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Inference for parameters identified by conditional moment restrictions using a generalized Bierens maximum statistic

Xiaohong Chen, Sokbae Lee, Myung Hwan Seo, Myunghyun Song

Abstract

Many economic panel and dynamic models, such as rational behavior and Euler equations, imply that the parameters of interest are identified by conditional moment restrictions. We introduce a novel inference method without any prior information about which conditioning instruments are weak or irrelevant. Building on Bierens (1990), we propose penalized maximum statistics and combine bootstrap inference with model selection. Our method optimizes asymptotic power by solving a data-dependent max-min problem for tuning parameter selection. Extensive Monte Carlo experiments, based on an empirical example, demonstrate the extent to which our inference procedure is superior to those available in the literature.

Inference for parameters identified by conditional moment restrictions using a generalized Bierens maximum statistic

Abstract

Many economic panel and dynamic models, such as rational behavior and Euler equations, imply that the parameters of interest are identified by conditional moment restrictions. We introduce a novel inference method without any prior information about which conditioning instruments are weak or irrelevant. Building on Bierens (1990), we propose penalized maximum statistics and combine bootstrap inference with model selection. Our method optimizes asymptotic power by solving a data-dependent max-min problem for tuning parameter selection. Extensive Monte Carlo experiments, based on an empirical example, demonstrate the extent to which our inference procedure is superior to those available in the literature.

Paper Structure

This paper contains 20 sections, 7 theorems, 68 equations, 4 figures, 9 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Closely related literature
  3. Test Statistic
  4. Bootstrap Critical Values
  5. Bootstrap Validity
  6. Consistency, Local Power and Calibration of lambda
  7. Consistency
  8. Local Power
  9. Calibration of lambda
  10. Implementation
  11. Inference with Pre-Estimated Parameters
  12. Choice of Penalty
  13. Inferring the Elasticity of Intertemporal Substitution
  14. Computation of the Test Statistic
  15. Computation Time
  16. ...and 5 more sections

Key Result

Lemma 1

Let Assumption assum0 hold. Then, $M\left(\theta,\gamma\right)=0$ if $\theta=\theta_{0}$ and $M\left(\theta,\gamma\right)\neq 0 \ for \ almost \ every \ \gamma \in \Gamma$ if $\theta\neq\theta_{0}$.

Figures (4)

  • Figure 1: Graphical Representation of Power Improvements via Penalization
  • Figure 2: Simulated Local Powers Computed Using PSO and GS
  • Figure 3: Power Curves of Competing Tests under the Baseline Specification
  • Figure A1: Testing Results

Theorems & Definitions (14)

  • Lemma 1: bierens1990consistent
  • Theorem 1
  • Theorem 2
  • Theorem 3
  • Lemma 2
  • Definition 1
  • Theorem 4
  • Theorem 5
  • proof : Proof of Theorem \ref{['thm:fixed p null']}
  • proof : Proof of Theorem \ref{['thm:fixed p null:bootstrap']}
  • ...and 4 more