Regression Systems with Random Coefficients: Estimation Procedures for the Unbalanced Panel Data Case

A framework for analyzing panel data characterized by a system of regression equations with random heterogeneity in intercepts and coefficients and unbalanced panel data is considered. A Maximum Likelihood (ML) procedure for joint estimation of all parameters is described. Since its implementation in numerical calculations is complicated, simplified procedures are presented. The simplifications in particular concern the estimation of the covariance matrices of the random coefficients. The application and ‘anatomy’ of the proposed algorithm for modified ML estimation is illustrated by using panel data for output, inputs and costs for 111 manufacturing firms observed up to 22 years.