The Mortensen-Pissarides (MP) search and matching model (Mortensen and Pissarides 1994; Pissarides 1985, 2000) studies the dynamics of unemployment in an environment where jobs are continuously created and destroyed. A sequence of papers by Costain and Reiter (2008), Hall (2005), and Shimer (2005) have questioned the model's ability to match the observed cyclical fluctuations of the unemployment rate in the United States. For example, Shimer shows that under a reasonable calibration strategy, the MP model predicts that the vacancy-unemployment ratio and the average labor productivity should have nearly the same volatility. In contrast, the standard deviation of the vacancy-unemployment ratio in the United States is almost 20 times as large as the standard deviation of the average labor productivity. This large discrepancy between the volatility implied by the model and the data constitutes an empirical puzzle, known as the unemployment volatility puzzle.
Pissarides (2009) shows that introducing fixed matching costs into the model (e.g., training costs) can significantly increase the volatility of labor-market outcomes, such as tightness and the job finding rate. He points out that this result is obtained without inducing a counterfactually low volatility in the wages of new jobs. In his quantitative exercise, Pissarides only considers sunk fixed matching costs and argues that non-sunk fixed training costs play a similar role. More in detail, Pissarides (2009, 1364) writes the following with respect to matching costs: "they are sunk once the wage bargain is concluded and the worker takes up the position, but this property is not important for the volatility, because training costs that are not sunk play a similar role." He shows that when these costs increase from 0% to 40% of average labor productivity, the volatility of the vacancies-unemployment ratio (measured by its elasticity) increases almost twofold, and it matches the observed volatility in the U.S. labor market.
In this paper, we evaluate the amplification mechanism of non-sunk fixed matching costs, and examine whether the cyclical volatility predicted by the model is substantially augmented. We show that when these costs are not sunk and, therefore, can be partially passed on to workers through lower wages, the volatility of the vacancy-unemployment ratio is approximately an order of magnitude less responsive to variations in these costs. Thus, from a quantitative standpoint, the contribution of matching costs in explaining labor-market volatility depends not only on the level, but also on what proportion of these costs is sunk. We also show that the model with fixed costs is equivalent to the standard model with lower labor productivity and nonconstant flow hiring costs. When we calibrate the model considering a share of sunk costs of 28% consistent with the empirical estimate of a small or a nearly neutral effect of training costs on the starting wage, the model is able to reproduce 96% of the observed volatility in the U.S. labor-market tightness. We observe, however, that this share of sunk costs introduces an unrealistic sensitivity to unemployment benefits (see Costain and Reiter 2008, for an explanation of this issue).
The paper is organized as follows. In Section II we incorporate non-sunk fixed costs in the standard MP model. Section III presents the calibration and the simulated elasticities. In Section IV, we present evidence related to the effect of training on the starting wage and check whether empirically reasonable training costs are able to match the volatility of unemployment. Finally, we present our conclusions in Section V.
II. THE MODEL
Given that our model is essentially the same as Pissarides' (2009), its presentation is reduced to a minimum. In this economy, there is a continuum of risk-neutral, infinitely lived workers and firms which discounts future payoffs at a common rate r; capital markets are perfect; and time is continuous. …