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

Abstract

We thank Maura Coughlin, Adam Karabatakis, and Miriam Larson-Koester for able research assistance. We received useful feedback from seminar participants at the HRS work-in-progress series, Bocconi University, University of Southampton, NYU CUSP, University of Michigan, Purdue University, Laval University, University of Oslo, Statistics Norway, University of Munich, and University of Padova, as well as from participants in the 2016 NYFed and ESRC RCMiSoC Workshop on Subjective Expectations. Giustinelli gratefully acknowledges support from the National Institute on Aging (NIA P01-AG10179 and P30-AG012846), the National Science NBER working papers are circulated for discussion and comment purposes. They have not been peer-reviewed or been subject to the review by the NBER Board of Directors that accompanies official NBER publications.© 2018 by Pamela Giustinelli, Charles F. Manski, and Francesca Molinari. All rights reserved. Short sections of text, not to exceed two paragraphs, may be quoted without explicit permission provided that full credit, including © notice, is given to the source. ABSTRACTA 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.

Dynamics and Heterogeneity of Subjective Stock Market Expectations

“…From a more technical perspective, the finite mixture model might get more unstable if too many types are added. One could also try to make the rounding model more realistic, for instance by adding additional types as in Kleinjans and van Soest (2014) or by using ideas developed in Giustinelli et al (2018).…”

“…The difference may be explained by the fact that the objective (retrospectively "correct") answers to the eight probability questions differ in magnitude (independent of expectation type). This might not be true in other settings, such as in Giustinelli et al (2018), where the objective probabilities might be closer (even though across different domains). Moreover, question-specific rounding may also be more able to explain differences in rounding patterns, such as depicted in Figure 4.…”

“…Second, we enrich this panel model by a response model that allows for nonresponse and rounding, inspired by Manski and Molinari (2010) and building on the paramteric framework of Kleinjans and van Soest (2014). Our paper is also related to current research on response behavior in probabilistic expectations questions (Giustinelli et al, 2018) and the econometric modeling of stock market beliefs by Drerup et al (2017) and von Gaudecker and Wogrolly (2018).…”

“…Response distribution for the Gain > 0% and Gain > 20% questions Note that previous research often assumes that rounding patterns in probabilistic expectation questions are constant across domains. For example, using data from the Health and Retirement Survey (HRS),Giustinelli et al (2018) make this assumption for different domains,…”

“…In addition, individuals also seem to round more in the center of the distribution than in the tails (cf Giustinelli et al, 2018)…”