Dynamic and Stochastic Search Equilibrium

Wage posting models are an appealing way of studying wage growth and dispersion, as firms offer high employment values to retain and poach more workers from other companies. In this paper, I study the business cycle properties of these types of models with random search. When abstracting from firm entry and exit, I show that productivity shocks do not generate fluctuations in labor market quantities (such as unemployment) because fear of competition for workers makes wages absorb most of these shocks. Even though separation rate shocks can generate large unemployment fluctuations, they generate a positive correlation between unemployment and hires and, depending on the recruiting cost function, these shocks may also generate a positive correlation between unemployment and vacancies. I show that introducing wage rigidity into the model increases the responses of labor market quantities to aggregate productivity shocks, but the size of these responses depends on how large (relative to productivity) the flow opportunity cost of employment is. To assess these models quantitatively, I propose a new algorithm that finds the steady state and computes transitional dynamics in seconds. Hence, integrating wage posting models with random search to larger models becomes possible (and easy) with this new algorithm.