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Panel Data Models Panel data: {ya,ru} i= T; ~ Advantage: Panel data allows us to construct and test more complicated and more re- alistic models than a single corss-section or a single time series would do ~ e.g., allows us to make inferences about the dynamics of change from cross-sectional evidence. ~ Important: exogenous determination of T;, i.c. why people drop out after a few years is unrelated with the phenomenon we are trying to explain (sample attrition bias) — Balanced Panel Data: if T; = T Yi: if T; differ: Unbalanced Panel Data. Our focus. will be on Balanced Panel Data for notational simplicity. — Typically, we will be concerned with situations where T is small and s large. — Disadvantage (practical): because we repeatedly observe the same units, it is usually no longer appropiate to assume that different observations are independent. Fur- thermore, panel data sets very often suffer from missing observations. Even if these: observations are missing in a random way, the standard analysis has to be adjusted Extensive discussion of the econometrics of panel data can be found in Hsiao (1986) and Baltagi (1995). The Static Linear Model In the panel data setting, we could specify a linear model as Yin = Cuba +6 where 3, measures the partial effects of xy, in period ¢ for unit i. This model is too general to be useful, and we put more structure on the coefficients. The standard assumption, used in many empirical cases, being that 4 is constant for all i and #, except — possibly - the intercept term: ya = ot a+ eu. This regression means that the effects of a change in x are the same for all units and all periods, but that the average level for unit i may be different from that for unit j. The a; thus capture the effects of those variables that are peculiar to the i-th individual and that are constant over time. 
