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Are Two Cheap, Noisy Measures Better Than One Expensive, Accurate One?

  • Martin Browning
  • Thomas Crossley

1. Survey responses are always subject to measurement error. In general surveys (and especially longitudinal surveys), there are severe constraints on the time that can be spent eliciting a less noisy response for any target variable. In this paper we consider when it may be better to consider multiple noisy measures of the target measure rather than improving the reliability of a single measure. 2. The Kotlarski result states that if the measurement errors in two measures of the same target variable are mutually independent and independent of the true value then we can recover the entire distribution of the quantity of interest, up to location. 3. We consider designing surveys to deliver measurement error with desirable properties. This shifts the emphasis from reliability (the signal to noise ratio for any given measure) to the joint properties of the multiple measures. 4. To illustrate our ideas, we consider a concrete example: the measurement of consumption inequality. A small simulation study suggests that the approach we propose has promise. The next step in this research agenda is experiments in survey data collection.

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File URL: http://www.aeaweb.org/articles.php?doi=10.1257/aer.99.2.99
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Article provided by American Economic Association in its journal American Economic Review.

Volume (Year): 99 (2009)
Issue (Month): 2 (May)
Pages: 99-103

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Handle: RePEc:aea:aecrev:v:99:y:2009:i:2:p:99-103
Note: DOI: 10.1257/aer.99.2.99
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  1. Erich Battistin & Richard Blundell & Arthur Lewbel, 2007. "Why is Consumption More Log Normal Than Income? Gibrat's Law Revisited," Boston College Working Papers in Economics 671, Boston College Department of Economics.
  2. Martin Browning & Thomas Crossley, 2009. "Are Two Cheap, Noisy Measures Better Than One Expensive, Accurate One?," American Economic Review, American Economic Association, vol. 99(2), pages 99-103, May.
  3. Martin Browning & Thomas F. Crossley & Guglielmo Weber, 2002. "Asking Consumption Questions in General Purpose Surveys," Social and Economic Dimensions of an Aging Population Research Papers 77, McMaster University.
  4. Richard Blundell & Luigi Pistaferri & Ian Preston, 2004. "Imputing consumption in the PSID using food demand estimates from the CEX," IFS Working Papers W04/27, Institute for Fiscal Studies.
  5. Cutler, David M & Katz, Lawrence F, 1992. "Rising Inequality? Changes in the Distribution of Income and Consumption in the 1980's," American Economic Review, American Economic Association, vol. 82(2), pages 546-51, May.
  6. Li, Tong & Vuong, Quang, 1998. "Nonparametric Estimation of the Measurement Error Model Using Multiple Indicators," Journal of Multivariate Analysis, Elsevier, vol. 65(2), pages 139-165, May.
  7. Skinner, Jonathan, 1987. "A superior measure of consumption from the panel study of income dynamics," Economics Letters, Elsevier, vol. 23(2), pages 213-216.
  8. Bound, John & Brown, Charles & Mathiowetz, Nancy, 2001. "Measurement error in survey data," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 5, chapter 59, pages 3705-3843 Elsevier.
  9. Martin Browning & Mette Gørtz, 2012. "Spending Time and Money within the Household," Scandinavian Journal of Economics, Wiley Blackwell, vol. 114(3), pages 681-704, 09.
  10. Susanne M. Schennach, 2004. "Estimation of Nonlinear Models with Measurement Error," Econometrica, Econometric Society, vol. 72(1), pages 33-75, 01.
  11. Richard Blundell & Ian Preston, 1998. "Consumption Inequality And Income Uncertainty," The Quarterly Journal of Economics, MIT Press, vol. 113(2), pages 603-640, May.
  12. Naeem Ahmed & Matthew Brzozowski & Thomas Crossley, 2006. "Measurement errors in recall food consumption data," IFS Working Papers W06/21, Institute for Fiscal Studies.
  13. Menno Pradhan, 2009. "Welfare Analysis with a Proxy Consumption Measure: Evidence from a Repeated Experiment in Indonesia," Fiscal Studies, Institute for Fiscal Studies, vol. 30(Special I), pages 391-417, December.
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