Repository files navigation

Measures of concentration and competition are important and give a firstinsight of a given market structure in a particular market. They areimportant to determine public policies and strategic corporatedecisions. However, in research and in practice the most commonly usedmeasure is the Herfindahl Hirschman Index. Various complementary oralternative measures exist, which - used as a set - might reduceuncertainty. The goal of theconcstats package is tooffer a set of alternative and/or additional measures for researchers insocial sciences and practitioners in institutions concerned withcompetition on a regular basis to better determine a given marketstructure and therefore reduce uncertainty with respect to a givenmarket situation. Various functions or groups of functions are availableto achieve the desired goal.

-concstats_concstats calculates a set of pre-selected concentrationand diversity measures in a one-step procedure.
-concstats_mstruct offers market structure measures, e.g. the sum ofTop3 or Top5 market shares.
-concstats_comp is a wrapper for concentration measures, e.g. theHerfindahl Hirschman Index.
-concstats_inequ offers diversity or inequality measures, e.g. theEntropy or the Palma ratio.
-concstats_shares is a helper function converting numeric vectors intoindividual shares.

A stable version of concstats is available on CRAN:

install.packages("concstats")# Market structure, concentration and inequality# measures

You can install the latest development version fromGitHub orR-universe.

# install.packages("devtools")devtools::install_github("ropensci/concstats")

install.packages("concstats",repos="https://ropensci.r-universe.dev")

In general, all functions of theconcstats package take numericvectors as input, that is, ideally relative market shares in decimalformat. However, the user can also use integers which are then convertedto decimal form.concstats_constats has one main function whichcalculates a set of pre-selected measures in a one-step procedure.

is a wrapper to calculate different structural measures. Within thisgroup are measures like the number of firms, numbers equivalent,cumulative Top 3 and Top 5 market share. The measures might becalculated as a group or individually. Theconcstats_top_df functionsalso take a data frame as input, since the ranking of firms might be ofinterest.

is a group wrapper to calculate different concentration measures. Withinthis group are measures like the Herfindahl-Hirschman index (HHI), thedual of the HHI, the Dominance or the Stenbacka index.

is a group of inequality and diversity measures, e.g. Entropy, Ginicoefficient, Palma ratio. Most functions offer a finite samplecorrection.

This is a basic example which shows you how to calculate an individualmeasure or a set of market structure and concentration measures:

library(concstats)## Create some simple datax<- c(0.4,0.2,0.25,0.1,0.05,0,0)concstats_hhi(x)# the Herfindahl-Hirschman Index#> [1] 0.275## if you need to convert your data into sharesx<- c(538572286.08,481096.77,161914143.03,128796268.59,69055940.72)concstats_shares(x,digits=5)#> [1] 0.59920 0.00054 0.18014 0.14329 0.07683concstats_dom(x)# the Dominance Index#> [1] 0.4127273## Our simple datax2<- c(0.35,0.4,0.05,0.1,0.06,0.04)# market shares of each firm in# the market (should sum up to 1)## Calculate a selected set of market structure and concentration measuresconcstats_concstats(x2,digits=2)# calculates a pre-selected set of measures#>         Measures Values#> 1          Firms   6.00#> 2 Nrs_equivalent   3.33#> 3        Top (%)  40.00#> 4       Top3 (%)  85.00#> 5       Top5 (%)  96.00#> 6            HHI   0.30#> 7    Entropy(RE)   0.79#> 8    Palma ratio   2.67

In this case, the result is a table with eight selected measures: 1)Number of firms, 2) Numbers equivalent of firms, 3) Top firm, share in%, 4) Top 3 firms, share in %, 5) Top 5 firms, share in %, 6) TheHerfindahl-Hirschman Index, in decimal form, 7) Normalized ShannonEntropy (RE), a value between 0 and 1, 8) Palma ratio, an inequalityscore which measures the ratio of the top 10 percent to the bottom 40percent.

Some functions are already implemented in other R packages. Thenon-exhaustive summary below is by no means a description of eachpackage.

• The Herfindahl Hirschman Index can be found in thehhi and thedivseg packages. Whilethehhi package has just one function, neither of both packagesoffer a normalized version of the measure.

• The latter offers as well functions for the Entropy, Gini and Simpsonmeasures.

• Theacid and theineq packages offerfunctions for inequality and competition measures, e.g. for theEntropy and Gini metric.

Some popular measures, e.g. Gini or the Herfindahl-Hirschman index havealso been implemented in Python.

However, almost none of these packages offer a normalized calculation ofthe respective measure, with the exception of theineq package. Other functionsare new implementations in R, e.g. Dominance Index, Palma ratio,Stenbacka Index, GRS measure, and the dual of the Herfindahl HirschmanIndex.

1. Chang, E. J., Guerra, S. M., de Souza Penaloza, R. A. & Tabak, B. M.2005) “Banking concentration: the Brazilian case” In FinancialStability Report. Brasilia: Banco Central do Brasil, 4:109-129.
2. Cobham, A. and A. Summer (2013). “Is It All About the Tails? ThePalma Measure of Income Inequality”, Center for Global Development,Washington, DC.
3. Garcia Alba Idunate, P. (1994). “Un Indice de dominancia para elanalisis de la estructura de los mercados”. , 61: 499-524.
4. Ginevicius, R. and S. Cirba (2009). “Additive measurement of marketconcentration”, , 10(3), 191-198.https://doi.org/10.3846/1611-1699.2009.10.191-198
5. Palma, J. G. (2006). “Globalizing Inequality: ‘Centrifugal’ and‘Centripetal’ Forces at Work”, DESA Working Paper No. 35.
6. Shannon, C. E. (1948). “A Mathematical Theory of Communication”,(Nokia Bell Labs).
7. Melnik, A., Shy, Oz, Stenbacka, R., (2008), “Assessing marketdominance”, , 68: pp. 63-72.
8. Simpson, E. H. (1949). “Measurement of Diversity”, , 163, 688.https://doi.org/10.1038/163688a0

The hexagon sticker is created by myself with thehexsticker package.A good overview and a lot of inspiration (adding badges, how to create awebpage and testing the package) comes fromCosima Meyer and DennisHammerschmidt.

If you have any questions or find any bugs requiring fixing, feel freeto open an issue or pull request.

Contributions are welcome! For more details on how to contribute to thispackage please see theCONTRIBUTINGfile.

Please note that this package is released with aContributor Code ofConduct. By contributing to thisproject, you agree to abide by its terms.