Sequential Estimation of Structural Models With a Fixed Point Constraint


  • Hiroyuki Kasahara,

    1. Dept. of Economics, University of British Columbia, Vancouver, British Colum- bia V6T 1Z1, Canada;
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  • Katsumi Shimotsu

    1. Faculty of Economics, University of Tokyo, 7-3-1, Hongo, Bunkyo-ku Tokyo, 113-0033, Japan;
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    • We are grateful to the co-editor and three anonymous referees whose comments greatly improved the paper. The authors thank Victor Aguirregabiria, David Byrne, Hide Ichimura, Kenneth Judd, Vadim Marmer, Lealand Morin, and seminar participants at the Bank of Japan, FEMES, New York Camp Econometrics, NASM, SITE, Vienna Macroeconomic Workshop, Boston University, Michigan, Montreal, Hitotsubashi, HKU, HKUST, Johns Hopkins, SETA, Tokyo, UBC, UWO, Yale, Yokohama National University, and Xiamen for helpful comments. The authors thank the SSHRC for financial support.


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 a local condition under which the nested pseudo likelihood (NPL) algorithm converges to a consistent estimator, and derive its convergence rate. We find that the NPL algorithm may not necessarily converge to a consistent estimator when the fixed point mapping does not have a local contraction property. To address the issue of divergence, we propose alternative sequential estimation procedures that can converge to a consistent estimator even when the NPL algorithm does not.