The Precision of Instrumental Variables Estimates With Grouped Data

This paper is an examination of a potential problem inherent in instrumental variables estimation in samples drawn from populations with a grouped structure. When data used in a regression model are drawn from such a population, the regression errors may not satisfy the assumption that they not be correlated. While the consequences of this correlation have been recognized previously in the context of ordinary least squares estimation where the values of the exogenous variables do not vary within group, little attention has been paid to the consequences of such correlation for instrumental variables estimation. In this paper I examine the consequences of intra-group correlation for instrumental variables estimation where the instruments (rather than the exogenous variables) have repeated values within groups. I first briefly summarize analytical results which demonstrate that ignoring the problem of the grouped structure will yield estimated standard errors which are understated. While the magnitude of the understatement depends on the size of the within-group variance relative to the total variance, even small amounts of within-group correlation result in understatement. I then perform simulations using different magnitudes of within-group correlation and various sample sizes and calculate the standard errors with and without accounting for the correlation. I find that with a data set comparable in size to many cross-sectional data sets used by empirical economists. even within-group variance only one-tenth the size of the total variance yields estimated standard errors that are as much as eight times too small relative to the correctly estimated standard errors. Finally, I describe two methods for estimating standard errors which account for the within-group correlation.