A Stata module for estimating dose response treatment models under (continuous) treatment endogeneity and heterogeneous response to observable confounders

Following in the footsteps of the Stata user-written command ivtreatreg, recently proposed by the author (Cerulli, 2012), the paper presents a new Stata routine— contreatreg—for estimating a Dose Response Treatment Model under continuous treatment endogeneity and heterogeneous response to confounders. Compared with similar models—and in particular the one proposed by Hirano and Imbens (2004) implemented in Stata by Bia and Mattei (2008)—this model does not need the normality assumption; it is well suited when many individuals have a zero-level of treatment, and it accounts for treatment endogeneity by exploiting a two-step instrumental-variables (IV) estimation. The model considers two groups: 1) untreated, whose level of the treatment (or dose) is zero; and 2) treated, whose level of the treatment is greater than zero. Treated units' outcome y responds to treatment by a function h(t), assumed to have a flexible polynomial form. contreatreg estimates the model’s dose response function, which is shown to be equal to the average treatment effect, given the level of treatment t (that is, ATE(t)), along with other causal parameters of interest, such as the ATE, ATET, ATENT, and ATE(x; t). An application on real data will be provided along with the command’s ado and help files.