Sticky Wage Models and Labor Supply Constraints∗

In New Keynesian models with sticky wages, the quantity of labor is solely determined by the demand side. Unions with monopsony power set the wage above what it takes to make agents work. If wages are sticky, however, a change of circumstances may make the demand for labor higher than agents’ willingness to work. Because of the simplicity of log-linearization, the literature implicitly assumes that the markup of wages over the willingness to work is large enough to ensure that workers always comply with the quantity of labor demanded. In this paper, we explore the extent to which this is the case and find that workers are required to work against their will about 10% of the time. Moreover, when we use, as proposed by traditional theory (Drèze (1975)), the minimum of the demand and supply of labor instead of the demand-determined quantity, we find that the typical parametrization yields a variance of hours around 25% lower (depending on the particular model). The Dreze equilibrium is hard to compute, yet we find that a boundedly rational use of log-linearization methods gives a good approximation. We estimate the Dreze equilibrium for a version of the Christiano, Eichenbaum, and Evans (2005) environment and find that it yields answers that are sharply different from the demanddetermined allocation: neutral productivity shocks go from accounting for 13% of the variance of employment to accounting for 70% of the variance of employment, to the detriment of the role played by investment specific technology shocks and monetary shocks. We conclude that when working with sticky wage economies, the appropriate procedure is to estimate the model using the approximated Dreze equilibrium.