92 Chapter 3 APPENDIX D. ANALYSES ON MODEL ASSUMPTIONS We conducted three sets of analyses to explore potential violations of the identifying assumption that confounding discontinuities at 18 and any manipulation of the running variable are time-invariant. First, Figure A2 shows age-trends in the proportion of individuals living with their parents (top) and for the average percentile of personal income (as a percentile of the overall population distribution; bottom). Dissimilar discontinuities at age 18 between the low and high deductible period, if any, would cast potential doubt on the identifying assumption of our empirical approach. The share of individuals living with their parents evolves virtually identical over age among both genders in both periods. Average income percentiles are not identical over the entire age range, but the age-trends and discontinuities differ not much. Figure A2. Age-trends in the proportion of individuals living with their parents (A) and average percentile of personal income in the population personal income distribution (B), by age in months. Second, we examine whether annual discontinuities in the low deductible period are time-invariant [12]. Figure A3 displays annual RDD estimates of mental health care takeup at age 18, obtained from estimating model (1) for each year separately. The resulting discontinuities are stable in the low deductible period (2009, 2010, 2011). Figure A3 also provides the annual RDD coefficient for 2012, which was excluded from the main study analysis due to the introduction of adult specialist care co-payments
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