A General Design-Based Framework and Estimator for Randomized Experiments
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.
Cite
@article{arxiv.2210.08698,
title = {A General Design-Based Framework and Estimator for Randomized Experiments},
author = {Christopher Harshaw and Fredrik Sävje and Yitan Wang},
journal= {arXiv preprint arXiv:2210.08698},
year = {2025}
}