Market Structure, Concentration and Inequality Measures


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Measures of concentration and competition are important and give a first insight of a given market structure in a particular market. They are important to determine public policies and strategic corporate decisions. However, in research and in practice the most commonly used measure is the Herfindahl Hirschmann Index. The goal of the concstats package is to offer a set of alternative and/or additional measures to better determine a given market structure and therefore reduce uncertainty with respect to a given market situation. Various functions or groups of functions are available to achieve the desired goal.

-concstats calculates a set of pre-selected concentration and diversity measures in a one-step procedure.
-mstruct offers market structure measures, e.g. the sum of Top3 or Top5 market shares.
-comp is a wrapper for concentration measures, e.g. the Herfindahl Hirschmann Index.
-inequ offers diversity or inequality measures, e.g. the Entropy or the Palma ratio.


You can install the development version from GitHub or:

install.packages("devtools") # a package for developing R packages

How to use concstats


has one main function which calculates a set of pre-selected measures in a one-step procedure.


is a wrapper to calculate different structural measures. Within this group are measures like the number of firms, numbers equivalent, cumulative Top 3 and Top 5 market share. The measures might be calculated as a group or individually.


is a group wrapper to calculate different concentration measures. Within this group are measures like the Herfindahl-Hirschmann index (HHI), the dual of the HHI, the Dominance or the Stenbacka index.


is a group of inequality and diversity measures, e.g. Entropy, Gini coefficient, Palma ratio.


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

## Create some simple data
share1 <- c(0.4, 0.2, 0.25, 0.1, 0.05, 0, 0)
share_hhi <- hhi(share1) # the Herfindahl-Hirschmann Index
#> [1] 0.275

share_dom <- dom(share1) # the Dominance Index
#> [1] 0.4127273

## Create some other simple data
share2 <- 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 measures
share2_con <- concstats(share2) # creates share2_con, a 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) The Herfindahl-Hirschmann Index, in decimal form, 7) Normalized Entropy (RE), a value between 0 and 1, 8) Palma ratio, an inequality score which measures the ratio of the top 10 percent to the bottom 40 percent.


  1. Chang, E. J., Guerra, S. M., de Souza Penaloza, R. A. & Tabak, B. M.
    1. Banking concentration: the Brazilian case. In Financial Stability Report. Brasilia: Banco Central do Brasil, 4: 109-129.
  2. Cobham, A. and A. Summer (2013). Is It All About the Tails? The Palma Measure of Income Inequality, Center for Global Development, Washington, DC.
  3. Garcia Alba Idunate, P. (1994). Un Indice de dominancia para el analisis de la estructura de los mercados. El Trimestre Economico, 61: 499-524.
  4. Ginevicius, R. and S. Cirba (2009). Additive measurement of market concentration, Journal of Business Economics and Management, 10(3), 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, The Bell System Technical Journal (Nokia Bell Labs).


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Contact and Issues

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


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