General Discussion

They did actually, they even address this in the study pretty early on and they also find the correlation persists in countries where the humans are being sourced from despite no changes in that nation's regulations. Human trafficking increases from legalized prostitution.

From the article that you didn't read:

This is because contrary to Akee, Bedi, et al.’s (2010) implicit underlying assumption, the legalization of prostitution is not equal to laxer enforcement of anti-trafficking laws and, conversely, the fact that prostitution is illegal does not imply stricter anti-trafficking enforcement. Human trafficking always remains illegal even if prostitution becomes legal. Moreover, by erroneously equating the legal status of prostitution with different levels of law enforcement with respect to human trafficking, Akee, Bedi, et al. (2010) overlook other demand and supply effects that the legalization of prostitution may have on human trafficking.

and

Akee, Bedi, et al. (2010) provide an excellent game-theoretic analysis on the effects of anti-trafficking law enforcement in source and destination countries between such country pairs. However, their analysis tells us nothing about the effect of the legalization of prostitution in itself. This is because contrary to Akee, Bedi, et al.’s (2010) implicit underlying assumption, the legalization of prostitution is not equal to laxer enforcement of anti-trafficking laws and, conversely, the fact that prostitution is illegal does not imply stricter anti-trafficking enforcement. Human trafficking always remains illegal even if prostitution becomes legal. Moreover, by erroneously equating the legal status of prostitution with different levels of law enforcement with respect to human trafficking, Akee, Bedi, et al. (2010) overlook other demand and supply effects that the legalization of prostitution may have on human trafficking. Jakobsson and Kotsadam’s (in press) paper is closer to our theoretical analysis in this regard as they directly focus on the supply and demand effects of legalizing prostitution. However, they only take into account the scale effect, i.e., the expansion of prostitution markets after legalization. As we will show below, there is an opposing substitution effect replacing illegal, forced prostitution with voluntary, legal prostitution, making the overall effect indeterminate.