Random Coefficients Models
Random coefficients models (RCM) are models in which the regression coefficients are random variables, the means, variances, and covariances of which are unknown parameters to estimate. The Hildreth and Houck model, which we discussed in Section 6.5.4, is a special case of RCM. The error components models, which we discussed in Section 6.6, are also special cases of RCM. We shall discuss models for panel data in which the regression coefficients contain individual-specific and time-specific components that are independent across individuals and over time periods. We shall discuss in succession models proposed by Kelejian and Stephan (1983), Hsiao (1974,1975), Swamy (1970), and Swamy and Mehta (1977). In the last subsection we shall mention several other related models, including so-called varying parameter regression models in which the time-specific component evolves with time according to some dynamic process. As RCM have not been applied as extensively as ECM, we shall devote less space to this section than to the last.