Synthetic Difference in Differences for Repeated Cross-Sectional Data

TL;DR

This paper adapts the synthetic difference-in-differences method for repeated cross-sectional data, improving causal effect estimation by incorporating a new weighting scheme that accounts for varying group sizes.

Contribution

It introduces a novel weighting approach for synthetic difference-in-differences in repeated cross-sectional data, enhancing estimator performance.

Findings

Improved estimator performance with the new weighting scheme.

Simulation results demonstrate better accuracy in causal effect estimation.

Method effectively handles varying group sizes in data.

Abstract

The synthetic difference-in-differences method provides an efficient method to estimate a causal effect with a latent factor model. However, it relies on the use of panel data. This paper presents an adaptation of the synthetic difference-in-differences method for repeated cross-sectional data. The treatment is considered to be at the group level so that it is possible to aggregate data by group to compute the two types of synthetic difference-in-differences weights on these aggregated data. Then, I develop and compute a third type of weight that accounts for the different number of observations in each cross-section. Simulation results show that the performance of the synthetic difference-in-differences estimator is improved when using the third type of weights on repeated cross-sectional data.