Since the data of host firms' aggregated output
in North America(
)
is not available statistically, it is estimated in the following way.
Under the assumption of (5-1-4), host firms' aggregated output in North America is:
At this time, the data of rate of capital share(¦Á), the
rate of labor share(¦Â), the rate of capital utilization( ¦Ñ )
and host firms' aggregated capital stock(
) are known,
the dataset of technological level(
) and host firms'
aggregated labor input (
) must be built
to estimate host firms' aggregated output ( 
).
First, the data of A (technological level in Cobb-Douglas function), can be estimated by:
Second, host firms' aggregated labor input ()
can be estimated by the first-order conditions of
optimization problem of the host firms in North America.
That is, host firms are assumed to decide their capital and labor
input so that their profits(denoted by 
) are maximized. That is:
where 
is what is called to be a nominal wage rate in North America
,
C(¡¦) is a cost function of capital.
Since P,A,¦Ñ,¦Á and ¦Â are assumed to be the same between
home firms' and host firms' aggregated production functions,
no asterisks(*) are put on these variables.
Since host firms are assumed to be competitive in both product market
and labor market as mentioned in (A1),
the first order condition of the optimization problem(5-4-3) is:
where ¦Á is a rate of capital share, ¦Â is a rate of labor share,
A is a technological level
in the Cobb-Douglas macro production function,
P is a products price(deflator),
is a nominal wage rate in North America,
is host firms' aggregated capital stock.
There arises a problem when one estimates host firms'
aggregated labor input (h*L*) by using (5-4-5).
It is about nominal wage rate in North America().
Statistically, there is not such data as a nominal wage rate
in North America. North America consists of a number of countries
that have different currencies. For simplicity,
data of a nominal wage rate in the United States are used
in this paper as in (5-4-5). One must bear in mind that
using the U.S. wage rate instead of the ``North American wage rate''
will bring about the following problem. Because of this,
we cannot estimate the actual values of MPK*s. So, it dose not
make any sense at all to compare MPK*s with MPKs directly.
For this reason, the regressable equation(4-1-b) is not used explicitly
in this paper. However, one can observe the movement of
MPK*s from 1984 to 1993, even though the values of MPK*s are not
``actual'' values. So, the equation(4-1-c) is used in this paper.
Now that the data of , , 
, ,
and 
are
available by the estimation above, host firms' aggregated output
in North America can be calculated by using the
(5-4-1).