Does faith lead to the social virtue of liberty? Yes, “man, by assenting to matters of faith, is raised above his nature,” as said Thomas Aquinas. Man’s natural state is self-sovereignty – impulse, savagery, and law unto himself. By “assenting to matters of faith”, as Aquinas put it, man accepts God as sovereign. As stated above, the sovereign is the authority, or law maker, to which a member of a society yields in order to gain his liberty, and liberty is one’s freedom of physical action within the limits of the law prescribed by the sovereign – in this case, the law of God. Without faith in God, there is no sovereign. Without the sovereign, there can be no liberty, by definition, because without the sovereign, that authority and law maker, we are instead a law unto ourselves and considered to be self-sovereign creatures of passion. Therefore, we can safely say that, yes, faith does lead to the social virtue of liberty.
As the determination of whether faith does-or-does-not lead to liberty is merely a matter of semantics, rather than searching for quantitative data on the link between liberty and faith, let us consider a study on the impact of religious liberty:
According to the study, descriptive evidence suggests that countries with higher levels of religious liberty benefit economically in a variety of ways, such as greater relative levels of economic development that result in better economic institutions, leading to more personal economic freedom, particularly property rights. Further, “increases in religious freedom are associated with robust increases in measures of human flourishing, even after controlling for time-invariant characteristics across space and time and a wide array of time-varying country-specific factors, such as economic activity and institutional quality.”
In fact, “countries that experienced the greatest growth in religious liberty between 2006 and 2018 also experienced the greatest growth in human flourishing.” A slightly modified version of the study’s Figure 1 can be found below, which provides “motivating evidence on the link between religious liberty and human flourishing.”

Yes, faith does lead to liberty.
Thanks for reading!