Does public housing occupancy increase unemployment?

In order to test for the effect of public housing occupancy on unemployment, we estimate a simultaneous probit model of unemployment and public housing. On a first sample, we instrument public housing with the gender composition of children. On a second sample, the instrument is the share of public housing at the city level. We also perform a robustness check that consists in measuring the correlation between unobservables that could explain the effect of public housing on unemployment. As the corresponding level of correlation is low, this check reinforces our result of no effect of public housing on unemployment.