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Sequential Estimation of Structural Models With a Fixed Point Constraint

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  • Hiroyuki Kasahara
  • Katsumi Shimotsu

Abstract

This paper considers the estimation problem of structural models for which empirical restrictions are characterized by a fixed point constraint, such as structural dynamic discrete choice models or models of dynamic games. We analyze the conditions under which the nested pseudo-likelihood (NPL) algorithm achieves convergence and derive its convergence rate. We find that the NPL algorithm may not necessarily converge when the fixed point mapping does not have a local contraction property. To address the issue of non-convergence, we propose alternative sequential estimation procedures that can achieve convergence even when the NPL algorithm does not. Upon convergence, some of our proposed estimation algorithms produce more efficient estimators than the NPL estimator.

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Bibliographic Info

Article provided by Econometric Society in its journal Econometrica.

Volume (Year): 80 (2012)
Issue (Month): 5 (09)
Pages: 2303-2319

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Handle: RePEc:ecm:emetrp:v:80:y:2012:i:5:p:2303-2319

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  1. Victor Aguirregabiria & Pedro Mira, 2007. "Sequential Estimation of Dynamic Discrete Games," Econometrica, Econometric Society, vol. 75(1), pages 1-53, 01.
  2. Ariel Pakes & Michael Ostrovsky & Steven Berry, 2007. "Simple estimators for the parameters of discrete dynamic games (with entry/exit examples)," RAND Journal of Economics, RAND Corporation, vol. 38(2), pages 373-399, 06.
  3. Patrick Bajari & Han Hong, 2006. "Semiparametric Estimation of a Dynamic Game of Incomplete Information," NBER Technical Working Papers 0320, National Bureau of Economic Research, Inc.
  4. Hiroyuki Kasahara & Katsumi Shimotsu, 2009. "Nonparametric Identification of Finite Mixture Models of Dynamic Discrete Choices," Econometrica, Econometric Society, vol. 77(1), pages 135-175, 01.
  5. Kasahara, Hiroyuki & Shimotsu, Katsumi, 2008. "Pseudo-likelihood estimation and bootstrap inference for structural discrete Markov decision models," Journal of Econometrics, Elsevier, vol. 146(1), pages 92-106, September.
  6. Per Krusell & Anthony A. Smith & Jr., 1998. "Income and Wealth Heterogeneity in the Macroeconomy," Journal of Political Economy, University of Chicago Press, vol. 106(5), pages 867-896, October.
  7. Jacek B. Krawczyk & Steffan Berridge, 1997. "Relaxation Algorithms in Finding Nash Equilibria," Computational Economics 9707002, EconWPA.
  8. Victor Aguirregabiria & Pedro Mira, 1999. "Swapping the Nested Fixed-Point Algorithm: a Class of Estimators for Discrete Markov Decision Models," Computing in Economics and Finance 1999 332, Society for Computational Economics.
  9. Hiroyuki Kasahara & Katsumi Shimotsu, 2006. "Nested Pseudo-likelihood Estimation and Bootstrap-based Inference for Structural Discrete Markov Decision Models," UWO Department of Economics Working Papers 20064, University of Western Ontario, Department of Economics.
  10. S. Rao Aiyagari, 1993. "Uninsured idiosyncratic risk and aggregate saving," Working Papers 502, Federal Reserve Bank of Minneapolis.
  11. Hiroyuki Kasahara & Katsumi Shimotsu, 2006. "Nonparametric Identification and Estimation of Finite Mixture Models of Dynamic Discrete Choices," UWO Department of Economics Working Papers 20065, University of Western Ontario, Department of Economics.
  12. V. Joseph Hotz & Robert A. Miller, 1992. "Conditional Choice Probabilities and the Estimation of Dynamic Models," Working Papers 9202, Harris School of Public Policy Studies, University of Chicago.
  13. Jonathan Levin (Stanford University) & Pat Bajari & Lanier Benkard, 2004. "Estimating Dynamic Models of Imperfect Competition," Econometric Society 2004 North American Winter Meetings 627, Econometric Society.
  14. Rust, John, 1987. "Optimal Replacement of GMC Bus Engines: An Empirical Model of Harold Zurcher," Econometrica, Econometric Society, vol. 55(5), pages 999-1033, September.
  15. Martin Pesendorfer & Philipp Schmidt-Dengler, 2008. "Asymptotic Least Squares Estimators for Dynamic Games -super-1," Review of Economic Studies, Oxford University Press, vol. 75(3), pages 901-928.
  16. Allan Collard-Wexler, 2006. "Demand Fluctuations and Plant Turnover in the Ready-Mix Concrete Industry," Working Papers 06-25, New York University, Leonard N. Stern School of Business, Department of Economics.
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Cited by:
  1. Victor Aguirregabiria & Chun-Yu Ho, 2008. "A Dynamic Oligopoly Game of the US Airline Industry: Estimation and Policy Experiments," Working Papers tecipa-337, University of Toronto, Department of Economics.
  2. Aguirregabiria, Victor & Nevo, Aviv, 2010. "Recent developments in empirical IO: dynamic demand and dynamic games," MPRA Paper 27814, University Library of Munich, Germany.
  3. Sumon Datta & K. Sudhir, 2012. "Does Reducing Spatial Differentiation Increase Product Differentiation? Effects of Zoning on Retail Entry and Format Variety," Cowles Foundation Discussion Papers 1851, Cowles Foundation for Research in Economics, Yale University, revised Sep 2012.

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