How to calculate competition (herfindahl-hirschman index)?

[gani davlatyov]

Hi everyone,
I am trying to identify how competitive the area (zip codes) is. I have the market shares of organizations across zip codes.
The HHI is calculated by squaring the market share of each organization in the area.

* Example generated by -dataex-. For more info, type help dataex
clear
input str5 zipcode float market_share
"00601"  94.93433
"00601" 3.7898686
"00601"  .3377111
"00601"  .9380863
"00602"  93.81937
"00602"  4.809576
"00602" 1.3710555
"00603" 1.3475177
"00603"  24.89362
"00603" 15.531915
"00603"  56.80851
"00603" 1.4184397
"00605" 37.735847
"00605" 18.867924
"00605"  43.39622
"00606" 19.980925
"00606"  80.01907
"00610"  66.85678
"00610"  33.14322
"00611" 13.064133
"00611"  86.93587
"00612"  .4781997
"00612"  7.735584
"00612"  .8720112
"00612"  63.26301
"00612"  8.579466
"00612" 15.583685
"00612" 2.2503517
"00612" 1.2376934
"00613"  16.37931
"00613"  70.97701
"00613" 12.643678
"00614"  17.28972
"00614"  72.66355
"00614"  10.04673
"00616"  5.148515
"00616"  47.92079
"00616" 12.871287
"00616" 34.059406
"00617"  .3344968
"00617"  .9307737
"00617"  .8726004
"00617"   7.35893
"00617"  89.86329
"00617"  .6399069
"00622"       100
"00623"       100
"00624"   .375728
"00624"  98.60981
"00624"  .3193688
"00624"  .6950967
"00627"  78.20222
"00627" 17.513758
"00627" .59350383
"00627" .22661056
"00627"  3.463904
"00631"  91.39151
"00631"  8.608491
"00637"  4.571429
"00637"  95.42857
"00638"  4.499487
"00638"  87.99648
"00638" 2.1984465
"00638"  1.568225
"00638"  3.737359
"00641" 2.0793223
"00641"  1.347709
"00641"  88.21717
"00641" 4.3896804
"00641"  .9241433
"00641" 3.0419714
"00646"  71.39507
"00646" 2.5791326
"00646"  3.048066
"00646"  2.344666
"00646" 14.771395
"00646"  5.861665
"00647"       100
"00650"   .458907
"00650" 1.2828536
"00650"  75.86566
"00650" 22.392574
"00652" 3.4552846
"00652" 18.495935
"00652" 10.162601
"00652"  67.88618
"00653"  1.978022
"00653"  98.02198
"00656"  68.90511
"00656"  5.839416
"00656" 25.255474
"00659" 17.126081
"00659"  79.79899
"00659"   .457757
"00659"  .4876107
"00659" 2.1295652
"00660"       100
end

Thank you for your help.

[Carlo Lazzaro]

Gani:
check if what follows does the trick (untested):

encode zipcode, g(num_zipcode)
bysort num_zipcode: g wanted=sum(market_share^2)

[gani davlatyov]

It worked.
Thank you so much for your help.

[gani davlatyov]

Now I am reviewing the results, it seems like this formula didn't work as I needed.
For example, when I look at the zip code area 00601, the HHI should be 9,027.8849

display (0.33771107^2)+(94.934334^2)+(3.7898686^2)+(0.9380 8633^2)
9027.8849

That number should be the same for all the organizations located within a certain zip code.

But the formula generated different HHI scores for each organization, within a zip code.

* Example generated by -dataex-. For more info, type help dataex
clear
input float ID str5 zipcode float(market_share hhi)
159 "00601"  .9380863   .880006
115 "00601"  94.93433  9013.408
117 "00601" 3.7898686 9027.7705
135 "00601"  .3377111  9027.885
128 "00602"  4.809576 23.132017
127 "00602"  93.81937  8825.205
135 "00602" 1.3710555  8827.085
125 "00603" 1.3475177  1.815804
135 "00603"  56.80851  3229.023
127 "00603"  24.89362  3848.715
159 "00603" 1.4184397  3850.727
128 "00603" 15.531915  4091.967
127 "00605" 37.735847  1423.994
128 "00605" 18.867924 1779.9927
135 "00605"  43.39622  3663.225
115 "00606" 19.980925  399.2373
128 "00606"  80.01907   6802.29
128 "00610"  33.14322  1098.473
127 "00610"  66.85678  5568.302
135 "00611" 13.064133 170.67157
159 "00611"  86.93587  7728.517
134 "00612"  .8720112  .7604036
141 "00612"  8.579466  74.36764
135 "00612"  63.26301  4076.576
159 "00612" 2.2503517   4081.64
114 "00612"  .4781997  4081.869
125 "00612"  7.735584  4141.708
152 "00612" 15.583685  4384.559
162 "00612" 1.2376934  4386.091
125 "00613"  16.37931 268.28183
135 "00613"  70.97701  5306.018
152 "00613" 12.643678  5465.881
152 "00614"  10.04673 100.93677
135 "00614"  72.66355  5380.928
125 "00614"  17.28972  5679.863
141 "00616" 12.871287 165.67004
152 "00616" 34.059406  1325.713
125 "00616"  5.148515 1352.2205
135 "00616"  47.92079 3648.6226
134 "00617"  .9307737  .8663397
125 "00617"  .3344968  .9782279
135 "00617"  .8726004 1.7396593
152 "00617"  89.86329   8077.15
162 "00617"  .6399069   8077.56
141 "00617"   7.35893  8131.714
128 "00622"       100     10000
128 "00623"       100     10000
124 "00624"  .3193688 .10199641
128 "00624"  .6950967  .5851559
117 "00624"  98.60981 9724.4795
115 "00624"   .375728  9724.621
125 "00627"  78.20222  6115.588
135 "00627" 17.513758   6422.32
159 "00627"  3.463904  6434.318
152 "00627" .22661056   6434.37
141 "00627" .59350383  6434.722
115 "00631"  91.39151  8352.408
159 "00631"  8.608491  8426.515
117 "00637"  4.571429  20.89796
128 "00637"  95.42857  9127.511
114 "00638"  4.499487  20.24538
141 "00638" 2.1984465  25.07855
162 "00638"  3.737359   39.0464
134 "00638"  87.99648  7782.427
152 "00638"  1.568225  7784.887
125 "00641"  1.347709 1.8163193
152 "00641"  .9241433   2.67036
159 "00641" 3.0419714  11.92395
135 "00641"  88.21717  7794.193
115 "00641" 2.0793223  7798.517
141 "00641" 4.3896804  7817.786
206 "00646"  5.861665 34.359116
152 "00646"  2.344666  39.85657
114 "00646"  71.39507  5137.113
134 "00646"  3.048066  5146.404
162 "00646" 14.771395  5364.598
119 "00646" 2.5791326   5371.25
128 "00647"       100     10000
152 "00650" 22.392574  501.4274
141 "00650"  75.86566  6257.026
134 "00650"   .458907  6257.237
135 "00650" 1.2828536  6258.882
141 "00652" 10.162601 103.27847
135 "00652" 18.495935  445.3781
152 "00652"  67.88618  5053.911
125 "00652" 3.4552846   5065.85
117 "00653"  1.978022  3.912571
128 "00653"  98.02198  9612.221
124 "00656"  5.839416 34.098778
117 "00656"  68.90511  4782.013
128 "00656" 25.255474  5419.853
152 "00659"  .4876107  .2377642
135 "00659"  79.79899  6368.116
125 "00659" 17.126081  6661.419
159 "00659" 2.1295652  6665.954
141 "00659"   .457757  6666.164
128 "00660"       100     10000
end

[Nick Cox]

sum() gives a cumulative or running sum, so it’s the last value you want from each zip code. Or use egen‘s total() function.

[gani davlatyov]

Thank you, Dr. Cox.
This produced what I needed:
bysort num_zipcode: egen hhi=total(market_share^2)

[Nick Cox]

Using percents means that the HHI runs on a scale from 0 (almost) to 10000. I find it more useful to convert to a numbers equivalent, the equivalent number of companies with equal shares, varying from 1 (monopoly) upwards. Each zip code should be plotted just one.

egen HHI = total(market_share^2), by(zipcode)
gen numbers_equivalent = 10000/HHI 
egen tag = tag(zipcode)

quantile numbers_equivalent if tag, scheme(s1color) ms(S) mc(blue) rlopts(lc(none)) yla(, ang(h))