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Identification of Stochastic Sequential Bargaining Models

Author

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  • Antonio Merlo

    () (Department of Economics, University of Pennsylvania)

  • Xun Tang

    () (Department of Economics, University of Pennsylvania)

Abstract

Stochastic sequential bargaining games (Merlo and Wilson (1995, 1998)) have found wide applications in various fields including political economy and macroeconomics due to their flexibility in explaining delays in reaching agreement. In this paper, we present new results in nonparametric identification of such models under different scenarios of data availability. First, with complete data on players’ decisions, the sizes of the surplus to be shared (cakes) and the agreed allocations, both the mapping from states to the total surplus (i.e. the "cake function") and the players’ common discount rate are identified, if the unobservable state variable (USV) is independent of observable ones (OSV), and the total surplus is strictly increasing in the USV conditional on the OSV. Second, when the cake size is only observed under agreements and is additively separable in OSV and USV, the contribution by OSV is identified provided the USV distribution satisfies some distributional exclusion restrictions. Third, if data only report when an agreement is reached but never report the cake sizes, we propose a simple algorithm that exploits exogenously given shape restrictions on the cake function and the independence of USV from OSV to recover all rationalizable probabilities for reaching an agreement under counterfactual state transitions. Numerical examples show the set of rationalizable counterfactual outcomes so recovered can be informative.

Suggested Citation

  • Antonio Merlo & Xun Tang, 2009. "Identification of Stochastic Sequential Bargaining Models," PIER Working Paper Archive 09-037, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
  • Handle: RePEc:pen:papers:09-037
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    References listed on IDEAS

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    2. Merlo, Antonio, 1997. "Bargaining over Governments in a Stochastic Environment," Journal of Political Economy, University of Chicago Press, vol. 105(1), pages 101-131, February.
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    5. Daniel Diermeier & Michael Keane & Antonio Merlo, 2005. "A Political Economy Model of Congressional Careers," American Economic Review, American Economic Association, vol. 95(1), pages 347-373, March.
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    More about this item

    Keywords

    Nonparametric identification; non-cooperative bargaining; stochastic sequential bargaining; rationalizable counterfactual outcomes;

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C35 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory

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