FDI and International Portfolio Investment - Complements or Substitutes? Preliminary Please do not quote

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1 FDI and International Portfolio Investment - Complements or Substitutes? Barbara Pfe er University of Siegen, Department of Economics Hölderlinstr. 3, Siegen, Germany Pone: +49 (0) pfe er@vwl.wiwi.uni-siegen.de JEL classi cation: F2, F23, G Keywords: FDI, Portfolio Investment, Risk Diversi cation, endogeneous Productivity. Introduction Preliminary Please do not quote Te recent World Investment Report 2006 igligts tat Foreign Direct Investment (FDI) ows and growing FDI stocks are now at an unparalleled level wit most going to industrial countries. At te same time ows of international portfolio investments (FPI) exceeded FDI ows twice at te beginning of te nineties wile more recently FPI growt slowed down and bot capital ows converged. Wat are te motives for rms to invest in one or te oter and ow are tey to be explained? Previous studies on FDI explained te motives for FDI wit di erential rates of return, di erences in interest rates and risk diversi cation. 2 Following Andersen and Hainaut (998) tese determinants lost explanatory power and recent teoretical and empirical studies document tat FDI is undertaken to exploit cost advantages (vertical FDI) 3 or to serve di erent markets locally to avoid trade costs (orizontal FDI). 4 If FDI no longer serves risk diversi cation, does FPI ten ll te gap and are tese capital ows complements rater tan substitutes? In te present paper I analyse weter rms coose FDI or FPI in te presence of stocastic productivity socks taking into account di erences in exibility of bot investments. In particular FDI is less volatile tan FPI and tis reduced volatility entails a iger rigidity of FDI. As FDI requires iger investment speci c costs it is not possible to adjust FDI to environmental canges every period. 5 In contrast, FPI bears lower xed costs and can be adjusted immediately to sort-term canges in te environment. However, as a result of te investor s control position FDI yields a iger return tan FPI. Hence, tere is a trade-o between volatility, exibility and iger return for rms deciding between FDI and FPI. I explore weter as a consequence of iger investment See WTO News, October See for example Dunning (973). 3 Grossman, Helpman, Szeidl (2005) discuss in wic states rms decide to outsource or o sore some of teir production stages. 4 See Helpman, Melitz, Yeaple (2003) for a detailed survey weter rms decide to serve a foreign market troug export or FDI. Studies of complex FDI strategies can be found for example in Helpman (2006) or Grossman, Helpmann, Szeidl (2003). 5 See Goldstein and Razin (2005) for a discussion of te di erent costs for FDI and FPI.

2 2 speci c xed costs and lower exibility in te case of FDI, small rms prefer FPI and larger rms invest in FDI. I sow tat te combined strategy dominates te isolated strategy always in times. Additionally wit combined international investment, tere is a iger incentive for rms to invest in r&d-investment and consequently rm productivity increase faster tan wit isolated international investment. Depending on te success-probability and te correlation between te various investment possibilities, even small rms (low productivity) invest in FDI. To model rm beaviour I use an oligopolistic competition framework wit uncertain rm productivity in combination wit a dynamic investment approac over a nite investment orizon. Tere are tree countries, ome and two foreign countries. Te rms are located in te ome country and decide to invest via FDI or FPI in te foreign countries. Tereby, tey face uncertainty about teir future productivity and returns on te respective investment. In particular, rm productivity is endogenous and follows a Poisson process. Te productivity of te di erent investment opportunities are correlated wit eac oter. Di erences in correlation betien FDI and ome production account for di erent forms of FDI. 6 Te reminder of te paper is organized as follows. In section two, I give a sort overview of te recent literature and empasize our contribution to. Section tree outlines te teoretical framework and derives te optimality conditions for te various investments strategies. Following tis, I present te numerical solution of te model and discuss te results in section four. Finally, section ve concludes. 2. Te Literature In te paper I link te information based trade-o literature between FDI and FPI by Goldstein and Razin (2005) (RG) and Albuquerque (2003) wit te rm-level Export and FDI approaces by Grossman, Helpman and Szeidl (2003) and Helpman, Melitz and Yeaple (2003). RG analyse te investors decision betien FDI and FPI under asymmetric information in a static model. 7 As a result of te information asymmetry te project revenue from FDI is iger tan from FPI. In te case of FDI te investor is also te manager of te foreign rm. Hence, e as a iger control of te production processes and can ensure tat te rm is run according to te investors interests. Tis is not te case if te investor cooses FPI. Tus te expected return of FPI is loir. I use tese di erent caracteristics sown by RG to motivate te costs, volatility and return of te di erent investment possibilities in te present paper. Additionally, I considered te ndings of Cuan, Perez-Quiraz and Popper (996). Tey provide an empirical analysis on te di erent caracterisitics of sort term and long term capital ows. Furtermore, in contrast to RG, I introduce a long-term investor in a dynamic setting. Tis investor as te possibility to adjust is portfolio periodically wit rigidity in FDI-sares. Hence, I also account for te di erent grades of exibility of bot investments. Alburquerque 6 Aizenman and Marion (200) as well as Markusen and Maskus (200) sow tat orizontal FDI is establised in countries similar in size and endowments, wile vertical FDI is te preferred investment in countries wit di erent caracteristics as te source country. 7 See also Razin, Mody and Sadka (2002) and Razin (2002).

3 3 (2003) analysises from a country perspective te risk-saring caracter of FDI and non- FDI capital ows for countries wit di erent degrees of nancial constraineds. Tereby, non-fdi ow adjustements arise from socks in te receiving country. One result is tat for nancially constrained countries FDI is less volatile tan non-fdi ows. Wit perfect enforcement, te di erence in volatility diminises. I modify tis approac by taking te rm perspective and consider socks on rm level as Ill as on ost country level. Actually, I always nd a iger volatility of non-fdi ows (FPI) tan FDI ows in my rm perspective model. Te rm reacts to any sort-term environment cange by adjusting FPI. Precisely, FPI as te main function to smoot risk wereas FDI mainly exploits gains from tecnology transfers. Uncertain rm productivity is decisive for te results of my model. Tis leads to te literature around Melitz (2003) or Grossman, Helpman and Szeidl (2003). Tey motivate te rms coice to export or engage in FDI wit di ering rm productivity. Melitz (2003) sows tat wit eterogeneous rms only te large rms (wit iger productivity) export. Small rms serve te domestic market only. Furtermore, Helpman, Melitz and Yeaple (2003) extend tis and nd tat rms wit iger productivity use iger integrated organisational production structures. Tey sow tat less productive rms only serve te domestic market, wit increasing productivity rms start to export and nally te most productive rms engage in FDI. In contrast to tis literature, in te present paper rm productivity is endogenous. Firms can pus teir productivity by investing in researc and development (r&d). Te success of te r&d-investment is uncertain. Moreover, I extend tese models by introducing FPI as a new form of investment possibility. 3. Teoretical Framework Firms optimize teir investment decisions in a continuous-time model. Inspired by Melitz (2003), te model is based on oligopolistic competition wit stocastic rm productive. Tere are tree symmetric countries. Two of tese countries are nortern countries East (ome country) and west (foreign). Te tird country is a soutern country (foreign). I consider a setting in wic a representative rm faces a coice between performing activities at ome (production and r&d-investment) and engaging in two alternative foreign investments: foreign portfolio investment (FPI) or foreign direct investment (FDI). Te initial position of eac rm is ome production and ome r&d investment. Based on tese ome activities te rm can additionally coose to invest internationally. Weter a rm decides to invest internationally depends on te rm s speci c productivity. In particular, te rm can increase its speci c productivity by investing in ome researc and development (r&d). Weter r&d-investment increases te rm s productivity is uncertain. Te cange of troug r&d-investment follows a Poisson-Process d = ( ) K dq. () In () is te amount of capital invested in r&d and K is te total stock of capital available to te rm. As obsolete tecnologies ave to be replaced, patent laws are renewed etc., even in case of successful r&d-investment, te growing rate of is smaller tan te invested rate of capital. Tese costs correspond to depreciation and are depicted by.

4 4 Finally q is a random variable tat equals wit probability dt and 0 oterwise. Hence, if r&d-investment is successfull, increases by ( ) K. Wit probability ( dt) r&d-investment fails and stays uncanged. As every rm, no matter if it engages in FDI, FPI or not, produces at ome and serves te ome market, I start wit te analysis of te ome country. 3.. Home 3... Demand and Production As I consider tree symmetric countries, te demand structure is similar in eac country. Consumers ave Dixit-Stiglitz preferences for di erentiated goods wit elasticity of substitution = > and 0 < ' <. Te price index for te ome country is ' R P = dji p j2j (j) R and te demand level is A = dji x j2j (j)' '. Tis generates te demand function x i = Ap i (2) for eac good variety produced by rm. 8 Firms use a single factor, capital, to produce output x x () = k. (3) Te superscript states tat tese are te values in te isolated "Home"-scenario. 9 According to (), rms also can use capital to invest in r&d and increase teir productivity K = k +. (4) As a consequence of monopolistic competition, rms coose te pro t maximising-price p t = ' t. (5) Were te rent for capital is set equal to one, is te pro t maximizing mark up and ' t are te marginal costs of a rm wit productivity t. Furtermore all rms ave xed costs of ome production equal to f and costs of r&d-investment equal to. Te xed costs f are te same for every rm but rms di er in teir productivity and ence in teir marginal costs. Additionally every rm cooses its own. Hence, te pro t of a rm at ome in period t is t ( t ) = p t t kt f + x t + t, 0 < <. (6) t Te rst term on te rigt and side equal te revenue from production and sales at te ome market, r t. Te second term on te rigt and side summarizes te costs of ome production and r&d investment. 8 For a detailed derivation see Dixit and Stiglitz (977). 9 Te following scenarios wit FPI, FDI and te combined investments are identi ed by te superscripts p, d, and c respectively.

5 5 Te expected value of rm pro ts is V ( t ) = maxe t ks ; s TZ t s ( s ) e (s t) ds. (7) subject to (2) - (5). Rearranging (7) yields te optimality condition V ( t ) dt = max t ( t ) dt + E t V dt (8) ks ; s wic states tat te mean required return of a rm equals te expected return. In period t te expected return consist of te maximized pro t at t and te expected gain or loss of te future pro t ow. To calculate te expected capital ow, I substitute () into dv yields E t dv = V () V () dt (9) wit ( ) K.0 Te rigt and sows te cange in te expected capital ow in case of successful r&d investment. Substituting (9) into (8) and divide by dt leads to V () = max () + V () V (). (0) ks ; s Tere are two important features about (0) wic one sould keep in mind toroug te following analysis. Firstly, all important informations about te past concerning current or future decisions are summarized in. How te rm reaced te present productivity does not matter at all. Secondly, coosing te optimal production and r&d-investment strategy wit respect to te problem starting at te current productivity level tat results from te initial rm strategies, is te optimal strategy no matter wat te initial strategy of te rm was Optimality Conditions for R&D-Investment and Production Strategies From (0) I can derive te optimality conditions for rm-strategies for r&d-investement and ome production. R&D-Investment Deriving te marginal valuation of r&d-investment from (0) yields () + V () = 0. () Te second part of te brackets of (0) disappears, as V () does not depend on te current. Rearranging () I get ( V () = r () ). (2) Te marginal valuation of r&d-investment is a perpetual ow equal to one minus te revenue canges caused by, discounted by te probability of successful r&d-investment. 0 For a detailed derivation see Appendix A.

6 6 Home Production Di erentiating te rigt and side of (0) wit respect to k, I obtain k () + V k () r k () + V k () V k () = 0 V k () = 0 V () = V () r (). (3) Te subscripts unequal to t stand for te partial derivation. For simplicity, in te following cases te derivation subscripts are sortened to (respectively p; d) instead of k (respectively k p ; k d ). Te marginal valuation of production-investment, in te case of r&d-investment equals te marginal valuation of production-investment wit no r&dinvestment minus te marginal revenue stream resulting from increased capital in production - discounted wit te probability of successful r&d-investment. It is V () minus te revenue stream, as te valuation of k in case of additional investment in r&d is observed. Observing just te valuation of k witout te increased productivity would be V () plus te revenue stream. An optimal strategy requires tat te marginal valuation of investment in production equals te marginal valuation of r&d-investment. I can derive an explicit marginal valuation for investment in production by equating (3) and (2), namely " # V () = + r r. (4) Similar to (2) te marginal valuation of investment in production equals a ow consisting of one plus te di erence between te revenue cange caused by te two investment decisions. Again, tis ow is discounted by te probability of successful r&d investment. From (4) I can see tat increasing productivity in te ome scenario also increases te marginal valuation of capital invested in te domestic production process dv () > 0. d Tis is very intuitive as rising productivity also increases te output produced by one unit capital and decreases te variable costs ( x ). Tese considerations are re ected in te second part of (4). Tere is a trade-o between investing in r&d or not. First of all, investing in r&d reduces te capital available to invest in domestic production. Tis e ect is negative. But secondly, r&d-investment increases productivity and as sown above iger productivity enforces te output of te employed production-capital and decreases te variable production costs. Hence, tere is also a positive e ect of r&d-investment on te marginal valuation of capital invested in ome-production Home and Foreign Portfolio Investment Production and FPI Now, I analyse te investment decision of te rm and give it an additional investment alternative, namely foreign portfolio investment (FPI). Wit FPI equation (4) canges to K t = k t + k p t + t. (5) For matematical details see Appendix B.

7 7 Tis sows tat te total capital available to a rm can be used to invest in domestic production, r&d-investment (te same as in te scenario above) and additionally k p is te capital invested in FPI. As te rm invests in FPI, it gains ownersip on a foreign rm. But te domestic rm as no - or only in nitely small - possibility to exert control over te foreign production and management process. Tus te domestic rm can not directly in uence te foreign revenue and te gained dividend r p t = t (k p t ) p, 0 < d <. (6) t is te return rate from FPI (or te productivity of capital invested in FPI). It varies d = dz (7) were dz is a Wiener process wit mean zero and unit variance. Following (6) and (7), te decision of ow muc capital to invest in FPI is te only impact te rm as. Investment in FPI requires to buy assets, time to select te appropriate assets, additional administration systems and e orts etc. All tese e orts are summarized as xed costs f p t for tis investment. Yet te pro t function for te rm (6) canges to t ( t ) = p t t k t f + x t + t + rp t t f p t. (8) Following te steps in te Home-scenario I get te multi-period optimization problem for te rm V p ( t ) dt = max t ( t ) dt + E t (dv p ) (9) ks ;k p t ; s subject to (2), (3), (5) and (5) - (7). As te rm is now in te FPI-scenario, te superscript canged to p and tere is one more control variable, namely k p t. Te beaviour of V p depends on two state variables t and t dv p = V p d + V p d + 2 V p (d) 2 + V p (d) (d). (20) Tus in case of FPI investment te expection of te cange in te expected capital ow consists of tree parts E (dv p ) = [V p () V p ()] dt V p dt + V p () ( ) dt. (2) Te rst part is similar to te expected capital ow in te Home-scenario. Additionally, te variations of te foreign return impacts V p. Tis impact occurs in te second term. Finally, te tird term accounts for common variations of ome productivity and foreign productivity tat can result from global or industry socks. Te direction of tis correlation depends on (dq) (dz ) 6= 0. If te rm invests FPI in te western country, is positive and is negative if te rm invests FPI in te soutern country.

8 8 In case of FPI, te present value of te rm pro t ows is V p () = max [ p () + [V p () V p ()] + "] (22) ks ;k p t ; s wit " " + " 2, " V p and " 2 V p () ( ). Te uncertain foreign productivity in uences te present value of te pro t ows twice. Firstly, te isolated variation of te foreign productivity " enters te capital ows and secondly, te common variation of ome and foreign productivity " 2 canges te capital ows. Wereas, te ome productivity cange is a discrete sock, " is continuous. Similar to (0), all necessary informations for any decision are summarised in and. Furter, any optimality of future decision on FPI, ome production or r&d-investment is independent of te rms initial decision Optimality Conditions wit FPI R&D-Investment Wit FPI te marginal valuation of r&d-investment canges to " # V p () = r (23) were p ) p ()() ). FPI does not ave any direct impact r&d-investment. In comparison to te pure Home-scenario, te marginal valuation of r&d-investment is reduced by. Tis e ect arises troug te common variation of te ome and foreign productivities. If te rm invests into closely related industries or even in te same industry (western country) ten te own risk is not reduced. Tus is positive and reduces te marginal valuation of r&d-investment sligtly but never completely compensates it. Contrary, wit investment in an dissimilar industry (Sout) te risk of r&d failure is diversi ed. is negative and increases te valuation of r&dinvestment. Home Production Te direct valuation of ome production is uncanged 2 3 V p () = V () 6 4 r () 7 5. (24) {z } >0 Following te optimality principle, I can equate te marginal valuation of investment in ome production wit te marginal valuation of r&d-investment and get " # V p () = + r r. (25) Similar to (23), te valuation canges by. Again, te cange depends on te industry invested in.

9 9 FPI Optimality requires tat te marginal valuation of FPI also equals te marginal valuation of investment in ome production and r&d-investment. Terefore I di erentiate (22) wit respect to k p rearranging it delivers V p p () = V p p () r p p + " p. (26) If te rm invests abroad into an industry located in similar country tan te ome country, ten te valuation of FPI is lower tan wit investment into a country wit di erent factor endowment, production structure etc. as te ome country. Obviously, te diversi cation of te risk increases te valuation of te investment abroad FPI vs Home Te results from deriving all optimality conditions for FDI are summarized in table : i r&d V p () = r i. ome V p () = r r fpi Vp p () = r i. rp p + " p Table: Optimality Conditions under FPI Table sows tat te direct e ect of FPI on te marginal valuation of investment in ome production is negative. Additional capital invested abroad reduces capital available for domestic production. No de nite statement about te indirect impact of FPI on domestic investment is possible. Investment into countries wit closely related industries (West) diminises te valuation of domestic production and investments in dissimilar countries (Sout) pus te valuation sligtly up. FPI as a similar impact on te valuation of r&d-investment For furter conclusions, I need te results from marginal valuation wit FDI and te combined international investment (CII) - including bot FPI and FDI. Hence, I derive tem in te next two sections Home and Foreign Direct Investment In te case of FDI, te ome rm takes ownersip as well as control over te foreign rm and tus can in uence te pro t of its FDI-investment. Following Markusen and Maskus (200) orizontal FDI takes place in a similar country - West and vertical FDI in te Sout - dissimilar country. Te coice of te FDI receiving country as a signi cant impact on te valuation of FDI. If te ome rm decides for FDI it also transfers intangible assets, as for example managerial skills, tecnology..., to te foreign rm. As a side e ect of tis asset transfer a part of te ome productivity directly enters te return of FDI r d t = 2 t a t k d t d ; 0 < a < ; 0 < d <. (27) Home productivity does not impact te foreign investment to te same extent, tan ome production. Tis can be caused by country speci c conditions or incomplete mobility of some ome skills. Te impact of ome productivity on FDI return increases wit

10 0 country similarity. is te foreign productivity wic is stocastic and varies wit d = dz. (28) Again, dz is Wiener process wit mean zero and unit variance. Te amount of capital invested in FDI is k d. Hence equation (4) becomes K t = k t + k d t + t. (29) Furter, FDI requires some speci c up-front costs like country and market researc, a merger or building a new plant. All tese activities are costly and summarized in f d, as te xed costs arising from FDI. Now te modi ed pro t function of te ome rm is t ( t ) = p t t k t f + x t + t t + rd t f d t. (30) It is important to keep in mind, tat te FDI x costs, f d exceed te FPI x costs, f p. Te dynamic optimization problem of te ome rm is V d () dt = max d () dt + E t dv d. (3) k ;k d ; Equation (3) is a function of te state variables ome productivity as well as foreign productivity : Te control variables are te tree investment purposes, k ; k d ;. As te derivation of te functional equation from (3) is very similar to te steps in te FPI-scenario, I leave te details to te matematical appendix C and get V d () = max d + V d () V d () + (32) k ;k d ; wit + 2, V d, 2 V d ( ) () and = (dz dq). Again, te uncertainty of te foreign productivity as two impacts on te present value of te pro t ows: te variation of te foreign productivity and te common variation of te foreign and te ome productivity 2. All necessary information for any decision are included in and Optimality Conditions wit FDI R&D-Investment Following te same steps as in te two previous scenarios I get te marginal valuation of additional r&d-investment " # V d () = r r d {. (33) First, tere is a additional impact of FDI on te marginal valuation of r&d-investment. It is a very small positive e ect troug a sligt increase in te foreign revenue. In comparison to te isolated ome-scenario, tis marginal cange in r d again increases te marginal valuation of r&d-investment.

11 Secondly, te in uence of on te foreign productivity is included in Te rst derivation is positive but very close to zero. Te second derivation - neglecting - would be always negative. Adding, te sign depends on te cosen kind of FDI. In te case of orizontal FDI { < 0 and under vertical FDI { > 0. Te overall e ect of orizontal FDI increases te valuation of domestic r&d-investment, vertical FDI decreases it. 2 Horizontal FDI is mostly undertaken among industrial countries. For tese countries, production structure, factor endowments and business-culture are relatively similar. Tus increased productivity at ome transfers very easily to te foreign a liate. On te oter and, vertical FDI is prevalent in countries wit di ering production and cost structures. Usually, te various production activities are distributed around several locations in di erent countries. A productivity increase at te ome location does not a ect a di erent production step located abroad as a similar production step located abroad. Terefore, te implementation of new tecnologies - developed for domestic production - is not as easy under vertical FDI as in te case of orizontal FDI. In contrast to te Home-scenario, te additional e ects of FDI pus te marginal valuation of r&d-investment up. Precisely, wit vertical FDI tis upward pusing e ect is smaller tan wit orizontal FDI. Home Production As expected from te previous section, ome production stays uncanged again V d () = V d r () (). (34) Substituting equation (33) into te marginal valuation of investment in ome production delivers " # V d () = + r r r d {. (35) Te canges in a ect directly te FDI revenue and te variations of te productivity of FDI. Te reduction of te marginal valuation of te investment in ome production is not as ig as under FPI. In te current case, r&d-investment does not only diminis te capital available for FDI it also increases te productivity of capital invested in te foreign rm. Furter, te sign of { depends on te kind of FDI undertaken. FDI To derive te optimality condition for FDI, I di erentiate (32) wit respect to k d. Tis yields Vd d () = Vd d r d () d + d. (36) 2 Markusen and Maskus (200) provide a analysis wic di erences and similarities of country / industry caracteristics lead to vertical or orizontal FDI. Additionally Grossman, Helpman and Szeidl (2003) sow tat under di erent cost structures in te observed countries, rm strategies canges from orizontal to vertical FDI and vice versa.

12 2 Equation (36) sows tat te marginal valuation of FDI in case of successful r&dinvesetment depends again on te kind of FDI undertaken. If te rm invests in orizontal FDI ten te term in te brackets remains positive and ence reduces te valuation. On te oter and, if te rm undertakes vertical FDI te sign of canges. But te indirect e ect troug is weaker tan te direct e ect of te canged revenue. Tus te valuation is still reduced but not as muc as in te case of orizontal FDI. Generally, I observe a decreasing marginal product of capital eiter invested in domestic production or invested in foreign production. Vertical FDI requires investment in di erent production steps. Hence, wit a negative correlation between domestic and foreign productivity at and, te decrease of te marginal product invested in FDI is damped FDI vs Home Table 2 summarizes te optimality conditions wit FDI: r&d ome = r&d fdi = r&d V d () = V d () = V d d () = r r rd { i r +rd { Table 2: Optimality Conditions under FDI i r d +rd d +r { + d i As discussed above, FDI puses te marginal valuation of r&d-investment (row one of table 2) up. Tis e ect is stronger wit orizontal FDI tan vertical FDI. Furter, tese e ects carry over to te evaluation of investment in ome-production wit respect to r&d-investment. From te second row of table 2, I see more closely ow te valuation of capital invested in ome production depends on te di erent e ects of FDI. Additional capital invested abroad decreases te marginal revenue of FDI no matter if te rm undertakes vertical or orizontal FDI. Tis e ect increases te valuation of investment in domestic production. Furter, FDI impacts te valuation of domestic production indirectly by te common variation of foreign and ome productivity. Tat impact is small but noneteless under vertical FDI it increases te valuation of investment into domestic production. In te case of vertical FDI te di erent stages of production of a good are geograpically separated. If te rm invests in a production activity abroad ten te nal good produced at ome becomes more valuable and terefore te positive e ect of te additional FDI arises. Tese e ects from te cosen FDI are reversed in comparison to te FDI-impact on r&d-investment. Finally, te marginal valuation of FDI wit respect to r&d (row tree, table 2) equals a perpetual ow of te di erence of canged revenues troug additional capital invested in FDI and r&d, discounted by te probability of successful r&d-investment. Te indirect e ects of r&d and FDI pus in te same direction. In te case of orizontal FDI, tere is a positive pus and wit vertical FDI, te valuation is sligtly reduced Home and Combined International Investment Finally, I analyse a combined international investment strategy for rms. Besides te usual ome activities of te rm, it also can invest in FPI as Ill as in FDI. Because tere.

13 3 are four di erent investment alternatives for capital, (4) canges to K t = k t + k p t + k d t + t. (37) Te return functions of te international investments are similar to te return functions under isolated international investment. Hence, te rm s pro t function wit combined international investment is c t ( t ) = p t t kt f + x t + t + r p t f p t + rt d ft d. (38) t Now, I transferring te it to te dynamic rm problem and get 3 V c () dt = max [ c () dt + E t (dv c )]. (39) k ;k p ;k d ; Te control variable in te dynamic combined optimization problem are te various investment purposes: investment in domestic production k, r&d-investment and te two international investment alternatives FPI k p and FDI k d. Furter, in te combined scenario te present value of te rms capital ows is a function of te tree state variables ome productivity, productivity of te portfolio investments and te productivity of te direct investment. Tese tree variables summarize all te necessary information for an optimal investment-decision in te present period. I need te functional equation of te optimizing problem (39) to derive te optimality conditions. Again, te steps are very similar to te isolated investment strategies and terefore, I neglect tem and directly turn to te functional equation V c () = max [ c + [V c () V c ()] + " + + ] (40) k ;k d ; were V c ( ) ( ) and = (dz ) (dz ). In (40) I ave te investment effects of te isolated international strategies combined. Additionally, te common variation of te two international investments is included troug Optimality Conditions wit Combined International Investment R&D-Investment Following (40), te optimality condition for r&d-investment canges sligtly in comparison to te isolated scenarios: V c () = " r r d { #. (4) Te rst part of te bracket stays uncanged. Also, te isolated e ects of te di erent investment possibilities, pd and { pd, are te same as above. But te interaction of FPI and FDI canges te impact of te isolated investment e ects. Te only new term is wose impact depends on te international investment interaction, too. Table 3 summarizes te e ects from te isolated strategies and adds te common e ects in case of CII 3 We will keep te detailed transforming-steps very sort as te necessary steps for te transformation are similar to te steps undertaken in te previous isolated section.

14 4 impact FPI impact FDI common impact western country 6 FPI / orizontal FDI > 0 { < 0 > 0 soutern country FPI / vertical FDI < 0 { > 0 > 0 western country FPI / vertical FDI > 0 { > 0 < 0 soutern country FPI / orizontal FDI < 0 { < 0 < 0 Table 3: Impact of di erent International Investment Possibilities. A combined strategy wit FPI in an soutern country and orizontal FDI dominates all oter investment combination wit respect to te impact of additional r&d-investment on te rms capital ows. Wit FPI in an unrelated country, te rm secures risk diversi cation and wit orizontal FPI te tecnology transfer is facilitated. Furter, bot investment possibilities are negatively correlated and tis puses te marginal valuation of r&d-investment additionally. I ave to keep in mind, tat tis is only te optimal combination wit respect to te impact of r&d-investment on te rm s capital ows. Home Production Analogue to te isolated investment possibilities, te impact of ome production does not cange V c () = V c r () (). (42) In combination wit te marginal valuation of r&d-investment, te impact of CII on te ome production valuation becomes clear " # V c () = + r r r d {. (43) I see from table 3, tat te optimal combination wit respect to r&d-investment is te optimal combination wit respect to te valuation of ome production in combination wit r&d. But I still cannot generalize tis optimal investment combination. CII First, I ave to examine te e ects on te various international investments and te combination of all e ects. As tere are all derived similarly to te isolated strategies, table 4 just summarizes te results r&d ome fdi fpi V c V c V c d () = V c p () = i r rd { () = i () = + r r rd { i. r rd rd d { + d + d i r rd rp p { + " p + p Table 4: Optimality Conditions under CII From table 4, I see tat eac marginal valuation increases wit negative correlation of te ome industry and te cosen industry for FPI ( < 0). Te risk of unsuccessful r&d-investment at ome can be propped up by te sort term portfolio-investment.

15 5 Also, { < 0 puses te respective valuation up. Tis negative sign for { arises under orizontal FDI. Overall, wit a facilitated tecnology transfer under orizontal FDI, r&d impacts te expected capital ows of te rm positively. Te variation e ects between te international investments (, p, d ) eiter support or decrease te strengt of te direct impact but never compensates it. Hence, bot international investments are mostly favoured wit FPI in a soutern country and orizontal FDI. For FPI, te risk diversi cation is te stronger e ect wit te igest impact on te rm decision. In particular, FPI is te more exible investment and can be adjusted almost costless. Terefore, it is te appropriate instrument to diversify a rm s risk. On te oter and, FDI reacts more sensitive to productivity canges and tus, is te favourable instrument to exploit productivity gains internationally. In CII, FPI can prop up te risk from ome production and FDI. Te relations between te ome country and te recipient countries are uncanged to te isolated investment scenarios for FPI as Ill as for FDI. Hence, I expect in CII te sare of FPI to adjust to sort-term environment canges wereas FDI stays uncanged. It is not possible to derive an explicit analytical solution for te respective international investment sares. Te de nite sares of FPI and FDI will be derived numerically. 4. Optimal Investment Strategies As a consequence of te previous ndings, in te following analysis I consider orizontal FDI and FPI in te Sout. Unfortunately, te problem as no tractable closed form solution. Hence, te solution must be approximated by numerical metods. I use recursive policy function iteration. Te rst run computes te solution for te isolated international investment strategies and determines te cut-o s at wic te rm canges from one strategy to anoter (ome, FPI or FDI). In te second run, I repeat te same steps for te combined international investment strategy. Precisely, wit CII te rm canges its strategy only once: from isolated ome production to FPI and FDI at te same time. I derive a bencmark case wit a depreciation of = 0; 3. A iger depreciation puses te start of international activity backwards in time and a lower depreciation pulls it forward. Te general results stay te same. Furter, te probability for successful r&d-investment varies and sows a signi cant impact on te rms decision to invest internationally or not. 4.. Isolated International Investment 4... Start of International Actvitiy Te rst international activity of te rm is FPI. As expected, FPI requires lower cut-o productivity tan FDI. However, te rm starts investing in FPI not until te probability of successful r&d is 0,3 or iger. Even ten, te international activity starts very late in time. Wit increasing r&d-probability, te rm undertakes international investment at an earlier stage. Tis is very intuitive, as wit ig success-probability te productivity increases more quickly. All tese results con rm te ndings in te recent literature. Firms wit low productivity stay isolated at te ome market. Wit a sligt increase in productivity te rst small international steps are made and nally, rms wit a remarkable ig productivity invest in FDI.

16 6 investmentsares wit r&d success probability 0,3 investmentsares wit r&d success probability 0,5 sare 00% 80% 60% 40% 20% r&d fdi fpi ome sare 00% 80% 60% 40% 20% r&d fdi fpi ome 0%,00000,0200,04244,06433,08668,35727,62247,75875,90649, %,00000,03500,0722,34923,68896,9254,82043,60578,789,83846 productivity/time productivity/time a Figure b Variation of Foreign Productivity Firstly, I observe canges in te FPI productivity. Table 5 in Appendix D sows tat neiter te productivity cut o s nor te cut-o time cange wit variations in FPI productivity. One migt ave expected tat wit iger foreign productivity te rm engages earlier in international investment. Tis is not te case. Te rm rst secures te ome production process and ten goes abroad. Furter, te rm does not reduce or increase its sare in FDI. Only te FPI sares increase wit iger FPI productivity. Tis migt seem intuitive, as only te FPIproductivity canges. Hence, te FDI sares are independent of te FPI productivity. Let s take a closer look on FDI-productivity canges, to see weter tis independence also old in te opposite direction. Table 6 in Appendix D sows tat wit a ig FDI-productivity te rm engages in international investment at an earlier stage in time, tan wit a lower FDI-productivity. Furter, te productivity cut-o is lower tan wit te bencmark productivity. Te only exceptions are te cases wit a very ig success probability of r&d investment. For tese cases te cut-o s are te same for te bencmark case and te ig FDI-productivity. Finally, wit varying FDI-productivity bot international sares cange in comparison to te bencmark case. In particular, te FPI sares vary only in comparison to te bencmark case. Tey also cange between te various cases of ig FDI-productivity wile te FDI sares stay almost te same. Again, only wit te ig r&d-probability te FDI sares cange between te di erent cases, but tey don t cange wit respect to te bencmark case. Tese are only results for te isolated investment scenario Combined International Investment In contrast to te isolated international investment strategy, te rm starts its international activities wit bot investment alternatives FPI and FDI at te same time. Even wit a low r&d-probability, te rm engages in its rst international investment. However, I ave to distinguis between te rst international investment and te investment in FDI. In bot cases, te rst international activity under CII takes place before te rst international rm activity under an isolated international investment strategy. Te rst international activity requires a lower r&d-probability under CII tan for te isolated international investments. At a moderate probability, te rm switces from ome to international investment (isol. FPI and combined FPI-FDI respectively at te same

17 7 time). Wit increasing probability te isolated investment even dominates te combined strategy in time. I ave to keep in mind, tat I comparing te rm starting isolated FPI against te rm starting combined FPI and FDI under CII. first international activity FDI switc period λ switc ci 02 switc iso fpi period λ switc cii switc iso a Figure 2 Now, I turn to te comparison of isolated FDI and te combined international investment. For te switc to FDI te picture canges as sown in gure 2b. Under CII te rm switces from ome production to international investment at a lower r&d-probability and at an earlier stage in time. Furter, wit increasing success-probability, CII still dominates te isolated investments in time. But, CII does not always dominate isolated FDI in productivity. Particularly, te productivity cut-o s for FDI under CII do not always lie below te cut-o s for isolated FDI. Te productivity cut-o s are analysed according to te at wic te rm switces from one strategy (for example ome) to anoter strategy (for example FDI). I compare te marginal impact of on te di erent discounted capital ows under a given productivity level. Figure 3 sows te di erent productivities for FDI cut o wit isolated FDI (iso) and CII-FDI (cii). productivity,8,6,4,2 0,8 0,6 0,4 0,2 0 FDI cut off positive correlation iso cii λ a b productivity,8,6,4,2 0,8 0,6 0,4 0,2 0 low negative correlation iso cii b λ productivity,6,4,2 0,8 0,6 0,4 0,2 0 ig negative correlation iso cii Figure 3 Tese results are supported by te previously ndings on te impact of te preferred c λ

18 8 FDI-FPI combination under te combined investment strategy. If I derive te impact of productivity on te di erent investment alternatives I get Home FPI FDI CII Valuation of productivity V V p V d V c () = (+) () = (+) V (+) () = V d () = (+) r () V p () () V c () r p + "p r d +rdd Table 7: Impact of Productivity i + d r c +rdc + " c + c + i i. From table 7, I see tat te productivity cut-o s increase from Home to FPI to FDI. For a given te discounted additional capital ows under CII exceed te one under isolated FDI. Te impact of and r d are very similar and in te respective scenario tey cancel eac oter out. Furtermore, te FDI impact also arises in te isolated as Ill as in te combined scenario. So, it also can be neglected. Finally, tere is one additional positive impact left under CII wic does not appear under any isolated strategy,. As I already examined above, te preferred combination of FDI and FPI is orizontal FDI and FPI country unrelated to te ome country. Tus, te correlation of FDI and FPI is negative and ence, as a positive impact on te additional discounted capital ows under CII. As FPI is very exible, it can prop up any sort time canges in te environment. Wereas under isolated FPI tere migt be a loss under environment canges. Tis additional "security" increases te value of eac unit productivity. Hence, wit a given productivity CII provides te rm wit iger discounted capital ows tan wit isolated FDI. However, wit te iger marginal valuation of a given, tere is also a iger incentive to invest in r&d under CII tan wit isolated FDI. Te additional capital from CII r&d investment exceeds te isolated FDI r&d investment by and (see table 4 and 2). Bot e ects ave a positive impact on te marginal valuation of CII r&d investment. 7 arises troug te negative correlation of te ome country and te FPI receiving country. Home risk can be diversi ed by FPI and additional r&d investment delivers a iger outcome tan witout FPI. results in te negative correlation of te FPI and FDI receiving country. Additional r&d investment increases te FDI return and consequently FDI will rise. Canges in te FDI receiving country will ten be propped up by FPI adjustments. Tis is not possible wit isolated FDI investments. Hence, is an additional positive e ect troug te combination of FDI and FPI. Te two risk-diversifying e ects and pus te marginal CII r&d-valuation above valuation wit isolated FDI. Terefore, te rm will invest more in r&d under CII tan wit isolated FDI and tis in turn leads to a faster growing ome productivity Variation of Foreign Productivity First of all, minor canges in te foreign productivities relation may diminis any international investment under isolated strategy completely. If bot productivities are very low or at least te FPI-productivity is very low ten te rm does not invest abroad. 7 { can be neglected, as it arises in bot investment strategies.

19 9 On te oter and, tese canges do not reduce international investment under CII totally. Te productivity cut-o canges as bot foreign productivities drift apart (negatively correlated) or move togeter (positively correlated). Te following gure 4 sows te variation of FPI and FDI sares in dependence on teir productivity relation., , , , , , , , , ,0000 0,00000 sare of CII FPI wit varying foreign productivities ig neg a pos corr low neg λ 9, , , , , , , ,00000, ,00000 sare of CII FDI wit varying foreign productivities ig neg pos corr Figure 4 Precisely, te cut-o is lower wit very di erent foreign productivities and raises as te productivities converge. Tis is sown in gure 5. productivity,8,6,4,2 0,8 0,6 0,4 0,2 0 ig neg CII cut off wit varying foreign productivity relation low neg pos corr λ Figure 5 If te foreign productivities move very close to eac oter ten te CII cut-o s may even lie below te isolated FDI cut-o s. Te rm prefers to invest in only one alternative instead of two and bears only te isolated costs instead of te combined costs. Furter, te additional e ects for CII in table 7 turn negative and reduce te discounted additional cas ows. Hence, FPI looses its diversi cation property wit similar moving productivities. Tis supports te statement, tat te rm uses FPI to diversify static FDI risk. Overall, te sare of FPI varies more toroug te canged productivities tan te FDI sares. Te latter are more or less stable. Additionally, FPI sares under CII uctuate even more tan under isolated international investment. Wereas, CII FDI is more stable tan isolated FDI. Figure 6 sows te variation of bot investments under te respective strategy wit varying investment cut o conditions. b low neg λ

20 20,50000 isolated international investment 0,2 combined international investment,00000 fdi 0,5 0, , 0,05 0,00000 fpi 0 fdi 0,50000, ,05 0, fpi,50000 a λ 0,5 b λ Figure 6 Hence wit CII, te rm reacts to sort-term canges in its environment by adjusting FPI and keeping FDI stable. Tus FPI does not necessarily increase wit FDI, but adjusts according to r&d-probability, depreciation and variation in bot foreign productivities. 5. Conclusion I ave sown in a dynamic investment setting tat te relation of FPI and FDI is complementary. Isolated FPI and FDI investments Ire compared to combined FPI and FDI investments. Te combined investment strategy dominates te isolated investments always in time. Furter, CII comprises a iger incentive to invest in r&d. Te risk diversifying e ect from additional FPI puses te marginal valuation of r&d investment above te valuation wit isolated investment strategies. Specially, tis is te case wit te combination of orizontal FDI and FPI in a country wit dissimilar structure tan te ome country. As a consequence, ome productivity increases muc faster and witout smaller relative opportunity costs tan under isolated investment strategies. Finally, tis leads to a iger productivity at a timely earlier FDI cut o. Te signi cant iger CII r&d investment tan isolated FDI r&d investment con rms tis observations. Furtermore, I also found tat rms adjust to sort-term canges via FPI and keep FDI stable. FPI can prop up small and medium sized canges and terefore, te valuation of FDI wit combined FPI is iger tan of isolated FDI. Hence, a combined FPI and FDI investment strategy increases te rms exibility. Te consequences are earlier international activity for medium sized as Ill as small sized rms and better adjustment to environment canges, especially trade liberalization. 6. References Andersen, P. S. and Hainaut, P. (998): Foreign Direct Investment and Employment in te Industrial Countries, Bank for International Settlements, Working Paper, No. 6. Aizenman, Josua and Marion, Nancy (200): "Te Merits of Horizontal versus Vertical FDI in te Presence of Uncertainty", NBER Working Paper, No Cuan, Punam; Perez-Quiros, Gabriel and Popper, Helen (996): International Capital Flows. Do Sort-Term Investment and Direct Investment Di er?, Te World Bank,

21 2 Policy Researc Working Paper No Dixit, Avinas K. and Pindyck, Robert S. (994):"Investment under Uncertainty", Princeton University Press. Dixit, Avinas K. and Stiglitz, J. (977): "Monopolistic Competition and Optimum Product Diversity", American Economic Review, Vol. 67, No. 3, Dunning, Jon H. (973): "Te Determinants of International Production", Oxford Economic Papers, New Series, Vol. 25, No. 3, p Goldstein, Itay and Razin, Assaf (2005): Foreign Direct Investment vs Foreign Portfolio Investment, NBER Working Paper No Grossman, Gene M.; Helpman, Elanan and Szeidl, Adam (2003): "Optimal Integration Strategies for te Multinational Firm", NBER Working Paper, No Grossman, Gene; Helpman, Elanan and Szeidl, Adam (2005): "Complementarities between Outsourcing and Foreign Sourcing", American Economic Review, Vol. 95 (2), p Helpman, Elanan (2006): Trade, FDI, and te Organization of Firms, Journal of Economic Literature, Vol. 64 (3), p Helpman, Elanan ;Melitz, Marc J.and Yeaple, Stepen R. (2003): Eport versus FDI, NBER Working Paper No Markusen, James R. and Maskus, Keit E. (200): "General-Equilibrium Approaces to te Multinational Firm: A Review of Teory adn Evidence", NBER Working Paper, No Melitz, Marc J. (2003):"Te Impact of Trade on Intra-Industry Reallocations and Aggregate Industry Productivity", Econometrica, Vol. 7, No. 6, Mody, Asoka; Razin, Assaf and Sadka, Efraim (2002): Te Role of Information in driving FDI: Teory and Evidence, NBER Working Paper, No Razin, Assaf (2002): FDI Contribution to Capital FLows and Investment in Capacity, NBER Working Paper, No WTO (996): Trade and foreign direct investment, New Report by WTO, UNCTAD (2006): World Investment Report 2006, ttp:// 7. Appendix 7.. Appendix A 7... Derivation of Expected Capital Flow Te value of te rm in te case witout international investment is a function of te state variable (productivity). dv = V d (44) Te state variable follows a poisson process wit q = wit prob. dt and q = 0 wit prob. ( dt): ) d = ( ) dq K (45)