Econometrica: Sep 2012, Volume 80, Issue 5

Sequential Estimation of Structural Models With a Fixed Point Constraint

https://doi.org/10.3982/ECTA8291
p. 2303-2319

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 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.
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Supplement to "Sequential Estimation of Structural Models with a Fixed Point Constraint"

This zip file contains the replication files for the manuscript.

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Supplement to "Sequential Estimation of Structural Models with a Fixed Point Constraint"

This supplement contains the following details omitted from the main paper due to space constraints: (A) proof of the results in the paper, (B) auxiliary results and their proof, (C) additional alternative sequential algorithms, (D) the convergence properties of the NPL algorithm for models with unobserved heterogeneity, and (E) additional Monte Carlo results.

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