1. Introduction
Economic growth in East Asia (Hong Kong, Singapore, South Korea, and Taiwan) took off in the 1960s, with an annual rate averaging over 5% in 1960–2008. East Asia's per capita income relative to the US increased from around 15% in 1960 to over 70% in 2010, while that of Latin America (LA) remained at around 30% over that period. Consequently, per capita income in LA, which was twice that of East Asia in 1960, fell to 42.8% of East Asia's income by 2010 (World Bank, 2011, pp. 22–23), a relative decline of nearly 80%. Many studies have examined the causes of the relative decline in LA and found that differences in productivity levels and growth played a major role in explaining differences in economic performance. For instance, Cole et al. (Reference Cole, Ohanian, Riascos and Schmidt2005) find that LA's low total factor productivity (TFP) explains its poor economic performance, with the low level of TFP due mainly to trade and other barriers to competition rather than a low level of human capital. Similarly, Kydland and Zarazaga (Reference Kydland and Zarazaga2002) find that Argentina's poor economic performance in the ‘lost decade’ of the 1980s was mainly due to a decline in TFP.Footnote 1
In this paper, we focus on TFP and its determinants, examining potential causes of the TFP gap between East Asia and LA. We contribute to the literature on the impact of North–South international technology diffusion in several ways. First, we develop a simple model that integrates the trade- and distance-focused models of technology diffusion and TFP. Second, we examine the impact of distance on TFP in the context of technology diffusion from G7 countries,Footnote 2 whether separately or jointly with trade. Third, we estimate the impact on TFP of raising LA's levels of trade openness, human capital, and governance to those of East Asia, and the extent to which doing so accounts for the TFP gap between the two regions. Finally, we use the estimated impact of distance on TFP to derive the impact of South America's remoteness to G7 countries relative to Mexico, and similarly for Singapore's greater distance relative to Hong Kong.
We find that (a) TFP increases with education, trade, governance, and trade's R&D content, and declines with North–South distance; (b) an increase in LA's education, trade and governance to East Asia's level raises its TFP by about 100% and accounts for about 75% of its TFP gap with East Asia; and (c) the TFP impact on South America relative to Mexico due to the former's greater distance to US–Canada (Europe) (Japan) (G7 as a whole) is −19.3 (−2.2) (−10.0) (−12.6)%.
The remainder of the paper is organized as follows. Section 2 presents the three technology diffusion model specifications. Section 3 describes the data and key variables in the South. Section 4 presents the empirical results. Section 5 presents data on South–North distance used in the simulations. Section 6 conducts a ‘nesting’ (and robustness) test to determine our preferred specification, and examines (i) the impact on LA's TFP and on the East Asia–LA TFP gap of raising LA's education, trade, and governance to East Asia levels; and (ii) the impact of South America's greater distance to the G7 than Mexico on the former's TFP relative to that of the latter, and similarly for the Singapore's TFP relative to that of Hong Kong. Section 7 concludes.
2. Empirical Framework
Our empirical analysis draws on Coe and Helpman's (Reference Coe and Helpman1995) seminal work on North–North trade-related technology diffusion and on Keller's (Reference Keller2002) model that incorporates the impact of North–North distance but abstracts from trade.Footnote 3 We integrate the Coe and Helpman (Reference Coe and Helpman1995) and Keller (Reference Keller2002) specifications of the technology diffusion process. This enables us to examine simultaneously the impact of both North–South trade-related and distance-related technology diffusion on South's TFP, as well as differences in the TFP impact for proximate and remote regions in the South.
Coe and Helpman (Reference Coe and Helpman1995) construct an index of ‘foreign R&D’, defined as the trade-weighted sum of developed trading partners’ R&D stocks, and find that it has a large and significant impact on TFP, which increases with the economy's openness, and on educational attainment and governance levels.Footnote 4 In this paper, the North comprises the G7 countries where most of the R&D is generated.Footnote 5 The G7 countries are indexed by k, and measures of foreign (Northern) R&D are denoted by NRD ij, where i indexes the developing countries and j = 1, 2, 3 indexes the three NRD measures, which are as follows.
-
Model 1: Linear Trade-Weighted R&D
The measure for country i is:
$$NRD_{i1} = \mathop \sum \limits_k RD_{ik1} = \mathop \sum \limits_k \left({\displaystyle{{M_{ik}} \over {VA_i}}} \right)RD_k, \;$$where M ik is the value of i's imports from k, and VA i is the value of i's GDP.
-
Model 2: Non-Linear Distance-Corrected R&D
Keller (Reference Keller2002) specified a measure of foreign R&D that includes the distance, Dist, between technology source and recipient countries but excludes trade. His measure of NRD is:
$$NRD_{i2} = \mathop \sum \limits_k RD_{ik2} = \mathop \sum \limits_k RD_k\,\ast\, e^{-\delta .Dist_{i, \;k}}.$$Keller does not specify the channel or channels through which technology diffusion takes place. Rather, his focus is on the impact of distance, with δ > 0 indicating that the impact of G7 R&D stocks on importing countries’ TFP declines with their distance from the G7 countries. The reason for the negative impact of distance on TFP is that some information cannot be standardized and/or codified. Thus, face-to-face communication is particularly important in those cases and in cases of imperfect information, which are key features of many creative activities and are important for productivity (e.g., see Storper and Venables, Reference Storper and Venables2004).
-
Model 3: Non-Linear Trade-Weighted Distance-Corrected R&D
Models (1) and (2) can be combined into a model that includes both distance and trade, as follows:
$$NRD_{i3} = \mathop \sum \limits_k RD_{ik3} = \mathop \sum \limits_k \left({\displaystyle{{M_{ik}} \over {VA_i}}} \right)\,\ast\, RD_k\,\ast\, e^{-\delta .Dist_{i, \;k}}.$$ Equation (3) says that foreign R&D in country i increases with its G7 trading partners’ R&D stocks, RD k increases with its openness to trade 
${{M_{ik}} \over {VA_i}}$, and (assuming δ > 0) declines with the distance, Dist i,k, from its G7 trading partners.
The three above models give three estimation equations, one for each value of j (j = 1, 2, 3):
$$\log ( {TFP_{it}} ) = \alpha + \beta \log ( {NRD_{ijt}} ) + \beta ^{Edu}Edu_{it} + \beta ^{Gov}Gov_{it} + \mathop \sum \limits_i \gamma _iD_i + \mathop \sum \limits_t \gamma _tD_t + \varepsilon _{it}$$where NRD i1t, NRD i2t, and NRD i3t are defined, respectively, in equations (1), (2), and (3) above, Edu it is country i's educational attainment, Gov it is a governance index, D i (D t) is a country (time) fixed effect, and 
$\varepsilon $ is an error term.Footnote 6
3. Data Description and Descriptive Statistics
The data cover the G7 and 30 developing countries, for the 32-year period 1976–2007, the period up to but excluding the Great Recession.Footnote 7 The G7 countries are split into three groups: United States and Canada (USC) in North America; France, Germany, Italy, and the UK in Europe; and Japan in Asia. This enables us to examine, among other things, the impact of distance on countries’ TFP. The 30 developing countries are collected into four groups: (1) Hong Kong (China), Singapore, and South Korea in East Asia;Footnote 8 (2) Mexico; (3) all countries of South America except Paraguay (as it lacked data for constructing industry-specific capital stocks); and (4) 17 developing countries outside East Asia and Latin America, namely: Bangladesh, Cameroon, Egypt, India, Indonesia, Jordan, Kenya, Kuwait, Malawi, Malaysia, Morocco, Nepal, Pakistan, the Philippines, Sri Lanka, Tunisia, and Turkey.
The production function is 
$Y = AL^\alpha K^{1-\alpha }$, where Y(A)(L)(K) is value added or GDP (total factor productivity TFP) (labor) (capital). Thus, log (TFP) = log (Y) − αlog(L) − (1 − α)log(K), where α is the labor share, measured as the ratio of the wage bill and GDP. Fixed capital formation used in the construction of capital stocks, value added, labor, and wages are from the World Bank database (Nicita and Olarreaga, Reference Nicita and Olarreaga2007), all reported in current US dollars at the 3-digit ISIC codes (Revision 2) and deflated by the US GDP deflator (1991 = 100).
Capital stocks are derived from the deflated fixed capital formation series using the perpetual inventory method with a 5% depreciation rate, and R&D stocks are constructed from R&D expenditures using the same method with a 10% depreciation rate. R&D expenditure for the G7 countries is taken from OECD ANBERD, with ISIC Revision 2 (2002) covering data from 1973 to 1998 and ISIC Revision 3 (2006) covering data from 1987 onward. As the two datasets have 12 overlapping years, we are able to match them. The governance index is from Kaufmann et al. (Reference Kaufmann, Kraay and Mastruzzi2011). It consists of an average of six governance indicators that range from −2.5 to 2.5.Footnote 9 Distance is defined as the shortest distance between countries’ capitals, measured in thousands of kilometers. Secondary school completion ratio for population aged 15 and older is obtained by annualizing the five-year averages in Barro and Lee (2013).Footnote 10 Bilateral trade data of the 30 developing countries with the G7 industrialized countries at the 4-digit ISIC 2 level are from World Bank data (a description is in Nicita and Olarreaga, Reference Nicita and Olarreaga2007).
We construct bilateral trade shares between the 30 developing countries and the G7 countries for the 32 sample years, and do so for 16 industries, which consist of six R&D-intensive and ten low-R&D-intensity industries.Footnote 11 These are then used to construct the NRD measures in equations (1), (2), and (3). Due to missing observations, our sample is unbalanced. It has 32 panels, with 1876 observations out of a total of 1920 observations, or over 97% of the total. All regressions in Section 5 include country and time fixed effects.
Table 1 shows average levels for 1976–2007 of log (TFP), governance, education, and trade openness, for the four regions of interest. Figures for country groups are weighted averages, where weights are based on countries’ GDP in the case of log (TFP), governance and openness, and on population in the case of education.
Table 1. Mean of key variables by region, 1976–2007 (Weighted average)
Notes: Regional averages weighted by GDP (population); M = imports (regional average weighted by GDP); Latin America = South America + Mexico.
East Asia's average log (TFP) in 1976–2007 is 2.93, which is 40% higher than Mexico's 2.10, 56% higher than South America's 1.88, and 46% higher than LA's 2.04. East Asia also has the highest governance level, with an average of 0.535, followed by South America (0.054) and Mexico (−0.269), and with the LA value equal to −0.027.Footnote 12 Educational attainment, defined as the percent of population aged 20 and above with a high school degree or more, is 45.8 in East Asia, 26.2 in South America, 24.3 Mexico, and 25.4 in LA. The East Asia–LA education gap is 20.6 percentage points or 82%. Trade openness (the share of imports in GDP) is 60% for East Asia and 30 (37) (33)% for South America (Mexico) (LA), with an East Asia–LA trade openness gap of 0.27 percentage points or 82%.
4. Empirical Results
Studies in the trade-related technology diffusion literature – including Coe and Helpman (Reference Coe and Helpman1995) – have estimated equation (1) by OLS, an exception being Coe et al. (Reference Coe, Helpman and Hoffmaister2008) who use panel co-integration estimation and the same data as Coe and Helpman (Reference Coe and Helpman1995) to estimate (1) and obtain similar results. As Coe et al. (Reference Coe, Helpman and Hoffmaister2008) state: ‘The new estimates confirm the key results reported in Coe and Helpman (Reference Coe and Helpman1995) about the impact of domestic and foreign R&D stocks on TFP.’ Based on this finding and following the literature, equation (1) is estimated by OLS. Keller (Reference Keller2002) estimated equation (2) by non-linear least-squares, which is the method used to estimate equations (2) and (3). Estimation results for the three models are presented in columns (1), (2), and (3) of Table 2, respectively, for the four relevant variables that matter for the simulations: trade, distance, education, and governance.Footnote 13
a t statistics in parenthesis.
b Significance level.
***+p < 0.001, ***p < 0.01, **p < 0.05.
Column (1) shows a positive impact of log(NRD i1), education and governance on log(TFP), with β = 0.325, β Edu = 0.0219, and β Gov = 0.587, all significant at the 0.1% level. The adjusted R 2 (based on robust standard errors) is 0.66. Column (2) also shows a positive impact of log(NRD i2), education and governance, and a negative one for distance (as δ > 0; see (2)). Coefficients (significance level) are: β = 0.234 (5%), β Edu = 0.0232 (1%), β Gov = 0.568 (0.1%), and δ = 0.722 (1%), and the adjusted R 2 is 0.61. Column (3) shows β = 0.285 for log(NRD i3), β Edu = 0.0221, β Gov = 0.536, and δ = 0.760, all significant at the 0.1% level. Thus, distance also has a negative impact on TFP in this specification. The adjusted R 2 is 0.91, which is higher by 25 (30) percentage points or 38 (49)% than the adjusted R 2 in column (1) ((2)). The elasticity of TFP with respect to trade openness towards the G7 countries is 
$\varepsilon _T = \beta = 0.285$.Footnote 14 With δ = 0.76, the elasticity of TFP with respect to distance is 
$\varepsilon _{Dist} = {-}\;\beta \delta = {-}\;0.217$.
The coefficients β Edu and β Gov are semi-elasticities. Using mean education and governance values, the elasticities are 
$\varepsilon _{Edu} = 0.609$, and 
$\varepsilon _{Gov} = 0.081$. Thus, education has the largest elasticity, trade has the second-largest (
$\varepsilon _T = 0.285$), and governance has the smallest. Note also that 
$\varepsilon _T$'s value of 0.285 is almost identical to the value of 0.290 obtained by Coe and Helpman (Reference Coe and Helpman1995).
North–South trade-related technology diffusion studies have estimated versions of Model 1 and have typically ignored distance as one of the determinants of TFP, while distance-related technology diffusion studies have ignored the impact of trade. The results shown in Table 2 indicate that the goodness-of-fit is significantly improved when both the trade-related and the distance-related impacts on TFP are incorporated into the analysis. Table 2 also shows that parameter estimates vary according to the equation being estimated, with the largest differences obtained for the β estimates, whose value in column (3) is equal to the average of the values in columns (1) and (2).Footnote 15
5. South–North Distance
This section presents information used in the simulations in Section 5 on the impact of developing countries or regions’ distance to the three G7 regions: US and Canada (USC), Europe's four largest economies, France, Germany, Italy, UK (Europe); and Japan.Footnote 16 Specifically, we compare the distances from Mexico to the three G7 regions with those from South America, and similarly compare the distances from Singapore to the three G7 regions with those from Hong Kong. The distance of South America to any of the three G7 regions is the sum of each South American country's distance weighted by its share in the region's GDP. The results are given in Table 3.
Table 3. Absolute and relative distance (in km)
Notes: aUS and Canada
b France, Germany, Italy, and the UK.
South America is 105.4% further from USC than Mexico (6,225 vs. 3,031 km, respectively). It is 9.0% further from Europe than Mexico (10,019 vs. 9,190 km), and it is 46.3% further from Japan than Mexico (16,518 vs. 11,294). As for Singapore, it is 18.5% further from USC than Hong Kong (15,528 vs. 13,099), 11.5% further from Europe than Hong Kong (10,722 vs. 9,620), and 84.4% further from Japan than Hong Kong (5317 vs. 2884).
Several observations are in order here. First, given that Mexico shares a border with USC, it is not surprising that the distance gap between South America and Mexico is, at 115.2%, largest in the case of the USC region. Second, for both the Americas and Asia, the distances to the three G7 country groups are greatest for the Southern-most regions, South America and Singapore, respectively, which makes sense as the three G7 regions, located between the 35° and 51° parallels, are further North than any of the developing countries or regions. Third, the gap in South America's and Mexico's distance to Europe is, at 2.3%, surprisingly small, especially when compared with the 49.2% gap in their distance to Japan. Mexico's latitude is 19.432° N and South America's is 15.540° S, a gap of 34.972° or 3882 km, implying a smaller distance from Mexico to both Europe and Japan. Mexico's longitude is 102.55° W and South America's is 58.70° W, a gap of 43.85° or 4182 km (at Mexico's latitude),Footnote 17 implying a smaller distance from Mexico to Japan but a greater distance to Europe. Thus, differences in latitude and longitude have opposite effects on Mexico's distance to Europe relative to that of South America but have reinforcing effects on Mexico's distance to Japan.
Similar results obtain with respect to Hong Kong and Singapore. The distance from Singapore to Europe (Japan) is 11.5 (84.4)% above that of Hong Kong. Singapore is 20.9672 degrees or 2293 km South of Hong Kong, implying a greater distance from the former to both Europe and Japan (and USC). Singapore is also 10.3496 degrees or 1148 km (at Singapore's latitude) West of Hong Kong, implying a smaller distance to Europe and a greater one to Japan.
6. Simulation Results
To undertake a simulation, we must select one of the three equations. We conduct two F-tests since Models 1 and 2 are nested in equation (3). The objective is to ascertain whether including both distance and trade in Model 3 improves the results in a statistically significant way relative to Models 1 and 2. The F-test value was compared to the critical value, F*, in the F-distribution table,Footnote 18 with F > F* in both cases (significant at the 1% level). Thus, the hypothesis that Model 3 is the preferred one cannot be rejected. Moreover, the adjusted R 2 is 0.91, which is 25 percentage points above the 0.66 value in Model 1 and 30 percentage points above the 0.61 value in Model 2. Hence, Model 3 is selected for the simulations.
We examine the impact on TFP of an increase in South America's, Mexico's, and LA's governance, education, and trade openness to East Asia's values, and the extent to which the difference in the levels of these variables accounts for their TFP gap with East Asia. Results are presented in Table 4. We also examine South America's TFP loss relative to Mexico due to its greater distance from the three G7 groups, and similarly for Singapore relative to Hong Kong. The results are presented in Tables 5 and 6, respectively. Values in Tables 4–6 are averages over the sample period.
Table 4. Impact on TFP of raising South America's and Mexico's Governance, Education and trade to east Asia's level (%)a
Table 5. South America's greater distance to the G7 relative to Mexico: impact on TFP (in %)a
Table 6. Singapore's greater distance to the G7 relative to Hong Kong: impact on TFP (in %)a
6.1 Governance
The value of the governance coefficient in (4.3) is 0.536. Average governance is −0.027 for LA and 0.535 for East Asia, with a gap of 0.562. Raising LA's governance to Asia's level raises its TFP by 0.536*0.562 = 0.308, i.e., by 30.8%. This amounts to a reduction in LA's TFP gap with East Asia of 23.1%. The same logic applies to all the other simulations. Thus, raising governance from South America's (Mexico's) level to that of East Asia raises TFP by 25.6 (46.1)%, which accounts for 19.1 (34.6)% of the gap in TFP.
6.2 Education
The coefficient for education is 0.0221, i.e., a one-percentage point increase in education raises TFP by 2.21%. LA's (South America's) (Mexico's) average level of education over the period 1976–2004 is 25.7 (26.2) (24.3), while that of East Asia is 45.8, with a gap equal to 20.1 (19.6) (21.5), Thus, the impact on TFP of increasing education to East Asia's level is equal to 44.4 (43.3) (47.5)%, which accounts for 33.5 (32.5) (35.8)% of the TFP gap.
6.3 Trade
TFP's elasticity with respect to NRD is equal to 0.285. This implies that raising LA's (South America's) (Mexico's) import-to-GDP ratio to East Asia's level raises TFP by 23.3 (27.5) (11.6)%, which accounts for 17.5 (20.6) (8.7)% of the TFP gap.
6.4 Total Impact of Governance, Education, and Trade
An increase in education, governance, and trade to East Asia's level raises TFP in South America (Mexico) (LA) by 96.4 (105.2) (98.6)%, which accounts for 72.2 (79.1) (74.1)% of the TFP gap with East Asia. Thus, the gap between LA and East Asia in the levels of education, governance, and trade accounts for about three quarters of the gap in their TFP. Note that based on the linear equation (1), the first regression shown in Table 2, the TFP gap between LA and East Asia would have been reduced by 80% rather than 74%, i.e., the remaining gap would have been estimated to be 20% rather than 26% of the actual gap.
6.5 Distance
This section examines the impact on South America's TFP of being farther than Mexico from each of the three G7 country groups, with results shown in Table 5, and does the same for Singapore and Hong Kong, with results shown in Table 6. The solutions for the TFP gap between South America and Mexico, and between Singapore and Hong Kong, due to the gap in their distance from each of the three G7 regions and from the G7 as a whole, are shown in Appendix 2. From equation (4.3), the elasticity of TFP with respect to distance is 
$\varepsilon _D = {-}\beta \delta $. With β =–0.285 and δ = 0.760, we have 
$\varepsilon _D = {-}0.217.$
The difference between South America's and Mexico's TFP due to the former's greater distance from USC is −0.217*1.152 = −0.250 or −25.0%, the impact for the greater distance from Japan is −0.217*0.492 = −0.107 or −10.7%, the impact for the greater distance from Europe is −0.217*0.023 = −0.005 or −0.5%, and the impact for the G7 as a whole is −15.9%. The figure for the impact on Singapore’ TFP relative to that of Hong Kong is −4.0% for distance from USC, −18.2% for distance from Japan, −2.5% for distance Europe, and −10.1% for distance from the G7 as a whole.
7. Conclusion
Our findings indicate that TFP increases with openness to trade, education, governance, and imports’ R&D content, and declines with distance. An increase in trade, governance, and education to East Asia's level just about doubles Latin America's TFP (+98.6%), which accounts for about three quarters (74.1%) of its TFP gap with East Asia. The gap in South America's TFP due to its greater distance, relative to Mexico, to ‘US and Canada’ (Japan) (Europe) (G7 as a whole) is −25.0 (−10.7) (−0.5) (−15.9)%. And the gap in Singapore's TFP due to its greater distance, relative to Hong Kong, to ‘US and Canada’ (Japan) (Europe) (G7 as a whole) is −4 (−18.2) (−2.5) (−10.1)%.
Thus, the results indicate, unsurprisingly, that South America's TFP gap relative to Mexico is greatest with respect to the ‘US and Canada’ region as the relative difference in distance is the largest and, similarly, Singapore's TFP gap relative to Hong Kong is greatest with respect to Japan. Distance is given and nothing can be done about that.Footnote 19 On the other hand, the results show that South America, Mexico, and Latin America as a whole could obtain a significant increase in productivity by raising their level of openness, particularly towards the North, improving the quality of governance and raising the level of education (i.e., raising the number of people who have access to education, raising the level of their education, and improving education's quality).
Acknowledgements
We would like to thank Magali Pinat, David Tarr, two anonymous referees, and participants at seminars at the World Bank and the University of Chile for helpful comments, and Wei Jiang of Nankai University for excellent research assistance.
Appendix 1
The sixteen industries consist of six R&D-intensive and ten low-R&D-intensity industries. The ISIC codes and names for the ‘low’ R&D group of industries, and their R&D intensity (in percent and in parenthesis) are (1) 32-Textiles, Apparel & Leather (0.4); (2) 33-Wood Products & Furniture (0.6); (3) 34-Paper, Paper Products & Printing (0.7); (4) 31-Food, Beverage & Tobacco (0.8); (5) 371-Iron & Steel (1.1); (6) 381-Metal Products (1.3); (7) 36-Non-Metallic Mineral Products (1.8); (8) 355/6-Rubber & Plastic Products (2.2); (9) 372-Non-Ferrous Metals (2.4); and (10) 39-Other Manufacturing (2.8).
Similarly, ISIC codes and names for ‘high’ R&D group of industries, and their R&D intensity (in percent) are 382-Non-Electrical Machinery, Office & Computing Machinery (7.9); (2) 383-Electrical Machinery and Communication Equipment (8.1); (3) 384-Transportation Equipment (8.1); (4) 385-Professional Goods (11.0); (5) 351/2-Chemicals, Drugs & Medicines (11.6); and (6) 353/4-Petroleum Refineries & Products (18.5).
Appendix 2
The difference in TFP between developing countries i and j due to the former's greater distance from G7 region g (g = 1, 2, 3) is:
$\;\Delta TFP_g = {{TFP_{i-g}} \over {TFP_{j-g}}}-1 = \varepsilon _D\left({{{DIST_{i-g}} \over {DIST_{j-g}}}-1} \right)$. For instance, the impact on South America's TFP due to its greater distance to Japan relative to Mexico is 
$\Delta TFP_g = \varepsilon _D\left({{{DIST_{SA-g}} \over {DIST_{Mex-g}}}-1} \right) = {-} 0.217\,\ast\, 0.492 = -0.107\;$or −10.7 %.
The overall impact on South America's TFP due to its greater distance to the three G7 regions relative to Mexico is 
$\Delta TFP_{SA} = \mathop \sum \limits_g \omega _{SA-g}\,\ast\, \Delta TFP_g{\rm \;} = \varepsilon _D\,\ast\, \mathop \sum \limits_g \left[{\omega_{SA-g}\left({{{DIST_{SA-g}} \over {DIST_{Mex-g}}}-1} \right)} \right]$, where 
$\omega _{SA-g}\equiv {{\left[{\left({{{M_{SA-g}} \over {VA_{SA}}}} \right)RD_g} \right]} \over {\mathop \sum \nolimits_g \left({{{M_{SA-g}} \over {VA_{SA}}}} \right)RD_g}}$, and 
$\mathop \sum \limits_g \omega _{SA-g} = 1$. Based on South America's trade-to-GDP ratio with each G7 region and each G7 region's R&D stock, we have ΔTFP SA = −15.9%.
