Eliciting subjective survival curves: Lessons from partial identification

When analyzing data on subjective expectations of continuous outcomes, researchers have access to a limited number of reported probabilities for each respondent from which to construct complete distribution functions. Moreover, reported probabilities may be rounded and thus not equal to true beliefs. Using survival expectations elicited from a representative sample from the Netherlands, we investigate what can be learned if we take these two sources of missing information into account and expectations are therefore only partially identified. We find novel evidence for rounding by checking whether reported expectations are consistent with a hazard of death that increases weakly with age. Only 39% of reported beliefs are consistent with this under the assumption that all probabilities are reported precisely, while 92% are if we allow for rounding. Using the available information to construct bounds on subjective life expectancy, we show that the data alone are not sufficiently informative to allow for useful inference in partially identified linear models, even in the absence of rounding. We propose to improve precision by interpolation between rounded probabilities. Interpolation in combination with a limited amount of rounding does yield informative intervals.