Herfindahl-Hirschman index in STATA

[Fredrik Azelius]

Hi,

I am writing a thesis regarding export diversification in the region of West Africa (ECOWAS). I have run regressions and got significant results. I would like to make Herfindahl-Hirschman index to strengthen my thesis. Is this index possible to make in STATA, or do I have to look elsewhere? If it is possible in STATA, how do I do? I know of the Command ssc install hhi, but i do not manage to get it working.

Thanks in advance!

[Emad Shehata]

In fact I am working now in such these models but under developing
I will send to you part of help file for calculation purpose:

WTM: Stata module to estimate Trade Indicators Models:

================================================== ====================
*** World Trade Models (WTM) ***
---------------------------------------------------------------------------
*** World Trade Matrix ***
* (1) (CTM) Commodity Trade Matrix
* (2) (CES) Commodity Export Share (%) in Total Commodity Export
* (3) (CIS) Commodity Import Share (%) in Total Commodity Import
--------------------------------------------------------------------
* (4) (TTM) Total Trade Matrix
* (5) (CESW) Country Export Share (%) in Total Trade Export
* (6) (CISW) Country Import Share (%) in Total Trade Import
--------------------------------------------------------------------
* (7) (CTS) Commodity Trade Share (%) in Total Trade
---------------------------------------------------------------------------
*** World Trade Revealed Comparative Advantage Models ***
* (8) (BRCA) Balassa Revealed Comparative Advantage Index
* (9) (SRCA) Symmetric Revealed Comparative Advantage Index
* (10) (WRCA) Weighted Revealed Comparative Advantage Index
* (11) (ARCA) Additive Revealed Comparative Advantage Index
* (12) (MI) Michelaye Index
* (13) (RO) Regional Orientation
---------------------------------------------------------------------------
*** World Trade Intra-Regional Models ***
* (14) (CIRXS) Commodity Intra-Regional Export Share
* (15) (CIRMS) Commodity Intra-Regional Import Share
* (16) (CIRTS) Commodity Intra-Regional Trade Share
* (17) (TIRXS) Total Intra-Regional Export Share
* (18) (TIRMS) Total Intra-Regional Import Share
* (19) (TIRTS) Total Intra-Regional Trade Share
---------------------------------------------------------------------------
*** (WTRGC) World Trade Regional Geographical Concentration Models ***
* (20) (RMS) Regional Market Share
* (21) (RGHI) Regional Gini-Hirschmann Index
* (22) (RHHI) Regional Hirschmann (Hirschmann-Herfindahl) Index
* (23) (NRHHI) Normalized Regional Hirschmann (Hirschmann-Herfindahl) Index
* (24) (TEI) Trade Entropy Index
---------------------------------------------------------------------------

* Example generated by -dataex-. To install: ssc install dataex
clear
input byte(c1_australia c2_newzland) int(c3_china c4_korea c5_asean c6_row) long w1_australia int w2_newzland long(w3_china w4_korea w5_asean w6_row)
0 4   3 168 441   777     0 3348   4878   5213   7070   41062
0 0   0   0   7     0  2564    0    777    659   1187    9633
0 0   0  54  18     2  6058  867      0  16243  23301  398969
0 0   0   0   1     0  2516  301  24232      0  17521  115477
0 0   0   0   6     3  9850 1130  24832  15950  80320  253262
5 3 150 339 960 12836 43045 7169 156819 103738 174227 4341696
end

(22) (RHHI) Regional Hirschmann (Hirschmann-Herfindahl) Index:

 RHHI = (Xji ÷ Xj)^2

where:
 Xji = Exports of Country (j) to Country (i)
 Xj  = Total Exports of Country (j)

    Regional Hirschmann-Herfindahl Index is a measure of the geographical concentration of exports.
    It tells us the degree to which a region or country’s exports are dispersed across different
    destinations.  High concentration levels are sometimes interpreted as an indication of
    vulnerability to economic changes in a small number of export markets. An alternative measure is
    the trade entropy index.

    * Definition: Regional Hirschmann-Herfindahl Index is defined as the sum across destinations of
    the squared export shares for the region under study to all destinations.

* (RHHI) Range: Regional Hirschmann-Herfindahl Index takes Range of values between (0 & 1).
 Higher values indicate that exports are concentrated on fewer markets.

 - (        RHHI < 0.01): High Competitive Index
 - (        RHHI < 0.15): UnConcentrated Index
 - ( 0.15 < RHHI < 0.25): Moderate Concentration
 - (        RHHI > 0.25): High Concentration

    A small index indicates a competitive industry with no dominant players.  If all countries have
    an equal share the reciprocal of the index shows the number of countries in the industry. When
    countries have unequal shares, the reciprocal of the index indicates the "equivalent" number of
    countries in the world.  Value of (RHHI) increases with the degree of concentration reaching its
    upper bound of 1 when all exports in the country is concentrated in one region.  RHHI takes the
    lowest value 1/N, when country export is evenly distributed across all the countries.

    * Limitations: Regional Hirschmann-Herfindahl Index index is subject to an aggregation bias – the
    more disaggregated the data from which it is calculated the better

===========================================================================
*** (1) (CTM) Commodity Trade Matrix ***

+---------------------------------------------------------------------------------------+
|      Country | c1_australia c2_newzland c3_china c4_korea c5_asean   c6_row |  TotalX |
|--------------+--------------------------------------------------------------+---------|
| c1_australia |            0           4        3      168      441      777 |    1393 |
|  c2_newzland |            0           0        0        0        7        0 |       7 |
|     c3_china |            0           0        0       54       18        2 |      74 |
|     c4_korea |            0           0        0        0        1        0 |       1 |
|     c5_asean |            0           0        0        0        6        3 |       9 |
|       c6_row |            5           3      150      339      960    12836 |   14293 |
|--------------+--------------------------------------------------------------+---------|
|       TotalM |            5           7      153      561     1433    13618 |   15777 |
+---------------------------------------------------------------------------------------+
 *** TotalX = Total Commodity Exports  *** TotalM = Total Commodity Imports

 In this example, the commodity will be Wheat.
 Trade Matrix for Wheat – Units US$ millions

1- Rows are Exporting Countries of wheat:
 - Wheat Exports from Australia to Korea               = (168) $US million.
 - Total Wheat Exports from Australia to all countries = (1393) $US million.

2- Columns are Importing Countries of wheat:
 - Wheat Imports to China from Australia           = (3) $US million.
 - Total Wheat Imports to China from all countries = (153) $US million.

    Note that the diagonal elements for single economies are zero. This is because, by definition, a
    country does not trade with itself. If the matrix contains aggregate regions (e.g., ASEAN),
    however, there will be non-zero elements on the diagonal. These represent the intra-regional
    exports of the group.  Note also that for convenience, it is common to put the row and column
    sums in the table.  Row sums are total exports of the product by the country/region in the row
    heading, while column sums are total imports of the product by the country/region in the column
    heading

===========================================================================
*** (22) (RHHI) Regional Hirschmann (Hirschmann-Herfindahl) Index ***
----------------------------------------------------------------------
  * (1) (CRHHI) Commodity Regional Hirschmann (Hirschmann-Herfindahl) Index ***

+---------------------------------------------+
|              Country |                CRHHI |
|----------------------+----------------------|
|         c1_australia |              0.42591 |
|----------------------+----------------------|
|          c2_newzland |              1.00000 |
|----------------------+----------------------|
|             c3_china |              0.59240 |
|----------------------+----------------------|
|             c4_korea |              1.00000 |
|----------------------+----------------------|
|             c5_asean |              0.55556 |
|----------------------+----------------------|
|               c6_row |              0.81170 |
+---------------------------------------------+
------------------------------------------------------------------
  * (2) (TRHHI) Total Regional Hirschmann (Hirschmann-Herfindahl) Index ***

+---------------------------------------------+
|              Country |                TRHHI |
|----------------------+----------------------|
|         w1_australia |              0.47435 |
|----------------------+----------------------|
|          w2_newzland |              0.46357 |
|----------------------+----------------------|
|             w3_china |              0.80649 |
|----------------------+----------------------|
|             w4_korea |              0.55575 |
|----------------------+----------------------|
|             w5_asean |              0.48193 |
|----------------------+----------------------|
|               w6_row |              0.81203 |
+---------------------------------------------+

+-------------------------------------------------------------------+
|              Country |                CRHHI                 TRHHI |
|----------------------+--------------------------------------------|
|         c1_australia |              0.42591               0.47435 |
|----------------------+--------------------------------------------|
|          c2_newzland |              1.00000               0.46357 |
|----------------------+--------------------------------------------|
|             c3_china |              0.59240               0.80649 |
|----------------------+--------------------------------------------|
|             c4_korea |              1.00000               0.55575 |
|----------------------+--------------------------------------------|
|             c5_asean |              0.55556               0.48193 |
|----------------------+--------------------------------------------|
|               c6_row |              0.81170               0.81203 |
+-------------------------------------------------------------------+
* Range: (0 < RHHI < 1).
 - Higher values indicate that exports are concentrated on fewer markets.
 - (        RHHI < 0.01): High Competitive Index
 - (        RHHI < 0.15): UnConcentrated Index
 - ( 0.15 < RHHI < 0.25): Moderate Concentration
 - (        RHHI > 0.25): High Concentration

Example: If we wish to know degree of geographical dispersion of Australia exports.
Regional Hirschmann-Herfindahl Index (RHHI) is appropriate. If (RHHI) has declined over time,
suggesting that Australia has diversified its export markets over the period.

+-------------------------------------------------------------------------+
|   Country | Australia Newzland  China   Korea   ASEAN     ROW |  TotalX |
|-----------+---------------------------------------------------+---------|
| Australia |         0     3348   4878    5213    7070   41062 |   61571 |
|  Newzland |      2564        0    777     659    1187    9633 |   14820 |
|     China |      6058      867      0   16243   23301  398969 |  445438 |
|     Korea |      2516      301  24232       0   17521  115477 |  160047 |
|     ASEAN |      9850     1130  24832   15950   80320  253262 |  385344 |
|       ROW |     43045     7169 156819  103738  174227 4341696 | 4826694 |
|-----------+---------------------------------------------------+---------|
|    TotalM |     64033    12815 211538  141803  303626 5160099 | 5893914 |
+-------------------------------------------------------------------------+

Australia’s bilateral exports = 0       3348    4878    5213    7070    41062
Australia total exports       = 61571
Australia export shares = (0/61571), (3348/61571), (4878/61571), (5213/61571), (7070/61571), (41062/61571)
Australia export shares =  0.0000     0.0544        0.0792        0.0847        0.1148        0.6669

RHHI = [(0.0000)^2 + (0.0544)^2 + (0.0792)^2 + (0.0847)^2 + (0.1148)^2 + (0.6669)^2]^0.5 = 0.47435

    Notes: This calculation illustrates the problem with aggregation bias. In this simplified trade matrix the rest of
    world is a single share. This type of aggregation will push the calculated Hirschmann index up. A Hirschmann index
    can also be calculated using import or trade shares. Regional Hirschmann index is sometimes called the
    Hirschmann-Herfindahl index (HHI).

[Fredrik Azelius]

Dear Emad,

thank you very much! I will try to make my own HHI with this information!

Fredrik

[Emad Shehata]

Dear Fredrik
all best wishes

[Nick Cox]

Emad: Note for your documentation the spelling Hirschman, not Hirschmann https://en.wikipedia.org/wiki/Albert_O._Hirschman

I don't understand the evident perception that this is a difficult problem that might even be beyond Stata.

Fredrik says nothing about his precise data structure, but here is one recent thread. on a similar topic.

http://www.statalist.org/forums/foru...imilar-regions

I'll steal Denis' data from that thread. Using a similar style to the entropy calculation there, it's one egen call to calculate proportions and another to add up their squares.

clear
input str35 Regios float ind int yr float emp
"Oost-Groningen" 0 1970 39000
"Oost-Groningen" 0 1973 36300
"Oost-Groningen" 0 1974 37400
"Oost-Groningen" 0 1975 34600
"Oost-Groningen" 0 1976 35700
"Oost-Groningen" 0 1977 34200
"Oost-Groningen" 0 1978 32900
"Oost-Groningen" 0 1979 32900
"Oost-Groningen" 0 1980 32500
"Oost-Groningen" 0 1981 29600
"Oost-Groningen" 0 1982 29400
"Oost-Groningen" 0 1983 27000
"Oost-Groningen" 0 1984 27800
"Oost-Groningen" 0 1985 27900
"Oost-Groningen" 0 1986 29400
"Oost-Groningen" 0 1987 28700
"Oost-Groningen" 0 1988 28600
"Oost-Groningen" 0 1989 28900
"Oost-Groningen" 0 1990 29600
"Oost-Groningen" 0 1991 29700
"Oost-Groningen" 0 1992 30300
"Oost-Groningen" 0 1993 30300
"Oost-Groningen" 1 1970   700
"Oost-Groningen" 1 1973   600
"Oost-Groningen" 1 1974   900
"Oost-Groningen" 1 1975   600
"Oost-Groningen" 1 1976   600
"Oost-Groningen" 1 1977   400
"Oost-Groningen" 1 1978   500
"Oost-Groningen" 1 1979   500
"Oost-Groningen" 1 1980   500
"Oost-Groningen" 1 1981   400
"Oost-Groningen" 1 1982   400
"Oost-Groningen" 1 1983   400
"Oost-Groningen" 1 1984   400
"Oost-Groningen" 1 1985   400
"Oost-Groningen" 1 1986   400
"Oost-Groningen" 1 1987   400
"Oost-Groningen" 1 1988   400
"Oost-Groningen" 1 1989   400
"Oost-Groningen" 1 1990   400
"Oost-Groningen" 1 1991   400
"Oost-Groningen" 1 1992   400
"Oost-Groningen" 1 1993   400
"Oost-Groningen" 2 1970     0
"Oost-Groningen" 2 1973     0
"Oost-Groningen" 2 1974     0
"Oost-Groningen" 2 1975     0
"Oost-Groningen" 2 1976     0
"Oost-Groningen" 2 1977     0
"Oost-Groningen" 2 1978     0
"Oost-Groningen" 2 1979     0
"Oost-Groningen" 2 1980     0
"Oost-Groningen" 2 1981     0
"Oost-Groningen" 2 1982     0
"Oost-Groningen" 2 1983     0
"Oost-Groningen" 2 1984     0
"Oost-Groningen" 2 1985     0
"Oost-Groningen" 2 1986     0
"Oost-Groningen" 2 1987     0
"Oost-Groningen" 2 1988     0
"Oost-Groningen" 2 1989     0
"Oost-Groningen" 2 1990     0
"Oost-Groningen" 2 1991     0
"Oost-Groningen" 2 1992     0
"Oost-Groningen" 2 1993     0
end

egen prop = pc(emp), by(Regios yr) prop
egen HHI = total(prop^2), by(Regios yr)
tabdisp yr Regios, c(HHI)  

. tabdisp yr Regios, c(HHI)  

--------------------------
          |     Regios    
       yr | Oost-Groningen
----------+---------------
     1970 |       .9653573
     1973 |       .9680085
     1974 |       .9541069
     1975 |       .9664902
     1976 |       .9674886
     1977 |        .977146
     1978 |       .9705081
     1979 |       .9705081
     1980 |       .9701561
     1981 |       .9736889
     1982 |       .9735147
     1983 |       .9712291
     1984 |       .9720336
     1985 |        .972131
     1986 |       .9735147
     1987 |       .9728864
     1988 |       .9727943
     1989 |       .9730691
     1990 |       .9736889
     1991 |       .9737751
     1992 |       .9742808
     1993 |       .9742808
--------------------------

[Emad Shehata]

Dear Nick
Thanks for correction spelling name of Hirschman

[Emad Shehata]

In fact many books and website write the name also "hirschmann"
You can search on google as "regional hirschmann"
But I will correct in the code to "hirschman"
Best Regards

[Nick Cox]

Emad: I am not an economist, but I am sure you're correct. That's a common error. Here are some more from my files:

Statistics typos: a miscellaneous list

This is a list of some common typos arising in statistical literature.

1. The following statisticians' surnames end with "s". Thus whatever is
attributed to them is tagged with (e.g.) Jeffreys or Jeffreys', but not
Jeffrey's.

Harold Jeffreys 1891-1989
Colin L. Mallows 1930-
John P. Mills fl.1926 (Mills ratio)
Samuel Stanley Wilks 1906-1964 (but note Martin Bradbury Wilk 1922-2013)
Frank Yates 1902-1994

2. Other surnames

Ole Eiler Barndorff-Nielsen 1935-
Carl Harald Cramér 1893-1985 (NB accent)
Student 1876-1937 was William Sealy Gosset (not Gossett).
Richard A. Leibler 1914-2003 (not Liebler)
George Pólya 1887-1985 (NB accent)
Alfréd Rényi 1921-1970 (NB accents)
Henry Scheffé 1907-1977 (NB accent)
Gideon Schwarz 1933- (not Schwartz) (BIC)
Hermann Amandus Schwarz 1843-1921 (not Schwartz) (Cauchy-Schwarz)

3. Families and non-families

Bernoulli family. There were lots of them.

Playfair family. John Playfair (1748-1819) was brother of William
Playfair (1759-1823).

Pearson family. Karl Pearson (1857-1936) was father of Egon S. Pearson
(1896-1980).

Coxes. Gertrude M. Cox (1900-1978) was unrelated to David R. Cox
(1924-).

Kendalls. Maurice G. Kendall (1907-1983) was unrelated to David G.
Kendall (1918-2007).

4. Bad Greek and Latin

"polychotomous" is bad Greek, probably arising from a misunderstanding
of "dichotomous", which is "dicho" + "tomous", not "di" + "chotomous".
"polytomous" is better.

"data" in Latin means "given things" and is a plural. What this implies
for modern languages is discussable.

"strata" in Latin is another plural. "stratum" is the singular.

Some people want to insist that "heteroskedastic" and "homoskedastic"
are the correct spellings. (There was no "c" in ancient Greek.) This
argument was published in Econometrica. Oddly enough, the spellings
"heteroscedastic" and "homoscedastic" are due to Karl Pearson, who was
no enemy of "k"; he changed his own name from Carl and founded the
journal Biometrika. Fans of "k" should promise to write of
mikroekonomics and makroekonomics on the grounds that all the pertinent
roots of those words are all Greek too.

5. Not yet idiomatic English (prejudices ahead)

The expressions "a data" (to mean a dataset) and "a code" (to mean a
program) are not yet part of standard English. They are already
collectives.

Using "skew" to mean "bias" is just bound to confuse.

[Emad Shehata]

Thanks so much dear Nick for these information

[Emad Shehata]

Dear Fredrik
In fact fortunately also you can use ineq module for Nick
to calculate directly Herfindahl-Hirschman index (HHI)

clear all
 input id it y
1 1970 39000
1 1973 36300
1 1974 37400
1 1975 34600
1 1976 35700
1 1977 34200
1 1978 32900
1 1979 32900
1 1980 32500
1 1981 29600
1 1982 29400
1 1983 27000
1 1984 27800
1 1985 27900
1 1986 29400
1 1987 28700
1 1988 28600
1 1989 28900
1 1990 29600
1 1991 29700
1 1992 30300
1 1993 30300
1 1970   700
1 1973   600
1 1974   900
1 1975   600
1 1976   600
1 1977   400
1 1978   500
1 1979   500
1 1980   500
1 1981   400
1 1982   400
1 1983   400
1 1984   400
1 1985   400
1 1986   400
1 1987   400
1 1988   400
1 1989   400
1 1990   400
1 1991   400
1 1992   400
1 1993   400
1 1970     0
1 1973     0
1 1974     0
1 1975     0
1 1976     0
1 1977     0
1 1978     0
1 1979     0
1 1980     0
1 1981     0
1 1982     0
1 1983     0
1 1984     0
1 1985     0
1 1986     0
1 1987     0
1 1988     0
1 1989     0
1 1990     0
1 1991     0
1 1992     0
1 1993     0
 end
 ineq y , by(it)

.  ineq y , by(it)

----------------------------------------------------------------------
    group |         it        freq     Simpson     entropy     dissim.
----------+-----------------------------------------------------------
        1 |   1970.000           3       0.965       0.089       0.649
        2 |   1973.000           3       0.968       0.083       0.650
        3 |   1974.000           3       0.954       0.111       0.643
        4 |   1975.000           3       0.966       0.086       0.650
        5 |   1976.000           3       0.967       0.084       0.650
        6 |   1977.000           3       0.977       0.063       0.655
        7 |   1978.000           3       0.971       0.078       0.652
        8 |   1979.000           3       0.971       0.078       0.652
        9 |   1980.000           3       0.970       0.079       0.652
       10 |   1981.000           3       0.974       0.071       0.653
       11 |   1982.000           3       0.974       0.071       0.653
       12 |   1983.000           3       0.971       0.076       0.652
       13 |   1984.000           3       0.972       0.074       0.652
       14 |   1985.000           3       0.972       0.074       0.653
       15 |   1986.000           3       0.974       0.071       0.653
       16 |   1987.000           3       0.973       0.073       0.653
       17 |   1988.000           3       0.973       0.073       0.653
       18 |   1989.000           3       0.973       0.072       0.653
       19 |   1990.000           3       0.974       0.071       0.653
       20 |   1991.000           3       0.974       0.071       0.653
       21 |   1992.000           3       0.974       0.069       0.654
       22 |   1993.000           3       0.974       0.069       0.654
----------------------------------------------------------------------

[Emad Shehata]

This index is usually known as the Simpson index in ecology
and as the Herfindahl index or Herfindahl–Hirschman index (HHI) in economics

https://en.wikipedia.org/wiki/Diversity_index
Part (Simpson index)

[Emad Shehata]

Simpson index is also known as the Hunter–Gaston index in microbiology

[Emad Shehata]

So, the conclusion is:

Simpson index (SI) in ecology
= Herfindahl index (HI) in economics
= Herfindahl–Hirschman index (HHI) in economics
= Hunter–Gaston index ( HGI) in microbiology

Gibbs–Martin index (GMI) of sociology, psychology and management
= Blau index (BI)
= Gini–Simpson index (GSI)

Blau index = 1 - Simpson index

Best regards

[Cynthia Nembi]

Hello to all. I am Cynthia NEMBI PhD student in economics. For my thesis I am working on "Income diversification of rural households in the Central African Republic. I used the inverse Herfindal index approach to measure income diversification, but when I run the command on stata, I find the same values everywhere. I know that this is not normal for these values. Can someone help me to unravel this problem?
I am enclosing the command and the results of my calculation. Thank you in advance.

hhi = psrsp psrast pautres psra psre psrcf psrpcc psrpc psrsg

where hhi is index Herfindal

"psrsp psrast pautres psra psre psrcf psrpcc psrpc psrsg " are the differences sources of income.

ihi = 1/hhi

where ihi is the Index Inverse Herfindal

[Cynthia Nembi]

Inverse Index Herfindal (IIH) in STATA

Hello to all. I am Cynthia NEMBI PhD student in economics. For my thesis I am working on "Income diversification of rural households in the Central African Republic. I used the inverse Herfindal index approach to measure income diversification, but when I run the command on stata, I find the same values everywhere. I know that this is not normal for these values. Can someone help me to unravel this problem?
I am enclosing the command and the results of my calculation. Thank you in advance.

hhi = psrsp psrast pautres psra psre psrcf psrpcc psrpc psrsg

where hhi is index Herfindal

"psrsp psrast pautres psra psre psrcf psrpcc psrpc psrsg " are the differences sources of income.

ihi = 1/hhi

where ihi is the Inverse Index Herfindal