More Results on the Exact Small Sample Properties of the Instrumental Variable Estimator - Woglom, Geoffrey (Econometrica, 2001)
generous referee; remaining errors are my own. The exact finite sample distribution for the two-stage least square estimator has been derived for quite general situations (see Phillips (1983) for a survey of the literature). Unfortunately, these general expressions do not lend themselves to easy interpretations. Consequently, a number of authors have looked at special cases to illustrate some of the problems that can arise when using asymptotic distribution results for finite samples. Two such special cases of note are: 1) The totally unidentified case, where the population covariance between the instruments and the endogenous variable is zero; 2) The very weakly correlated case (first stage R2 much less than the inverse of the sample size) with one equation and one endogenous regressor. Nelson and Startz ’ (1990a&b) pioneered the study of the very weakly correlated case. Their work dramatized the substantial differences that can arise between the exact distribution of the IV estimator and the asymptotic distribution. They argue that: 1) the IV estimate will be concentrated around a value more biased than the plim of the OLS estimate and the ratio of the two biases falls as the correlation between the endogenous variable and