Heterogeneous effects of tariff and nontariff trade-policy barriers in quantitative general equilibrium

Egger, Peter; Erhardt, Katharina Article Heterogeneous effects of tariff and nontariff trade-policy barriers in quantitative general equilibrium Quantitative Economics Provided in Cooperation with: The Econometric Society Suggested Citation: Egger, Peter; Erhardt, Katharina (2024) : Heterogeneous effects of tariff and nontariff trade-policy barriers in quantitative general equilibrium, Quantitative Economics, ISSN 1759-7331, The Econometric Society, New Haven, CT, Vol. 15, Iss. 2, pp. 453-487, https://doi.org/10.3982/QE1994 This Version is available at: https://hdl.handle.net/10419/320303 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. Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in EconStor may be saved and copied for your personal and scholarly purposes. You are not to copy documents for public or commercial purposes, to exhibit the documents publicly, to make them publicly available on the internet, or to distribute or otherwise use the documents in public. If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by-nc/4.0/ Quantitative Economics 15 (2024), 453–487 1759-7331/20240453 Heterogeneous effects of tariff and nontariff trade-policy barriers in quantitative general equilibrium Peter H. Egger Department of Management, Technology, and Economics, ETH Zürich, CEPR, and CESifo Katharina Erhardt DICE, Heinrich Heine University Düsseldorf and CESifo Structural quantitative work in international economics typically models trade costs as a log-linear function of exogenous trade-policy variables. We propose a structural approach that allows for a nonparametric relationship and for treating tariff and nontariff trade-policy variables as potentially endogenous. The data reject the assumption of log-linearity of trade costs in both tariffand nontariffpolicy variables. We assess the effects of a unilateral increase of US tariffs on Chinese imports by 10 percentage points and document that the estimated effects on real bilateral trade-flow changes would be substantially underestimated by standard approaches. Keywords. Trade policy, gravity models, semiparametric methods, nonparametric methods, generalized propensity scores. JEL classification. C14, F13, F14. 1. Introduction Virtually every announcement of a trade-policy intervention is followed by an attempt to quantify its economic consequences. Economists achieve this by employing parameterizations of structural models, predominantly general-equilibrium models, which formalize the impact of trade-policy shocks. Countless studies have aimed at quantifying the effect of trade liberalizations in this spirit.1One important insight gained from this work is that the economic outcome responses to a uniform trade-policy shock differ across countries due to their distinct fundamentals. However, despite incorporating rich mechanisms that produce heterogeneous responses across countries, conventional Peter H. Egger: [email protected] Katharina Erhardt: [email protected] We gratefully acknowledge numerous helpful comments on earlier versions of the manuscript by three anonymous reviewers as well as by Chad Bown, Lorenzo Caliendo, Arnaud Costinot, Jonathan Eaton, Alfonso Flores-Lagunes, and Georg Schaur. We are also thankful for comments from participants at several seminars (University of Salzburg, University of Würzburg, University of Oxford, University of Mannheim) and conferences (Villars Workshop on International Economics, PRONTO Workshop in Paris, DEGIT in Nottingham, EEA in Geneva, ETSG in Paris, Stoos Sinergia Workshop, TRISTAN workshop in Bayreuth). 1See, for example, recent work on Brexit by Breinlich et al. (2016), the Transatlantic Trade and Investment Partnership (TTIP) by Felbermayr, Aichele, and Heiland (2016), or the 2018 trade war between the US and China by Fajgelbaum, Goldberg, Kennedy, and Khandelwal (2019). ©2024 The Authors. Licensed under the Creative Commons Attribution-NonCommercial License 4.0. Available at http://qeconomics.org.https://doi.org/10.3982/QE1994 454 Egger and Erhardt Quantitative Economics 15 (2024) quantitative general-equilibrium models often impose at least three important restrictive assumptions. First, they impose a homogeneous and log-linear relationship between trade-policy variables and ad valorem trade costs and a log-linear direct relationship between ad valorem trade costs and trade flows.2Heterogeneous trade-cost effects emerge only indirectly, and mainly through general-equilibrium repercussions, that is, through effectson consumer and producer prices (see, e.g., Eaton and Kortum (2002), Anderson and van Wincoop (2003), Arkolakis, Costinot, and Rodriguez-Clare (2012)). This paper demonstrates that the data appear to reject a log-linear direct relationship between trade policy and trade flows and illustrates that assuming it depresses the heterogeneity of equilibrium responses to trade-policy changes.3 A second customary restriction lies in the focus on trade policy through tariffs alone.4Nontariff barriers to trade are associated with the application of specific checking routines at borders and the implementation of standards and procedures with an intent to protect domestic suppliers (see Anderson (2016)). Nontariff policy regulations have become extremely important since the Uruguay Trade Round (see Horn, Mavroidis, and Sapir (2010)). They have garnered attention and become the focus of interest in the context of the “new” protectionism since the beginning of the Economic and Financial Crisis (Bown (2011), Baldwin and Evenett (2012), Bown and Crowley (2013)). The use of nontariff measures is relevant if tariffs and nontariff barriers are set jointly and not independently by policymakers, and if their partial effects depend on each other. We will allow for the latter and document that responses to tariff changes tend to depend on nontariff provisions and vice versa.5 A final customary but restrictive assumption is that trade-policy measures are treated as randomly assigned to countries rather than chosen with an economic rationale.6Economic theory hypothesizes that countries choose tariffs based on their fundamentals (see Bond (1990), Bond and Syropoulos (1996), Bagwell and Staiger (1999,2004), Ossa (2011,2014), Felbermayr, Jung, and Larch (2013), Caliendo, Feenstra, Romalis, and Taylor (2015)). 2Eaton and Kortum (2002) and Henderson and Millimet (2008) consider nonparametric direct effects of geography on trade costs and trade flows, but the results do not point to any strong nonlog-linearity of the direct effects at large geographical distance. The findings of Hillberry and Hummels (2008) suggest, however, that geography induces nonlog-linear effects over short distances. 3In a recent study, Adão, Costinot, and Donaldson (2017) emphasize the importance of relaxing functional form restrictions in general equilibrium models of trade but do not consider nonparametric trade costs. 4See, for example, Romalis (2007)orCaliendo and Parro (2015). 5Related to this, Caliendo, Opromolla, Parro, and Sforza (2021) suggest that, in quantitative models of migration, it is insufficient to control for direct migration costs alone, but other policy domains need to be be considered, too. 6See, for example, Eaton and Kortum (2002)orCaliendo and Parro (2015). If at all, endogeneity of trade policy is mostly considered through the (binary) membership of countries in preferential trade agreements (see 2007 (2007,2009)). With the exception of Egger, Larch, Staub, and Winkelmann (2011) and Egger et al. (2011), related work on endogenous trade agreements is concerned with the direct (partial) rather than the total (direct plus indirect) effects on economic outcome. Quantitative Economics 15 (2024) Heterogeneous effects of trade policy 455 The present paper puts forward a quantitative framework and analysis of tradepolicy effects on trade costs and trade flows in a unified framework to relax the aforementioned three assumptions. It builds on a multicountry, multisector quantitative framework that is consistent with a wide range of trade models (compare Arkolakis, Costinot, and Rodriguez-Clare (2012), Costinot and Rodriguez-Clare (2014)). To address the aforementioned concerns, the paper suggests implementing the following multistep approach. First, trade data—here, for 115 countries and 128 sectors—are decomposed to extract information on exogenous producer-country-sector fundamentals as well as total ad valorem trade frictions. Second, machine-learning algorithms are used to decompose tariff and nontariff policy barriers into their deterministic (predicted) and residual (random) parts. In line with the literature on optimal trade policy (Bond and Syropoulos, 1996), Ossa (2011,2014), Felbermayr, Jung, and Larch (2013), we impose that trade policy and trade flows depend on the same fundamentals in their reduced form. Third, we estimate the link function of ad valorem trade costs on tariff and nontariff barriers, using the joint density of their random components. This approach is a multivariate generalization of the dose-response-function estimation in Flores, Flores-Lagunes, Gonzalez, and Neumann (2012). We present evidence of a nonlog-linear mapping of the trade-policy variables with ad valorem trade costs. We find that the marginal effect of an increase in tariffs is very strong for very low and medium tariff barriers, while it is much weaker and even close to zero for very high tariff barriers, especially, when nontariff barriers are high. Nontariff barriers increase trade costs, in particular, for very low initial levels of nontariff barriers. For medium levels of nontariff barriers, marginal effects on trade costs can actually be trade-cost-reducing, which is owed to the beneficial effects of some technical barriers to trade. These patterns are consistent with tariff and nontariff avoidance at high levels of these costs (see Fisman and Wei (2004), Javorcik and Narciso (2008), Sequeira (2016), and Demir and Javorcik (2018)), and with a lacking usage of granted preferential tariffs at low most favored nation tariff levels (see Herin (1986), Francois, Hoekman, and Manchin (2006), Estevadeordal, Freund, and Ornelas (2008), Fugazza and Nicita (2013), Krishna, Salamanca, Suzuki, and Martincus (2021)). To demonstrate the importance of these nonlinearities, we feed the estimated trade-policy gradients into a quantitative multicountry, multisector general-equilibrium model of trade and evaluate the effect of a unilateral increase in US tariffs on Chinese imports of 10 percentage points. The effects of this particular policy change would be severely underestimated by a customary modeling of trade costs as log-linear in tariffs compared to the flexible-gradient approach proposed in this paper. The average reduction across all treated sector-level US import shares from China is about 7 percentage points larger with the flexible-gradient approach and total US imports from China (evaluated at benchmark income levels) fall by 6% as compared to only 3% under an ad valorem specification. 456 Egger and Erhardt Quantitative Economics 15 (2024) 2. The effect of trade policy in gravity models of international trade Quantitative work in international economics on the effect of trade-policy changes is almost exclusively based on gravity models for at least three reasons: (i) the empirical success of structural gravity estimation (Head and Mayer,2014), (ii) the wide range of theoretical general-equilibrium trade models leading to a gravity equation including models with appealing microfoundations (Costinot and Rodriguez-Clare,2014), and (iii) the parsimonious nature that allows researchers to quantify the (welfare) consequences of changes in fundamentals relying on only very few key parameters—in particular, estimates of the so-called trade elasticity—while still being able to take into account general-equilibrium effects.7 Consider the simplest case of such a gravity model—a single-sector Armington model where different countries are endowed with a fixed quantity, Qi, of distinct goods and each country is populated by a representative consumer with constant elasticity of substitution (CES) preferences over these goods. Bilateral trade flows, Xij , between an exporter iand an importer jwill be given by the well-known CES demand for the exporter’s good, which is a function of the good’s price (mill price, Pii, times ad valorem trade costs, Dij ), the price index in j,Pj, and the importer’s total expenditure (which equals income), Yj. The elasticity αis a linear function of the elasticity of substitution specified in the CES preferences: Xij =(PiiDij )αYj Pj (1) Note that bilateral sales consist of an exporter-specific part, an importer-specific component, and bilateral trade costs. The mill price of exporter i’s good, Pii, is the total value of the good country iis endowed with, Yi, divided by total endowment Qi,Pii =Yi/Qi. While the quantity is exogenously given, the price of the good is endogenously determined in general equilibrium. The importer-specific part consists of total expenditure of partner country j,Yj, divided by the price index prevailing in that country, Pj.8The price index itself is a function of mill prices Pkk of all countries, k=1...J, and trade costs Dkj between all countries k=1...Jand j. Using this model for trade-policy analysis, it is customary to assume that ad valorem trade costs, Dij , are proportional to ad valorem tariffs. Then the direct effect of tariffs on trade—the effect before general-equilibrium adjustments of prices and income—is log-linear and governed by α. Note that this direct effect is uniform for all countries and irrespective of their fundamentals. Hence, a reduction in tariffs would have the same direct effect in a country irrespective of its previous tariff level, its implementation of non-tariff barriers or how hard it is to actually apply preferential market access formalities. Only once general-equilibrium adjustments are taken into account, heterogeneous effects of trade policy can emerge through the endogenous adjustment of mill prices. 7We provide details on the general equilibrium formulation of the specific parsimonious trade model outlined in this paper in a Supplemental Appendix (Egger and Erhardt (2024)) to this paper. 8Note that we abstract from tariff revenues here; this is relaxed later. Quantitative Economics 15 (2024) Heterogeneous effects of trade policy 457 While the Armington model is admittedly stylized, the general structure of bilateral trade flows outlined above holds for a wide range of models some of them incorporating sophisticated micro-theoretical mechanisms. In these so-called gravity models, trade flows, Xs ij , between an exporter iand an importer jwithin a sector sdepend multiplicatively on three components: supply-potential factors that are exporter-sector-specific, As i, demand-potential factors that are importer-sector-specific, Bs j, and friction factors that vary at the sector-country-pair level, Ds ij , and whose impact on trade flows is governed by the trade elasticity, αs: Xs ij =As iBs jDs ij αs.(2) Theoretical models resulting in a gravity-type model for international trade flows differ mainly with respect to the structural interpretation of the exporter-sector-specific component, As i, and the importer-sector-specific component, Bs j, but not with respect to the bilateral component, Ds ij .9This bilateral component is typically simply referred to as “iceberg-type” trade costs and assumed to encompass all potential frictions to trade in some unspecified way.10 Absent any theoretical guidance, most empirical work assumes a log-linear trade-cost function. Just as above, modeling changes in ad valorem tariffs will lead to the same restrictive, uniform direct effects on trade flows irrespective of the underlying complex micro-theoretical mechanisms. How can we better understand how bilateral trade costs Ds ij and trade policy are related? To begin, we can obtain an estimate of these costs in logs,  ds ij ,11 by decomposing product-level bilateral exports (in logs) into their product-level importer and exporterspecific components: xs ij =as i+bs j+αsds ij ,(3) estimating a linear fixed-effects regression to obtain estimates of as iand bs jand using trade elasticities from the literature (Kee, Nicita, and Olarreaga (2008)) to back out an estimate of bilateral sector-specific trade costs:  ds ij =1 αsxs ij − as i− bs j.(4) Our objective is to comprehend the nature of trade costs further. To this end, we will extend the notion of trade policy beyond its focus on tariffs taking into account nontariff barriers and allow for potentially nonlinear effects of trade policy on trade costs. On the one hand, nontariff policy regulations have become extremely important since the Uruguay Trade Round (see Horn, Mavroidis, and Sapir (2010)) and they have recently become the focus of interest in the context of the “new” protectionism since 9In the simple Armington model above, for instance, Ai=(Yi/Qi)αand Bj=Yj/Pj. 10Note that we restrict our analysis to trade models featuring a constant trade elasticity and that this assumption has consequences, for example, for welfare. 11Throughout the paper, hats will indicate estimates and lowercase letters, x, will refer to the log of a variable, X. 458 Egger and Erhardt Quantitative Economics 15 (2024) the beginning of the Economic and Financial Crisis (Bown (2011), Baldwin and Evenett (2012), Bown and Crowley (2013)). Nontariff barriers to trade are associated with the application of specific checking routines at borders and the implementation of standards and procedures with an intent to protect domestic suppliers (see Anderson (2016)). In contrast to tariffs, certain nontariff barriers might also have trade-enhancing effects, for example, by establishing trust in products through standards or decreasing transaction costs (WTO (2012)). On the other hand, several studies question the assumption of log-linear trade costs based on at least five arguments. First, the nexus between tariff and nontariff barriers and trade costs is affected by misdeclarations at customs (see, e.g., Demir and Javorcik (2018), Fisman and Wei (2004), Javorcik and Narciso (2008), Sequeira (2016)). Second, a nonlog-linear relationship between trade-policy variables and trade costs emerges once some trade-policy measures alter prices nonproportionately (as is the case with specific tariffs) rather than proportionately (see, e.g., Hummels and Skiba (2004), Irarrazabal, Moxnes, and Opromolla (2015)). Third, work on the size and role of preference margins suggests that available preferential market access is underused (see, e.g., Herin (1986), Francois, Hoekman, and Manchin (2006), Estevadeordal, Freund, and Ornelas (2008), Fugazza and Nicita (2013), Krishna et al. (2021)). Fourth, the uncertainty about expected applied tariff and nontariff barriers may induce nonlog-linear effects of trade policy on trade costs (see, e.g., Handley and Limao (2017), Handley and Limao (2015), Pierce and Schott (2016), and Crowley, Song, and Meng (2016)). Finally, nonlinearities in the relationship between trade-policy instruments and effective trade costs may relate to the incomplete but trade-cost-dependent penetration of consumer markets (see, e.g., Arkolakis (2010)).12 In a first step, we will evaluate how trade costs,  ds ij , vary along the dimensions of two measures of trade policy: tariffs, τs ij =ln(1+ts ij ), and nontariff barriers, ηs ij =ln(1+ns ij ), each expressed in ad valorem terms, in a potentially nonlinear way using a higher-order polynomial approximation while controlling for customary exogenous trade barriers and 4-digit sector fixed effects.13 In this exercise, we treat τs ij and ηs ij as exogenous determinants of  ds ij . We illustrate the results graphically in Figure 1. The upper panel illustrates a socalled dose-response function: it states how log statutory applied tarriffand nontariffbarrier ad valorem rates map into effective log ad valorem trade costs ds ij .Thetwolower panels represent the two-dimensional average gradient of the dose-response function with respect to the two policy variables averaging over the respective other trade-policy variable. The gradient function corresponds to the marginal effects of tariff and nontariff trade policy at different levels of trade policy. What these figures suggest is that, for tariffs, the gradient is flatter at the lower and the higher end of the support, and for 12That the trade-cost function may be nonlinear in its arguments finds also strong support in the literature assessing distance effects on trade (Hillberry and Hummels,2008). 13Data on 4-digit sectoral trade flows, xs ij ,tobackout ds ij and applied tariffs, ts ij , at the country-pair-sector level for the year 2011 are taken from the Trade Analysis Information System (TRAINS) Database contained in the World Bank’s WITS Database. Data on ad valorem equivalents of nontariff barriers, ns ij , are available from Kee, Nicita, and Olarreaga (2016). For more details, see the respective data description in Section 4. Quantitative Economics 15 (2024) Heterogeneous effects of trade policy 459 Figure 1. Trade costs as a flexible polynomial function of trade policy. nontariff barriers, it also flattens out at the higher end. This is consistent with the evasion/avoidance as well as the underusage arguments from earlier work. However, this evidence must be taken with a grain of salt as (i) it makes an ad hoc (polynomial) functional form assumption and (ii) it treats the trade-policy measures τs ij and ηs ij as exogenous. While the latter is true for many empirical studies on the effects of trade policy in quantitative trade models, earlier work considers their endogeneity in theory as well as in empirical analyses (see Bond and Syropoulos (1996), Ossa (2011, 2014), Felbermayr, Jung, and Larch (2013), Caliendo et al. (2015)). The next section proposes an approach towards modeling trade costs as a flexible function of trade-policy variables that are jointly determined with trade flows by the same exogenous fundamentals as in the just-mentioned earlier work. 3. Econometric methodology In modeling the dependence of trade costs on tariff and nontariff trade-policy barriers, we want to permit a sufficiently flexible functional form and to control for the fundamentals, which jointly determine trade flows and trade policy (see Bond (1990), Bond 460 Egger and Erhardt Quantitative Economics 15 (2024) and Syropoulos (1996), Ossa (2011,2014), Felbermayr, Jung, and Larch (2013), Caliendo et al. (2015)).14 In this context, it is important to note that structural trade models in the quantitative literature we wish to speak to do not only permit decomposing trade flows into their supply, demand, and friction components as outlined in equation (2). They also identify measures of the endogenous components in supply factors, and hence, they permit identifying composite measures of the exogenous fundamentals of trade flows and policy. Specifically, in customary quantitative trade models, there is a fundamental driver of trade at the exporter-sector level, which we will denote by Fs i. This could be an exogenous endowment as in the simple Armington model, a supply-side parameter such as productivity (see Eaton and Kortum (2002)) or a demand-side parameter like preferences for this particular country-sector’s good (see Anderson and van Wincoop (2003)). This component is exogenous to the model. Moreover, in gravity-type general equilibrium models, endogenous factor prices ensure that markets clear. We denote this endogenous component by Ws i. The sensitivity of trade flows to these country-sectorspecific factor prices is governed by an elasticity, which is typically identical to (or at least, codetermined by) the trade elasticity αs. Note that all three components of the export-sectorspecific component of trade flows in equation (2) are log-additive in endogenous (Ws i) and exogenous determinants (Fs i) of exporter potential:15 As i=Fs iWs iαs.(5) This structural decomposition is important, as a large body of work on endogenous trade policy considers the fundamentals behind the (optimal) choice of trade-policy parameters to be the same as the ones behind the endogenous factor and output prices, which co-determine supply and demand, and hence, trade flows (see Bond and Syropoulos (1996), Baier and Bergstrand (2004), Bond, Riezman, and Syropoulos (2004), Ossa (2011,2014), Felbermayr, Jung, and Larch (2013), Caliendo et al. (2015)). According to this literature, all that matters for the systematic determination of trade policy are the sector-country-pair natural trade costs, the sector-country fundamental drivers of supply potential, and the sector-level trade elasticities. Conditional on these factors, trade policy is stochastically independent of orrandom to trade flows. The reason is that, upon a complete decomposition of trade flows in a generic general-equilibrium setting 14The endogeneity of trade-policy barriers can be addressed by either instrumental-variable (IV) estimation or approaches relying on an assumption of conditional mean independence (CMI). IV estimation in the present context would require that shifters of trade policy could be found, which are independent of any other measurable or unmeasurable trade-cost factors. CMI, by contrast, requires us to model the endogenous component of trade-policy variables observed in the data. Using outside instruments in a multicountry quantitative general-equilibrium setting appears unnatural while the literature suggests that trade-policy variables are conditionally—on the fundamentals determining the endogenous model outcomes jointly with policy—mean independent. 15Adão, Costinot, and Donaldson (2017) establish a quantitative trade model supporting nonparametric effects of preferences and technology—both of which are ingredients of Fs i—on trade flows in sfrom ito j. The interest here is on a nonparametric link between endogenous trade policy and overall trade costs on the one hand, and trade flows on the other hand, an issue which is not addressed in Adão, Costinot, and Donaldson (2017). Hence, the two approaches appear complementary to each other. Quantitative Economics 15 (2024) Heterogeneous effects of trade policy 467 Table 2. Examples of estimated country-sector sales fundamentals versus estimated countrysector fixed effects in the data. Sector Structural Metal Motor Vehicles Structural Metal Motor Vehicles Country ˆ fs iˆ as i China −22.86 6.30 5.38 5.22 Germany −20.74 11.21 3.99 7.60 Japan −23.21 10.90 0.39 7.66 United States −21.14 9.95 3.66 6.44 Mexico −27.19 6.89 −0.26 3.92 India −27.13 6.36 1.73 4.24 Brazil −25.61 5.15 −0.31 2.49 helps us learning the subset of relevant (polynomial and interaction) terms of these factors, which are numerous for every sector and country pair. This part of the analysis is interested in separating the conditional mean of tariff and nontariff policy measures from the stochastic part, νs τ,ij and νs η,ij : τs ij =gτqs ij +νs τ,ij ,ηs ij =gηqs ij +νs η,ij . (10) It is crucial to allow for a high degree of flexibility in estimating gm(·). We achieve this by applying a powerful approach that estimates the relationship nonparametrically using multivariate adaptive regression splines (MARS) following Friedman (1991). In order to account for any country-specific characteristics in policy formation, we allow for fixed effects across importing countries jand exporting countries i.27 The model selection of the MARS model along with cross-validation statistics is presented in Figure 2. The selected model is able to explain 50% of the variation in τs ij and 39% of the variation in ηs ij . Up to almost one-half of the basic variables in qs ij as well as the importing-country and exporting-country fixed effects are chosen as predictors and enter the model in a total of 223 and 188 terms (such as interactions or powers), respectively. A fundamental concern with respectto machine-learning algorithms is overfitting.28 Note that the employed algorithm contains a backward passage in which a subset of previously selected regressors (e.g., polynomial terms or interaction terms) is deleted to avoid overfitting. We can assess the degree of overfitting by means of cross-validation. Specifically, in the present context we generate 5-fold cross-validated models for tariff and nontariff trade barriers. For each fold, the algorithm builds a MARS model with the 27The MARS algorithm applied in this context has two steps. Forward passage: After estimating an intercept, piecewise-linear basis functions of the covariates are added iteratively (allowing for interactions). Backward passage: In order to avoid overfitting, a subset of the previously selected terms is deleted, and the final model is selected based on the minimization of the generalized cross-validation (GCV) score. 28In fact, underfitting would be much more of a concern economically than overfitting here, because what is key is that the residual is not systematically informed by the exogenous fundamentals. However, statistically, one may still care about overfitting. 468 Egger and Erhardt Quantitative Economics 15 (2024) Figure 2. Model selection of gτ(·)and gη(·). in-fold data (90% of the complete data) and uses this model to measure the R2from predictions made on the out-of-fold data (10% of the complete data). The mean of these out-of-fold R2statistics amounts to 0.494 (with a standard deviation of 0.0.20) for the tariff model (gτ(qs ij )) and 0.289 (with a standard deviation of 0.138) for the nontariff model (gη(qs ij )). These statistics are quite close to the R2statistics of the model estimated on the full data, in particular, for tariffs. While we abstain from an in-depth analysis of the reduced-form models for the two trade-policy variables τs ij and ηs ij here, we discuss some relationships in a Supplemental Appendix to this paper. The residuals νs ij =(νs τ,ij ,νs η,ij )of the regressions in equation (10) serve as estimates of the two conditional (quasi-randomized) tariff and nontariff trade-policy-treatment variables whose joint density has to be estimated. For most of the subsequent analysis, we estimate the joint density of the latter assuming a bivariate normal distribution and estimate the parameters of the distribution by maximum likelihood (see, e.g., Imai and Van Dyk (2004), Hirano and Imbens (2004), Kluve, Schneider, Uhlendorff, and Zhao (2012), for the assumption of normal densities in the context of univariate-continuoustreatment-effects estimation). We conduct an alternative nonparametric estimation that allows for a maximum degree of flexibility following Li and Racine (2006). The estimated bivariate density by one of the aforementioned methods serves as an estimate of the propensity of getting randomly assigned to a specific tuple of tariff and non-tariff-barrier levels for any country pair and sector. The density as a compact (propensity) score can be obtained not only for observed but even for potential (hypothetical) trade-policy treatment levels. We will refer to this density as generalized propensity score. However, this compact score is only meaningful, if the covariates in qs ij are similar for all units {ij s }with a similar level of the estimated joint density. Towards an assessment of the latter, we enforce a common support and discard observations with extreme joint-density-score values. Specifically, we follow Flores et al. (2012) in defining the common support and extend their methodology to multivariate treatments.29 29Details regarding the definition of the common support can be found in the Supplemental Appendix. Quantitative Economics 15 (2024) Heterogeneous effects of trade policy 469 Besides ensuring common support, we will test if for any observation with the same GPS the probability of a specific level of trade-policy treatment is independent of the observable determinants qs ij following Hirano and Imbens (2004). For each covariate in qs ij ,wemayconductat-test under the null hypothesis that the mean of the covariate is the same across groups that correspond to different levels of trade policy. Specifically, we perform such a test unconditionally versus conditionally on the GPS. The respective test statistics are reported in the Supplemental Appendix. We show that conditioning on the GPS improves the share of balanced covariates (at the 5% level) from 31% to 96%. We use the stochastic component of the two trade-policy measures in a control function which is employed in a second step, where the functional form of the causal relationship between the trade-policy measures and overall sector-country-pair trade costs are in the limelight. This step determines what we will call the dose-response function. 5.2 Estimating partial (direct) effects of trade policy on trade costs and trade flows In this subsection, we estimate the effect of tariff and nontariff trade-policy variables on bilateral trade costs, ds ij , as obtained from the procedure in equation (3). The corresponding model to estimate the so-called unit-level dose-response of derived trade costs ˆ ds ij to the trade-policy barriers in ms ij reads ˆ ds ij =kms ij ,rms ij +controlss ij θ+ξs ij . (11) We additionally condition on a linear function of all covariates in this step of the analysis through the inclusion of controlss ij in equation (11), as suggested by Imai and Van Dyk (2004). Note that this is not the same as assuming a linear relationship between natural trade barriers and trade costs—in fact, we are agnostic about their impact on trade costs beyond their (potentially nonlinear) relationship and interaction with endogenous trade policy. We then estimate the functional form of k(·)in equation (11)byapolynomial approximation whose order is chosen based on the Aikake information criterion (AIC). We allow for both policy variables, their interaction, the GPS as well as any interaction with the GPS to enter the unit-level dose-response function up to a polynomial of order 10. The estimated coefficients do not have any economic meaning. However, the polynomial model provides us with a functional form of k(·)in equation (11) that allows for evaluating the average causal effect of changes in tariff and nontariff trade-policy variables on trade costs at any potential level of the policy variables in the outset. Hence, we can define a grid of trade-policy levels for which we are interested in the level of trade costs and estimate the latter using the functional form of equation (11). Figure 3plots the bivariate distribution of the trade-policy data on the such defined grid of m=(τ,η) and shows that the majority of the data is located at relatively low levels of policy trade barriers but that there is variation in the tariff and as well as the nontariff barrier dimension. 470 Egger and Erhardt Quantitative Economics 15 (2024) Figure 3. Distribution of the data across the 25 ×25 grid. We evaluate the expected conditional dose-response function,k(m)=E[k(m, r(m,qs ij ))], as an average from the size-nsample through ˆ k(m)=1 n i∈J  j∈J  s∈S ˆ km,ˆ rm,qs ij , (12) where Jand Sdenote the sets of countries and sectors in the data. Figure 4displays the average dose-response function (12)aswellasthe95%confidence bounds that are based on 100 bootstrap samples for the estimation based on a normally distributed GPS in the left panel and the estimation based on a nonparametriFigure 4. Average dose-response function of log trade costs and log trade-policy variables with 95% confidence bounds. Quantitative Economics 15 (2024) Heterogeneous effects of trade policy 471 Figure 5. Gradients w.r.t τand w.r.t. ηwith 95% confidence bounds for different levels of trade policy (normal density). cally distributed GPS in the right panel.30 The two variants of the GPS estimation are of minor importance for the overall shape of the dose-response function. As expected, trade costs are generally increasing in the two trade-policy variables. The effect is, however, strongly nonlinear and depends on the level of trade policy in the outset. In order to investigate the nonlinearities in more detail, we present the gradient of the average dose-response function with respect to τand ηin Figure 5. For a better illustration, we present three slices of the gradient in each dimension. Each slice corresponds to either low (grid points 1–5), medium (grid points 11–15), or high (grid points 21–25) levels of tariff or nontariff barriers, respectively. Note that the gradient is referring to the change in log trade costs, ˆ ds ij , in response to a change in policy barriers by one grid-point difference in the dose-response function, which amounts to 0.02. To put the gradient into context, recall that the customary assumption in most general equilibrium models of trade is that trade policy enter trade costs log-linearly in an ad valorem fashion. Hence, ad valorem tariffs increase trade costs one for one. Translated to the grid defined in this exercise, a one-grid-point change in tariffs should increase log trade costs by 0.02 at any point on the grid. This is far below the maximum gradient of 0.3 obtained in this exercise pointing to a role of tariffs beyond the pure ad valorem effect. At the same time, the gradient is effectively zero for some 30The bootstrap was conducted as follows. 100 bootstrap samples of the total sample (see Table 1)were drawn ensuring that all importer-sector combinations exist in each bootstrap sample. This corresponds to importer-sector block-bootstrapping, and all steps of the procedure are estimated for each bootstrap sample. This leads to differently-sized bootstrap samples that are then used in the subsequent steps. This procedure accounts for the imprecision in the measurement of estimated (derived) variables that are used in later stages, such as log sales fundamentals, ˆ fs i,ortradecosts, ˆ ds ij . 472 Egger and Erhardt Quantitative Economics 15 (2024) Figure 6. Gradients w.r.t τand w.r.t. ηwith 95% confidence bounds for different levels of trade policy—technical versus nontechnical trade barriers (normal density). parts of the grid and a substantial share of the observations is placed in exactly those parts of the grid. The results suggest that trade policy is rather ineffective in these cases. For reference, we also plot the gradient of the “naive” regression underlying Figure 1for different slices and adjusted to the scaling such that the gradient refers to the change in log trade costs w.r.t. a one-grid-point change. We refer to this as “naive gradient” in Figure 5. The reference illustrates that this approach entails a poor approximation for the marginal effect of changes in trade policy, in particular, in tariffs, both in terms of effect size and shape as a function of tariff levels. Quantitative Economics 15 (2024) Heterogeneous effects of trade policy 473 The different panels in Figure 5illustrate nicely that a given change in trade policy has a very different effect depending on where in the outset trade policy lies at the moment of evaluation and that these differences are particularly stark when considering large-scale trade-policychanges. A change in tariff policy has a very strong positive effect on trade costs for very low levels of tariff barriers when nontariff barriers are medium to high. This marginal effect is substantially smaller for very low levels of tariff and nontariff barriers, which might be explained by unused preference margins (see Herin (1986), Francois, Hoekman, and Manchin (2006), Estevadeordal, Freund, and Ornelas (2008), Fugazza and Nicita (2013)). The effort to comply with any requirements in order to obtain a preferential tariff treatment might be simply too burdensome, especially, when the gains from compliance are rather low, leading to an unused preference margin and to a less pronounced marginal impact of tariffs on trade costs and trade flows. In contrast, there is virtually no marginal effect of a change in tariffs when tariffs are around 10%. The marginal effect of a change in tariffs remains zero also beyond a tariff level of 15% for high levels of nontariff barriers. However, the marginal effect becomes strongly positive for low and medium levels of non-tariff barriers as we move beyond 15% and fades slowly out as we approach a level of 40%. The result that the marginal effect of a change in tariffs fades out for high tariff levels and, in particular, in case of high nontariff barriers, is well in line with the literature on avoidance strategies for high barriers to trade (see Fisman and Wei (2004), Javorcik and Narciso (2008), Sequeira (2016), Demir and Javorcik (2018)). The pattern is rather different when considering the marginal effect with respect to nontariff barriers. We observe a very strong effect for low levels of nontariff barriers, in particular, when tariffs are high. By contrast, we observe basically no or even negative marginal effects for intermediate levels of ηacross all levels of tariff barriers and a strong marginal increase in trade costs for high levels of nontariff trade barriers when tariffs are low. As mentioned in the Introduction, in contrast to tariffs, nontariff barriers might entail a decrease in trade costs, in particular, in the case of nontechnical measures. Since, the data on the ad valorem equivalents of nontariff barriers allow for differentiating between technical and nontechnical barriers to trade, we analyze their differential effects in Figure 6. While the gradient of tariff barriers is basically unchanged in the two subanalyses, we see that the negative gradient in the nontariff-barrier dimension is almost entirely driven by technical barriers to trade (compare WTO (2012)). Figure 6suggests that technical barriers to trade have a strong marginal impact on trade costs for low policy barriers, but a negative effect for intermediate levels of technical barriers in place. We take this result as support for the notion that, while nontariff measures are costly on average, there exists an intermediate level of, particularly, nontechnical barriers to trade where a higher level may actually be trade enhancing. 5.3 Putting the estimated trade-policy gradients in context The nonlinear relationship of trade costs and trade policy might stem from various sources (cf. Section 2). We cannot include measures of these sources in the regressions explicitly, because they are partly functions of trade policy, and hence, endogenous just 474 Egger and Erhardt Quantitative Economics 15 (2024) like trade policy itself.31 However, putting these measures in context with the gradient may shed light on the roots of the variation in trade-cost responses to trade policy. We do so in Figure 7. We start with the role of trade-policy uncertainty. Earlier work has demonstrated that such uncertainty is an important factor in determining the actual effect of trade policy. For instance, the findings in Handley and Limao (2015)andPierce and Schott (2016) suggest that trade-policy changes contain a signal about future trade-policy uncertainty. We hypothesize that trade-policy uncertainty affects the shape of the trade-cost function and it varies across tariff levels. In order to proxy for uncertainty, we use the unexplained variation from a first-order autoregressive regression, where we regress the annual applied tariff level for any country pair and sector on its lagged value in all years between 2001 and 2011 for each tariff cell using TRAINS data. The left panel of Figure 7suggests that a lower level of tariff predictability, that is, a higher tariff uncertainty, is associated with higher applied tariff levels. In particular, the measure of tariff uncertainty rises substantially more strongly for tariff levels beyond 10–20%. The latter is exactly where the gradient of trade costs with respect to tariffs τis strongly positive. Further potential rationales for a heterogeneous impact of tariffs on trade costs are avoidance strategies at high tariffs on the one hand, and the nonuse of available tariff preferences at low most-favored nation tariffs on the other hand (see Herin (1986), Francois, Hoekman, and Manchin (2006), Estevadeordal, Freund, and Ornelas (2008), Fugazza and Nicita (2013)). We would assume tariff avoidance strategies to be more prevalent in countries with high levels of corruption (see Fisman and Wei (2004), Javorcik and Narciso (2008), Sequeira (2016), Demir and Javorcik (2018)). We proxy for the lack of corruption by taking a measure of transparency at the country level for 2006 from Transparency International as an inverse measure of corruption. We map the latter to tariffs by the respective countries’ densities at different products and levels of tariffs. In order to proxy for the nonuse of available tariff preferences, we use the preference margin (the difference between the most favored nation tariff and the principally-available minimum tariff in a trade agreement). The results in Figure 7suggest the following. First, the gradient is positively correlated with a greater transparency in the lowand high-tariff range, while at medium tariffs, transparency is negatively related to a higher gradient of trade costs w.r.t. tariffs. This is consistent with avoidance being negatively correlated with transparency. Second, the tariff gradient is relatively independent of the preference margin at low tariff levels. The latter is consistent with an underexploitation of tariff preferences at low tariff levels. A further important determinant of the effectiveness of trade policy is the presence of rules of origin, which impose more restrictions and costs on the access to preferential treatment in trade agreements, in particular, regarding nontariff barriers. Krishna et al. (2021) show that the fixed costs of meeting rules of origin decrease with the experience of the firm in obtaining preferential tariffs. Generally, we would expect that the impact of changes in trade policy is stronger, whenever fewer rules of origins are in place. We 31For example, the “tariff water,” the gap between bound and applied tariffs, or the correlation between lagged and contemporaneous tariffs as a measure of tariff variation in time or tariff uncertainty are both functions of applied tariffs. Quantitative Economics 15 (2024) Heterogeneous effects of trade policy 475 Figure 7. Gradients and potential covariates. assess the role of rules of origin for the trade-cost gradient with respect to trade policy using the product-level incidence of rules of origin in the North American Free Trade Area (NAFTA) based on data compiled by Conconi, García-Santana, Puccio, and Venturini (2018). We summarize the associated findings in the right panel of Figure 7.The figure suggests that the gradient of trade costs w.r.t. nontariff barriers is negatively associated with the prevalence of rules-of-origin provisions at different nontariff barrier levels. Overall, the relationship between trade policy and trade costs identified in this paper is well aligned with evidence in the literature on trade-policy setting and uncertainty as well as corruption, tariff avoidance, and trade-policy stringency. 5.4 Quantification of total (general-equilibrium) effects of trade policy on trade flows A key insight of quantitative trade models is that even homogeneous partial effects of tariff and nontariff barriers on trade costs materialize in heterogeneous responses of economic outcomes through general equilibrium responses. However, heterogeneous partial treatment effects of trade-policy variables as portrayed in Figure 5will add to and amplify the heterogeneity of total trade-cost treatment effects in general equilibrium. This subsection is concerned with a quantification of this amplification of the total trade-policy treatment effects.32 To illustrate the relevance of our estimates, we will analyze the effect of a unilateral increase of US tariffs on all Chinese imports by 10 percentage points—a policy change that was discussed and partly implemented in a similar vein over the last years. In particular, we are interested in comparing the estimated outcomes based on a homogeneous gradient of trade costs with respect to tariffs (assuming a one-for-one response of log 32For this analysis, it is necessary to focus on a somewhat more aggregated sample of the data used above. The reason is that a general-equilibrium analysis needs to rely on a full data set for all country pairs and sectors covered, while this was not necessary with the analysis of partial trade-policy treatment effects on the treated. Therefore, we focus on a subset of 41 individual countries and one rest of the world (ROW) for 97 sectors in the respective analysis. 476 Egger and Erhardt Quantitative Economics 15 (2024) trade costs, ds ij ,toachangeinτs ij ) and the one corresponding to the flexible gradient as estimated above. Throughout the analysis, we keep the deficit share in terms of total spending constant for any country.33 Details on the computation of the general equilibrium are delegated to the Supplemental Appendix. In the context of the experiment—an increase of US tariffs on Chinese imports—the actual change in trade costs resulting from the increase in tariffs is on average 19%, and thus 9 percentage points higher than the pure ad valorem effect of tariffs alone (which is 10%). This implies that the majority of affected trade flows between China and the US lies in an area of the gradient where the response of trade costs to a change in tariffs is particularly strong. Indeed, the average tariffs levied on these flows in the benchmark economy lie at 5%, which is exactly the domain featuring strong marginal responses in Figure 5. The share of US spending on Chinese goods drops by roughly one percentage point due to this policy change. Holding total US spending at the benchmark level, this amounts to a decrease of Chinese imports by more than 6% (95% confidence interval ranging from 7.2% to 4.8%). An effect that is substantially larger than the one implied by the customary ad valorem specification in which the drop in imports is less than 3%.34 The share of US income generated through tariffs increases by 50% in the nonparametric exercise whereas the increase is 54% in the ad valorem specification, which illustrates the additional impact of tariffs in increasing trade costs beyond the pure ad valorem effect. These aggregate numbers hide, however, substantial heterogeneity across import shares from different Chinese sectors as illustrated in the left panel of Figure 8.Onaverage, for treated sectors—sectors that were subject to nonzero tariffs in the benchmark— the change in import flows (at US benchmark income levels) is 7 percentage points lower (significant at the 5% level) in the nonparametric specification compared to the ad valorem specification. In some sectors, the import shares drop by more than 50% in the nonparametric case illustrating the wide range of responses under the nonparametric specification as compared to the ad valorem exercise, which exhibits substantially less variation. Note that for 92% of all bilateral trade share changes the differences between the nonparametric specification and the ad valorem specification is significant at the 5% level. The experiment of a unilateral increase in tariffs by the US toward Chinese imports reveals that customary (ad valorem) approaches of evaluating the policy change would severely underestimate the implied effects of this particular policy change. How far the two different specifications diverge depends on the respective status quo of trade policy, which differs across countries and sectors. To illustrate how large the divergence is on average, let us consider an alternative experiment that implies a change in trade costs for all tariff-treated trade flows in the data and not only Chinese imports to the 33Note that trade imbalances do not affect the key insights regarding the response function of trade costs and trade-policy variables. 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The Journal checked the data and codes included in the package for their ability to reproduce the results in the paper and approved online appendices.