Parametric representation of the top of income distributions: Options, historical evidence, and model selection

Abstract

Empirical distributions of top incomes suffer from statistical problems affecting the measurement of inequality and its trend. Researchers and practitioners have been increasingly noting parametric regularities across income distributions and turning to parametric functions to approximate or supplement the observed distributions, both for descriptive purposes and for correcting distributional statistics derived from data. The proliferation of distinct branches of modeling literature has highlighted the need to compare the alternative modeling options, and develop systematic tools to discriminate between them. This paper reviews the state of methodological and empirical knowledge regarding the adoptable parametric functions, and lists references and statistical programs allowing practitioners to apply these models to microdata in household surveys and administrative registers, or grouped‐records data from national accounts statistics. Implications for modeling the distributions of other economic outcomes including consumption and wealth, and incomes below the topmost tail, are drawn. For incomes, a handful of distribution functions hold promise for modeling the top tails based on theoretical and empirical properties—namely the extreme values distributions, the generalized Pareto, the Singh–Maddala and the generalized beta type 2. Understanding these functions in relation to other commonly invoked alternatives is a contribution of this review.

The Impact of Top Incomes Biases on the Measurement of Inequality in the United States

“…While the one‐parameter Pareto distribution is thought to approximate the dispersion of top incomes well, it has been outperformed by other modelling techniques in some countries, and it is not representative of incomes in the middle or bottom of the income distribution (Hlasny, 2021a,b). Blanchet and Fournier (2017) show that the inverted Pareto coefficients estimated across different income cutoffs have a non‐constant (U‐shaped) profile – or a ‘generalized Pareto curve’ – in contrast to the Pareto law.…”

Bottom Incomes and the Measurement of Poverty and Inequality

“…Income surveys are known to exhibit a variety of systematic problems that may bias the measurement of income poverty or inequality such as sampling errors, unit and item nonresponse, under-reporting, and top coding by statistical agencies. These issues are known to affect the top tail of the distribution and bias the measurement of inequality, an issue that has generated a significant body of literature covering high-and low-income countries (Atkinson et al, 2011;Cowell and Victoria-Feser, 1996;Hlasny and Verme, 2018b;Hlasny, 2020;Jenkins et al, 2011). These contributions propose parametric and nonparametric methods to correct inequality measurement based on known top income properties (Hlasny, 2021) or information derived from sources external to surveys (such as tax registers or national accounts).…”