Specification Testing in Models with Many Instruments

16 Pages Posted: 16 Aug 2009

See all articles by Stanislav Anatolyev

Stanislav Anatolyev

New Economic School; CERGE-EI

Nikolay Gospodinov

Federal Reserve Bank of Atlanta

Date Written: September 1, 2008

Abstract

This paper studies the asymptotic validity of the Anderson-Rubin (AR) test and the J test of overidentifying restrictions in linear models with many instruments. When the number of instruments increases at the same rate as the sample size, we establish that the conventional AR and J tests are asymptotically incorrect. Some versions of these tests, that are developed for situations with moderately many instruments, are also shown to be asymptotically invalid in this framework. We propose modifications of the AR and J tests that deliver asymptotically correct sizes. Importantly, the corrected tests are robust to the numerosity of the moment conditions in the sense that they are valid for both few and many instruments. The simulation results illustrate the excellent properties of the proposed tests.

Keywords: Instrumental variables, many instruments, Bekker's asymptotics, Anderson-Rubin test, test for overidentifying restrictions

JEL Classification: C12, C21

Suggested Citation

Anatolyev, Stanislav and Gospodinov, Nikolay, Specification Testing in Models with Many Instruments (September 1, 2008). Econometric Theory, Forthcoming. Available at SSRN: https://ssrn.com/abstract=1452689

Stanislav Anatolyev (Contact Author)

New Economic School ( email )

Skolkovskoe shosse, 45
Moscow, 121353
Russia

CERGE-EI ( email )

P.O. Box 882
7 Politickych veznu
Prague 1, 111 21
Czech Republic

Nikolay Gospodinov

Federal Reserve Bank of Atlanta ( email )

Atlanta, GA 30309
United States

HOME PAGE: https://www.frbatlanta.org/research/economists/gospodinov-nikolay.aspx?panel=1

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