Chapters 1 through 11 discussed basic econometric analysis using SAS. This chapter introduces additional analytical methods within the context of what was covered in the previous chapters.
12.1 ITERATIVE FGLS ESTIMATION UNDER HETEROSCEDASTICITY
In Section 5.6, we introduced FGLS estimation where we assumed that the variance of the disturbances is a function of one or more explanatory variables. For example, we assumed that , where zi = income. The estimation was done over two steps, where in step 1, the OLS residuals were used in a regression with log(zi) to get an estimate of α. The weights using α were calculated resulting in the two-step FGLS estimator.
We can very easily iterate the two-step estimation process to convergence. The method involves recomputing the residuals using the first set of FGLS estimators and then using these residuals to recompute the FGLS estimates. The iteration continues until the difference between the most recent FGLS estimates does not differ from the estimates computed in the previous stage. Program 9 in Appendix E gives IML code to carry out these computations on the credit card data set, which was used in Chapter 5 with zi = income. The analysis results are given in Output 12.1. As discussed in Greene (2003), the asymptotic properties of the iterated FGLS are similar to those of the FGLS.