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Sequential Estimation of Structural Models With a Fixed Point Constraint

  • Hiroyuki Kasahara
  • Katsumi Shimotsu

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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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. 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.
  2. Hotz, V.J. & Miller, R.A., 1991. "Conditional Choice Probabilities and the Estimation of Dynamic Models," GSIA Working Papers 1992-12, Carnegie Mellon University, Tepper School of Business.
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  7. 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.
  8. 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.
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  11. 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.
  12. Krusell, P & Smith Jr, A-A, 1995. "Income and Wealth Heterogeneity in the Macroeconomic," RCER Working Papers 399, University of Rochester - Center for Economic Research (RCER).
  13. 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.
  14. 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.
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  16. 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.
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