Conditional Selective Inference for the Selected Groups in Panel Data

TL;DR

This paper introduces a new selective inference method for testing differences in group-specific slopes in panel data after clustering, addressing the bias caused by using the same data for clustering and testing.

Contribution

It proposes a valid conditional inference approach that accounts for the selection process in clustering, extending to covariate differences and GMM frameworks.

Findings

Method shows good finite sample performance in simulations.

Applied to economic growth and CO2 emissions, revealing new insights.

Provides an R package for implementation.

Abstract

We consider the problem of testing for differences in group-specific slopes between the selected groups in panel data identified via k-means clustering. In this setting, the classical Wald-type test statistic is problematic because it produces an extremely inflated type I error probability. The underlying reason is that the same dataset is used to identify the group structure and construct the test statistic, simultaneously. This creates dependence between the selection and inference stages. To address this issue, we propose a valid selective inference approach conditional on the selection event to account for the selection effect. We formally define the selective type I error and describe how to efficiently compute the correct p-values for clusters obtained using k-means clustering. Furthermore, the same idea can be extended to test for differences in coefficients due to a single covariate and can be incorporated into the GMM estimation framework. Simulation studies show that our method has satisfactory finite sample performance. We apply this method to explore the heterogeneous relationships between economic growth and the $CO_2$ emission across countries for which some new findings are discovered. An R package TestHomoPanel is provided to implement the proposed selective inference framework for panel data.