lorenz_curve {EconGeo}

Plot a Lorenz curve from regional industrial counts

Description

This function plots a Lorenz curve from regional industrial counts. This curve gives an indication of the unequal distribution of an industry accross regions.

Usage

lorenz_curve(mat, plot = TRUE, pdf = TRUE, pdf_location = NULL)

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).

plot

Logical; shall the curve be automatically plotted? Defaults to TRUE. If set to TRUE, the function will return x y coordinates that you can latter use to plot and customize the curve.

pdf

Logical; shall a pdf be saved? Defaults to FALSE. If set to TRUE, a pdf with all will be compiled and saved to R's temp dir if no 'pdf_location' is specified.

pdf_location

Output location of pdf file

Value

If 'plot = FALSE', the function returns a list with two components: - 'cum.reg': A vector of cumulative proportions of regions. - 'cum.out': A vector of cumulative proportions of industrial output. If 'plot = TRUE', the function generates a plot of the Lorenz curve and does not return a value.

Author(s)

Pierre-Alexandre Balland [e-mail]

References

Lorenz, M. O. (1905) Methods of measuring the concentration of wealth, Publications of the American Statistical Association 9: 209–219

See Also

hoover_gini, locational_gini, locational_gini_curve, hoover_curve, gini

Examples

## generate vectors of industrial count
ind <- c(0, 10, 10, 30, 50)

## run the function
lorenz_curve (ind)
lorenz_curve (ind, plot = FALSE)

## generate a region - industry matrix
mat = matrix (
c (0, 1, 0, 0,
0, 1, 0, 0,
0, 1, 0, 0,
0, 1, 0, 1,
0, 1, 1, 1), ncol = 4, byrow = TRUE)
rownames(mat) <- c ("R1", "R2", "R3", "R4", "R5")
colnames(mat) <- c ("I1", "I2", "I3", "I4")

## run the function
lorenz_curve (mat)
lorenz_curve (mat, plot = FALSE)

## run the function by aggregating all industries
lorenz_curve (rowSums(mat))
lorenz_curve (rowSums(mat), plot = FALSE)

## run the function for industry #1 only (perfect equality)
lorenz_curve (mat[,1])
lorenz_curve (mat[,1], plot = FALSE)

## run the function for industry #2 only (perfect equality)
lorenz_curve (mat[,2])
lorenz_curve (mat[,2], plot = FALSE)

## run the function for industry #3 only (perfect unequality)
lorenz_curve (mat[,3])
lorenz_curve (mat[,3], plot = FALSE)

## run the function for industry #4 only (top 40% produces 100% of the output)
lorenz_curve (mat[,4])
lorenz_curve (mat[,4], plot = FALSE)

## Compare the distribution of the #industries
oldpar <- par(mfrow = c(2, 2))  # Save the current graphical parameter settings
lorenz_curve (mat[,1])
lorenz_curve (mat[,2])
lorenz_curve (mat[,3])
lorenz_curve (mat[,4])
par(oldpar)  # Reset the graphical parameters to their original values

## Save output as pdf
lorenz_curve (mat, pdf = TRUE)

## To specify an output directory for the pdf,
## specify 'pdf_location', for instance as '/Users/jones/lorenz_curve.pdf'
## lorenz_curve(mat, pdf = TRUE, pdf_location = '/Users/jones/lorenz_curve.pdf')