Test of Hypotheses with Panel Data

The question of whether to pool the data or not naturally arises with panel data. The restricted model is the pooled model given by (2.3) representing a behavioral equation with the same parameters over time and across regions. The unrestricted model, however, is the same behavioral equation but with different parameters across time or across regions. For example, Cornwell and Rupert (1988) estimate a mincer wage equation based on a panel of 595 individuals drawn from the Panel Study of Income Dynamics (PSID) and observed over the period 1976–82. In this case, the question of whether to pool or not boils down to the question of whether the parameters of this mincer wage equation vary from one year to the other over the seven years of available data. One can have a behavioral equation whose parameters may vary across countries. For example, Baltagi and Griffin (1983) considered panel data on motor gasoline demand for 18 OECD countries. In this case, one is interested in testing whether the behavioral relationship predicting demand is the same across the 18 OECD countries, i.e., the parameters of the prediction equation do not vary from one country to the other.