Identification of Stochastic Sequential Bargaining Models

43 Pages Posted: 22 Oct 2009

See all articles by Antonio Merlo

Antonio Merlo

University of Pennsylvania - Department of Economics; Rice University

Xun Tang

Rice University - Department of Economics

Date Written: October 15, 2009

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 non-parametric 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 counter-factual 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

Merlo, Antonio M. and Tang, Xun, Identification of Stochastic Sequential Bargaining Models (October 15, 2009). PIER Working Paper No. 09-037, Available at SSRN: https://ssrn.com/abstract=1492217 or http://dx.doi.org/10.2139/ssrn.1492217

Antonio M. Merlo

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

Xun Tang (Contact Author)

Rice University - Department of Economics ( email )

6100 South Main Street
Houston, TX 77005
United States