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Type: Journal article
Title: On bootstrap validity for specification tests with weak instruments
Author: Doko Tchatoka, F.
Citation: The Econometrics Journal, 2015; 18(1):137-146
Publisher: Wiley
Issue Date: 2015
ISSN: 1368-4221
Statement of
Firmin Doka Tchatoka
Abstract: We study the asymptotic validity of the bootstrap for Durbin–Wu–Hausman tests of exogeneity, with or without identification. We provide an analysis of the limiting distributions of the proposed bootstrap statistics under both the null hypothesis of exogeneity (size) and the alternative hypothesis of endogeneity (power).We show that when identification is strong, the bootstrap provides a high-order approximation of the null limiting distributions of the statistics and is consistent under the alternative hypothesis if the endogeneity parameter is fixed. However, the bootstrap only provides a first-order approximation when instruments are weak. Moreover, we provide the necessary and sufficient condition under which the proposed bootstrap tests exhibit power under (fixed) endogeneity and weak instruments. The latter condition may still hold over a wide range of cases as long as at least one instrument is relevant. Nevertheless, all bootstrap tests have low power when all instruments are irrelevant, a case of little interest in empirical work. We present a Monte Carlo experiment that confirms our theoretical findings.
Keywords: Bootstrap validity; Durbin–Wu–Hausman tests; Edgeworth expansion; exogeneity testing; weak instruments
Rights: © 2014 Royal Economic Society. Published by John Wiley & Sons Ltd, 9600 Garsington Road, Oxford OX4 2DQ, UK and 350 Main Street, Malden, MA, 02148, USA
RMID: 0030030969
DOI: 10.1111/ectj.12042
Appears in Collections:Economics publications

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