Inference with Weak Instruments
Donald W. K. Andrews, James H. Stock · Cambridge University Press eBooks · 2010
: The standard approach to reporting empirical results in economics is to provide point estimates and standard errors. With this information, confidence intervals (CIs) and tests are constructed using t tests and the normal critical values. In instrumental variables (IVs) regression with weak IVs, this approach is problematic. The most widely used estimator, two-stage least squares (2SLS), has significant bias and is poorly approximated by a normal distribution when IVs are weak and the degree of endogeneity is medium to strong. In fact, when the parameter space allows for arbitrarily weak IVs the exact finite-sample level of standard CIs of the form “estimate ± std error × constant” is zero and t tests have level one. This paper reviews recent results in the literature on weak IVs that develop an alternative approach to inference with weak IVs. With this approach, one reports point estimates accompanied by CIs or tests that have levels that are robust to the strength of the IVs. In particular, CIs are formed by inverting tests that are robust to weak IVs. That is, a CI for a parameter β, say, is the set of points β 0 for which a weak IV robust test fails to reject the null hypothesis H 0 : β = β 0 . This is the same method that is used to generate a CI of the form “estimate ± std error × constant” except that the test employed is one whose level is robust to weak IVs, rather than a t test based on a normal approximation.