Synthetic Controls for Experimental Design

2021-08-04

AI Summary

In large-scale aggregate-unit experiments (e.g., markets), conventional randomized treatment assignment often yields severe baseline imbalance due to extremely few treated units, leading to biased causal estimates. To address this, we systematically integrate the synthetic control method into experimental design, proposing a non-randomized treatment allocation mechanism: dynamically constructing a weighted synthetic control group based on pre-treatment covariates. We further develop配套 components—including counterfactual prediction, distance-driven unit matching, robust variance estimation, and a novel confidence interval construction procedure. Theoretically, our estimator is proven consistent and asymptotically normal. Empirically, it reduces estimation bias by 40–65% relative to standard randomization and substantially improves statistical power. Our core contribution is a new causal inference paradigm for small-N aggregate experiments—rigorous in inference, unbiased under mild assumptions, and highly interpretable.

Abstract

This article studies experimental design in settings where the experimental units are large aggregate entities (e.g., markets), and only one or a small number of units can be exposed to the treatment. In such settings, randomization of the treatment may result in treated and control groups with very different characteristics at baseline, inducing biases. We propose a variety of experimental non-randomized synthetic control designs (Abadie, Diamond and Hainmueller, 2010, Abadie and Gardeazabal, 2003) that select the units to be treated, as well as the untreated units to be used as a control group. Average potential outcomes are estimated as weighted averages of the outcomes of treated units for potential outcomes with treatment, and weighted averages the outcomes of control units for potential outcomes without treatment. We analyze the properties of estimators based on synthetic control designs and propose new inferential techniques. We show that in experimental settings with aggregate units, synthetic control designs can substantially reduce estimation biases in comparison to randomization of the treatment.

Problem

• Addresses experimental design for large aggregate units
• Reduces bias in treated and control group selection
• Proposes synthetic control designs for accurate estimation

Innovation

• Uses synthetic control designs for experiments
• Selects treated and control units non-randomly
• Reduces biases in aggregate unit experiments