REAT (version 1.2.1)

herf: Herfindahl-Hirschman coefficient

Description

Calculating the Herfindahl-Hirschman coefficient of concentration, standardized and non-standardized

Usage

herf(x, coefnorm = FALSE)

Arguments

x

A numeric vector (e.g. dataset of sales turnover or size of firms)

coefnorm

logical argument that indicates if the function output is the non-standardized or the standardized Herfindahl-Hirschman coefficient (default: coefnorm = FALSE, that means the non-standardized Herfindahl-Hirschman coefficient is returned)

Value

A single numeric value of the Herfindahl-Hirschman coefficient ($\frac{1}{n} < HHI < 1$) or the standardized Herfindahl-Hirschman coefficient ($0 < HHI* < 1$).

Details

The Herfindahl-Hirschman coefficient is a popular measure of statistical dispersion, especially used for analyzing concentration in markets, regarding sales turnovers or sizes of $n$ competing firms in an industry. This indicator is e.g. used as a measure of market power and distortions of competition in the governmental competition policy. The coefficient ($HHI$) varies between $\frac{1}{n}$ (parity resp. no concentration) and $1$ (complete concentration). Because the minimum of $HHI$ is not equal to 0, also a standardized coefficient ($HHI*$) with a minimum equal to 0 can be calculated alternatively.

References

Doersam, P. (2004): “Wirtschaftsstatistik anschaulich dargestellt”. Heidenau : PD-Verlag.

Lessmann, C. (2005): “Regionale Disparitaeten in Deutschland und ausgesuchten OECD-Staaten im Vergleich”. ifo Dresden berichtet, 3/2005. https://www.cesifo-group.de/link/ifodb_2005_3_25-33.pdf.

See Also

cv, gini, herf.eq

Examples

# Example from Doersam (2004):
sales <- c(20,50,20,10)
# sales turnover of four car manufacturing companies
herf(sales)
# returns the non-standardized HHI (0.34)
herf(sales, coefnorm=TRUE)
# returns the standardized HHI (0.12)

# Regional disparities in Germany:
gdp <- c(460.69, 549.19, 124.16, 65.29, 31.59, 109.27, 263.44, 39.87, 258.53, 
645.59, 131.95, 35.03, 112.66, 56.22, 85.61, 56.81)
# GDP of german regions 2015 (in billion EUR)
herf(gdp)
# returns the HHI (0.125)
herf.eq(gdp)
# returns the HHI equivalent number (7.988733)