feasible GLS

[fboehlandt]

Hi everyone,
I have a pretty straight-forward question regarding weighted least squares: I would like to do feasible GLS where heteroskedasticity is modelled as follows:
Var(u|x)=sigma^2*exp(delta0+delta1x1+delta2x2+...+deltakxk)
where x1, x2, ... , xk denote the independent variables in the model. I noticed that there is no option for feasible GLS in the stimation dialogue. Thus, I estimated the weighting function h first and then used it in the weighted regression. I'm just wondering if there is a shortcut for feasible GLS using the common model for heteroskedasticity above (I like to avoid running dummy regressions). Thanks for your reply

[fboehlandt]

This is not in direct response to the above question but it does refer to feasable GLS Estimation with AR(1) Errors. I have come across posts enquiring about Cochrane-Orcutt (CO) or Prais-Winston (PW) estimation. The following code should do the trick. Here the underlying assumpions:
1. serial correlation with strictly exogenous errors
2. no lagged dependent variables
The timeseries should be renamed as follows if you do not want to make changes to the code:
1. all independent variables should be grouped in 'xs' (without an intercept dummy)
2. the dependent variable should be renamed 'y'

And here the code for PW:

Code: Select all

group xsp 'Run OLS y c xs equation e1.ls y c xs e1.makeresid resid_ols 'Run OLS residuals c residuals(-1) equation e2.ls resid_ols c resid_ols(-1) !p = e2.@coefs(2) 'removing serial correlation form y and xs %c = "x0" smpl @all series {%c} = 1 xs.add {%c} for !i = 1 to xs.@count %xname = xs.@seriesname(!i) %newx = "p" + %xname %yp = "yp" series {%newx} = {%xname} series {%yp} = y smpl @first @first '<-- CO {%newx} = {%xname}*(1 - !p^2)^(1/2) '<-- CO {%yp} =y*(1 - !p^2)^(1/2) '<-- CO smpl @first+1 @last {%newx} = {%xname} - !p*{%newx}(-1) '<--CO replace: '{%newx} = {%xname} - !p*{%xname}(-1) {%yp} = y - !p*{%yp}(-1) "<--CO replace: {%yp} = y - !p*y(-1) xsp.add {%newx} next 'Run OLS yp xsp (intercept in xsp) equation e3.ls yp xsp xs.drop {%c} smpl @all

e3 contains the final results and coefficient estimates. The autocorrelation coefficient p can be found as slope coefficient in e2. If you prefer to use CO you may delete/edit the lines marked '<-- CO. Note that this will result in one less observation in estimation. Lastly, consider that both PW and CO do not account for heteroscedasticity and consider AR(1) errors only. Thus, I recommend consulting the forum for more up-to-date treatments in time series regression. However, PW and CO are still very popular.

[fboehlandt]

In particular, Newey-West HAC consistent estimators using the Bartlett kernel are commonly used (and easily done in Eviews). Note that HAC estimators yield the same coefficient estimates as OLS but higher/lower standard errors