  There has been considerable recent interest in estimating heterogeneous
causal effects. In this paper, we study conditional average partial causal
effects (CAPCE) to reveal the heterogeneity of causal effects with continuous
treatment. We provide conditions for identifying CAPCE in an instrumental
variable setting. Notably, CAPCE is identifiable under a weaker assumption than
required by a commonly used measure for estimating heterogeneous causal effects
of continuous treatment. We develop three families of CAPCE estimators: sieve,
parametric, and reproducing kernel Hilbert space (RKHS)-based, and analyze
their statistical properties. We illustrate the proposed CAPCE estimators on
synthetic and real-world data.
