Herfindahl-Hirschman Index (HHI) with Panel data

[Anuradha Saikia]

Hello everyone. I have a dataset of different firms in panel form. I want to take HHI s a control variable but I am not sure how to do it . HHI wont be individual values for each firm in each year. Is it possible to take HHI in panel data form.

[Jared Greathouse]

No idea what HHI is or why you'd want it, but presuming it's just a matter of arithmetic, yeah of course Stata can do it as far as I know. Do you know the formula to calculate such an index? And if so, show me your example data as well as what you tried to calculate the index.

[Nick Cox]

Jared Greathouse HHI as in the thread title is the Herfindahl-Hirschman Index.

Anuradha Saikia There are many threads on that here, but what you want is a sum of squared probabilities. Here is code for HHI of investment by year in the Grunfeld data.

webuse grunfeld, clear 

egen double total = total(invest), by(year)

egen double HHI = total((invest/total)^2), by(year)

format total %3.2f 

format HHI %04.3f 

tabdisp year, c(total HHI)

----------------------------------
     Year |      total         HHI
----------+-----------------------
     1935 |     727.46       0.286
     1936 |    1016.07       0.283
     1937 |    1224.81       0.273
     1938 |     775.55       0.242
     1939 |     805.26       0.265
     1940 |    1132.65       0.280
     1941 |    1397.19       0.263
     1942 |    1226.65       0.277
     1943 |    1177.90       0.285
     1944 |    1209.25       0.276
     1945 |    1241.59       0.266
     1946 |    1613.59       0.267
     1947 |    1471.35       0.250
     1948 |    1539.48       0.240
     1949 |    1392.44       0.259
     1950 |    1510.61       0.272
     1951 |    1995.83       0.248
     1952 |    2240.33       0.257
     1953 |    2755.83       0.292
     1954 |    2737.81       0.337
----------------------------------

For another approach, see (e.g.) entropyetc from SSC, which gives code for this problem:

entropyetc company [aw=invest], by(year)

[Anuradha Saikia]

Hii Jared Greathouse .This is the definition of HHI."The Herfindahl-Hirschman Index is an index that measures the market concentration of an industry. A highly concentrated industry is one where only a few players in the industry hold a large percentage of the market share, leading to a near-monopolistic situation. A low degree of concentration means that the industry is closer to a perfect competition scenario, where many firms of more or less equal size share the market." To calculate the Herfindahl-Hirschman Index, we take the percentage market share of each firm in an industry, square that number, and then add all the squares together.

[Jared Greathouse]

Nick Cox Well yes, what I really meant to say was "What does this HHI map on to in the real world"? I presume it's a kind of economic index. What is it anyways?


EDIT: Okay I see. interesting.

[Anuradha Saikia]

Thank you Nick Cox . But can HHI be for firm level. Its only at time series level right not at panel data form. For example there cannot for HHI for firm A in years from 2005-2021. Then HHI for firm B from the same industry for period 205-2021.

[Jared Greathouse]

I suspect the issue here is to use some combination of egen or the bysort prefix; can you post your example data using dataex? Anuradha Saikia

[Nick Cox]

Generically this measure is just a sum of squared proportions (with use of percentages the same idea). Market concentration is an example of its application. It can be used for many purposes and earlier uses long predate its re-invention by Herfindahl. The mention of Hirschman is a courtesy, perhaps reflecting the fact that Hirschman claimed priority over Herfindahl for essentially the same idea, which he suggested in another guise. Much earlier than either H, this is one of several quite measures invented by Gini. One of these years I hope to encounter it as the solution to a routine probability problem in some 19th century text.

[Nick Cox]

#6 I am not an economist, and I may be misunderstanding. But I see the point of looking at firms in some sector as a snapshot in time, as measuring the state of a sector somewhere between monopoly and perfect competition. I am unsure of the meaning of looking at a firm in a series of years, if that is what you are asking, but the calculation would be just the same commands with different variables. .The formula admits many interpretations, but not market concentration if you focus on individual firms.

[Anuradha Saikia]

Thank you Nick. I got the clarity now.