Many models of statistical discrimination assume rational expectations. Consider instead a model in which expectations about strangers of a given race or other salient characteristic have a random error around rational expectations. Unlike the case for stock market expectations where mean-zero idiosyncrasies to beliefs around a rational expectations mean reduce the welfare of the investor holding inaccurate beliefs, but have no direct effect on prices, variance in beliefs about strangers of a given race or other salient characteristic are likely to have a systematic negative effect on groups that are in low esteem on average, simply because key actions are non-linear in perceptions. The example I have in mind is calling the police on an African-American individual because one perceives them as suspicious. Variance around the mean is likely to push more observers into beliefs based on circumstances plus skin color that are negative enough to lead them to call 911 and ask the police to check things out.

In the video above (which I have highlighted on this blog before), Baratunde Thurston is eloquent about the many different innocent activities that, when interacted with negative enough beliefs about a race, lead to someone calling the police.

All of this is to argue that while statistical discrimination plus random error in beliefs might, to some readers, sound relatively innocent, it is far from innocent in its effects.

I have a couple of other blog posts that are closely related to this one. “The Right Amount of Wokeness” pursues the theme of variance in a different way. “Enablers of White Supremacy” pursues the theme of statistical discrimination in a different way.