Inequality by Population Groups and Income Sources

• Published date: 01 June 2021
• Author: Carlos Gradín
• Date: 01 June 2021
• DOI: http://doi.org/10.1111/roiw.12470

481

© 2020 UNU-WIDER. Review of Income and Wealth published by John Wiley & Sons Ltd on behalf

of International Association for Research in Income and Wealth

IINEQUALITY BY POPULATION GROUPS AND INCOME SOURCES:

ACCOUNTING FOR INEQUALITY CHANGES IN SPAIN DURING THE

RECESSION

by Carlos Gradín*

United Nations University World Institute for Development Economics Research (UNU-WIDER)

I discuss a new approach which decomposes inequality into the contributions of population groups by

income sources. I estimate a matrix with rows and columns which indicate different population groups

and income sources, respectively, with each element indicating the marginal change in the inequality

contribution of a group (as measured by the Recentered Influence Function) when an income source is

added and with all contributions adding up to overall inequality. The approach can be used to analyze

the contributions of groups and sources to the trend in inequality over time (or between distributions),

disentangling the effect of changes in the composition of the population by groups and changes in

their income distribution by sources. An empirical application characterizes the distributional change

in Spain following the Great Recession, highlighting the disequalizing role of the massive increase in

unemployment or the equalizing effect of social protection through different population groups.

JEL Codes: D31, H24, J64

Keywords: decomposition, Great Recession, income sources, inequality, population groups

1. IntroduCtIon

The analysis of inequality requires the combination of measures which quan-

tify the phenomenon and analytical tools that identify the type of distributional

changes which drive inequality trends. Among these tools, the analysis of inequal-

ity by population groups and by income sources has played an important role in

understanding which characteristics of households or individuals (e.g. place of

residence, ethnicity, education, labor market attachment, etc.) and which income

sources (e.g. earnings, capital income, social benefits, taxes, etc.) most contribute to

explaining inequality at a given moment in time and, more importantly, its changes

over time and the differences across countries or regions. These simple decomposi-

tions have produced a prolific literature investigating the properties of the different

approaches (for a review, see Chakravarty, 2009).

The literature has identified the different ways in which overall inequality

indices can be aggregated as a function of inequalities between groups and within

Note: This study has been prepared within the UNU-WIDER project “Inequalities—

measurement, implications, and influencing change.”

*Correspondence to: Carlos Gradín, United Nations University World Institute for Development

Economics Research (UNU-WIDER) Katajanokanlaituri 6 B, FI-00160 Helsinki, Finland

(gradin@wider.unu.edu).

Review of Income and Wealth

Series 67, Number 2, June 2021

DOI: 10.1111/roiw.12470

This is an open access article under the terms of the Creative Commons Attribution-NonCommercial-

ShareAlike License, which permits use and distribution in any medium, provided the original work is

properly cited, the use is non-commercial and the content is offered under identical terms.

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Review of Income and Wealth, Series 67, Number 2, June 2021

482

© 2020 UNU-WIDER. Review of Income and Wealth published by John Wiley & Sons Ltd on behalf

of International Association for Research in Income and Wealth

groups, with additively decomposable measures (characterized by Shorrocks, 1984)

becoming the most popular in empirical analyses. More recently, this approach has

been extended by attributing to each group its contribution to overall inequality

or to each between-group or within-group component (Gradín, 2020). However,

the literature has also investigated how different income sources contribute to

total inequality depending on how they change inequality after adding that source

(i.e. marginal approaches, following Musgrave and Thin, 1948) or based on their

association with total income, that is, natural decomposition of indices that can

be written as the weighted sum of incomes (e.g. Shorrocks, 1982; Morduch and

Sicular, 2002). These analyses have been recently complemented with the use of

regression-based techniques that identify the contribution to inequality of several

household characteristics at a time, by directly regressing the log of income, and

then, using decomposition properties of the variance of logs (Fields, 2003; Yun,

2006), by reweighting (DiNardo et al., 1996), or by linearizing inequality indices

using their “recentered influence function” (RIF) (Firpo et al., 2007, 2009). These

methods have become quite popular in distributional analysis, producing a decom-

position of distributional changes into compositional and structural effects as an

extension of the Blinder–Oaxaca method applied to average differentials in income

between two distributions. However, there is little integration of these different

tools that have been developed in different branches of the literature.

This paper, therefore, proposes a simple approach to analyze inequality that

integrates the joint analysis of population groups and income sources, in a way that

is consistent with the use of RIF regression-based decompositions. In doing so, it

extends the approach in Gradín (2020) and estimates the contribution of a group

to inequality through a specific income source based on the marginal change in the

RIF contribution of the group when the source is added. This provides a consistent

decomposition with several attractive properties. Given that each group contribu-

tion can be expressed as the product of the group population share and the average

contribution of the group (based on its distribution), this enables the implemen-

tation of a Blinder–Oaxaca-type decomposition of the differential in inequality

between two distributions into a compositional effect (changes in population sizes)

and a structural effect (changes in the distribution of groups by income source).

That is, this is an application of the extended Blinder–Oaxaca decomposition pro-

posed by Firpo et al. (2007, 2009). This decomposition can also be implemented in

two stages, by computing the aggregate decomposition using reweighting and the

detailed decomposition using RIF, making sure that distributional contributions

are independent of group sizes. Given that the approach is integrated into the RIF-

regression framework (with or without reweighting), the decomposition can be

estimated conditional on other covariates too. It can also refer to overall inequality

and to the between-group or within-groups terms separately (which in the case of

additively decomposable indices will add up to the overall level).

The approach is illustrated using an empirical analysis of the changes in income

inequality in Spain after the Great Recession. This is a particularly interesting case to

study because of the magnitude of changes in overall inequality, employment, and

incomes. Indeed, Spain witnessed a large increase in inequality after being severely hit

by the Great Recession when the housing bubble burst, triggering a dramatic financial

crisis that affected households, businesses, and the public sector. Real per capita gross