Bargaining with Commitment between Workers and Large Firms

I study bargaining between workers and large firms when commitment to long-term contracts is feasible. The marginal surplus associated with a match is split in a pre-determined ratio, analogously to generalized Nash bargaining. Commitment avoids the over-hiring inefficiency identified by Stole and Zwiebel (1999a,b) and Smith (1999). However, even under the Hosios (1990) condition, the equilibrium is still not constrained efficient since large firms search too intensively relative to small firms. If workers can direct their search to firms by size, or if firms can hire workers instantaneously at constant marginal cost, the equilibrium is constrained efficient if the Hosios condition applies. The pattern of growth rates of firms by size can be used to identify how firms bargain with workers.