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Identification-robust inference for endogeneity parameters in linear structural models

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  • Doko Tchatoka, Firmin
  • Dufour, Jean-Marie

Abstract

We provide a generalization of the Anderson-Rubin (AR) procedure for inference on parameters which represent the dependence between possibly endogenous explanatory variables and disturbances in a linear structural equation (endogeneity parameters). We focus on second-order dependence and stress the distinction between regression and covariance endogeneity parameters. Such parameters have intrinsic interest (because they measure the effect of "common factors" which induce simultaneity) and play a central role in selecting an estimation method (because they determine "simultaneity biases" associated with least-squares methods). We observe that endogeneity parameters may not be identifiable and we give the relevant identification conditions. We develop identification-robust finite-sample tests for joint hypotheses involving structural and regression endogeneity parameters, as well as marginal hypotheses on regression endogeneity parameters. For Gaussian errors, we provide tests and confidence sets based on standard-type Fisher critical values. For a wide class of parametric non-Gaussian errors (possibly heavy-tailed), we also show that exact Monte Carlo procedures can be applied using the statistics considered. As a special case, this result also holds for usual AR-type tests on structural coefficients. For covariance endogeneity parameters, we supply an asymptotic (identification-robust) distributional theory. Tests for partial exogeneity hypotheses (for individual potentially endogenous explanatory variables) are covered as instances of the class of proposed procedures. The proposed procedures are applied to two empirical examples: the relation between trade and economic growth, and the widely studied problem of returns to education.

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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 40695.

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Date of creation: 16 Aug 2012
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Handle: RePEc:pra:mprapa:40695

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Keywords: Identification-robust confidence sets; endogeneity; AR-type statistic; projection-based techniques; partial exogeneity test;

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Cited by:
  1. Doko Tchatoka, Firmin, 2012. "Specification tests with weak and invalid instruments," Working Papers, University of Tasmania, School of Economics and Finance 15063, University of Tasmania, School of Economics and Finance, revised 26 Jun 2012.
  2. Doko Tchatoka, Firmin, 2012. "On the validity of Durbin-Wu-Hausman tests for assessing partial exogeneity hypotheses with possibly weak instruments," Working Papers, University of Tasmania, School of Economics and Finance 15061, University of Tasmania, School of Economics and Finance, revised 06 Jul 2012.
  3. Firmin Doko Tchatoka & Jean-Marie Dufour, 2014. "Identification-robust inference for endogeneity parameters in linear structural models," CIRANO Working Papers, CIRANO 2014s-17, CIRANO.
  4. Xu Cheng & Zhipeng Liao, 2012. "Select the Valid and Relevant Moments: A One-Step Procedure for GMM with Many Moments," PIER Working Paper Archive 12-045, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.

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