Abstract
To gauge inequality in living standards, the distribution of lifetime income is likely to be more relevant than the distribution of current income. Yet, empirical studies of income inequality are typically based on observations of income for one or a few years. In this paper, we exploit a unique data set with nearly career-long income histories to assess the role of so-called life-cycle bias in empirical analysis of income inequality that uses current income variables as proxies for lifetime income. We find evidence of substantial life-cycle bias in estimates of inequality based on current income. One implication is that cross-sectional estimates of income inequality are likely to be sensitive to the age composition of the sample. A decomposition of the life-cycle bias into income mobility and heterogeneous profiles reveal the importance of two explanations that have been put forth to explain the disagreement between current and lifetime inequality.
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Notes
There are, however, a few studies that use income data over a longer period. A notable example is Björklund (1993), who uses long panel data on income from Sweden to compare the distributions of annual and long-term income. He finds that the inequality in long-run income is around 35–40 % lower than in the cross-sections of annual income. Burkhauser and Poupore (1997) report reductions in income inequality indices of about 15–20 % when the accounting period was extended from 1 to 6 years. Using income data for a whole decade, both Gittleman and Joyce (1999) and Aaberge et al. (2002) find that cross-sectional inequality indices overstate inequality in long-run income by 25–30 %. The focus of these studies is how income mobility reduces inequality in long-run income, and they do not study the issue of life-cycle bias in studies of inequality that use current income as a proxy for lifetime income.
Because of the small scale of the U.S. panel surveys, much of the early research relied on simple models that impose economically implausible restrictions (see the discussions in Baker and Solon 2003). Using rich administrative data, Haider (2001), Baker and Solon (2003), Moffitt and Gottschalk (2012), and Blundell et al. (2014) go beyond earlier models by allowing for key aspects in the evolution of labour income over time and across the life-cycle.
Although the formal retirement age is 67 years, many individuals retire around age 65.
The annual real interest rates on borrowing and savings are computed from Norwegian official statistics on interest rates on loans and deposits in commercial banks over the period 1967–2006.
For a given \(u,\, N(u)\) is the ratio of the mean income of the poorest 100u per cent of the population and the overall mean. By inserting for the Lorenz curve in N(u) it follows straightforwardly that the scaled conditional mean curve is a representation of inequality that is equivalent to the Lorenz curve.
Since \(C_1\), G, and \(C_3\) have a common theoretical foundation and complement each other with regard to sensitivity to changes in the lower and upper part of the income distribution, Aaberge (2007) calls them Gini’s Nuclear Family.
For studies of intergenerational income mobility taking this approach to correct for life-cycle bias, see the review of Black and Devereux (2011).
In comparison, Haider and Solon (2006) find that \(\lambda _{t }\) comes close to 1 when individuals are in their early 40s (and mid 30s), whereas Böhlmark and Lindquist (2006) report that \(\lambda _{t}\) is approximately 1 when individuals are aged 46–53 (and around age 33). It should be noted, however, that these two studies measure income in logs rather than levels. When measuring income in logs, our estimate of \(\lambda _{t}\) is equal to 1 around age 40.
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We thank two anonymous referees, the editor and Anders Björklund for helpful comments.
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Aaberge, R., Mogstad, M. Inequality in current and lifetime income. Soc Choice Welf 44, 217–230 (2015). https://doi.org/10.1007/s00355-014-0838-3
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DOI: https://doi.org/10.1007/s00355-014-0838-3