124 Chapter 4 Figure 2. Subgroup analysis for admission to supported housing, total expenditure and working in the next calendar year: by age, personal income and mental disorder diagnosis. Robustness Analysis We test the robustness of our main specification in five ways. First, results are robust to the stepwise inclusion of different sets of individual/application controls in the main specification, as well as controlling for age as dummies and additional controls for mental health disorder diagnosis and need at the time of application, as proxied by the care intensity requested (columns 2-6 in Table A2 of the appendix). Second, results are also robust to changing the minimum number of cases by assessor/type of assessment procedure from 30 to 15 or to 45, when constructing the leniency instrument (columns 7-8 in Table A2). Third, the effect size is slightly reduced after including all the applications likely to be reassessments of recent eligibility status by removing the requirement that individuals had not been eligible for supported housing in the past 365 days (column 9 in Table A2). Fourth, we find similar results when using the unadjusted version of the leniency measure (column 10 in Table A2) and when residualising leniency by quarter of the year (Table A10 of the appendix). Last, we replace the residualised leniency by a vector of assessor fixed effects, using the unbiased jackknife instrumental variables estimator (UJIVE) [36]. Following Maestas et al. [15], Dahl et al. [16] and Bakx et al. [14], we have opted for the residualised leave-oneout leniency instrument in our main specification; but Hull [37] argues that the implied dimension reduction procedure of the assessor fixed effects instruments may result in
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