Privately Efficient Bargaining between Workers and Large Firms

I propose a model of bargaining between workers and large firms that resembles the Stole and Zwiebel (1996a,b) model, but has the desirable feature that workers and firms behave in a privately efficient manner. I assume that on hiring, firms and workers can contract to behave efficiently in the future, while maintaining the assumption that the marginal surplus associated with the match is split in a constant ratio. I show that the equilibrium of the model is constrained efficient under my bargaining assumption if the Hosios (1990) condition holds; in Stole and Zwiebel’s bargaining model, the incentive of firms to extract rent from their existing employees by over-hiring means that the equilibrium is never constrained efficient in the absence of taxes. I show that the two models cannot be distinguished from data only on the worker side of the market, such as wages and job-finding rates; data on firm profitability is required. The model is tractable enough to allow aggregate fluctuations to be studied easily, and a variant of it has rich predictions for wage dynamics. I find that a benchmark version of the model generates behavior of key labor market variables such as market tightness and the unemployment rate that is similar to what arises in a comparably-calibrated Mortensen-Pissarides model, although the model does have the ability to account for much richer dynamics of employment at the firm level. JEL Codes: E24, J41, J64. ∗Addresses: Harkness 232, Department of Economics, University of Rochester, Box 270156, Rochester, NY 146270156; [email protected]. I also thank Mark Bils, Philipp Kircher, Rafael Lopes de Melo, and seminar participants at Rochester and the Richmond Fed for very helpful comments. The fault for the large set of remaining imperfections is, of course, my own.