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Abstract
The paper develops a general equilibrium model of international production and trade. Technology is carried across borders by multinational producers and the set of technologies being used in a particular country is endogenous. Production locations are chosen based on the costs of production and getting the product to market. A producer may manufacture its product in its home country, target market country, or a third country. Estimated model parameters describe the states of technology in different countries, barriers to international investment, and trade costs. It is found that the barriers to international trade and investment are highly correlated. The model is used to measure the extent of technology diffusion across countries, study the relationship between international production and trade, investigate the effects of free-trade agreements (FTAs) on offshoring, and to quantify the welfare effects of international production and trade.
Acknowledgements
I would like to thank Tolga Ergün, Nikos Sagias, Boris Ivlev, and the anonymous referees for helpful comments and suggestions. I would also like to acknowledge excellent research assistance by Giulio Girardi.
Notes
1. The international investment literature distinguishes between the horizontal FDI, when firms establish production in foreign countries in order to circumvent trade costs, and vertical FDI, when firms do it in order to take advantage of cheaper inputs. In the latter case, the output of the foreign plant may be sold back to the home country or to a third country (a scenario called export-platform FDI). The model of this paper allows for all of these possibilities.
2. The data show great variability of strategies that multinationals use to serve various markets. From data on the US foreign affiliates, we know that while most of the foreign affiliates' output is typically sold locally (66% of output in an average country), there is significant heterogeneity across host countries (it varies between 22% in Bermuda and 95% in India). The rest of output is sold to the home country and third countries (11% and 23%), but again there is significant heterogeneity (the percentage output sold locally varies between 22% in Bermuda and 95% in India; the percentage sold to the US varies between 0.2% in Greece and 46% in Barbados); It is also interesting to compare two different ways to serve a foreign market: trade and local production, by looking at the ratio of the merchandise exports to the local sales of the foreign affiliates. The most striking feature of this data is how much it varies across countries. Some countries, such as Bermuda (0.08), Poland (0.11), and the UK (0.15), are served mostly by multinational production. Other countries, such as Israel (5.5), Costa Rica (2.65), and Korea (2.24), are served mostly through exports (Mataloni and Yorgason 2002; BEA database).
3. The data show that most of the R&D is done in the home country (87% for the US) (Mataloni and Yorganson 2002; BEA database).
4. Their model and the model of this paper were developed contemporaneously.
5. RRC estimate international trade and production costs using cost functions that relate those costs to distance, common language, etc. As the result, their measures of international trade and production costs are positively correlated by design. The model of this paper does not need to use cost functions, so that the international trade and investment costs do not have to correlate.
6. This section will not assume specific distributional forms for the random variables, but will derive the results in the general case. Section 2.4 will impose distributional forms and derive the expressions that will be put to data.
7. This specification is equivalent to using ‘iceberg’ costs for international investment, an approach that has been previously used by the empirical literature on FDI as well as the more recent models of FDI with heterogeneous producers.
8. The unbounded supports of the distributions of z(j) and φ(j) mean that the model cannot replicate zero trade or investment flows between countries. Ramondo (2008) and Chor (2010) develop models where zero trade or FDI flows are made possible by bounding the support of the technology distributions. While allowing unbounded supports limits the applicability of the model to large countries or country blocks, it also reduces the complexity of the model and makes it more tractable.
9. So, the productivity achieved in production is a product of two random variables, zh and φ ih . Ramondo and Rodríguez-Clare (2009), on the other hand, model the productivity achieved in production as a random variable drawn from a multivariate distribution with one dimension representing the home country and the other representing the country of production. Their approach results in many more parameters (than the model of this paper) that need to be estimated, so they have to impose additional restrictions on the parameters. On the other hand, RRC's approach results in expressions for international production and trade that are more compact than those derived in this paper. Of course, the solutions to their model as well as the model of this paper have to be obtained numerically.
10. The assumption of identical factor shares in all countries is of course counterfactual, as shares do vary across countries. However, it is a common assumption in the literature and, as the results in Section 4.1 illustrate, it is not a bad approximation.
11. Why cannot φ ih be the same for all goods j, same as trade cost dni ? If φ ih were the same for all goods j, then for a given pair of countries {n,h} there would have been only one (for all goods j) production location i* that gives the minimum cost to market (a ‘knife's edge’ scenario, where several production locations give the same cost to market, is possible, but not realistic). An implication is that for a given pair of countries, there could only be trade or IP (FDI), but not both. In fact, for some country pairs, there could be no trade or investment (all production would take place in a third country). When φ ih is random, different producers from h may choose different ways of serving market n.
12. Note that for given n and i, events Anih across different h's are mutually exclusive. In other words, two producers from any two locations h 1 and h 2 cannot establish manufacturing facilities in the same location i in order to supply the same product j to the same market n. Therefore χ nih are additive across origins h. Also, for given n and h events Anih across different i's are mutually exclusive, since a producer from h would not establish affiliates in more than one location i in order to supply the same market n. Therefore χ nih is additive across production locations i.
13. It is also possible to derive the volume of sales of h producers (manufacturing anywhere in the world) in n. Let be the probability that a producer from h (manufacturing anywhere in the world) sells in n. Therefore, χ
nh
X
n
is the volume of sales of h firms in n. The expression for χ
nh
simplifies considerably. The second term in the expression for χ
nih
disappears, and the probability that a producer from h (manufacturing anywhere) is the least-price supplier in n is simply
.
14. So is not a probability that a firm located in i has come from h (or a fraction of firms located in i that has come from h), because some affiliates may sell to more than one destination.
15. When the model is simulated (as in Section 7), the model parameters are Kn, Ln
, , Λ
n
, Ψ
ih
, θ, dni
, α, β, σ, and ϕ
n
, while the endogenous variables are π
ni
, kih, Qn, Xn, wn, rn
, and pn
.
16. Because some markets n are more expensive to serve than others, more productive producers will be competitive in more markets than less productive producers.
17. There is a large literature that looks at producer-level heterogeneity in trade. This literature finds that exporters are a minority and more productive than non-exporters. More productive exporters sell to more destinations than less productive exporters (Aw, Chung, and Roberts 1998; Clerides, Lach, and Tybout, 1998; Bernard and Jensen 1999; Eaton, Kortum, and Kramarz 2004).
18. The superscript ‘export’ is not necessary, but is added for convenience.
19. Similarly, of the firms that serve a specific number of destinations, the fraction of pure exporters (not engaged in IP) declines as the number of destinations rises.
20. There are several studies of producer heterogeneity in international production. They find that only a small fraction of firms engage in FDI and that these firms are more productive than the exporting firms (Helpman, Melitz, and Yeaple 2004; Tomiura 2007).
21. The mean and variance of a Fréchet random variable are , for θ > 1 and
, for θ > 2, where Γ is the Gamma function.
22. The technology being used to make good j and the implementation procedure for this technology both represent best available practices. Therefore, it is reasonable to represent them by extreme-value distributions.
23. Note that a product of two Weibull random variables cannot be approximated by a Weibull random variable (Sagias and Tombras 2007).
24. Most of international production occurs in developed countries: 70% of the world FDI inflows are received by industrial countries and 70% of the US MOFAs (by output) are in the G7 countries (Mataloni and Yorgason 2002; UNCTAD 2004, 2005; BEA database).
25. The size of international production can be measured in several ways. It can be measured by the cumulative investment made by the MNCs into their affiliates. This measure is called the stock of FDI and is calculated from the annual FDI flows reported in national accounts. The size of IP can also be measured by the output, sales, employment, or reported assets of the affiliates. There are advantage and disadvantage to using each of these measures. FDI flows are available for a wide range of countries and years, but are volatile and may be inaccurate because investments are often routed through the third countries. Industry distribution of FDI may be inaccurate for a similar reason: investments are often routed through holding companies in other industries. In addition, the FDI stocks reported by statistical agencies do not take into account changes in asset and currency values. The data on affiliates' output, sales, employment, and assets is collected by industrial surveys and reflects ownership and industry more accurately than FDI flows. However, this data is available for only a few countries and years.
26. Note that the market clearing conditions are implied by equation (21). This can be seen by taking the sum of equation (21) over h and remembering that
, and
.
27. Note that while equations (20) and (21) are solved as a system, the trade costs are primarily identified from equation (20) (since it sums over the sources of technology s), while implementation factors are primarily identified from equation (21) (since it sums over the destination of exports n). Therefore, trade costs are primarily determined by trade flows, while implementation factors are primarily determined by the size of international production.
28. The share of intermediate goods in output is then 0.7. The implied shares of capital and labor in value added are 0.35 and 0.65. The 20% gross rate of return assumes a 10% net return and 10% depreciation rate.
29. The value of parameter σ has a negligible effect on the parameter estimates or simulation results. For example, choosing a σ between 1.1 and 10 changes the relative price levels by less than 1%.
30. Lower θ results in higher variance of the technology distribution, thus increasing the probability that a country has a producer that can be competitive in foreign markets. To fit the existing trade and IP values, the model offsets this effect by setting higher trade and IP costs.
31. The simulation results presented in this paper are robust to the value of θ. Consider, for example, two cases: (a) a low θ and the corresponding high estimates of dni, n ≠ i and (b) a high θ and the corresponding low estimates of dni , n ≠ i. Then, in each case, consider performing a counterfactual experiment that sets dni = 1, ∀n, i (i.e. free trade). Such an experiment is performed in Section 8.2. As in Eaton and Kortum (2002), parameter θ determines the response of trade flows to changes in trade costs: higher θ means smaller response. So, moving to free trade results in approximately the same predicted changes of trade flows in both cases. In case (a), changes in trade costs are large, but trade flows are not sensitive to changes in trade costs. In case (b), changes in trade costs are small, but trade flows are very sensitive to changes in trade costs. Welfare changes are also approximately similar in both cases since they are a function of the changes in trade. The same logic applies to simulating free IP and autarky.
32. Note that this is not an econometric estimation. There are zero degrees of freedom.
33. The model estimates high export trade costs for Japan because of low import shares for Japanese manufactures shown in . For example, the share of Japanese manufactures in the Europe is 0.015, which is about a half of the US's share (0.031). Since the Japan has a slightly higher average productivity than the US () and lower manufacturing wage than the US (), its low share in Europe is explained by high trade costs.
34. We cannot simply add up the local sales in the European or the ROW countries to obtain the local sales of the US affiliates in Europe and the ROW. Consider, for example, the sales of the US affiliates located in France to Italy. These sales are local sales for Europe, but will be classified as sales to third countries in the BEA's data.
35. Changing the value of parameter θ has a negligible effect on the percentages inferred by the model.
36. Unfortunately, this result cannot be compared against data because Statistics Canada does not report data on the operations of foreign affiliates in Canada. Also, note that this result does not mean that Canada's imports are greater than its output, because Canadian output includes the output of foreign affiliates located in Canada, which is substantial.
37. This means, for example, that producers do not choose an export-platform location to serve the ROW based on the lowest cost of production.
38. While the labor compensation in Canada, Europe, Japan, and the US is seven to 10 times greater than in the ROW, it constitutes only 20% of the cost of production. Since the prices of capital and intermediate goods are fairly similar in all countries, the differences in the costs of production are not as great; there is certainly anecdotal evidence that operating in the US is not much more expensive than operating in China (which dominates the ROW data). For example, an article in the L.A. Times (Lee 2008) tells a story of a Chinese businessman opening a printing-plate factory in South Carolina. He explains that land costs less than 1/4 of what it does in southeast China, electricity rates are about 75% lower, and there are no blackouts. While the South Carolina labor costs are higher ($12–13/h vs. $2/h), they are partially offset by payroll tax credits from the state government (the differences in land costs, electricity costs, and tax incentives are captured in the model by the differences in the expected implementation factors). The bottom line? ‘I was surprised,’ said the businessman. ‘The gap is not as large as I thought.’
39. They use a gravity-like equation to estimate the trade costs.
40. This result also serves as a check of the model of this paper.
41. In terms of fractions of labor forces employed by foreign affiliates, λ ih .
42. This evidence includes the fact the most of the output of international production is sold locally (see Sections 4.2 and 4.3). Since local sales are usually interpreted as the result of horizontal FDI, their prevalence can be taken as evidence of prevalence of horizontal FDI. Irarrazabal, Moxnes and Opromolla (2008) reconcile the horizontal IP theory with gravity results by requiring foreign affiliates to buy intermediate inputs from the headquarters. Ramondo and Rodríguez-Clare (2009) use a similar mechanism in their model, but still find that trade and IP are substitutes. The model of this paper imposes no such requirements on the affiliates. Instead, this section explains that the gravity results and theory are not contradictory.
43. The correlation coefficient excludes the diagonal entries.
44. The slope of the relationship between trade costs and implementation factors on is close to −1. The relationship between trade costs and implementation factors tightens significantly if the country pairs involving ROW are excluded (ρ becomes −0.77).
45. The empirical literature on the determinants of FDI is reviewed in Blonigen (2005).
46. Keller and Yeaple (2009) show how distance may matter in IP activity.
47. There are several caveats to this finding. First, trade and IP are partial (weak) substitutes (Ramondo and Rodríguez-Clare [2009] get the same result, even though they require foreign affiliates to buy a portion of their intermediate goods from their home country). Second, even though trade and IP are substitutes on the net, there are both substitution and complimentarity effects between the two. Trade and IP are substitutes because they are two alternative ways to serve foreign markets. The complimentarity effects work though the output. For example, lower investment barriers increase output, which stimulates trade (including trade in intermediate goods) (Blonigen [2001] also finds evidence of complimentarity and substitution effects between trade and FDI.). Lower trade costs lead to higher output in both countries, including the output of the remaining foreign affiliates. However, these complimentarity effects are smaller than the substitution effects. Third, trade and IP are substitutes in the sense that changing trade or IP barriers moves trade and IP in opposite directions. A change in another parameter may move trade and IP in the same direction. For example, increasing Λ h leads to greater exports from h and greater IP by h affiliates (simulations results are available from the author upon request). Fourth, the prediction of the model regarding trade and IP being substitutes is for the existing levels of barriers to trade and investment. For example, if trade is free, then lowering barriers to international production increases IP, but does not decrease trade. Similarly, if there are no barriers to international production, then decreasing barriers to trade increases trade, but does not decrease international production.
48. The US affiliates in the ROW also increase their exports to the US much more than the other affiliates in the ROW. For example, the ROW's own domestic affiliates increase exports to the US only five-fold.
49. The source of this data is the BEA database on the activity of the US foreign affiliates.
50. Countries can also enter into stand-alone (i.e. not part of FTAs) agreements that reduce investment barriers outside of the FTAs. The examples include bilateral investment treaties (BITs) and double-taxation treaties (DTTs). The empirical evidence on the effects of BITs on FDI is mixed, though it seems that developing countries, especially those considered to have risky business environments, increase their FDI inflows by signing BITs (Neumayer and Spess, 2004; Swenson 2005).
51. Arkolakis, Costinot and Rodríguez-Clare (2010) show that these gains from trade can be obtained from a large class of trade models.
52. Trade costs are held at their base values, presented in .
53. Eaton and Kortum (2002) reach the same conclusion for international trade.
54. Regardless of whether the international trade is free or not.