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Kolm index (absolute inequality)

Source: R/kolm.R
iq_kolm.Rd

Computes the Kolm index, the only standard inequality measure that is translation-invariant (absolute). Adding the same amount to every income leaves the index unchanged. All other indices in this package are scale-invariant (relative): multiplying every income by the same factor leaves them unchanged.

Usage

iq_kolm(
  x,
  weights = NULL,
  alpha = 1,
  na.rm = FALSE,
  ci = FALSE,
  R = 1000L,
  level = 0.95
)

Arguments

x

Numeric vector of incomes.

weights

Optional numeric vector of survey weights.

alpha

Numeric. Inequality aversion parameter (> 0). Default 1.

na.rm

Logical. Remove NA values? Default FALSE.

ci

Logical. Compute bootstrap confidence intervals? Default FALSE.

R

Integer. Number of bootstrap replicates. Default 1000.

level

Numeric. Confidence level. Default 0.95.

Value

An S3 object of class "iq_kolm" with elements:

value

Numeric. The Kolm index.

alpha

Numeric. The inequality aversion parameter used.

n

Integer. Number of observations.

se, ci_lower, ci_upper, level

Bootstrap CI fields, NULL unless ci = TRUE.

Details

Higher alpha gives more weight to inequality at the bottom of the distribution. The index is always non-negative and equals zero only under perfect equality. The Kolm index is well-defined for any real values, including negatives.

References

Kolm, S.-C. (1976). "Unequal Inequalities II." Journal of Economic Theory, 13(1), 82–111.

Examples

d <- iq_sample_data("income")
iq_kolm(d$income, alpha = 1)
#> 
#> ── Kolm Index (absolute inequality) ────────────────────────────────────────────
#> • Value: 46736.2301
#> • Alpha: 1
#> • Observations: 1000

# With bootstrap CIs
iq_kolm(d$income, alpha = 1, ci = TRUE, R = 200)
#> 
#> ── Kolm Index (absolute inequality) ────────────────────────────────────────────
#> • Value: 46736.2301
#> • Alpha: 1
#> • Observations: 1000
#> • Bootstrap 95% CI: [43092.8954, 49430.9832]

# Higher aversion to inequality at the bottom
iq_kolm(d$income, alpha = 2)
#> 
#> ── Kolm Index (absolute inequality) ────────────────────────────────────────────
#> • Value: 46739.684
#> • Alpha: 2
#> • Observations: 1000