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Testing for Weak Instruments in Linear IV Regression

Testing for Weak Instruments in Linear IV Regression August 2001 (This revision: February 2003) James H. Stock Department of Economics, Harvard University and the National Bureau of Economic Research and Motohiro Yogo* Department of Economics, Harvard University ABSTRACT Weak Instruments can produce biased IV estimators and hypothesis tests with large size distortions. But what, precisely, are weak Instruments , and how does one detect them in practice? This paper proposes quantitative definitions of weak Instruments based on the maximum IV estimator bias, or the maximum Wald test size distortion, when there are multiple endogenous regressors.

2. The IV Regression Model, the Proposed Test Statistic, and Weak Instrument Asymptotics 2.1. The IV Regression Model We consider the linear IV regression model (1.1) and (1.2), generalized to have n included endogenous regressors Y and K1 included exogenous regressors X: y = Yβ + Xγ + u, (2.1) Y = ZΠ + XΦ + V, (2.2)

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