  There is interest in learning about the causal effect of family planning (FP)
on empowerment related outcomes. Experimental data related to this question are
available from trials in which FP programs increase access to FP. While program
assignment is unconfounded, FP uptake and subsequent empowerment may share
common causes. We use principal stratification to estimate the causal effect of
an intermediate FP outcome on a primary outcome of interest, among women
affected by a FP program. Within strata defined by the potential reaction to
the program, FP uptake is unconfounded. To minimize the need for parametric
assumptions, we propose to use Bayesian Additive Regression Trees (BART) for
modeling stratum membership and outcomes of interest. We refer to the combined
approach as Prince BART. We evaluate Prince BART through a simulation study and
use it to assess the causal effect of modern contraceptive use on employment in
six cities in Nigeria, based on quasi-experimental data from a FP program trial
during the first half of the 2010s. We show that findings differ between Prince
BART and alternative modeling approaches based on parametric assumptions.
