There is an active discussion in the literature on whether the standard search and matching model (Mortensen and Pissarides (1994), Pissarides (1985, 2000)) is consistent with U.S. business cycle facts. The issue that received the most attention is whether the model can generate the volatility of labor market variables (e.g., vacancies, unemployment) that is quantitatively consistent with the data. Shimer (2005) proposed a calibration of the model that implied that the model generates only a small volatility in the variables of interest. Hagedorn and Manovskii (2006), on the other hand, propose a different calibration strategy, and find that the model does generate a volatile labor market.
However, assessing the model’s performance along other dimensions reveals additional empirical shortcomings. First, in the data, the standard deviation of wages is higher than the elasticity of wages with respect to productivity. In the model, regardless of the calibration strategy used, they are virtually identical. Gertler and Trigari (2005) propose to fix this problem by postulating staggered wage contracting. Since only a fraction of firms is allowed to adjust wages in a given month, wages are relatively non-responsive to contemporaneous productivity changes. Since workers are assumed to have a large bargaining weight, when a firm is able to adjust wages, the adjustment is large.
As an alternative possibility, in this paper we follow Benhabib, Rogerson, and Wright (1991), Hall (1997), McGrattan, Rogerson, and Wright (1997), among others, in assuming that the value of non-market activity includes, among other components, the stochastic value of home production. We incorporate this feature into the MP model and show that allowing for stochastic non-market activity adds an additional (to fluctuations of productivity) source of wage fluctuations to the model. We find that, since the standard deviation of wages is higher than the elasticity, both of them can be matched in the extended model.
A second shortcoming is that in the data, the correlation between current productivity and vacancies is maximized when vacancies one or two quarters ahead are considered. In the model, regardless of the calibration strategy used, the correlation is maximized for contemporaneously measured vacancies. A related third shortcoming is that the correlation between contemporaneously measured labor market tightness (the ratio of vacancies to unemployment) and productivity is close to 1 in the model but is much lower in the data (the precise number depends, as we document in this paper, on the employment measures used to define productivity.
But independent of measurement, the number is significantly lower than 1 and can be as low as 0.39 as reported in Shimer (2005)). We show that these empirical shortcomings of the MP model can be corrected by incorporating time to build into the model (Kydland and Prescott (1982)). Specifically, we add a lag in vacancy posting so that vacancies created by firms today enter the labor market with a short delay. Such a lag is natural if it takes firms some time to adjust productive capacity in response to a change in productivity. It may also arise if it takes firms time to infer that an aggregate productivity change has occurred.
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The Cyclical Behavior of Unemployment, Vacancies and Wages
