Robust Inference Methods for Latent Group Panel Models under Possible Group Non-Separation
We develop robust inference methods for general linear hypotheses in linear panel data models with latent group structure in the coefficients. We employ a selective conditional inference approach based on the conditional distribution of coefficient estimates given the group structure estimated from the data. The resulting inference procedures remain valid even when group separation fails (i.e., when the distributional properties of the group-specific coefficients are not established) and, because they account for uncertainty in estimating the group structure, they also improve on conventional asymptotic procedures in finite samples when separation does hold. Our tests are exactly valid under Gaussian errors with known variances and asymptotically valid under general error distributions. Unlike much of the post-clustering inference literature, which focuses on testing group homogeneity, our framework accommodates arbitrary linear restrictions on the group-specific coefficients. Inverting the conditional tests yields selective confidence sets with valid coverage conditional on the estimated group structure. We illustrate the methods through Monte Carlo simulations and an application to growth convergence clubs. Simulations demonstrate accurate size control and good power in finite samples, including in the presence of serial correlation and cross-sectional dependence. The applications show sharp differences between the traditional inference methods and robust methods proposed in this paper, illustrating the importance of taking the estimated group structure into account.