114 Chapter 4 compliers is not feasible, we follow Dahl et al. [16] and Dobbie et al. [32] to estimate the proportion of marginal applicants in our study, and their characteristics as a group. Provided the monotonicity and independence assumptions hold, the share of always takers – those that would always be considered eligible regardless of assessor leniency – can be obtained from the eligibility decisions of the least lenient assessor. Analogously, the share of never-takers – those that would never be granted eligibility no matter which assessor they are assigned to – can be derived from the decisions of the most lenient assessor. The group characteristics of the compliers are obtained by first defining subgroups based on characteristics potentially relevant for the assessor to utilize discretionary power. The relative likelihood that the compliers have these characteristics compared to the overall population of applicants equals the first-stage subgroup coefficient divided by the overall first-stage coefficient [15]. The LATE are meaningful from a policy perspective. Compliers are the individuals who might have received a different decision had their application been assigned to a different assessor. These individuals likely resemble those affected by marginal changes in future supported housing eligibility policy. Eligibility is a key policy tool for determining who should receive each type of long-term mental health care. Hence, our findings are informative about access to the system rather than using supported housing, as individuals might not move into supported housing despite being eligible. For instance, individuals or the family might not accept the need to move into supported housing – as the application is often placed by a social worker or a provider – or they might not be willing to pay the co-payments. Furthermore, eligible individuals usually only move into supported housing after some time because they need to find a suitable provider or make other arrangements. Conversely, those who are ineligible may re-apply, for instance when their situation changes drastically, and become eligible and be admitted at a later point in time. The group of compliers may change during the study period and we control for the half-year period of the application to deal with any variation over time in either the population composition or assessor leniency, both within-assessor or between earlyobservation-period and late-observation-period assessors. The effects we estimate should be interpreted as the weighted average over substantial treatment effect heterogeneity among the compliers with our instrument. Changes in composition and effect heterogeneity over time do not lead to biased estimators, but they do lead to a specific interpretation of the population of compliers which are represented by the compliers in our study. Relevance of the instrument Leniency has a strong impact on eligibility: the share of individuals granted eligibility for supported housing ranges from 36% in the first percentile to 100% in the 99th percentile (average 86%, standard deviation 13%). The standard deviation of the residualised leniency
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