Random coefficients in regression equation systems: The case with unbalanced panel data

We consider a framework for analyzing panel data characterized by: (i) a system of regressions equations, (ii) random individual heterogeneity in both intercepts and slope coefficients, and (iii) unbalanced panel data, i.e., panel data where the individual time series have unequal length. A Maximum Likelihood (ML) procedure for joint estimation of all parameters is described. Since it is complicated to implement in numerical calculations, we consider simplified procedures, in particular for estimating the covariance matrices of the random coefficients. An algorithm for modified ML estimation of all parameters is presented.