Partial Distributional Policy Effects Under Endogeneity

Rothe (Econometrica 80, 2269–2301 2012) introduces a new class of parameters called ‘Partial Distributional Policy Effects’ (PPE) to estimate the impact on the marginal distribution of an outcome variable due to a change in the unconditional distribution of a single covariate. Since the strict exogeneity assumption of all covariates makes this approach less applicable in empirical research, we propose the identification of the PPEs for a continuous endogenous explanatory variable using the control variable approach developed by Imbens and Newey (Econometrica 77, 1481–1512 2009). We also apply this proposed control variable PPE approach to investigate how poverty and black-white racial wage gaps contribute to the steep increase in the incarceration rate of black men over the period 1980-2010. Our control variable PPE estimates suggest that although the fall in the racial wage gap does not explain the changes in the incarceration rate of black men, changes in the poverty rate contribute about one-third of the steep increase in the incarceration rate at the upper-tail of the distribution.