That they're just crawling out of a deep hole ? It is perfectly normal for countries that get "enabled" suddenly to experience double or even triple digit growth.

After all, when you make 5c, another 5c is a 3-digit improvement. Their economies suck beyond belief currently, and they're waking up, slowly.

These not-really-all-that-totalitarian-any-more countries should be experiencing 20% or 30% growth a year, yet they don't.

"But the main mistake of Hassett is that he does not correct his analysis for confounding variables: unfree countries are much poorer than free countries, so it is easy for them to catch up."

Which begs the question: Why do unfree poor countries outperform free poor countries? Doesn't this undermine the neocon thesis that all countries ought to be democracies NOW, regardless of their stage of cultural/economic development?

I'd say this is a false correlation.

Since most non-democratic countries also happen to be undeveloped hell-holes, there is a lot more of room for rapid growth.

Two controlled economies showed incredible growth in the last 100 years.  Currently China and in the 1950's the USSR.  I think central control can crush local corruption and create rapid growth up to a point but as the economhy matures a Milton Freidman style economy is the only way forward.  Japan and France seem to both have stumbed here. 

As Snorri Godhi says, it is easy to rise quickly if the starting position is low enough so these short term gains may not be as impressive as they seem.  The wealth of the unfortunate citizens of repressive regimes is still below that of their freer counterparts.

It may also be no coincidence that there has been some relaxation in many repressive countries since the fall of the Berlin wall (the start point for Hassett's data), politically as well as economically.  Can this be measured quantitavely, and how does that relaxation compare with the growth rates?

"The unfree governments now understand that they have to provide a good economy to keep citizens happy, and they understand that free-market economies work best."

Kevin Hassett managed to put 2 pieces of nonsense into a single sentence:
1) The unfree governments now understand that they have to provide a good economy to keep citizens happy: unfree governments have always understood that they have to provide a good economy to keep citizens happy; certainly, Roman emperors understood that. It didn't help in the long run.
2) they understand that free-market economies work best: so how come politically unfree countries are also economically unfree? (a fact that Bassett acknowledges in the main body of the article.)

But the main mistake of Hassett is that he does not correct his analysis for confounding variables: unfree countries are much poorer than free countries, so it is easy for them to catch up. As they begin to catch up with free countries, it becomes more and more difficult to keep up. Besides, the population will start to demand more freedom.