Geodesic Synthetic Control Methods for Random Objects and Functional Data

TL;DR

This paper develops a novel causal inference method extending synthetic control techniques to outcomes in geodesic metric spaces, enabling analysis of complex data types like distributions, networks, and functional data.

Contribution

It introduces a geodesic synthetic control and difference-in-differences method that generalizes existing approaches to non-Euclidean data with a double robustness property.

Findings

Effectively applied to real-world data such as employment changes post-earthquake.

Analyzed fertility patterns following abortion policy changes in East Germany.

Studied demographic impacts of the Soviet Union's collapse.

Abstract

We introduce a geodesic synthetic control method for causal inference that extends existing synthetic control methods to scenarios where outcomes are elements in a geodesic metric space rather than scalars. Examples of such outcomes include distributions, compositions, networks, trees and functional data, among other data types that can be viewed as elements of a geodesic metric space given a suitable metric. We extend this further to geodesic synthetic difference-in-differences that builds on the established synthetic difference-in-differences for Euclidean outcomes. This estimator generalizes both the geodesic synthetic control method and a previously proposed geodesic difference-in-differences method and exhibits a double robustness property. The proposed geodesic synthetic control method is illustrated through comprehensive simulation studies and applications to the employment composition changes following the 2011 Great East Japan Earthquake, and the impact of abortion liberalization policy on fertility patterns in East Germany. We illustrate the proposed geodesic synthetic difference-in-differences by studying the consequences of the Soviet Union's collapse on age-at-death distributions for males and females.