Pension eligibility rules and the local causal effect of retirement on cognitive functioning

We propose an identification framework to evaluate the exclusion restriction in a fuzzy regression discontinuity setting, by adopting results from the literature on partial identification with invalid instrumental variables. With this framework, we provide new estimates of the effect of retirement on cognitive functioning and the first empirical analysis of the validity of an age‐based instrumental variable for retirement. Point estimates suggest an insignificant negative effect of retirement on cognitive functioning. Partial identification regions qualify this finding by suggesting that if retirement is, in fact, detrimental for cognitive functioning, then large drops are unlikely. Second, data alone cannot identify the sign of the treatment effect. In fact, our results support improvements in cognitive functioning 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 cut‐off in regression discontinuity designs.