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Instrumental variables estimation and inference in the presence of many exogenous regressors

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  • Stanislav Anatolyev

Abstract

We consider a standard instrumental variables model contaminated by the presence of a large number of exogenous regressors. In an asymptotic framework where this number is proportional to the sample size, we study the impact of their ratio on the validity of existing estimators and tests. When the instruments are few, the inference using the conventional 2SLS estimator and associated t and J statistics, as well as the Anderson-Rubin and Kleibergen tests, is still valid. When the instruments are many, the LIML estimator remains consistent, but the presence of many exogenous regressors changes its asymptotic variance. Moreover, the conventional bias correction of the 2SLS estimator is no longer appropriate. We provide asymptotically correct versions of bias correction for the 2SLS estimator, derive its asymptotically correct variance estimator, extend the Hansen-Hausman-Newey LIML variance estimator to the case of many exogenous regressors, and propose asymptotically valid modi cations of the J overidenti cation tests based on the LIML and bias corrected 2SLS estimators.
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  • Stanislav Anatolyev, 2013. "Instrumental variables estimation and inference in the presence of many exogenous regressors," Econometrics Journal, Royal Economic Society, vol. 16(1), pages 27-72, February.
    • Handle: RePEc:wly:emjrnl:v:16:y:2013:i:1:p:27-72
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    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models

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