Synthetic Controls for Experimental Design

TL;DR

This paper explores the use of synthetic control methods for experimental design involving large aggregate units, demonstrating their ability to reduce bias compared to randomization.

Contribution

It introduces synthetic control-based experimental designs for aggregate units, analyzing their properties and proposing new inferential techniques.

Findings

Synthetic control designs reduce bias in experimental settings with aggregate units.

They outperform randomization in terms of bias reduction.

New inferential methods improve the reliability of estimates.

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.