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

A growing number of surveys elicit respondents' expectations for future events on a 0-100 scale of percent chance. These data reveal substantial heaping at multiples of 10 and 5 percent, suggesting that respondents round their reports. This paper studies the nature of rounding by analyzing response patterns across expectations questions and waves of the Health and Retirement Study. We discover a tendency by about half of the respondents to provide more refined responses in the tails of the scale than the center. Only about five percent provide more refined responses in the center than the tails. We find that rounding varies across question domains, which range from personal health to personal finances to macroeconomic events. We develop a two-stage framework to characterize person-specific rounding. The first stage uses observed responses to infer respondents' rounding practice in each question domain and scale segment. The second stage replaces each original point response with an interval, representing the range of possible values of the respondent's true latent belief implied by the degree of rounding inferred in the first stage. We study how the inferred rounding types in the first stage vary with respondent characteristics, including age and cognitive abilities