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Uncertainty causes rounding: an experimental study

Published online by Cambridge University Press:  14 March 2025

Paul A. Ruud ,
Daniel Schunk  and
Joachim K. Winter
Paul A. Ruud*
Affiliation:
Department of Economics, Vassar College, 124 Raymond Ave, Poughkeepsie, NY 12604-0708, USA
Daniel Schunk*
Affiliation:
Department of Economics, University of Mainz & University of Zurich, Jakob-Welder Weg 4, 55128 Mainz, Germany
Joachim K. Winter*
Affiliation:
Department of Economics, University of Munich, Ludwigstr. 33, 80539 Munich, Germany
*
[email protected]
[email protected]
[email protected]
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Abstract

Rounding is a common phenomenon when subjects provide an answer to an open-ended question, both in experimental tasks and in survey responses. From a statistical perspective, rounding implies that the measured variable is a coarsened version of the underlying continuous target variable. Since the coarsening process is non-random, inference from rounded data is generally biased. Despite the potentially severe consequences of rounding, little is known about its causes. In this paper, we focus on subjects’ uncertainty about the target variable as one potential cause for rounding behavior. We present a novel experimental method that induces uncertainty in a controlled way, thus providing causal evidence for the effect of subjects’ uncertainty on the extent of rounding. Then, we specify and estimate a mixture model that relates uncertainty and rounding. The results suggest that an increase in the exogenous level of uncertainty translates into higher variance of the subjects’ beliefs, which in turn results in more rounding.

Keywords

RoundingExperimental methodologyIndividual decision-makingEconometric analysis of experimental dataUncertaintySurvey response

JEL classification

C91: Laboratory, Individual Behavior C81: Methodology for Collecting, Estimating, and Organizing Microeconomic Data • Data Access
Type
Original Paper
Information
Experimental Economics , Volume 17 , Issue 3 , September 2014 , pp. 391 - 413
Copyright
Copyright © 2013 Economic Science Association

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Footnotes

We would like to thank the referees, seminar participants at UC Berkeley, the Universities of Mannheim, Munich, Tilburg, and Zurich, as well as participants of various conferences and in particular of the workshop on “Subjective Beliefs in Econometric Models”, as well as Ernst Fehr and Charles Manski for their helpful comments and suggestions.

Electronic Supplementary Material The online version of this article (doi:https://doi.org/10.1007/s10683-013-9374-8) contains supplementary material, which is available to authorized users.

References

Battistin, E., Miniaci, R., & Weber, G. (2003). What do we learn from recall consumption data?. The Journal of Human Resources, 38(2), 354–385. 10.2307/1558748CrossRefGoogle Scholar
Bellemare, C., Bissonnette, L., & Kröger, S. (2010). Bounding preference parameters under different assumptions about beliefs: a partial identification approach. Experimental Economics, 13, 334–345. 10.1007/s10683-010-9244-6CrossRefGoogle Scholar
Bruhin, A., Fehr-Duda, H., & Epper, T. (2010). Risk and rationality: uncovering heterogeneity in probability distortion. Econometrica, 78, 1375–1412. 10.3982/ECTA7139Google Scholar
Bruine de Bruin, W., Fischhoff, B., Millstein, S. G., & Halpern-Felsher, B. L. (2000). Verbal and numerical expressions of probability: “It’s a fifty-fifty chance”. Organizational Behavior and Human Decision Processes, 81(1), 115–131. 10.1006/obhd.1999.2868CrossRefGoogle Scholar
Engelberg, J., Manski, C. F., & Williams, J. (2009). Comparing point predictions and subjective probability distributions of professional forecasters. Journal of Business & Economic Statistics, 27, 30–41. 10.1198/jbes.2009.0003CrossRefGoogle Scholar
Fischhoff, B., & Bruine de Bruin, W. (1999). Fifty-fifty = 50 %?. Journal of Behavioral Decision Making, 12, 149–163. 10.1002/(SICI)1099-0771(199906)12:2<149::AID-BDM314>3.0.CO;2-J3.0.CO;2-J>CrossRefGoogle Scholar
Foley, J., van Dam, A., Feiner, S., & Hughes, J. (1995). Interactive computer graphics: principles and practice, Reading: Addison-Wesley.Google Scholar
Heitjan, D. F. (1994). Ignorability in general incomplete-data models. Biometrika, 81, 701–708. 10.1093/biomet/81.4.701CrossRefGoogle Scholar
Heitjan, D. F., & Rubin, D. B. (1991). Ignorability and coarse data. The Annals of Statistics, 19(4), 2244–2253. 10.1214/aos/1176348396CrossRefGoogle Scholar
Hey, J. D., Lotito, G., & Maffioletti, A. (2010). The descriptive and predictive adequacy of theories of decision making under uncertainty/ambiguity. Journal of Risk and Uncertainty, 41, 81–111. 10.1007/s11166-010-9102-0CrossRefGoogle Scholar
Hoderlein, S., & Winter, J. (2010). Structural measurement errors in nonseparable models. Journal of Econometrics, 157, 432–440. 10.1016/j.jeconom.2010.03.044CrossRefGoogle Scholar
Hsu, M., Bhatt, M., Adolphs, R., Tranel, D., & Camerer, C. F. (2005). Neural systems responding to degrees of uncertainty in human decision-making. Science, 310, 1680–1683. 10.1126/science.1115327CrossRefGoogle ScholarPubMed
Kahneman, D., & Tversky, A. (2000). Choices, values, and frames, New York: Cambridge University Press.CrossRefGoogle Scholar
Kleinjans, K. J., & van Soest, A. (2013, forthcoming). Rounding, focal point answers and nonresponse to subjective probability questions. Journal of Applied Econometrics. doi:10.1002/jae.2321CrossRefGoogle Scholar
Manski, C. F. (2004). Measuring expectations. Econometrica, 72(5), 1329–1376. 10.1111/j.1468-0262.2004.00537.xCrossRefGoogle Scholar
Manski, C. F., & Molinari, F. (2010). Rounding probabilistic expectations in surveys. Journal of Business & Economic Statistics, 28, 219–231. 10.1198/jbes.2009.08098CrossRefGoogle ScholarPubMed
Pudney, S. (2007). Heaping and leaping: survey response behavior and the dynamics of self-reported consumption expenditure. Unpublished manuscript, University of Essex.Google Scholar
Rustichini, A., Dickhaut, J., Ghirardato, P., Smith, K., & Pardo, J. (2005). A brain imaging study of the choice procedure. Games and Economic Behavior, 52(2), 257–282. 10.1016/j.geb.2004.08.005CrossRefGoogle Scholar
Tourangeau, R., Rips, L. J., & Rasinski, K. (2000). The psychology of survey response, Cambridge: Cambridge University Press 10.1017/CBO9780511819322CrossRefGoogle Scholar
von Gaudecker, H.-M., van Soest, A., & Wengström, E. (2011). Heterogeneity in risky choice behavior in a broad population. The American Economic Review, 101, 664–694. 10.1257/aer.101.2.664CrossRefGoogle Scholar
Wright, D. E., & Bray, I. (2003). A mixture model for rounded data. Statistician, 52(1), 3–13. 10.1111/1467-9884.00338CrossRefGoogle Scholar
Yaniv, I., & Foster, D. P. (1995). Graininess of judgement and uncertainty: an accuracy-informativeness trade-off. Journal of Experimental Psychology. General, 124, 424–432. 10.1037/0096-3445.124.4.424CrossRefGoogle Scholar
Yaniv, I., & Foster, D. P. (1997). Precision and accuracy of judgmental estimation. Journal of Behavioral Decision Making, 10, 21–32. 10.1002/(SICI)1099-0771(199703)10:1<21::AID-BDM243>3.0.CO;2-G3.0.CO;2-G>CrossRefGoogle Scholar
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