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A Weak Instrument F-Test in Linear IV Models with Multiple Endogenous Variables

Eleanor Sanderson and Frank Windmeijer

Bristol Economics Discussion Papers from School of Economics, University of Bristol, UK

Abstract: We consider testing for weak instruments in a model with multiple endogenous variables. Unlike Stock and Yogo (2005), who considered a weak instruments problem where the rank of the matrix of reduced form parameters is near zero, here we consider a weak instruments problem of a near rank reduction of one in the matrix of reduced form parameters. For example, in a two-variable model, we consider weak instrument asymptotics of the form π1=δπ2 + c/sqrt(n) where π1 and π2 are the parameters in the two reduced-form equations, c is a vector of constants and n is the sample size. We investigate the use of a conditional first-stage F-statistic along the lines of the proposal by Angrist and Pischke (2009) and show that, unless δ=0, the variance in the denominator of their F-statistic needs to be adjusted in order to get a correct asymptotic distribution when testing the hypothesis H0: π1=δπ2. We show that a corrected conditional F-statistic is equivalent to the Cragg and Donald (1993) minimum eigenvalue rank test statistic, and is informative about the maximum total relative bias of the 2SLS estimator and the Wald tests size distortions. When δ=0 in the two-variable model, or when there are more than two endogenous variables, further information over and above the Cragg-Donald statistic can be obtained about the nature of the weak instrument problem by computing the conditional first stage F-statistics.

Keywords: weak instruments; multiple endogenous variables; F-test. (search for similar items in EconPapers)
JEL-codes: C12 C36 (search for similar items in EconPapers)
Pages: 29 pages
Date: 2014-06-30, Revised 2015-05-27
New Economics Papers: this item is included in nep-ecm
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Citations: View citations in EconPapers (28)

Forthcoming in Journal of Econometrics.

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Related works:
Journal Article: A weak instrument F-test in linear IV models with multiple endogenous variables (2016) Downloads
Working Paper: A weak instrument F-test in linear IV models with multiple endogenous variables (2015) Downloads
Working Paper: A weak instrument F-test in linear IV models with multiple endogenous variables (2015) Downloads
Working Paper: A weak instrument F-test in linear IV models with multiple endogenous variables (2013) Downloads
Working Paper: A Weak Instrument F-Test in Linear IV Models with Multiple Endogenous Variables (2013) Downloads
Working Paper: A weak instrument F-test in linear IV models with multiple endogenous variables (2013) Downloads
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