A General Design-Based Framework and Estimator for Randomized Experiments

TL;DR

This paper introduces a flexible design-based framework for causal inference in randomized experiments, enabling analysis of complex causal questions including interference, with new estimators and variance methods.

Contribution

It presents a novel, expressive framework for causal inference that handles interference and other complex scenarios, along with new estimators and variance estimation techniques.

Findings

Framework accommodates interference and complex causal questions

Provides conditions for unbiasedness and consistency of estimators

Includes conservative variance estimators for confidence intervals

Abstract

We describe a design-based framework for drawing causal inference in general randomized experiments. Causal effects are defined as linear functionals evaluated at unit-level potential outcome functions. Assumptions about the potential outcome functions are encoded as function spaces. This makes the framework expressive, allowing experimenters to formulate and investigate a wide range of causal questions, including about interference, that previously could not be investigated with design-based methods. We describe a class of estimators for estimands defined using the framework and investigate their properties. We provide necessary and sufficient conditions for unbiasedness and consistency. We also describe a class of conservative variance estimators, which facilitate the construction of confidence intervals. Finally, we provide several examples of empirical settings that previously could not be examined with design-based methods to illustrate the use of our approach in practice.