# Gini coefficient of spatial industry concentration Calculating the Gini coefficient of spatial industry concentration based on regional industry data (normally employment data) ```r gini.conc(e_ij, e_j, lc = FALSE, lcx = "% of objects", lcy = "% of regarded variable", lctitle = "Lorenz curve", le.col = "blue", lc.col = "black", lsize = 1, ltype = "solid", bg.col = "gray95", bgrid = TRUE, bgrid.col = "white", bgrid.size = 2, bgrid.type = "solid", lcg = FALSE, lcgn = FALSE, lcg.caption = NULL, lcg.lab.x = 0, lcg.lab.y = 1, add.lc = FALSE, plot.lc = TRUE) ``` ## Arguments - `e_ij`: a numeric vector with the employment of the industry $i$ in region $j$ - `e_j`: a numeric vector with the employment in region $j$ - `lc`: logical argument that indicates if the Lorenz curve is plotted additionally (default: `lc = FALSE`, so no Lorenz curve is displayed) - `lcx`: if `lc = TRUE` (plot of Lorenz curve), `lcx` defines the x axis label - `lcy`: if `lc = TRUE` (plot of Lorenz curve), `lcy` defines the y axis label - `lctitle`: if `lc = TRUE` (plot of Lorenz curve), `lctitle` defines the overall title of the Lorenz curve plot - `le.col`: if `lc = TRUE` (plot of Lorenz curve), `le.col` defines the color of the diagonale (line of equality) - `lc.col`: if `lc = TRUE` (plot of Lorenz curve), `lc.col` defines the color of the Lorenz curve - `lsize`: if `lc = TRUE` (plot of Lorenz curve), `lsize` defines the size of the lines (default: 1) - `ltype`: if `lc = TRUE` (plot of Lorenz curve), `ltype` defines the type of the lines (default: `"solid"`) - `bg.col`: if `lc = TRUE` (plot of Lorenz curve), `bg.col` defines the background color of the plot (default: `"gray95"`) - `bgrid`: if `lc = TRUE` (plot of Lorenz curve), the logical argument `bgrid` defines if a grid is shown in the plot - `bgrid.col`: if `lc = TRUE` (plot of Lorenz curve) and `bgrid = TRUE` (background grid), `bgrid.col` defines the color of the background grid (default: "white") - `bgrid.size`: if `lc = TRUE` (plot of Lorenz curve) and `bgrid = TRUE` (background grid), `bgrid.size` defines the size of the background grid (default: 2) - `bgrid.type`: if `lc = TRUE` (plot of Lorenz curve) and `bgrid = TRUE` (background grid), `bgrid.type` defines the type of lines of the background grid (default: `"solid"`) - `lcg`: if `lc = TRUE` (plot of Lorenz curve), the logical argument `lcg` defines if the non-standardized Gini coefficient is displayed in the Lorenz curve plot - `lcgn`: if `lc = TRUE` (plot of Lorenz curve), the logical argument `lcgn` defines if the standardized Gini coefficient is displayed in the Lorenz curve plot - `lcg.caption`: if `lcg = TRUE` (displaying the Gini coefficient in the plot), `lcg.caption` specifies the caption above the coefficients - `lcg.lab.x`: if `lcg = TRUE` (displaying the Gini coefficient in the plot), `lcg.lab.x` specifies the x coordinate of the label - `lcg.lab.y`: if `lcg = TRUE` (displaying the Gini coefficient in the plot), `lcg.lab.y` specifies the y coordinate of the label - `add.lc`: if `lc = TRUE` (plot of Lorenz curve), `add.lc` specifies if a new Lorenz curve is plotted (`add.lc = "FALSE"`) or the plot is added to an existing Lorenz curve plot (`add.lc = "TRUE"`) - `plot.lc`: logical argument that indicates if the Lorenz curve itself is plotted (if `plot.lc = FALSE`, only the line of equality is plotted)) ## Details The **Gini coefficient of spatial industry concentration** ($G_{i}$) is a special spatial modification of the Gini coefficient of inequality (see the function `gini()`). It represents the rate of spatial concentration of the industry $i$ referring to $j$ regions (e.g. cities, counties, states). The coefficient $G_{i}$ varies between 0 (perfect distribution, respectively no concentration) and 1 (complete concentration in one region). Optionally a Lorenz curve is plotted (if `lc = TRUE`). ## Returns A single numeric value ($0 < G_{i} < 1$) ## References Farhauer, O./Kroell, A. (2013): Standorttheorien: Regional- und Stadtoekonomik in Theorie und Praxis . Wiesbaden : Springer. Nakamura, R./Morrison Paul, C. J. (2009): Measuring agglomeration . In: Capello, R./Nijkamp, P. (eds.): **Handbook of Regional Growth and Development Theories**. Cheltenham: Elgar. p. 305-328. ## Author(s) Thomas Wieland ## See Also `gini`, `gini.spec` ## Examples ```r # Example from Farhauer/Kroell (2013): E_ij <- c(500,500,1000,7000,1000) # employment of the industry in five regions E_j <- c(20000,15000,20000,40000,5000) # employment in the five regions gini.conc (E_ij, E_j) # Returns the Gini coefficient of industry concentration (0.4068966) data(G.regions.emp) # Concentration of construction industry in Germany # based on 16 German regions (Bundeslaender) for the year 2008 construction2008 <- G.regions.emp[(G.regions.emp$industry == "Baugewerbe (F)" | G.regions.emp$industry == "Insgesamt") & G.regions.emp$year == "2008",] # only data for construction industry (Baugewerbe) and all-over (Insgesamt) # for the 16 German regions in the year 2008 construction2008 <- construction2008[construction2008$region != "Insgesamt",] # delete all-over data for all industries gini.conc(construction2008[construction2008$industry=="Baugewerbe (F)",]$emp, construction2008[construction2008$industry=="Insgesamt",]$emp) # Concentration of financial industry in Germany 2008 vs. 2014 # based on 16 German regions (Bundeslaender) for 2008 and 2014 finance2008 <- G.regions.emp[(G.regions.emp$industry == "Erbringung von Finanz- und Vers.leistungen (K)" | G.regions.emp$industry == "Insgesamt") & G.regions.emp$year == "2008",] finance2008 <- finance2008[finance2008$region != "Insgesamt",] # delete all-over data for all industries gini.conc(finance2008[finance2008$industry == "Erbringung von Finanz- und Vers.leistungen (K)",]$emp, finance2008[finance2008$industry=="Insgesamt",]$emp) finance2014 <- G.regions.emp[(G.regions.emp$industry == "Erbringung von Finanz- und Vers.leistungen (K)" | G.regions.emp$industry == "Insgesamt") & G.regions.emp$year == "2014",] finance2014 <- finance2014[finance2014$region != "Insgesamt",] # delete all-over data for all industries gini.conc(finance2014[finance2014$industry == "Erbringung von Finanz- und Vers.leistungen (K)",]$emp, finance2014[finance2014$industry=="Insgesamt",]$emp) ```

gini.conc function