tailieunhanh - Book Econometric Analysis of Cross Section and Panel Data By Wooldridge - Chapter 7

Estimating Systems of Equations by OLS and GLS Introduction This chapter begins our analysis of linear systems of equations. The first method of estimation we cover is system ordinary least squares, which is a direct extension of OLS for single equations. In some important special cases the system OLS estimator turns out to have a straightforward | Estimating Systems of Equations by OLS and GLS Introduction This chapter begins our analysis of linear systems of equations. The first method of estimation we cover is system ordinary least squares which is a direct extension of OLS for single equations. In some important special cases the system OLS estimator turns out to have a straightforward interpretation in terms of single-equation OLS estimators. But the method is applicable to very general linear systems of equations. We then turn to a generalized least squares GLS analysis. Under certain assumptions GLS or its operationalized version feasible GLS will turn out to be asymptotically more efficient than system OLS. However we emphasize in this chapter that the efficiency of GLS comes at a price it requires stronger assumptions than system OLS in order to be consistent. This is a practically important point that is often overlooked in traditional treatments of linear systems particularly those which assume that explanatory variables are nonrandom. As with our single-equation analysis we assume that a random sample is available from the population. Usually the unit of observation is obvious such as a worker a household a firm or a city. For example if we collect consumption data on various commodities for a sample of families the unit of observation is the family not a commodity . The framework of this chapter is general enough to apply to panel data models. Because the asymptotic analysis is done as the cross section dimension tends to infinity the results are explicitly for the case where the cross section dimension is large relative to the time series dimension. For example we may have observations on N firms over the same T time periods for each firm. Then we assume we have a random sample of firms that have data in each of the T years. The panel data model covered here while having many useful applications does not fully exploit the replicability over time. In Chapters 10 and 11 we explicitly consider