Basic Linear Unobserved E¤ects Panel Data Models In Chapter 7 we covered a class of linear panel data models where, at a minimum, the error in each time period was assumed to be uncorrelated with the explanatory variables in the same time period. For certain panel data applications this assumption is too strong. | Basic Linear Unobserved Effects Panel Data Models In Chapter 7 we covered a class of linear panel data models where at a minimum the error in each time period was assumed to be uncorrelated with the explanatory variables in the same time period. For certain panel data applications this assumption is too strong. In fact a primary motivation for using panel data is to solve the omitted variables problem. In this chapter we study population models that explicitly contain a time-constant unobserved effect. The treatment in this chapter is modern in the sense that unobserved effects are treated as random variables drawn from the population along with the observed explained and explanatory variables as opposed to parameters to be estimated. In this framework the key issue is whether the unobserved effect is uncorrelated with the explanatory variables. Motivation The Omitted Variables Problem It is easy to see how panel data can be used at least under certain assumptions to obtain consistent estimators in the presence of omitted variables. Let y and x x1 x2 . xK be observable random variables and let c be an unobservable random variable the vector y x1 x2 . xK c represents the population of interest. As is often the case in applied econometrics we are interested in the partial effects of the observable explanatory variables xj in the population regression function E y xi X2 . xk c In words we would like to hold c constant when obtaining partial effects of the observable explanatory variables. We follow Chamberlain 1984 in using c to denote the unobserved variable. Much of the panel data literature uses a Greek letter such as a or f but we want to emphasize that the unobservable is a random variable not a parameter to be estimated. We discuss this point further in Section . Assuming a linear model with c entering additively along with the xj we have E y x c bo xfi c where interest lies in the K x 1 vector p. On the one hand if c is uncorrelated with .
