Stochastic Search Equilibrium
We analyze a stochastic equilibrium contract-posting model. Firms post employment contracts, wages contingent on all payoﬀ-relevant states. Aggregate productivity is subject to persistent shocks. Both employed and unemployed workers search randomly for these contracts, and are free to quit at any time. An equilibrium of this contract-posting game is Rank-Preserving [RP] if larger ﬁrms oﬀer a larger value to their workers in all states of the world. We show that every equilibrium is RP, and equilibrium is unique, if ﬁrms diﬀer either only in their initial size, or also in their ﬁxed idiosyncratic productivity but more productive ﬁrms are initially larger, in which case turnover is always eﬀicient, as workers always move from less to more productive ﬁrms. The RP equilibrium stochastic dynamics of ﬁrm size provide an explanation for the empirical ﬁnding that large employers are more cyclically sensitive (Moscarini and Postel-Vinay, 2009). RP equilibrium computation is tractable, and we simulate calibrated examples.
Moscarini, Giuseppe and Postel-Vinay, Fabien, "Stochastic Search Equilibrium" (2010). Cowles Foundation Discussion Papers. 2082.