Random Coefficients Models

Abstract

Consider a linear regression model of the form $$ y = \underline {\beta '} \underline x + u, $$ where y is the dependent variable and x is a K x 1 vector of explanatory variables.1 The variable u denotes the effects of all other variables that affect the outcome of y but are not explicitly included as independent variables. The standard assumption is that u behaves like a random variable and is uncorrelated with x. However, the emphasis of panel data is often on the individual units over time. In explaining human behaviour, the list of relevant factors may be extended ad infinitum. The effect of these factors that have not been explicitly allowed for may be individual specific and time varying. In fact, one of the crucial issues in panel data analysis is how the differences in behaviour across individuals and/or through time should be modeled.