the following equation:21
M\OU = (I + s11×n - diag(s))MOU
(31)
where M\OU, MOU and s are (n× 1) vectors, I is the (n×n) identity matrix, diag(s) is
the (n × n) diagonal matrix of s and 11×n is a ones-vector. With si ≤ 1 for each element
in s we know that the term in brackets is positive definite. Rearranging terms yields:
MOU = (I + s11×n - diag(s))-1M\OU
(32)
MOU is the vector of the adjusted MOUs for all MNPs in country l at time z.
Note that data for smaller firms are at least partially based on Merrill Lynch estimations.
Thus, it might be the case that dependent on the estimation data for smaller MNPs
there is a lower statistical variance over time or also cross-sectional dependence on the
estimation methodology used for getting information about these MNPs.
A.5 Calculation of actual MOUs
The relation between the given MOUs of MNP i and the actual MOUs is given as follows:
M\OUi = siXMOUj + MOUi
j
(33)
For any MNP i the MOUs given in the Merrill Lynch European wireless matrix are its
actual MOUs plus the incoming MOUs from all other providers. Thus, for all providers
the relationship is the following:
M\OU 1 = 1
M\OU2 = s2
M\OU3 = s3
MOU1+s1 MOU2+s1 MOU3+...
(34)
MOU1+ 1 MOU2+s2 MOU3+...
MOU1+s3 MOU2+ 1 MOU3+...
We can rewrite this equation system in matrix notation as follows:
-—~—-
M\OU = smatMOU
M\OU1
M\U 2
MMOU 3
...
|
1 |
s1 |
s1 |
|
s2 |
1 |
s2 |
|
s3 |
s3 |
1 |
...
...
...
...
/
M OU1
MOU2
MOU3
...
(35)
21 How one gets from (30) to (31) is shown in the next subsection.
38