INTRODUCTION

Suppose we have sample observations of characteristics of N individuals over T time periods denoted by yit, xkit, i = 1, …, N, t = 1, …, T, k = 1, …, K. Conventionally, observations of y are assumed to be the random outcomes of some experiment with a probability distribution conditional on vectors of the characteristics x and a fixed number of parameters θ, f(y ∣ x, θ). When panel data are used, one of the ultimate goals is to use all available information to make inferences on θ. For instance, a simple model commonly postulated is that y is a linear function of x. Yet to run a least-squares regression with all NT observations, we need to assume that the regression parameters take values common to all cross-sectional units for all time periods. If this assumption is not valid, as shown in Section 1.2, the pooled least-squares estimates may lead to false inferences. Thus, as a first step toward full exploitation of the data, we often test whether or not parameters characterizing the random outcome variable y stay constant across all i and t.

A widely used procedure to identify the source of sample variation is the analysis-of-covariance test. The name “analysis of variance” is often reserved for a particular category of linear hypotheses that stipulate that the expected value of a random variable y depends only on the class (defined by one or more factors) to which the individual considered belongs, but excludes tests relating to regressions.