Behavior of estimators as the number of periods and cohorts grows

Ascertain how the proposed estimators for the counterfactual distribution and derived quantile treatment effects behave as the number of time periods T (and the number of treatment cohorts R) increases, particularly when per-cohort sample sizes become small.

Background

The paper evaluates finite-sample performance of the proposed nonparametric estimators via Monte Carlo experiments and notes theoretical expectations for good performance when the sample size is large relative to the number of periods and cohorts. However, the implications when the number of periods (and, consequently, cohorts) grows are not theoretically characterized.

This uncertainty is practically important because increasing T can fragment the sample across many cohorts, reducing per-cohort sample sizes and potentially affecting estimator bias, variance, and inference.