The Cure Can Be Worse than the Disease: A Cautionary Tale Regarding Instrumental Variables

Abstract

In this paper we draw attention to two problems associated with the use of instrumental variables (IV) whose importance for empirical work has not been fully appreciated. First, using potential instruments that explain little of the variation in the: endogenous explanatory variables can lead to large inconsistencies of the IV estimates even If only a weal< relationship exists between the Instruments and the error in the structural equation. Second. In finite samples. IV estimates are biased in the same direction as ordinary least squares (OLS) estimates. The magnitude of the bias of IV estimates approaches that of OLS estimates as the R[squared] between the instruments and the potentially endogenous explanatory variable approaches O. To illustrate these problems with IV estimation we reexamine the results of the recent provocative paper by Angrist and Krueger "Does Compulsory School Attendance Affect Schooling and Earnings?" and find evidence that their IV estimates of the effects of educational attainment on earnings are possibly both inconsistent and suffer from finite sample bias. To gauge the severity of both problems we suggest that both the partial R[squared] and the F statistic on the excluded instruments from the first stage estimation be reported when using IV as approximate guides to the quality of the IV estimates.