We elicit numerical expectations for late-onset dementia and long-term-care (LTC) outcomes in the US Health and Retirement Study. We provide the first empirical evidence on dementia-risk perceptions among dementia-free older Americans and establish important patterns regarding imprecision of subjective probabilities. Our elicitation distinguishes between precise and imprecise probabilities, while accounting for rounding of reports. Imprecise-probability respondents quantify imprecision using probability intervals. Nearly half of respondents hold imprecise dementia and LTC probabilities, while almost a third of precise-probability respondents round their reports. These proportions decrease substantially when LTC expectations are conditioned on hypothetical knowledge of the dementia state. Among rounding and imprecise-probability respondents, our elicitation yields two measures: an initial rounded or approximated response and a post-probe response, which we interpret as the respondent's true point or interval probability. We study the mapping between the two measures and find that respondents initially tend to over-report small probabilities and under-report large probabilities. Using a specific framework for study of LTC insurance choice with uncertain dementia state, we illustrate the dangers of ignoring imprecise or rounded probabilities for modeling and prediction of insurance demand.

中文翻译：

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精确概率还是不精确概率？与迟发性痴呆相关的调查反应的证据


我们在美国健康与退休研究中得出了对迟发性痴呆和长期护理 (LTC) 结果的数字预期。我们提供了关于无痴呆症老年人对痴呆症风险认知的第一个经验证据，并建立了有关主观概率不精确的重要模式。我们的启发区分了精确概率和不精确概率，同时考虑了报告的四舍五入。不精确概率的受访者使用概率区间来量化不精确性。近一半的受访者对痴呆症和长期护理的概率持不精确的态度，而近三分之一的受访者对他们的报告持精确概率的态度。当长期护理预期以痴呆状态的假设知识为条件时，这些比例会大幅下降。在四舍五入和不精确概率的受访者中，我们的启发产生了两种度量：初始四舍五入或近似响应和探测后响应，我们将其解释为受访者的真实点或区间概率。我们研究了这两种衡量标准之间的映射，发现受访者最初倾向于多报小概率而少报大概率。使用特定框架来研究不确定痴呆状态下的长期护理保险选择，我们说明了忽视保险需求建模和预测的不精确或舍入概率的危险。