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Identification of Stochastic Sequential Bargaining Models

  • Antonio Merlo


    (Department of Economics, University of Pennsylvania)

  • Xun Tang


    (Department of Economics, University of Pennsylvania)

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.

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Paper provided by Penn Institute for Economic Research, Department of Economics, University of Pennsylvania in its series PIER Working Paper Archive with number 09-037.

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Length: 43 pages
Date of creation: 15 Oct 2009
Date of revision:
Handle: RePEc:pen:papers:09-037
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  1. David Benjamin, 2008. "Recovery Before Redemption," 2008 Meeting Papers 531, Society for Economic Dynamics.
  2. Daniel Diermeier & Michael Keane & Antonio Merlo, 2002. "A Political Economy Model of Congressional Careers," PIER Working Paper Archive 04-037, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 01 Sep 2004.
  3. repec:cup:cbooks:9780521576475 is not listed on IDEAS
  4. Emmanuel Guerre & Isabelle Perrigne & Quang Vuong, 2000. "Optimal Nonparametric Estimation of First-Price Auctions," Econometrica, Econometric Society, vol. 68(3), pages 525-574, May.
  5. Carlos Diaz-Moreno & Jose E. Galdon-Sanchez, 2000. "Collective bargaining under complete information," LSE Research Online Documents on Economics 19337, London School of Economics and Political Science, LSE Library.
  6. Philip A. Haile & Han Hong & Matthew Shum, 2003. "Nonparametric Tests for Common Values in First-Price Sealed-Bid Auctions," Cowles Foundation Discussion Papers 1445, Cowles Foundation for Research in Economics, Yale University.
  7. Matthew Shum, 2000. "Nonparametric Tests for Common Values," Econometric Society World Congress 2000 Contributed Papers 1598, Econometric Society.
  8. Merlo, Antonio, 1997. "Bargaining over Governments in a Stochastic Environment," Journal of Political Economy, University of Chicago Press, vol. 105(1), pages 101-31, February.
  9. Athey, Susan & Haile, Philip A., 2007. "Nonparametric Approaches to Auctions," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 60 Elsevier.
  10. Patrick Bajari & Han Hong & John Krainer & Denis Nekipelov, 2006. "Estimating Static Models of Strategic Interaction," NBER Working Papers 12013, National Bureau of Economic Research, Inc.
  11. Binmore, Ken & Osborne, Martin J. & Rubinstein, Ariel, 1992. "Noncooperative models of bargaining," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 1, chapter 7, pages 179-225 Elsevier.
  12. Merlo, Antonio & Wilson, Charles A, 1995. "A Stochastic Model of Sequential Bargaining with Complete Information," Econometrica, Econometric Society, vol. 63(2), pages 371-99, March.
  13. Yasutora Watanabe, 2005. "Learning and Bargaining in Dispute Resolution: Theory and Evidence from Medical Malpractice Litigation," 2005 Meeting Papers 440, Society for Economic Dynamics.
  14. Daniel Diermeier & Hulya Eraslan & Antonio Merlo, 2003. "A Structural Model of Government Formation," Econometrica, Econometric Society, vol. 71(1), pages 27-70, January.
  15. David Benjamin & Mark L. J. Wright, 2009. "Recovery Before Redemption: A Theory Of Delays In Sovereign Debt Renegotiations," CAMA Working Papers 2009-15, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.
  16. Hülya K. K. Eraslan, 2008. "Corporate Bankruptcy Reorganizations: Estimates From A Bargaining Model," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 49(2), pages 659-681, 05.
  17. Antonio Merlo & Charles Wilson, 1997. "Efficient delays in a stochastic model of bargaining," Economic Theory, Springer, vol. 11(1), pages 39-55.
  18. Haile,P.A. & Tamer,E.T., 2000. "Inference with an incomplete model of English auctions," Working papers 18, Wisconsin Madison - Social Systems.
  19. Ran Bi, 2008. "“Beneficial†Delays in Debt Restructuring Negotiations," IMF Working Papers 08/38, International Monetary Fund.
  20. Athey,S. & Haile,P.A., 2000. "Identification of standard auction models," Working papers 13, Wisconsin Madison - Social Systems.
  21. Laffont, Jean-Jacques & Vuong, Quang, 1996. "Structural Analysis of Auction Data," American Economic Review, American Economic Association, vol. 86(2), pages 414-20, May.
  22. Songnian Chen & Gordon B. Dahl & Shakeeb Khan, 2005. "Nonparametric Identification and Estimation of a Censored Location-Scale Regression Model," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 212-221, March.
  23. Xun Tang, 2009. "Estimating Simultaneous Games with Incomplete Information under Median Restrictions," PIER Working Paper Archive 09-023, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
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