If we focus only on consistency, it is necessarily better to use IV than OLS if the correlation between z and u is smaller than that between x and u.

Question

Quizplus · Accepted Answer

Consistency of an estimator depends on whether it targets the true parameter as the sample size increases, not directly on the correlation between instruments or explanatory variables and the error term. IV (Instrumental Variables) is used over OLS (Ordinary Least Squares) when there is endogeneity in the explanatory variables (x correlated with u), by finding instruments (z) that are correlated with x but uncorrelated with u. The comparison of correlation sizes between z and u and x and u does not directly determine the superiority of IV over OLS in terms of consistency; it's the endogeneity issue and the instrument's validity that matter.

If We Focus Only on Consistency, It Is Necessarily Better