Welfare Measurement and Measurement Error

Abstract

The approximate effects of measurement error on a variety of measures of inequality and poverty are derived. They are shown to depend on the measurement error variance and functionals of the errorcontaminated income distribution, but not on the form of the measurement error distribution, and to be accurate within a rich class of error-free income distributions and measurement error distributions. The functionals of the error-contaminated income distribution that approximate the measurement error induced distortions can be estimated. So it is possible to investigate the sensitivity of welfare measures to alternative amounts of measurement error and, when an estimate of the measurement error variance is available, to calculate corrected welfare measures. The methods are illustrated in an application using Indonesian household expenditure data.

Micro-Level Estimation of Poverty and Inequality

“…Clearly because expenditures are measured with error this may differ from a measure based on true expenditures. See Chesher and Schluter (2002) for methods to estimate the sensitivity of welfare measures to mismeasurement in y. u ch = c + ch complete enumeration areas are added, independently of previous EAs.…”

Inequality, Poverty, and the Intra-Household Allocation of Consumption in Senegal

“…Such level of measurement error is highly unlikely. Bound et al, 2001, give much lower orders of magnitude for measurement error in income, closer to 20%, and this is the range considered by Chesher and Schluter, 2002 in their application to Indonesian data. Hence, it is unlikely that measurement error explains the high observed inequality in the PSF survey.…”

J-Divergence Measurements of Economic Inequality

“…It is of interest to note that if both the observed income and the contamination terms are log-normal this implies that the true income distribution also has this form. Further the J-divergence of a log-normal distribution is simply equal to σ 2 y and hence this form of measurement error simply leads to an overstatement of inequality by σ 2 λ (see Chesher and Schluter (2002) or van Praag et al (1983) for similar results). The intuition behind this finding is clear: even when uncorrelated with income, data contamination introduces a new source of variation that acts via Jensen's inequality to increase the overall inequality (Arnold, 1980).…”

“…It is of interest to note that if both the observed income and the contamination terms are log‐normal this implies that the true income distribution also has this form. Further the J ‐divergence of a log‐normal distribution is simply equal to and hence this form of measurement error simply leads to an overstatement of inequality by (see Chesher and Schluter () or van Praag et al . () for similar results).…”