have greater influence in the estimate obtained A common specification is that the variance is proportional to one of the regressors or its square. If then the transformed regression model for the gls is y=B:+B1 B2 If the variance is proportional to k instead of zk, then the weight applied to each observations is 1/vEk instead of 1/k 4 Estimation when o contains unknown pa rameters The general form of the heteroscedastic regression model has too many parameters to estimate by ordinary method. Typically, the model is restricted by formulat- ing a292 as a function of a few parameters, such as a?=aag or a2=o2[]2 Write this as R(a), FGLS based on a consistent estimator of R (a)is asymptot ally equivalent to gLs. The new problem is that we must first find consistent estimators of the unknown parameters in Q(a). Two methods are typically used, two step GLs and maximum likelihood 4.1 Two-Step Estimation For the heteroscedastic model. the GLS estimator is i=1 The two step estimators are computed by first obtaining estimators of, usually using some function of the Ols residuals. then the Fgls will be i=1 a2have greater influence in the estimate obtained. A common specification is that the variance is proportional to one of the regressors or its square. If σ 2 i = σ 2x 2 ik, then the transformed regression model for the GLS is y xk = βk + β1  x1 xk  + β2  x2 xk  + ... + ε xk . If the variance is proportional to xk instead of x 2 k , then the weight applied to each observations is 1/ √ xk instead of 1/xk. 4 Estimation When Ω Contains Unknown Pa￾rameters The general form of the heteroscedastic regression model has too many parameters to estimate by ordinary method. Typically, the model is restricted by formulat￾ing σ 2Ω as a function of a few parameters, such as σ 2 i = σ 2x α i or σ 2 i = σ 2 [x 0 iα] 2 . Write this as Ω(α), FGLS based on a consistent estimator of Ω(α) is asymptot￾ically equivalent to GLS. The new problem is that we must first find consistent estimators of the unknown parameters in Ω(α). Two methods are typically used, two step GLS and maximum likelihood. 4.1 Two-Step Estimation For the heteroscedastic model, the GLS estimator is β˜ = "X N i=1  1 σ 2 i  xix 0 i #−1 "X N i=1  1 σ 2 i  xiyi # . The two step estimators are computed by first obtaining estimators σˆ 2 i , usually using some function of the OLS residuals, then the FGLS will be βˇ = "X N i=1  1 σˆ 2 i  xix 0 i #−1 "X N i=1  1 σˆ 2 i  xiyi # . 6