The paper describes the methodology of residual discrimination and applies it to measures, such as punishment, where the dependent variable is truncated, bounded, or otherwise limited in the range of values it can assume. A test for the effect of equal punishment on recidivism is constructed. The methodology is then applied to the Federal Parole Board's data set on all Federal felony offenders released from adult correctional institutions in 1972. The findings indicate that blacks served in excess of 5 more months in prison compared to identically qualified whites. The analysis demonstrates that this punishment severity disparity cannot be justified on the grounds that blacks are more criminal or are more likely to recidivate. There were no racial disparities in the certainty of punishment, but racial differentials in preprison employment experiences were revealed. Tabular study data and 41 references are provided.