Gravity with Intermediate Goods Trade

Sujin, Sujin; Song, E. Young Article Gravity with Intermediate Goods Trade East Asian Economic Review (EAER) Provided in Cooperation with: Korea Institute for International Economic Policy (KIEP), Sejong-si Suggested Citation: Sujin, Sujin; Song, E. Young (2017) : Gravity with Intermediate Goods Trade, East Asian Economic Review (EAER), ISSN 2508-1667, Korea Institute for International Economic Policy (KIEP), Sejong-si, Vol. 21, Iss. 4, pp. 295-315, https://doi.org/10.11644/KIEP.EAER.2017.21.4.332 This Version is available at: https://hdl.handle.net/10419/316528 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. 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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by/4.0/ PISSN 2508-1640 EISSN 2508-1667 an open access journal East Asian Economic Review vol. 21, no.4 (December 2017) 295-315 http://dx.doi.org/10.11644/KIEP.EAER.2017.21.4.332 ⓒ Korea Institute for International Economic Policy Gravity with Intermediate Goods Trade Sujin Jang Metro Seoul [email protected] E. Young Song Department of Economics Sogang University [email protected] This paper derives the gravity equation with intermediate goods trade. We extend a standard monopolistic competition model to incorporate intermediate goods trade, and show that the gravity equation with intermediates trade is identical to the one without it except in that gross output should be used as the output measure instead of value added. We also show that the output elasticity of trade is significantly underestimated when value added is used as the output measure. This implies that with the conventional gravity equation, the contribution of output growth can be substantially underestimated and the role of trade costs reduction can be exaggerated in explaining trade expansion, as we demonstrate for the case of Korea’s trade growth between 1995 and 2007. Keywords: Gravity Equation, Gross Output, Intermediate Goods Trade, Global Value Chains, Fragmentation JEL Classification: F12, F14, F15 I. INTRODUCTION Last several decades saw a huge increase in the trade of intermediate goods across countries. This phenomenon was driven by the rise of global supply chains, also called by various other names, such as fragmentation, unbundling, or vertical specialization of production. A production process is broken into a number of parts, which then are relocated in various countries of the world. As a result, unfinished products cross borders multiple times before they reach a final user, and trade volume increases relative to value added produced by trade. ID ID 296 Sujin Jang and E. Young Song ⓒ Korea Institute for International Economic Policy The new aspect of world trade can be understood by investigating world inputoutput tables or analyzing a computable general equilibrium model embodying worldwide input-output structure. Hummels, Ishii and Yi (2001), Yi (2003), Johnson and Noguera (2012), Bridgman (2012), and Koopman, Wang and Wei (2014) are notable examples in this line of research. An alternative approach is to modify the gravity equation to encompass intermediate goods trade. The gravity equation states that bilateral trade is proportional to the product of the masses of trading pairs, and is inversely related to trade costs between them. It has been the most powerful and popular tool for estimating the determinants of bilateral trade flows. The gravity model gained more traction in recent years since Eaton and Kortum (2002), Anderson and van Wincoop (2003), and Chaney (2008) strengthened its theoretical foundation by rigorously deriving it from muti-country Ricardian, Chamberlinian, and heterogeneous firms trade models. Modifying the gravity equation to incorporate intermediates trade should start from a simple observation that trade is measured in gross sales, while GDP is measured in value added. Most theoretical studies on the gravity equation assume the world without intermediates goods, and thus ignore the difference between gross sales and value added. Most empirical studies estimating the gravity equation use GDP to measure the mass of a country, either because trade theories ignoring the presence of intermediate goods justify its use, or because data on gross output are not easily available. However, one can conjecture that to obtain reliable results, either trade in terms of value added should be regressed on value added output, or trade in gross sales should be regressed on gross output. The former approach, as exemplified by Aichele and Heiland (2014), would require a complicated task of collapsing the inverse matrix coefficients of input-output tables into a manageable number of explanatory variables. Reduced gravity equations would be modelspecific or their coefficients would be difficult to link to structural parameters. In this paper, we take the latter approach of explaining gross trade by gross output. A number of researchers have estimated the gravity equation by regressing gross trade on gross output because it made more intuitive sense (e.g., Wei, 1996 and Novy, 2013). However, they do not offer any theoretical justification. The paper by Baldwin and Taglioni (2011), to our knowledge, is the first study that formally derives the gravity equation with intermediate goods trade, and emphasizes the importance of using gross output as the mass variable. We build Gravity with Intermediate Goods Trade 297 ⓒ 2017 East Asian Economic Review upon their results, and show that the mass variable of the gravity equation with intermediated goods trade should be gross output for the exporter, and gross output plus net imports for the importer. 1 We derive this result in a general setting where the ratio of value added to gross output responds to economic variables such that using value added as the mass variable generates errors-in-variables bias. Most trade models with intermediate goods (e.g., Krugman and Venables, 1996; Eaton and Kortum, 2002; Baldwin and Taglioni, 2011) assume that the production function for gross output is of Cobb-Douglas, and thus the ratio of value added to gross output is fixed. Under this assumption, value added is a perfect proxy for gross output, and the question that we raise in this paper becomes meaningless. A convenient feature of our gravity equation is that it holds both for aggregate trade and for sectoral level trade. A number of empirical studies on gravity estimate the gravity equation at sectoral level. Some studies aim to demonstrate that the elasticity of trade with respect to output, trade costs, or exchange rate volatility varies depending on the nature of goods, while others try to capture a trade pattern specific to an industry. Rauch (1999), Feenstra et al. (2001), Evans (2003), Saito (2004), Baldwin et al. (2005), and Anderson et al. (2014) are just a few such examples. In this line of research, it has never been entirely clear which mass variable should be used for the exporter and which for the importer. This paper provides a rigorous answer to this question. In addition, this paper tests whether the use of gross output as the mass variable improves the performance of the gravity equation over the popular practice of using value added as the mass variable. Baldwin and Taglioni (2011) also conduct a similar comparison. Because data on gross output are not widely available, they suggest using the sum of GDP and intermediate goods trade as a proxy, and show that the proxy performs better than GDP in gravity equation estimations. In this paper, we use gross output data from the World Input-Output Table (Timmer et al., 2015), and explicitly show that fluctuations in gross output to value added ratio generate downward bias in the estimation of the mass variable coefficient when value added is used as the mass variable. This implies that if we use the conventional gravity equation with value added as the mass variable, the contribution of output 1 Baldwin and Taglioni (2011) show that the mass variable for the exporter should be gross output, as we confirm here, and the one for the importer should be GDP plus the total costs of production, which is different from ours. In addition, we derive the gravity equation that holds both for aggregate trade and for sectoral level trade under a more general setting. 298 Sujin Jang and E. Young Song ⓒ Korea Institute for International Economic Policy growth can be substantially underestimated, and the role of trade costs reduction can be significantly exaggerated in explaining trade expansion. We demonstrate this possibility using the case of Korea’s trade growth between 1995 and 2007. This paper is organized as follows. In section II, we derive the gravity equation in the presence of intermediate goods trade from a monopolistic competition model with intermediate goods trade. In section III, we estimate the gravity equation, and compare the empirical performance of value added and gross output as the mass variable. Section III briefly concludes this paper. II. THEORY To introduce intermediate goods trade into the gravity theory, we utilize the framework used by Krugman and Venables (1996), Eaton and Kortum (2002), and Baldwin and Taglioni (2011). The essence of the idea is the assumption that each firm produces a good (or a service) that can be used both as an intermediate good and as a final good. We incorporate the idea into the monopolistic competition model by Krugman (1979) and Anderson and van Wincoop (2003), where all firms located in the same country are assumed to be symmetrical. There are 𝐾 industries in the world. Goods produced in industry 𝑚 are differentiated from each other and indexed on an interval 𝑁𝑚. Each firm produces only one good so that we can index firms by the index of goods. Firms located in country 𝑖 produces a subset of 𝑁𝑚, and let 𝑛𝑖𝑚 be its measure. Free entry prevails everywhere and the profit of each firm is equal to zero. To produce 𝑞 units of an industry 𝑚 good in country i, 𝑓𝑖𝑚+𝑎𝑖𝑚 𝑞 units of 𝑍𝑖𝑚 are required. 𝑓𝑖𝑚 is the fixed cost of production, and 𝑎𝑖𝑚 is the marginal cost, both measured in the unit of 𝑍𝑖𝑚. 𝑍𝑖𝑚 is a composite good, which is produced by a CES production function using local labor 𝐿𝑖𝑚 and composite intermediate goods 𝐺𝑖𝑚𝑘 (𝑘=1,…,𝐾): 𝑍𝑖𝑚=[(𝛼𝑚𝐿)1 𝜀𝑚 (𝐿𝑖𝑚)𝜀𝑚−1 𝜀𝑚+∑(𝛼𝑚𝑘)1 𝜀𝑚 (𝐺𝑖𝑚𝑘)𝜀𝑚−1 𝜀𝑚 𝐾 𝑘=1 ]𝜀𝑚 𝜀𝑚−1, (1) Gravity with Intermediate Goods Trade 299 ⓒ 2017 East Asian Economic Review 𝜀𝑚 is the elasticity of substitution among labor and composite inputs, and is assumed to be greater than one. 𝐺𝑖𝑚𝑘, composite intermediate good 𝑘 used in industry 𝑚 of country 𝑖, in turn, is made by assembling industry 𝑘 goods produced all over the world. 𝐺𝑖𝑚𝑘 =[ ∫𝑔𝑖𝑚 (𝑠)𝜎𝑘−1 𝜎𝑘 𝑠∈𝑁𝑘𝑑𝑠]𝜎𝑘 𝜎𝑘−1. (2) 𝑔𝑖𝑚 (𝑠) (𝑠∈𝑁𝑘) is the input of an industry 𝑘 good into composite intermediate good 𝐺𝑖𝑚𝑘. 𝜎𝑘 is the elasticity of substitution between 𝑔𝑖𝑚’s, and is greater than one. We assume that individual goods entering composite intermediate goods are tradable, but composite goods themselves are not tradable. Equation (2) implicitly assumes that 𝜎𝑘 does not depend on 𝑚, the industry that uses intermediate inputs. As we will see soon, this is a crucial assumption. The unit cost of 𝐺𝑖𝑚𝑘 is given by the following price index: 𝑃𝑖𝑘= [∫ (𝑝𝑖(𝑠))1−𝜎𝑘𝑑𝑠 𝑠∈𝑁𝑘]1 1−𝜎𝑘. (3) 𝑝𝑖 (𝑠) is the price of good s in country i. Denoting the wage rate in country i by 𝑊𝑖, using (1), the unit cost of 𝑍𝑖𝑚 can be written as: 𝑉𝑖𝑚= [𝛼𝑚𝐿(𝑊𝑖)1−𝜀𝑚+ ∑𝛼𝑚𝑘 (𝑃𝑖𝑘)1−𝜀𝑚 𝐾 𝑘=1 ]1 1−𝜀𝑚. (4) Thus the total cost of a country i firm producing 𝑞 units of an industry 𝑚 good is given by: 𝐶𝑖𝑚=(𝑓𝑖𝑚+𝑎𝑖𝑚 𝑞) 𝑉𝑖𝑚. (5) 300 Sujin Jang and E. Young Song ⓒ Korea Institute for International Economic Policy Denoting the marginal cost by 𝑐𝑖𝑚, 𝑐𝑖𝑚= 𝑎𝑖𝑚 𝑉𝑖𝑚. (6) Applying Shephard’s lemma to (4), we can obtain the shares of labor and composite intermediate goods in the total cost of a country 𝑖 firm in industry 𝑚: 𝛾𝑖𝑚𝐿 ≡𝑊𝑖 𝐿𝑖 𝑚 𝐶𝑖𝑚 =𝛼𝑚𝐿(𝑊𝑖 𝑉𝑖𝑚)1−𝜀𝑚 , (7) 𝛾𝑖𝑚𝑘 ≡𝑃𝑖𝑘 𝐺𝑖𝑚𝑘 𝐶𝑖𝑚 =𝛼𝑚𝑘(𝑃𝑖𝑘 𝑉𝑖𝑚)1−𝜀𝑚 . (8) Using (3), (4), and (8), we can derive the value of good 𝑠 that enters composite intermediate good 𝑘 used in industry 𝑚 of country 𝑖. 𝑝𝑖(𝑠) 𝑔𝑖𝑚(𝑠) =(𝑝𝑖(𝑠) 𝑃𝑖𝑘)1−𝜎𝑘𝛾𝑖𝑚𝑘 𝐶𝑖𝑚 for 𝑠∈𝑁𝑘. (9) The representative household in country i maximizes the following utility function. 𝑈𝑖=[∑(𝛼ℎ𝑘)1 𝜀ℎ𝐾 𝑘=1 (𝐺𝑖ℎ𝑘)𝜀ℎ−1 𝜀ℎ]𝜀ℎ 𝜀ℎ−1. (10) Here, superscript ℎ denotes the household, and 𝐺𝑖ℎ𝑘 is composite good 𝑘 consumed by the household as a final good. Again, it is made of industry 𝑘 goods produced all over the world: 𝐺𝑖ℎ𝑘 =[ ∫𝑔𝑖ℎ (𝑠)𝜎𝑘−1 𝜎𝑘 𝑠∈𝑁𝑘𝑑𝑠]𝜎𝑘 𝜎𝑘−1. (11) Gravity with Intermediate Goods Trade 301 ⓒ 2017 East Asian Economic Review Composite final good 𝑘 is assumed to be made in the same way as composite intermediate good 𝑘 used by industries. Equation (10) assumes that no direct labor is used to produce household utility. This restriction is not necessary, but we adopt it as it conforms to the structure of input-output tables. Using the same method as before, we can show that 𝑝𝑖(𝑠) 𝑔𝑖ℎ(𝑠) =(𝑝𝑖(𝑠) 𝑃𝑖𝑘)1−𝜎𝑘𝛾𝑖ℎ𝑘 𝐸𝑖 for 𝑠∈𝑁𝑘. (12) 𝐸𝑖 is the final expenditure of a country i, and is equal to its GDP plus its net imports. 𝛾𝑖ℎ𝑘 is the share of composite good 𝑘 in final expenditure, and is given by 𝛾𝑖ℎ𝑘 ≡𝑃𝑖𝑘 𝐺𝑖ℎ𝑘 𝐸𝑖 =𝛼ℎ𝑘(𝑃𝑖𝑘 𝑉𝑖ℎ)1−𝜀ℎ, (13) 𝑉𝑖ℎ= [∑𝛼ℎ𝑘 (𝑃𝑖𝑘)1−𝜀ℎ 𝐾 𝑘=1 ]1 1−𝜀ℎ. (14) To maximize the profit, a firm sets its price as a markup over the marginal cost, the markup rate determined by the price elasticity of its demand. By CES demand functions given in (9) and (12), the price elasticity for an industry 𝑘 good is given by 𝜎𝑘. Thus, 𝑝𝑖𝑗 𝑘= 𝜏𝑖𝑗 𝑘𝜎𝑘 𝜎𝑘−1 𝑐𝑖𝑘 . (15) 𝑝𝑖𝑗 𝑘 is the price of an industry 𝑘 good produced in country i and sold in country j. Here 𝜏𝑖𝑗 𝑘 (≥1) represents an iceberg-type transportation cost, and a firm in country i has to produce 𝜏𝑖𝑗 𝑘 units of a good to sell one unit in country j. Note that 𝑝𝑗(𝑠)= 𝑝𝑖𝑗 𝑘 if 𝑠∈𝑁𝑘 and 𝑠 is produced in country i. 302 Sujin Jang and E. Young Song ⓒ Korea Institute for International Economic Policy By (9)and (12), the value of good 𝑠 produced in industry 𝑘 of country 𝑖 and sold in country j, both as an intermediate good and as a final good, is determined by: 𝑥𝑖𝑗(𝑠)= (𝑝𝑖𝑗 𝑘 𝑃𝑗𝑘)1−𝜎𝑘 (∑𝛾𝑗𝑚𝑘𝑛𝑗𝑚𝐶𝑗𝑚 𝐾 𝑚=1 +𝛾𝑗ℎ𝑘𝐸𝑗). (16) Equation (16) is crucial for our result below. The essential feature of the equation that allows the gravity equation to follow from it is that demand for good 𝑠 in country 𝑗 is mutiplicatively separable between relative price (𝑝𝑖𝑗 𝑘𝑃𝑗𝑘 ⁄)1−𝜎𝑘 and total expenditure on good (∑𝛾𝑗𝑚𝑘𝑛𝑗𝑚𝐶𝑗𝑚 𝐾 𝑚=1 +𝛾𝑗ℎ𝑘𝐸𝑗). This property, in turn, follows from our assumption that composite input 𝑍𝑚 for producing an industry 𝑚 good is produced by a nested CES function of subinputs 𝐺𝑚𝑘’s given in (1), and the additional assumption that 𝜎𝑘, the elasticity of substitution between individual industry 𝑘 goods in the production of subinput 𝐺𝑚𝑘 , does not depend on 𝑚, as assumed in (2). The rest of derivation is straightforward. Because 𝑥𝑖𝑗(𝑠) is identical for all industry 𝑘 firms in country 𝑖, the total value of industry 𝑘 goods exported from country 𝑖 to country 𝑗 is equal to: 𝑋𝑖𝑗 𝑘=𝑛𝑖𝑘(𝑝𝑖𝑗 𝑘 𝑃𝑗𝑘)1−𝜎𝑘 (∑𝛾𝑗𝑚𝑘𝑛𝑗𝑚𝐶𝑗𝑚 𝐾 𝑚=1 +𝛾𝑗ℎ𝑘𝐸𝑗). (17) From the assumption that the profit of each firm is zero, the total costs incurred by industry 𝑚 firms in country 𝑗 (𝑛𝑗𝑚𝐶𝑗𝑚) is equal to the gross output of industry 𝑚 in country j, which we denote by 𝐺𝑂𝑗𝑚. Then we can show that: ∑𝛾𝑗𝑚𝑘𝑛𝑗𝑚𝐶𝑗𝑚 𝐾 𝑚=1 +𝛾𝑗ℎ𝑘𝐸𝑗= 𝐺𝑂𝑗𝑘+ 𝐼𝑀𝑗𝑘−𝐸𝑋𝑗𝑘 . (18) Equation (18) is an accounting identity that holds in any input-output model: the total value of industry 𝑘 goods used in a country, both as intermediates and final goods, must be equal to the total value of industry 𝑘 goods supplied to the country, Gravity with Intermediate Goods Trade 309 ⓒ 2017 East Asian Economic Review Table 2. Continued ln 𝑋𝑖𝑗 (4) (5) (6) Common Currency -0.08*** (0.03) -0.07** (0.03) -0.07** (0.03) RTA 0.18*** (.04) 0.19*** (.04) 0.19*** (.04) Fixed Effects year exporterimporter year exporterimporter year exporterimporter R2 0.44 0.45 0.45 Obs. 20,274 20,274 20,274 Note: Some bilateral costs variables in Tables 1 and 2 are dropped because they are constant over time. The intercepts are not reported. The numbers in the parentheses are robust standard errors clustered by country-pairs. R2s are from within regressions. As we emphasized before, our gravity equation holds both for aggregate trade and for industry level trade. Relying on this feature, we estimated gravity equations for 14 manufacturing industries. Regression results vary a lot from industry to industry. However, in almost all industries, using valued added alone as the mass variable results in the underestimation of its coefficient, and using gross output instead significantly raises the estimated coefficient. In addition, in all industries, the estimated coefficient of ln (𝐺𝑂𝑖𝐺𝑂𝑗) (𝑉𝐴𝑖𝑉𝐴𝑗 ⁄) is large and significant at 1 percent when it is included together with ln𝑉𝐴𝑖𝑉𝐴𝑗. Table 3 reports results for three selected industries. To save space, the results when ln𝐺𝑂𝑖𝐺𝑂𝑗 alone is used as the mass variable are not reported. Cokes and refined petroleum industry represents the case where the coefficient of the mass variable is the most underestimated when value added alone is included as the mass variable. The estimated coefficient of ln𝑉𝐴𝑖𝑉𝐴𝑗 is equal to 0.20, but it increases to 0.77 when ln (𝐺𝑂𝑖𝐺𝑂𝑗) (𝑉𝐴𝑖𝑉𝐴𝑗 ⁄) also is included. The huge increase probably stems from the fact that oil price changes caused big swings of gross output to value added ratio in the oil-using industry. Basic and fabricated metals industry represents a median case. The coefficient of ln𝑉𝐴𝑖𝑉𝐴𝑗 modestly increases from 0.81 to 1.00 when ln (𝐺𝑂𝑖𝐺𝑂𝑗) (𝑉𝐴𝑖𝑉𝐴𝑗 ⁄) is included. Though not reported, similar results hold for most other industries. General machinery industry is selected as the case where the coefficient of the mass variable is the 310 Sujin Jang and E. Young Song ⓒ Korea Institute for International Economic Policy least underestimated with value added used as the mass variable. It increases from 0.84 to 0.87 with the inclusion of ln (𝐺𝑂𝑖𝐺𝑂𝑗) (𝑉𝐴𝑖𝑉𝐴𝑗 ⁄). This small increase is not observed in the other industries. We also ran regressions for individual manufacturing industries controlling for exporter-importer pair fixed effects. Though we do not report here, the coefficients of the mass variables change little. Table 3. Value Added Vs. Gross Output in the Gravity Equation in Selected Industries Cokes and Refined Petroleum Basic and Fabricated Metals General Machinery ln 𝑋𝑖𝑗 (7) (8) (9) (10) (11) (12) ln 𝑉𝐴𝑖𝑉𝐴𝑗 0.20*** (0.03) 0.77*** (0.06) 0.81*** (0.05) 1.00*** (0.05) 0.84*** (0.05) 0.87*** (0.05) ln (𝐺𝑂𝑖𝐺𝑂𝑗) (𝑉𝐴𝑖𝑉𝐴𝑗 ⁄) 0.88*** (0.06) 1.19*** (0.12) 0.73*** (0.11) ln𝑁𝑒𝑡 𝐼𝑚𝑝𝑜𝑟𝑡𝑠𝑗 0.19* (0.11) -0.12 (0.13) 0.69*** (0.12) 0.04 (0.13) 0.66*** (0.10) 0.08 (0.12) ln Distance -2.38*** (0.10) -2.36*** (0.10) -1.68*** (0.08) -1.68*** (0.08) -1.37*** (0.07) -1.37*** (0.07) Contiguity 0.65*** (0.23) 0.66*** (0.23) 0.31* (0.17) 0.31* (0.17) 0.26 (0.18) 0.25 (0.18) Common language -0.04 (0.21) -0.05 (0.21) 0.37** (0.17) 0.37** (0.17) 0.18 (0.15) 0.17 (0.15) Colony 0.56** (0.22) 0.58** (0.22) 0.29 (0.21) 0.29 (0.21) 0.47** (0.21) 0.47** (0.21) Common Currency -0.52*** (0.14) -0.50*** (0.14) -0.41*** (0.08) -0.41*** (0.08) -0.61*** (0.08) -0.58*** (0.08) RTA -0.20 (0.14) -0.12 (0.14) 0.09 (0.10) 0.09 (0.10) -0.07 (0.09) -0.05 (0.09) Fixed Effects year exporter importer year exporter importer year exporter importer year exporter importer year exporter importer year exporter importer R2 0.74 0.74 0.84 0.84 0.85 0.85 Obs. 20,274 20,274 20,274 20,274 20,274 20,274 Note: The intercepts are not reported. The numbers in the parentheses are robust standard errors clustered by country-pairs. Gravity with Intermediate Goods Trade 311 ⓒ 2017 East Asian Economic Review The question that we are pursuing here is whether we should use value added or gross output to correctly estimate the elasticity of trade with respect to output. The literature on the gravity equation, however, has moved away from the issue. The gravity equation is mainly used as a tool for evaluating the effect on trade volume of shocks reducing trade barriers, such as free trade agreements, currency unions, or lower transportation costs. Therefore, researchers’ interests converged on correctly estimating the elasticities of trade with respect to trade frictions. These elasticities can be consistently estimated in the gravity equation without specifying the mass variable. Instead of using ln𝑉𝐴𝑖𝑉𝐴𝑗 as a single regressor, we could place ln𝑉𝐴𝑖 and ln𝑉𝐴𝑗 as separate regressors, and let them be subsumed by exporter and importer fixed effects. One research area where this strategy is not workable is to decompose observed trade volume changes into component parts: the contribution of output changes, the contribution of transportation costs changes, and the contribution of trade policy changes. Notable examples in this line of research are Baier and Bergstrand (2001), Estevadeordal, Frantz, and Taylor (2003), and Novy (2013). Here we have to correctly specify the mass variable and correctly estimate its coefficient not to underestimate the role of output and hence overestimate the role of trade frictions in trade volume changes. 5 To get a sense on how important the correct specification of the mass variable is in decomposing trade expansion, we construct Table 4. Column (1) shows the growth of Korea’s manufactured exports to the world and its top 10 importers between 1995 and 2007. Columns (2) and (3), respectively, display the ratio of percentage increase in value added to percentage increase in exports, and the ratio of percentage increase in gross output to percentage increase in exports. Column (4) shows the ratio of percentage increase in importer’s net imports to percentage increase in exports. The numbers in the third row, which accounts for Korea’s exports to the world, are obtained by calculating the weighted averages of the numbers corresponding to individual countries, each weight given by the average share of an importer in Korea’s total exports during the period. 6 The row shows that Korea’s manufactured exports grew 113% during the period, and 75% of the 5 Correctly estimating the output elasticity of trade is also important in understanding the recent slowdown of world trade relative to GDP growth. See Constantinescu, Mattoo and Ruta (2015). 6 The World Input-Output Database provides Korea’s exports to 39 other countries and the rest of the world. The rest of the world accounts for 26 percent of Korea’s total exports. 312 Sujin Jang and E. Young Song ⓒ Korea Institute for International Economic Policy growth can be attributed to the growth of valued added produced by Korea and its trading partners. The number increases to 84% when gross output is used instead of value added as the output variable. This is because the ratio of gross output to value added increased in Korea and other countries. Column (4) shows that the part explained by importer’s net imports is small at -1.4%. The following rows report results for individual countries. They vary a lot from country to country. However, we can notice that for all countries, the part explained by gross output is larger than that by valued added. The part explained by importer’s net imports is large in some countries. Table 4. Decomposing Korea’s Manufacturing Export Growth Between 1995 and 2007 (Unit: percent) Importer ∆ln𝑋𝑖𝑗 ∆ln(𝑉𝐴𝑖𝑉𝐴𝑗ln𝑉𝐴𝑊 ⁄) ∆ln𝑋𝑖𝑗 ∆ln(𝐺𝑂𝑖𝐺𝑂𝑗ln𝐺𝑂𝑊 ⁄) ∆ln𝑋𝑖𝑗 ∆ln𝑁𝑒𝑡 𝐼𝑚𝑝𝑜𝑟𝑡𝑠𝑗 ∆ln𝑋𝑖𝑗 0.89×(2) (1) (2) (3) (4) (5) World 112.9 74.9 83.5 -1.4 66.7 USA 50.7 118.6 137.1 10.6 105.6 China 191.3 91.8 103.0 -3.1 81.7 Japan 28.0 -25.4 20.3 -12.9 -22.6 Taiwan 103.4 47.6 58.3 -17.0 42.4 Germany 79.4 66.0 72.8 -20.0 58.8 RUS 217.3 68.2 72.7 0.9 60.7 CAN 68.0 116.4 144.0 10.6 103.6 MEX 241.0 53.3 54.4 2.3 47.4 GBR 70.8 77.9 99.0 15.1 69.3 AUS 109.8 71.9 87.9 5.2 64.0 Column (5) was obtained by multiplying 0.89, the estimated coefficient of ln𝑉𝐴𝑖𝑉𝐴𝑗 in Tables 1 and 2, to column (2). Thus, the gravity equation using value added as the mass variable would have attributed 67% of Korea’s export growth to increases in the output scales of Korea and its partners, implying that the contribution of lower trade costs can be as large as 33%. The number increases to 84% when we use gross output as the mass variable, reducing the room for the contribution of trade costs to 16%. This increase is due to the increase in gross Gravity with Intermediate Goods Trade 313 ⓒ 2017 East Asian Economic Review output to value added ratio, and the increase in the estimated coefficient of the mass variable. The increase is not large, but substantial. IV. CONCLUSION In this paper, we propose a simple solution to the problem of estimating the gravity equation in the presence of intermediate goods trade. All we have to do is to use gross output in place of value added as the mass variable. This method can reduce bias coming from fluctuations in gross output to value added ratio, which would naturally arise in the world where intermediate goods are heavily traded through global supply networks. Through some empirical exercises, we show that bias is not quite large, but significant for the gravity equation in manufacturing trade. However, huge bias can arise for an industry level gravity equation, as we demonstrate in the case of petroleum refining industry. We also show that this bias can result in exaggerating the role of reduced trade barriers in explaining the recent expansion of world trade. In the case of Korea’s export growth between 1995 and 2007, the possible contribution of reduced trade barriers shrinks from 33% to 16% of Korea’s total export growth. This suggests that the effect of trade policy changes like the Korea- US FTA or the Korea-EU FTA could be substantially overestimated with the conventional gravity equation using GDP as the mass variable. One limitation of our study is that our empirics focused only on the period in which world trade rapidly expanded with the rise of global value chains. It will be an interesting exercise to test whether our findings are still valid for the period after 2011, in which world trade shrank relative to GDP. 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