Detection Boundaries for Panel Slope Homogeneity Tests Under Small-Group Heterogeneity

TL;DR

This paper analyzes the power of slope-homogeneity tests in panel data, especially when heterogeneity is confined to small groups, providing guidelines on their effectiveness under various conditions.

Contribution

It offers a theoretical characterization of when slope-homogeneity tests can detect small-group heterogeneity in panel data.

Findings

Power decreases as group size shrinks and deviations diminish.

Detectability depends on panel dimensions and deviation rates.

Monte Carlo simulations confirm theoretical results.

Abstract

Empirical researchers often use slope-homogeneity tests to assess whether slopes can be treated as common across units. A key difficulty is that heterogeneity may be concentrated in a small number of units, so that a failure to reject homogeneity may reflect limited power rather than true homogeneity. We quantify this issue by analyzing the power of standard slope-homogeneity tests under doubly local alternatives - alternatives in which only small groups of units depart from the common slope and the magnitude of the deviations shrinks with sample size. We characterize detectability as a function of panel dimensions, the size of the departing groups, and the rate at which deviations shrink. The results tell the researcher clearly when homogeneity tests are informative and when they will miss small-group heterogeneity. A Monte Carlo study confirms the theory.