This paper considers the finite sample distribution of the 2SLS estimator and derives bounds on its exact bias in the presence of weak and/or many instruments. We then contrast the behavior of the exact bias expressions and the asymptotic expansions currently popular in the literature, including...

This paper estimates the impact of elite school attendance on long-run outcomes including completed education, income and fertility. Our data consists of individuals born in the 1950s and educated in a UK district that assigned students to either elite or non-elite secondary schools. Using...

This paper shows how a weighted average of a forward and reverse Jackknife IV estimator (JIVE) yields estimators that are robust against heteroscedasticity and many instruments. These estimators, called HFUL (Heteroscedasticity robust Fuller) and HLIM (Heteroskedasticity robust limited...

This paper estimates the impact of elite school attendance on long- run outcomes including completed education, income and fertility. Our data consists of individuals born in the 1950s and educated in a UK dis- trict that assigned students to either elite or non-elite secondary schools. Using...

Instrumental Variables (IV) methods identify internally valid causal effects for individuals whose treatment status is manipulable by the instrument at hand. Inference for other populations requires homogeneity assumptions. This paper outlines a theoretical framework that nests causal...

This paper analyzes conditions under which various single-equation estimators are asymptotically normal in a simultaneous equations framework with many weak instruments. In particular, our paper adds to the many instruments asymptotic normality literature, including papers by Morimune (1983),...

We examine instrumental variables estimation in situations where the instrument is only observed for a sub-sample, which is fairly common in empirical research. Typically, researchers simply limit the analysis to the sub-sample where the instrument is non-missing. We show that when the...

Many empirical studies specify outcomes as a linear function of endogenous regressors when conducting instrumental variable (IV) estimation. We show that tests for treatment effects, selection bias, and treatment effect heterogeneity are biased if the true relationship is non-linear. These...

An emerging literature on the geography of bohemians argues that a region’s lifestyle and cultural amenities explain, at least partly, the unequal distribution of highly qualified people across space, which in turn, explains geographic disparities in economic growth. However, to date, there...

An emerging literature on the geography of bohemians argues that a region's lifestyle and cultural amenities explain, at least partly, the unequal distribution of highly qualified people across space, which in turn, explains geographic disparities in economic growth. However, to date, there has...