Estimating the Number of Components in Panel Data Finite Mixture Regression Models with an Application to Production Function Heterogeneity

This paper develops statistical methods for determining the number of components in panel data finite mixture regression models with regression errors independently distributed as normal or more flexible normal mixtures. We analyze the asymptotic properties of the likelihood ratio test (LRT) and information criteria (AIC and BIC) for model selection in both conditionally independent and dynamic panel settings. Unlike cross-sectional normal mixture models, we show that panel data structures eliminate higher-order degeneracy problems while retaining issues of unbounded likelihood and infinite Fisher information. Addressing these challenges, we derive the asymptotic null distribution of the LRT statistic as the maximum of random variables and develop a sequential testing procedure for consistent selection of the number of components. Our theoretical analysis also establishes the consistency of BIC and the inconsistency of AIC. Empirical application to Chilean manufacturing data reveals significant heterogeneity in production technology, with substantial variation in output elasticities of material inputs and factor-augmented technological processes within narrowly defined industries, indicating plant-specific variation in production functions beyond Hicks-neutral technological differences. These findings contrast sharply with the standard practice of assuming a homogeneous production function and highlight the necessity of accounting for unobserved plant heterogeneity in empirical production analysis.