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This paper develops the likelihood ratio-based test of the null hypothesis ofa M0-component model against an alternative of (M0 + 1)-component model in thenormal mixture panel regression by extending the Expectation-Maximization (EM)test of Chen and Li (2009a) and Kasahara and Shimotsu (2015) to the case ofpanel data. We show that, unlike the cross-sectional normal mixture, thefirst-order derivative of the density function for the variance parameter inthe panel normal mixture is linearly independent of its second-orderderivatives for the mean parameter. On the other hand, like the cross-sectionalnormal mixture, the likelihood ratio test statistic of the panel normal mixtureis unbounded. We consider the Penalized Maximum Likelihood Estimator to dealwith the unboundedness, where we obtain the data-driven penalty function viacomputational experiments. We derive the asymptotic distribution of thePenalized Likelihood Ratio Test (PLRT) and EM test statistics by expanding thelog-likelihood function up to five times for the reparameterized parameters.The simulation experiment indicates good finite sample performance of theproposed EM test. We apply our EM test to estimate the number of productiontechnology types for the finite mixture Cobb-Douglas production function modelstudied by Kasahara et al. (2022) used the panel data of the Japanese andChilean manufacturing firms. We find the evidence of heterogeneity inelasticities of output for intermediate goods, suggesting that productionfunction is heterogeneous across firms beyond their Hicks-neutral productivityterms.

Testing the Number of Components in Finite Mixture Normal Regression Model with Panel Data