74 Chapter 3 deductible applies. This, in practice, implies imposing how individuals adjust their mental health care use in the months before and after facing the deductible within the same calendar year, when our yearly binary outcome captures only the extensive margin of consumption. Instead, our approach of excluding observations with partial deductibles avoids such assumptions, by comparing those paying the full deductible in the calendar year of their 18th birthday (228 months) with those paying no deductible at all in the previous calendar year (216 months). This set-up implies that our estimation strategy uses up to two observations for individuals born in January to November – one for the year she turns 17 and another for the year she turns 19 – and one additional observation for individuals born in December – which pay no deductible (yet) in the year they turn 18. While our main model in (1) presents effect estimates of the deductible increase in absolute terms, i.e. in percentage point (pp) changes, we also calculate relative effect sizes by dividing ^δ by the average mental health care use at 228 months - the first full deductible observation. Age* itm is centered at 228 months. We estimate all models separately by gender to account for different age and time trends in mental health services utilization. All models present clustered standard errors at the individual level. We conduct three analyses to explore potential violations of the identifying assumption that confounding discontinuities at 18 and any manipulation of the running variable are timeinvariant. First, we focus on two potential major discontinuities at the age of 18: living situation and personal income. We find no indication that the proportion of individuals living with their parents (Figure A2 in appendix D) or the average income (Figure A2.B in appendix D) evolved dissimilarly in the low and high deductible periods. Additionally, and following Grembi et al. [23], Figure A3 shows no evidence of time-varying annual RDD of mental health care use at age 18 in the low deductible period (2009, 2010 and 2011). Finally, while age cannot be manipulated, adolescents might anticipate the deductible introduction in the last months/year of the exemption; and therefore change their mental health care consumption already before turning 18. While this violates the identifying assumptions of the standard RDD framework, difference-in-discontinuity can overcome such anticipatory behaviour provided it is time-invariant. Our estimates in Table A1 provide supportive evidence of time-invariant anticipatory behaviour in the low versus high deductible periods, indicating that differences in this behaviour over time are not driving our results. Subgroup and sensitivity analyses We also conduct subgroup analyses of the effects of increasing deductibles on mental health care use ( Yi ) following two different approaches. First, we study heterogeneous effects by income. We interact month of age polynomials, intercepts and discontinuities in model (1) with quartiles of standardised disposable household income at age 17. Second, we focus only on the subpopulation of mental health care users at the age of 17. This subgroup analysis sheds light on the impact of the deductible increase on treatment
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