# Enabling Decision Making with the Modified Causal Forest: Policy Trees for Treatment Assignment
## 3 Empirical Studies
### Study 1: Oregon Health Insurance Experiment  
In 2008, Oregon initiated a lottery with limited spots to provide low-income individuals access to its Medicaid program. This lottery offers an opportunity to examine the impact of expanding access to public health insurance within a randomised controlled setting. Researchers analysed various outcomes over the two years following the experiment, including healthcare utilisation, financial strain, health status, labour market outcomes, and political participation. Extensive studies have been conducted by [14; 15; 16; 17; 18; 19; 20; 21], among others. Overall, findings suggest that access to Medicaid leads to an increase in healthcare utilisation and a decrease in financial strain and depression, albeit without statistically significant improvements in physical health or labour market outcomes. This analysis follows [14] and specifically focuses on the impact of being selected in the lottery on primary care visits during the first year post-selection. We rely on survey data collected within the experimental setting, given that the hospital records are not publicly available. The end-line survey, conducted after 12 months, was completed by 23,777 individuals. The outcome is measured by a binary variable indicating if primary care has been utilised during the year. Among the several outcomes available (e.g., emergency room usage or drug prescription), we choose primary care utilisation because of its importance from a policy perspective. Indeed, primary care visits may lead to preventive care for more serious diseases and, consequently, prevention of more expensive medical care. After dropping observations with missing values, the size of our dataset is 23,527 observations, with 50% of the individuals having Medicaid health insurance. As in [14], our intention-to-treat specification incorporates additional features, such as socio-demographic factors, which are valuable for exploring heterogeneity and informing policy, even though they are not essential for identifying causal effects. On the contrary, although assignment to the lottery is random, all family members of randomly selected individuals can apply for Medicaid. Therefore, the probability of receiving treatment depends on the number of family members, which we include as a control variable. Tables 1 and 4 in Appendix A describe the 11 variables used for data analysis. We evaluate the distribution of the IATEs to detect potential effect heterogeneity. Figure 1 displays a density plot of the IATEs, ranging from \(-0.13\) to \(0.37\), with a mean value of \(0.07\) and an average standard error of \(0.1\). The variation in the effects justifies our following analysis for decision making, aiming at expanding the number of primary care visits by optimising the treatment allocation process. Table 1 provides details on welfare, measured as utilisation of primary care visits and allocation shares of individuals for various policies. We compare the results of the policy trees with our two baseline policies, namely the observed and random treatment allocations. In this study, we examine both unconstrained and constrained policy trees. Given the lack of specific cost information for Medicaid insurance, we assume that only approximately half of the population (as in the empirical data) can be covered by this health insurance. The algorithm enforces constraints by finding a cost value to subtract from the policy score. It adjusts the treatment costs to ensure that the allocation of observations to treatments does not exceed the maximum treatment shares. We build our constrained policy trees by specifying either the depth of a first optimal tree (constrained optimal policy tree) or, optionally, specifying, in addition, the depth of a second optimal policy tree (constrained sequentially optimal policy tree). In the latter case, the second tree is built within the strata  
obtained from the leaves of the first tree. The final policy tree will not be optimal.