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Long-Term Contracting in a Changing World

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  • Alessandro Pavan

Abstract

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.

Suggested Citation

  • Alessandro Pavan, 2007. "Long-Term Contracting in a Changing World," Discussion Papers 1456, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  • Handle: RePEc:nwu:cmsems:1456
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    References listed on IDEAS

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    1. Battaglini, Marco & Coate, Stephen, 2008. "Pareto efficient income taxation with stochastic abilities," Journal of Public Economics, Elsevier, vol. 92(3-4), pages 844-868, April.
    2. Péter Eső & Balázs Szentes, 2007. "Optimal Information Disclosure in Auctions and the Handicap Auction," Review of Economic Studies, Oxford University Press, vol. 74(3), pages 705-731.
    3. Marco Battaglini, 2005. "Long-Term Contracting with Markovian Consumers," American Economic Review, American Economic Association, vol. 95(3), pages 637-658, June.
    4. Pascal Courty & Li Hao, 2000. "Sequential Screening," Review of Economic Studies, Oxford University Press, vol. 67(4), pages 697-717.
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    Citations

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    Cited by:

    1. Krähmer, Daniel & Strausz, Roland, 2015. "Ex post information rents in sequential screening," Games and Economic Behavior, Elsevier, vol. 90(C), pages 257-273.
    2. Raphael Boleslavsky & Maher Said, 2013. "Progressive Screening: Long-Term Contracting with a Privately Known Stochastic Process," Review of Economic Studies, Oxford University Press, vol. 80(1), pages 1-34.
    3. Penta, Antonio, 2015. "Robust dynamic implementation," Journal of Economic Theory, Elsevier, vol. 160(C), pages 280-316.
    4. Deb, Rahul, 2008. "Optimal Contracting Of New Experience Goods," MPRA Paper 9880, University Library of Munich, Germany.

    More about this item

    Keywords

    asymmetric information; stochastic process; dynamic mechanism design; long-term contracting;

    JEL classification:

    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • L1 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance

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