Policy Research Working Paper 10634 Quantifying Economic Impacts of Trade Agreements with Heterogeneous Trade Elasticities Hiau Looi Kee Alessandro Nicita Development Economics Development Research Group December 2023 Policy Research Working Paper 10634 Abstract Bilateral trade relationships between countries vary across less elastic compared to products from other trading part- products. Such heterogeneity poses challenges when assess- ners. The findings also show substantial heterogeneity in ing the economic impacts of trade agreements. This paper the elasticities across products and a negative correlation estimates bilateral trade elasticities at the product level and between these elasticities and tariffs. These factors mitigate explores these impacts using a hypothetical no-deal Brexit the extent of trade welfare losses compared to a scenario as an example. The findings indicate that the European using homogeneous elasticities. Union’s demand for the United Kingdom’s products is often This paper is a product of the Development Research Group, Development Economics. It is part of a larger effort by the World Bank to provide open access to its research and make a contribution to development policy discussions around the world. Policy Research Working Papers are also posted on the Web at http://www.worldbank.org/prwp. The authors may be contacted at hlkee@worldbank.org. The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent. Produced by the Research Support Team Quantifying Economic Impacts of Trade Agreements ∗ with Heterogeneous Trade Elasticities Hiau Looi Kee† Alessandro Nicita‡ World Bank UNCTAD Keywords: Welfare gains from trade, trade elasticities, Brexit JEL Classification Numbers: F10, F14 ∗ We thank James Anderson, David Baqaee, Chad Bown, Lorenzo Caliendo, Alonso de Gortari, Svetlana Deminova, Rob Feenstra, Penny Goldberg, Beata Javorcik, Aaditya Mattoo, Paul Romer and participants in the World Bank’s Policy Research Talk for feedback and comments. Alejandro Feraros provides excellent research assistance. Research for this paper has in part been supported by the World Bank’s Multidonor Trust Fund for Trade and Development. The authors declare that they have no relevant or material financial interests that relate to the research described in this paper. The results and opinions presented in this paper do not represent the views of our institutions, the Executive Directors, or the countries they represent. † Development Research Group, The World Bank; 1818 H ST NW, Washington, DC 20433. Tel: 1-202-473 4155; Fax: 1-202-522 1159; Email: hlkee@worldbank.org. ‡ United Nations Conference on Trade and Development, Switzerland. Email: Alessandro.Nicita@un.org 1 Introduction One of the reasons for a country to join a trade agreement is the potential welfare gains from trade.1 Trade agreements may also foster deeper ties among the partnering countries, which may further amplify the welfare gains from trade.2 On the flip side, do we expect larger welfare loss when countries with closer ties withdraw from existing trade agreements or face higher tariffs? Quantifying the potential impacts of existing trade agreements requires detailed knowledge of how trade may respond to trade policy changes given the specific trading relationship of these partnering countries in different industries. In other words, to study the trade and welfare impacts of existing trade agreements, we need partner country specific trade elasticities. These estimates do not exist. The objective of this paper is to fill the gap in the literature regarding the product- level trade elasticities with bilateral variations. As an application, this paper studies a hypothetical No-Deal Brexit. We first estimate the detailed bilateral trade elasticities of the European Union (EU) with respect to imports from its top 100 trading partners, including the United Kingdom (UK), at the HS 6-digit level.3 We then evaluate the welfare and trade impacts, based on these trade elasticity estimates. While the actual Brexit is governed by the Trade and Cooperation Agreement between the EU and the UK, which came into effect in 2022 and provides for free trade in goods, findings based on a No-Deal Brexit are still informative as they provide a clean policy experiment to isolate the impacts of sudden tariff hikes on trade and welfare losses of countries that are closely linked through existing 1 Standard trade models have emphasized that when countries specialize in producing and exporting products according to their comparative advantage, there may be efficiency and consumption gains. See Krugman, Obstfeld and Melitz (2022) for a textbook treatment. 2 See World Bank (2020) and Fernandes, Kee and Winkler (2022). 3 In this paper we estimate import demand elasticities, which is the percentage change in quantity imported with respect to a one percent change in import price. The (negative) import demand elasticity equals trade elasticity when prices and quantities of other products are held fixed. See Section A1 of the Appendix for the proof. Throughout this paper, we use the terms import demand elasticities and trade elasticities interchangeably when there is no confusion. 1 trading relationships. In addition, the findings could be timely and relevant in other similar instances, such as in quantifying the trade effects of the ongoing US-China trade tensions, or the current Russian Federation-Ukraine war. To assess the economic impacts of trade agreements, this paper adapts the partial equi- librium approach of Feenstra (1995), which is a simplification of Anderson and Neary (1992). This approach is rich in product and country level heterogeneity, and does not depend on the modeling choices, preference and production structures. We show that trade and welfare impacts depend on the size of the country specific trade elasticities, as well as the correlation between the elasticities and the tariffs. Our approach complements a general equilibrium gravity framework, which takes into account substitution of products and changes in income. These models are rich in the general equilibrium effects, often assume homogeneous trade elasticites across countries, with some models also assume heterogeneous elasticities across industries.4 Our analysis shows that in a No-Deal Brexit, the exports from the UK to the EU would decrease by 6.4 percent while the welfare losses to both the EU and the UK, measured in terms of their GDPs, would be less than 1 percent. These impacts are tapered by the relatively low EU-UK specific trade elasticity estimates, as well as the negative correlation between the EU-UK specific trade elasticities and the EU’s tariffs. Without accounting for heterogeneous elasticities, the trade losses would have been higher, resulting in approximately a 7.8% decline. Our findings of heterogeneous elasticities collaborate well with some recent studies. The heterogeneous elasticity estimates across products are consistent with the findings of Imbs and Mejean (2017). The low EU-UK elasticity estimate is consistent with the findings of Chen and Novy (2022) and de Gortari (2019), who show that bilateral trade is less sensitive 4 For general equilibrium models with industries heterogeneity, see Melitz and Redding (2015), Caliendo and Parro (2015). 2 to trade costs if the exporting country provides a larger share of the destination country’s imports, and the trading of specialized inputs which are less elastic. The inherent market power of the EU as it pertains to the UK’s products may also contribute to the low bilateral demand elasticity, as shown in Juarez (2023), based on evidence from Colombia. Soderbery (2021) takes a similar general approach as this paper, except his focus is on heterogeneous pass-through rates across countries and how trade impacts are shaped by importer market power. The result of negative correlation between tariffs and elasticities speak to Caliendo and Feenstra (2022) and the classic optimal tariff models showing that the relationship between tariffs and elasticities could affect the welfare gains from trade.5 In addition, our results are validated by several robustness checks. First, we find larger trade and welfare losses when we replace the heterogeneous elasticities with the homoge- neous elasticities. This is because the estimated EU-UK trade elasticities are about 30 percent lower than the homogeneous EU elasticities across all trading partners. Ex ante, smaller elasticities imply smaller losses, and the homogeneous elasticities remove the negative correlation between tariffs and trade elasticities, which pushes up losses. Next, we find that using different elasticity estimates from the existing literature does not qualitatively change our results. Then, we reshuffle the heterogeneous elasticities in such a way that there is no correlation between tariffs and elasticities. In this case, the welfare and trade impacts are much larger, demonstrating the importance of considering the possibility of correlation between tariffs and elasticities. We also further break down the trade and losses to the industry level. The results suggest lower losses for the machinery and transport equipment sectors, which are more integrated between the EU and the UK.6 5 Empirical evidence supporting the optimal tariff theory can be found in Broda, Limao and Weinstein (2008), who estimate export supply elasticities at a disaggregated level and find strong evidence that import- ing countries set higher tariffs on products that face inelastic export supply. Here in this paper we focus on estimating import demand elasticities and studying how the correlation between these elasticities and tariffs may affect the calculations of the gains from trade. 6 In the Appendix, we further extend our analysis to include some general equilibrium forces such as the 3 This paper contributes to several strands of trade literature. First, it builds on the theo- retical framework of Anderson and Neary, to show that heterogeneous trade elasticities affect welfare and trade calculations when there is any correlation between trade elasticity and tar- iffs.7 Second, this paper relates to the empirical literature on quantifying the impact of trade agreements, by focusing on the micro-level evidence of tariffs and elasticities and building the overall impacts from the ground up.8 Third, this paper contributes to the optimal tariffs literature by estimating the empirical relationship between tariffs and elasticities.9 Finally, this paper contributes to research analyzing the trade impacts of trade agreements, such as Brexit.10 Rather than predicting trade by using gravity models, this paper uses bilateral trade elasticity estimates to quantify the impacts, which prove to be relevant. The paper proceeds as follows. Section 2 presents the trade elasticity estimations. Section 3 provides a description of the data used in the analysis. Section 4 presents the results of the elasticity estimation. Section 5 describes the theoretical framework. Section 6 presents the trade and welfare impacts of a No-Deal Brexit, while Section 7 presents the robustness checks. Section 8 concludes. Mathematical derivations and details are in the Appendix. availability of substitutes, input-output linkages, as well as the positive income effects due to the increase in tariff revenues. Including these general equilibrium channels do not alter the overall results of this paper which lend credibility to our partial equilibrium approach for our current context. 7 Anderson and Neary (1992, 1994, 1996, 2003 and 2007), Feenstra (1995). 8 Melitz and Redding (2015), Caliendo and Parro (2015) and Ossa (2015). 9 Broda, Limao and Weinstein (2008); Bagwell and Staiger (2011). 10 Baldwin (2016), Bloom and Mizen (2017), Dhingra, Huang, Ottaviano, Sampson and Van Reenen (2016), Gudgin, Coutts, Gibson and Buchanan (2017), and Lawless and Morgenroth (2019). Specifically, for general equilibrium models, Dhingra, Huang, Ottaviano, Pessoa, Sampson, and Van Reenen (2016) find that Brexit could lower the UK’s income by 2.3 percent. The partial equilibrium approach taken by Lawless and Morgenroth (2019), based on sector level median elasticity estimates from Imbs and Mejean (2017), finds that Brexit may result in significantly different impacts across countries and sectors. 4 2 Estimating Trade Elasticities 2.1 Translog GDP Function Approach The estimating framework of this paper is based on the translog GDP function approach.11 This approach has the following advantages. First, it allows the construction of bilateral trade elasticities at the product level for each trading partner. The differences in market power across countries may cause differences in trade elasticities. This implies that trade elasticities could have bilateral variations and may be partner country specific. We can thereby evaluate the trade impact of Brexit without imposing homogeneous trade elasticities across trading partners. The second advantage is that the translog GDP function relies not only on the variations in tariffs, but also the variations in unit values to estimate trade elasticities. Nearly 25 percent of HS 6-digit products imported by the EU face zero MFN tariff throughout the sample period which provides neither time series nor cross sectional variations in data. By taking into account the variations of the unit values, this approach permits the retention of these products in the estimation of trade elasticities. Finally, this approach allows to correct for the potential selection and endogeneity biases using a multi- step methodology developed in Semykina and Wooldridge (2010). The translog GDP function was first derived by Diewert (1974) and was adapted to an international setting by Kohli (1978, 1991) to estimate the US aggregate import demand and export supply functions. Harrigan (1997) incorporated productivity into the GDP function to study the impact of productivity and endowment in affecting the international specialization of the OECD countries at a sectoral level. Subsequently, Kee, Nicita and Olarreaga (2008) built on these works to estimate import elasticities at a disaggregate HS 6-digit product level 11 Alternatively, one could run a cross sectional gravity regression of bilateral imports on bilateral tariffs, controlling for importer and exporter fixed effects. The estimated coefficient on tariffs is the aggregate trade elasticity. See ACR (2012) for details. 5 for a wide range of countries. For the current application, we explicitly introduce the ad valorem tariffs into the GDP function, and thus allow tariffs to affect the imports of products in GDP through product prices.12 Let’s denote ln Gt (pt , v t ) as the translog GDP function of a small open economy, facing ad valorem tariff-inclusive price, pt , factor endowment, v t , with n and k index goods, and m and l index factors:13 1N N ln G pt , v t = a00 +N t n=1 a0n ln pn + ank ln pt t n ln pk 2 n=1 k=1 1M M +M m=1 b0m t ln vm + t t l=1 bml ln vm ln vl 2 m=1 +N M t t n=1 m=1 cnm ln pn ln vm . (1) t For each period, t, the net output vector q t = (q1 t , q2 t , ..., qN ) is chosen to maximize GDP, with positive elements denoting outputs, which include exports, and negative numbers denoting inputs, which include imported goods as in Kohli (1991). To reduce the number of translog parameters, we apply a semiflexible functional form developed by Diewert and Wales (1988) to reparametrize ln Gt (pt , v t ) so that ln Gt (pt , v t ) satisfies homogeneity and symmetry restrictions, with respect to prices and factor endow- ments. The Envelope theorem implies that, at the equilibrium, the share of good n in GDP at period t is pt t t t n qn ( p , v ) pt t vm st t t n p ,v ≡ = a 0n + a nn ln n + M c m̸=l,m=1 nm ln , ∀n = 1, ..., N. (2) Gt ( p t , v t ) pt k vlt Note that if good n is an input, as in the case of imports, then st n < 0 is the negative share of n in GDP, while if good n is an output, such as exports, then st n > 0 is the positive share 12 Please refer to Feenstra (2015) for standard textbook treatments of the GDP function approach. 13 The exposition below closely follows Kee, Nicita and Olarreaga (2008). Please refer to Section A4 of the Appendix. 6 of n in GDP. In Equation (2) , ln pt ∑ ak ln pt k = k̸=n k̸=n ak k is a weighted average of the log prices of all non-n goods. For every good n, ln pt k can be constructed using the GDP deflator net of the price of good n, adjusted by the share of non-n goods,14 t −1 −n = ln p − s ln pt n ln pn / 1 − s t ¯t t ¯t ¯t n , where s t n = 0 . 5 sn + sn . (3) This approximation introduces an additive error term to reflect measurement error in each share equation, κt n : pt t vm n , ∀n = 1, ..., N. n st t t n p ,v = a0n + ann ln t + M m ̸ = l,m =1 c nm ln t + κt (4) p −n vl Equation (4) forms the basis to estimate the translog parameter, ann , which is used to construct the own-price elasticity, εnn , t ∂qn ( pt , v t ) pt nn ≡ n εt (5) ∂ptn q t n ann = + st n−1 ≤ 0 , ∀ st n < 0. (6) stn Please note that εnn is also the (negative) trade elasticity when the prices and quantities of other goods are held constant.15 Likewise, the cross-price elasticity for good −n is: −ann εt n−nd = + st −nd . (7) st nd 14 Caves, Christensen and Diewert (1982). 15 Please refer to Section A1 of the Appendix for the proof. 7 2.2 Econometric Issues There are a number of issues that needs to be addressed. The first involves the endogeneity of tariff-inclusive relative prices. Following Equation (4), we regress the share of each good n on their tariff-inclusive relative prices and the endowments of the EU, where the share of each good n is constructed based on the trade value of each HS 6-digit good from each trading partner, relative to the GDP of the EU. In this specification, the tariff-inclusive pt relative prices of HS 6-digit products, ln ptnd , could be endogenous to the share of each −n good, st nd , which could lead to inconsistent estimates. Moreover, if the small open economy assumption is violated, an increase in tariffs may also cause foreign prices to change and affect pt ln ptnd . To address these endogeneity issues, we use the tariff-inclusive relative price of the −n pt United States (US), ln ptnd,U S , as the instrument in a Fixed Effects Two Stage Least Square −n,U S (FE-2SLS) regression. The identification assumption is that relative prices are affected by common shocks: while the price of a product in the EU and the US could be correlated due to the world market conditions, the share of each good in the GDP of the EU should not be correlated with the trade policy and prices of the US a priori. One of the reasons the US prices and the EU prices are correlated is because they faced the common exogeneous shocks, such as productivity/technology, and climate/weather/natural disaster/pandemic, as well as China shocks and the wars in other countries. These exogeneous events affect product prices in the world markets hence caused the US and EU prices to move together. At the same time the US prices should not be affecting or influenced by the share of UK products in the EU’s imports; hence, they are consistent with the exclusion restrictions and acceptable as 8 an instrumental variable for the EU prices: 1st stage : ∀n = 1, ..., N, pt pt nd,U S vt ln tnd n n = βd + βt + βn ln t + βv ln mt + et nd , (8) p −n p−n,U S vl 2nd stage : ∀n = 1, ..., N, t pt vm st nd , ∀n = 1, ..., N, n n nd = a0d + αt + ann ln nd + c nm ln + κt (9) pt −n v t l pt pt where ln ptnd denotes the predicted value of ln ptnd from the first stage regression, Equation −n −n (8) . The dependent variable in the second stage regression is the share of the imported product in the GDP of the EU (which is by construction negative or zero). The right-hand side variables include the predicted tariff-inclusive relative price of this product, the relative endowments of the EU, together with year fixed effects an t and exporting country fixed effects an 0d . Equation (9) forms the base-line for our elasticity estimates. The second econometric issue is the potential selection bias due to EU imports being not random. In fact, it is well documented that international trade is often highly concentrated (Helpman, Melitz and Rubinstein, 2008). Within our sample of bilateral imports of the 5000 HS 6-digit level products between the EU and its top 100 partners, nearly 75 percent of the product-exporting country observations are zeros, while the UK exports nearly all but 200 products to the EU. The issue of sample selection bias cannot be ignored. To correct for sample selection, we use a multi-step sample selection model for panel data, developed in Semykina and Wooldridge (2010). This approach is particularly suitable for panel data with endogenous right-hand-side variables and unobserved heterogeneity that can be controlled by panel fixed effects. Semykina and Wooldridge (2010) also provide a selection bias test which allows us to identify products that need such corrections. t To test for selection bias, we define a dummy variable, Dnd that indicates the presence 9 of trade for each HS 6-digit product, n, in year t, from exporting country, d,    1, if st < 0 t nd Dnd =   0, otherwise. t t In other words, Dnd = 1 if country d exports product n to the EU; and Dnd = 0 if country d does not export product n to the EU.16 We then apply the following procedure: First, for each HS 6-digit product n and each year t, we run a cross sectional probit regression: t P Dnd = 1|znd t t = Φ znd ¯nd ζ t , δt + z (10) where the dependent variable equals one if there is non-zero trade between the EU and the partner country in that year, and zero otherwise. The right-hand-side variables of this t t probit regression include znd ¯nd . Matrix znd , and z represents all the exogenous right-hand-side variables and instruments, which are the tariff-inclusive relative price of the product in the ¯nd represents the cross years averages of the US and the relative endowments. The variable z tariff-inclusive relative price of the US for product n coming from partner country d, and the cross years average relative endowments of the EU. The resulting estimates are used to obtain ˆt = λ zt δ the inverse Mills ratio, λ ˆt + z ˆt + z ˆt = ϕ z t δ ¯nd ζ ¯nd ζ ˆt + z ˆt /Φ z t δ ˆt , with ¯nd ζ nd nd nd nd ϕ (.) and Φ (.) denoting the pdf and cdf of a normal distribution. t Second, for Dnd = 1, the tariff-inclusive relative price of the product in the US and the inverse Mills ratio are then used as instruments to estimate the following FE-2SLS regression 16 Please refer to Section A5 of the Appendix on how relative prices could determine zero trade. 10 for every product, n : 1st stage : ∀n = 1, ..., N, pt pt t ln tnd n n nd,U S = βd + βt + βn ln t ˆ t + βv ln vm + et , + βλ λ (11) nd nd p −n p−n,U S vlt 2nd stage : ∀n = 1, ..., N, t pt ˆ t + cnm ln vm + κt . st n n nd = a0d + αt + ann ln nd + ρ λ nd nd (12) pt −n vlt Third, we use the t-statistic with heteroskedasticity robust standard error to test H0 : ρ = 0. Selection bias is present if ρ is tested to be statistically significant. For the products that have non-zero trade and for which the selection bias has tested pos- itive, we correct for such bias by using the tariff-inclusive relative price of the US, the partner country average tariff-inclusive relative price of the US, and average relative endowments as instruments in the following Pooled 2SLS regression: 1st stage : ∀n = 1, ..., N, pt pt t ln tnd n nd,U S = βt + βn ln t ˆ t + βn ln pnd,U S + βv ln vm + βv ln vm + et , (13) + βλ λ nc nd p −n p−n,U S p−n,U S vlt vl 2nd stage : ∀n = 1, ..., N, t pt ˆ t + an pnd,U S vm vm st n nd = αt + ann ln nd t + ρ λ nc ¯ ln + c nm ln t + cnm ln + κt nd , (14) p −n p−n,U S vl vl ¯ denotes the average value of x. Note that in this pooled 2SLS specification, partner where x country fixed effects are replaced with country averages in both the first and second stages. Finally, given the assumption that products from different exporting countries are dif- ferentiated, each of these HS 6-digit-exporter pairs should have unique translog parameters, ann and cnm . However, there are only 8 years of data for each HS 6-digit-exporter pair, which is too limited in terms of degrees of freedom. Thus, for each HS 6-digit product, we pool 11 across all exporting countries and years to implement the above specification, by estimating the average ann and cnm for all exporting countries. Specifically, let each n represent an HS 6-digit product, and n′ represent the same HS 6-digit product from an exporting country. Then each country’s unique an′ n′ is ann plus a mean-zero error term, κt 2n′ . Likewise, cn′ m is 17 cnn plus a mean-zero error term, κt 3n ′ : an′ n′ = ann + κt t 2n′ , with E κ2n′ = 0 or E (an′ n′ ) = ann , cn′ m = cnn + κt t 3n′ , with E κ3n′ = 0 or E (cn′ m ) = cnn , ptn′ t vm ptn′ t vm st t t n′ p , v = a0n′ + ann ln + M m̸=l,m=1 c n ′ m ln + κ t 1n ′ + κ t 2n ′ ln + κ t 3n ′ ln . pt −n ′ vlt pt −n ′ vlt The above specification is possible because the error terms κt t 2n′ and κ3n′ are not correlated with relative prices and endowments. 3 Data The analysis of this paper uses HS 6-digit panel data sets which consist of the EU’s MFN ad valorem tariffs and trade with its 100 top trading partners for the period between 2010 and 2017. Using panel data allows elasticities estimates to be based on variation both across countries and across time. One advantage of using panel data is that it allows us to obtain estimates in cases where there is insufficient tariffs’ variation in the cross section setup or for HS-6 digit products with no consistent trade throughout the sample period. Trade and tariff information originate from the World Bank World Integrated Trade Solution (WITS). The World Bank’s World Development Indicators provides the data on endowments and GDP. Table 1 presents some summary statistics of the EU trade policies with respect to products from the UK, under the assumption of MFN ad valorem tariffs 17 The error terms are mean-zero because we are estimating the average ann for each product n. 12 between the EU and the UK.18 4 Results: Bilateral Elasticity Estimation This section discusses bilateral trade elasticity, constructed from the estimated translog parameter, ann : ann εnnd = + snd − 1. snd We restrict the estimated elasticities to be non-positive as well as winsorize to drop the outliers. Missing elasticity estimates are replaced with the averages within the exporting partner country and product groups.19 Overall, the bilateral trade elasticities for the UK appear to be well estimated. The average first stage F-statistic is 12.38, while the average t-statistic for the estimated bilateral elasticity is -2.60. Table 2 summarizes the results for the exports from the UK. The sample average import elasticity estimate for an HS 6-digit product imported from the UK to the EU is -13.9, with a sample median of -1.76 and a standard deviation of 38.8. This indicates that there is a wide range of trade responsiveness across all products, which highlights the importance of allowing trade elasticities to vary across products when calculating trade 18 The EU MFN tariff schedule includes ad valorem tariffs and specific duties. The conversion from specific duties to ad-valorem tariffs is automated in WITS and relies on reference prices (world prices) and price elasticities, both of which may not be representative of EU-UK trade. Therefore, the analysis of this paper discards the products subject to specific duties (about five percent of HS-6 digits products). 19 Thus, for each product n, the difference in bilateral elasticities across trading partners is due to the difference in the share of these partners in the GDP of the EU, snd . However, this does not imply that partner countries with a larger share will face a less elastic import demand in the EU, since ann could be positive or negative empirically. Specifically, ∂εnnd ann = − 2 + 1. ∂snd snd ∂εnnd If ann > s2 nd , then ∂snd < 0, implying that an exporting country with a smaller share in magnitude (given that snd < 0) will face a more elastic demand in the EU (given that εnnd < 0). The converse is also true. ∂εnnd If ann < s2 nd , then ∂snd > 0, which implies that an exporting country with a smaller share in magnitude (given that snd < 0) will face a less elastic demand in the EU ( given that εnnd < 0). The size of ann depends on the regressions and could be positive or negative empirically. 13 impacts and the welfare gains from trade. For comparison purposes, our import weighted average elasticity is 3.9, similar to the trade elasticity estimate of Simonovska and Waugh (2014) of 4. The results also indicate heterogeneity of elasticities across trading partners, with a me- dian elasticity of -20 and standard deviation of 70. In fact, relative to the rest of the exporting countries, the import demand for UK products is found to be less elastic. Column (1) of Table 3 formally tests the hypothesis that all partner countries have the same elasticity for each HS 6-digit product and the hypothesis was rejected with high t-statistics. On average, the elasticity of the UK is 30 percent lower than that of the other exporting countries for the same HS 6-digit product. This differential is statistically and economically significant, which highlights the importance of estimating bilateral trade elasticities, rather than imposing the same elasticities across all trading partners. UK-EU relatively small trade elasticities are consistent with Novy (2013) and Chen and Novy (2022) who find that bilateral trade is less sensitive to trade costs if the exporting country provides a larger share of the destination country’s imports.20 In addition, the inherent market power of the EU as it pertains to UK’s products could also lead to lower bilateral demand elasticities.21 20 As a robustness check for the results of substantially lower elasticities for the UK we run a series of gravity regressions excluding one exporting country at a time. Results show that excluding the UK from the regression significantly increases the magnitude of the coefficient on distance, implying that the UK faces a lower elasticity in the EU than other exporting countries. Please refer to Section A6 of the Appendix for details. 21 Soderbery (2021) takes a similar general approach as this paper, except his focus is on heterogeneous pass-through rates across countries and how trade impacts are shaped by importer market power. Please also refer to Juarez (2023) for evidence relating importer market power to low pass-through elasticity, based on evidence from Colombia. 14 5 Theoretical Framework 5.1 The Bilateral Trade Restrictiveness Index To show how heterogeneous elasticities may affect welfare calculations, we build on the Trade Restrictiveness Index (TRI) framework developed by Anderson and Neary (1994, 1996). For any importing country, with different trade policies on different products, the TRI is the uniform tariff equivalent that would generate welfare or dead-weight loss at the observed levels. Feenstra’s (1995) simplification of TRI is a linear approximation around the equilibrium without imposing any preference structure which proves to be convenient. Kee, Nicita and Olarreage (2007) adapt Feenstra’s approach to construct the multilateral-TRI for a wide range of countries. In Section A2 of the Appendix, we derive the bilateral-TRI of the EU (indexed by c) with respect to imports from the UK (indexed by d). Then with some algebraic manipulations, we show that the bilateral-TRI can be decomposed into the following 3 terms:22 2 2 1/2 TRIcd = τ ¯cd + σcd + ρ2 cd , (15) 2 where τ ¯cd , σcd and ρ2 cd are the average tariff, the variance of tariffs, and the covariance between tariffs and trade elasticity, respectively.23 Equation (15) indicates that the TRI will be higher if the bilateral tariffs have a higher average, a large variance or a high correlation with the bilateral trade elasticity. Thus, if trade elasticity is homogeneous, then the TRI only depends on import weighted average tariffs and the variance of tariffs.24 It is straightforward to write the deadweight loss (DWL) of trade policy in terms of the 22 Both the tariff and the TRI are expressed in ad valorem terms as x/(1+x). See Section A2 of the Appendix for details. 23 Please refer to Section A2 of the Appendix for the definitions of these variables. 24 Please note that in this paper, we used the term heterogeneity to refer to the differences in the bilateral product level import demand elasticities. This is in contrast to the existing papers which often use a single homogeneous elasticity for all products and all trading partners. Differences in tariffs will affect DWL and 2 welfare calculations through σcd , which is the variance of tariffs. 15 decomposition of the TRI:25 1 2 2 1 2 DWLcd = ¯ + σcd τ Mcd ε ¯cd + ρ Mcd ε ¯cd , in level, or (16) 2 cd 2 cd Tariff-Induced DWL Heterogeneity-Induced DWL DWLcd 1 2 2 1 = ¯cd + σcd τ ¯cd + ρ2 ε ¯cd , in share, ε (17) Mcd 2 2 cd where Mcd ≡ n ¯cd is the import weighted pncd qncd is the total imports of c from d, and ε average import elasticity, which is negative by definition. Therefore, the higher is the average tariff, or the variance of tariffs, or the covariance between tariffs and elasticity, the larger is the magnitude of the DWL. Conversely, if the average tariff is lower, or the variance of tariffs is lower, or if higher tariffs are levied on less elastic products, then an increase in tariffs will generate a smaller welfare loss.26 Equation (16) shows that heterogeneous trade elasticity will affect the welfare calcula- tion through its correlation with the tariffs, ρ2 cd . Let’s define the first term of (16) as the Tariff-Induced DWL, and the second term of (16) as the Heterogeneity-Induced DWL. If trade elasticities are homogeneous, then the DWL equals the Tariff-Induced DWL, and the Heterogeneity-Induced DWL is zero. If trade elasticities are positively correlated with tariffs, then the DWL is larger than the Tariff-Induced DWL in magnitude, and the Heterogeneity- Induced DWL is negative. Conversely, if trade elasticities are negatively correlated with tariffs, then the DWL is smaller than the Tariff-Induced DWL in magnitude, and the Heterogeneity-Induced DWL is positive.27 25 See Section A2 of the Appendix. 26 Please note that a positive deadweight loss is a welfare loss. It effectively measures the price effect of a tariff increase. 27 Please refer to the Proposition 1 in Section A2 of the Appendix for the relationship between DWL and the heterogeneity in trade elasticities. 16 5.2 The Bilateral Overall Trade Restrictiveness Index To show how heterogeneous elasticities may affect trade impact calculations, we build on the multilateral Overall Trade Restrictiveness Index (OTRI) framework, developed by Kee, Nicita and Olarreaga (2009), based on the Mercantilist Trade Restrictiveness Index of Ander- son and Neary (2003). For any importing country, with different trade policies on different products, the OTRI is the uniform tariff equivalent that would generate imports at the ob- served levels. Here, we define the OTRI as the uniform ad valorem tariff of country c (the EU) with respect to imports from country d (the UK), facing bilateral tariff τcd . In Section A3 of the Appendix, we derive and decompose the bilateral-OTRI into the following two terms: OT RI cd = τ ¯cd + ρcd , (18) ¯cd and ρcd are the average tariff and the covariance of tariffs and the negative trade where τ elasticity, respectively.28 From Equation (18), it is evident that the OTRI is higher when the bilateral trade policy of c on products from d has a higher average or a high correlation with the bilateral trade elasticity. Unlike the TRI, the OTRI is not affected by the variance of tariffs. It is straightforward to write the trade impact of trade policy in terms of the decompo- sition of the OTRI:29 ∆Mcd = ¯cd Mcd (1 + ε τ ¯cd ) + ¯cd ) ρcd Mcd (1 + ε , in level, or (19) Tariff-Induced Trade Impact Heterogeneity-Induced Trade Impact ∆Mcd ¯cd (1 + ε = τ ¯cd ), in share. ¯cd ) + ρcd (1 + ε (20) Mcd Thus, the higher is the average tariff, or the covariance between tariffs and trade elasticity, 28 Please refer to Section A3 of the Appendix for the definitions of these variables. 29 See Section A3 of the Appendix. 17 the greater is the magnitude of the trade impact of the restrictive trade policy. Conversely, if the average tariff is lower, or if tariffs and trade elasticities are negatively correlated, then moving from free trade to restrictive trade between c and d will generate a smaller trade loss. Equation (19) shows the trade impact for the UK is affected by the correlation between heterogeneous trade elasticities and tariffs. Let’s define the first term of (19) as the Tariff-Induced trade impact, and the second term of (19) as the Heterogeneity-Induced trade impact. If trade elasticities are homogeneous, then the trade impact equals the Tariff-Induced trade impact, and the Heterogeneity-Induced trade impact is zero. If trade elasticities are positively correlated with tariffs, then the trade impact is larger than the Tariff-Induced trade impact in magnitude, and the Heterogeneity-Induced trade impact is negative. Conversely, if trade elasticities are negatively correlated with tariffs, then the trade impact is smaller than the Tariff-Induced trade impact in magnitude, and the Heterogeneity-Induced trade impact is positive.30 In the empirical section, we construct TRI and OTRI to calculate the DWL and trade impact resulting from the increase in tariffs between the EU and the UK in the event of a No- Deal Brexit. Moreover, we decompose the DWL and trade impact into various components to assess how the presence of heterogeneous elasticities may affect the results. 6 Trade and Welfare Impacts of a No-Deal Brexit Based on the heterogeneous elasticity estimates, the first column of Table 4 presents the potential TRI, welfare change, OTRI and trade impact on the EU of a No-Deal Brexit. Moving from no tariff to the MFN ad valorem tariff will result in the bilateral TRI to be about 4.41 percent, and may cause the welfare of the EU to drop less than 1 percent, the 30 Please refer to the Proposition 2 in Section A3 of the Appendix for the relationship between trade impact and the heterogeneity in trade elasticities. 18 equivalent of a loss of US$ 0.55 billion. Likewise, moving from no tariffs to the MFN tariffs will increase the EU’s OTRI with respect to the UK’s products to 2.29 percent, and may cause the EU-UK trade to decrease by 6.38 percent, equivalent to a loss of about US$ 10.2 billion, or less than 1 percent of the UK’s GDP. The second and third columns of Table 4 present the decompositions of DWL and trade impacts post-Brexit into the part that is induced by tariffs and the part that is induced by the heterogeneity of trade elasticities, according to (16) and (19). The Tariff-Induced DWL and trade impact are found to be larger in magnitude relative to the overall DWL and trade impact, while the Heterogeneity-Induced DWL and trade impact are positive. This is because, for the EU, the covariance between tariff and trade elasticity is negative, meaning higher tariffs are placed on less elastic products, while lower tariffs are placed on more elastic products.31 The resulting positive heterogeneity-induced impacts reduce the overall sizes of welfare and trade loss. This case nicely provides the empirical support for Propositions 1 and 2 of Sections A2 and A3 of the Appendix when ρcd < 0. Ignoring the Heterogeneity-Induced welfare change and trade impact leads to biases in the overall changes. Finally, the EU’s relatively inelastic import demand for products from the UK implies that other countries, including developing or transition economies, may not be affected in a significant way. The EU in the short run will continue to import products from the UK despite the higher tariffs, so there may not be large trade diversion to other countries. However, in the long run, firms may relocate to countries that face lower or no tariffs in the EU market, such as Ireland and Poland. That may result in larger trade and welfare 31 This is an empirical finding with good theoretical justifications rooted in the optimal tariff model: in order to minimize deadweight loss, countries with market power will levy higher tariffs on products that have lower elasticities, leading to the negative correlation. However, this negative correlation between tariff and elasticity does not always hold empirically. Regression results show that, controlling for exporter fixed effects and HS 6-digit product fixed effects, the partial correlation between the EU’s bilateral applied tariffs and the estimated bilateral elasticities is positive. This implies that the EU tends to impose lower tariffs on less elastic products across trading partners. This is likely due to the EU’s preferential tariffs for developing countries, which tend to export agriculture products that have low elasticities. 19 impacts. 7 Robustness Checks 7.1 Homogeneous Elasticities The first robustness test is to compute trade and welfare effects assuming homogeneous elasticities across the EU’s trading partners. This is done by setting the UK elasticities equal to the mean across all countries within the same HS 6-digit product. The results are presented in Table 5. Given that on average, the elasticity facing the UK’s exports to the EU is 30 percent smaller than the sample mean, this results in larger trade and welfare losses and highlights the important of using UK specific bilateral trade elasticities. The second robustness check is to compare the resulting trade and welfare effects with those obtained using homogeneous elasticities across products. The results are presented in Table 6. In Column (1), we assume that for all products, the elasticity is equal to the import weighted average elasticity of the sample, which is -3.85. In this case, the TRI and OTRI are 4.60 percent and 2.81 percent, respectively. Because of the homogeneous trade elasticity, there is no covariance between tariffs and elasticity, the overall welfare and trade changes are exactly equal to the Tariff-Induced welfare and trade changes of Table 4.32 Columns (2) and (3) of Table 6 show the results by setting the homogeneous trade elasticity to -4 and -8, values commonly assumed in the existing literature. In both cases, the levels of TRI and OTRI remain the same as the first column, despite differences in the levels of homogeneous elasticity. This is because with the homogeneous elasticities, the 32 This finding provides the empirical support for Propositions 1 and 2 of Sections A2 and A3 of the Appendix. The result further demonstrates the upward bias (in magnitude) for the calculations of the overall welfare and trade impacts assuming homogeneous trade elasticities when in fact there is a negative correlation between tariff and elasticity. 20 levels of TRI and OTRI only depend on tariffs, according to Equations (15) and (18).33 However, welfare and trade changes are larger in magnitude because they increase with size of the average elasticities, according to Equations (16) and (19). This shows that the upward biases are even larger (in magnitude) for the calculations of the overall welfare and trade impacts when the assumed homogeneous trade elasticity is larger. 7.2 Different Elasticity Estimates As an additional robustness check, we substitute our trade elasticity estimates with the esti- mates from Caliendo and Parro (2015) and then of Ossa (2015). There are some fundamental differences between these trade elasticity estimates. First, their estimates are at more ag- gregated sectoral levels: 2-digit ISIC Rev. 3 for Caliendo and Parro (2015) with 20 sectors, and 3-digit SITC for Ossa (2015) with 200 industries. Our elasticity estimates are at the HS 6-digit level for about 5000 products. Second, their elasticity estimates are homogeneous across countries, while ours are specific to each bilateral importer-exporter pair.34 Finally, the elasticity estimates from Caliendo and Parro (2015), denoted as θ, capture the percent- age change in the trade value of a sector with respect to a one percent increase in the tariff, while the elasticity estimates of Ossa (2015), denoted as σ, are defined as the elasticity of substitution from the CES aggregate. Our elasticities, denoted as ε, measure the percentage change in the imported quantity of a product with respect to a one percentage increase in its price. The following relationship holds for these elasticities (ignoring the differences in 2 33 Equations (15) and (18) can be verified empirically when elasticities are homogeneous: TRI = 2 2 (0.046/1.046) = 0.0019. τ ¯2 = (0.027) = 0.0007 is the square of the import weighted average of tar- 2 iff/(1+tariff); σ = 0.0012, and ρ = 0. Thus, TRI does not depend on the levels of the average homoegeneous elasticity. Likewise, OTRI = (0.028/1.028) = 0.027 = τ ¯, suggesting that OTRI does not depend on the levels of the average homogeneous elasticity. 34 For example, Caliendo and Parro (2015) have one elasticity estimate for “Auto” industry for all countries, while we have an elasticity estimate for HS 870332, which is “Vehicles principally designed for the transport of persons (excl. of 87.02 & 8703.10-8703.24), with C-I internal combustion piston engine (diesel/semi-diesel), of a cylinder capacity >1500cc but not >2500cc” imported by the EU from the UK. 21 product aggregation and country bilateral variations):35 −θ − 1 = −σ = ε < 0. (21) To compare the results obtained using these different elasticities, we first aggregate the EU MFN tariff schedule, from the HS 6-digit level to both the corresponding ISIC and SITC levels. We then use these elasticities to calculate TRI, deadweight loss, OTRI and trade impact accordingly, with adjustments based on (21). Columns (4) and (5) of Table 6 present the results. Overall, while these elasticities are fundamentally different, the results are remarkably consistent with trade losses of 5 to 8 percent, and welfare losses of less than 1 percent. Column (6) of Table 6 presents the result when we purposely reshuffle the heterogeneous trade elasticities to minimize the correlation between trade elasticities and tariffs. This is to show that even with heterogeneous elasticities, if there is no negative correlation between tariffs and elasticities, the welfare and trade impacts calculations will be larger in magnitude: the UK’s potential trade loss from Brexit is around 33 percent, and the EU’s welfare loss is about 1.2 percent. Both of these impacts are larger than the results presented in Table 4 when the empirical negative correlations between tariffs and elasticities are allowed. 7.3 Sectoral Impacts In this robustness check we show how heterogeneous elasticities result in very diverse sectoral effects. Table 7 presents the sectoral breakdown of the trade impact post-Brexit. The first two columns show the composition of the UK’s exports to the EU by SITC sectors. Nearly 60 percent of the UK’s exports to the EU are in the Machinery and Transport Equipment 35 Please refer to Section A1 of the Appendix for the proof. 22 sector, and the Chemical sector. If these sectors were to face MFN tariffs of about 3 percent, the drop in their exports would be about 1.6 percent to 2.8 percent. These two sectors also have relatively low import elasticities (around -1.6). Across all sectors, there is a negative correlation between MFN tariffs and trade elasticities, which is the reason why the aggregate trade impacts of a No-Deal Brexit are not larger. Thus the sectoral results presented in Table 7 are consistent with the aggregate results presented in Table 4. 8 Concluding Remarks This paper presents a way to quantify the trade and welfare impacts of trade policy changes, taking into account the heterogeneity in trade elasticities. This is motivated by the empirical observations that bilateral trade between countries tend to respond differently facing trade policy shocks, in part due to the varying trading relationships between these countries. Our partial equilibrium approach is rich in product and country heterogeneity, and complements the existing general equilibrium gravity framework, which often assumes homogeneity across countries in evaluating trade and welfare impacts. As an illustration, this paper studies a hypothetical No-Deal Brexit, in which the EU was to impose MFN tariffs on products imported from the UK. Trade elasticities are estimated at the detailed product level that vary across the EU’s top 100 trading partners, including the UK. The results show that exports from the UK to the EU would decrease by 6.4 percent, while both the EU and the UK would experience short-run welfare losses of less than 1 percent, measured in terms of their GDP. The impacts would be larger if the trade elasticities are homogeneous. This is because of the low bilateral EU-UK trade elasticities. The negative correlation between the elasticities and the EU’s tariffs further tapers the impacts of a No-Deal Brexit. The findings suggest that an increase in trade barriers between 23 highly interconnected economies may result in lower short-term welfare losses than those suggested by trade models using aggregated data with homogeneous trade elasticities. In this vein, our results would suggest that the current US-China trade disputes with tariff hikes may not impact trade significantly in the short run due to their existing trading relationship. Long-term impacts may involve relocation of firms, which is beyond the scope of the current paper. References [1] Anderson, J., Neary, P. (1992). “Trade reforms with quotas, partial rent retention and tariffs”, Econometrica 60(1): 57-76. [2] Anderson, J., Neary, P. (1994). “Measuring the restrictiveness of trade policy”, World Bank Economic Review 8(2): 151-69. [3] Anderson, J., Neary, P. (1996). “A new approach to evaluating trade policy”, Review of Economic Studies 63(1): 107-25. [4] Anderson, J., Neary, P. (2003). “The Mercantilist index of trade policy”, International Economic Review 44(2): 627-49. [5] Anderson, J., Neary, P. (2007). “Welfare versus market access: the implications of tariff structure for tariff reform”, Journal of International Economics 71(1): 187-205. [6] Anderson, J., Yotov, Y. (2016). “Terms of trade and global efficiency effects of free trade agreements, 1990–2002,” Journal of International Economics 99: 279-98. 24 [7] Bagwell, K., Staiger, R. (2011). “What Do Trade Negotiators Negotiate About? Empir- ical Evidence from the World Trade Organization.” American Economic Review 101(4): 1238-73. [8] Baldwin, R. (2016). “Brexit Beckons: Thinking ahead by leading economists,” http://voxeu.org/content/brexit-beckons-thinking-ahead-leading-economists. [9] Blackorby, C., Russell, R. (1981). “The Morishima Elasticity of Substitution; Symmetry, Constancy, Separability, and its Relationship to the Hicks and Allen Elasticities,” Review of Economic Studies 48: 147-58. [10] Bloom, N., Mizen, P. (2017). “New survey evidence on the impact of Brexit on UK firms,” Voxeu: http://voxeu.org/article/new-survey-evidence-impact-brexit-uk-firms. [11] Broda, C., Limao, N., Weinstein, D. (2008). “Optimal Tariffs and Market Power: The Evidence.” American Economic Review 98 (5): 2032-65. [12] Caliendo, L., Feenstra, R. (2022). “Foundation of the Small Open Economy Model with Product Differentiation.” Working paper. [13] Caliendo, L., Parro, F. (2015). “Estimates of the Trade and Welfare Effects of North American Free Trade Agreement.” The Review of Economic Studies 82(1): 1-44. [14] Caves, D, Christensen, L., Diewert, E. (1982). “Multilateral Comparisons of Output, Input, and Productivity using Superlative Index Numbers.” Economic Journal 92: 73- 86. [15] Chen, N. and D. Novy (2022). Gravity and Heterogeneous Trade Cost Elasticities. Economic Journal 132(644): 1349–77. 25 [16] de Gortari, A. (2019). “Disentangling Global Value Chains,” NBER Working Paper 25868. [17] Diewert, E. (1974). “Applications of Duality Theory”, pp. 106-171 in Frontiers of Quan- titative Economics, Volume II, M. Intriligator and D. Kendrick, eds., Amsterdam: North-Holland. [18] Diewert, E., Wales, T. (1988). “A Normalized Quadratic Semiflexible Function Form,” Journal of Econometrics 37: 327-42. [19] Dhingra, S., Huang, H., Ottaviano, G., Sampson, T., Van Reenen, J., (2016) “The Costs and Benefits of Leaving the EU: Trade Effects,” CEP working paper 1478. [20] Feenstra, R. (1995). “Estimating the effects of trade policy,” in Handbook of Interna- tional Economics, vol. 3 (G. Grossman and K. Rogoff, eds.), Amsterdam: Elsevier. [21] Feenstra, R. (2015). Advanced International Trade: Theory and Evidence, 2e, Princeton University Press. [22] Fernandes, A., Kee, H. L., Winkler, D. (2022) “Determinants of Global Value Chain Participation: Cross-Country Evidence,” World Bank Economic Review 36(2): 329–360. [23] Grinols, E. (1984). “A Thorn in the Lion’s Paw: Has Britain Paid Too Much for Common Market Membership?” Journal of International Economics 16: 271-93. [24] Gudgin, G., Coutts, K., Gibson, N., Buchanan, J. (2017). “The Role of Gravity Models in Estimating the Economic Impact of Brexit,” Centre for Business Research, University of Cambridge, Working Paper No. 490. [25] Harrigan, J. (1997). “Technology, Factor Supplies, and International Specialization: Estimating the Neoclassical Model,” American Economic Review 87(4): 475-94. 26 [26] Helpman, E., Melitz, M., Rubinstein, Y. (2008). “Estimating trade flows: trading part- ners and trading volumes.” Quarterly Journal of Economics 123(2): 441-87. [27] Imbs, J., Mejean, I. (2017). “Trade Elasticities”, Review of International Economics 25(2): 383-402. [28] Juarez, L. (2023). “Buyer Market Power and Exchange Rate Pass-through”. Job Market Paper, University of Michigan. [29] Kee, H.L., Nicita, A., Olarreaga, M. (2008). ‘Import demand elasticities and trade distortions’, Review of Economics and Statistics 90(4): 666–82. [30] Kee, H.L., Nicita, A., Olarreaga, M. (2009). ‘Estimating Trade Restrictiveness Indices,” Economic Journal 119: 172–99. [31] Kohli, U. (1991). Technology, Duality, and Foreign Trade: The GNP Function Approach to Modeling Imports and Exports, The University of Michigan Press, Ann Arbor. [32] Krugman, P., Obstfeld, M., Melitz, M. (2022). International Trade: Theory and Policy 12e. Pearson. [33] Krugman, P. (1981). Intraindustry Specialization and the Gains from Trade. Journal of Political Economy 89(5): 959-73. [34] Melitz, M., Redding, S. (2015). “New Trade Models, New Welfare Implications.” Amer- ican Economic Review 105(3): 1105-46. [35] Novy, D. (2013). International Trade without CES: Estimating Translog Gravity, Jour- nal of International Economics 89(2): 271-282. [36] Lawless, M., Morgenroth, E. (2019) “The product and sector level impact of a hard Brexit across the EU,” Contemporary Social Science 14(2): 189-207. 27 [37] Ossa, R. (2015). “Why trade matters after all.” Journal of International Economics 97(2): 266-77. [38] Semykina, A., Wooldridge, J. (2010). “Estimating Panel Data Models in the Presence of Endogeneity and Selection,” Journal of Econometrics 157: 375-80. [39] Simonovska, Ina and Michael Waugh (2014). “The elasticity of trade: Estimates and evidence,” Journal of International Economics 92(1), 34-50. [40] Soderbery, Anson (2021). “Trade restrictiveness indexes and welfare: A structural ap- proach,” Canadian Journal of Economics 54(3), 1018-1045. [41] World Bank (2020). World Development Report 2020: Trading for Development in the Age of Global Value Chains, the World Bank. Table 1: Summary Statistics of Trade Policies of EU for a No-Deal Brexit MFN ad valorem tariff % Maximum 74.9 Minimum 0 Import weighted average 2.95 Import weighted variance 15.17 Table 2: Summary Statistics of the Estimated Trade Elasticities of the EU UK All Mean -13.90 -47.80 Median -1.76 -20.55 Standard Deviation 38.81 70.28 Maximum -0.004 -0.000 Minimum -427.60 -444.38 Observations 5,050 417,580 28 Table 3: Dependent Variables: Estimated Trade Elasticities (1) UK 34.42*** (0.57) Constant -48.21*** (0.01) HS 6-digit product FE Yes Observation 417,580 Table 4: Potential Short-Run Impact of Brexit Overall Tariff- Heterogeneity- Induced Induced EU’s Bilateral-TRI wrt the UK (%) 4.41 Welfare change of the EU (%) -0.34 -0.37 0.03 Welfare change of the EU ($B) -0.55 -0.60 0.05 EU’s Bilateral-OTRI wrt the UK (%) 2.29 Trade impact of the UK (%) -6.38 -7.81 1.43 Trade impact of the UK ($B) -10.2 -12.5 2.28 Table 5: Robustness Check Using Homogeneous Elasticities Across All Partner Countries Overall Tariff- Heterogeneity- Induced Induced EU’s Bilateral-TRI wrt the UK (%) 5.20 Welfare change of the EU (%) -5.52 -4.36 -1.17 Welfare change of the EU ($B) -8.83 -6.97 -1.86 EU’s Bilateral-OTRI wrt the UK (%) 3.26 Trade impact of the UK (%) -139.38 -120.76 -18.62 Trade impact of the UK ($B) -223 -193 -29.8 Table 6: Robustness Checks with Different Elasticities Homogeneous Elasticities from Reshuffled Elasticity Caliendo-Parro Ossa Elasticities -3.85 -4 -8 (2015) (2015) w/ no Correlation (1) (2) (3) (4) (5) (6) EU’s Bilateral-TRI wrt the UK (%) 4.60 4.60 4.60 2.91 4.01 4.48 Welfare change of the EU (%) -0.37 -0.39 -0.77 -0.15 -0.20 -1.22 Welfare change of the EU ($B) -0.60 -0.62 -1.23 -0.26 -0.31 -1.95 EU’s Bilateral-OTRI wrt the UK (%) 2.81 2.81 2.81 2.35 2.23 2.77 Trade impact of the UK (%) -7.81 -8.20 -19.1 -8.13 -5.68 -33.0 Trade impact of the UK ($B) -12.5 -13.1 -30.6 -14.48 -8.69 -52.7 29 Table 7: Potential Short-Run Impacts of Brexit by Sectors SITC Rev 4 Export Import Weighted Average OTRI Trade Impact Sector Description $Bil. % MFN Tariff (%) Elasticity % $Bil. % 0 Food and live animals 4.39 2.74 8.51 -13.33 6.09 -3.10 -70.79 1 Beverages and tobacco 2.57 1.61 1.93 -1.14 14.37 -0.05 -1.76 2 Crude materials 3.03 1.89 0.47 -18.63 0.05 -0.03 -0.91 3 Mineral fuels 19.29 12.06 0.75 -10.69 0.16 -0.30 -1.56 4 Animal and veg. oils 0.37 0.23 5.64 -26.56 7.80 -0.69 -185.02 5 Chemicals 28.75 17.97 2.65 -1.69 4.21 -0.80 -2.80 6 Manufacturing material 16.42 10.27 2.60 -4.59 3.52 -2.01 -12.21 7 Machinery and transport 67.00 41.89 3.38 -1.60 2.67 -1.04 -1.56 8 Misc. manufacturing 17.20 10.75 3.82 -2.95 6.95 -2.18 -12.69 9 Other Commodities 0.93 0.58 0.00 -0.49 0.00 0.00 0.00 30 Appendix A1 Trade Elasticities vs. Import Demand Elasticities Trade elasticities equal (negative) import demand elasticities when prices and quantities of other products do not change. Let xi = pi qi , the trade elasticity is defined as xi ∂ ln xj σ−1 ≡ − pi ∂ ln pj xi pi ∂ xj pj = − pi xi ∂ pj xj 1 xj ∂xi xj pi = − 1 , assuming xj and pj are constant, pj ∂pi pj xi ∂xi pi = − ∂pi xi ∂pi qi pi = − ∂pi pi qi ∂qi 1 = − qi + p i ∂pi qi ∂qi pi = −1 − ∂pi qi = −1 − εi ==> σ = −εi , ∀i. A2 The Bilateral Trade Restrictiveness Index Let’s define pncd , qncd , εncd , τncd as the bilateral import price, quantity, import elasticity (negative) and the ad valorem tariff of product n of country c from country d, respectively. 1 The bilateral-TRI of country c with respect to products from country d is  2  1 /2 τncd T RIcd  (1/2) n pncd qncd εncd 1+τncd  =   (A1) 1 + T RIcd (1/2) n pncd qncd εncd 2 1 /2 (1/2) ˜ncd pncd qncd εncd τ x T RI cd = n ˜≡ , with x or (1/2) n pncd qncd εncd 1+x ∑ ( )2 1/ 2 τ (1/2) pncd qncd εncd 1+ncd n τncd ∑ (1/2) n pncd qncd εncd T RIcd = ( )2 1/2 (A2) ∑ τncd (1/2) n pncd qncd εncd 1+τncd 1− ∑ (1/2) n pncd qncd εncd By definition, the numerator inside the parentheses of (A1) is the bilateral dead-weight loss (DWL) of the trade policy of c with respect to products from d. Let’s define Mcd ≡ n pncd qncd as the total imports of c from d, then, pncd qncd sncd = , Mcd is the share of each product n in the total imports of c from d. With some algebraic manip- ulations, the TRI can be decomposed into the following three terms: 2 2 1/2 TRIcd = τ ¯cd + σcd + ρ2 cd , (A3) 2 where τ ¯cd is the import weighted average tariff/(1 + tariff), σcd is the import weighted variance of tariff/(1 + tariff), and ρ2 cd is the import weighted covariance between the square of tariff/(1 + tariff) and import elasticity (re-scaled by the import weighted average import 2 ¯cd ).36 Equation (A3) indicates that the TRI will be higher when the bilateral tariff elasticity, ε of c on products from d has a higher average, a large variance or a high correlation with the bilateral import elasticity re-scaled by mean. Note that while import elasticity is non- positive, a re-scaled elasticity is by construction positive, which facilitates the interpretation that a higher correlation implies that larger tariffs are levied on more elastic products. When import elasticity is homogeneous, TRI only depends on import weighted average tariffs and the variance of tariffs: 2 2 2 TRIcd = τ ¯cd + σcd if εncd is constant. It is straightforward to construct the DWL of trade policy from (A1) and (A3) : 1 DWLcd ≡ pncd qncd εncd τ 2 ˜ncd < 0, given that εncd ≤ 0 2 n 1 2 = TRIcd Mcd ε ¯cd , 2 1 2 2 1 2 = τ ¯cd + σcd ¯cd + Mcd ε ¯cd ρ Mcd ε , in level, or (A4) 2 2 cd Tariff-Induced DWL Heterogeneity-Induced DWL DWLcd 1 2 2 1 = τ ¯cd + σcd ¯cd + ρ2 ε ¯cd , in share. ε (A5) Mcd 2 2 cd Thus, the higher the TRI is (which could be due to a higher average tariff, a higher variance 36 To be clear, τ ¯cd ≡ ˜ncd , sncd τ n 2 2 σcd ≡ τncd − τ sncd (˜ ¯cd ) n ε ¯cd ≡ sncd εncd < 0 n εncd 2 εncd εncd ¯cd ε ρ2 cd = Cov ˜ncd , where ,τ > 0 and E = = 1. ¯cd ε ¯cd ε ¯cd ε ¯cd ε 3 of tariffs, or a higher covariance between tariffs and elasticity), the larger is the magnitude of the DWL. The converse is true as well, if the average tariff is lower, or the variance of tariffs is lower, or if higher tariffs are levied on less elastic products, then moving from free trade to restrictive trade will generate a smaller welfare loss. Equation (A4) shows that heterogeneous import elasticity will affect the welfare calcu- lation through its correlation with the tariffs, ρ2 cd . Let’s define the first term of (A4) as the Tariff-Induced DWL, and the second term of (A4) as the Heterogeneity-Induced DWL. The following proposition summarizes the relationship between DWL and the heterogeneity in import elasticities. Proposition 1 Given an importing country, c, and an exporting country, d, the dead weight loss (DWL) moving from free to restricted trade due to c imposing differential tariffs on products from d depends on the bilateral import elasticities and tariffs, such that: 1. if import elasticities are homogeneous, then the DWL equals the Tariff-Induced DWL, and the Heterogeneity-Induced DWL is zero; 2. if import elasticities are heterogeneous and are positively correlated with tariffs (after re-scaling), which is when higher tariffs are levied on the more elastic product, then the DWL is larger than the Tariff-Induced DWL in magnitude, and the Heterogeneity- Induced DWL is negative; 3. if import elasticities are heterogeneous and are negatively correlated with tariffs (after re-scaling), which is when higher tariffs are levied on the less elastic product, then the DWL is smaller than the Tariff-Induced DWL in magnitude, and the Heterogeneity- Induced DWL is positive. Proof. From (A4) , given ε ¯cd < 0 4 1 2 2 1. when import elasticities are homogeneous ==>ρ2 cd = 0 ==> DWLcd = ¯ + σcd τ ¯cd , Mcd ε 2 cd Tariff-Induced DWL 1 2 and ¯cd ρ Mcd ε = 0; 2 cd Heterogeneity-Induced DWL 2. when higher tariffs are levied on more elastic products such that ρ2 cd > 0 ==> 1 2 1 2 |DW Lcd | > 2 ¯cd + σcd τ ¯cd , and Mcd ε ρ Mcd ε¯cd < 0; 2 2 cd Heterogeneity-Induced DWL Tariff-Induced DWL cd < 0 ==> |DW Lcd | < 3. when higher tariffs are levied on less elastic products such that ρ2 1 2 2 1 2 τ ¯cd + σcd Mcd ε¯cd , and ρ Mcd ε ¯cd > 0. 2 2 cd Heterogeneity-Induced DWL Tariff-Induced DWL A3 The Bilateral Overall Trade Restrictiveness Index We define the OTRI as the uniform ad valorem tariff of the EU (indexed by c) with respect to imports from the UK (indexed by d), facing world price pn for each good n with bilateral tariff τncd and import quantity qncd : ∂pncd pncd pncd = pn (1 + τncd ) ==> = pn = ∂τncd (1 + τncd ) {OT RIcd | n pncd qncd (τncd ) =n pncd qncd (OT RIcd )} , (A6) with pncd , qncd , εncd , τncd represent the bilateral import price, quantity, demand elasticity (negative) and the ad valorem tariff of product n of c from d, respectively. Total differenti- 5 ating Equation (A6) with respect to tariff and evaluating at equilibrium gives us: ∂pncd ∂qncd (τncd ) ∂pncd n qncd (τncd ) τncd + pncd τncd ∂τncd ∂pncd ∂τncd ∂pncd ∂qncd (τncd ) ∂pncd = n qncd (τncd ) OT RIcd + pncd OT RIcd ∂τncd ∂pncd ∂τncd τncd OT RIcd n pncd qncd [1 + εncd ] = n pn qncd [1 + εncd ] 1 + τncd 1 + OT RIcd x n pn qncd (1 + εncd )˜ τncd = OT RI cdn pn qncd (1 + εncd ), with x ˜≡ 1+x p q n n ncd (1 + ε )˜ τ ncd ncd OT RI cd = or p q n n ncd (1 + εncd ) τncd n mncd (1 + εncd ) 1+τncd OTRIcd = 1 . (A7) n mncd (1 + εncd ) 1+τncd Equation (A7) takes into account the bilateral import elasticities of all products n, εncd , bilateral trade policy, τncd , and bilateral trade value, mncd . By definition, the numerator of (A7) is the bilateral trade impact of d due to the trade policy τncd of c, when c is moving from free to restricted trade with d. With some simple algebraic manipulations, it can be shown that the OTRI can be decomposed into two terms: OT RI cd = τ ¯cd + ρcd , (A8) 1 + εncd ρcd = Cov ˜ncd ,τ 1+ε ¯cd ¯cd is the import weighted average tariff/(1+tariff) and ρcd is the where, similar to the TRI, τ import weighted covariance between tariff/(1+tariff) and (1+trade elasticity) (re-scaled by its mean). From (A8) it is evident that the OTRI is higher when the bilateral trade policy of c on products from d has a higher average or a high correlation with the bilateral trade elasticity. Unlike the TRI, the OTRI is not affected by the variance of tariffs. To construct the bilateral trade impact of c on d moving from free to restrictive trade 6 based on bilateral tariff τncd , we use (A7) and (A8) : ∆Mcd ≡ ˜ncd < 0 pncd qncd (1 + εncd ) τ n ¯cd ) = OT RI cd Mcd (1 + ε = τ ¯cd ) + ¯cd Mcd (1 + ε ¯cd ) ρcd Mcd (1 + ε , in level, or (A9) Tariff-Induced Trade Impact Heterogeneity-Induced Trade Impact ∆Mcd ¯cd (1 + ε = τ ¯cd ), in share. ¯cd ) + ρcd (1 + ε (A10) Mcd Thus, the higher is the OTRI (which could be due to a higher average tariff or a higher covariance between tariffs and (re-scaled) elasticity), the greater is the magnitude of the trade impact of the restrictive trade policy. The converse is true as well. If the average tariff is lower, or if tariffs and (re-scaled) elasticities are negatively correlated, then moving from free trade to restrictive trade between c and d will generate a smaller trade loss. Equation (A9) shows that the trade impact for the UK is affected by the correlation between heterogeneous trade elasticities and tariffs. We summarize those relationships in the proposition below. Proposition 2 Given an importing country, c, and an exporting country, d, the trade impact moving from free to restricted trade due to c imposing tariffs on products from d depends on the bilateral import elasticities and tariffs, such that: 1. if import elasticities are homogeneous, then the trade impact equals the Tariff-Induced Trade Impact, and the Heterogeneity-Induced Trade Impact is zero; 2. if import elasticities are heterogeneous and are positively correlated with tariffs (after re-scaling), which is when higher tariffs are levied on more elastic products, then the overall trade impact is larger than the Tariff-Induced Trade Impact in magnitude, and Heterogeneity-Induced Trade Impact is negative; 7 3. if import elasticities are heterogeneous and are negatively correlated with tariffs (after re-scaling), which is when higher tariffs are levied on less elastic products, then the overall trade impact is smaller than the Tariff-Induced Trade Impact in magnitude, and the Heterogeneity-Induced Trade Impact is positive. Proof. From (A9) , if (1 + ε ¯cd ) < 0, 1. when import elasticities are homogeneous ==> ρcd = 0 ==> ∆Mcd = τ ¯cd ) , ¯cd Mcd (1 + ε Tariff-Induced Trade Impact and ¯cd ) ρcd Mcd (1 + ε = 0; Heterogeneity-Induced Trade Impact 2. when higher tariffs are levied on more elastic products such that ρcd > 0 ==> |∆Mcd | > |τ ¯cd )| , and ¯cd Mcd (1 + ε ¯cd ) ρcd Mcd (1 + ε < 0; Tariff-Induced Trade Impact Heterogeneity-Induced Trade Impact 3. when higher tariffs are levied on less elastic products such that ρcd < 0 ==>|∆Mcd | < |τ ¯cd )| , and ¯cd Mcd (1 + ε ¯cd ) ρcd Mcd (1 + ε > 0. Tariff-Induced Trade Impact Heterogeneity-Induced Trade Impact A4 Translog GDP Function Approach Let’s define Gt (pt , v t ) be the GDP function of a small open economy, facing ad valorem tariff- inclusive price, pt , factor endowment, v t , and the strictly convex production set defined by St : Gt pt , v t = max t pt · q t : q t , v t ∈ St q t For each period, t, the net output vector q t = (q1 t , q2 t , ..., qN ) is chosen to maximize GDP, with positive elements denoting outputs, which include exports, and negative numbers denoting inputs, which include imported goods (see Kohli, 1991). We consider imported 8 goods and competing domestically produced goods as differentiated products. Similarly, domestic products sold in the domestic market are differentiated from products sold in foreign markets (i.e., exported). To implement the above GDP function empirically, we assume that Gt (pt , v t ) follows a translog functional form, with n and k index goods, and m and l index factors: 1N N ln G pt , v t = a00 +N t n=1 a0n ln pn + ank ln pt t n ln pk 2 n=1 k=1 1M M +M t m=1 b0m ln vm + t bml ln vm ln vlt 2 m=1 l=1 +N M t t n=1 m=1 cnm ln pn ln vm , (A11) which satisfy the following homogeneity and symmetry restrictions, with respect to prices and factor endowments: n=1 cnm = 0, ank = akn , ∀n, k = 1, ..., N, m = 1, ..., M. (A12) N N n=1 a0n = 1, k=1 ank =N m=1 cnm = 0, bnk = bkn , ∀n, k = 1, ..., N, m = 1, ..., M. (A13) N N n=1 b0n = 1, k=1 bnk =M The Envelope theorem implies that at the equilibrium, the derivative of ln G (pt , v t ) with respect to ln pt n is the share of good n in GDP at period t : pt t t t n qn ( p , v ) st t t n p ,v ≡ = a0 n + N t M t k=1 ank ln pk +m=1 cnm ln vm Gt ( pt , v t ) n +k̸=n ank ln pk +m=1 cnm ln vm , ∀n = 1, ..., N, = a0n + ann ln pt t M t (A14) where st t n is the share of good n in GDP (sn < 0 if good n is an input, as in the case of imports). We further apply a semiflexible functional form developed by Diewert and Wales (1988) specifically designed to handle translog models with a large number of goods, by 9 reparametrizing the translog function with the following constraints: ank = γan ak , ∀n ̸= k, (A15) ann = −γan ak . (A16) k̸=n The resulting share equation for each good n is pt t vm st t t n p ,v = a0n + ann ln n +M m̸=l,m=1 cnm ln , ∀n = 1, ..., N, pt k vlt where ln pt ∑ ak ln pt k = k̸=n k̸=n ak k is a weighted average of the log prices of all non-n goods. Thus with this reparametrization, the resulting share equation of good n depends linearly on the log price of good n relative to an average price of all non-n goods, and the relative endowments. This significantly reduces the number of variables on the right-hand side from N + M, to M. For every good n, we approximate the average price with the observed Tornqvist price index of all non-n goods, ln p−n , which is the share-weighted average prices of all non-n goods. It is constructed using the GDP deflator net of the price of good n, adjusted by the share of non-n goods,37 t −1 −n = ln p − s ln pt n ln pn / 1 − s t ¯t t ¯t ¯t n , where s t n = 0 . 5 sn + sn . (A17) 37 Caves, Christensen and Diewert (1982) show that the GDP deflator of a translog GDP function with time invariant parameters is a Tornqvist price index. Thus, we can derive the aggregate price of all non-n goods by using the GDP deflator, ln pt , net of the price of good n, adjusted by the share of all non-n goods: ln pt ≡ ¯t s t ¯t k ln pk = s n ln pn + 1 − s t ¯t t n ln p−n =⇒ k ln pt −n = ln pt − s ¯tn ln pn / 1 − s t ¯tn . 10 This approximation introduces an additive error term to reflect measurement error in each share equation, κt n : ¯t s 1 t −1 −n ≡ k ln pt ln pt ¯t k , where s k = s + st k̸=n ¯t k̸=n s k 2 k k t t ln pt k = ln p−n + κn , (A18) pt t vm n , ∀n = 1, ..., N. n st t t n p ,v = a0n + ann ln + M c m̸=l,m=1 nm ln + κt (A19) pt −n v t l Equation (A19) forms the basis to estimate the translog parameter, ann , which is necessary to construct the own-price import elasticity, εnn , t ∂qn ( pt , v t ) pt nn ≡ n εt (A20) ∂pt n q t n ann = t + st n−1 ≤ 0 , ∀ st n < 0, (A21) sn and the cross-price elasticity for good −n : −ann εt n−nd = + st −nd . (A22) st nd A5 Positive Trade and Relative Prices t In Section 5.2, we first define a dummy variable, Dnd that indicates the presence of trade for each HS 6-digit product, n, in year t, from exporting country, d,    1, if st < 0 t nd Dnd =   0, otherwise. 11 In other words, Dnd = 1 if the following share equation for imported good n from d is negative: ptnd t vm st t t nd p , v = a0n + ann ln t + M c m̸=l,m=1 nm ln t + κt nd < 0. p−nd vl Alternatively, if there is no trade from exporting country, d′ , then Dnd′ = 0 or ptnd′ t vm st nd′ ≥ 0. t t M nd′ p , v = a0n + ann ln + m̸=l,m=1 c nm ln + κt pt −nd ′ v t l The comparison of d to d′ clarifies that the differences are driven in part by differences in relative prices, as well as the unobserved error terms: pt ptnd′ st t t nd p , v − st t t nd′ p , v = ann ln t nd − ln t nd − κnd′ < 0. + κt t p−nd p−nd′ Assuming that the unobserved error terms are random. If ann is positive, and Dnd = 1 while Dnd′ = 0, then it implies that the relative price of d is lower than that of d′ . In other words, countries that do not export product n to the EU are those countries with higher tariff-inclusive prices. This could be due to a higher tariff, higher variable trade costs or higher production costs. Conversely, if ann is negative, and Dnd = 1 while Dnd′ = 0, then it implies that the relative price of d is higher than that of d′ . In this case, countries that do export product n to the EU are those countries with higher tariff-inclusive prices, which could signal better product quality or very specific products. Indeed, the results of our estimation reveal that about 10 percent of the HS 6-digit products have negative ann estimates. These products are concentrated in the electronics, machinery and equipment industries (HS 84, 85, 90), which may indicate the imports of special parts and components at a higher price to ensure quality and fit. 12 A6 Cross Country Comparison of Trade Elasticities To show that trade elasticities of the UK for products imported to the EU are indeed different than the trade elasticities of other trading partners, we conduct the following thought ex- periment. We exclude one exporting country at a time to run about 100 gravity regressions, regressing the log of the aggregate bilateral trade on the log of the GDP of the exporting country and the log of the distance between the exporting country and the EU. In this spec- ification, the log of distance is used as a proxy for variable trade costs, so its coefficient has the interpretation of the trade elasticity. Each bar in Figure A1 represents the absolute value of the estimated trade elasticity when we drop the country on the X-axis. Note that not all country names are listed in the figure as it would not be legible. Excluding the UK from the regression significantly increases the estimated trade elasticity. The coefficient represented by the green bar (omitting the UK from the regression sample) is significantly larger than the coefficient represented by the red bar (regression sample with the UK). This implies that the UK faces a lower elasticity in the EU relative to other exporting countries. Figure A1: Trade Elasticity Estimates 13 A7 Income and Cross-Price Effects The analysis thus far only takes into account own-price elasticities, and thus may be con- sidered partial equilibrium in nature. While our analysis allows for heterogeneity across products and trading partners, some general equilibrium forces are missing, such as linkages across products, tariff revenue and possible terms-of-trade impacts. Anderson and Yotov (2016) find that terms-of-trade effects via changes in factor prices play a minor role in eval- uating the effects of the free trade agreements of the 1990s using nested CES/Cobb-Douglas preferences. In this section, we will focus on incorporating product linkages and tariff revenue into the calculation of trade and welfare impacts. When the price of a product increases due to a tariff, the demand for products that are either complements in consumption or are inputs in the production will decrease. This will lead to negative cross-price elasticities as well as magnify the negative trade impact. Conversely, the cross-price elasticities of substitutes will be positive therefore reducing the negative trade impact. On the other hand, while the welfare loss of the EU due to tariff increases will also lead to a decrease in demand for all normal goods, which will further exacerbate the negative trade impact, tariff revenue collected when distributed back to the consumers may generate positive income effect and increase the demand for all normal goods, possibly reducing the negative trade impact. There may also be tariff revenue collected due to the potential trade diversion effect when the EU switches from importing from the UK to importing from other countries.38 Thus, a priori, it is not clear whether the general equilibrium effect of tariff increases due to Brexit will be larger than the partial equilibrium effect. It depends on the magnitude of cross-price elasticity and income elasticity. In the 38 Grinols (1984) studies the potential welfare impact of the UK’s joining the European Economic Com- munity (EEC) and shows that in some years Britain would have been better off, by 34 percent of GDP, trading on its own. Its average losses were greater than 1.5 percent of GDP. Moreover, a feasible alternative arrangement is described in which Common Market association would benefit both Great Britain and other Common Market countries without harming non-Common Market countries. 14 interest of making our analysis comparable with the existing literature that focuses on general equilibrium effects, we will introduce these different forces in our OTRI framework. First, we assume that all the tariff revenue collected will be distributed back to the EU consumers who will use the full amount to buy products imported from the UK. This is equivalent to assume that all imported products from the UK are normal goods with an income elasticity of 1, and the EU consumers will not use the collected tariff revenue from UK products on other goods. If we define Tncd as the tariff revenue collected from good n, then this assumption implies that τncd Tncd = pncd qncd (A23) 1 + τncd ∂ ln qncd = 1. ∂ ln Tncd Therefore, the increase in tariff τncd will raise tariff revenue Tncd , which will be distributed back to consumers, who will use the tariff revenue collected to buy more of the imported good ncd. Second, we assume that the negative income effect due to the welfare loss from the tariff increase has a negligible impact on imports. Given the rather small size of deadweight loss listed in Table 4, which is about 0.5 percent of total imports from the UK, this assumption seems reasonable. Third, we assume that there is no general price increase due to the tariff increase on the UK’s products. Considering that the EU’s total imports from the UK is less than 1 percent of the EU’s GDP, this assumption also seems reasonable. To keep the analysis tractable, and following the notation of Section 2, for every n good, we define a non-n good, −n, which is a composite of all other goods in the economy, including both domestic and imported goods. Using the GDP deflator, p, we can construct the price of −n good according to Equation (3). We omit the time subscript since there is only one 15 year of data for this part of the analysis: ln p−ncd = (ln p − sncd ln pncd ) / (1 − sncd ) , (A24) ∂ ln p−ncd sncd = − , (A25) ∂ ln pncd 1 − sncd with the general price level, ln p, fixed by Assumption 3. The demand for each imported product, n, depends on its price, pncd , and the price of the non-n good, p−ncd , as well as tariff revenue, Tncd , qncd (pncd , p−ncd , Tncd ) . (A26) The cross-price elasticity of good n with respect to the price increase in good −n is defined by Equation (7): −ann −ann εn−ncd = + s−ncd = + 1 − sncd = −εncd , sncd sncd which is the negative of own-price elasticity. To find the trade impact in this general equi- librium set up, we need to first define the general equilibrium OTRI (GEOTRI): {GEOT RIcd | n pncd qncd (pncd , p−ncd , Tncd ) =n pncd qncd (pncd , p−ncd , GEOT RIcd )} . Total differentiation of the above equation with respect to τncd , results in the following for the right-hand side: ∂pncd ∂qncd ∂pncd ∂qncd ∂p−ncd ∂pncd ∂qncd ∂Tncd n qncd τncd + pncd τncd + pncd τncd + pncd τncd , ∂τncd ∂pncd ∂τncd ∂p−ncd ∂pncd ∂τncd ∂Tncd ∂τncd where the first two terms are the same as before, capturing the own-price impact on trade 16 value when a tariff increases. The last two terms are the new general equilibrium effects, capturing the cross-price and income effects on trade value resulting from the increase in tariffs. Combining the four terms on the right-hand side and comparing that with the GEOTRI uniform tariff on the left-hand side: εncd τncd εncd GEOT RIcd n pncd qncd 2+ = n pncd qncd 2+ 1 − sncd 1 + τncd 1 − sncd 1 + GEOT RIcd εncd τncd GEOT RIcd n pncd qncd 2+ 1−sncd 1+τncd = . 1 + GEOT RIcd εncd n pncd qncd 2 + 1−sncd εncd It is clear that including cross-price effects inflates the elasticities, 1−sncd , while including τncd tariff revenue increases imports by exactly the same amount, pncd qncd 1+ τncd . Likewise, it can be shown that the general equilibrium TRI (GETRI) is derived as the following:  2  1/ 2 εncd τncd GET RIcd  (1/2) n pncd qncd 1 + 1−sncd 1+τncd  =  . 1 + GET RIcd (1/2) n pncd qncd 1 + εncd 1−sncd Table A1 presents the results with three scenarios: (1) own-price and cross-price effects; (2) own-price and income effects; (3) own-price, cross-price and income effects. With only own-price and cross-price effects and without considering the positive income effect due to tariff revenue, the trade and welfare effects presented in Column (1) are slightly larger than the partial equilibrium result presented in Table 4. This finding is consistent with Ossa (2015) and Caliendo and Parro (2015) where they include input-output linkages and find that welfare gains from trade are generally higher. Column (2) only considers the positive income effect due to the redistributed tariff revenues. Here the trade and welfare impacts are smaller because the positive income effect softens the blow of tariff hikes due to a No-Deal Brexit. Column (3) includes both cross-price and income elasticities, so the resulting trade 17 and welfare impacts lie between the scenarios of Columns (1) and (2). Overall our general equilibrium results are broadly consistent with the findings of the existing literature. Table A1: Potential General Equilibrium Short-Run Impacts of Brexit Own-Price Effect + Cross-Price Effect Income Effect Cross-Price & Income Effects EU’s Bilateral-TRI wrt the UK (%) 4.37 4.34 4.29 Welfare change of the EU (%) -0.34 -0.25 -0.25 Welfare change of the EU ($B) -0.55 -0.39 -0.40 EU’s Bilateral-OTRI wrt the UK (%) 2.24 2.00 1.95 Trade impact of the UK (%) -6.40 -3.64 -3.67 Trade impact of the UK ($B) -10.2 -5.83 -5.86 18