Free markets don't necessarily mean free societies.
The study, authored by Paola Giuliano, an economics professor at UCLA, Prachi Mishra, an economist at the International Monetary Fund (IMF), and Antonio Spilimbergo, an economist at the IMF, found that though there is a strong correlation between democracy and capitalism, it's likely because adopting democracy leads to economic reform. The authors concluded that "there is no evidence that economic reforms pave the way for political reforms."
The study's findings have an example in China. The country has been booming after opening some of its markets to the world, but is still run by an authoritarian Communist regime, practices censorship, and jails and tortures people for dissent.
Mishra told the Wall Street Journal that in the cases where a free society and a free economy seem to be correlated, it's likely because democracy leads to economic reforms because "democracies fall to private interest groups."
The study's authors analyzed data from more than 150 countries between 1960 and 2004. The data included statistics on market reforms, financial sector reforms, and political reforms, among other information.