SlowGuess/NeurIPS_2023_OCR huggingface dataset:
Because the Oregon Health Insurance Study expanded access to enroll in Medicaid, a social safety net program, the effective treatment policy is in the space of encouragement to enroll in insurance (via access to Medicaid) rather than direct enrollment. This encouragement structure is shared by many other interventions in social services that may invest in nudges to individuals to enroll, tailored assistance, outreach, etc., but typically do not automatically enroll or automatically initiate transfers. Indeed this so-called administrative burden of requiring eligible individuals to undergo a costly enrollment process, rather than automatically enrolling all eligible individuals, is a common policy design lever in social safety net programs. Therefore we expect many beneficial interventions in this consequential domain to have this encouragement structure.
We preprocess the data by partially running the Stata replication file, obtaining a processed data file as input, and then selecting a subset of covariates. These covariates include household information that affected stratified lottery probabilities, socioeconomic demographics, medical status and other health information.
In the notation of our framework, the setup of the optimal/fair encouragement policy design question is as follows:
-  $X$  covariates (baseline household information, socioeconomic demographics, health information)
- A race (non-white/white), or gender (female/male)
These protected attributes were binarized.
-  $R$  encouragement: lottery status of expanded eligibility (i.e. invitation to enroll when individual was previously ineligible to enroll)
-  $T$ : whether the individual is enrolled in insurance ever
Note that for  $R = 1$  this can be either Medicaid or private insurance while for  $R = 0$  this is still well-defined as this can be private insurance.
-  $Y$ : number of doctor visits
This outcome was used as a measure of healthcare utilization. Overall, the study found statistically significant effects on healthcare utilization. An implicit assumption is that increased healthcare utilization leads to better health outcomes.
We subsetted the data to include complete cases only (i.e. without missing covariates). We learned propensity and treatment propensity models via logistic regression for each group, and used gradient-boosted regression for the outcome model. We first include results for regression adjustment identification.
In Figure 3 we plot descriptive statistics. We include histograms of the treatment responsivity lifts  $p_{1|1a}(x,a) - p_{1|0a}(x,a)$ . We see some differences in distributions of responsivity by gender and race. We then regress treatment responsivity on the outcome-model estimate of  $\tau$ . We find substantially more heterogeneity in treatment responsivity by race than by gender: whites are substantially more likely to take up insurance when made eligible, conditional on the same expected treatment effect heterogeneity in increase in healthcare utilization. (This is broadly consistent with health policy discussions regarding mistrust of the healthcare system).
Next we consider imposing treatment parity constraints on an unconstrained optimal policy (defined on these estimates). In Figure 4 we display the objective value, and  $\mathbb{E}[T(\pi) \mid A = a]$ , for gender and race, respectively, enumerated over values of the constraint. We use costs of 2 for the number of doctors visits and 1 for enrollment in Medicaid (so  $\mathbb{E}[T(\pi) \mid A = a]$  is on the scale of probability of
Figure 3: Distribution of lift in treatment probabilities  $p_{1|1,a} - p_{1|0,a} = P(T = 1 \mid R = 1, A = a, X) - P(T = 1 \mid R = 0, A = a, X)$ , and plot of  $p_{1|1,a} - p_{1|0,a}$  vs.  $\tau$ .
Figure 4: Policy value  $V(\pi^{\lambda})$ , treatment value  $\mathbb{E}[T(\pi^{\lambda}) \mid A = a]$ , for  $A =$  race, gender.
enrollment). These costs were chosen arbitrarily. Finding optimal policies that improve disparities in group-conditional access can be done with relatively little impact to the overall objective value. These group-conditional access disparities can be reduced from 4 percentage points (0.04) for gender and about 6 percentage points (0.06) for race at a cost of 0.01 or 0.02 in objective value (twice the number of doctors' visits). On the other hand, relative improvements/compromises in access value for the "advantaged group" show different tradeoffs. Plotting the tradeoff curve for race shows that, consistent with the large differences in treatment responsivity we see for whites, improving access for blacks. Looking at this disparity curve given  $\lambda$  however, we can also see that small values of  $\lambda$  can have relatively large improvements in access for blacks before these improvements saturate, and larger  $\lambda$  values lead to smaller increases in access for blacks vs. larger decreases in access for whites.