Stochastic Search Equilibrium

We study equilibrium wage and employment dynamics in a class of popular search models with wage posting, in the presence of aggregate productivity shocks. Firms offer and commit to (Markov) contracts, which specify a wage contingent on all payoff-relevant states, but must pay equally all of their workers, who have limited commitment and are free to quit at any time. We find sufficient conditions for the existence and uniqueness of a stochastic search equilibrium in such contracts, which is Rank Preserving [RP]: larger and more productive firms offer more generous contracts to their workers in all states of the world. On the RP equilibrium path, turnover is always efficient as workers always move from less to more productive firms. The resulting stochastic dynamics of firm size provide an intuitive explanation for the empirical finding that large employers have more cyclical job creation (Moscarini and Postel-Vinay, 2012). Finally, computation of RP equilibrium contracts is tractable