Doko Tchatoka, Firmin and Dufour, JeanMarie (2012): Identificationrobust inference for endogeneity parameters in linear structural models.

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Abstract
We provide a generalization of the AndersonRubin (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 secondorder 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 leastsquares methods). We observe that endogeneity parameters may not be identifiable and we give the relevant identification conditions. We develop identificationrobust finitesample 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 standardtype Fisher critical values. For a wide class of parametric nonGaussian errors (possibly heavytailed), 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 ARtype tests on structural coefficients. For covariance endogeneity parameters, we supply an asymptotic (identificationrobust) 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.
Item Type:  MPRA Paper 

Original Title:  Identificationrobust inference for endogeneity parameters in linear structural models 
Language:  English 
Keywords:  Identificationrobust confidence sets; endogeneity; ARtype statistic; projectionbased techniques; partial exogeneity test 
Subjects:  C  Mathematical and Quantitative Methods > C3  Multiple or Simultaneous Equation Models ; Multiple Variables C  Mathematical and Quantitative Methods > C5  Econometric Modeling > C52  Model Evaluation, Validation, and Selection C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General > C12  Hypothesis Testing: General C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General > C15  Statistical Simulation Methods: General 
Item ID:  40695 
Depositing User:  Firmin Doko Tchatoka 
Date Deposited:  16 Aug 2012 12:28 
Last Modified:  23 Aug 2016 02:11 
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URI:  https://mpra.ub.unimuenchen.de/id/eprint/40695 