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01-12-2021 | Original Research

Population Changes and the Measurement of Inequality

Authors: Lidia Ceriani, Paolo Verme

Published in: Social Indicators Research | Issue 2/2022

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Abstract

Population changes in countries with little natural growth tend to occur via migration channels and among poorer individuals such as refugees and economic migrants, or richer individuals such as international white collar workers or global entrepreneurs. These migratory flows are increasing in size, they are difficult to capture in censuses and surveys, and they potentially bias the measurement of inequality. This paper provides a formal treatment of the impact of population changes on the measurement of inequality when changes occur to the extremes of an income distribution. It provides the conditions under which inequality is expected to increase or decrease and determines the relative importance of including or excluding selected observations at the top or at the bottom. An application to US data illustrates the mathematical results and shows that including or excluding observations from the extremes can bias the measurement of inequality significantly.

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Available only for authorised users

https://www.iom.int/wmr/chapter-2.

See also Cowell and Flachaire (2007a) for a general framework that considers extreme observations on both ends of the income distribution.

PovcalNet is an interactive computational tool that allows to replicate the calculations made by the World Bank’s researchers in estimating the extent of absolute poverty in the world. http://iresearch.worldbank.org/PovcalNet/povOnDemand.aspx.

Note that the literature on inequality decomposition generally considers the population as fixed but the same simplified formulation of the Gini index can be applied if we consider B as a new group added to the original population, which is what we have been considering in this paper.

Also relevant to cite is Bourguignon (2018) who expands on this literature showing how to derive analytical expressions for the quantile function and the Lorenz curves when income or population masses change at the top. In particular, he considers the case of correcting the Gini index for under-sampling (missing observations) at the top, which is equivalent to our case of adding individuals at the top. While the author shows that deriving the quantile function and Lorenz curve expression is complex, the paper can be regarded as a general treatment of Gini corrections for top income biases. Our results can therefore be seen as a special case of this particular literature. Adding populations to the extremes can also be be seen as merging populations. One article that studied inequality when two populations are merged is Stark and Yitzhaki (1988).

https://www2.census.gov/programs-surveys/cps/techdocs/cpsmar16.pdf.

Note that these populations are smaller than the official US population size as some groups of people such as prisoners are excluded from the survey.

These observations were removed because negative incomes often belong to non-poor households (Hlasny et al. 2021). The breakdown by state is as follows: AK (1), AL (5), CA (6), DE (1), FL (3), GA (1), HI (4), IL (2), LA (5), MA (1), MI (4), MN (1), MT (3), ND (3), SD (3), TX (7), VA (1), VT (1), WI (1), WY (5).

Estimated from Table 1. Annual Estimates of the Resident Population for the United States, Regions, States, and Puerto Rico: April 1, 2010 to July 1, 2018 wired at: https://www.census.gov/data/tables/time-series.

Or 1.183m people: https://www.migrationpolicy.org/programs/data-hub/us-immigration-trends.

Note that this percentage is derived from the US data and should not be assumed to be a general law applicable to other countries.

Available on request.

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Title: Population Changes and the Measurement of Inequality
Authors: Lidia Ceriani
Paolo Verme
Publication date: 01-12-2021
Publisher: Springer Netherlands
Published in: Social Indicators Research / Issue 2/2022
Print ISSN: 0303-8300
Electronic ISSN: 1573-0921
DOI: https://doi.org/10.1007/s11205-021-02849-7

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