115 The effects of supported housing for individuals with mental disorders measure is lower (9%), but still considerable. Figure 1 indicates a positive monotonic relationship between residualised leniency (x-axis) and rate of eligibility to supported housing (y-axis on the right). Consistent with Figure 1, the first-stage coefficients indicate a strong and precisely estimated impact of residualised leniency on eligibility, which we observe regardless of the specification used (Table A2 of the appendix). Being assigned to a one standard deviation more lenient assessor increases the probability of being eligible for supported housing by 8.6 pp (0.978 x 0.088) (Table A2). Furthermore, the first stage yields a Cragg-Donald F-statistic of 415.35. Validity The Dutch institutional context, and in particular the allocation of applications to assessors, makes a violation of the instrument independence assumption unlikely8. Applicants cannot choose the assessors, and assessors cannot choose the applications they review. Hence, assessors only interact with individuals and their families for the purpose of the needsassessment. Once the eligibility is granted assessors have no other role in the pathway to utilization. Eligibility and provision of supported housing are taken care of by different parts of the Dutch long-term care system: eligibility is decided upon by the independent needs-assessment agency, while long-term care is provided by private organizations that are contracted by a regional single payer. This means that the assessor’s leniency should not be correlated with the outcomes of interest other than through the eligibility granted for supported housing. We report means of observed characteristics for each quartile of residualised leniency and find no indication of systematic or meaningful associations between such observed characteristics and residualised leniency (Tables S3 and S4 of the appendix). Monotonicity In order to interpret our 2SLS estimates as LATE we must also assume average monotonicity, meaning that one application that is denied eligibility by the most lenient assessor would also be denied eligibility by the strictest assessor. Similarly, an application that is granted eligibility by the strictest assessor would also be granted eligibility by the most lenient one [15, 33]. We do not have sufficient evidence to reject average monotonicity based on the positive relationship between residualised leniency and the probability of being eligible to supported housing in all major subgroups (Table 2, column 1) [33]. We further confirm average monotonicity using alternative “reverse-sample” instruments. These instruments are computed as the residualised leniency excluding the observations in the respective subgroup (e.g. we estimate the first-stage for young adults based on assessor´s residualised leniency constructed only with observations of 8 The Dutch government announcement in 2012 to reduce the number of inpatient mental health treatments (Trimbos-instituut, 2021) – which is in line with the ongoing trend of deinstitutionalization (Fakhoury and Priebe 2007, Thornicroft and Henderson 2016, Chow and Priebe 2016, Ravelli 2006) – could pose a threat to the identification of the LATEs. Our approach of controlling for half-year periods when constructing the residualised instrument and when applying the 2SLS estimates accounts for these changes. In the same way, we account for regional offices tackling the different nature of the applications by geography. 4
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