Tail and Center Rounding of Probabilistic Expectations in the Health and Retirement Study.

We study rounding of numerical expectations in the Health and Retirement Study (HRS) between 2002 and 2014. We document that respondent-specific rounding patterns across questions in individual waves are quite stable across waves. We discover a tendency by about half of the respondents to provide more refined responses in the tails of the 0-100 scale than the center. In contrast, only about five percent of the respondents give more refined responses in the center than the tails. We find that respondents tend to report the values 25 and 75 more frequently than other values ending in 5. We also find that rounding practices vary somewhat across question domains and respondent characteristics. We propose an inferential approach that assumes stability of response tendencies across questions and waves to infer person-specific rounding in each question domain and scale segment and that replaces each point-response with an interval representing the range of possible values of the true latent belief. Using expectations from the 2016 wave of the HRS, we validate our approach. To demonstrate the consequences of rounding on inference, we compare best-predictor estimates from face-value expectations with those implied by our intervals.