Abstract
The standard approach to indirect inference estimation considers that the auxiliary parameters, which carry the identifying information about the structural parameters of interest, are obtained from some recently identified vector of estimating equations. In contrast to this standard interpretation, we demonstrate that the case of overidentified auxiliary parameters is both possible, and, indeed, more commonly encountered than one may initially realize. We then revisit the “moment matching” and “parameter matching” versions of indirect inference in this context and devise efficient estimation strategies in this more general framework. Perhaps surprisingly, we demonstrate that if one were to consider the naive choice of an efficient Generalized Method of Moments (GMM)-based estimator for the auxiliary parameters, the resulting indirect inference estimators would be inefficient. In this general context, we demonstrate that efficient indirect inference estimation actually requires a two-step estimation procedure, whereby the goal of the first step is to obtain an efficient version of the auxiliary model. These two-step estimators are presented both within the context of moment matching and parameter matching.
Highlights
Twenty-five years ago, with the publication of their manuscript on “Efficient Method of Moments”(hereafter, EMM), Gallant and Tauchen (1996) made a seminal contribution to the field of simulation-based estimation and inference
We demonstrate that efficient indirect inference estimation requires a two-step estimation procedure, whereby the goal of the first step is to obtain an efficient version of the auxiliary model
Demonstrate that, for well-chosen weighting matrices used for moment matching, indirect inference estimators based on score matching will be asymptotically equivalent to indirect inference estimators based on the direct matching of auxiliary parameters
Summary
Twenty-five years ago, with the publication of their manuscript on “Efficient Method of Moments”. Several authors, including Gallant and Long (1997), Andersen and Lund (1997) (hereafter, AL), and Gallant et al (1997), have carefully discussed the choice of auxiliary model in the context of EMM, namely through the use of some SNP score generator Not surprisingly they find that, as in any moment matching exercise, to achieve good finite-sample performance of the indirect inference estimator “it is important to conserve on the number of elements in the score generator” (AL), that is, on the number of moments to match within estimation. Our focus of interest is the asymptotic variance of the resulting indirect inference estimator of structural parameters To this end, the present paper demonstrates the relevant way to measure the information content of the moments we wish to match. Proofs of certain results are detailed in the Appendix A
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