st: Calculating an Index

["Pavlos C. Symeou" <p.symeou@gmail.com>]

Dear Statlisters,

Nick and Antonios kindly responded to a similar problem I 
encountered last week. I hope I can also find some assistance with 
the following problem which is a bit more complex. I don't know 
much about programming (e.g. using mata) I would appreciate it if 
you could explain your code so that I can adjust it in future 
problems. This way I will avoid to annoy you with similar problems.

Here it goes. I have data for a number of firms for multiple years 
per firm. Each firm operates in a number of markets each year. A 
market's identifier is denoted by a 3-digit number. I want to 
calculate a new variable "index" as follows:

1) for each company-year I take the sales_ratio of each market and 
multiply it with each other market's sales ratio:

a) If the identifiers of the two markets are the same, then I 
multiply their product with 1.
b) If the identifiers of the two markets have the same first 2 
digits (i.e. they differ in the 3rd digit), then I multiply their 
product with 2.
c) If the identifiers of the two markets have the same first digit 
but differ in all others, then I multiply their product with 3.
d) If the identifiers of the two markets differ in the first digit, 
then I multiply their product with 4.

The "index" variable equals the sum of a, b, c, and d.

From the example data below, the Index for Firm 1 in Year 1996 
should be:
(0.071 * 0.14 * 4) + (0.071 * 0.071 * 4) + (0.071 * 0.29 * 4) + 
(0.14 * 0.071 * 3) + (0.14 * 0.29 * 3) +(0.071 * 0.29 * 2) = 0.335

firm_id    year    market    sales_ratio
1    1996    262    .071
1    1996    349    .14
1    1996    353    .071
1    1996    357    .29
1    1997    382    .36
1    1997    733    .071
1    1997    262    .5
1    1997    353    .5
1    1998    349    .15
1    1998    357    .31
1    1998    365    .077
1    1998    382    .38
1    1998    733    .077
2    1996    349    .13
2    1996    357    .27
2    1996    365    .067
2    1996    366    .067
2    1996    371    .067
2    1996    382    .33
2    1996    733    .067

Best wishes,

Pavlos
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