Finite Population Inference for Factorial Designs and Panel Experiments with Imperfect Compliance

This paper develops a finite population framework for analyzing causal effects in settings with imperfect compliance where multiple treatments affect the outcome of interest. Two prominent examples are factorial designs and panel experiments with imperfect compliance. I define finite population causal effects that capture the relative effectiveness of alternative treatment sequences. I provide nonparametric estimators for a rich class of factorial and dynamic causal effects and derive their finite population distributions as the sample size increases. Monte Carlo simulations illustrate the desirable properties of the estimators. Finally, I use the estimator for causal effects in factorial designs to revisit a famous voter mobilization experiment that analyzes the effects of voting encouragement through phone calls on turnout.