Kakwani progressivity index

Measures the progressivity of a tax or transfer system. A positive value indicates progressivity (the rich pay a larger share than their income share); a negative value indicates regressivity. Zero means proportional.

Usage

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

Arguments

pre_tax

Numeric vector of pre-tax incomes (non-negative by default).

tax

Numeric vector of tax payments (same length as pre_tax). Positive values are taxes paid; negative values are transfers received.

weights

Optional numeric vector of survey weights.

na.rm

Logical. Remove NA values? Default FALSE.

ci

Logical. Compute bootstrap confidence intervals on the Kakwani and Reynolds-Smolensky indices? Default FALSE.

R

Integer. Number of bootstrap replicates. Default 1000.

level

Numeric. Confidence level. Default 0.95.

negatives

Character. "error" (default) aborts on negative pre-tax incomes; "keep" permits them.

Value

An S3 object of class "iq_kakwani" with elements:

kakwani

Numeric. The Kakwani index (-1 to 1).

gini_pre

Numeric. The pre-tax Gini coefficient.

concentration_tax

Numeric. The concentration coefficient of taxes.

reynolds_smolensky

Numeric. The Reynolds-Smolensky index (pre-tax Gini minus post-tax Gini).

gini_post

Numeric. The post-tax Gini coefficient.

avg_tax_rate

Numeric. Average effective tax rate.

n

Integer. Number of observations.

kakwani_ci, rs_ci

Lists with lower and upper (or NULL).

Details

The Kakwani index equals the concentration coefficient of the tax minus the pre-tax Gini coefficient: K = C_T - G_pre.

The post-tax Gini is computed on pre_tax - tax directly. Households whose post-tax income is negative are kept as-is, so the post-tax Gini may exceed 1 in distributions with extreme tax burdens. Pass negatives = "error" to abort on negative pre-tax incomes.

References

Kakwani, N. C. (1977). "Measurement of Tax Progressivity: An International Comparison." The Economic Journal, 87(345), 71–80.

Reynolds, M. and Smolensky, E. (1977). Public Expenditures, Taxes, and the Distribution of Income. New York: Academic Press.

Examples

set.seed(1)
pre <- iq_sample_data("income")$income
# Progressive tax: higher rate for higher incomes
tax <- pre * (0.10 + 0.15 * (pre / max(pre)))
iq_kakwani(pre, tax)
#> 
#> ── Fiscal Progressivity (Progressive) ──────────────────────────────────────────
#> • Kakwani index: 0.0646
#> • Reynolds-Smolensky index: 0.0092
#> • Pre-tax Gini: 0.43
#> • Post-tax Gini: 0.4208
#> • Tax concentration coefficient: 0.4946
#> • Average tax rate: 12.5%
#> • Observations: 1000

# With bootstrap CIs
iq_kakwani(pre, tax, ci = TRUE, R = 200)
#> 
#> ── Fiscal Progressivity (Progressive) ──────────────────────────────────────────
#> • Kakwani index: 0.0646
#> • Reynolds-Smolensky index: 0.0092
#> • Pre-tax Gini: 0.43
#> • Post-tax Gini: 0.4208
#> • Tax concentration coefficient: 0.4946
#> • Average tax rate: 12.5%
#> • Observations: 1000
#> • Bootstrap 95% CIs:
#>   Kakwani: [0.0484, 0.081]
#>   Reynolds-Smolensky: [0.0066, 0.0121]