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Robust Inference Methods for Latent Group Panel Models under Possible Group Non-Separation

This paper presents 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, deriving the conditional distribution of coefficient estimates given the group structure estimated from the data. Our procedure provides valid inference under possible violations of group separation, where distributional properties of group-specific coefficients remain unestablished. Furthermore, even when group separation does hold, our method demonstrates superior finite-sample properties compared to traditional asymptotic approaches. This improvement stems from our procedure's ability to account for statistical uncertainty in the estimation of group structure. We demonstrate the effectiveness of our approach through Monte Carlo simulations and apply the methods to two datasets on: (i) the relationship between income and democracy, and (ii) the cyclicality of firm-level R&D investment.

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