More Topics in Linear Unobserved E¤ects Models This chapter continues our treatment of linear, unobserved e¤ects panel data models. We first cover estimation of models where the strict exogeneity Assumption fails but sequential moment conditions hold. A simple approach to consistent estimation involves differencing combined with instrumental variables methods. | More Topics in Linear Unobserved Effects Models This chapter continues our treatment of linear unobserved effects panel data models. We first cover estimation of models where the strict exogeneity Assumption fails but sequential moment conditions hold. A simple approach to consistent estimation involves differencing combined with instrumental variables methods. We also cover models with individual slopes where unobservables can interact with explanatory variables and models where some of the explanatory variables are assumed to be orthogonal to the unobserved effect while others are not. The final section in this chapter briefly covers some non-panel-data settings where unobserved effects models and panel data estimation methods can be used. Unobserved Effects Models without the Strict Exogeneity Assumption Models under Sequential Moment Restrictions In Chapter 10 all the estimation methods we studied assumed that the explanatory variables were strictly exogenous conditional on an unobserved effect in the case of fixed effects and first differencing . As we saw in the examples in Section strict exogeneity rules out certain kinds of feedback from yit to future values of xit. Generally random effects fixed effects and first differencing are inconsistent if an explanatory variable in some time period is correlated with uit. While the size of the inconsistency might be small something we will investigate further in other cases it can be substantial. Therefore we should have general ways of obtaining consistent estimators as N co with T fixed when the explanatory variables are not strictly exogenous. The model of interest can still be written as yit Xitb Ci Uit t 1 2 . T but in addition to allowing ci and xit to be arbitrarily correlated we now allow uit to be correlated with future values of the explanatory variables xi t 1 xi t 2 . xiT . We saw in Example that uit and xitt 1 must be correlated because xitt 1 yit. Nevertheless there .
