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This paper proposes a new class of heterogeneous causal quantities, named\textit{outcome conditioned} average structural derivatives (OASD) in a generalnonseparable model. OASD is the average partial effect of a marginal change ina continuous treatment on the individuals located at different parts of theoutcome distribution, irrespective of individuals' characteristics. OASDcombines both features of ATE and QTE: it is interpreted as straightforwardlyas ATE while at the same time more granular than ATE by breaking the entirepopulation up according to the rank of the outcome distribution.  One contribution of this paper is that we establish some close relationshipsbetween the \textit{outcome conditioned average partial effects} and a class ofparameters measuring the effect of counterfactually changing the distributionof a single covariate on the unconditional outcome quantiles. By exploitingsuch relationship, we can obtain root-$n$ consistent estimator and calculatethe semi-parametric efficiency bound for these counterfactual effectparameters. We illustrate this point by two examples: equivalence between OASDand the unconditional partial quantile effect (Firpo et al. (2009)), andequivalence between the marginal partial distribution policy effect (Rothe(2012)) and a corresponding outcome conditioned parameter.  Because identification of OASD is attained under a conditional exogeneityassumption, by controlling for a rich information about covariates, aresearcher may ideally use high-dimensional controls in data. We propose forOASD a novel automatic debiased machine learning estimator, and presentasymptotic statistical guarantees for it. We prove our estimator is root-$n$consistent, asymptotically normal, and semiparametrically efficient. We alsoprove the validity of the bootstrap procedure for uniform inference on the OASDprocess.

Identification and Auto-debiased Machine Learning for Outcome Conditioned Average Structural Derivatives