Identification and Estimation of Conditional Average Partial Causal
  Effects via Instrumental Variable
Yuta Kawakami Manabu Kuroki Jin Tian
There has been considerable recent interest in estimating heterogeneous
causal effects. In this paper, we introduce 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. 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.