A tale of two Ginis in the US, 1921–2012

Abstract

Following a methodology by Jantzen and Volpert (2012), we use IRS Adjusted Gross Income data for the US (1921–2012) to estimate two Gini indices representing inequality at the bottom and the top of the income distribution, and to calculate the overall Gini as a function of the parameters underlying the two indices. A steady increase in the overall Gini since the Second World War actually hides two different periods of distributional changes. First, the increase in inequality from the mid 1940s to the late 1970s is driven by rising inequality at the bottom of the income distribution that more than offsets a decrease in inequality at the top. The implication is that middle-income earners gained relative to high-incomes, and especially relative to low-income earners. Second, the rise in the Gini after 1981 is driven by rising inequality at the top. Third, top-driven inequality follows a U-shaped trajectory consistent with Piketty and Saez (2003, 2006). Fourth, the welfare effects of the different distributional changes behind increasing inequality can be evaluated in light of the Lorenz-dominance criterion by Atkinson (1970): we argue that the rise in inequality since 1981 is much more likely to be associated with a social welfare loss net of compensating growth.

Keywords:

• Inequality
• income distribution
• Gini index

JEL Classifications:

• D3
• D63

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Correction

Acknowledgements

We thank Robert Jantzen and Klaus Volpert for comments on an earlier version of the manuscript, the editor and two anonymous referees for comments that greatly improved the paper, and the conference participants at the Eastern Economic Association Annual Meetings 2015 and the XIX FMM Conference, Berlin 2015. The usual disclaimer applies.

Notes

1. It can be conjectured that entropy-based indices such as I[0] and I[2] as discussed by Jenkins (2009) and used by Schneider (2013) show similar patterns as JV’s G ₀ and G ₁. Furthermore, the Theil index (I[1]) used by Galbraith (2012) for a compelling illustration of the increase in inequality since the 1940s (as well as the co-movements with the stock market in the US) is already known to basically replicate the general trend in the Gini series.

2. Average growth lowers to 3.1% per year if the sample is restricted to the 1945–1980 period. Notice that this is harmless for our analysis: if the two periods are actually characterized by similar average growth rates, welfare comparisons à la Atkinson are actually even more appropriate.

3. Goldin and Katz (2007) offer an analysis of educational wages back to 1890, but they do not pay attention to the detailed distributional changes that are central to our work.

4. Shorrocks (1983) uses a ‘generalized’ Lorenz curve that rescales the range of the Lorenz curve using mean income per capita.

5. Asymptotic right self-similarity is also consistent with recently popular parametric distribution such as the GB2 or Dagum (see Kleiber and Kotz 2003).

6. denotes the Gamma function.

7. Specifically, we need only assume a smooth social welfare function that exhibits diminishing returns to income.

8. Based on sequential Chow tests for breaks and choosing the year(s) with the largest test statistic (i.e., an informal Quandt Likelihood Ratio test). Break dates are based on and . Formal tests suggested that first differences of the parameters were stationary and no further lags were necessary.

9. Large fluctuations mean that its first difference is not statistically different from zero.