Servile labor disappeared because it could not stand the competition of free labor; its unprofitability sealed its doom in the market economy. -Ludwig von Mises1
Slavery, as opposed to free labor, is far less efficient.2 Mistreated workers have much lower productivity than workers with good workspaces and good pay.3 Slaves had to have their living accommodations taken care of, despite how minimal those accommodations were sometimes. You had to have security to keep slaves from running away. This higher demand for security set prices higher for guards, which meant other types of businesses unassociated with slavery had to pay more. In many places, people were required by law to take part in slave hunts, whether it be directly or through the socialized costs of public slave hunters, which resulted in many man-hours lost in other markets.4 And of course, there was the postponed use of labor-saving devices, whether it be to force harder labor on slaves or to protect slave investments. It just requires some basic economic analysis to come to this conclusion.
Due to the civil war and many other factors such as laws, it's difficult to see the economic effects of abolishing slavery. We do know that slave owners suffered economically, but entrepreneurs not a part of the slave-related businesses did not.5 The slavers only suffered economically because they lost their investments, and laborers, especially former slaves, tended not to want to work for plantations that formerly had slaves. So, abolishing slavery was bad for some people financially, but only because slavery was around in the first place.
The best example of free labor improving an economy is Russia, where serfdom was abolished in the 1860s. Russia kept incredible economic records and there wasn't much else going on at the time, so we can reach much more conclusive empirical data without the need for speculation. According to a 2018 study by Andrei Markevich, "..substantial increases in agricultural productivity, industrial output, and peasants' nutrition in Imperial Russia as a result of the abolition of serfdom in 1861"6
There aren't as many good studies about American slavery currently, but there is a forthcoming one by Trevon Logan and Richard Hornbeck. It is probably going to be quite groundbreaking in the field. Logan wrote an article on Bloomberg about his research back in February:
"..instead of destroying wealth, emancipation actually delivered the largest positive productivity shock in U.S. history. Under conservative assumptions about the value of non-working time to enslaved people, we estimate that the productivity gain was roughly 10% to 20% of gross domestic product."7
Mises, Ludwig von, Human Action (1949), p. 625.
Datta, M. N., & Bales, K. “Slavery is Bad for Business: Analyzing the Impact of Slavery on National Economies.” The Brown Journal of World Affairs. 19. (2013), pp. 205–223.
Bellet, Clement & Neve, Jan-Emmanuel & Ward, George, “Does Employee Happiness Have an Impact on Productivity?” SSRN Electronic Journal, (2019)
Thornton, Mark A. “Rothbard on the Economics of Slavery.” Quarterly Journal of Austrian Economics. 22. (2020), pp. 565-578.
Ager, Philipp, Leah Boustan, and Katherine Eriksson, "The Intergenerational Effects of a Large Wealth Shock: White Southerners after the Civil War." American Economic Review. 111. 11. (2021), pp. 3767-3794.
Markevich, Andrei, and Ekaterina Zhuravskaya, "The Economic Effects of the Abolition of Serfdom: Evidence from the Russian Empire." American Economic Review. 108. (4-5), (2018), pp. 1074-1117.
Logan, Trevon, “Slavery Was Never an American Economic Engine” Bloomberg (2022)