Long-Term Relationships: Static Gains and Dynamic Inefficiencies

Abstract

Do contractual frictions matter when firms are engaged in repeated interactions? This paper argues that long-term relationships, which allow firms to (partly) overcome the static costs associated with low contractibility, will under certain circumstances create dynamic inefficiencies. We consider the repeated interaction between final good producers and intermediate input suppliers, where the provision of the intermediate input is noncontractible. A producer/supplier pair can be a good match or a bad match, with bad matches featuring lower productivity. This allows us to build a cooperative equilibrium where producers can switch suppliers and start cooperation immediately with new suppliers. Every period, one supplier has the opportunity to innovate, and in the baseline model, innovations are imitated after one period. We show that (i) innovations need to be larger to break up existing relationships in the cooperative equilibrium than in either a set-up where the input is contractible or when we preclude cooperation in long-term relationships, (ii) the rate of innovation in the cooperative equilibrium is lower than in the contractible case, and may even be lower than in the non-cooperative equilibrium and (iii) cooperation may reduce welfare. Next, we assume that the frontier technology diffuses slowly to suppliers (instead of after one period). In that case, for sufficiently slow diffusion, the innovation rate in the cooperative equilibrium may be higher than even in the contractible case. Finally, we show that cooperation may also increase relationship specific innovations.

Keywords: Contractibility, Innovation, Repeated Game, Relational Contract

JEL Classification: C73, K12, L14, O31, O43