hence the rate at which unemployed workers find jobs, is in turn determined endogenously by firms’ collective vacancy decisions.

In the simplest version of the Mortensen-Pissarides matching model, the job destruction decision, i.e. the probability with which employed workers become unemployed, is treated as exogenous: all matches end with probability d per period. Mortensen and Pissarides (1994) extend this simple model to endogenize the job destruction decision.

A central feature of this model is that the matched worker and firm are in a bilateral monopoly situation. That is, an employed worker could always leave her job and find another employer; however, because search is time-consuming, workers are impatient, and all jobs are identical, she prefers to work for her current employer. Likewise, a firm could fire an employee and attempt to hire another one, but this will take time and will not yield a better match. There are many wages consistent with the pair agreeing to match, and so the model provides little guidance as to how wages are determined. Pissarides (1985) assumes wages satisfy an axiomatic Nash bargaining solution. A worker’s threat point is unemployment and a firm’s threat point is a vacancy. The two agents split the gains from production in excess of this threat point.

From the perspective of a matched worker and firm, wage bargaining is a zero sum game with distributional but not allocational consequences, and so the Nash bargaining assumption might seem innocuous. But from an aggregate perspective, wage bargaining matters. Firms’ expectations of future wages is crucial to their job creation decisions, which balance the up-front cost of creating a vacancy against the expected profits from employing workers. If firms anticipate having to pay high wages in the future, they will be reluctant to create vacancies today, reducing job creation and raising the unemployment rate.

Although the central role that wage bargaining plays in the determination of employment and unemployment rates in the Mortensen-Pissarides model is sometimes seen as a shortcoming, I will argue below that the bilateral monopoly situation is the reason why we can use the model to think about a different type of shock that looks to be a promising explanation for at least some part of business cycle fluctuations. In a reduced form model, these shocks amount essentially to changes in workers’ bargaining power.

Quantitative Behavior

In Shimer (2002a), I examine a stochastic version of this simple model, with shocks driven by a first-order autoregressive process for productivity, p, and the job destruction rate, d. At any point in time, the state of the economy is described by the current level of productivity, the current job destruction rate, and the current unemployment rate. In principle, the curse of dimensionality should make this problem very difficult to handle computationally. But I show that the equilibrium vacancy-unemployment ratio and wage can be expressed as functions only of the first two state variables, productivity and the job destruction rate. Moreover, both functions are easy to compute numerically — and in some special cases, analytically. After computing the vacancy-unemployment ratio at each productivity level and job destruction rate, I simulate a large number of paths and recover the stochastic properties of unemployment, vacancies, and wages in response to these exogenous shocks.I choose model parameters to match as many macro/labor facts as possible. Due to its simplicity, the model cannot replicate some standard business cycle facts (Cooley and Prescott 1995). For example, there is no investment or capital in this model; and the risk-neutrality assumption implies the intertemporal elasticity of substitution is infinite. But there are a number of other facts that the model potentially can match. One that is particularly important is the cyclical behavior of vacancies and unemployment. The correlation between the detrended time series for the two variables is strongly negative, -0.88 (Abraham and Katz 1986, Blanchard and Diamond 1989), and they have approximately the same standard deviation of the percent deviation from trend. That is, if unemployment is 17 percent below trend (5 percentage points instead of 6 percentage points), vacancies are approximately 17 percent above trend. This means that the vacancy-unemployment ratio, and hence the ease of finding a job, is strongly procyclical. On the other hand, wages and productivity are much less variable and much less correlated with either vacancies or unemployment.

I next consider the behavior of the model economy in response to a productivity shock. Qualitatively, this raises the profit from a filled job p – w, encouraging firms to create vacancies. A higher vacancy-unemployment ratio decreases the rate at which vacancies are filled, restoring the zero profit condition. It also makes it easier for workers to find jobs, lowering the unemployment rate. Under reasonable parameter restrictions, vacancies and unemployment move in opposite directions, along a downward sloping “Beveridge curve,” consistent with the previously mentioned fact. But quantitatively, almost all of a productivity shock accrues to workers in the form of higher wages, leaving only a muted response of vacancies and unemployment. Equivalently, it takes an unrealistically large productivity shock to generate reasonable movements in vacancies and unemployment. The model offers little amplification of the underlying shocks.

I also consider the economy’s response to a job destruction shock. This has a direct effect on the unemployment rate because the employment-to-unemployment transition rate increases. It also has an indirect effect: a decline in the expected future duration of jobs discourages vacancy creation. This raises average unemployment duration and further increases the unemployment rate. Moreover, the increase in unemployment duration tends to reduce wages slightly, mitigating the decline in profits. In net, I find a large response of the unemployment rate to a job destruction shock but little movement in the vacancy-unemployment ratio or wages. As a result, vacancies and unemployment are counterfactually positively correlated in response to such shocks, while wages are realistically rigid.

If one only wanted to explain a subset of the data, the model behaves quite well. For example, Blanchard and Diamond (1989), Mortensen and Pissarides (1994) and Cole and Rogerson (1999) find that the model can match the behavior of unemployment and vacancies (as well as some other variables), but do not examine the behavior of wages. Essentially, these papers introduce unrealistically large productivity shocks in order to generate fluctuations. On the other hand, Ramey and Watson (1997) and Pries (2002) assume that job finding rates are constant and exogenous or equivalently that the vacancy-unemployment ratio is acyclical. Both models generate large unemployment changes associated with only moderate wage fluctuations. Similarly, in the Lucas and Prescott (1974) search model, workers seek production opportunities available in an exogenously-determined supply. Models in this framework (e.g. Gomes, Greenwood, and Rebelo 2001) therefore cannot explain why the vacancy-unemployment ratio is procyclical, although they are again capable of matching the cyclical behavior of wages. It is only by looking simultaneously at the behavior of unemployment, vacancies, wages, and productivity that the difficulty of matching the business cycle facts emerges. The lesson to take away from this is that it is important to explore models quantitatively along as many dimensions as possible.

Alternative Wage Setting Assumptions

Wage flexibility, particularly wage flexibility in new jobs, is central to these results. Suppose there was a productivity increase, but firms did not expect wages in new jobs to change. This would amplify the effect on firm entry, since firms would enjoy all of the productivity increase in the form of higher profits. Conversely, if firms anticipated declining wages without an associated change in productivity, this would also lead to an increase in entry and a decline in the unemployment rate. Moreover, quantitatively both of these effects are likely to be big. For example, firms’ economic profits are at least an order of magnitude smaller than their wage bill, so a one percent decline in wages leads to at least a ten percent increase in profits and an associated spurt in job creation. (On the other hand, rigidity of wages in old jobs, perhaps due to implicit or explicit wage contracts, has no effect on job creation.)An assertion that that rigid real wages amplify productivity shocks and that wage shocks are an important source of business cycle fluctuations is unsatisfactory. From a theoretical perspective, one would like to know why real wages are rigid in response to productivity shocks and yet sometimes change in the absence of such shocks. From a normative perspective, it is impossible to analyze a change in labor market policies in the absence of a policy-invariant model of wages. The important next step is therefore to develop alternative models of wage determination from first principles, which do not have a strong link between wage and productivity movements.

One feature of the labor market that may be important in this regard is asymmetric information. A firm knows more about its productivity than does an employee, while a worker knows more about her outside opportunities than does her employer. For a worker to signal that she has a good outside opportunity is costly. She must leave the firm. Likewise, for a firm to credibly signal that it has low productivity is costly. It must typically lay off some workers or sharply reduce the hours of existing employees. The wage also plays an important role, conveying information to the worker about the firm’s productivity — it is at least willing to pay her wage — and to the firm about the worker’s outside opportunities — she is at least willing to work at that wage.

In Shimer (2002b), I develop a simple model with one-sided asymmetric information. A worker does not know how productive her job is. She is able to make take-it-or-leave-it wage demands, but is reluctant to ask for too high a wage because, if the firm refuses her demand, she is laid off. There are two important determinants of wages in this model. First, workers examine the hazard rate of the productivity distribution. If the hazard rate is large, asking for a higher wage is risky, i.e. it results in a substantial increase in the layoff probability. Second, workers consider how long it will take to get another job offer. If job offers are scarce, workers will be reluctant to risk demanding a high wage. This also feeds back into firm behavior. If firms anticipate that workers will demand high wages, they will create few jobs, making job offers scarcer and suppressing wage demands. In parametric examples, I find that an increase in mean productivity raises wages and reduces unemployment, much as in a model with symmetric information. An increase in the variance of productivity lowers wages and has an ambiguous effect on unemployment, an effect that is absent from models with symmetric information. If recessions are periods of low mean productivity and high variance, as Storesletten, Telmer, and Yaron (2001) suggest, we would observe little variation in wages and significant declines in employment.

The wage setting regime, i.e. workers making take-it-or-leave-it wage demands, is important for these results. Since there is no reason to believe that this is an accurate characterization of wage setting in reality, relaxing this assumption is desirable. Of course, any other wage-setting assumption faces the same criticism. An alternative possibility is to focus on Pareto optimal incentive-compatible mechanisms in an economy with two-sided asymmetric information. Here the tools developed in the endogenous incomplete markets literature (e.g. Spear and Srivastava 1987, Thomas and Worrall 1990, Atkeson and Lucas, 1992) are likely to prove useful. It is an open question whether such a model predicts significant employment fluctuations in response to modest exogenous shocks.

References