Why does xtgls not report an R-squared statistic?

The R-squared statistic is an ordinary least squares (OLS) concept that is useful because of the unique way it breaks down the total sum of squares into the sum of the model sum of squares and the residual sum of squares. When you estimate the model’s parameters using generalized least squares (GLS), the total sum of squares cannot be broken down in the the same way, making the R-squared statistic less useful as a diagnostic tool for GLS regressions. Specifically, an R-squared statistic computed from GLS sums of squares need not be bounded between zero and one and does not represent the percentage of total variation in the dependent variable that is accounted for by the model. Also, eliminating or adding variables in a model does not always increase or decrease the computed R-squared value.