A few years ago, I was teaching at HEC Montréal and I explained that putting people in prison – by statistical definition – did reduce unemployment. My students were shocked that I would say that. I told them that it was important to know definitions like that because you can then analyze the BS that politicians and pundits can spew.
And the case of Black-Americans is the best example, especially with regards to the wage gap. In recent years, I have seen pundits (left and right) use the slightly increasing ratio of black-to-white wages as a tool to promote their favored political narrative (i.e. the BS that I am referring to).
But, at the same time, the incarceration rates of Blacks has increased dramatically. Tell me, do you think that the socio-economic features of blacks in jail are distributed the same way as the socio-economic features of blacks not in jail? Of course not, criminals tend to be clustered disproportionately at the bottom of the income ladder. However, when its time to collect the wage statistics for blacks and whites, you are basically considering only the wages of blacks not in jail (i.e. blacks who are in the top centiles of the wage distribution). So, you’re basically committing a sin of statistical composition.
Some bloggers have caught on to that – the wage ratio is going up at the same pace as the incarceration rate for blacks. But they caught on after the work of scholars like Becky Pettit and Bruce Western came along (here and here and see graph below that illustrates the effect of correcting for incarceration on the employment rate of blacks).
When I look at this evidence, I understand why some people are pissed off at the conditions of Black Americans. It throws in doubt the contention that there has been racial convergence in America. At the same time, I wonder if the lack of recognition given to this statistical issue is a form of cognitive dissonance. If you claim that the convergence is mostly an artifice of composition fallacies, then what does it say about the policies of the last 30-40 years?