hoover_gini {EconGeo}

Compute the Hoover Gini

Description

This function computes the Hoover Gini, named after Hedgar hoover_ The Hoover index is a measure of spatial inequality. It ranges from 0 (perfect equality) to 1 (perfect inequality) and is calculated from the Hoover curve associated with a given distribution of population, industries or technologies and a reference category. In this sense, it is closely related to the Gini coefficient and the Hoover index. The numerator is given by the area between the Hoover curve of the distribution and the uniform distribution line (45 degrees line). The denominator is the area under the uniform distribution line (the lower triangle).

Usage

hoover_gini(mat, pop)

Arguments

mat

An incidence matrix with regions in rows and industries in columns. The input can also be a vector of industrial regional count (a matrix with n regions in rows and a single column).

pop

A vector of population regional count

Value

The Hoover Gini value(s). If the input matrix has a single column, the function returns a numeric value representing the Hoover Gini index. If the input matrix has multiple columns, the function returns a data frame with two columns: "Industry" (names of the industries) and "hoover_gini" (corresponding Hoover Gini values).

Author(s)

Pierre-Alexandre Balland [e-mail]

References

Hoover, E.M. (1936) The Measurement of Industrial Localization, The Review of Economics and Statistics 18 (1): 162-171

See Also

hoover_curve, locational_gini, locational_gini_curve, lorenz_curve, gini

Examples

## generate vectors of industrial and population count
ind <- c(0, 10, 10, 30, 50)
pop <- c(10, 15, 20, 25, 30)

## run the function (30% of the population produces 50% of the industrial output)
hoover_gini(ind, pop)

## generate a region - industry matrix
mat <- matrix(
  c(
    0, 10, 0, 0,
    0, 15, 0, 0,
    0, 20, 0, 0,
    0, 25, 0, 1,
    0, 30, 1, 1
  ),
  ncol = 4, byrow = TRUE
)
rownames(mat) <- c("R1", "R2", "R3", "R4", "R5")
colnames(mat) <- c("I1", "I2", "I3", "I4")

## run the function
hoover_gini(mat, pop)

## run the function by aggregating all industries
hoover_gini(rowSums(mat), pop)

## run the function for industry #1 only
hoover_gini(mat[, 1], pop)

## run the function for industry #2 only (perfectly proportional to population)
hoover_gini(mat[, 2], pop)

## run the function for industry #3 only (30% of the pop. produces 100% of the output)
hoover_gini(mat[, 3], pop)

## run the function for industry #4 only (55% of the pop. produces 100% of the output)
hoover_gini(mat[, 4], pop)