Herfindahl-Index

[Kirsten Weitz]

Hello,

i need the industry concentration (Herfindahl Index), calculated as the sum of squared market shares (based on annual sales (WC01001)) in the firm's industry sector (SIC-Code) per year. The index is between 0 (perfect competition) and 10.000 (monopoly) since market shares in percentage are multiplied by 100.


How can I get the herfindahl index for each year?

I have the following sheet:

isin	company_name	year	WC01001	SIC_Code
BSP951331318	UNITED INTERNATIONAL	2014	1757001	1
BSP951331318	UNITED INTERNATIONAL	2015	1758568	1
BSP951331318	UNITED INTERNATIONAL	2016	1998846	1
CH0136071542	Cavotec SA	2015	2167291	3
CH0136071542	Cavotec SA	2016	2002564	3
CH0136071542	Cavotec SA	2017	2049372	3
CH0256424794	Oriflame Cosmetics S.A	2015	11307275	5
CH0256424794	Oriflame Cosmetics S.A	2016	11828624	5
CH0256424794	Oriflame Cosmetics S.A	2017	13154648	5
DK0010006329	SANTA FE GROUP A/S	2014	2520000	12
DK0010006329	SANTA FE GROUP A/S	2015	2786839	12
DK0010006329	SANTA FE GROUP A/S	2016	2520217	12
DK0010008028	F E BORDING A/S	2014	621147	3
DK0010008028	F E BORDING A/S	2015	610803	3
DK0010008028	F E BORDING A/S	2016	627518	3
DK0010025113	ARKIL HOLDING A/S	2014	2871394	12
DK0010025113	ARKIL HOLDING A/S	2015	3346768	12
DK0010025113	ARKIL HOLDING A/S	2016	3017006	12
DK0010027671	NTR HOLDING AS	2014	89500	2
DK0010027671	NTR HOLDING AS	2015	89500	2
DK0010027671	NTR HOLDING AS	2016	80100	2
DK0010125848	RIAS A/S	2014	279346	5
DK0010125848	RIAS A/S	2015	265806	5
DK0010125848	RIAS A/S	2016	266244	5
DK0010128008	SILKEBORG IF INVEST	2014	59363	12
DK0010128008	SILKEBORG IF INVEST	2015	61597	12
DK0010128008	SILKEBORG IF INVEST	2016	61183	12
DK0010129089	BRD KLEE A/S	2014	154191	9
DK0010129089	BRD KLEE A/S	2015	157089	9
DK0010129089	BRD KLEE A/S	2016	174743	9
DK0010181759	CARLSBERG A/S	2014	64506000	1
DK0010181759	CARLSBERG A/S	2015	65354000	1
DK0010181759	CARLSBERG A/S	2016	62614000	1
DK0010201102	KOEBENHAVNS	2014	3867500	12
DK0010201102	KOEBENHAVNS	2015	4061900	12
DK0010201102	KOEBENHAVNS	2016	4421900	12
DK0010212224	Intermail AS	2014	416016	3
DK0010212224	Intermail AS	2015	366955	3
DK0010212224	Intermail AS	2016	330700	3

[Jorrit Gosens]

It's possible to calculate this manually, but there is also a program for it: https://ideas.repec.org/c/boc/bocode/s457512.html

In the future, please provide an example of your data with dataex (see the FAQ on how and why: https://www.statalist.org/forums/help#stata

* Example generated by -dataex-. To install: ssc install dataex
clear
input str12 isin str22 company_name int year long WC01001 byte SIC_Code
"BSP951331318" "UNITED INTERNATIONAL"   2014  1757001  1
"BSP951331318" "UNITED INTERNATIONAL"   2015  1758568  1
"BSP951331318" "UNITED INTERNATIONAL"   2016  1998846  1
"CH0136071542" "Cavotec SA"             2015  2167291  3
"CH0136071542" "Cavotec SA"             2016  2002564  3
"CH0136071542" "Cavotec SA"             2017  2049372  3
"CH0256424794" "Oriflame Cosmetics S.A" 2015 11307275  5
"CH0256424794" "Oriflame Cosmetics S.A" 2016 11828624  5
"CH0256424794" "Oriflame Cosmetics S.A" 2017 13154648  5
"DK0010006329" "SANTA FE GROUP A/S"     2014  2520000 12
"DK0010006329" "SANTA FE GROUP A/S"     2015  2786839 12
"DK0010006329" "SANTA FE GROUP A/S"     2016  2520217 12
"DK0010008028" "F E BORDING A/S"        2014   621147  3
"DK0010008028" "F E BORDING A/S"        2015   610803  3
"DK0010008028" "F E BORDING A/S"        2016   627518  3
"DK0010025113" "ARKIL HOLDING A/S"      2014  2871394 12
"DK0010025113" "ARKIL HOLDING A/S"      2015  3346768 12
"DK0010025113" "ARKIL HOLDING A/S"      2016  3017006 12
"DK0010027671" "NTR HOLDING AS"         2014    89500  2
"DK0010027671" "NTR HOLDING AS"         2015    89500  2
"DK0010027671" "NTR HOLDING AS"         2016    80100  2
"DK0010125848" "RIAS A/S"               2014   279346  5
"DK0010125848" "RIAS A/S"               2015   265806  5
"DK0010125848" "RIAS A/S"               2016   266244  5
"DK0010128008" "SILKEBORG IF INVEST"    2014    59363 12
"DK0010128008" "SILKEBORG IF INVEST"    2015    61597 12
"DK0010128008" "SILKEBORG IF INVEST"    2016    61183 12
"DK0010129089" "BRD KLEE A/S"           2014   154191  9
"DK0010129089" "BRD KLEE A/S"           2015   157089  9
"DK0010129089" "BRD KLEE A/S"           2016   174743  9
"DK0010181759" "CARLSBERG A/S"          2014 64506000  1
"DK0010181759" "CARLSBERG A/S"          2015 65354000  1
"DK0010181759" "CARLSBERG A/S"          2016 62614000  1
"DK0010201102" "KOEBENHAVNS"            2014  3867500 12
"DK0010201102" "KOEBENHAVNS"            2015  4061900 12
"DK0010201102" "KOEBENHAVNS"            2016  4421900 12
"DK0010212224" "Intermail AS"           2014   416016  3
"DK0010212224" "Intermail AS"           2015   366955  3
"DK0010212224" "Intermail AS"           2016   330700  3
end

To install the program:

ssc install hhi

Code to calculate the hhi:

hhi WC01001, by (year SIC_Code)
sort year SIC_Code

And multiply by 100 if you want the HHI as a percentage rather than fraction.

[Nick Cox]

See also e.g. entropyetc from SSC. With the same example data, and knowing Simpson == Herfindahl,

. entropyetc comp [w=WC] , by(SIC year)
(analytic weights assumed)

----------------------------------------------------------------------
    Group |  Shannon H      exp(H)     Simpson   1/Simpson     dissim.
----------+-----------------------------------------------------------
   1 2014 |      0.122       1.130       0.948       1.054       0.897
   1 2015 |      0.121       1.129       0.949       1.054       0.897
   1 2016 |      0.138       1.148       0.940       1.064       0.892
   2 2014 |      0.000       1.000       1.000       1.000       0.923
   2 2015 |      0.000       1.000       1.000       1.000       0.923
   2 2016 |      0.000       1.000       1.000       1.000       0.923
   3 2014 |      0.673       1.961       0.520       1.925       0.846
   3 2015 |      0.826       2.283       0.526       1.900       0.769
   3 2016 |      0.838       2.312       0.515       1.942       0.769
   3 2017 |      0.000       1.000       1.000       1.000       0.923
   5 2014 |      0.000       1.000       1.000       1.000       0.923
   5 2015 |      0.109       1.116       0.955       1.047       0.900
   5 2016 |      0.106       1.112       0.957       1.045       0.901
   5 2017 |      0.000       1.000       1.000       1.000       0.923
   9 2014 |      0.000       1.000       1.000       1.000       0.923
   9 2015 |      0.000       1.000       1.000       1.000       0.923
   9 2016 |      0.000       1.000       1.000       1.000       0.923
  12 2014 |      1.114       3.045       0.340       2.938       0.763
  12 2015 |      1.117       3.056       0.337       2.966       0.763
  12 2016 |      1.101       3.006       0.349       2.868       0.763
----------------------------------------------------------------------