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Measurement Error Bias in Estimates of Income and Income Growth among the Poor: Analytical Results and a Correction Formula

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  • Paul Glewwe

Abstract

In any population, income growth among the poor may be higher or lower than overall income growth. Estimates of income growth among the poor are almost always based on household surveys, but income and expenditure data in those surveys are almost always measured with error. This article uses the assumption that income follows a lognormal distribution to demonstrate that such measurement error can lead to biased estimates of the mean income of the poor and the growth of that mean income over time. In particular, when both income and the measurement error are lognormally distributed, (i) measurement error leads to underestimation of the mean income among the poor at any point in time, (ii) increases (decreases) in measurement error over time, for a given level of inequality, lead to underestimation (overestimation) of income growth among the poor, and (iii) increases (decreases) in inequality over time, for a given level of measurement error, lead to overestimation (underestimation) of income growth among the poor. This article derives a correction formula that calculates the mean income of the poor as a function of the mean of the observed income of the poor, the variance of observed (log) income, and the variance of the (log of) measurement error. This formula can then be used to calculate consistent estimates of income growth among the poor. This article also presents several simulations that relax the assumptions that measurement errors are lognormally distributed, have a mean of zero, and are uncorrelated with income. Relaxing these assumptions has little effect on the results, which implies that the derivations are robust to many different types of measurement error.

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  • Paul Glewwe, 2007. "Measurement Error Bias in Estimates of Income and Income Growth among the Poor: Analytical Results and a Correction Formula," Economic Development and Cultural Change, University of Chicago Press, vol. 56(1), pages 163-189, October.
    • Handle: RePEc:ucp:ecdecc:v:56:y:2007:p:163-189
    DOI: 10.1086/520559
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    1. Sen, Amartya, 1973. "On Economic Inequality," OUP Catalogue, Oxford University Press, number 9780198281931.
    2. John Gibson & Jikun Huang & Scott Rozelle, 2003. "Improving Estimates of Inequality and Poverty from Urban China's Household Income and Expenditure Survey," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 49(1), pages 53-68, March.
    3. Sen, Amartya, 1997. "On Economic Inequality," OUP Catalogue, Oxford University Press, number 9780198292975.
    4. Menno Pradhan, 2001. "Welfare Analysis with a Proxy Consumption Measure – Evidence from a Repeated Experiment in Indonesia," Tinbergen Institute Discussion Papers 01-092/2, Tinbergen Institute.
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    1. repec:dau:papers:123456789/5143 is not listed on IDEAS
    2. Dwayne Benjamin & Loren Brandt & Brian McCaig, 2017. "Growth with equity: income inequality in Vietnam, 2002–14," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 15(1), pages 25-46, March.
    3. Pina-Sánchez Jose & Koskinen Johan & Plewis Ian, 2019. "Adjusting for Measurement Error in Retrospectively Reported Work Histories: An Analysis Using Swedish Register Data," Journal of Official Statistics, Sciendo, vol. 35(1), pages 203-229, March.
    4. Paul Glewwe & Hai-Anh Hoang Dang, 2011. "Was Vietnam's Economic Growth in the 1990s Pro-Poor? An Analysis of Panel Data from Vietnam," Economic Development and Cultural Change, University of Chicago Press, vol. 59(3), pages 583-608.
    5. Pina-Sánchez, Jose & brunton-smith, ian & Buil-Gil, David & Cernat, Alexandru, 2022. "rcme: A Sensitivity Analysis Tool to Explore the Impact of Measurement Error in Police Recorded Crime Rates," SocArXiv sbc8w, Center for Open Science.
    6. Filho, Irineu de Carvalho & Chamon, Marcos, 2012. "The myth of post-reform income stagnation: Evidence from Brazil and Mexico," Journal of Development Economics, Elsevier, vol. 97(2), pages 368-386.
    7. Charlotte Guénard & Sandrine Mesplé‐Somps, 2010. "Measuring Inequalities: Do Household Surveys Paint A Realistic Picture?," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 56(3), pages 519-538, September.
    8. Pina-Sánchez, Jose & Buil-Gil, David & brunton-smith, ian & Cernat, Alexandru, 2021. "The impact of measurement error in models using police recorded crime rates," SocArXiv ydf4b, Center for Open Science.
    9. Shelley Clark & Caroline W. Kabiru & Sonia Laszlo & Stella Muthuri, 2019. "The Impact of Childcare on Poor Urban Women’s Economic Empowerment in Africa," Demography, Springer;Population Association of America (PAA), vol. 56(4), pages 1247-1272, August.

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