Static Panel Data Models1 Class Notes

A sizeable part of econometric activity deals with empirical description and forecasting, but another aims at quantifying structural or causal relationships. Structural relations are needed for policy evaluation and for testing theories. The regression model is an essential tool for descriptive and structural econometrics. However, regression lines from economic data often cannot be given a causal interpretation. The reason is that sometimes we expect correlation between explanatory variables and errors in the relation of interest. One example is the classical supply-and-demand simultaneity problem due market equilibrium. Another is measurement error: if the explanatory variable we observe is not the variable to whom agents respond but an error ridden measure of it, the unobservable term in the equation of interest will contain the measurement error, which will be correlated with the regressor. Finally, there may be correlation due to unobserved heterogeneity. This has been a pervasive problem in cross-sectional regression analysis. If characteristics that have a direct effect on both leftand right-hand side variables are omitted, explanatory variables will be correlated with errors and regression coefficients will be biased measures of the structural effects. Thus, researchers have often been confronted with massive cross-sectional data sets from which precise correlations can be determined but that, nevertheless, had no information about parameters of policy interest. This is an abridged version of Part I in Arellano (2003).