Yagan Hazard (Paris School of Economics)

Abstract. The evaluation of many policies of interest (e.g., educational and training programs) inevitably face incomplete treatment group take-up. Estimation of causal effects in these controlled or natural “experiments with imperfect compliance” usually relies on an Instrumental Variable (IV) strategy, which often yields imprecise and thus possibly uninformative inference when compliance rates are low. We tackle this problem by proposing a Test-and-Select estimator that exploits covariate information to restrict estimation to a subpopulation with non-zero compliance. We derive the asymptotic properties of our proposed estimator under standard and weak-IV-like asymptotics, and study its finite sample properties in Monte Carlo simulations. We provide conditions under which it dominates the usual 2SLS estimator in terms of precision. Under an assumption on the degree of treatment effect heterogeneity, our estimator remains first-order unbiased with respect to the Local Average Treatment Effect (LATE) estimand, setting it apart from alternatives in the burgeoning literature on the use of first-stage heterogeneity to improve the precision of IV estimators. This robustness to treatment effect heterogeneity and the potential for precision gains are illustrated using Monte Carlo simulations and two empirical applications. Applying this new estimation procedure to the returns to schooling example (where compulsory schooling laws serve as instruments for educational attainment), we document that our methodology reduces standard errors by 12% to 48% depending on specifications.