Several recent papers (Shimer 2003a, 2003b; Costain and Reiter 2003; Hall 2003) have shown that general equilibrium labor market models have a hard time generating the degree of cyclical volatility in unemployment and vacancies that is observed in the data. These papers have suggested that rigid wages may help to resolve this puzzle. However, little progress has been made in incorporating microfoundations for wage stickiness into these models, and it remains an open question whether the quantitative effects of wage stickiness are large when a consistent model of wage stickiness is used. This paper studies a dynamic matching model with downward wage rigidity. Like Mortensen and Pissarides (2001) and Jansen (2001), we generalize the standard Mortensen and Pissarides (1994) model by assuming that workers' effort is imperfectly observable. To avoid shirking, firms therefore prefer to pay their workers incentive compatible wages. Jansen (2001) showed that in this context, the incentive compatibility constraint acts as a lower-bound on the negotiated wage, which always binds on the least productive jobs, but need not bind on the most productive jobs. Job destruction decisions are therefore driven by the minimum incentive compatible wage, resulting in inefficient separations. Previous papers using this framework have focused on the steady state. Here, we explore the implications of this type of downward wage rigidity for the cyclical properties of job creation, job destruction and unemployment. We start from the reasonable assumption that the disutility of effort (in our case the loss of leisure) is related to average productivity but less cyclical than actual productivity. Given this assumption, the surplus of jobs exhibits substantially more cyclical volatility than in standard matching models with transferable utility. The downward wage rigidity therefore accentuates the counter-cyclical pattern of job destruction and the pro-cyclical pattern of job creation, giving us some of the labor market volatility that is missing in other matching models. Moreover, as long as the incentive compatibility constraint does not bind on all jobs, this does not lead to a substantial increase in the average unemployment rate. It is important to point out that in our paper, incorporating an incentive compatible wage has consequences which may be surprising, given the conventional wisdom about ``efficiency wage'' models. In macroeconomic models without matching frictions, the higher unemployment during recessions makes it easier to motivate workers, decreasing the wage and therefore smoothing unemployment fluctuations (Kimball 1994). In a matching model, too, wages fall in recessions. But the more important point in a matching context is that both the total match surplus, and the share of this surplus received by firms, is smaller in recessions. The incentive compatibility problem is therefore particularly harmful for employment in recessions.
