Palma ratio

Computes the Palma ratio: the share of total income received by the top 10 percent divided by the share received by the bottom 40 percent.

Usage

iq_palma(
  x,
  weights = NULL,
  na.rm = FALSE,
  ci = FALSE,
  R = 1000L,
  level = 0.95,
  negatives = c("error", "keep")
)

Arguments

x

Numeric vector of incomes.

weights

Optional numeric vector of survey weights.

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.

negatives

Character. "error" (default) aborts on negatives; "keep" permits them.

Value

An S3 object of class "iq_palma" with elements:

palma

Numeric. The Palma ratio.

top10_share

Numeric. Share of income held by the top 10 percent.

bottom40_share

Numeric. Share of income held by the bottom 40 percent.

n

Integer. Number of observations.

se, ci_lower, ci_upper, level

Bootstrap CI fields, NULL unless ci = TRUE.

Details

The Palma ratio is motivated by Palma's (2011) observation that the "middle" 50 percent (deciles 5–9) tends to capture a remarkably stable share of income across countries, so inequality is driven by what happens at the tails. A Palma ratio of 1 means the top 10 percent and bottom 40 percent receive equal shares.

Distributions containing negative values may produce a non-positive bottom-40 share, in which case the Palma ratio is undefined. The function returns NA with a warning rather than aborting.

References

Palma, J. G. (2011). "Homogeneous Middles vs. Heterogeneous Tails, and the End of the 'Inverted-U': It's All About the Share of the Rich." Development and Change, 42(1), 87–153.

Examples

d <- iq_sample_data("income")
iq_palma(d$income)
#> 
#> ── Palma Ratio ─────────────────────────────────────────────────────────────────
#> • Palma ratio: 2.1528
#> • Top 10% share: 31.5%
#> • Bottom 40% share: 14.6%
#> • Observations: 1000

# With bootstrap CIs
iq_palma(d$income, ci = TRUE, R = 200)
#> 
#> ── Palma Ratio ─────────────────────────────────────────────────────────────────
#> • Palma ratio: 2.1528
#> • Top 10% share: 31.5%
#> • Bottom 40% share: 14.6%
#> • Observations: 1000
#> • Bootstrap 95% CI: [1.8718, 2.4882]

# Equal distribution: Palma = 0.25/0.40 = 0.625
iq_palma(rep(100, 100))
#> 
#> ── Palma Ratio ─────────────────────────────────────────────────────────────────
#> • Palma ratio: 0.25
#> • Top 10% share: 10%
#> • Bottom 40% share: 40%
#> • Observations: 100