INSTITUTE OF ECONOMIC STUDIES WORKING PAPER SERIES W 06 : 12 December 2006 Substitution between inward and outward foreign direct investment

This paper offers a new combination of the knowledge-capital and the gravity models. The model combination is applied to a small, remote country, which allows for testing of a corner case. Furthermore, the substitution effects between inward and outward foreign direct investment (FDI) are estimated, by use of a simultaneous equation system, and the estimates indicate that inward and outward FDI can be considered to be substitutes for each other.


Introduction
So far the gravity and knowledge capital (KK) models have primarily been tested for bilateral flows of foreign direct investment (FDI) between range of countries (Davies et al., 2008;Davies and Kristjánsdóttir, 2010;Kristjánsdóttir, 2010;Kristjánsdóttir, 2012a;Kristjánsdóttir 2012b).This paper, however, offers a testing of inward and outward flow of a single small remote country, and rather than testing the models separately, they are combined.Another feature of the analysis here is that the new equation specification makes it possible to analyze inward and outward flow simultaneously.The key country in question, Iceland, is an island far from all countries, with a Mid-Atlantic location equidistant from the US and Europe.Further factors adding to this unique case study are the small size of the Icelandic economy and the highly skilled labor force, which are combined to create the perfect KK model corner case.
In recent years, it has been popular to capture the volume of export flowing between countries by means of a gravity model (Bergstrand, 1985) and more recently a popular way of capturing FDI has either been with means of a gravity model or a KK model (Markusen et al., 1996;Carr et al., 2001).Helpman (1984) introduced the general equilibrium model for vertical FDI, and Markusen (1984) presented a general equilibrium model for horizontal FDI.Markusen et al. (1996) laid out the theoretical background of the KK model by combining the Helpman (1984) and Markusen (1984) general equilibrium models.Then, Carr et al. (2001) went on and presented an econometric specification of the KK model.Helpman (1998) finds the gravity model primarily suitable for similar countries that have considerable intra-industry trade with each other.This implies that the model does better for horizontal activities.However, the KK model is designed to cover both horizontal and vertical incentives for investment.In the Carr et al. (2001) specification of the KK model, endowments Helga Kristjánsdóttir, 2012.are accounted for by including skill differences, country size differences, and trade and investment costs.The gravity and KK models are partly based on the proposition of the Heckscher-Ohlin model, implying that countries will export goods that intensively use their relatively abundant factors, with skill differences as a proxy for differences in relative factor endowments.This paper introduces a new combination of the KK and gravity model that allows for inclusion of additional endowments in the KK model.Moreover the substitution effects between in-and outward FDI are estimated, by using a simultaneous equation system.I analyze these functions for the case country, Iceland, using data that spans from 1989 to 2001.The highlight of this data is that estimates indicate that inward and outward FDI can be considered substitutes of each other.
The paper is organized as follows.Section 1 introduces related literature.Section 2 constructs a model specification taking into account some of the features of the KK model and the gravity model, allowing for inclusion of endowment measures for this case.In section 3, estimation results are introduced.The final section concludes.

Literature
This paper seeks to explain to what extent trade and foreign direct investment (FDI) are substitutes.This paper also seeks to bring in the factor-proportions hypothesis implying that multinationals seek vertical production integration across countries to take advantage of different factor prices resulting from relative differences in factor supplies across countries.For this purpose I use some combinations of the gravity model and the knowledge capital (KK) model, which enables me to account for distance, population and gross domestic product.Also skillness is included together with additional proxies to account for factor endowments in the economy.The gravity model is a macro model by nature, however, Bergstrand (1985) provided microfoundations of the model.Some important contributions of the KK model include incorporation of source endowments as part of its components and other factors such as investment cost and trade cost to account for both horizontal and vertical motives for FDI.Just as soon the KK model was put forward it gained a lot of publicity and debate, and has been tested by several economists.
In a well known paper, Brainard (1997) proxies outward and inward FDI separately as the share of affiliate sales in total exports.Another more recent example of a share measure can be found in a paper by Slaughter (2000), where he constructs an investment share variable as the share which accounts for an FDI proxy (measured as majority owned affiliates) in overall multinational investment.

Basic model presentation
International firms are generally faced with the trade-off between producing in the domestic or foreign market, dependent on whether the marginal cost of supplying the foreign market is lower if production facilities are located abroad.This could be because wages are lower abroad, because of transport cost, tariffs, or simply because of the cost of overcoming governmental instability when entering a new market.Firms have incentive to start undertaking FDI if they find that entering a foreign market will increase their profits.By expanding their operations internationally they become multinationals.The specification presented in equation ( 1) presents the simultaneous equations of (1a) and (1b).The hypothesis tested seeks to answer is whether or not foreign direct investment (FDI) from country i to country j increases with an increase in the reverse FDI, that is the FDI from country j to country i.This is tested by using a three stage least squares (3SLS) simultaneous estimation (Snider, 2005).Equation ( 1) is combined of equation (1a) and equation (1b), with the endogenous variables inward FDI and outward FDI as functions of each other, as well as being functions of other relevant variables for inward and outward FDI.
More specifically, then in the first specification in equation (1a), the dependent variable is FDI ij,t (foreign direct investment (FDI) from country i to j over time t).The explanatory variables in equation (1a) are also listed here.FDI ji,t is the foreign direct investment (FDI) from country j to i over time t.Oil t is the world oil price over time t.Fin_Risk j,t is the financial risk in country j over time t.Exchr j,t is the exchange rate of country j over time t.Openness j,t is the openness of country j over time t.CO 2 _Manuf i,t-1 is the greenhouse gas omission allowance in the manufacturing industry in country i.Lagged by one time period denoted as t-1.Gas omission presented in carbohydrate equivalence, thousands of tons.
As for equation (1b) the dependent variable is FDI ji,t (foreign direct investment (FDI) from country j to i over time t).The explanatory variables for equation (1b) are also listed here.FDI ij,t is the foreign direct investment (FDI) from country i to j over time t.GDP j,t is the gross domestic product (GDP) of country j over time t.GDP i,t is the gross domestic product (GDP) of country i over time t.Skillness i,t are the skills in country i over time t, as measured by the International Labor Organization (ILO).Openness i,t is the openness of country i over time t.Generally in the gravity model presented by Bergstrand (1985) the "origin" or "source" country is denoted with i, while the "recipient", or "host" country is denoted with j.Here the j country is a single country (Iceland), however the source country i varies for different countries.
Since I prefer to estimate the equation in a linear format, and change the notation, I now present it in a log-linear format as shown in equation ( 2).The basic model specification (specification 1) in a loglinear format for the three-stage estimation for systems of simultaneous equations, can now be presented as follows:  The simultaneous equation system allows me to estimate the substitutability between inward FDI denoted by ij, and outward FDI denoted by ji.When transferring the equation system to a loglinear format I apply an inverse hyperbolic sine function (Johnston, 1949), rather than applying the natural logarithm function.The procedure transfers positive data in a similar way as the natural logarithm, however the conventional logarithm procedure does not function on zeros or negatives, but this procedure does.I, therefore, choose this procedure since it allows me to transform the data into a log-linear format without truncating zeros or negatives.The possibility of being able to transform zeros and negatives is important, since those values occasionally show up in the data.Transformation by means of an inverse hyperbolic sine (IHS) function, rather than a logarithm function, has been used in studies on household wealth.The procedure has been found to provide a suitable in transforming household wealth data by Burbidge et al. (1988).Based on the fact that some households hold zero or negative net worth as explained by Carroll et al. (1999).The inverse hyperbolic sine function is presented in Figure 1 as sinh -1 (x) = ln(x + (1 + x 2 ) 0.5 .
Source: Author's computations.Note: All regressions presented here are obtained from using STATA version 8.0.

Estimation results
The regression results from estimating the equations simultaneously for inward and outward FDI, are presented in Table 2.In equation (2b), outward FDI (FDI ji,t ) is presented as function of some or all the following variables in the basic specification: inward foreign direct investment (FDI ij,t ), the recipient country's gross domestic product (GDP j,t ), the investing country's gross domestic product (GDP i,t ), skillness of the investing country (Skillness i,t ).
The overall results from estimating all the equations in a simultaneous equations system are presented in Table 2.The results indicate that inward FDI is positively affected by outward FDI, and vice versa.This is as could be expected in the sense that there may be some complementary effects between inward and outward FDI, driving multinationals to increase their FDI, as result of increased multinational activities.
Let us then look at the explanatory variables.The explanatory variables coefficients for inward FDI are estimated to be similar in sign, size and significance, and the same holds for the variables explaining outward FDI.
I find inward FDI to be negatively affected by oil world prices, which is also as could be expected since increase energy prices is likely to halter investment incentives in the power industry, especially when hydropower price is tagged to world oil prices like in the case of hydropower price in Iceland.Inward FDI is also found to be negatively affected by financial risk in the host country which is certainly as could be expected, since more financial risk in host is likely to reduce investment incentives in host.The third explanatory variable for inward FDI, that is the host country exchange rates, is also estimated to be negative.This is also as could be expected since it reflects on higher barriers for foreign investors when entering the host market.Also the openness variable is estimated to be negative, which indicates that investment decreases as the economy becomes more open.This is surprising, since one would expect FDI to increase with increased openness.However, the variable is only estimated to be significant in one of the three cases, which diminishes the results.
Finally the last variable for greenhouse gas omission, presented in carbohydrate equivalence, is estimated to be positive.That is as could be expected, since more pollution allowance for the manufacturing industry is likely to positively influence investment incentives.
Outward estimates indicate that outward FDI is positively affected by inward FDI, and both host and home country's gross domestic production (GDP) which is in line with the gravity model based on Newton's hypothesis that as the mass of objects increases, the more flow is between them.One of the interesting results is how much positive effects skillness is estimated to have on outward FDI.Finally, openness in the recipient country is estimated to have positive effects on outward FDI.That is as could be expected, since foreign markets can be expected to attract more FDI with an increase in openness.

Conclusion
This paper applies a combination of a knowledge capital (KK) model and a gravity model to analyze the substitution between inward and outward foreign direct investment.The study focus is on bilateral flows flowing in and out of the case country Iceland, a very remote small island in the middle of the Atlantic.A combination of a gravity model and KK model is well suited for this case since then remoteness, endowments and economics of scale can be accounted for.Estimating a country like Iceland by the KK model framework provides an opportunity to look at one corner of the KK model diagram, due to the smallness of the country and its highly skilled labor.Also, the use of Iceland as a case country allows for additional variable inclusion, since the country is rich in endowments like power resources, and human capital.
I also use a log-linear functional form derived from using a hyperbolic sine function, which enables me to incorporate both zeros and negatives.
The usage of simultaneous equation system allows for estimating in-and outflow of FDI as a function of each other.Taken together, estimates indicate that inward and outward FDI can be considered to be substitutes of each other.This is because inward FDI and outward FDI are estimated to be significant in explaining each other, when estimated simultaneously as a function of each other together with a set of variables.

Table 1 .
Variable definition Variable DefinitionFDIij,t Foreign direct investment (FDI) from country i to j over time t.FDIji,tForeign direct investment (FDI) from country j to i over time t.GDPj,tGross domestic product (GDP) of country j over time t.GDPi,tGross domestic product (GDP) of country i over time t.CO2_Manufi,t-1 Greenhouse gas omission allowance in the manufacturing industry in country i.Lagged by one time period denoted as t-1.Gas omission presented in carbohydrate equivalence, thousands of tons.Opennessj,t Openness of country j over time t.Opennessi,t Openness of country i over time t.Oilt World oil price over time t.Skillnessi,t Skills in country i over time t, as measured by the International Labor Organization (ILO).Fin_Riskj,t Financial risk in country j over time t.Exchrj,t Exchange rate of country j over time t.The way I choose to estimate this, is by determining to which extent inward FDI is a function of outward FDI, and vice versa.More specifically, I use a simultaneous equations model, which allows me to estimate simultaneously inward FDI as function of outward FDI, and outward FDI as function of inward FDI.More specifically this procedure allows me to avoid the possible simultaneity which might exist among explanatory variables.I base the model presentation on the gravity equation Bergstrand (1985) and the KK model equation (Carr et al., 2001), allowing me to account for economic sizes as well as transport costs and other factors.The basic specification for equation (1) goes as follows:

Table 2 .
Empirical findings for simultaneous equation system ) is presented as function of some or all the variables in the basic specification: outward FDI (FDI ji,t ), world oil prices (Oil t ), financial risk in the recipient country j (Fin_Risk j,t ), exchange rate of country j (Exchr j,t ), openness of the recipient country j (Openness j,t ).