The J-curve and The Rise and Decline of Nations

The link goes to a book review of The J Curve: A New Way to Understand
Why Nations Rise and Fall, by Ian Bremmer. In the book, Bremmer plots authoritarian states on the left side of the J, and democratic states on the right. He argues that very authoritarian states on the top of the left side of the J must, in order to liberalize, descend through increasing instability at the bottom of the curve and then ascend on the right. As they ascend the right side of the J, the states will see less instability. The process can also happen in the reverse direction, and states can become mired in the middle of the curve.
This strikes me as an interesting idea, particularly given the discussion we had in class of Olson's Rise and Decline. In Olson's theory, the more stability in a state, the more organizations have evolved which rely upon and promote that stability. He even uses the word sclerotic to describe the state of Great Britain in the early '80s. I suspect Bremmer would put Great Britain all the way at the top-right side of the J. Conversely pre-war Japan and Germany would have been placed near the top of the left side -- their defeat dropped them to the bottom of the curve, and then they clawed their way up the right.
The period of highest growth for Japan, Germany and the UK were probably as they completed the 'turn' onto the vertical part of the curve. South Korea and India seem to be making or to have just completed this turn as well. I suspect Iraq is at the bottom of the J, with the potential to go either way. And China, as the reviewer, Tim Worstall, points out, seems to straddle the curve; politically on the authoritarian side, and economically on the free side.