herf {REAT}

Herfindahl-Hirschman coefficient

Description

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

Usage

herf(x, coefnorm = FALSE, output = "HHI", na.rm = TRUE)

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)

output

argument to state the output. If output = "HHI" (default), the Herfindahl-Hirschman coefficient is returned (standardized or non-standardized). If output = "eq", the Herfindahl-Hirschman coefficient equivalent number is returned

na.rm

logical argument that indicates whether NA values should be excluded before computing results

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 especially used as a measure of market power and distortions of competition in the governmental competition policy (Roberts 2014). But the coefficient is also utilized as a measure of geographic concentration of industries (Lessmann 2005, Nakamura/Morrison Paul 2009).

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. The equivalent number (which is the inverse of the Herfindahl-Hirschman coefficient) reflects the theoretical number of economic objects (normally firms) where a calculated coefficient is \frac{1}{n}, which means parity (Doersam 2004). In a regional context, the inverse of HHI is also used as a measure of diversity (Duranton/Puga 2000).

Value

A single numeric value of the Herfindahl-Hirschman coefficient (\frac{1}{n} < HHI < 1) or the standardized Herfindahl-Hirschman coefficient (0 < HHI* < 1) or the Herfindahl-Hirschman coefficient equivalent number (H_{eq} >= 1).

Author(s)

Thomas Wieland

References

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

Duranton, G./Puga, D. (2000): “Diversity and Specialisation in Cities: Why, Where and When Does it Matter?”. In: Urban Studies, 37, 3, p. 533-555.

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

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.

Roberts, T. (2014): “When Bigger Is Better: A Critique of the Herfindahl-Hirschman Index's Use to Evaluate Mergers in Network Industries”. In: Pace Law Review, 34, 2, p. 894-946.

See Also

cv, gini

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)
herf(sales, output = "eq")
# returns the HHI equivalent number (2.94)

# 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)