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

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  • Martin Browning
  • Thomas Crossley

Abstract

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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  • 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.
    • 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. Martin Browning & Thomas F. Crossley & Guglielmo Weber, 2003. "Asking consumption questions in general purpose surveys," Economic Journal, Royal Economic Society, vol. 113(491), pages 540-567, November.
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    8. 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 546-551, May.
    9. 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.
    10. 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.
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    2. 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.
    3. Battistin, Erich & De Nadai, Michele & Krishnan, Nandini, 2020. "The Insights and Illusions of Consumption Measurements," CEPR Discussion Papers 14730, C.E.P.R. Discussion Papers.
    4. 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.
    5. John Sabelhaus & David Johnson & Stephen Ash & David Swanson & Thesia I. Garner & John Greenlees & Steve Henderson, 2014. "Is the Consumer Expenditure Survey Representative by Income?," NBER Chapters, in: Improving the Measurement of Consumer Expenditures, pages 241-262, National Bureau of Economic Research, Inc.
    6. Thomas F. Crossley & Joachim K. Winter, 2014. "Asking Households about Expenditures: What Have We Learned?," NBER Chapters, in: Improving the Measurement of Consumer Expenditures, pages 23-50, National Bureau of Economic Research, Inc.
    7. Keshav Dogra & Olga Gorbachev, 2016. "Consumption Volatility, Liquidity Constraints and Household Welfare," Economic Journal, Royal Economic Society, vol. 126(597), pages 2012-2037, November.
    8. Matthieu Stigler & David Lobell, 2021. "Optimal index insurance and basis risk decomposition: an application to Kenya," Papers 2111.08601, arXiv.org, revised Mar 2023.
    9. Jaqueson K Galimberti & Stefan Pichler & Regina Pleninger, 2023. "Measuring Inequality Using Geospatial Data," The World Bank Economic Review, World Bank, vol. 37(4), pages 549-569.
    10. J. Vernon Henderson & Adam Storeygard & David N. Weil, 2012. "Measuring Economic Growth from Outer Space," American Economic Review, American Economic Association, vol. 102(2), pages 994-1028, April.
    11. Orazio Attanasio & Erik Hurst & Luigi Pistaferri, 2012. "The Evolution of Income, Consumption, and Leisure Inequality in The US, 1980-2010," NBER Working Papers 17982, National Bureau of Economic Research, Inc.
    12. Zhang, Ping & Shi, XunPeng & Sun, YongPing & Cui, Jingbo & Shao, Shuai, 2019. "Have China's provinces achieved their targets of energy intensity reduction? Reassessment based on nighttime lighting data," Energy Policy, Elsevier, vol. 128(C), pages 276-283.
    13. Tilottama Ghosh & Sharolyn J. Anderson & Christopher D. Elvidge & Paul C. Sutton, 2013. "Using Nighttime Satellite Imagery as a Proxy Measure of Human Well-Being," Sustainability, MDPI, vol. 5(12), pages 1-32, November.
    14. Corrado, L. & Weeks, M., 2010. "Identification Strategies in Survey Response Using Vignettes," Cambridge Working Papers in Economics 1031, Faculty of Economics, University of Cambridge.
    15. Zhao, Da & Wu, Tianhao & He, Qiwei, 2017. "Consumption inequality and its evolution in urban China," China Economic Review, Elsevier, vol. 46(C), pages 208-228.
    16. Doppelhofer, G. & Moe Hansen, O-P. & Weeks, M., 2017. "Determinants of long-term economic growth redux: A Measurement Error Model Averaging (MEMA) approach," Cambridge Working Papers in Economics 1702, Faculty of Economics, University of Cambridge.
    17. Orazio Attanasio & Erik Hurst & Luigi Pistaferri, 2014. "The Evolution of Income, Consumption, and Leisure Inequality in the United States, 1980–2010," NBER Chapters, in: Improving the Measurement of Consumer Expenditures, pages 100-140, National Bureau of Economic Research, Inc.
    18. Matthieu Stigler & David Lobell, 2024. "Optimal index insurance and basis risk decomposition: an application to Kenya," American Journal of Agricultural Economics, John Wiley & Sons, vol. 106(1), pages 306-329, January.
    19. Doppelhofer, Gernot & Hansen, Ole-Petter Moe & Weeks, Melvyn, 2016. "Determinants of long-term economic Growth redux: A Measurement Error Model Averaging (MEMA) approach," Discussion Paper Series in Economics 19/2016, Norwegian School of Economics, Department of Economics.

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    JEL classification:

    • C83 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - Survey Methods; Sampling Methods

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