期刊
JOURNAL OF ECONOMETRICS
卷 190, 期 2, 页码 212-221出版社
ELSEVIER SCIENCE SA
DOI: 10.1016/j.jeconom.2015.06.004
关键词
Weak instruments; Multiple endogenous variables; F-test
资金
- Economic and Social Research Council [RES-343-28-0001]
- European Research Council [DEVHEALTH-269874]
- Medical Research Council [MC_UU_12013/9]
- ESRC [ES/H005331/1] Funding Source: UKRI
- MRC [MC_UU_12013/9] Funding Source: UKRI
- Economic and Social Research Council [RES-343-28-3001] Funding Source: researchfish
- Medical Research Council [MC_UU_12013/9] Funding Source: researchfish
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 pi(1) = delta pi(2) + c/root n where pi(1) and pi(2) 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 delta = 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 H-0 : pi(1) = delta pi(2). 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 delta = 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. (C) 2015 Elsevier B.V. All rights reserved.
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