calculating related and unrelated diversification with the entropy measure.

[smi...@gmail.com]

Hello all, Im trying to use the entropy measure to calculate related and unrelated diversification and Im having a real go of it. 

Im using the Palepu 1985 measures where: 

Total diversification =

 DT = sum across groups - Pi* In(1 /Pi)

Related diversification = 

DRj  = sum across groups -  Pi(of j)*ln(1/Pi(of j))

Total related diversification = 

DR = sum across groups - DRj*Pj

Unrelated diversification = 

DU = sum across groups - Pj*ln(1/Pj)

In the paper, he even posts a table to illustrate hypothetical calculations. However, I can not for the life of me reproduce them. 

For example: 

                                                                          Sales                                                                                   Diversification Index

                                    Group 1 (2-digit)                                     Group 2 (2-digit) 

Total                          Seg1       Seg2                              Seg1      Seg2       Seg3                          Total         Related       Unrelated

100                          100                                                                                                                          0                0                     0

100                           95              5                                                                                                         .2                .2                     0

100                           90             10                                                                                                       .32              .32

100                           80             10                                    10                                                               .64              .32                 .32

100                           70             20                                   10                                                                 .80             .48                  .32 

100                          60            10                                     10          10              10                               1.23             .62                 .61

For example...For the second row, I keep trying the following 

=95/100*(log(100/95)) = .021

=5/100*(log(100/5)) = .065

.065+.021 = .086, which does not equal .2 

Can anyone help with this? Before I can write code to calculate this across firms, I need to get my head wrapped around it conceptually first. So I can at least go back and calculate a few to make sure things line up. I attached the article Im using for reference. 

Thanks to anyone who can help!

[joost impink]

Hi,

It looks like you didn't use the segments fractions correctly ( 95% is 95/100, not 100/95).

S1: 95% = 0.95
S2: 5% = 0.05

DT = 0.95 x ln ( 1 / 0.95 ) + 0.05 x ln ( 1 / 0.05 ) = 0.02 (rounded)

Best Regards,

Joost

[joost impink]

On second thought -- you do have the formula correct -- but you used log instead of natural log.

0.95*LOG(1/0.95)+0.05*LOG(1/0.05) = 0.86
0.95*LN(1/0.95)+0.05*LN(1/0.05) = 0.20

:)

[smi...@gmail.com]

Joost, 

Thank you - you definitely saved me further headache on this, can't believe I overlooked such a small detail! Another question for you while I am at it. 

When calculating related and unrelated diversification scores for firms do you treat primary and secondary SICs differently? Or do you just do it BY firm BY year and BY primary sic? 

Ive attached a screenshot of the data for an example:

Let's take Abbott Laboratories, which has 5 segments in 1999 - the 5 segments are listed under 5 primary SICs (however, only 3 are unique). Of the 3 primary SIC codes that are identical, two 

have a secondary SIC code and the other one does not. Should I compute related and unrelated diversification as though all of the sales in the primary SIC segments "2834" are identical? In effect,

aggregating the three segments' sales for SIC code "2834" in order to then compute related and unrelated diversification? 

My hunch is that this is what should be done since it is really a proxy and theyll be pluses/minuses to any approach. 

What do you think/advise? 

Thanks for your help!

[joost impink]

hi,

It has been a while but at some point I needed to construct related/unrelated diversification, and I remember I only used SIC1 (ignoring SIC2).

Also there may be prior research to follow? (assuming the papers have enough detail to replicate)

Best Regards,

Joost

[smi...@gmail.com]

Thanks for your swift reply!

I haven't found prior work that goes into sufficient detail. However, I imagine it is best to just use sic1 (ignoring sic2) since trying to account for both the primary and secondary SIC could result in

double counting and some other issues. 

Thanks again for your comments!