Efficiency and labor market dynamics in a model of labor selection

We characterize efficient allocations and business cycle fluctuations in a labor selection model. Due to forward-looking hiring and labor supply decisions, efficiency entails both static and intertemporal margins. We develop welfare-relevant measures of marginal rates of transformation and efficiency along each margin that nest their counterparts in frictionless labor markets. In a calibrated version of the model, efficient fluctuations feature highly volatile unemployment and job-finding rates, in line with empirical evidence. We show analytically in a simplified version of the model that volatility arises from selection effects, rather than general equilibrium effects. We also develop sufficient conditions on wages, which are independent of the wage-determination process, that decentralize efficient allocations. Unlike the Hosios condition for matching models, there is no simple restriction on Nash bargaining that guarantees that Nash wages can support efficient allocations. Cyclical fluctuations in the Nash-bargaining economy display even larger amplification of productivity shocks into labor market outcomes than in the efficient economy, without extreme assumptions about bargaining shares, inflexibility of wages, or the size of surpluses that govern labor demand. The results establish normative and positive foundations for DSGE labor selection models.