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

Pedro Picchetti

Abstract

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.

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

Abstract

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.
Paper Structure (14 sections, 10 theorems, 104 equations, 5 tables)

This paper contains 14 sections, 10 theorems, 104 equations, 5 tables.

Table of Contents

  1. Introduction
  2. Factorial Designs
  3. Framework and Target Parameters
  4. Identification
  5. Estimation and Inference
  6. Panel Experiments
  7. Framework and Assumptions
  8. Identification
  9. Estimation and Inference
  10. Monte Carlo Simulations
  11. Factorial Designs
  12. Panel Experiments
  13. Application - GOTV Experiment
  14. Conclusion

Key Result

Theorem 1

Under Assumptions 1-5, and for any $\textbf{d}\in\left\{0,1\right\}^{p+1}$.

Theorems & Definitions (10)

  • Theorem 1
  • Theorem 2
  • Theorem 3
  • Theorem 4
  • Theorem 5
  • Theorem 6
  • Lemma 1
  • Lemma 2
  • Lemma 3
  • Lemma 4