R/locational.Gini.r

In PABalland/EconGeo: Computing Key Indicators of the Spatial Distribution of Economic Activities

#' Compute the locational Gini coefficient from regions - industries matrices
#'
#' This function computes the locational Gini coefficient as proposed by Krugman from regions - industries matrices. The higher the coefficient (theoretical limit = 0.5), the greater the industrial concentration. The locational Gini of an industry that is not localized at all (perfectly spread out) in proportion to overall employment would be 0.
#' @param mat An incidence matrix with regions in rows and industries in columns
#' @keywords concentration inequality
#' @export
#' @examples
#' ## generate a region - industry matrix
#' mat = matrix (
#' c (100, 0, 0, 0, 0,
#' 0, 15, 5, 70, 10,
#' 0, 20, 10, 20, 50,
#' 0, 25, 30, 5, 40,
#' 0, 40, 55, 5, 0), ncol = 5, byrow = T)
#' rownames(mat) <- c ("R1", "R2", "R3", "R4", "R5")
#' colnames(mat) <- c ("I1", "I2", "I3", "I4", "I5")
#'
#' ## run the function
#' locational.Gini (mat)
#' @author Pierre-Alexandre Balland \email{p.balland@uu.nl}
#' @seealso \code{\link{Hoover.Gini}}, \code{\link{locational.Gini.curve}}, \code{\link{Hoover.curve}}, \code{\link{Lorenz.curve}}, \code{\link{Gini}}
#' @references Krugman P. (1991) \emph{Geography and Trade}, MIT Press, Cambridge (chapter 2 - p.56)


locational.Gini <- function (mat)

{

  loc.Gini <- function (mat, col = 1) {
    share_city_total = rowSums (mat) / sum (mat)
    ind <- mat[,col]
    pop <- share_city_total
    oind <- order(ind/pop)
    ind <- ind[oind]
    pop <- pop[oind]
    cind <- cumsum(ind)/max(cumsum(ind))
    cpop <- cumsum(pop)/max(cumsum(pop))
    nn = length (cind)
    (sum(cind[-1] * cpop[-nn]) - sum(cind[-nn] * cpop[-1]))/2

  }

  y  <- NULL;
  for (i in unique(1:ncol(mat)))
  {
    tmp <- loc.Gini (mat, i)
    y <- rbind(y, tmp)
  }

  x = data.frame (colnames (mat),  y[,1])
  colnames (x) = c ("Industry", "Loc.Gini")
  return (x)

}