MI Double Feature: Multiple Imputation to Address Nonresponse and Rounding Errors in Income Questions


  • Joerg Drechsler Institute for Employment Research
  • Hans Kiesl
  • Matthias Speidel Kompetenzzentrum Empirische Methoden Institut für Arbeitsmarkt- und Berufsforschung der Bundesagentur für Arbeit Regensburger Str. 100 90478 Nürnberg




Obtaining reliable income information in surveys is difficult for two reasons. On the one hand, many survey respondents consider income to be sensitive information and thus are reluctant to answer questions regarding their income. If those survey participants that do not provide information on their income are systematically different from the respondents - and there is ample of research indicating that they are - results based only on the observed income values will be misleading. On the other hand, respondents tend to round their income. Especially this second source of error is usually ignored when analyzing the income information.

In a recent paper, Drechsler and Kiesl (2014) illustrated that inferences based on the collected information can be biased if the rounding is ignored and suggested a multiple imputation strategy to account for the rounding in reported income. In this paper we extend their approach to also address the nonresponse problem. We illustrate the approach using the household income variable from the German panel study "Labor Market and Social Security''.


Clementi F, Gallegati M (2005). "Pareto's law of income distribution: Evidence for Germany, the United Kingdom, and the United States." In A Chatterjee, S Yarlagadda, B Chakrabarti (eds.), Econophysics of wealth distributions, pp. 3-14. Milan: Springer.

Drechsler J, Kiesl H (2014). "Beat the heap - an imputation strategy for valid inferences from rounded income data." IAB Discussion Paper 2/2014.

Eurostat (2013). "Glossary: Equivalised disposable income - Statistics Explained (2013/6/2)." http://epp.eurostat.ec.europa.eu/statistics_explained/index.php/Glossary:Equivalised_disposable_income>.

Gelman A, Carlin JB, Stern HS, Rubin DB (2004). "Bayesian Data Analysis." Second edition. London: Chapman and Hall.

Graf M, Nedyalkova D (2013). "Modeling of income and indicators of poverty and social exclusion using the generalized beta distribution of the second kind." Review of Income and Wealth, online first.

Heitjan D (1994). "Ignorability in General Incomplete-Data Models." Biometrika, 81, 701-708.

Heitjan D, Rubin D (1990). "Inference from Coarse Data Via Multiple Imputation with Application to Age Heaping." Journal of the American Statistical Association, 85, 304-314.

Huttenlocher J, Hedges LV, Bradburn NM (1990). "Reports of elapsed time: bounding and rounding processes in estimation." Journal of Experimental Psychology: Learning, Memory, and Cognition, 16(2), 196-213.

Little RJA, Rubin DB (2002). "Statistical Analysis with Missing Data". Second edition. New York: John Wiley and Sons.

Manski CF, Molinari F (2010). "Rounding Probabilistic Expectations in Surveys." Journal of Business & Economic Statistics, 28, 219-231.

Pischke JS (1995). "Measurement error and earnings dynamics: Some estimates from the PSID validation study." Journal of Business & Economic Statistics, 13(3), 305-314.

Raghunathan TE, Lepkowski JM, van Hoewyk J, Solenberger P (2001). "A multivariate technique for multiply imputing missing values using a series of regression models." Survey Methodology, 27, 85-96.

Rubin DB (1976). "Inference and missing data." Biometrika, 63, 581-590.

Rubin DB (1978). "Multiple imputations in sample surveys." In Proceedings of the Section on Survey Research Methods of the American Statistical Association, pp. 20-34. Alexandria, VA: American Statistical Association.

Rubin DB (1987). "Multiple Imputation for Nonresponse in Surveys". New York: John Wiley and Sons.

Ruud PA, Schunk D, Winter JK (2013). "Uncertainty causes rounding: an experimental study." Experimental Economics, pp. 1-23.

TrappmannM, Gundert S,Wenzig C, Gebhardt D (2010). "PASS: a household panel survey for

research on unemployment and poverty." Schmollers Jahrbuch. Zeitschrift fur Wirtschafts und Sozialwissenschaften, 130, 609-622.

Wang H, Heitjan DF (2008). "Modeling heaping in self-reported cigarette counts." Statistics in medicine, 27(19), 3789-3804.

Wang H, Shiffman S, Grith SD, Heitjan DF (2012). "Truth and memory: Linking instantaneous and retrospective self-reported cigarette consumption." The annals of applied

statistics, 6(4), 1689-1706.



How to Cite

Drechsler, J., Kiesl, H., & Speidel, M. (2015). MI Double Feature: Multiple Imputation to Address Nonresponse and Rounding Errors in Income Questions. Austrian Journal of Statistics, 44(2), 59-71. https://doi.org/10.17713/ajs.v44i2.77