Inference for Two-Stage Extremum Estimators

Aristide Houndetoungan and Abdoul Haki Maoude ()
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Abdoul Haki Maoude: Université de Cergy-Pontoise, THEMA

No 2024-01, THEMA Working Papers from THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise

Abstract: We present a simulation-based approach to approximate the asymptotic variance and asymptotic distribution function of two-stage estimators. We focus on extremum estimators in the second stage and consider a large class of estimators in the first stage. This class includes extremum estimators, high-dimensional estimators, and other types of estimators (e.g., Bayesian estimators). We accom- modate scenarios where the asymptotic distributions of both the first- and second-stage estimators are non-normal. We also allow for the second-stage estimator to exhibit a significant bias due to the first-stage sampling error. We introduce a debiased plug-in estimator and establish its limit- ing distribution. Our method is readily implementable with complex models. Unlike resampling methods, we eliminate the need for multiple computations of the plug-in estimator. Monte Carlo simulations confirm the effectiveness of our approach in finite samples. We present an empirical application with peer effects on adolescent fast-food consumption habits, where we employ the proposed method to address the issue of biased instrumental variable estimates resulting from the presence of many weak instruments.

Keywords: Hypothesis Testing; Two-stage Estimators; Semiparametric and Nonparametric Methods; Resampling Methods; High-Dimensional Asymptotics (search for similar items in EconPapers)
JEL-codes: C12 C13 C14 C15 C55 (search for similar items in EconPapers)
Date: 2024
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