Can racially unbiased police perpetuate long-run discrimination?

We develop a stylized dynamic model of highway policing in which a non-racist police officer exhibits a cognitive bias: relative overconfidence. The officer is given incentives to arrest criminals but faces a per stop cost that increases when the racial mix of her stops differs from that of the population. By observing the racial composition of jail inmates, she estimates crime rates of each race. Her overconfidence regarding eventual incarceration of criminals is shown to lead her to overestimate the crime rate of one race causing the long-run racial composition of the jail population to deviate from the “fair” one.