Does the augmented Solow growth model work for oil producers?

Oil producing countries are usually excluded from economic growth estimations based on the augmented Solow model. The reason is that much of their economic growth is not from accumulation of capital, but rather from sales of a natural asset.

I tested the augmented Solow model on a panel of 24 oil producing countries, with a GMM System estimator and a variety of instrument sets of lagged variables to correct for endogeneity. The fit of the model, measured by parameter uncertainty, was quite good. The parameters on the returns to capital and education were both far lower than for estimates of all countries, with returns to education particularly low by comparison. So it looks like it is sensible to exclude oil producers when analysing growth models, but the Solow model could have merit in describing part of growth in oil producers too. It's probably a small amount though.