Long-term relationships : Static gains and Dynamic ineffi ciencies

This paper formalizes the idea that firms can (partly) overcome the static costs associated with low contractibility by engaging in long-term relationships, but that the rigidity of these relationships may lead to strong dynamic ineffi ciencies. Specifically, we consider the repeated interaction between a final good producer and an intermediate input supplier. A pair producer/supplier can be a good match or a bad match and the nature of the match does not change over time. As a consequence, learning that a match is good increases the value of the relationship and creates the potential for cooperation in general equilibrium. We then allow for innovation on the supplier side and show (i) that innovations need to be larger for a new supplier with superior technology to break up existing relationships than in either a set-up where the input is contractible or when we preclude cooperation in long-term relationships, and (ii) that the rate of innovation is lower than in the contractible case, and may be lower than when cooperation is precluded in the noncontractible setting. We then show that, when innovation is exogenous, cooperation in long-term relationships may overcome most of the welfare loss associated with non-contractibility, but that, once innovation is endogenized, welfare is much lower in the noncontractible case than in the contractible case, and can even be lower if cooperation occurs in long-term relationships than if it does not. However, we show that far from the technological frontier, the establishment of long-term relationships can turn out to be a good substitute to high contractibility. An analysis of patents data in the US provide motivational evidence to our work. JEL.