Vector correlation to create relatedness measure

[Laura Irrgang]

Hello all,

I am currently trying to create a technological relatedness measure using International Patent Classification Codes (IPC). I have already created vectors for each firm in a given year which represent the number of IPC classes the firm has filed patents in.

The technological relatedness measure which I am trying to recreate is:

where f represents the vectors of the firms i and j (apex indicates the transposed vector). TechRel should represent the uncentered correlation between the two vectors and assumes value =1 if the patent activities coincide and 0 if the vectors are orthogonal.

My data currently looks like this:

* Example generated by -dataex-. For more info, type help dataex
clear
input double fyear long(gvkey gvkey2) float(vec1sum vec2sum vec1sum2 vec2sum2) str12 d1
2012  10016  10000 0 0 0 0 "1000010016"
2012  10115  10000 0 0 0 0 "1000010115"
2012  10000  10453 0 0 0 0 "1000010453"
2012  10000  10519 0 0 0 0 "1000010519"
2012  10860  10000 0 0 0 0 "1000010860"
2012  10983  10000 0 0 0 0 "1000010983"
2012 110566  10000 0 0 0 0 "10000110566"
end

Since I have patents in 184 IPC classes in my dataset I only included the first two variables of my vectors in this example.

I don't really know how to compute this measure. In the end I want to have the variable technological relatedness for each firm-pair.

Any help would be greatly appreciated!