Synthetic Decomposition for Counterfactual Predictions

TL;DR

This paper introduces a novel method for counterfactual prediction using synthetic decomposition, leveraging data from source regions to improve predictions in a target region, especially when policies extend beyond existing support.

Contribution

It proposes a new transferability condition and a synthetic outcome-policy relationship to enhance counterfactual predictions across regions.

Findings

Develops a procedure for constructing confidence intervals for counterfactuals.

Applies method to predict teenage employment in Texas after policy change.

Proves asymptotic validity of the proposed confidence intervals.

Abstract

Counterfactual predictions are challenging when the policy variable goes beyond its pre-policy support. However, in many cases, information about the policy of interest is available from different ("source") regions where a similar policy has already been implemented. In this paper, we propose a novel method of using such data from source regions to predict a new policy in a target region. Instead of relying on extrapolation of a structural relationship using a parametric specification, we formulate a transferability condition and construct a synthetic outcome-policy relationship such that it is as close as possible to meeting the condition. The synthetic relationship weighs both the similarity in distributions of observables and in structural relationships. We develop a general procedure to construct asymptotic confidence intervals for counterfactual predictions and prove its asymptotic validity. We then apply our proposal to predict average teenage employment in Texas following a counterfactual increase in the minimum wage.