In this repository we provide the code for the BCF-IV function and for the application part of the paper "Heterogeneous causal effects with imperfect compliance: a novel Bayesian machine learning approach" by F.J. Bargagli-Stoffi, K. De Witte and G. Gnecco. This function discovers the effect heterogeneity and provides two ways to estimate the heterogeneous causal effect (two-stage least squares and method-of-moments) in scenarios where the assignment mechanism is irregular. The BCF-IV function directly builds on the Bayesian Causal Forest algorithm by Hahn, Murray and Carvalho.

The function takes as inputs:

• y: the outcome variable;
• w: the reception of the treatment variable (binary);
• z: the assignment to the treatment variable (binary);
• max_depth: the maximal depth of the tree generated by the function;
• n_burn: the number of iterations discarded by the BCF-IV algorithm for the burn-in;
• n_sim: the number of iterations used by the BCF-IV algorithm to get the posterior distribution of the estimands;
• binary: this option should be set to TRUE when the outcome variable is binary and to FALSE if the outcome variable is either discrete or continuous.

The mm_bcf_iv function returns the discovered sub-population, the conditional complier average treatment effect (CCACE), the p-value for this effect, the p-value for a weak-instrument test, the proportion of compliers, the conditional intention-to-treat effect (CITT) and the proportion of compliers in the node.

More details on the R code for the BCF-IV function can be found here.

source("bcf-iv.R")

bcf_iv(y, w, z, x, max_depth = 2, n_burn= 2000, n_sim= 2000, binary = TRUE)

mm_bcf_iv(y, w, z, x, max_depth = 2, n_burn= 2000, n_sim= 2000, binary = TRUE)

• Falco J. Bargagli-Stoffi, Kristof De Witte, Giorgio Gnecco. Heterogeneous causal effects with imperfect compliance: a novel Bayesian machine learning approach. [link]
• P. Richard Hahn, Jared S. Murray, Carlos Carvalho. Bayesian regression tree models for causal inference: regularization, confounding, and heterogeneous effects. [link]