R/spec.coeff.r

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

#' Compute the Hoover coefficient of specialization from regions - industries matrices
#'
#' This function computes the Hoover coefficient of specialization from regions - industries matrices. The higher the coefficient, the greater the regional specialization. This index is closely related to the Krugman specialisation index.
#' @param mat An incidence matrix with regions in rows and industries in columns
#' @keywords specialization
#' @export
#' @examples
#' ## generate a region - industry matrix
#' set.seed(31)
#' mat <- matrix(sample(0:100,20,replace=T), ncol = 4)
#' rownames(mat) <- c ("R1", "R2", "R3", "R4", "R5")
#' colnames(mat) <- c ("I1", "I2", "I3", "I4")
#'
#' ## run the function
#' spec.coeff (mat)
#' @author Pierre-Alexandre Balland \email{p.balland@uu.nl}
#' @seealso \code{\link{Krugman.index}}
#' @references Hoover, E.M. and Giarratani, F. (1985) \emph{An Introduction to Regional Economics}. 3rd edition. New York: Alfred A. Knopf (see table 9-4 in particular)

spec.coeff <- function(mat) {
  share_tech_city <- mat / rowSums (mat)
  share_tech_total <- colSums (mat) / sum (mat)
  x <- matrix (share_tech_total,
               nrow = nrow (share_tech_city),
               ncol = length (share_tech_total), byrow = T)
  K <- rowSums (abs (share_tech_city - x))
  K = K/2
  return (K)
}