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April 1998, Vol. 121, No. 4
Alan B. Krueger and Aaron Siskind
In a clever and influential paper, William Nordhaus provides an estimate of the extent of bias in the Consumer Price Index (CPI) by comparing the net proportion of families that report an improvement in their financial situation with changes in real median income.1 Specifically, he bases his analysis on time-series data collected by the University of Michigans Institute for Social Research (ISR) in its Survey of Consumers. Among other things, this survey, which is used to measure consumer confidence, asks respondents whether their families financial situation improved or worsened in the past year.
Nordhaus reasons that if real median household income rises in a particular year, more respondents should report becoming better off than worse off, and if real median income falls, more respondents should report becoming worse off than better off. In this view, constant real median income should be associated with an equal number of families reporting financial gains and losses. Nordhaus estimates the implied bias in the CPI by determining the growth rate of real median income that is associated with an equal number of families reporting an improvement, compared with a decline, in their financial situation. His point estimate suggests that the CPI is biased upwards by 1.5 percentage points. This is a novel approach to deriving an independent estimate of any bias in the CPI.
Nordhaus method makes sense if the entire distribution of income moves with the median. But if the distribution of income changes in ways that are not related to the median, his approach could understate or overstate the bias in the CPI.
The following hypothetical example illustrates this point. Suppose the income distribution consists of five families that are ranked in order of their income in the base year. Suppose further that the family with the lowest income experiences a decline in (correctly measured) real income, the next two families experience no change in real income, and the top two families experience real-income growth. In this scenariowhich might roughly mirror the U.S. income distribution over the last two decadesthe median income is unchanged, so Nordhaus reliance on the median would imply an equal number of families with real income gains and losses.2
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1 William Nordhaus, "Quality Changes in Price Indexes," Journal of Economic Perspectives, Winter 1998, pp. 5968.
2 Between 1974 and 1994, the percent change in average household income for each quintile was 7 percent for the lowest quintile, 3 percent for the second quintile, 1 percent for the middle quintile, 9 percent for the fourth quintile, and 31 percent for the top quintile, using the CPI-U-XL to deflate income. (See Historical Income Tables for Households (U.S. Department of Commerce, Bureau of the Census, various years), table H3; also on the World Wide Web at <www.census.gov/hhes/income/histinc/h03.html>.)
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