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 …first show, through a simple discrete 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 the study of the dynamics of the optimal mechanism can be significantly simplified by assuming the shocks are independent over time. When the sets of possible types in any two adjacent periods satisfy a certain overlapping condition (which is always satisfied with a continuum of types) and some additional regularity conditions hold, then the optimal mechanism is the same irrespective of whether the shocks are the buyer’s private information or are observed also by the seller. These conditions are satisfied, for example, in the case of an AR(1) process, a Brownian motion, but also when shocks have a multiplicative effect as it is often the case in financial applications. Furthermore, the distortions in the optimal quantities are independent of the distributions of the shocks and, when the buyer’s payoff 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 does it greatly simplify the analysis, it is actually without loss of generality.asymmetric information, stochastic process, dynamic mechanism design, long-term contracting

Long-Term Contracting in a Changing World

I study the properties of optimal long-term contracts in an environment in which the agents 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 buyers 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 buyers 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 e¤ect 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 buyers 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.asymmetric information, stochastic process, dynamic mechanism design, long-term contracting

On the Optimality of Privacy in Sequential Contracting

This paper considers an environment where two principals sequentially contract with a common agent and studies the exchange of information between the two bilateral relationships. We show that when (a) the upstream principal is not personally interested in the decisions taken by the downstream principal, (b) the agent’s exogenous private information has a "vertical" structure in the sense that the sign of the single crossing condition is the same for upstream and downstream decisions, and (c) preferences in the downstream relationship are separable, then the upstream principal optimally commits to full privacy, whatever price the downstream principal is willing to pay to receive information. On the contrary, when any of the above conditions is violated, the upstream principal may find it strictly optimal to disclose a (noisy) signal of the agent’s exogenous type and/or the result of his upstream contractual activity, even if she can not make the downstream principal pay for the information she receives. We also show that disclosure does not necessarily reduce the equilibrium payoff of the agent and may lead to a Pareto improvement for the three players.contractual and informational externalities, mechanism design, optimal disclosure policy, sequential common agency, exogenous and endogenous private information

On the Optimality of Privacy in Sequential Contracting

This paper studies the exchange of information between two principals who contract sequentially with the same agent, as in the case of a buyer who purchases from multiple sellers. We show that when (a) the upstream principal is not personally interested in the downstream level of trade, (b) the agent’s valuations are positively correlated, and (c) preferences in the downstream relationship are separable, then it is optimal for the upstream principal to offer the agent full privacy. On the contrary, when any of these conditions is violated, there exist preferences for which disclosure is strictly optimal, even if the downstream principal does not pay for the information. We also examine the effects of disclosure on welfare and show that it does not necessarily reduce the agent’s surplus in the two relationships and in some cases may even yield a Pareto improvement. The paper describes this condition and its implications.contractual and informational externalities, mechanism design, optimal disclosure policies, sequential common agency games, exogenous and endogenous private information.

Managerial Turnover in a Changing World

We characterize a firm's profit-maximizing turnover policy in an environment where managerial productivity changes stochastically over time and is the manager's private information. Our key positive result shows that the productivity level that the …firm requires for retention declines with the manager's tenure in the …firm. Our key normative result shows that, compared to what is efficient, the profit-maximizing policy either induces excessive retention (i.e., inefficiently low turnover) at all tenure levels, or excessive firing at the early stages of the relationship followed by excessive retention after sufficiently long tenure.managerial turnover, termination clauses, dynamic mechanism design, adverse selection, moral hazard

Tilting the Supply Schedule to Enhance Competition in Uniform-Price Auctions

Uniform-price auctions of a divisible good in fixed supply admit underpricing equilibria, where bidders submit high inframarginal bids to prevent competition on prices. The seller can obstruct this behavior by tilting her supply schedule and making the amount of divisible good on offer change endogenously with its (uniform) price. Precommitting to an increasing supply curve is a strategic instrument to reward aggressive bidding and enhance expected revenue. A fixed supply may not be optimal even when accounting for the cost to the seller of issuing a quantity different from her target supply.Uniform-price auction, divisible good, strategic role of the seller, endogenous supply, Treasury and IPO auctions

Monopoly with Resale

This paper examines the intricacies associated with the design of revenue-maximizing mechanisms for a monopolist who expects her buyers to resell. We consider two cases: resale to a third party who does not participate in the primary market and inter-bidder resale, where the winner resells to the losers. To influence the resale outcome, the monopolist must design an allocation rule and a disclosure policy that optimally fashion the beliefs of the participants in the secondary market. Our results show that the revenue-maximizing mechanism may require a stochastic selling procedure and a disclosure policy richer than the simple announcement of the decision to trade.information linkage between primary and secondary markets, optimal disclosure policy, stochastic allocations, mechanism design.

Tilting the Supply Schedule to Enhance Competition in Uniform- Price Auctions

Uniform-price auctions of a divisible good in fixed supply admit underpricing equilibria, where bidders submit high inframarginal bids to prevent competition on prices. The seller can obstruct this behavior by tilting her supply schedule and making the amount of divisible good on offer change endogenously with its (uniform) price. Precommitting to an increasing supply curve is a strategic instrument to reward aggressive bidding and enhance expected revenue. A fixed supply may not be optimal even when accounting for the cost to the seller of issuing a quantity different from her target supply.uniform-price auction, divisible good, strategic role of the seller, endogenous supply, Treasury and IPO auctions.

On the Use of Menus in Sequential Common Agency

We illustrate, by means of two examples, why assuming the principals offer simple menus (i.e. collections of payoff-relevant alternatives) as opposed to more general mechanisms may preclude a complete characterization of the set of equilibrium outcomes in certain sequential contracting environments. We then discuss how refinements of the solution concept, or enrichments of the menus that allow for recommendations, may restore the possibility of using menus to obtain a complete equilibrium characterization.Sequential contracting, mechanism design, menus theorems.