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Identification of structural models in the presence of measurement error due to rounding in survey responses

Listed author(s):
  • Stefan Hoderlein

    (Boston College)

  • Bettina Siflinger

    ()

    (University of Mannheim)

  • Joachim Winter

    ()

    (University of Munich)

Distortions in the elicitation of economic variables arise frequently. A common problem in household surveys is that reported values exhibit a significant degree of rounding. We interpret rounding as a filter that allows limited information about the relationship of interest to pass. We argue that rounding is an active decision of the survey respondent, and propose a general structural model that helps to explain some of the typical distortions that arise out of this active decision. Specifically, we assume that there is insufficient ability of individuals to acquire, process and recall information, and that rational individuals aim at using the scarce resources they devote to a survey in an optimal fashion. This model implies selection and places some structure on the selection equation. We use the formal model to correct for some of the distorting effects of rounding on the relationship of interest, using all the data available. Finally, we show how the concepts developed in this paper can be applied in consumer demand analysis by exploiting a controlled survey experiment, and obtain plausible results.

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Paper provided by Boston College Department of Economics in its series Boston College Working Papers in Economics with number 869.

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Date of creation: 19 Jan 2015
Handle: RePEc:boc:bocoec:869
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  1. F. Thomas Juster & Richard Suzman, 1995. " An Overview of the Health and Retirement Study," Journal of Human Resources, University of Wisconsin Press, vol. 30, pages s7-s56.
  2. Hoderlein, Stefan, 2011. "How many consumers are rational?," Journal of Econometrics, Elsevier, vol. 164(2), pages 294-309, October.
  3. Erich Battistin & Raffaele Miniaci & Guglielmo Weber, 2003. "What Do We Learn from Recall Consumption Data?," Journal of Human Resources, University of Wisconsin Press, vol. 38(2).
  4. Susanne M. Schennach, 2012. "Measurement error in nonlinear models - a review," CeMMAP working papers CWP41/12, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  5. James J. Heckman & Edward Vytlacil, 2005. "Structural Equations, Treatment Effects, and Econometric Policy Evaluation," Econometrica, Econometric Society, vol. 73(3), pages 669-738, 05.
  6. Arthur Lewbel, 2001. "Demand Systems with and without Errors," American Economic Review, American Economic Association, vol. 91(3), pages 611-618, June.
  7. Huber, Martin & Melly, Blaise, 2011. "Quantile Regression in the Presence of Sample Selection," Economics Working Paper Series 1109, University of St. Gallen, School of Economics and Political Science.
  8. Philipson, Tomas, 2001. "Data Markets, Missing Data, and Incentive Pay," Econometrica, Econometric Society, vol. 69(4), pages 1099-1111, July.
  9. S. M. Schennach & Yingyao Hu, 2013. "Nonparametric Identification and Semiparametric Estimation of Classical Measurement Error Models Without Side Information," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(501), pages 177-186, March.
  10. Hoderlein, Stefan & Winter, Joachim, 2010. "Structural measurement errors in nonseparable models," Journal of Econometrics, Elsevier, vol. 157(2), pages 432-440, August.
  11. Charles F. Manski, 2004. "Measuring Expectations," Econometrica, Econometric Society, vol. 72(5), pages 1329-1376, 09.
  12. McFadden, Daniel, 2012. "Economic juries and public project provision," Journal of Econometrics, Elsevier, vol. 166(1), pages 116-126.
  13. Yingyao Hu & Susanne M. Schennach, 2008. "Instrumental Variable Treatment of Nonclassical Measurement Error Models," Econometrica, Econometric Society, vol. 76(1), pages 195-216, 01.
  14. Kristin J. Kleinjans & Arthur Van Soest, 2014. "Rounding, Focal Point Answers And Nonresponse To Subjective Probability Questions," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 29(4), pages 567-585, 06.
  15. Sims, Christopher A., 2003. "Implications of rational inattention," Journal of Monetary Economics, Elsevier, vol. 50(3), pages 665-690, April.
  16. Imbens, Guido W & Angrist, Joshua D, 1994. "Identification and Estimation of Local Average Treatment Effects," Econometrica, Econometric Society, vol. 62(2), pages 467-475, March.
  17. Stefan Hoderlein & Enno Mammen, 2007. "Identification of Marginal Effects in Nonseparable Models Without Monotonicity," Econometrica, Econometric Society, vol. 75(5), pages 1513-1518, 09.
  18. Hayfield, Tristen & Racine, Jeffrey S., 2008. "Nonparametric Econometrics: The np Package," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 27(i05).
  19. Manski, Charles F. & Molinari, Francesca, 2010. "Rounding Probabilistic Expectations in Surveys," Journal of Business & Economic Statistics, American Statistical Association, vol. 28(2), pages 219-231.
  20. Deaton, Angus S & Muellbauer, John, 1980. "An Almost Ideal Demand System," American Economic Review, American Economic Association, vol. 70(3), pages 312-326, June.
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