A short note on measuring subjective life expectancy: survival probabilities versus point estimates

The study of subjective life expectancy (SLE) is important in the context of economic choice behaviour [1], predicting mortality [2] and investment in future health [3]. Such individual subjective expectations may contain information not captured by their objective, actuarial counterparts [4]. Therefore, subjective longevity beliefs are increasingly elicited in order to better understand peoples’ decisions in various life domains, including health.

However, the measurement of SLE is not straightforward. In general, two elicitation approaches can be distinguished: the non-probabilistic and the probabilistic approach.¹ The first approach concerns the direct measurement of individuals’ subjective estimates of expected lifetime, typically asking for a point estimate. While this method is simple and straightforward to administer, it does not provide information regarding the uncertainty of reaching the specified age [5]. The second elicitation approach asks people for their subjective survival probability (SSP), i.e. their assessment of the probability of surviving to a certain target age. SSPs are used in various large-scale household surveys such as, for example, the Health Retirement Study (HRS) and the Survey of Health, Ageing and Retirement in Europe (SHARE). Research using such data has focused on their accuracy compared to actuarial data, their predictive power for actual mortality, and their relevance in the context of economic decisions [6‐8]. SSPs capture uncertainty and allow for computing survival probability distributions, but do not inform directly about SLE, and their elicitation is cognitively demanding [9], leading to inconsistencies [10]. Rounding and focal point answers are common phenomena in both approaches, but remain underexplored [11, 12].

The comparison of results from studies using these different approaches requires the comparison of both elicitation techniques. This helps to understand possible differences between elicitation methods. Moreover, considering the unresolved issues with both approaches, studying different elicitation techniques remains important. Only a few studies have directly related both approaches. Hamermesh [13] first employed both approaches in a single survey, using two unrepresentative samples, and found slightly higher estimates (i.e. 0.5–1 year) when probability estimates were used. Recently, Wu et al. [14] evaluated the consistency of both approaches among Australian respondents aged between 50 and 74 years and indicated that ‘even for those individuals who consistently evaluated their survival probabilities, very few choose life expectancies matching their personal beliefs of survival probabilities’.

In this short note, we report on one of the few studies providing a head-to-head comparison of both elicitation formats administered in one study sample. We show the distribution of responses from both approaches and focus on focal point answers, rounding and the consistency of answers. We compare both formats and relate them to relevant background characteristics of respondents such as health, lifestyle, and age of death of next of kin. Furthermore, we highlight possible consequences of sequential questioning (when eliciting SSPs).

From our initial sample of 1223 respondents we excluded 156 (12.8 %) who completed the online questionnaire in <15 min. This minimal completion time for the questionnaire was determined on the basis of a pilot-test of the questionnaire. Next, we selected the respondents who answered all SSP questions for age 60 and above, i.e. those aged between 20 and 59 years (n = 878).⁵ For reasons of consistency and to enable the envisaged comparisons between approaches, we consecutively excluded respondents who had: a SLE point estimate lower than the current age (n = 3); a SLE lower than 60 or higher than 100 (because we did not have SSPs for those ages) (n = 37); provided the same answers to all five SSP questions (n = 25), including 19 respondents reporting a 50 % chance to all five target ages; an increasing SSP for higher ages (n = 24); or a distribution of SSP answers that did not intersect 50 % within the 60–100 years age range (n = 52). Finally, 737 respondents (60.3 %) remained for further analyses. Compared to the initial sample of 1223, this led to slightly more centred distributions for age and education and an underrepresentation of men. The sample characteristics are shown in Table 1.

Using point estimates, mean SLE was 80.2 years (SD = 8.3). Figure 1 shows the frequency distribution of SLE point estimates. In line with earlier studies, approximately 40 % of answers were rounded to tens, and 70 % to fives. Peaks were observed at ages 75, 80 and 85.

Mean SSP declined from 87.6 % (SD = 13.6) at target age 60 to 13.4 % (SD = 15.5) at target age 100 (see Fig. 2). More than 75 % of responses to the five probability questions were multiples of ten, while almost 95 % were multiples of five. A “50 %” answer was most often observed for the SSP questions at target ages 80 and 90 (around 18 % of responses for both ages).

The mean point estimate obtained from the SSPs was 83.6 (SD = 9.3), which is on average 3.4 years (SD = 8.7) higher than the SLE point estimate. The SLE point estimate and the point estimate obtained from SSPs were correlated (r = 0.52, p < 0.001).

Individual differences between SLE and SSP point estimates ranged from −32 to +40 (Fig. 3), and the distribution showed a slight positive skew. Finally, the certainty score for the SLE point estimate derived from SSPs was 58.8 %.

In this short note, we presented estimations of subjective life expectancy based on two elicitation techniques, using a representative sample of the Dutch population aged 18–65 years in terms of age, gender and education level. On average, respondents were more optimistic (about 3.5 years) about their longevity when expressed in survival probabilities, using the 50 % chance point to calculate a SSP point estimate. Despite this difference, variables associated with SLE and SSP point estimates were very similar and their coefficient signs were plausible. Gender, age and socioeconomic variables like education and income were not strongly associated with the SLE and SSP point estimates. We found that age turned insignificant after introducing health indicators in the SLE model (results not shown here), which is not uncommon [7]. SLE and SSP point estimates were more similar for younger respondents and respondents with a higher socioeconomic status. This may reflect a higher capability of handling probability scores.

Some limitations of this study and the methods used are noted before highlighting the implications of our findings. First, this study was web-based and performed in one single country. This limits its generalizability. Second, excluding respondents with inconsistent answers from further analyses may have induced a selection bias in our results. Excluded respondents more often had a lower income and were male.

Nonetheless, we emphasise some important findings. First, inconsistencies in survival probabilities across target ages (i.e. same answers to all five SSP questions, increasing SSP for higher ages) were quite common (n = 49). Inconsistencies in SLE estimates (i.e. lower SLE than their current age) were less common (n = 3). Obviously, besides the difficulty of SSP estimates, this may reflect the fact that respondents answered five SSP questions but only one SLE question, providing greater opportunity for inconsistencies.

Second, rounding and focal point answers were common, as observed before [11, 12]. One in five respondents reported a SLE point estimate of exactly 80 years, for instance. While this may reflect a genuine expectation, it may also emanate from uncertainty, imprecision, or a tendency to provide focal answers. SSP responses also showed clear rounding issues. Here, special attention is required for a “50 %” answer. Bruine de Bruin et al. [20] for example, suggested that such “50/50” answers may indicate high uncertainty (similar to “donʼt know”) rather than a genuine probabilistic belief. Respondents reporting a 50 % chance for all five target ages (n = 19) were excluded from the analyses in this paper. Therefore, we expect that the remaining 50 % answers are more likely to represent a genuine probabilistic belief than high uncertainty, and thus to contain valuable information. Nevertheless, given that the SSP point estimate was determined using the probability of 50 %, this deserves more attention in future studies. Adjusting for probability weighting [21] may also be important.

Third, sequential questioning may lead to anchoring [22]. Here, the probability of reaching the first target age given by respondents may have influenced probabilities at subsequent target ages. We tested this by comparing SSPs of respondents aged 50–59 (included in the current sample) with those of respondents aged 60–69 (excluded from the current sample). The younger group of respondents started with 60 as first target age, the older group with 70 as first target age. Interestingly, the answers of both groups resulted in very similar probability distribution curves, starting at almost the same probability, but the latter starting 10 years later (Fig. 4). While this may relate to a rational shift of expectations, it may also signal anchoring.

Our results relate well to existing literature. For instance, the explanatory variables significantly associated with subjective life expectancy were largely in line with those reported by Hamermesh [13]. Moreover, the difference found between the two methods (probability estimates being higher than point estimates) was in the same direction as reported by Hamermesh [13], albeit somewhat larger. This may relate to methodological differences between the studies (e.g., Hamermesh [13] used unrepresentative samples from the US, in which academic economists and male respondents were overrepresented, two instead of five target ages, and a different method of deriving subjective survival curves). Inconsistencies between these elicitation formats were also observed by Wu et al. [14].⁶

In conclusion, an increasing amount of research aims to understand (the formation of) subjective longevity expectations and their relation to health behaviours and outcomes. Different elicitation methods are used across studies. The results of the current study suggest that findings may not be directly comparable across studies, especially in certain subgroups of the population. Future work may compare both approaches in relation to objective survival expectations and predicting economic choice behaviour. More research on how to measure subjective expectations is therefore warranted.