Partial Identification of the Causal Effect of Retirement on Cognition

Abstract

We propose an identification framework to empirically evaluate the validity of the exclusion restriction in a Regression Discontinuity setting. We embed recent results from the literature on partial identification with invalid instrumental variables into a Fuzzy Regression Discontinuity Designs underpinned by assumptions that allow the interpretation of the Discontinuity Design as a type of local randomized experiment with non-compliance. We use this setting to provide the first empirical analysis of the validity of an age-based instrumental variable for retirement (eligibility for the US Social Security Retirement Pension, SSRP). The point estimates suggest an insignificant negative LATE of 8.6% within +/-9 months around the SSRP. Partial identification regions qualify this finding by, first, suggesting that if retirement is, in fact, detrimental for the memory score, then drops beyond 8% are unlikely. Second, data alone cannot identify the sign of the treatment effect. In fact, our data supports improvements in the memory score of up to 16\% following retirement. The bounds analysis suggest that, when studying the impact of retirement, the validity of eligibility as an instrumental variable depends on the time period considered for the analysis and that violations of the exclusion restriction are likely already in very small intervals of +/-8 months around the SSRP age.