Calculate Kakwani and Modified Kakwani Index

Source: R/formulas.R

The Kakwani Index (KI) and the Modified Kakwani Index (MKI) are Gini-based methods to measure vertical equity.

These methods first order properties by sale price (ascending), then calculate the Gini coefficient for sale values and assessed values (while remaining ordered by sale price). The Kakwani Index then calculates the difference (Gini of assessed - Gini of sale), and the Modified Kakwani Index calculates the ratio (Gini of Assessed / Gini of Sale).

For the Kakwani Index:

  • KI < 0 is regressive

  • KI = 0 is vertical equity

  • KI > 0 is progressive

For the Modified Kakwani Index:

  • MKI < 1 is regressive

  • MKI = 1 is vertical equity

  • MKI > 1 is progressive

mki(assessed, sale_price, na.rm = FALSE)

ki(assessed, sale_price, na.rm = FALSE)

mki_met(x)

Arguments

assessed

A numeric vector of assessed values. Must be the same length as sale_price.

sale_price

A numeric vector of sale prices. Must be the same length as assessed.

na.rm

Default FALSE. A boolean value indicating whether or not to remove NA values. If missing values are present but not removed the function will output NA.

x

Numeric vector of sales ratio statistic(s) to check against IAAO/Quintos standards.

Functions

  • mki(): Returns a numeric vector containing the MKI of the input vectors.

  • ki(): Returns a numeric vector containing the KI of the input vectors.

  • mki_met(): Returns TRUE when input meets Quintos paper standards (between 0.95 and 1.05).

References

Quintos, C. (2020). A Gini measure for vertical equity in property assessments. Journal of Property Tax Assessment & Administration, 17(2). Retrieved from https://researchexchange.iaao.org/jptaa/vol17/iss2/2.

Quintos, C. (2021). A Gini decomposition of the sources of inequality in property assessments. Journal of Property Tax Assessment & Administration, 18(2). Retrieved from https://researchexchange.iaao.org/jptaa/vol18/iss2/6

See also

Other formulas: cod(), prb(), prd()

Examples

# Calculate MKI
mki(ratios_sample$assessed, ratios_sample$sale_price)
#> [1] 0.911457

# Calculate KI
ki(ratios_sample$assessed, ratios_sample$sale_price)
#> [1] -0.03599249