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In estimating the causal effect of a continuous exposure or treatment, it isimportant to control for all confounding factors. However, most existingmethods require parametric specification for how control variables influencethe outcome or generalized propensity score, and inference on treatment effectsis usually sensitive to this choice. Additionally, it is often the goal toestimate how the treatment effect varies across observed units. To address thisgap, we propose a semiparametric model using Bayesian tree ensembles forestimating the causal effect of a continuous treatment of exposure which (i)does not require a priori parametric specification of the influence of controlvariables, and (ii) allows for identification of effect modification bypre-specified moderators. The main parametric assumption we make is that theeffect of the exposure on the outcome is linear, with the steepness of thisrelationship determined by a nonparametric function of the moderators, and weprovide heuristics to diagnose the validity of this assumption. We apply ourmethods to revisit a 2001 study of how abortion rates affect incidence ofcrime.

Estimating heterogeneous effects of continuous exposures using Bayesian tree ensembles: revisiting the impact of abortion rates on crime