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.

中文翻译：

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养老金资格规则和退休对认知功能的当地因果影响*

我们通过采用无效工具变量部分识别的文献结果，提出了一个识别框架来评估模糊回归不连续设置中的排除限制。有了这个框架，我们就退休对认知功能的影响提供了新的估计，并对基于年龄的退休工具变量的有效性进行了首次实证分析。点估计表明退休对认知功能的负面影响微不足道。部分识别区域通过表明如果退休实际上对认知功能有害，则不太可能大幅下降，从而使这一发现得到证实。其次，仅凭数据无法确定治疗效果的迹象。事实上，我们的结果支持退休后认知功能的改善。