113 The effects of supported housing for individuals with mental disorders Figure 1. Distribution of assessors´ residualised leniency and its effect on eligibility to supported housing. Notes: Estimates of eligibility are obtained using a local linear regression of residualised leniency on each eligibility decision Two-stage least squares regression approach We use residualised leniency (Leniencyi) as an instrumental variable in a two-stage least squares (2SLS) regression approach, to estimate the effects of becoming eligible to supported housing on the outcomes. Equation (3) provides the first-stage regression while γ1 in equation (4) is the coefficient of interest. (3) Eligibilit yi =β0 +β1Leniencyi +Cont rol s IV i ′ β C+ε i (4) yi =γ0 +γ1 ^ Eligibilit y i +Cont rol s IV i ′ C+n i The vector of Controls IV i includes dummies for regional office, type of assessment and half-year periods, and an additional set of controls related to the applicant and the application discussed in more detail in Section Empirical implementation. Interpretation γ1 represents the LATE for those individuals whose eligibility may be influenced by the assessor’s residualised leniency: the compliers. While identification of the individual 4
RkJQdWJsaXNoZXIy MjY0ODMw