Repeated sampling of different individuals but the same clusters to improve precision of difference-in-differences estimators: the DISC design

TL;DR

The DISC design is a sampling approach that improves the precision of difference-in-differences estimators by sampling different individuals within the same clusters over time, offering a practical alternative to cohort designs.

Contribution

This paper introduces the DISC sampling scheme, combining elements of cohort and repeated cross-sectional designs to enhance estimator precision in DID analyses.

Findings

DISC design yields higher precision than RCS in DID estimators.

Variance reduction is more significant with higher intraclass correlation.

Sample size and ICC influence the efficiency gains of DISC over RCS.

Abstract

We describe the DISC (Different Individuals, Same Clusters) design, a sampling scheme that can improve the precision of difference-in-differences (DID) estimators in settings involving repeated sampling of a population at multiple time points. Although cohort designs typically lead to more efficient DID estimators relative to repeated cross-sectional (RCS) designs, they are often impractical in practice due to high rates of loss-to-follow-up, individuals leaving the risk set, or other reasons. The DISC design represents a hybrid between a cohort sampling design and a RCS sampling design, an alternative strategy in which the researcher takes a single sample of clusters, but then takes different cross-sectional samples of individuals within each cluster at two or more time points. We show that the DISC design can yield DID estimators with much higher precision relative to a RCS design, particularly if random cluster effects are present in the data-generating mechanism. For example, for a design in which 40 clusters and 25 individuals per cluster are sampled (for a total sample size of n=1,000), the variance of a commonly-used DID treatment effect estimator is 2.3 times higher in the RCS design for an intraclass correlation coefficient (ICC) of 0.05, 3.8 times higher for an ICC of 0.1, and 7.3 times higher for an ICC of 0.2.