Identification of Stochastic Sequential Bargaining Models, Second Version

47 Pages Posted: 24 Mar 2010

See all articles by Xun Tang

Xun Tang

Rice University - Department of Economics

Antonio Merlo

University of Pennsylvania - Department of Economics; Rice University

Date Written: March 11, 2010

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 an agreement. In this paper, we present new results in nonparametric identification of such models under different scenarios of data availability. First, we give conditions for an observed distribution of players’ decisions and agreed allocations of the surplus, or the "cake", to be rationalized by a sequential bargaining model. We show the common discount rate is identified, provided the surplus is monotonic in unobservable states (USV) given observed ones (OSV). Then the mapping from states to surplus, or the "cake function", is also recovered under appropriate normalizations. Second, when the cake is only observed under agreements, the discount rate and the impact of observable states on the cake can be identified, if the distribution of USV satisfies some exclusion restrictions and the cake is additively separable in OSV and USV. Third, if data only report when an agreement is reached but never report the size of the cake, we propose a simple algorithm that exploits shape restrictions on the cake function and the independence of USV to recover all rationalizable probabilities for agreements under counterfactual state transitions. Numerical examples show the set of rationalizable counterfactual outcomes so recovered can be informative.

Keywords: Nonparametric Identification, Non-Cooperative Bargaining, Stochastic Sequential Bargaining, Rationalizable Counterfactual Outcomes

JEL Classification: C14, C35, C73, C78

Suggested Citation

Tang, Xun and Merlo, Antonio M., Identification of Stochastic Sequential Bargaining Models, Second Version (March 11, 2010). PIER Working Paper No. 10-008, Available at SSRN: https://ssrn.com/abstract=1571298 or http://dx.doi.org/10.2139/ssrn.1571298

Xun Tang

Rice University - Department of Economics ( email )

6100 South Main Street
Houston, TX 77005
United States

Antonio M. Merlo (Contact Author)

University of Pennsylvania - Department of Economics ( email )

Ronald O. Perelman Center for Political Science
133 South 36th Street
Philadelphia, PA 19104-6297
United States
215-898-7933 (Phone)
215-573-2057 (Fax)

HOME PAGE: http://www.ssc.upenn.edu/~merloa

Rice University ( email )

6100 South Main Street
Houston, TX 77005-1892
United States

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