Panel Data Analysis with Stata Part 1 Fixed Effects and Random Effects Models

The present work is a part of a larger study on panel data. Panel data or longitudinal data (the older terminology) refers to a data set containing observations on multiple phenomena over multiple time periods. Thus it has two dimensions: spatial (cross-sectional) and temporal (time series). The main advantage of panel data comes from its solution to the difficulties involved in interpreting the partial regression coefficients in the framework of a cross-section only or time series only multiple regression. Depending upon the assumptions about the error components of the panel data model, whether they are fixed or random, we have two types of models, fixed effects and random effects. In this paper we explain these models with regression results using a part of a data set from a famous study on investment theory by Yehuda Grunfeld (1958), who tried to analyse the effect of the (previous period) real value of the firm and the (previous period) real capital stock on real gross investment. We consider mainly three types of panel data analytic models: (1) constant coefficients (pooled regression) models, (2) fixed effects models, and (3) random effects models. The fixed effects model is discussed under two assumptions: (1) heterogeneous intercepts and homogeneous slope, and (2) heterogeneous intercepts and slopes. We discuss all the relevant statistical tests in the context of all these models.