Inequality Measurement, Decomposition, and Poverty Analysis • inequality

A technical working paper for this package can be found here.

Measure income and wealth inequality in R. Gini coefficients with confidence intervals, Theil indices, Atkinson indices, Palma ratios, Lorenz curves, poverty measures, tax progressivity, and more. All functions accept optional survey weights, and every measure now exposes bootstrap confidence intervals via ci = TRUE.

What’s new in 0.2.0

This release responds to feedback from Frank Cowell and Emmanuel Flachaire on the v0.1.0 release.

Bootstrap CIs on every measure. iq_theil, iq_atkinson, iq_sgini, iq_palma, iq_hoover, iq_kolm, iq_percentile_ratio, iq_polarisation, iq_shares, iq_concentration, iq_kakwani, and iq_poverty all gain ci, R, and level arguments. iq_compare() runs a single bootstrap loop and propagates CIs to every row.
Negative values supported. Gini, S-Gini, top shares, Palma, Hoover, Wolfson, Kakwani, and iq_compare() accept negatives = "keep" for distributions containing negatives (wealth, post-tax income).
Raffinetti et al. (2017) normalised Gini. iq_gini(x, negatives = "keep", normalised = TRUE) rescales the index back into [0, 1] when negatives are present.
Wagstaff correction added to iq_concentration alongside the existing Erreygers correction.
iq_kakwani bug fix. The post-tax Gini no longer takes the absolute value of negative net incomes, so the Reynolds-Smolensky index is honest under high tax burdens.

Installation

# install.packages("devtools")
devtools::install_github("charlescoverdale/inequality")

Why this package?

The main CRAN package for inequality measurement (ineq) was last updated in 2014. It computes basic Gini and Theil indices but has no support for survey weights, no confidence intervals, no subgroup decomposition, no poverty measures, no Palma ratio, and no tax progressivity analysis.

inequality fills these gaps. You bring income or wealth data from any source (household surveys, tax records, administrative data, simulations) and the package handles measurement, decomposition, and comparison. Every function accepts optional weights, returns a clean S3 object with a print method, and cites the underlying academic paper.

Quick start

library(inequality)

# Built-in sample data: 1000 synthetic incomes
d <- iq_sample_data("income")

# How unequal is this distribution?
iq_gini(d$income)
#> -- Gini Coefficient --
#> * Gini: 0.43
#> * Observations: 1000

# With confidence intervals
iq_gini(d$income, ci = TRUE)
#> -- Gini Coefficient --
#> * Gini: 0.43
#> * Observations: 1000
#> * Bootstrap 95% CI: [0.4085, 0.453]

What can it do?

Compare indices side by side

iq_compare(d$income)
#> -- Inequality Comparison (n = 1000) --
#> * Gini              0.4300
#> * Theil T (GE1)     0.3307
#> * Theil L (GE0)     0.3241
#> * Atkinson (e=0.5)  0.1506
#> * Atkinson (e=1.0)  0.2768
#> * Palma ratio       2.1668
#> * Hoover            0.3126
#> * P90/P10           7.83
#> * P80/P20           3.92

Who gets what? Income shares

iq_shares(d$income)
#> -- Income Shares --
#> * Bottom 50%: 21.2% of income (50% of population)
#> * P50-P90:    47.1% of income (40% of population)
#> * P90-P99:    24.0% of income (9% of population)
#> * Top 1%:      6.6% of income (1% of population)

Between-group vs within-group inequality

d <- iq_sample_data("grouped")
iq_decompose(d$income, d$group)
#> -- Between-Within Decomposition (Theil T (GE(1))) --
#> * Total: 0.463
#> * Between: 0.116 (25.1%)
#> * Within: 0.347 (74.9%)

Poverty measurement

d <- iq_sample_data("income")
iq_poverty(d$income, line = 20000)
#> -- Poverty Measures (line = 20000) --
#> * Headcount (FGT0): 18.2%
#> * Poverty gap (FGT1): 0.0521
#> * Severity (FGT2): 0.0198
#> * Sen index: 0.0912
#> * Watts index: 0.0634

Is a tax progressive?

pre_tax <- d$income
tax <- pre_tax * (0.10 + 0.15 * (pre_tax / max(pre_tax)))
iq_kakwani(pre_tax, tax)
#> -- Fiscal Progressivity (Progressive) --
#> * Kakwani index: 0.1832
#> * Reynolds-Smolensky index: 0.0421

Lorenz curve and growth incidence

# Lorenz curve
lc <- iq_lorenz(d$income)
plot(lc)

# Growth incidence curve
panel <- iq_sample_data("panel")
gic <- iq_growth_incidence(panel$income_t0, panel$income_t1)
plot(gic)

Functions

Inequality indices

Function	What it measures
`iq_gini()`	Gini coefficient (bootstrap or asymptotic CIs)
`iq_sgini()`	Extended Gini family (adjustable inequality aversion)
`iq_theil()`	Theil T, Theil L, and generalised entropy GE(alpha)
`iq_atkinson()`	Atkinson index (with equally distributed equivalent income)
`iq_kolm()`	Kolm index (absolute inequality, translation invariant)
`iq_palma()`	Palma ratio (top 10% share / bottom 40% share)
`iq_hoover()`	Hoover index (Robin Hood index, Pietra index)
`iq_percentile_ratio()`	P90/P10, P80/P20, or custom ratios

Distribution and decomposition

Function	What it measures
`iq_lorenz()`	Lorenz curve with plot method
`iq_shares()`	Income shares by quantile (top 1%, top 10%, etc.)
`iq_decompose()`	Between-within group decomposition (GE family)
`iq_concentration()`	Concentration index with optional Erreygers correction
`iq_polarisation()`	Wolfson bipolarisation index

Poverty

Function	What it measures
`iq_poverty()`	FGT family (headcount, gap, severity), Sen and Watts indices
`iq_growth_incidence()`	Growth incidence curve (is growth pro-poor?)

Fiscal

Function	What it measures
`iq_kakwani()`	Kakwani progressivity + Reynolds-Smolensky redistribution

Utilities

Function	What it does
`iq_compare()`	All major indices in one table
`iq_sample_data()`	Built-in synthetic data for examples

Where to find inequality data

Source	Coverage	R package
World Bank PIP	Global poverty and inequality	`pipr`
World Inequality Database	Top income shares, 100+ countries	`wid`
Luxembourg Income Study	Harmonised household surveys	`lissyrtools`
OECD Income Distribution	OECD member Gini, P90/P10, shares	`readoecd`
Eurostat EU-SILC	European household income	`eurostat`
UK Family Resources Survey	UK income distribution	Download CSV
US Current Population Survey	US income and poverty	`ipumsr`
UN WIDER WIID	Cross-country inequality database	Download CSV

Package	Description
hmrc	UK income tax data (Income Tax by income range)
ato	Australian Taxation Office (income distributions)
ons	UK Office for National Statistics data (household income, ASHE)
ukhousing	UK Land Registry, EPC, and planning data (housing wealth)
ivcheck	IV diagnostics (for distributional treatment effects)
inflationkit	Inflation analysis (real-terms incomes)

Issues

Report bugs or request features at GitHub Issues.

Keywords

inequality, Gini, Theil, Atkinson, Kolm, Lorenz, Palma, Kakwani, poverty, FGT, decomposition, income distribution, wealth, survey weights, economics, progressivity

inequality