hoover_index {EconGeo}

Compute the Hoover index

Description

This function computes the Hoover index, named after Hedgar Hoover. The Hoover index is a measure of spatial inequality. It ranges from 0 (perfect equality) to 100 (perfect inequality) and is calculated from the Lorenz curve associated with a given distribution of population, industries or technologies. In this sense, it is closely related to the Gini coefficient. The Hoover index represents the maximum vertical distance between the Lorenz curve and the 45 degree line of perfect spatial equality. It indicates the proportion of industries, jobs, or population needed to be transferred from the top to the bottom of the distribution to achieve perfect spatial equality. The Hoover index is also known as the Robin Hood index in studies of income inequality.

Computation of the Hoover index: H=1/2\sum _{ i=1 }^{ N }{ \left| \frac { { E }_{ i } }{ { E }_{ total } } -\frac { { A }_{ i } }{ { A }_{ total } } \right| }

Usage

hoover_index(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; if this argument is missing an equal distribution of the reference group will be assumed.

Value

The Hoover index value(s) as either a numeric value or a data frame with two columns: "Industry" (names of the industries) and "hoover_index" (corresponding Hoover index 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, hoover_gini, 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_index(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_index(mat, pop)

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

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

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

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

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