University of Washington - Department of Economics
This paper establishes a unifying principle for spurious inference in weakly identified models. The â€˜Zero Information Limit Conditionâ€™ (ZILC) requires that the precision of a parameter estimate go to zero as an identifying parameter approaches a critical value. If ZILC holds, standard errors will be understated. The â€˜weak instrumentâ€™ problem in IV/GMM is one example; others include ARMA and non-linear regression models. Surprisingly, the size of t-tests may be either too large or too small, depending on the correlation between reduced form coefficients in the common linear representation shared by ZILC models. Weak identification does not imply spurious inference if ZILC does not hold.