Short answers, pulled from the story.
Democratization from a non-democratic regime is usually preceded by a fall in GDP, followed by volatile but rising growth in the long run. Authoritarian regimes tend to show the opposite pattern, growing quickly at first and then declining over time.
The causal direction changes by country. In some nations economic growth has promoted democracy, while in others democracy has promoted growth, and research on post-socialist nations found that rising political freedom had little to no effect on economic growth even though growth influenced political freedom.
The 2008 meta-analysis found that democracy has no direct effect on economic growth but has strong indirect effects. Democracy was linked to higher human capital accumulation, lower inflation, lower political instability, and higher economic freedom.
Chile, Hong Kong, Taiwan, Singapore, and South Korea achieved rapid economic growth from once-impoverished starting points without democratic institutions. They shared relatively free markets, little protectionism except in South Korea, and secure property rights under the rule of law.
117 out of 191 independent states currently declare themselves democratic. This follows a democratic revolution that has swept much of the world over the past two decades.
Ancient Athens, in the 4th century B.C., showed a highly positive correlation between democracy and economic growth through markets, trial by jury, civil liberties, and free speech, first documented by Xenophon. Rome built an even larger economic boom on its iron production and Pax Romana trade routes, though debasing its coins to fund military competition eventually pushed it back toward a barter economy.