Long-term contracting in a changing world

I study the properties of optimal long-term contracts in an environment in which the agent.s type evolves stochastically over time. The model stylizes a buyer-seller relationship but the results apply quite naturally to many contractual situations including regulation and optimal income-taxation. I .rst show, through a simple example, that distortions need not vanish over time and need not be monotonic in the shock to the buyer.s valuation. These results are in contrast to those obtained in the literature that assumes a Markov process with a binary state space. e.g. Battaglini, 2005. I then show that when the sets of possible types in any two adja-cent periods satisfy a certain overlapping condition (which is always satis.ed with a continuum of types), then the dynamics of the optimal mechanism can be signi.cantly simpli.ed by as-suming the shocks are independent over time. Under certain regularity conditions, the optimal mechanism is then the same irrespective of whether the shocks are the buyer.s private informa-tion or are observed also by the seller. These conditions are satis.ed, for example, in the case of an AR(1) process, a Brownian motion, but also when shocks have a multiplicative eþect as it is often the case in .nancial applications. Furthermore, the distortions in the optimal quantities are independent of the distributions of the shocks and, when the buyer.s valuation is additively separable, they are also independent of whether the shocks are transitory or permanent. Finally, I show that assuming the shocks are independent not only greatly simpli.es the analysis but is actually without loss of generality with a continuum of types.