# Enabling Decision Making with the Modified Causal Forest: Policy Trees for Treatment Assignment
## 3 Empirical Studies
### Study 1: Oregon Health Insurance Experiment
However, its performance in terms of welfare is comparable to that of an optimal tree with the same depth, with the advantage of reduced computational time. For example, in this application, the runtime for a constrained optimal policy tree of depth-4 is 3 min and 3 s, whereas a constrained sequentially optimal policy tree takes only 30 s. Additional details on the runtime comparison of the policy trees can be found in Appendix A.3.1 of Appendix A. Note that the policytree package of [22] also provides sequentially optimal policy trees, which are referred to as _hybrid policy trees_ by the authors. In Table 1, all the policy trees show an increase in welfare with respect to the baseline policies. The unconstrained policy trees achieve the highest welfare, increasing the probability of primary care visits from 51.70% to 54.97%. They allocate almost all individuals to the treatment, which can be interpreted as access to Medicaid insurance for nearly everyone. \begin{table}
\begin{tabular}{l c c c} \hline \hline
**Policy** & \begin{tabular}{c} **Welfare (\%)** \\ **Primary Care Visits** \\ \end{tabular} & \
\begin{tabular}{c} **Treatment Shares (\%)** \\ **Medicaid No** \\ \end{tabular} &
\begin{tabular}{c} **Medicaid Yes** \\ \end{tabular} \\ \hline Observed & 51.70 & 49.98 & 50.02 \\ Random & 51.45 & 50.16 & 49.84 \\ \hline Unconstrained optimal policy tree & & & \\ Depth-2 & 54.97 & 0 & 100 \\ Depth-3 & 54.97 & 0 & 100 \\ \hline Constrained optimal policy tree & & & \\ Depth-2 & 52.88 & 53.56 & 46.44 \\ Depth-3 & 53.48 & 51.75 & 48.25 \\ Depth-4 & 53.51 & 52.18 & 47.82 \\ \hline Constrained sequentially optimal policy trees & & & \\ Depth-2+1 & & 52.68 & 57.06 & 42.93 \\ Depth-3+1 & & 53.54 & 50.30 & 49.69 \\ \hline \hline \end{tabular} Note: The table shows empirically observed, randomly assigned, and optimal treatment allocations of individuals. The optimal policy trees are unconstrained and constrained. The final constrained trees add a sequential optimal sub-tree (+1). The constraint is implemented as a limit imposed on the treatment shares, as observed within the empirical dataset. The outcome represents primary care visits. The treatment is being extracted from the lottery, which allows one to apply for Medicaid, the public health insurance programme.  
\end{table} 
Table 1: Treatment allocations: Oregon health insurance experiment. Figure 1: Distribution of IATE. Mean (average standard error) of the IATEs: 0.07 (0.1). Compared to the unconstrained policy trees, those with the capacity constraint always report a small decrease in the probability of primary care visits, allocating a significantly lower proportion of individuals to the treatment. Constrained optimal policy trees and constrained sequentially optimal policy trees, with a last sequentially optimal sub-tree of the same depth, show comparable and stable results in terms of welfare achieved. From a computational point of view, such findings may be relevant for large datasets, since policy trees with sequentially optimal layers reduce computation time while performing similarly well. Figure 2 presents the allocation rules of a constrained optimal policy tree with a depth of 2. Notably, even at this relatively shallow depth, the policy tree demonstrates improvements in welfare compared to the observed allocations and the simplest allocation rules. Individuals with age between 37 and 51 years old (38% of the sample) are assigned to Medicaid. Additionally, individuals older than 51 living in metropolitan areas, constituting 9% of our sample, are also allocated to the program. Conversely, individuals younger than 36 and older than 51 who do not live in metropolitan areas are excluded from the program. For reference, note that the age ranges from 20 to 63.