پویایی های بهینه سرمایه گذاری خارجی در حضور تاثیرات فن آوری

In this paper we present a dynamic model of a firm which is deciding whether to outsource parts of its production to a less developed economy where wages and the level of technology are lower. Outsourcing reduces production costs but is associated with spillovers to foreign potential competitors. Spillovers over time increase productivity of firms in the foreign country and make them stronger competitors on the common market. The paper analyzes the inter-temporally optimal behavior of the firm and shows that two outcomes are possible in the long-run. One outcome is that there is one steady state where the firm invests a positive amount in the foreign country and the other outcome is a continuum of steady states with no investment. The paper then derives conditions such that it is optimal for the firm to invest in the foreign country and characterizes different types of optimal dynamic investment patterns. In addition, using numerical dynamic optimization methods, the effect of the speed of technology adoption and of the wage differential on total labor income in the home country is studied taking into account the transition dynamics.

With the decline of communism at the end of the 20th century, Central and Eastern European economies have become more open and more attractive for foreign capital. At the same time, the high growth rates of Asian countries such as China or India have also attracted foreign investors more frequently. Although most of foreign direct investment (FDI) is still undertaken in industrialized countries such as the US, Great Britain, France, Italy, and the Netherlands, just to mention a few, more and more direct investment flows to the newly industrializing countries (NICs) in Central and Eastern Europe and to Asian economies. According to the UNCTAD 2007 World Investment Report, the highest increase in FDI inflows from 2005 to 2006 among all regions occurred in South-East Europe with a growth of 74%. One important motivation for firms to invest in NICs is to get access to these markets; however, recent empirical evidence suggests that cost considerations have gained importance relative to market entry motives for foreign investment and are now in many cases the main factor influencing the location decisions of firms (see Kinkel and Lay, 2004).1 From a political perspective, FDI is highly appreciated in the countries where the investment is undertaken. An important aspect in this respect is the expectation that FDI does not only generate income for local firms and workers but also raises the productivity of local producers in the industry where investment takes place and also in vertically related industries. Hence, many NICs hope that spill-overs will reduce the gap to the technological frontier and that may help make the whole economy benefit from the new investments. Firms in developed countries are, of course, aware that their activities in foreign countries may prove negative in the long-run while their competitors benefit from their superior production technology. Hence, the firms will put great importance on the protection of intellectual property rights when investing in less developed countries. The effects of the protection of intellectual property rights have been studied in the economics literature in the context of endogenous growth models. For example, Parello (2008) demonstrates that stronger protection of intellectual property rights reduces the rate of technology transfer to less developed countries since it implies a smaller rate of imitation. In contrast to that, Dinopoulos and Segerstrom (2009) show that stronger protection of intellectual property rights raises international technology transfer within multinational firms and proves to be beneficial for less developed economies. But even if property rights are observed, there seems to be evidence that FDI is associated with positive spill-overs although the empirical evidence concerning the existence of positive horizontal spill-overs from FDI is mixed2 (see e.g. Görg and Greenaway, 2004). Thus, recent empirical studies find positive horizontal spillovers from FDI using firm level data from Hungary (Halpern and Murakozy, 2007), Romania (Smarzynska and Spatareanu, 2008), and from 17 emerging market economies (Gorodnichenko et al., 2007). Several channels of spill-overs have been discussed in the literature, most prominently the demonstration effect, labor turnover (both inducing horizontal spill-overs), and vertical linkages (see e.g. Saggi, 2002). So, while the firm that undertakes FDI may gain in the short-run from lower costs in NICs, spill-over effects can raise productivity of (potential) competitors in foreign countries. In particular in industries where markets have become globalized, such improvements of the competitiveness of foreign producers might severely affect future revenues of the firm. Therefore, a firm thinking about FDI faces a trade-off between short-run cost advantages and losing its competitive edge on the (global) market in the long-run. A dynamic view is needed to analyze the trade-off described above, and in this contribution we present a theoretical model of a firm that faces the corresponding inter-temporal optimization problem. In contrast to other contributions within that line of research (see our literature review below), we assume that firms in the home country and in the foreign country compete on the same market. Most existing theoretical work relies on the market opening motive for FDI and assumes a local market in the foreign country. In our framework, the firm under consideration operates on an oligopolistic market and may move some of its production by investing in physical capital in a NIC. Such investment, however, goes along with positive spill-overs which raise the productivity of competitors of the firm in the NIC. The incentive to invest in the foreign country are cost reductions due to lower wages there. Our assumption is that firms in less developed countries may be able to catch-up to the technology level of developed economies in line with arguments proposed by Nelson and Phelps (1966) and applied to the technology transfer problem by Boucekkine et al. (2006), for example. However, in contrast to those studies, where the technological gap does not vanish in the long-run, we allow for a different outcome. In our setting, the long-run outcome may be either that foreign firms catch-up to the firm in the developed country implying that they produce with the same technology or firms in the foreign countries always lag behind. Which of these two situations turns out to be optimal depends on the initial technology level in the less developed country among other things. While most contribution in the literature do not explicitly study the dynamics of the model, our goal with this paper is to pay special attention both to the long-run outcome of our model as well as to its transition dynamics. In particular, we are interested in the question of how the transient and the long-run outcomes are affected by economic factors like the initial productivity and wage gap between the regions or the spillover rate. A main finding of our study in this respect is that there are two classes of co-existing steady-states: one with and one without FDI, and that small changes in the economic factors mentioned above might induce that the long-run outcome jumps from one type to the other. The insight that there might be a non-continuous shift between an FDI and a non-FDI regime is a new finding in this area of research that is based on our dynamic approach. This insight has important implications for economic policy design. The best way to reach certain policy goals might be to influence the system so that the initial state moves into the basin of attraction of a steady state that is desired by the policy-maker. Although we do not explicitly consider the role of a policy maker in our model, we give some indication of such type of analysis by examining the impact of key parameters on current and accumulated labor income and on accumulated firm profits. In terms of transient investment dynamics, our dynamic approach allows us to address an issue raised by empirical observations about the dynamic patterns of foreign investment. Using data from German manufacturing firms, Kinkel and Maloca (2008) report that about 17% of the firms who have moved (parts of) their production abroad in 2000/2001 re-transferred it back to Germany within the following five years. Obviously, such a pattern of investment followed by disinvestment might be due to incorrect expectations about production conditions in the foreign country or actual changes in these conditions, but, as we show in this study, under certain conditions it might also correspond to intertemporally optimal behavior in the presence of technological spillovers. In particular, we demonstrate that such non-monotone investment patterns are optimal if the initial technology gap between the two countries is sufficiently large. In order to characterize the optimal investment paths and their dependency on parameters and initial conditions we combine an analytical and a numerical approach. Steady-state outcomes can be fully described by analytical means, and we can also analytically provide some characterization of the basins of attraction of the co-existing steady states. To gain additional insights about the transient dynamics and the sensitivity with respect to key parameters of the firm's and workers income streams under optimal investment, a numerical dynamic programming algorithm with grid adaptation in the state-space is used. Considering the theoretical literature dealing with FDI, one realizes that most contributions are multi-stage models with a small number of stages or focus on the steady sate of dynamic models (a survey of theoretical models is presented by Cheng, 1984; Saggi, 2002). Several papers study the entry mode decision between FDI and exporting in multi-stage oligopoly settings (see e.g. Petit and Sanna-Randaccio, 2000, Glass and Saggi, 2002 and Mattoo et al., 2004) or multi-sector models (e.g. Helpman et al., 2004). A contribution which presents a truly dynamic model analyzing FDI strategies under technology differences is the paper by Das (1987). She presents a model where multinational firms transfer technology to their subsidiaries in foreign countries and where firms in the host country benefit from the technology transfer. In this respect, our model will be related to the one presented by Das (1987). However, the motivation and the main issues of our paper are very different since neither cost reduction motives or interregional wage differences nor global competition effects are issues (Das, 1987). The focus there is on the intertemporally optimal price and quantity path of the subsidiaries that are only active in the (local) foreign market. Also, the question of whether the multinational firm should invest in FDI is not in the scope of that paper. Other dynamic models that deal with technology transfer as a result of FDI in an oligopolistic market are the papers by Wang and Blomstrom (1992), Lin and Saggi (1999), and Petit et al. (2000). The focus of these contributions is rather on the level of technology to be transferred (Wang and Blomstrom, 1992), on the timing of FDI (Lin and Saggi, 1999) and on the question of how the choice between export and foreign direct investment affects the incentive to innovate (Petit et al., 2000). The rest of the paper is organized as follows. In the next section we present the theoretical model. In Section 3 we analyze the long-run behavior of the investment policy of the firm and in Section 4 we study transitional dynamics. Section 5 concludes and points to possible extensions of the model. Appendix A briefly describes an example of our model with linear demand and all proofs are given in Appendix B.

In this paper, we have presented a dynamic model of a firm which competes with local and foreign firms in an oligopolistic market. The firm has an incentive to invest and produce in a developing country because of lower unit costs there but raises the technology level of its potential competitors in the developing economy by investing, due to spill-overs of investment. Our analysis shows that there are two possible types of long run outcomes—a catch-up scenario in which the domestic firm invests abroad and the productivity of the foreign competitors in the long run matches the productivity of the domestic subsidiary in country F, and a no-innovation scenario in which the domestic firm decides against FDI. In the absence of an initial capital stock in the foreign country, positive investment is optimal if the technological gap is either very large or very small. Furthermore, we have shown that an implication of the co-existence of these two scenarios is a non-continuous dependence of key variables like long-run foreign capital, long-run prices, or accumulated domestic labor income on parameters of the model. We have focused on the impact of changes in the initial productivity gap or in the domestic wage level and have shown that a slight decrease in the domestic wage level or a slight increase of the initial productivity gap might have substantial positive effects on the domestic labor income by inducing the transition from a catch-up scenario to a no-investment scenario. Furthermore, depending on the initial level of the productivity gap, a marginal decrease of the wage level, which does not lead to a transition between scenarios, might have negative (in the no innovation scenario) or positive (in the catch-up scenario) effects on domestic labor income. If we assume that even without FDI the productivity gap will slowly close over time, these findings suggest that the qualitative effect of changes in the wage level might change radically over time. Clearly, this has implications for wage policy if domestic labor income is of concern. Finally, we have shown under which circumstances patterns of positive foreign investment followed by disinvestment correspond are in accordance with intertemporally optimal behavior of the investing firm. The fact that we consider a scenario where only one of the firms in country H has the opportunity to invest abroad might be seen as a severe restriction of our analysis. However, this is not the case. A straightforward extension of our model where all m firms in country H can invest leads to a differential game model, and it is easy to show that no matter whether symmetric open-loop or stationary Markovian Nash equilibria are considered, 10 there is again a unique catch-up steady state where each investor holds exactly the steady-state foreign capital stock calculated in our single investor setup. Furthermore, for all values of the technology gap where a single potential investor should abstain from FDI, there is an (open-loop or stationary Markovian Nash) equilibrium where all potential investors abstain from investing. 11 The intuition for this result is straightforward. In a scenario with several potential investors, deviation of a single firm from the zero investment strategy might induce positive investments of the other potential investors which has a negative impact on the deviators’ profit. Accordingly, incentives to start positive foreign investments in a setup with multiple potential investors are smaller than in the scenario considered in this paper where no other firm can invest abroad. Therefore, the main qualitative findings derived for the single investor case carry over to a scenario with multiple potential investors. As to future research, several extensions of the model should be considered. In the current analysis, the level of the technology associated with the direct foreign investment was considered as given. It would be interesting to study optimal investment behavior allowing for an endogenous determination and dynamic changes of the technological level the firm uses in the foreign country. Furthermore, the choice of R&D investments of the firms in the foreign country might be incorporated into the analysis. There is empirical evidence and much discussion in the literature about the fact that a firm's ability to absorb technological spillovers depends positively on its R&D activities (see e.g. Cohen and Levinthal, 1989). Taking into account such effects would make the spillover intensity λλ an endogenous variable and generate strategic effects between the competitors in the different countries.