Linear instrumental variable estimators, such as two-stage least squares (TSLS), are commonly interpreted as estimating non-negatively weighted averages of causal effects, referred to as local average treatment effects (LATEs). We examine whether the LATE interpretation actually applies to the types of TSLS specifications that are used in practice. We show that if the specification includes covariates—which most empirical work does—then the LATE interpretation does not apply in general. Instead, the TSLS estimator will, in general, reflect treatment effects for both compliers and always/never-takers, and some treatment effects for the always/never-takers will necessarily be negatively weighted. We show that the only specifications that have a LATE interpretation are “saturated” specifications that control for covariates non-parametrically, implying that such specifications are both sufficient and necessary for TSLS to have a LATE interpretation, at least without additional parametric assumptions. This result is concerning because, as we document, empirical researchers almost never control for covariates nonparametrically, and rarely discuss or justify parametric specifications of covariates. We apply our results to thirteen empirical studies and find strong evidence that the LATE interpretation of TSLS is far from accurate for the types of specifications actually used in practice. We offer concrete recommendations for practice motivated by our theoretical and empirical results.

Abstract: We study a size-contingent law in Norway that grants workers the right to board representation in firms with 30 or more employees. To analyze the impact of the law, we embed the regulation into an equilibrium model of the labor market. We show how to use behavioral responses to the regulation to identify (i) the direct effects of the policy on regulated firms and workers, (ii) the distortions from firms adjusting their size to avoid the regulation, and (iii) the equilibrium effects in the labor market. We evaluate these effects on both firms profit and production as well as worker compensation, including wages and non-wage amenities.

Empirical researchers often use instrumental variables (IVs) to estimate a local average treatment effect (LATE), which reflects causal effects for the instrument-specific compliers. The subpopulation of compliers is often small and may not represent the actual subpopulation of interest, raising concerns about the external validity of the LATE. We develop a systematic approach for assessing the generalizability of LATEs. The approach uses the marginal treatment effect representation to link LATEs directly to alternative target parameters. These parameters can be bounded under the usual nonparametric IV assumptions. We demonstrate how these bounds can be significantly tightened by using nonparametric shape restrictions derived from economic theory or by imposing parametric structure. We examine the external validity of LATEs in three applications in development and labor economics. In each one, we demonstrate how to transparently trade-off stronger assumptions for sharper conclusions. The results reveal examples in which LATEs appear to generalize, as well as other examples in which LATEs do not generalize. Our findings show how researchers can use the marginal treatment effect framework not only to interpret IV estimates, but also to discipline and assess claims about their external validity.

We study how firms trade off formal education and relevant work experience in hiring, combining a large-scale employer survey, an embedded survey experiment, and matched employer–employee registry data for more than 10,000 Norwegian firms.