# Hoover.index: Compute the Hoover index In PABalland/EconGeo: Computing Key Indicators of the Spatial Distribution of Economic Activities

## 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∑ _{ i=1 }^{ N }{ ≤ft| \frac { { E }_{ i } }{ { E }_{ total } } -\frac { { A }_{ i } }{ { A }_{ total } } \right| }

## Usage

 1 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. pdf Logical; shall a pdf be saved to your current working directory? Defaults to FALSE. If set to TRUE, a pdf with all Hoover indices will be compiled and saved to your current working directory.

## Author(s)

Pierre-Alexandre Balland p.balland@uu.nl

## References

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

Hoover.curve, Hoover.Gini, locational.Gini, locational.Gini.curve, Lorenz.curve, Gini
  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 ## 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 = T) 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)