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

Stanislav Anatolyev ()

No w0162, Working Papers from Center for Economic and Financial Research (CEFIR)

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, and the associated Hahn–Hausman test is not valid. 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 Hahn–Hausman and J tests based on the LIML and bias corrected 2SLS estimators.

Keywords: instrumental variables regression; many instruments; many exogenous regressors; 2SLS estimator; LIML estimator; bias correction; t test; J test; Anderson–Rubin test; Kleibergen test; Hahn–Hausman test (search for similar items in EconPapers)
JEL-codes: C12 C21 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-ecm
Date: 2011-03
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