Survey response in probabilistic questions and its impact on inference

• We model expectations of a continuous variable and response to probabilistic items.
• We apply the model to the retirement income replacement rate (RR) of Dutch employees.
• We find reporting behavior: few focal answers but substantial rounding.
• Also modeling reporting behavior matters for the covariate effects on the median RR.
• Response behavior and expectations are persistent at the level of the individual.

We develop a panel data model of expectations of a continuous outcome variable elicited on a percentage-chance scale. The model explains the location and dispersion of the subjective distributions by socio-economic covariates and unobserved factors. Moreover, it accounts explicitly for non-response, non-informative focal answers, and recall and rounding errors. We apply the model to the expected retirement income replacement rate of Dutch wage workers. We find that incorporating these features of the answering process increases the size and significance of relationships with covariates. The estimates indicate substantial rounding but few focal answers. Respondents tend to stick to a certain answering strategy: non-response, rounding and especially non-informative focal answers are characterized by substantial unobserved heterogeneity across individuals.