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

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  • Stanislav Anatolyev

    ()
    (New Economic School)

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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Bibliographic Info

Paper provided by Center for Economic and Financial Research (CEFIR) in its series Working Papers with number w0162.

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Length: 48 pages
Date of creation: Mar 2012
Date of revision:
Handle: RePEc:cfr:cefirw:w0162

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Keywords: instrumental variables regression; many instruments; many exogenous regressors; 2SLS estimator; LIML estimator; bias correction; t test; J test; Anderson–Rubin test; Kleibergen test;

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  1. Hasselt, Martijn van, 2010. "Many Instruments Asymptotic Approximations Under Nonnormal Error Distributions," Econometric Theory, Cambridge University Press, vol. 26(02), pages 633-645, April.
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Cited by:
  1. Michal Kolesár & Raj Chetty & John N. Friedman & Edward L. Glaeser & Guido W. Imbens, 2011. "Identification and Inference with Many Invalid Instruments," NBER Working Papers 17519, National Bureau of Economic Research, Inc.

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