The Cyclical Behavior of Equilibrium Unemployment and Vacancies
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The Cyclical Behavior of Equilibrium Unemployment and Vacancies By ROBERT SHIMER* This paper argues that the textbook search and matching model cannot generate the observed business-cycle-frequency fluctuations in unemployment and job vacancies in response to shocks of a plausible magnitude. In the United States, the standard deviation of the vacancy-unemployment ratio is almost 20 times as large as the standard deviation of average labor productivity, while the search model predicts that the two variables should have nearly the same volatility. A shock that changes average labor productivity primarily alters the present value of wages, generating only a small movement along a downward-sloping Beveridge curve (unemployment- vacancy locus). A shock to the separation rate generates a counterfactually positive correlation between unemployment and vacancies. In both cases, the model exhibits virtually no propagation. (JEL E24, E32, J41, J63, J64) In recent years, the Mortensen-Pissarides cyclical behavior of two of its central elements, search and matching model has become the unemployment and vacancies, which are both standard theory of equilibrium unemployment highly variable and strongly negatively corre- (Dale Mortensen and Chris Pissarides, 1994; lated in U.S. data. Equivalently, the model can- Pissarides, 2000). The model is attractive for a not explain the strong procyclicality of the rate number of reasons: it offers an appealing de- at which an unemployed worker finds a job. scription of how the labor market functions; it is I focus on two sources of shocks: changes in analytically tractable; it has rich and generally labor productivity and changes in the separation intuitive comparative statics; and it can easily rate of employed workers from their job. In a be adapted to study a number of labor market one-sector model, a change in labor productiv- policy issues, such as unemployment insurance, ity is most easily interpreted as a technology or firing restrictions, and mandatory advanced no- supply shock. But in a multi-sector model, a tification of layoffs. Given these successes, one preference or demand shock changes the rela- might expect that there would be strong evi- tive price of goods, which induces a change in dence that the model is consistent with key real labor productivity as well. Thus these business cycle facts. On the contrary, I argue in shocks represent a broad set of possible this paper that the model cannot explain the impulses. An increase in labor productivity relative to the value of nonmarket activity and to the cost * Department of Economics, University of Chicago, of advertising a job vacancy makes unemploy- 1126 East 59th Street, Chicago IL 60637 (e-mail: ment relatively expensive and vacancies rela- [email protected]). A previous version of this paper tively cheap.1 The market substitutes toward was entitled “Equilibrium Unemployment Fluctuations.” I thank Daron Acemoglu, Robert Barro, Olivier Blanchard, vacancies, and the increased job-finding rate V. V. Chari, Joao Gomes, Robert Hall, Dale Mortensen, pulls down the unemployment rate, moving the Christopher Pissarides, two anonymous referees, the editor economy along a downward sloping Beveridge Richard Rogerson, and numerous seminar participants for curve (vacancy-unemployment or v-u locus). comments that are incorporated throughout the paper. This But the increase in hiring also shortens unem- material is based upon work supported by the National Science Foundation under grants SES-0079345 and SES- ployment duration, raising workers’ threat point 0351352. I am grateful to the Alfred P. Sloan Foundation in wage bargaining, and therefore raising the for financial support, to the Federal Reserve Bank of Min- neapolis for its hospitality while I worked on an early version of this paper, and to Mihai Manea, and especially 1 The interpretation in this paragraph and its sequel Sebastian Ludmer, for excellent research assistance. builds on discussions with Robert Hall. 25 26 THE AMERICAN ECONOMIC REVIEW MARCH 2005 expected present value of wages in new jobs. choice of whether to open a new vacancy. The Higher wages absorb most of the productivity equilibrium vacancy rate depends on the unem- increase, eliminating the incentive for vacancy ployment rate, on labor market tightness, and on creation. As a result, fluctuations in labor pro- the expected present value of wages in new ductivity have little impact on the unemploy- employment relationships. Wages, in turn, are ment, vacancy, and job-finding rates. determined by Nash bargaining, at least in new An increase in the separation rate does not matches. In principle, the wage in old matches affect the relative value of unemployment and may be rebargained in the face of aggregate vacancies, and so leaves the v-u ratio essentially shocks or may be fixed by a long-term employ- unchanged. Since the increase in separations ment contract. Section II A describes the basic reduces employment duration, the unemploy- model, while Section II B derives a forward- ment rate increases, and so therefore must va- looking equation for the v-u ratio in terms of cancies. As a result, fluctuations in the model parameters. separation rate induce a counterfactually posi- Section II C performs simple analytical com- tive correlation between unemployment and parative statics in some special cases. For ex- vacancies. ample, I show that the elasticity of the v-u ratio Section I presents the relevant U.S. business with respect to the difference between labor cycle facts: unemployment u is strongly coun- productivity and the value of nonmarket activity tercyclical, vacancies v are equally strongly pro- or “leisure” is barely in excess of 1 for reason- cyclical, and the correlation between the two able parameter values. To reconcile this with variables is Ϫ0.89 at business cycle frequen- the data, one must assume that the value of cies. As a result, the v-u ratio is procyclical and leisure is nearly equal to labor productivity, so volatile, with a standard deviation around its market work provides little incremental utility. trend equal to 0.38 log points. To provide fur- The separation rate has an even smaller impact ther evidence in support of this finding, I exam- on the v-u ratio, with an elasticity of Ϫ0.1 ine the rate at which unemployed workers find according to the comparative statics. Moreover, jobs. If the process of pairing workers with jobs while shocks to labor productivity at least in- is well-described by an increasing, constant duce a negative correlation between unemploy- returns-to-scale matching function m(u,v), as in ment and vacancies, separation shocks cause Pissarides (1985), the job finding rate is f ϭ both variables to increase, which tends to gen- m(u,v)/u, an increasing function of the v-u ratio. erate a positive correlation between the two I use unemployment-duration data to measure variables. Similar results obtain in some other the job-finding rate directly. The standard devi- special cases. ation of fluctuations in the job-finding rate Section II D calibrates the stochastic model to around trend is 0.12 log points and the correla- match U.S. data along as many dimensions as tion with the v-u ratio is 0.95. Finally I look at possible, and Section II E presents the results. the two proposed impulses. The separation rate The exercise confirms the quantitative predic- is less correlated with the cycle and moderately tions of the comparative statics. If the economy volatile, with a standard deviation about trend is hit only by productivity shocks, it moves equal to 0.08 log points. Average labor produc- along a downward-sloping Beveridge curve, but tivity is weakly procyclical and even more sta- empirically plausible movements in labor pro- ble, with a standard deviation about trend of ductivity result in tiny fluctuations in the v-u 0.02 log points. ratio. Moreover, labor productivity is perfectly In Section II, I extend the Pissarides’s (1985) correlated with the v-u ratio, indicating that the search and matching model to allow for aggre- model has almost no internal propagation mech- gate fluctuations. I introduce two types of anism. If the economy is hit only by separation shocks: labor productivity shocks raise output shocks, the v-u ratio is stable in the face of in all matches but do not affect the rate at which large unemployment fluctuations, so vacancies employed workers lose their job; and separation are countercyclical. Equivalently, the model- shocks raise the rate at which employed workers generated Beveridge curve is upward-sloping. become unemployed but do not affect the pro- Section II F explores the extent to which the ductivity in surviving matches. In equilibrium, Nash bargaining solution is responsible for there is only one real economic decision: firms’ these results. First I examine the behavior of VOL. 95 NO. 1 SHIMER: UNEMPLOYMENT AND VACANCIES 27 wages in the face of labor productivity and productivity shocks. This distinguishes the separation shocks. An increase in labor produc- present model from those based upon intertem- tivity encourages firms to create vacancies. The poral labor supply decisions (Robert E. Lucas, resulting increase in the job-finding rate puts Jr., and Leonard Rapping, 1969). Thus this pa- upward pressure on wages, soaking up virtually per explores the extent to which a combination all of the shock. A decrease in the separation of search frictions and aggregate shocks can rate also induces firms to create more vacancies, generate plausible fluctuations in unemploy- again putting upward pressure on wages and ment and vacancies if labor supply is inelastic. minimizing the impact on the v-u ratio and It suggests that search frictions per se scarcely job-finding rate. On the other hand, I examine a amplify shocks. The paper does not examine version of the model in which only workers’ whether a search model with an elastic labor bargaining power is stochastic.