In this section, a theoretical model, on which the following empirical study is based, is introduced. This model is in part based on Horaguchi(1992) and Takenaka et al.(1989) in ways that FDI's movement is seen as a byproduct of the dynamic optimizations of multinational firms. Horaguchi(1992) tries to explain the Japanese foreign direct investment in Asia by introducing the general model where the MNCs chooses either exporting, licensing or FDI. Horaguchi(1992) also formalized a dynamic optimization of the Japanese MNCs. For empirical usefulness, Horaguchi(1992)'s rigorous choice model between export, licensing and FDI is not used in this paper.
Takenaka et al.(1989) also introduces a dynamic optimization model and estimates what Takenaka et al.(1989) calls ``marginal q'' of domestic and foreign production. In his empirical study, Takenaka et al.(1989) assumes that (1)the capital share rate remains unchanged over time and (2) the sum of capital share rate and labor share rate is one. Since these assumptions seem to be arbitrary and strong, they are not put forward in this paper.
The following model is made simple enough to be applied to the empirical studies.
This model considers the ``representative''
Japanese multinational
firm, which has two production locations:
domestic(Japan) and foreign(North America).
Parent firms in Japan are called, in this paper, ``home firms'' and
affiliates in North America are called ``host firms''.
A combination of ``home firms'' and ``host firms'' is called, in
this paper, a multi-national corporation(MNC).
The MNCs are assumed, in the following model, to maximize the
present value of sum of net-cash flows that they get
from both the domestic and foreign production activities.
In this theoretical model,
the following 9 assumptions about the MNC's activities
and market structures are explicitly introduced.
(A1)Both home firms and host firms are assumed to act as price-takers in both products markets and factors market. This means that they take product prices and factor's prices (nominal wage rate, for example) as exogenously given. This assumption will be used to estimate host firms' aggregated labor input(h*L*) by the first-order condition, which is expressed by the equation(5-4-4), of the optimization behavior of host firms in North America..
(A2)The Japanese market and the North American market are assumed to be completely separated. Only capital moves from home firms in Japan to host firms in North America by taking forms of FDI. This assumption seems to be too strong. But this assumption cannot help but be accepted in order to simplify the FDI model.
(A3)Home firms in Japan are assumed to transfer only capitals to their host firms in North America. Some would say that this assumption is unrealistic and ignores the important things, by pointing out that home firms are surely transferring ``technology'' to host firms. Surely, technology transferring is important as a determinant of FDIs, as Wakasugi(1994) also pointed out. Since there is a confusion about the concept of ``technology'' among economists and management experts, this ``technology'' trenferring issue is not analyzed explicitly in this paper. At this stage, it could be possible to say that ``technology'' is embodied in capital and ``technology'' is transferred from home firms to host firms by ``riding on'' capitals.
(A4)The production technologies of home firms and host firms are assumed to be the same. This assumption will lead to considering parameters(say, technological level, the capital share rate and the labor share rate) of home firms' and host firms' macro production functions to be the same in the following empirical work. Some would think this assumption is strange and confusing. In some literatures on FDI, a difference of ``technologies'' of domestic and foreign production is one of major motivations for FDIs. Wakasugi(1994) says that ``a major factor of sharp increase of Japan's FDI in manufacturing sector in the recent decades was vigorous innovations of Japanese firms.'' Is assuming home firms' and host firms' ``technologies'' to be the same unrealistic and unacceptable?
In discussing this issue, one must consider what ``technology'' means. Moreover, one must bear in mind that what macroeconomists call ``technology'' and what management experts call ``technology'' are the two different things. In macroeconomics literatures, on the one hand, ``technology'' is represented in the structures of macro production functions: parameters of production functions. ``Technology levels'' are considered to be what cannot be explained by the factor inputs. In management literatures, on the other hand, ``technology'' is such things as organization structures, business process efficiencies, new products development, human resource management, research and development and so on.
Assuming the parameters of home firms' and host firms' macro production functions to be the same is not saying that what is called ``technology differences'' are not important in determining FDIs.
(A5)The MNCs are assumed to evaluate both domestic and foreign production in its currency(in this paper, yen.) Due to this assumption, in estimating host firms' variables in the following empirical work, all host firms' variables(K*, Y*, h*L*) are to be evaluated in the Japanese yen.
(A6)The MNCs are assumed to face an exogenous constraint of total investment. This assumption can be rewritten by:
where 
is a domestic investment of the Japanese
MNCs, 
is a FDI flow from home firms in Japan
to host firms in North America
and 
is an available investment to the Japanese
MNCs at time t. In other words, the domestic investment
and the FDI flow at time t is a completely trade-off. The
representative Japanese MNC will, given the available
investment quantity constraint, decide how much to invest domestically
and how much
to invest in North America. To be exact, this assumption has
some problem. But it is considered to be
acceptable for simplicity. This assumption
will be used in the capital constraint conditions of the following
optimizations.
(A7)Both home firms and host firms are assumed to get labor inputs locally. This means that there assumes to be no movements of labors(workers) between home firms and host firms. This assumption can be seen acceptable if one considers the level of capital movement between home and host firms, compared with that of labor movement.
(A8)Some amount of costs are assumed to be needed for home firms to accumulate domestic investment and to transfer them to host firms. These adjustment costs are assumed to be totally borne by the home firms. This assumption will lead to introducing what are called ``investment adjustment cost functions'' in the following model.
(A9) The discounted accumulation of the FDI flows from home firms in Japan to host firms in North America is assumed to be the capital inputs in host firm's production functions. This assumption is clearly unrealistic, because the local re-investments by host firms in North America are not taken into considerations. However, in this model, local re-investments by host firms in North America is not considered explicitly due to the shortages of that data and the utility of simplicity.
These assumptions, from (A1) to (A9), are put forward to make the following empirical work simple enough to be handled. The researchers of FDI who take the managerial approach would consider these assumptions unrealistic, but it can be thought to be acceptable in this macroeconomic empirical study.