# Interpretation of R-squared when using FGLS

Context: I am analyzing time series and cross-sectional data using Stata's xtpcse command which corrects for autocorrelation in panel data using a Prais–Winsten transformation (and additionally correcting the standard errors for heteroskedasticity)

Question: I need goodness-of-fit measure and the xtpcse command reports R-squared, but I am unsure about the correct interpretation.

For example, in Wooldrigde's well-known introductory econometrics textbook it says:

Finally, an R-squared is reported for the Prais-Winsten estimation that is well below the R-squared for the OLS estimation in this case. However, these R-squareds should not be compared. For OLS, the R-squared, as usual, is based on the regression with the untransformed dependent and independent variables. For Prais-Winsten, the R-squared comes from the final regression of the transformed dependent variable on the transformed independent variables. It is not clear what this R2 is actually measuring; nevertheless, it is traditionally reported.
(Wooldridge, 2012: Introductory Econometrics: A Modern Approach, p. 426)

• So what exactly is R-squared "measuring" in this context, after the dependent and independent variable have been transformed, compared to the usual OLS interpretation (% of variation explained by the model)?
• Is it still a useful measure of goodness-of-fit when comparing different models with different independent variables included?
• If not what are the alternatives (because of all the transformations AIC, BIC etc., are not available as postestimation commands when using xtpcse)?