Does being accused of being a criminal make a person more likely to be one?

Take for example the fact that the majority of people in the western (white European, anglo-saxon) world consider black and african people to be prone to , robbery, and other vicious and animalistic behaviors. If these blacks are not genetically more susceptible to and other violent crimes, then, could it be possible that carrying around that stigma for all of ones life might give one more of a reason to actually live out the stereotypes? I of course am not implying that that would be rational thinking or any excuse at all to carry out these atrocious acts. But if you are raised being told that you're a criminal, or future rapist, psychologically could this have a self fulfilling prophecy?