Efficiency in Job-Ladder Models

This paper examines the efficiency of a decentralized equilibrium in a broad class of random-search job-ladder models. We decompose the source of inefficiency into two margins: (i) the investment margin, that is, the difference between the private and social benefit of job creation given the surplus of a match, and (ii) the valuation margin, that is, the difference between the private valuation and the social valuation of a match surplus. In the presence of on-the-job searches, the well-known Hosios condition no longer guarantees the market equilibrium aligns with the efficient allocation along both margins. On-the-job searches contribute to the overvaluation of the match surplus in market equilibrium, especially at the top of the job ladder. Consequently, the decentralized equilibrium with the Hosios condition features excess creation of vacancies in the steady state. On-the-job searches also lead to excess volatility in unemployment in response to aggregate productivity shocks. Quantitatively, we find a significant difference between the equilibrium outcome and the efficient allocation under standard calibration. We also consider several decentralizations of the efficient allocation to shed light on the optimal policies under the frictional labor market.