Instrumental Variables in the Long Run

In the study of long-run economic growth, it is common to use historical or geographical variables as instruments for contemporary endogenous regressors. We study the interpretation of these conventional instrumental variable (IV) regressions in a general, yet simple, framework. Our aim is to estimate the long-run causal effect of changes in the endogenous explanatory variable. We find that conventional IV regressions generally cannot recover this parameter of interest. To estimate this parameter, therefore, we develop an augmented IV estimator that combines the conventional regression with a separate regression estimating the degree of persistence in the endogenous regressor. Importantly, our estimator can overcome a particular violation of the exclusion restriction that can arise when there is a time gap between the instrument and the endogenous explanatory variable. We apply our results to estimate the long-run effect of institutions on economic performance and the long-run effect of Protestantism on human capital accumulation. In both cases, we find economically significant long-run effects that are smaller than those in the existing literature, demonstrating that our results have important quantitative implications for the field of long-run economic growth. We also use our framework to examine related empirical techniques. We find that two prominent regression methodologies - using gravity-based instruments for trade and including ancestry-adjusted variables in linear regression models - have related issues of interpretation. In the latter case, this problem can be overcome by including both unadjusted and adjusted measures in the regression model