Estimating gravity equations for trade in value added: A structural perspective

Heiland, Inga; Šváb, Patrik Article — Published Version Estimating gravity equations for trade in value added: A structural perspective Economics Letters Provided in Cooperation with: Kiel Institute for the World Economy – Leibniz Center for Research on Global Economic Challenges Suggested Citation: Heiland, Inga; Šváb, Patrik (2025) : Estimating gravity equations for trade in value added: A structural perspective, Economics Letters, ISSN 1873-7374, Elsevier, Amsterdam, Vol. 254, pp. 1-5, https://doi.org/10.1016/j.econlet.2025.112476 This Version is available at: https://hdl.handle.net/10419/330838 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. http://creativecommons.org/licenses/by/4.0/ Contents lists available at ScienceDirect Economics Letters journal homepage: www.elsevier.com/locate/ecolet Estimating gravity equations for trade in value added: A structural perspective Inga Heilanda,b,c,∗, Patrik Šváb d aNorwegian University of Science and Technology Trondheim, Klæbuveien 72, 7030 Trondheim, Norway bUniversity of Oslo, Norway cKiel Institute for the World Economy, Kiellinie 66, 24105 Kiel, Germany dFaculty of International Relations, Prague University of Economics and Business, nám. Winstona Churchilla 1938/4, 130 67 Prague 3, Czech Republic A R T I C L E I N F O Dataset link:replication package (Original data ) JEL classification: F12 F15 Keywords: Structural gravity Trade in value added A B S T R A C T A large number of recent papers employ value-added trade data alongside traditional gross measures of trade to estimate the impact of various trade costs on bilateral trade. Value-added gravity equations are typically justified by referencing the theoretical and empirical merits of traditional gravity equations for gross trade. Contradicting this notion, we use theory and simulations to show that value-added gravity equations are misspecified when the gross trade gravity equation is correct. Consequently, estimates from value-added gravity equations are difficult to interpret and prone to omitted variables bias. 1. Introduction Many recent papers employ value-added (VA) trade data alongside with traditional gross measures of trade to estimate the impact of various trade costs on bilateral trade.1 VA gravity equations are typically justified by citing the theoretical and empirical merits of traditional gravity equations for gross trade. Contradicting this view, we demonstrate that if bilateral gross trade follows gravity, the bilateral VA trade gravity equations are misspecified. We employ a simple model of gross trade and VA trade to pinpoint the origin of the misspecification and conduct simulation exercises to assess the importance of the issues in a controlled setting. Our results indicate that both the external and internal validity of partial trade cost elasticities estimated with reduced-form VA gravity equations are limited. Specifically, we point out three issues. We use indicators for regional trade agreements (RTAs) to illustrate them, but our findings apply to any trade cost variable. First, the theoretical general gravity equation for VA trade, which we derive from a structural gravity model for ∗Corresponding author at: Norwegian University of Science and Technology Trondheim, Klæbuveien 72, 7030 Trondheim, Norway. E-mail address: [email protected] (I. Heiland). 1Our search of the Web of Science and the OECD iLibrary returned 35 published academic papers and 4 policy reports (listed in the Appendix) that employ reduced-form gravity equations with measures of bilateral VA trade flows as the left-hand-side variable. 2Our definition of general and structural gravity equations follows Head and Mayer (2014). 3In several of these papers, the issue of third-country effects is discussed, though only a few papers attempt to tackle the misspecification problem, using either the methodology proposed by Noguera (2012) (see Laget et al., 2020; Kang and Gapay, 2024) or non-structurally motivated interaction terms (Mulabdic et al., 2017; Boffa et al., 2019; Sanguinet et al., 2022). gross trade2, implies that the partial effects of RTAs are not comparable across samples, agreements, and time periods, and are not informative for future agreements. Second, the theory implies that trade cost changes have heterogeneous effects on bilateral VA trade between third countries. This implies that the estimated partial elasticities of RTAs for member countries are confounded by indirect effects on non-member countries. Third, changes in other determinants of trade between third countries happening elsewhere in the world will bias the RTA estimate unless both members’ and non-members’ GVCs are equally exposed to the third-country shock. Given that countries’ GVCs are very different, such biases are generally likely and ambiguous in direction. We are not the first to point out that trade cost elasticities obtained from reduced-form VA gravity equations are problematic from a structural point of view; Noguera (2012) derived a theory-grounded log-linear VA gravity equation with control terms for indirect trade cost effects. However, the majority of empirical studies have continued to use simple log-linear estimation models.3 Moreover, we show that https://doi.org/10.1016/j.econlet.2025.112476 Received 26 March 2025; Received in revised form 26 June 2025; Accepted 27 June 2025 Economics Letters 254 (2025) 112476 Available online 9 July 2025 0165-1765/© 2025 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license ( http://creativecommons.org/licenses/by/4.0/ ). I. Heiland and P. Šváb the indirect effects of a potentially prohibitively large set of other third-country shocks – including country-specific ones like productivity growth and infrastructure development – also confound estimates of the partial effects of trade cost shocks on VA trade. 2. A general gravity equation for value added 2.1. The theoretical model We set up a model of bilateral trade between 𝑁 countries, indexed by 𝑖, 𝑗, 𝑘, 𝑛, ℎ. Our analysis rests on two core assumptions. (A1). Final goods trade 𝐶𝑖𝑛 and intermediate goods trade 𝐴𝑖𝑛 from country 𝑖 to country 𝑛 follow general gravity equations, respectively given by 𝐶𝑖𝑛 =𝜋𝑖𝑛𝐶𝑛and 𝐴𝑖𝑛 =𝜋𝑖𝑛𝐴𝑛with 𝜋𝑖𝑛 =𝜏−𝜀 𝑖𝑛 𝛹𝑖𝛷𝑛 𝛷𝑛= 𝑁 ∑ ℎ=1 𝜏−𝜀 ℎ𝑛 𝛹ℎ , where 𝐴𝑛=∑𝑖𝐴𝑖𝑛 and 𝐶𝑛=∑𝑖𝐶𝑖𝑛.4 A1 stipulates that trade shares 𝜋𝑖𝑛 are identical for final and intermediate goods, implying that total trade also follows a general gravity equation: 𝑋𝑖𝑛 =𝜏−𝜀 𝑖𝑛 𝑋𝑛 𝛹𝑖𝛷𝑛 ,(1) where 𝑋𝑛=𝐴𝑛+𝐶𝑛. (A2). For every country 𝑛, the ratio of VA to output, denoted by 𝑣𝑛, is constant. A2 implies that the ratio of expenses for intermediates to country 𝑛’s output is (1 − 𝑣𝑛) and A1 and A2 together imply that the share of intermediates sourced directly from 𝑖 in output of 𝑛 is 𝑎𝑖𝑛 =𝜋𝑖𝑛(1 − 𝑣𝑛). We use 𝐚 to denote the 𝑁×𝑁 matrix of direct input coefficients 𝑎𝑖𝑛 and 𝐁= (𝐈−𝐚)−1 to denote the corresponding Leontief inverse with typical element 𝑏𝑖𝑛. Definition 1. VA exports from 𝑖 to 𝑛, 𝑉 𝐴𝑖𝑛, are defined as VA that originates in 𝑖 and is consumed in 𝑛. This definition follows Johnson and Noguera (2012) and leads us to the following result: Proposition 1. Under A1 and A2, bilateral VA exports are given by 𝑉 𝐴𝑖𝑛 =𝑣𝑖𝐶𝑛 𝛷𝑛(𝑁 ∑ ℎ 𝑏𝑖ℎ𝜏−𝜀 ℎ𝑛 𝛹ℎ),(2) where 𝑏𝑖ℎ =𝑓[{𝜏𝑗𝑘, 𝛹𝑗, 𝛷𝑘, 𝜈𝑘}𝑁 𝑗,𝑘=1 , 𝜀]. Proof. It follows from 𝐴2 and Definition 1 that 𝑉 𝐴𝑖𝑛 =𝑣𝑖(∑𝑁 ℎ𝑏𝑖ℎ𝐶ℎ𝑛). Substituting 𝐶ℎ𝑛 and 𝜋ℎ𝑛 from A1 yields (2). The dependency of 𝑏𝑖ℎ on the trade cost, multilateral resistance terms, and value added coefficients of other countries is due to the fact that 𝑏𝑖ℎ is a function of all input coefficients in 𝐚. Proposition 1 has two important implications. First, 𝑉 𝐴𝑖𝑛 is not log-proportional to 𝜏𝑖𝑛. Second, 𝑉 𝐴𝑖𝑛 depends in a non-trivial way on the determinants of trade between third countries. Intuitively, this is because VA from 𝑖 reaches 𝑛 embodied in goods processed elsewhere. The indirect nature of VA flows is, of course, well known and variants 4Trade shares 𝜋 of this form are implied, e.g., by the model of Eaton and Kortum (2002) or the Armington model of Anderson and Van Wincoop (2003) of (2) have been employed to quantify the impact of trade cost changes on VA trade in computable general equilibrium models.5 The purpose of deriving (2) is to enable a structural interpretation of the coefficients that are estimated by ad-hoc VA gravity equations. This allows us to pinpoint a set of problematic issues that arise under the commonly employed reduced-form approach.6 2.2. Estimating the impact of RTAs on (VA) trade To map our setup directly into commonly used panel estimation frameworks, we add a time dimension indexed by 𝑡 and employ two additional assumptions: (A3). Bilateral trade costs depend on RTAs and a vector of other observable trade barriers 𝑍𝑖𝑛𝑡 according to 𝜏𝑖𝑛𝑡 = exp {𝛿𝑅𝑇 𝐴𝑖𝑛𝑡 +𝜈𝑍𝑖𝑛𝑡}.(3) Combining (4) and (3), we derive the empirical gravity equation for gross trade ln 𝑋𝑖𝑛𝑡 =𝛽𝑋𝑅𝑇 𝐴𝑖𝑛𝑡 +𝜈𝑍𝑖𝑛𝑡 +𝛾𝑖𝑡 +𝛾𝑛𝑡 +𝛾𝑖𝑛 +𝑢𝑖𝑛𝑡.(4) where 𝛾𝑖𝑡, 𝛾𝑛𝑡, 𝛾𝑖𝑛 are fixed effects. Henceforth, we use 𝜻𝒊𝒏𝒕 to denote the vector of covariates in (4). (A4). Exogeneity of the covariates E[𝑢𝑖𝑛𝑠|𝜻𝑖𝑛𝑡]= 0 for 𝑠, 𝑡 = 1,…, 𝑇 . Under A4, (1) and (4) imply that the elasticity of gross trade to a trade cost change that is due to a change in RTA membership is 𝛽𝑋=𝜕E[ln 𝑋𝑖𝑛𝑡|𝜻𝒊𝒏𝒕] 𝜕𝑅𝑇 𝐴𝑖𝑛𝑡 = −𝜀𝛿. (5) In analogy to (4), VA gravity equations employ (variants of) the empirical model ln 𝑉 𝐴𝑖𝑛𝑡 =𝛽𝑉 𝐴𝑅𝑇 𝐴𝑖𝑛𝑡 +𝜈𝑉 𝐴𝑍𝑖𝑛𝑡 +𝛾𝑖𝑡 +𝛾𝑛𝑡 +𝛾𝑖𝑛 +𝜖𝑖𝑛𝑡 (6) to estimate 𝛽𝑉 𝐴 =𝜕E[ln 𝑉 𝐴𝑖𝑛𝑡|𝜻𝒊𝒏𝒕] 𝜕𝑅𝑇 𝐴𝑖𝑛𝑡 . However, the theoretical VA gravity Eq. (2) implies several issues that complicate the estimation of (6). Issue (1): Coefficient heterogeneity. According to (2) and (3), the elasticity of VA trade to a change in RTA membership is 𝜕ln 𝑉 𝐴𝑖𝑛𝑡 𝜕𝑅𝑇 𝐴𝑖𝑛𝑡 =𝜕ln 𝑉 𝐴𝑖𝑛𝑡 𝜕(ln 𝜏−𝜀 𝑖𝑛𝑡 )(−𝜀𝛿)(7) where 𝜕ln 𝑉 𝐴𝑖𝑛𝑡 𝜕(ln 𝜏−𝜀 𝑖𝑛𝑡 )=𝜕(ln 𝐶𝑛𝑡∕𝛷𝑛𝑡) 𝜕(ln 𝜏−𝜀 𝑖𝑛𝑡 )+𝜔𝑖𝑖𝑛𝑡 +∑ ℎ 𝜔𝑖ℎ𝑛𝑡 (𝜕ln 𝑏𝑖ℎ𝑡 𝜕(ln 𝜏−𝜀 𝑖𝑛𝑡 )−𝜕ln 𝛹ℎ𝑡 𝜕(ln 𝜏−𝜀 𝑖𝑛𝑡 )) and 𝜔𝑖ℎ𝑛𝑡 =𝑏𝑖ℎ𝑡𝜏−𝜀 ℎ𝑛𝑡𝛹−1 ℎ𝑡 ∑𝑗𝑏𝑖𝑗𝑡𝜏−𝜀 𝑗𝑛𝑡𝛹−1 𝑗𝑡 . Note that 𝜕ln 𝑉 𝐴𝑖𝑛𝑡 𝜕𝑅𝑇 𝐴𝑖𝑛𝑡 depends on characteristics of the pair 𝑖, 𝑛. Thus, the best we can aim for by estimating (6) is the sample average of 𝜕E[ln 𝑉 𝐴𝑖𝑛𝑡|𝜻𝑖𝑛𝑡] 𝜕𝑅𝑇 𝐴𝑖𝑛𝑡 for the pairs whose RTA status changes. The magnitude of this average effect, which we denote with 𝛽𝑉 𝐴,𝑡𝑟𝑒𝑎𝑡𝑒𝑑, will depend on the set of country pairs and the time period included in the estimation, even if the actual data were generated by a process consistent with A1–A4. In contrast,  𝛽𝑋,𝑡𝑟𝑒𝑎𝑡𝑒𝑑 estimates −𝜀𝛿 under A1–A4, independent of the sample composition. 5E.g., Johnson and Noguera (2017) and Felbermayr et al. (2022) employ quantitative trade models featuring gravity in intermediate and final goods trade to structurally estimate the partial effect of RTAs on gross trade and then calculate the corresponding changes in the world input–output matrix and the new VA trade flows. 6While our focus is on VA exports, the logic we outline extends to related measures such as the domestic VA content of exports or imports or the carbon content of trade. Economics Letters 254 (2025) 112476 2 I. Heiland and P. Šváb Issue (2): Lack of control group. Under A2, VA exports from 𝑗 reach 𝑘 via every possible route. This implies that a reduction in 𝜏𝑖𝑛, e.g., due to a bilateral RTA between 𝑖 and 𝑛 also benefits VA trade from 𝑗 to 𝑘 that travels via 𝑖 and 𝑛. Formally, except for knife-edge cases, 𝜕ln 𝑉 𝐴𝑗𝑘𝑡 𝜕ln(𝜏−𝜀 𝑖𝑛𝑡 )≠0 ∀ 𝑖, 𝑛, 𝑗, 𝑘. (8) For example, for two countries 𝑗, 𝑘, which are not part of the RTA, the effect is 𝜕ln 𝑉 𝐴𝑗𝑘𝑡 𝜕(ln 𝜏−𝜀 𝑖𝑛𝑡 )=𝜕ln(𝐶𝑘𝑡∕𝛷𝑘𝑡) 𝜕(ln 𝜏−𝜀 𝑖𝑛𝑡 )+∑ ℎ 𝜔𝑗ℎ𝑘𝑡 (𝜕ln 𝑏𝑗ℎ𝑡 𝜕(ln 𝜏−𝜀 𝑖𝑛𝑡 )−𝜕ln 𝛹ℎ𝑡 𝜕(ln 𝜏−𝜀 𝑖𝑛𝑡 )) Like the partial effect on the ‘‘treated’’ country pairs, the effect on ‘‘untreated’’ pairs is heterogeneous. Issue 2 implies that, under A1–A4, we will never be able to recover the (sample-dependent) 𝛽𝑉 𝐴,𝑡𝑟𝑒𝑎𝑡𝑒𝑑 . Hence, we will at best be able to identify the difference between the average effect of the RTA on members’ VA trade with each other and the average effect on all other, indirectly affected pairs:  𝛽𝑉 𝐴 = 𝛽𝑉 𝐴,𝑡𝑟𝑒𝑎𝑡𝑒𝑑 − 𝛽𝑉 𝐴,𝑢𝑛𝑡𝑟𝑒𝑎𝑡𝑒𝑑.(9) Issue (3): Omitted variables bias. The non-zero cross derivatives in (8) imply more generally that the effect of a given RTA cannot be identified separately from any trade cost change happening elsewhere in the world. Since 𝜕ln 𝑉 𝐴𝑖𝑛𝑡 𝜕ln(𝜏−𝜀 𝑗𝑘𝑡) is non-zero and pair specific, i.e., not absorbed by exporter and importer fixed effects, any trade cost change across the world that coincides with the change in 𝑅𝑇 𝐴𝑖𝑛 will bias the coefficient  𝛽𝑉 𝐴, except in special cases. Moreover, omitted variables bias is not limited to trade cost. In fact, even changes in the countryspecific parameters 𝛹ℎ and 𝑣ℎ, that influence 𝑉 𝐴𝑖𝑛𝑡 through the Leontief coefficients in (2), will bias the coefficient if they coincide with the formation of the RTA. 3. Quantification of heterogeneity and bias 3.1. Methodology In this section, we demonstrate the quantitative importance of the abovementioned issues in a controlled simulation setting where A1–A4 hold. We use a variant of the model of Aichele and Heiland (2018) to simulate the exact partial and general equilibrium effects of a hypothetical RTA on gross trade and VA trade.7 The model satisfies A1 and A2, and we simulate trade cost shocks that satisfy A3 and A4. Specifically, we assume that the set of countries 𝐵 ⊂ 𝑁 forms an RTA that reduces trade cost among members by 10% (𝛿=.9) and a trade elasticity 𝜀= −5. The model yields counterfactual changes  𝑋𝑖𝑛 =𝑋′ 𝑖𝑛∕𝑋0 𝑖𝑛, where 𝑋0 𝑖𝑛 (𝑋′ 𝑖𝑛) is gross bilateral trade in the baseline (counterfactual) equilibrium, and, analogously, counterfactual changes in VA trade,  𝑉 𝐴𝑖𝑛 =𝑉 𝐴′ 𝑖𝑛∕𝑉 𝐴0 𝑖𝑛 for 𝑖, 𝑛 ∈𝑁. Our assumptions imply that we can recover the partial effect of the RTA on gross trade from the regression ln  𝑋𝑖𝑛 =𝛽𝑋𝑅𝑇 𝐴𝑖𝑛 +𝜇𝑖+𝜇𝑛+𝑢𝑖𝑛,(10) where 𝑅𝑇 𝐴𝑖𝑛 equals one for 𝑛, 𝑖 ∈𝐵, 𝑛 ≠𝑖 and zero otherwise. 𝛽𝑋 observes 𝑒𝛽𝑋=𝛿𝜀. In analogy to (10), we set up the ad-hoc log linear estimation equation ln  𝑉 𝐴𝑖𝑛 =𝛽𝑉 𝐴𝑅𝑇 𝐴𝑖𝑛 +𝜇𝑖+𝜇𝑛+𝜀𝑖𝑛 (11) to study the properties of  𝛽𝑉 𝐴. 7The model baseline is calibrated to match production and bilateral trade of 65 countries and the rest of the world in the OECD ICIO database in 2018. Fig. 1. BRICS, effects on RTA-members vs. Non-members. 3.2. Results First, we focus on the extent of heterogeneity that is concealed by the average partial effect (issue 1). To that end, we simulate the following scenario: Scenario 1 (‘‘𝐵𝑅𝐼𝐶𝑆’’). We assume that the BRICS countries (Brazil, Russia, India, China, and South Africa) form an RTA that reduces trade costs between RTA members by 10%. To quantify the heterogeneity, we calculate the distribution of the partial VA trade effects of the RTA across all possible quadruples with one treated pair. Starting with gross trade as a reference point, A1 implies ln ( 𝑋𝑖𝑛∕ 𝑋𝑖𝑗  𝑋𝑘𝑛∕ 𝑋𝑘𝑗 )=𝛽𝑋if 𝑅𝑇 𝐴𝑖𝑛 = 1, 𝑅𝑇 𝐴𝑖𝑗 , 𝑅𝑇 𝐴𝑘𝑛, 𝑅𝑇 𝐴𝑘𝑗 ≠1. (12) The partial trade effect is constant across members of the RTA and independent of the composition of the control group. In contrast, every RTA member experiences a different partial VA trade effect, and so does every non-member. Hence, the distribution of ln ( 𝑉 𝐴𝑖𝑛∕ 𝑉 𝐴𝑖𝑗  𝑉 𝐴𝑘𝑛∕ 𝑉 𝐴𝑘𝑗 )for 𝑅𝑇 𝐴𝑖𝑛 = 1, 𝑅𝑇 𝐴𝑖𝑗 , 𝑅𝑇 𝐴𝑘𝑛, 𝑅𝑇 𝐴𝑘𝑗 ≠1 (13) is non-degenerate. Fig. 1 (dashed blue line) shows the distribution of the RTA effects across quadruples. The partial VA effects are smaller than the partial effect on gross trade on average, but span a wide range. Fig. 2 plots the distribution of the RTA effects on the control groups, calculated as ln ( 𝑉 𝐴𝑖𝑛∕ 𝑉 𝐴𝑖𝑗  𝑉 𝐴𝑘𝑛∕ 𝑉 𝐴𝑘𝑗 )for 𝑅𝑇 𝐴𝑖𝑛, 𝑅𝑇 𝐴𝑖𝑗 , 𝑅𝑇 𝐴𝑘𝑛, 𝑅𝑇 𝐴𝑘𝑗 ≠1.(14) As implied by (8), the effects are non-zero and heterogeneous across pairs. Table 1 shows the estimate of 𝛽𝑉 𝐴 from (11) in column 1. The implied average partial VA trade change is (𝑒𝛽𝑉 𝐴 − 1) ∗ 100% = 54.97%. To illustrate that the estimate of the VA trade cost elasticity depends on the composition of the estimation sample, we analyze two additional scenarios: Scenario 2: ‘‘𝐵𝑅𝐼𝐶𝑆 +𝑇 𝑇 𝐼𝑃 ’’. In parallel with the formation of the 𝐵𝑅𝐼𝐶𝑆 agreement as defined in Scenario 1, another RTA (called ‘‘TTIP’’) is formed between the U.S. and all EU27 members, which also reduces trade costs between members by 10%. Economics Letters 254 (2025) 112476 3 I. Heiland and P. Šváb Fig. 2. BRICS, effects on Non-members. Table 1 Partial VA trade effects under different scenarios. 1.𝐵𝑅𝐼𝐶𝑆 2.𝐵𝑅𝐼𝐶𝑆 +𝑇 𝑇 𝐼𝑃 3.𝐵𝑅𝐼𝐶𝑆2001 4.𝐵𝑅𝐼𝐶𝑆 +𝑈𝑆 𝛽𝑉 𝐴 0.4381 0.4474 0.4476 0.4402 Note: In all four scenarios, the partial trade effect on gross trade is 𝛽𝑋= 0.5268. Scenario 3: ‘‘𝐵𝑅𝐼𝐶𝑆2001’’. Like in Scenario 1, the BRICS countries form an RTA, but now we calibrate the model baseline with data from 2001 instead of 2018. In both new scenarios, we find partial average VA effects that are approximately 1.5 percentage points larger than in the baseline scenario (see columns 2, 3). By construction, the partial effect on gross trade are identical. To demonstrate the issue of omitted variables bias, we study the following scenario: Scenario 4: ‘‘𝐵𝑅𝐼𝐶𝑆 +𝑈𝑆’’. In addition to the BRICS agreement as in Scenario 1, a positive infrastructure shock occurs in the USA which reduces trade costs between the U.S. and all destinations (including the U.S. itself) by 50%. Column 4 shows that the estimated partial VA trade effect of 𝐵𝑅𝐼𝐶𝑆 is affected by the infrastructure shock occurring elsewhere in the world. This occurs despite the fact that the direct effect on BRICS countries’ and non-BRICS countries’ VA trade with the US is absorbed by the country fixed effects in (11). In contrast, in the gross trade regression, the country fixed effects perfectly control for the infrastructure shock. 4. Discussion and conclusions Before concluding, we would like to discuss the assumptions underlying our framework. A3 is a widespread and fairly harmless loglinearity assumption. A4, in contrast, is likely to fail when confronted with real-world data. However, we adopt it for practical purposes only, because we want to demonstrate the challenges associated with VA gravity estimates for variables whose effects on gross trade can be cleanly identified using OLS with fixed effects. A1 and A2 warrant more discussion. A2 implies that the VA composition of exported goods is identical across destinations, effectively ruling out the possibility that different inputs are used for different destination markets. If we had real data on value added content, we could more accurately measure country-pair specific exposure to the treatment or confounding shocks. The empirical issues caused by heterogeneous exposure, however, would persist. The same holds for relaxing A1 by allowing for differences between trade shares of final and intermediate goods or multiple sectors. Finally, we do not intend for our analysis to suggest that gross trade gravity equations are correct. Instead, we want to point out that the use of reduced-form VA gravity equations should not be justified by referencing the theoretical and empirical merits of gravity equations for gross trade. We think the misspecification issues outlined here are relevant beyond our stylized framework because they arise from the multilateral nature of VA trade and the uniqueness of each country’s GVC, which is an empirical fact. Consequently, we believe that the effects of trade cost changes on VA trade are better studied using a structural model of trade in final and intermediate goods. Declaration of Generative AI and AI-assisted technologies in the writing process During the preparation of this work the authors used ChatGPT-4 to improve the language. After using this tool, the authors reviewed and edited the content as needed and take full responsibility for the content of the published article. Funding Funded by the European Commission through its Horizon Europe research and innovation programme under grant agreement number 101061123. Views and opinions expressed are however those of the authors only and do not necessarily reflect those of the European Union or the European Research Executive Agency (REA), the granting authority. Neither the European Union nor the granting authority can be held responsible for them. Appendix List of academic papers and policy reports estimating gravity equations with value added trade flows Academic papers Blind et al. (2018)Sanguinet et al. (2022) Boffa et al. (2019)Sharma et al. (2023) Böhmecke-Schwafert and Blind (2023) Sharma et al. (2024) Chen et al. (2022)Thang et al. (2021) Díaz-Mora et al. (2022)Tokas (2021) Doan and Le (2021)Tokas (2022) Fertő et al. (2024)Wang and Thangavelu (2021) Hayakawa and Mukunoki (2023) Wolszczak-Derlacz and Lu (2022) Johnson and Noguera (2017) Yang (2022) Kang and Gapay (2024)Yang (2023) Laget et al. (2020)Yang and Liu (2024) Le et al. (2022)Zaninović (2022) Lee (2019)Zaninović and Bugarčić (2023) Lu and Wolszczak-Derlacz (2024) Zaninović et al. (2024) Mulabdic et al. (2017)Zhang et al. (2024) Njike (2021)Zhao (2022) Olczyk and Kordalska (2017) Zhong et al. (2022) Pahl and Timmer (2019) Policy reports Cadestin et al. (2016) Jouanjean et al. (2017) Moïsé and Sorescu (2015) OECD (2021) Economics Letters 254 (2025) 112476 4 I. Heiland and P. Šváb Data availability I have shared the link to my data/code at the Attach File step replication package (Original data) (Github) References Aichele, R., Heiland, I., 2018. Where is the value added? Trade liberalization and production networks. J. Int. Econ. 115, 130–144. Anderson, J.E., Van Wincoop, E., 2003. Gravity with gravitas: A solution to the border puzzle. Am. Econ. Rev. 93 (1), 170–192. Blind, K., Mangelsdorf, A., Niebel, C., Ramel, F., 2018. Standards in the global value chains of the European single market. Rev. Int. 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