Inequality, Redistribution and Optimal Trade Policy: A Public Finance Approach

Transcription

1 Inequality, Redistribution and Optimal Trade Poliy: A Publi Finane Approah Roozbeh Hosseini University of Georgia Federal Reserve Bank of Atlanta roozbeh@uga.edu Ali Shourideh Carnegie Mellon University ashourid@andrew.mu.edu Otober 16, 2018 Abstrat In this paper, we explore the relationship between optimal trade and redistributive poliies when the gains from trade are unequally distributed. We use a ompetitive trade model with input-output linkages where trade affets the relative wages and the realloation of workers aross various setors is fritional. We study how inome taxes and trade poliies should be designed in order to balane the effiieny gains from trade with the osts assoiated with the resulting inreased inequality. We show that for a large lass of global prodution strutures, the global trade of goods and servies must be undistorted even when personal taxes are inomplete. In other words, barriers to trade suh as tariffs are never optimal. In ontrast, produer taxes in the form of value-added taxes VAT) that are differentially levied on different setors play a ruial role in redistributing the gains from trade. We provide formulas that highlight the main determinants of optimal VAT and non-linear inome taxes. Finally, in a quantitative version of our model, we study the optimal response to the rise of China in international trade. Our quantitative analysis establishes that differential VAT taxes play the main role of redistributing the gains from trade, while inome taxes do not. We would like to thank Laurene Ales, Andy Atkeson, Mostafa Beshkar, Ariel Burstein, V. V. Chari, Pablo Fagelbaum, Hugo Hopenhayn, Brian Kovak, Ahmad Lashkaripour, Chris Sleet, Florian Sheuer, Aleh Tsyvinski, Jonathan Vogel, and various onferene and seminar partiipants. We speially thank Ivan Werning and Arnaud Costinot for their extensive omments on an earlier version of our paper. We are also thankful to Simon Galle, Andres Rodriguez- Clare and Moises Yi for sharing their data and odes with us. The views expressed herein are those of the authors and not neessarily those of the Federal Reserve Bank of Atlanta or the Federal Reserve System. 1

2 1 Introdution Reent evidene suggests that international trade and global realloation of prodution has signifiantly hanged the alloation of labor and inequality of inome in the United States. 1 Aording to Autor et al. 2013), the import ompetition reated by China s entrane into the World Trade Organization WTO) has led to a signifiant deline in manufaturing employment in the United States. Under this narrative, the import ompetition stemming from China s relatively high produtivity in manufaturing together with the inability of workers to move to setors or loations with omparative advantage due to the speialization of their skills) is at the root of this problem. Given suh distributional effets of free trade and modern governments desire for redistribution, an important question arises: How should a redistributive poliy be designed to distribute these unequal gains from trade? In partiular, as governments have a variety of poliy instruments at their disposal i.e., tariffs, inome taxes, prodution taxes, et.), what poliy instruments must be used to ahieve this goal? In this paper, we set out to answer these questions from a theoretial and quantitative perspetive. We study a multi-ountry ompetitive model of trade where global prodution ours through input-output linkages and workers exhibit skill speialization and imperfet mobility. In this environment, we show that for a large lass of prodution funtions, tariffs and other distortions to free trade are not optimal. Instead, setor-speifi VAT taxes should be used to redistribute the gains from the global realloation of prodution. Finally, we provide a quantitative assessment of the government response in a version of the model alibrated to the reent rise of China in international trade. Using this quantitative framework, we show that, unlike VAT, inome taxes do not play an essential role in redistributing the gains from trade. In our model, prodution is done ompetitively aross ountries where goods produed in one ountry an be used for prodution in others. Thus, prodution ours through a network of input-output linkages aross loations. We assume that workers are heterogeneous in terms of their ability to move aross prodution units, à la Roy 1951). In partiular, we assume that the population of workers is divided into groups e.g., differing by their skills), eah of whih has a pattern of setor-speifi produtivities. As a result, their setoral hoie is determined by this pattern together with wages and an idiosynrati produtivity shok. We assume that that these idiosynrati produtivity shoks have a type-2 extreme value distribution, whih allows us to haraterize the elastiity matrix of workers setoral hoie in response to hanges in setoral wages in a tratable fashion. We use our model to study the oint determination of the optimal trade poliy and redistributive inome taxes. The key restrition is that personal inome taxes an depend only on inome and not on other harateristis of workers. In order for ountries to be able to fully realize the global gains from trade, we onsider the determination of trade under ooperation among ountries. That is, we haraterize the world Pareto frontier when the obetive funtion within eah ountry exhibits redistributive motives. One an interpret these poliies as being determined under a trade agreement where the outome of the negotiations is effiient. In this environment, we first investigate the optimality of free trade or effiieny of the alloation of goods aross ountries. We show that in our benhmark model, the alloation of 1 There is a large literature trying to understand the effet of trade on inequality in developed and developing ountries. Papers inlude Goldberg and Pavnik 2007), Verhoogen 2008), Helpman et al. 2010), Lagakos and Waugh 2013), Helpman et al. 2017), Artuç et al. 2010), and Caliendo et al. 2017), among many others. 2

3 intermediate inputs aross ountries and setors is effiient. We refer to this effiieny as pseudoeffiieny of prodution sine we do not allow for realloation of labor aross setors in ontrast with the standard notion of prodution effiieny). This result resembles the seminal prodution effiieny result of Diamond and Mirrlees 1971), despite that at the personal level, taxes are inomplete and thus the assumptions of Diamond and Mirrlees 1971) do not hold in this framework. Intuitively, we obtain this result beause in our baseline model, the intermediate inputs do not diretly affet the distribution of labor produtivity in the eonomy. Sine the distribution of labor produtivity determines the deadweight loss of inome taxation, it is effiient not to distort prodution. Our analysis further identifies the onditions under whih the undistorted alloation of goods aross setors fails to be optimal. Suh alloation ours when the degree of substitution between labor and other fators intermediate inputs) varies for workers with different skills. Having established the pseudo-effiieny of prodution, we study the best mix of instruments that an redistribute the gains from trade. We show that, in general, using produer taxes is a powerful tool to redistribute the gains from trade. These taxes must take the form of a value-added tax under whih firms must be allowed to dedut the ost of intermediate input from their tax bill. We show that when the labor fore exhibits skill speialization i.e., when groups of workers differ in terms of their omparative advantage aross setors), VAT taxes must be different aross setors. We provide formulas that desribe the key omponents of optimal VAT taxes. These omponents inlude the soial marginal value of inreasing the inome of workers in a setor, the fisal externality of raising VAT taxes on inome tax revenue, and the setoral reloation effet of raising VAT taxes. In addition to VAT taxes, inome taxes remain a viable to tool to redistribute the gains from trade. While our theoretial analysis identifies VAT taxes as a potential poliy instrument to redistribute the gains from trade, its importane ompared to that of inome taxes is a quantitative question. To answer it, we use the reent rise of China in global prodution the China shok) as an example to test the importane of eah poliy instrument. In partiular, we onsider a variant of the quantitative framework developed by Galle et al. 2017) 2 to measure the distribution of hanges in welfare aused by the China shok aross different groups of workers in the United States whih are distinguished by their Commuting Zone see Autor et al. 2013)) and eduation. In our baseline quantitative exerise, we look for optimal poliies that ompensate the losers from the China shok while keeping the winners as well off as they were prior to the shok. 3 Our quantitative exerise provides two main insights: First, VAT taxes are an integral part of optimal poliies to ompensate groups of workers that lose from the China shok; seond, optimal inome taxes do not play a role in redistributing the gains from trade. Regarding optimal VAT taxes, our results suggest signifiant variation aross setors, with Textile & Leather and Eletrial Equipment reeiving large subsidies, while setors suh as Coke & Petroleum and Transport Equipment paying VAT taxes. The sign and the magnitude of the VAT taxes are fairly orrelated with the employment hange in that setor as well as the distribution of the welfare hanges of the groups of workers onentrated in eah setor. This is mainly beause the data suggest there is signifiant speialization of skill among a selet group of workers. As for inome taxes, our main result is that they do not play a role in redistributing gains from 2 Our main differene is that we allow for an endogenous intensive margin of labor supply and government poliies. Adusting for these differenes, we obtain welfare alulations that broadly line up with theirs. 3 Additionally, we solve for optimal poliies that ensure a least level of gain from the China shok for all groups of workers. Our results remain fairly unhanged. 3

4 trade. In partiular, we show that marginal inome taxes are zero for all levels of inome above 10% of the average inome. This result is mainly beause the distribution of welfare hanges resulting from the China shok is almost unorrelated with group inomes. In other words, the gains and losses from the rise of China are mainly determined by the patterns of skill speialization rather than inome. Therefore, inome taxes are not benefiial to redistributing the gains from the China shok. Our results have very stark impliations for the design and struture of trade agreements and domesti poliy response to suh agreements. VAT taxes are already prevalent in many ountries, with the United States being an important exeption. The standard reasoning for using them is that they keep prodution effiient while they raise signifiant revenue. In our paper, we show that in addition to suh benefits, when imposed differentially on different setors, VAT taxes an also be used very effetively to redistribute the gains from trade aross different groups of workers. The European Union as a large free trade area already has a entralized VAT tax system whih determines how muh VAT different setors in different ountries must pay. Our analysis suggests that in the presene of distributional onerns in trade agreements, VAT taxes must be utilized to ensure that the gains from trade are distributed more equally aross the population. Additionally, our analysis identifies the onditions required for optimality of VAT taxes and free trade. As we show, optimality of free trade requires labor provided by different types of workers to have the same degree of substitution with intermediate inputs. This implies that measuring the heterogeneity in substitution of intermediate inputs is a ruial element of trade poliies and should be subet to further empirial studies. 1.1 Related Literature Our paper builds on and makes a ontribution to several strands of literature in publi finane and international trade. The publi finane literature has lassially studied the problem of the optimal design of diret and indiret taxes. This dates bak to the work by Ramsey 1927) as well as later work by Diamond and Mirrlees 1971), Atkinson and Stiglitz 1976), and Deaton 1981). The seminal work by Diamond and Mirrlees 1971) has established the optimality of prodution effiieny under onstant returns to sale and a rih tax struture. While later studies suh as that of Naito 1999) 4 have shown that departures from prodution effiieny ould be neessary when the tax struture is inomplete and under ertain assumptions about prodution funtions, the preise theoretial and quantitative determinants of optimal distortions to prodution are still not fully explored. 5 To our knowledge, our paper is one of the few that study the determinants of optimal produer taxes in an eonomy with inomplete diret taxes, speifially, an eonomy where inome taxes do not depend on workers setoral hoie. Our main ontribution to this literature is the identifiation of the main fore that leads to the failure of prodution effiieny; see Proposition 4 below. Our analysis provides a ondition that an be measured and tested empirially. Moreover, we provide a framework that enapsulates quantitative models of international trade and thus allows us to 4 For other papers along this line of researh, see Guesnerie 1998), Spetor 2001), and Jaobs 2015). 5 Saez 2004) argues that in the long-run, workers swith to setors with higher wages and thus there is no need for distortions to prodution. This is in ontrast with Naito 1999) s result on lak of prodution effiieny. In a world where the tehnology frontier keeps expanding, it is hard to imagine that suh differentials diminish even in the long-run. 4

5 quantitatively assess the importane of various poliies. As our model inludes a disrete hoie by workers i.e., the setoral hoie by workers), our paper builds on the literature on optimal inome taxation in presene of setoral hoie. These papers inlude Saez 2002), Rothshild and Sheuer 2013), and Gomes et al. 2017). Our main ontribution to this line of researh is providing a fairly tratable framework using disrete hoie with extreme value distribution. Moreover, our paper is related to a more reent literature on optimal taxation in trade and spatial models e.g., Costinot and Werning 2018), Lyon and Waugh 2017), Fagelbaum and Gaubert 2018), and Ales and Sleet 2017)). Costinot and Werning 2018) study an eonomy where new tehnologies that do not employ labor are introdued into an eonomy that is otherwise similar to our model. They show that in suh an eonomy prodution ineffiieny arises similar to Naito 1999) and provide novel formulas that govern optimal taxes. They map these formulas into suffiient statistis that are measurable in the data and alulate optimal values of distrotions to prodution effiieny. In ontrast, our analysis highlights that unequal gains from trade or new tehnologies) do not neessarily lead to ineffiieny of prodution, sine they ould be aused by speialization of the labor fore. Furthermore, our quantitative analysis highlights the importane of VAT taxes in redistributing the gains from trade. 6 Lyon and Waugh 2017) study an optimal inome taxation problem in a small open eonomy where pries move exogenously and workers move aross setors. They show that progressive inome taxes an be used to redistribute the gains from trade. Our fous instead is on a more general lass of poliy instruments, namely we allow for poliies that diretly affet produers. In Fagelbaum and Gaubert 2018) and Ales and Sleet 2017) the role of taxes is to orret externalities. While our paper is somewhat related to the literature on optimal trade poliy e.g., Bagwell and Staiger 1999), Opp 2010), Costinot et al. 2015), and Beshkar and Lashkaripour 2017) among others), our paper is different in that this literature often assumes strategi motives of the government as the main determinant of trade poliies. As a result, these poliies help governments manipulate their terms of trade in their favor. In our setup, this motive is shut down intentionally to fous on optimal poliies under ooperation. Thus, our paper is mainly related to the design of trade agreements and disussion of the type of industrial poliies allowed under suh agreements. In the trade literature, our paper is also related to the work by Dixit and Norman 1980) and Dixit and Norman 1986), who show that it is always possible to redistribute gains from trade with lump-sum and proportional taxes. While their analysis is insightful, it does not identify the main poliy instruments that are required to redistribute gains from trade. In ontrast, we provide a theoretial and quantitative analysis of optimal poliy instruments whih are benefiial in redistributing gains from trade. Our quantitative exerise builds upon reent models in the international trade literature that try to measure and aount for hanges differential hanges in welfare and employment aused by the rise of China, as doumented by Autor et al. 2013). These inlude Caliendo et al. 2015) and Galle et al. 2017). More speifially, we use a variant of the model in Galle et al. 2017) to perform our quantitative exerise. To do so, we allow for the intensive margin of labor supply in their environment as well as redistributive taxes. The rest of the paper is organized as follows: In setion 2 we desribe a general model of trade 6 We oneture that these insights arryover for other forms of tehnologial hange as well but we leave suh an analysis for future work. 5

6 with imperfet mobility. In setion 3 we desribe and haraterize the optimal poliy problem in suh a model, and in setion 4, we disuss the determinants of optimal poliies. In setion 5, we present our quantitative results. We onlude in setion 6. 2 A Model of Trade with Imperfet Mobility In this setion, we provide the basi framework of analysis in this paper. This framework is based on an eonomy where workers movement aross setors an be ostly, as in the model proposed by Roy 1951). This framework allows us to provide our basi theoretial result on optimal trade poliy and optimal inome taxes. Geography. Prodution and onsumption our in N C ountries, and eah ountry is represented by {1,, N C }. In eah ountry there is a unit ontinuum of workers who are potentially heterogeneous with respet to their working opportunities, as we larify below. Prodution. There are a total of N goods produed globally. In partiular, suppose that eah good, i {1,, N}, an be produed in ountry aording to the prodution funtion Yi = G i L i, { } Q N i =1), where L i is the total effetive units of labor in this setor, and Q i is the total amount of good used in prodution of good i in ountry. We assume that the above prodution funtion exhibits onstant returns to sale with respet to all fators, the marginal produt of eah intermediate good onverges to infinity as its quantity goes to zero, and G i is stritly onave with respet to all its inputs. Moreover, the produers of eah good are prie takers; they take as given the pries of their produts, their inputs, and the wages of their workers. Workers and Setoral Choie. In eah ountry there is a unit ontinuum of workers. 7 They are assumed to have preferenes over a vetor of onsumption goods x = x 1,, x N ), where x i is the onsumption of good i. Aside from hoosing a onsumption bundle x, workers an work in firms that produe a good and hoose how muh effort to put in their work. This hoie of working status depends on the workers types and their idiosynrati produtivity shok. In partiular, a worker draws a type θ Θ, whih is distributed aording to probability measure µ. A worker of type θ an hoose to work in setor with labor produtivity given by z = a θ) ɛ, where ɛ is a random variable that is distributed i.i.d. and aording to a Fréhet distribution given by H ɛ) = Pr ɛ ɛ) = e ɛ σ for σ > 0. In other words, a worker is identified by a group θ and idiosynrati produtivity type ɛ = ɛ 1,, ɛ N ). The group θ an be assoiated with eduation, loation, and other harateristis of a worker. We let the.d.f. of ɛ be given by H ɛ) = N =1 H ɛ ). 7 We an also work with a version of our model where ountries are heterogeneous in their population, in whih ase, i µ i = M, {1,, N C }. 6

7 Finally, the utility of a worker that onsumes a bundle x and supplies l units of labor and works in setor is given by U x) v l). 1) We assume that workers preferenes satisfy the following properties: Assumption 1. The prefenes of workers in ountry satisfy the following: 1. The utility from onsumption, U x) is stritly onave, homotheti, and inreasing. Moreover, its implied indiret value funtion is linear in wealth. 2. The disutility of effort v ) satisfies v l) = l1+1/ε 1+1/ε. 3. The parameter governing the distribution of ɛ satisfies σ > 1 + ε. The above assumptions on preferenes are mainly made for tratability of the analysis. The homothetiity assumption implies that Atkinson and Stiglitz 1976) and Deaton 1981) s result on uniform ommodity taxation applies and onsumers in eah ountry must pay the same taxes on onsumption of different goods. Moreover, the fat that the indiret utility funtion assoiated with U is linear in wealth implies that there is no inome effet whih simplifies the analysis of optimal taxes. 8 Finally, the last part of the assumption ensures that the 2mean produtivities are well-defined. The above assumptions about the struture of worker mobility are made to allow for a somewhat general struture yet maintain tratability. In partiular, our speifiation of produtivity is flexible enough to allow for various patterns of mobility: 1. Absolute Advantage: Suppose that a θ) = α β θ). That is, a worker of type θ, whose β θ) is high, is on average more produtive in all setors. In this sense, workers with high β θ) have an absolute advantage over those with low β θ). 2. Speialization: Suppose that a θ) = α θ) ψ l θ)) 2 In this setting, a worker of type θ is on average most produtive in setor l θ) {1,, N}. For setors whose index is different from a worker s most produtive setor, the worker experienes an average loss in produtivity given by ψ l θ)) 2. The parameter ψ ontrols a worker s extent of speialization. Additionally, the assumption of Fréhet distribution implies that the labor supply in eah setor an be haraterized in a fairly tratable way. We will disuss this tratability when we analyze the properties of equilibrium. 8 It is fairly straightforward to extend the results to non-homotheti preferenes but we skip this for the ease of exposition. 7

8 Markets. We assume that for eah good i {1,, N}, there is a ompetitive market where the produers of this good in ountry sell their produt, while the produers of other goods and onsumers purhase their demand from this market. The market prie of good i is given by ˆp i. Seemingly, the assumption above suggests that all goods are traded in all ountries and trade is free and, therefore, our speifiation annot handle trade osts. As we will larify later, this literal interpretation of the model is at best inomplete. In partiular, we argue that our speifiation is general enough and an enompass a model with ieberg trade osts à la Samuelson, non-tradable goods, autarky, et. In addition to markets for goods and servies, we also assume that in eah ountry there are ompetitive labor markets. This implies that there is a wage assoiated with working in setor in ountry, whih is given by w, {1,, N}, {1,, N C }. Governments and Poliies. We assume that in eah ountry, there is a government that has aess to inome taxes, produer taxes, and onsumer taxes. In partiular, we assume that the government in ountry imposes a general non-linear tax on earnings given by T y) where y is a worker s labor inome. Moreover, upon onsumption of good i by a onsumer in ountry, the government imposes an ad-valorem tax rate given by t x, i. Finally, a produer of good i in ountry faes a tax rate of t p, i on its revenue and a tax rate t p, i, on its purhases of intermediate inputs of good. For now, we assume that governments do not have any expenditure and therefore must have a balaned budget. Given the above struture for the global eonomy, a ompetitive equilibrium given governments poliies an be defined as: i) onsumption, leisure alloations together with { setoral hoie by eah worker in group θ and idiosynrati type ɛ = ɛ 1,, ɛ N ), ˆx θ, ɛ), ˆl } θ, ɛ), θ, ɛ) ; ii) prodution in eah setor, L i, { Qi} N ; iii) vetor =1 θ Θ,ɛ R N + of pries, ˆp = ˆp 1,, ˆp N ), and wages, w = {wi } N i=1, suh that: 1. Workers in eah ountry maximize utility, taking as given pries and government poliies: ˆx θ, ɛ), ˆl θ, ɛ), θ, ɛ) arg max x,l, U x) v l) subet to N i=1 ˆp i 1 + t x, i ) x i w a θ) ɛ l T w a θ) ɛ l ) 2. Firms maximize their profits, taking as given pries and government poliies: L i, { Qi} arg max ˆp i 1 t p, i ) G i L,Q i ) L, {Q i } N =1 wi L N =1 ) 1 + t p, i ˆp Q i 8

9 3. Government budget onstraint holds: N C =1 4. Markets lear: N C i ˆp i t x, i Yi + =1 Θ ɛ L i = N C =1 N i=1 N =1 N C + =1 ˆp t p, i Q i + Θ x i θ, ɛ) dh ɛ) dµ + Θ R N + ɛ N C =1 N i=1 ˆp i t x, i x i θ, ɛ) dh ɛ) dµ Θ ɛ T w θ,ɛ)a θ,ɛ) θ) ɛ l θ, ɛ) ) dh ɛ) dµ = 0 N C =1 k=1 N N C Q ki = =1 G i L i, { }) Q i, i, 2) a θ,ɛ) θ) ɛ θ,ɛ)l θ, ɛ) 1 [ θ, ɛ) = i] dh ɛ) dµ, i, 3) Note that in our definition of equilibrium, we have a single budget onstraint for the governments. In other words, our equilibrium onept allows for transfers aross ountries. As a result and in general trade an be unbalaned. In our environment, imposing a budget balane introdues additional distortions, whih we want to abstrat from. In our quantitative exerise, we study the role of these inter-government transfers. Generality of the Model. As we have laimed before, our model enompasses various versions of the models that are popular in the international trade literature. Here, we provide some remarks to illustrate this: 1. Ieberg trade osts: While we have assumed that markets are ompetitive, it is possible to map a trade model with ieberg osts into the setup above. In partiular, onsider a model with ieberg trade osts. In order to map suh a model into our setup, we first extend the set of goods so that eah good is produed in a different ountry. That is, we define an extended set of goods {1,, N} and partition it into goods produed in eah ountry given by I where C I = {1,, N}, I I =. =1 Let i) be the ountry in whih good i is produed. Suppose that the ieberg ost of shipping good i I from ountry to is given by d, i with d, i = 1 for all and i I. We then refer to x i, onsumption of good i in ountry, as this onsumption inluding the ieberg trade ost. Similarly, Q i is defined by the intermediate input demand of setor in ountry of good i whih inludes the ieberg ost d, i. Given this relabeling, the utility funtions and prodution funtions in any ountry are given by ) x U x) = U 1 x 2 x N,,, d 1), 1 d 2), 2 d N), N Yi = G i L i, { Q i d ), 9 }), i I

10 Note that in the above we relied heavily on the extension of the set of goods so that eah good is produed in a unique ountry. This is often possible in neolassial models of trade. For example, in an Armington model, eah ountry produes a set of differentiated produts that are imperfet substitutes and hene, no extension is neessary. In Riardian models, suh as that of Dornbush et al. 1977) or Eaton and Kortum 2002), the goods produed in eah ountry are perfet substitutes and thus the set of goods an be easily relabeled so that ertain lasses of goods are perfetly substitutes in utility and prodution funtions. For example, if the set of goods are loth and wine and the set of ountries are England and Portugal, we an extend the set of goods to be English Wine, Portuguese Wine, English Cloth and Portuguese Cloth. In this ase, the wine and loth produed in eah ountry are perfet substitutes for all onsumers and produers. Note that the types of trade osts are tehnologial as opposed to government imposed. In partiular, the goal of the paper is to find the optimal government-imposed trade osts given the tehnologial ones. 2. Non-tradable goods: It is fairly straightforward to see that the non-tradable goods are aptured in our model by requiring ertain goods to be produed and used by onsumers or produers) in one ountry. That is, the non-tradable goods do not enter the utility of workers and prodution funtion of firms in other ountries. 3. Two layers of mobility: It is possible to extend the above model to allow for ostless mobility aross some setors, similar to the models in Caliendo et al. 2017) and Galle et al. 2017). In partiular, one an partition the set of goods in ountry into setors Ii, i = 1,, NJ where N J i=1 I i = {1,, N}. We then assume that idiosynrati produtivity shoks ɛ s are the same for all goods produed in the same setor, Ii. This is the approah taken when we use a quantitative version of this model. Given the above disussion, it is easy to see that various neolassial models of trade suh as the Armington model, and Riardian models of Dornbush et al. 1977) and Eaton and Kortum 2002) are speial ases of our general model. Generality of the Poliies Despite the fous of our paper on trade poliy, we have not expliitly introdued tariffs in the above environment. This is in part beause tariffs are a speial ase of onsumer and produer taxes. To see this, suppose that the government in ountry imposes an ad valorem tariff, τi, on good i whih is on net being imported into ountry. Therefore, if the international) market prie of good i is ˆp i, the prie faed by produers and onsumers in ountry is ˆp i 1 + τi ). In other words, a tariff imposes a tax on the use of a good, by onsumer and produers, while at the same time, it imposes a subsidy on the prodution/making of good i in ountry. That is, under this tariff, we have: t x, i = τ i, t p, i = τ i, t p, i = τ i. The above example illustrates that the indiret ommodity) tax poliies onsidered in our model inlude the possibility of tariff. Another way to see this is to realize that in the presene 10

11 of tariffs,τ i, the onsumer prie vetor in ountry is given by 9 ˆp = 1 + τ 1) 1 + t x, 1 ) ˆp 1,, 1 + τ N) 1 + t x, N ) ˆp N) while the set of after tax/tariff pries faed by produers in setor i is given by 1 t p, i ) 1 + τi ) ˆp i, { ) ) } 1 + t p, 1 + τ N ˆp. =1 Sine onsumers and produers are only about after tax/tariff pries, it is possible to redefine onsumer and produer taxes so that the resulting equilibrium alloations and pries will be the same as the ones in the eonomy with tariffs. Beause of this equivalene of tax systems, we fous our attention to indiret tax poliies that involve only onsumer and produer taxes. 2.1 Charateriation of Equilibria In this setion, we provide a haraterization of alloation that an arise in ompetitive equilibria, whih are distorted by government poliies. This haraterization helps us in solving the optimal taxation problem in Setion 3. We first observe that the workers setoral hoie is independent of taxes and depends only on wages. In other words, a worker identified by θ, ɛ) hoses the setor that gives the worker the highest labor produtivity. That is, θ, ɛ) arg max wa θ) ɛ This is beause personal inome taxes depend only on total inome and not on wages or the setor in whih a worker works. 10 We an then define labor produtivity for a worker given by z = max w a θ) ɛ. Given this level of labor produtivity whih is determined by the setoral hoie of the worker, a worker s hoie of earning is simply given by max V zl T zl) ; q ) v l) l where q = ˆp t x, 1 ),, ˆp N 1 + t x, N )) is the after-tax vetor of pries faed by onsumers in ountry, and V I; q) is the indiret utility of a worker in ountry with after-tax inome I who faes after-tax vetor of pries q. This illustrates a key property that signifiantly simplifies the analysis of optimal taxes in this paper: The earning deision depends only on the labor produtivity of an individual together with inome tax T, while the setoral hoie deision of a worker only depends on wages. This separation of deisions allows us to express the distribution { }) of types in eah setor and inome level in a tratable fashion. Partiularly, let λ z, θ; w be the density of workers of type θ in setor that have produtivity z. In the Appendix, we show that the extreme value assumption about the distribution of ɛ implies that i λ z, θ; { w }) = σ z 1 σ w a θ) ) σ e z σ iw i a i θ))σ 9 This partiular way of defining tariffs works as a tax on imports and subsidy on exports. 10 A similar separation result emerges in Rothshild and Sheuer 2013). 11

12 Similarly, if we define λ z, θ; { w }) as the distribution of labor produtivity among workers of type θ, then λ z, θ; { }) w = σ z 1 σ i wi a i θ)) σ e z σ iwi a i θ))σ In other words, the distribution of labor produtivity among workers of type θ is Fréhet with a mean value of Γ ) [ 1 1 σ i w i a i θ)) σ] 1 σ and shape parameter σ. Moreover, onditional on setoral hoie, the distribution of labor produtivity is Fréhet with a shape parameter of σ and the same mean value. The extreme value assumption also implies the fration of workers of type θ that work in setor is given by Λ θ) = w a θ) ) σ i w i a i θ))σ. The parameter σ is related to the elastiity of mobility of workers aross setors with respet to wages. When σ = 0, the fration of workers in setor is given by µ ; that is, workers are attahed to setors and annot move aross them. At the other extreme where σ =, only setors in whih a θ) w = max k a k θ) w k holds will have a non-zero measure of workers of type θ. In addition to these distributions, reall that by Assumption 1, the indiret utility funtion assoiated with U x), whih we denote by V I; q), is linear in I. As a result a prie index ν q) exists so that V I; q) = I + ν q) ϑ q). Therefore, the hoie of work effort by a worker of type θ, ɛ), ˆl θ, ɛ), must satisfy ˆl θ, ɛ) arg max l z θ, ɛ) l T z θ, ɛ) l) ν q ) v l) This implies that effort depends only on labor produtivity z; we refer to this as l z). Finally, we an alulate the welfare of workers of type θ as follows: û θ) = 0 u z) λ z, θ; { w }) dz where u z) = zl z) T zl z)) v l z)). We an thus summarize the neessary and suffiient ν q ) onditions that alloations in an equilibrium must satisfy in the following proposition: Proposition 1. In any equilibrium, the alloation of onsumption ˆx θ, ɛ), effort ˆl θ, ɛ), and setoral hoie θ, ɛ) satisfy the following: i. Setoral hoie is independent of inome taxes, i.e., θ, ɛ) = arg max ɛ a θ) w, ii. If we let z θ, ɛ) = max ɛ a θ) w be the labor produtivity of a worker of type θ, ɛ), then effort hoie of a worker of type θ, ɛ) depends only on the worker s labor produtivity z. That is, a funtion l z) exists suh that ˆl θ, ɛ) = l z θ, ɛ)). 12

13 iii. A funtion I z) must exist suh that z arg max ẑ I ẑ) ν q ) v ẑl ) ẑ) and ˆx θ, ɛ) = x I z) ; q ), where x I; q) = x 1 I; q),, x N I; q)) is the demand funtion assoiated with the utility funtion U x). The funtion I z) represents the disposable inome of a worker with labor produtivity z. The above proposition is useful in solving the optimal taxation problem, sine it simplifies the onstraint set of the problem. In what follows, we use this haraterization of equilibria in order to disuss the solution of the optimal taxation problem. 2.2 Winners and Losers of Trade As Galle et al. 2017) have shown, the above model an be used to shed light on the distribution of welfare gains of trade. In partiular, depending on the pattern of speialization, a reorganization of prodution in the global eonomy an generate winners and losers. This reorganization of prodution ould ome from a produtivity shok to ertain setors outside of a partiular ountry; the literature often models the rise of China what we refer to as the China shok) in the prodution of manufaturing goods as an inrease in manufaturing produtivity see Caliendo et al. 2017) and Galle et al. 2017), among others). In order to provide a better understand of the effet of suh a disturbane, we disuss how a hange in the struture of wages something that an be aused by a trade shok) affets the welfare of workers. The following lemma desribes the main result: Lemma 1. Consider an infinitesimal hange in wages in ountry, given by δw. Then, the infinitesimal hange in the welfare of workers of type θ is given by ) δû θ) = δu 0) + σ Λ θ) δw z u ) z) λ z, θ; { w w }) dz 4) where Λ θ) is the fration of workers of type θ in setor in ountry. The proof an be found in the Appendix. The above formula illustrates that whether a group of workers of type θ beomes a winner or loser from a trade shok depends on the distribution of workers aross setors and on relative hanges of wages. For example, if the trade shok auses wages in manufaturing to deline, the groups that lose the most or win the least) are those that have a high fration of workers in manufaturing. To the extent that Λ θ) is determined by the funtion a θ), the pattern of speialization determines the gains and losses from trade. For example, suppose that a θ) exhibits absolute advantage, i.e., a θ) = αβ θ). Then, in this ase, z Λ θ) = a θ) w ) σ k a k θ) w k )σ = α w ) σ k α k w k )σ In other words, the distribution of workers aross setors is independent of their types, θ. This implies that when δu 0) = 0, either all workers gain from trade or all workers lose from it, 13

14 albeit to a varying degree given equation 4). 11 Note that the response of welfare depends on how the utility of workers with zero labor produtivity hanges, in other words, on the response of transfers to the trade shok. As we will show in the next setion, the optimal poliy response to a trade shok also depends on the degree of speialization aross different groups of workers. 3 The Optimal Poliy Problem The model developed in the previous setion larifies the type of poliies that an be used by the governments in eah ountry. Furthermore, it highlights how various groups of workers an be differentially affeted from international trade and global reloation of prodution. In this setion, we desribe the optimal poliy problem faed by these governments under ooperation and derive formulas that govern the behavior of the optimal trade poliy. Starting with the government in eah ountry, we assume that the government evaluates the alloation of resoures aross workers of types θ aording to a soial welfare funtion given by g θ) û θ) dµ Θ where g θ) > 0 is the welfare weight on workers of group θ. For now, we assume that g θ) is an exogenous welfare weight. In setion 5 where we study the problem of ompensating the losers from a trade shok, these welfare weights arise from onstraints that ensure that eah group of worker s utility is at least as high as its pre-shok level. Our main assumption about the determination of poliy is that it is determined under ooperation. In partiular, we assume that the optimal trade poliy problem is given by N C max ψ g θ) û θ) dµ 5) {t p,,t x,,t } =1,,NC =1 where û θ) is the utility profile arising from a ompetitive equilibrium of the eonomy desribed above given the poliy hoies {t p,, t x,, T } =1,,NC. One way to rationalize this assumption is to onsider trade agreements whereby governments negotiate with eah other on oordination of their tax poliies. We assume that the outome of this negotiation proess is effiient in that it is equivalent to maximizing a weighted average of aggregate welfare in eah ountry. Equation 5) represents suh an obetive, where ψ > 0 is the welfare weight of ountry implied by the negotiation proess. Given this obetive for the government, the optimal taxation problem for the government is to maximize soial welfare given that the utility profile û θ) arises from a ompetitive equilibrium, as defined above. As in Atkinson and Stiglitz 1976) or Diamond and Mirrlees 1971), it is often onvenient to write this problem in terms of after-tax) onsumer and produer pries defined by qi = ˆp i 1 + t x, i ) ) p i = ˆp i 1 t p, i ), p i = ˆp 1 + t p, i 11 When u z) = Az α for some A and α, then the perent hange inrease in welfare for all the groups will be the same. An example of this is the laissez-faire eonomy where u z) z 1+ε. In this ase, 4) beomes the basis of the formulas provided by Galle et al. 2017). 14 Θ

15 where qi is the after-tax prie paid by a worker/onsumer for good i in ountry while p i and { } p N i are the after-tax pries faed by produers of good i. Note that produer pries affet =1 the prodution deision of firms. However, sine the set of taxes on produers is general enough, we an show that any demand vetor for intermediate inputs by a firm i in ountry, { } Q N i =1, an be implemented by arefully hoosing the vetor of produer taxes, { } t p, N i. =1 Following the haraterization of equilibria in setion 2.1 and the disussion above, the optimal poliy problem an be stated as in the following proposition: Proposition 2. Any solution of the optimal taxation problem and its assoiated onsumer and produer pries and wages must solve the following optimization problem subet to Θ 0 N C max ψ q,{i z),l z),u z)},w,{q i} =1 x i q ; I z)) λ z, θ; w ) dzdµ + 1 w Θ Λ θ) 0 Θ g θ) C 0 =1 k=1 N Q ki = u z) λ z, θ; w ) dzdµ C =1 V q ; I z)) v l z)) = u z) l z) v l z)) z zl z) λ z, θ; w ) dzdµ = L G i P) L i, { } Q N i =1), i 6) = u ) z) 7) where Λ θ) = ) a θ) w σ / [ i a i θ) wi ) σ ]. Conversely, any solution of the above optimization problem that satisfies d zl z)) /dz 0 an be used to onstrut a solution of the optimal taxation problem. The proof of this proposition is relegated to the Appendix. As the above proposition establishes, the only restritions that ompetitive equilibrium imposes on alloations is feasibility and optimal hoie of labor supply. The reasoning for the above proposition is straightforward. Given that onsumption is alulated using the demand funtion of households, the households budget onstraints must be satisfied. Furthermore, sine feasibility is satisfied, these onditions imply that the government budget onstraint must hold. Finally given that onsumption omes from the demand funtion and optimality of hoie of labor supply, the onsumption and labor supply alloation must satisfy optimality for workers. Note that in the above, we are not hoosing produer pries, beause of two reasons: First, as we mentioned above, by hoosing intermediate quantities { Qi}, one effetively hooses a vetor of produer taxes { ti} p that implement suh intermediate quantities. Seond, the labor demand by firms is determined by p G i i L = w i Therefore, given intermediate quantities and aggregate labor supply, a hange in produer pries implemented by a hange in produer tax t i) translates into a hange in wage wi. Thus, hoosing 15

16 the vetor wages w is equivalent to hoosing after-tax pries {p i}. This disussion also larifies the role of ommodity taxes in this model. Speifially, produer taxes redistribute resoures to workers in a ertain setor. At the same time, they hange the labor supply of workers, by affeting the intensive and extensive margin of labor supply, and thus reate distortions. This is also true for earnings taxes, although earnings taxes redistribute resoures aross different produtivity levels z. The above planning problem finds a balane between the redistribution and distortions via produer taxes and earnings taxes. Finally, sine onsumer and produer pries are suffiient to haraterize alloations, the atual produer and onsumer taxes are indeterminate. This result is standard, as it is typially irrelevant whether to tax onsumer or produers. Optimal alloations, however, determine the ratio 1 tp i 1+t x i = p i q i. Remark. While in the above, we have assumed that the optimal poliies are determined under ooperation, there are alternative formulations of the problem that an result in the same outome. An example of this is a model of one small open eonomy where the entire vetor of relative pries is exogenously determined. In this ase, sine the ountry annot affet interntional pries, it will at very similarly to a ountry that is ooperating with the rest of the world, i.e., it has no motives for terms of trade manipulations Properties of Optimal Poliies In this setion, we disuss the qualitative features of optimal redistributive and trade poliies. We start our disussion by analyzing prodution effiieny and then we disuss the determinants of optimal poliies. 4.1 Prodution Effiieny In this setion, we disuss the prodution effiieny properties of optimal alloations, i.e., those that are the solution of the optimal poliy problem P). Sine the seminal result of Diamond and Mirrlees 1971), it is known that when the government has aess to a rih set of tax instruments, one for every good that households are about inluding leisure and onsumption goods), then prodution must be effiient, i.e., it is optimal to not distort firms prodution deision. In our ontext, this result would translate into optimality of free-trade as it implies that firms deision to use intermediate inputs is undistorted. Note that despite the generality of their result, it does not apply in our setting sine the government does not have aess to a rih set of taxes. In partiular, the appliation of the result of Diamond and Mirrlees 1971) to our environment requires the government to be able to tax workers in different setors differently. A question that arises then is whether produtive effiieny holds in our environment. In what follows, we show that a version of prodution effiieny holds, whih in turn leads to optimality of VAT taxes. { Consider an alloation of prodution aross ountries given by {l z), λ z, θ; w ) }, { } } Q z R +,θ Θ i, Yi with 1 i, N {1,,C} Y i = G i zl z) λ z, θ; w ) dzdµ, { Q i} ). 12 See Bagwell and Staiger 1999) for an interpretation of this assumption using the reiproity assumption often used in trade agreements. 16

17 We { all } this alloation psuedo-prodution effiient if there does not exist an alternative ˆQ i, Ŷ i suh that i,, Ŷ i = G i { } ) zl z) λ z, θ; w ) dzdµ, ˆQ i C =1 Ŷ i C N =1 =1 ˆQ i C =1 Y i C N Q i, i {1,, N} =1 =1 with the inequality holding stritly for at least one setor and one ountry. This notion of prodution effiieny is a somewhat weaker notion, sine it does not allow for reshuffling of labor aross setors. The following proposition establishes a key property that alloations that with pseudo-prodution effiieny must exhibit. { {l Lemma 2. A prodution alloation z), λ z, θ; w ) }, { } } Q z R +,θ Θ i, Yi 1 i, N {1,,C} is effiient if and only if there exists a vetor of positive numbers {ρ i } i {1,,N} suh that { Q i } i,, arg max { ˆQ i} [ N C ρ i i=1 where L i = zl z) λ i z, θ; w ) dzdµ. =1 G i { }) L i, ˆQ i The proof is relegated to the Appendix. The proof of the above lemma uses a standard separating hyper-plane argument to show the laim. We an think about the vetor ρ i s as the vetor of pries. The above laim then states that for prodution to be pseudo-effiient, the marginal rate of transformation between any two inputs must be equated aross all setors and ountries. Given the above lemma, our prodution effiieny result is fairly straightforward: Corollary { 1. Consider the solution of the optimization problem P). Then the prodution alloation {l z), λ z, θ; w ) }, { } } Q z R +,θ Θ i, Yi is pseudo-effiient. 1 i, N {1,,C} Proof. We know that at the optimum, Lagrange multipliers {ρ i } i {1,,N} should exist for resoure onstraints 6). Then, at the optimum, the optimality ondition for eah Q i satisfies ρ i G i Q i = ρ sine G i satisfies the Inada ondition with respet to eah intermediate input. Note further that eah ρ i > 0. This is beause a uniform inrease in inome of all workers in a ountry that likes good i inreases welfare. Sine all G i s are stritly onave, the above ondition is equivalent to the ondition stated in lemma 2. This onludes the proof. The key feature of our model whih leads to this result despite the inompleteness of inome taxes, is that different kinds of labor are perfet substitutes in the prodution funtion. This implies that the wage of a worker of type θ whose produtivity is z and works in setor is the 17 C =1 N =1 ˆQ i ] 8)

18 marginal produt of labor in setor multiplied by z. As a result, relative wages are independent of the intermediate quantities. Consequently, distortions to alloation of intermediate goods annot affet the deadweight loss of inome taxation and, as a result, it must not be distorted. The effiieny properties of prodution imply that taxes on firms must be designed so that all setors fae the same after tax-pries. This means that any sales taxes paid by firms in setor on their sales must be partially offset by a subsidy on intermediate inputs. One implementation of effiieny would be to have the sales tax rate be equal to the subsidy rate on intermediate inputs. In other words, optimal prodution taxes take the form of a VAT tax. We, thus, have the following proposition: Proposition 3. Optimal alloations in P) an be implemented by VAT taxes where Proof. In any ompetitive equilibrium, we have t i = t i, i, {1,, N}. ˆp i 1 t i) G i Q i = ˆp 1 + t i ) Sine pries in a ompetitive equilibrium an be freely piked, we set ˆp i = ρ i where ρ i is the Lagrange multiplier on the resoure onstraint 6). Then, the pseudo-effiieny of prodution implies that 1 + t i = 1 1 t i whih in turn implies that t i = t i, i,. As we illustrate below and in our numerial results, setor-speifi VAT taxes play an important role in redistributing gains from trade aross different groups in the population. Remark. It is important to ompare our results to other results in the literature on prodution effiieny, for example, those of Naito 1999) and Costinot and Werning 2018) as they have shown that distortions to prodution effiieny an be optimal. This is beause a hange in the alloation of intermediate goods affets relative wages and thus an redue the deadweight loss from taxation of inome. Our disussion above on the interplay between alloation of intermediate inputs and relative wages larifies the main fores behind the differene between our results and those of Naito 1999) and Costinot and Werning 2018). In partiular, one an onsider a more general prodution funtion of the form G i {L i θ)}, { }) Q i where L i θ) = Θ R N + [ ] a i θ) ɛ i l θ, ɛ) 1 i arg max w θ) a θ) ɛ dh ɛ) dµ 9) where in the above w i θ) is the wages of workers in setor i ountry. In this ase, it is possible to find onditions so that prodution remains pseudo-effiient. The following proposition states this result: Proposition 4. Suppose that good i in ountry is produed using the prodution funtion Yi = G i {L i θ)}, { }) Q i where L i θ) is the total effetive labor supply of workers of type θ in setor 18

19 i defined by 9). Then under optimal poliies, prodution is pseudo-effiient when the following ondition holds: = 0, i, {1,, N}, θ, θ Θ. Q i G i L θ) G i L θ ) The proof is relegated to the appendix. In other words, for distortions to prodution to be optimal, it must be that the intermediate inputs have different degrees of substitution with different types of labor, e.g., the intermediate inputs must be omplements to some types of skills and substitutes for others. Our analysis here basially implies that in order to understand the best poliy response to the redistribute gains from trade, this differene in substitution must be identified. The literature has often disussed the unequal effet of international trade; see for example, Autor et al. 2013), Galle et al. 2017), among many others. However, it is still unknown whether this results from speialization of workers or from the fat that traded inputs are potentially omplimentary to some skills and substitute to others. In other words, it ould be that ertain groups in the United States are worse off from the rise of China due to this substitution. When intermediate inputs an be produed in China heaper, they substitute for the labor of some groups in the prodution funtion and thus wages of suh groups drop. Our analysis highlights the need for suh identifiation. In our quantitative exerise, we fous on the speialization story, based on the work of Galle et al. 2017), and show how to design VAT taxes in order to redistribute the gains from trade. 4.2 Optimal VAT Taxes As we have shown, prodution taxes must take the form of VAT taxes. Here, we desribe the behavior of optimal VAT taxes and their role in redistributing the gains from trade aross workers of different groups. The following proposition desribes the determinants of optimal VAT taxes: Proposition 5. Optimal VAT taxes, t, satisfy t σ 1) 1 t Y = [ 1 W ] Y 10) + Λ y [ 1 τl ) 1 + ε ) σ ε z τl ) ] λ dzdµ + Λ i Λ [ y σ 1 ε + ε z τ ] l ) λ dzdµ 1 t i i 1 τl where W is the soial marginal value of inreasing the inome of workers in setor by 1% and is given by W g θ) Λ θ) 1 τl = z)) y z) λ z, θ) dzdµ g θ) dµ Λ θ) ; y z) λ z, θ) dzdµ y z) is the before-tax inome of a worker with produtivity z; τl z) is the marginal inome tax rate for a worker with labor produtivity z; and Y is total labor inome earned in setor, i.e., Y = Λ y λdzdµ. 19

20 The above formula haraterizes optimal VAT taxes. Its intuition is best understood by onsidering a 1% derease in VAT tax on setor i in ountry and onsidering its impat on government budget and welfare. The left hand side of the equation is the hange in government revenue due to the behavioral response of workers to a 1% derease in taxes. The term σ 1 an then be thought of as the elastiity of labor supply to this tax hange; this term aptures three effets: When VAT tax in setor delines and as a result its wages inrease, workers respond by hoosing setor more frequently - with elastiity σ ; by providing more hours with elastiity ε ; and by reduing the produtivity in that setor with elastiity 1 + ε. The superimposition of these effets leads to an elastiity of σ 1. The right hand side of the equation aptures the osts of this hange. The first term is the mehanial derease in government revenue net of its welfare effet. 13 The seond term is related to the fisal externality of hanging VAT taxes on the revenue from inome taxes. Finally, the last term aptures the fat that a redution in VAT taxes in setor auses an inrease in produtivity of other setors sine less produtive workers in move out of other setors and into setor. We refer to the former as the reloation effet. The above formula has the following important impliations: Optimal taxes are independent of the pattern of trade. As the above formula shows, trade or, more generally, the parameters of tehnology aross ountries, only affet optimal taxes through their effet on the distribution of inome. In other words, in this model, the soure of inequality is irrelevant for optimal taxes. Moreover, trade elastiities and the network struture of trade do not affet optimal taxes diretly. A stark illustration of this an be done by onsidering the model in whih the distribution of workers aross setors is irrelevant for their produtivity, i.e., σ = 1 + ε and when inome taxes are linear. Under this restrition, the formula for optimal produer taxes beomes t ε = 1 τ 1 t l 1 + ε ) W Note that this formula also holds when we ignore general equilibrium effets and assume that produer taxes do not affet the struture of wages. In fat, when we set W = 0, i.e., when the government does not are about workers in a setor, the above formula is simply the tax rate at the peak of Laffer urve, 1 ) 1 t 1 τ ) = 1 + ε. ε In other words, general equilibrium effets and, as a result, the global proess of prodution) are irrelevant for optimal VAT taxes. The main reason behind this result is that even though we have assumed away setor-speifi inome taxes, our tax struture is quite rih, i.e., it has enough flexibility. A rih tax shedule implies that the value of eah good to the government in eah ountry is simply the prie of that good. In other words, the government in eah ountry an perturb its tax shedule onsumer taxes and produer taxes) and inrease only the supply of one partiular good that is, either used or produed in eah ountry) by a small amount. 13 We have W = g Λ 1 τ l ) y λ dzdµ. Notie that there is no ompositional effet on welfare beause of the extreme value assumption. This assumption implies that the welfare of all the workers of the same type onditional on their setoral hoie is independent of their setoral hoie. 20

21 Sine all taxes are at the optimum, this perturbation of taxes has no first-order effet and, thus, the valuation of the government is proportional to the prie of this good. That eah government marginal valuation of eah good is simply its prie implies that the government an simply ignore the general equilibrium effet and use urrent pries to evaluate the hange in demand and supply oming from perturbation of t p,. Optimal taxes depend on the speialization of workfore. So far we have emphasized the role of speialization in generating winners and losers from trade shoks. Here, we show how speialization affets optimal VAT taxes. To do so, we onsider the ase without speialization, i.e., when there is absolute advantage. In this ase, as disussed in setion 2.2, the fration of workers in setor of type θ, Λ θ) is independent of θ. As a result, we an write the formula 10) as t σ 1) Λ 1 t Y = [ 1 W ] Λ Y + Λ y [ 1 τl ) 1 + ε ) σ ε z τl ) ] λ dzdµ + Λ iλ [ y σ 1 ε + ε z τ ] l ) λ dzdµ 1 t i i 1 τl Note that in the above, we have used the fat that Λ is independent of θ. In the Appendix, we show that W is the same for all setors. Roughly speaking, this is beause the distribution of workers aross different setors is idential. We an thus write it as t σ 1) =1 W 1 t + 1 y [ 1 τ Y l ) 1 + ε ) σ ε z τl ) ] λ dzdµ + 1 Λ [ i y σ 1 ε + ε z τ ] l ) λ dzdµ Y 1 t i 1 τl i Thus, t is independent of. In other words, VAT taxes will not be used to redistribute resoures aross different groups, and we have the following proposition: Proposition 6. Suppose a θ) = α β θ). Then optimal VAT taxes are equal. The proof is relegated to the Appendix. The above proposition highlights the main fores behind using VAT taxes to redistribute the gains from trade. When the distribution of workers aross setors is the same, VAT taxes annot prove a useful tool to redistribute the gains of trade. This is beause VAT taxes in this model work similar to other tags as disussed by Akerlof 1978), wherein the setoral hoie of a worker an be used as a signal of that worker s group θ. With absolute advantage, setors and θ are unorrelated. Thus, VAT taxes annot be used as a tag. However, in the presene of speialization, losers from trade are often onentrated in setors that do not experiene gains from trade. As a result, VAT taxes an be used to redistribute the gains from trade to the groups of workers that are onentrated in setors whose wages deline. 21

22 Finally, we should mention how our results on prodution taxes ompare to other forms of taxation of firms and, most importantly, the so-alled border tax adustments. Sine our VAT taxes are non-uniform aross setors, an impliation of this result is that border tax adustments wherein firms dedut their exports from their tax bill but annot do so for imports are suboptimal. In fat, border tax adustments reate a wedge between the prie paid for domesti inputs and the prie paid for foreign inputs Optimal Inome Taxes As we have desribed above, the tools that are optimally hosen by the government to redistribute the gains from trade are VAT taxes and inome taxes. To the extent that a group of workers average inome is orrelated with whether that group loses or wins from a trade shok, non-linear inome taxes an be used to redistribute the gains from trade. Here, we desribe the determinants of optimal inome taxes. Before desribing optimal taxes, it is useful to define the unonditional distribution of labor produtivity f z) given by z f z) = λ z, θ; w ) dµ, F z) = f ẑ) dẑ Θ 0 f z) = λ z, θ; w ) dµ = Λ λ dµ Θ In the above, f z) is the ountrywide density of labor produtivity, while f z) is the same for eah setor. The following proposition desribes optimal inome taxes: Proposition 7. Optimal inome taxes must satisfy Θ τl z) 1 t z) 1 = 1 F z) zf z) 1 + 1ε ) [1 W ẑ)] z df ẑ) 1 F z) 11) where 1 1 t z) = W z) = f z) f z) 1 1 t Θ g θ) λ z, θ; w ) dµ f z) g θ) dµ. The proof is relegated to the Appendix. The above formula is reminisent of the lassi formula that haraterizes optimal non-linear taxes see Mirrlees 1971), Diamond 1998), and Saez 2001)). It is, however, modified to allow for a differene from the anonial model. Sine the distortions to the deision to earn inome are reated by both VAT taxes and inome taxes, the right hand side of the equation ontains the labor wedge, τ l, and a weighted average of VAT taxes t z). This weighted average depends on the 14 This point is also shown originally by Grossman 1980); also see Dixit 1985). For a related disussion, see Costinot and Werning 2017). 22

23 level of labor produtivity, sine the setoral omposition of the labor fore at eah produtivity level hanges and the VAT differs aross setors. Additionally, the soial welfare weights, W, depend on the omposition of types at eah labor produtivity level, their welfare weights, and their orrelation with inome. To see this, onsider the hypothetial ase where g θ) and λ z, θ; w ) are unorrelated, i.e., g θ) dµ λ z, θ; w ) dµ = g θ) λ z, θ; w ) dµ. Then W z) = g θ) dµ λ z, θ; w ) dµ f z) g θ) dµ = λ z, θ; w ) dµ f z) In other words, the right hand side of 11) is zero. That is, the only role of inome taxes is to anel out the effet of VAT taxes on the labor supply. This ase identifies the importane of the orrelation between θ and labor produtivity in the ability of inome taxes to redistribute the gains from trade. As we argue in our quantitative exerise, the fat that the gains from trade are not perfetly orrelated with inome redues the importane of redistributive inome taxes and emphasizes the role of VAT taxes as a powerful mehanism to redistribute the gains from trade. Another extreme ase is the one with absolute advantage. In this ase, VAT taxes aross all setors are equal. As a result, we an simply set them to zero and then the above formula beomes idential to the lassi Mirrlees-Diamond-Saez formula. In essene, the best ase for using nonlinear inome taxes to redistribute the gains from trade an be made in an eonomy where the distribution of workers aross setors is the same. Our theoretial analysis has highlighted a few important qualitative features: 1. Prodution taxes should resemble VAT taxes. 2. In the presene of speialization, differential VAT taxes an be useful in redistributing the gains from trade. 3. Non-linear inome taxes are useful to redistribute the gains from trade to the extent that inome is orrelated with the gains from trade. These theoretial insights point toward a need for a quantitative evaluation of the fores involved. In partiular, it is important to understand whih poliy tools are the right ones to redistribute the gains from trade. In what follows, we pursue a quantitative analysis to shed light on this issue. = 1. 5 A Quantitative Exerise In this setion, we provide a quantitative evaluation of the optimal poliy response to a trade shok, namely, the rise of China in the global goods market China shok heneforth). To do so, we use a quantitative framework, based on the work of Galle et al. 2017), whih an be used to measure the differential impat of the China shok on the welfare of different types of workers. We use this framework to quantitatively assess the optimal poliies that are Pareto improving, i.e., keep workers at least as well off as the eonomy with the China shok. 23

24 5.1 A Model of Trade with Intermediate Goods Our applied framework losely follows Galle et al. 2017). The world eonomy onsists of C ountries in eah of whih prodution ours in N setors. There are two types of goods in eah setor of ountry. Firms in eah setor in ountry an produe many varieties of tradable intermediate goods and one variety of non-tradable omposite good. In partiular, in eah setor there is a ontinuum of intermediate goods represented by ω [0, 1]. The output of a variety ω in setor in ountry is given by the following onstant returns to sale prodution funtion: a ω ) ) L χ N ) Q γ,k,k, whih uses labor and the omposite good that is produed domestially, as in Caliendo and Parro 2015). Following Eaton and Kortum 2002), we assume a has a Fréhet distribution with CDF e A z ν. Parameter A is the average effiieny of prodution in setor, ountry. Parameter ν is the dispersion of produtivity aross varieties and will be the elastiity of trade flow to hanges in trade osts. The omposite good in setor, ountry is produed by ombining intermediate goods ω aording to the prodution funtion: [ ] ρ r ω ) 1 1 ρ 1 ρ dω, where r ω ) is the amount of intermediate goods of variety ω used in the prodution of the omposite goods. The omposite good, while non-tradable, an be produed using intermediate goods varieties produed in any ountries in order to minimize the ost of prodution. Additionally, the omposite good is used in the domesti prodution of intermediate goods and for domesti onsumption. We assume trade aross ountries is ostly, and we expliitly model this as an ieberg ost à la Samuelson 1954). More speifially, we denote the ost of shipping an intermediate good k=1 produed in setor from ountry to ountry as d, 1 with d, = 1. This means for one unit of good to arrive at ountry, d, unit must be shipped from ountry. Finally, we assume that the governments impose VAT taxes t on intermediate goods produed in setor and ountry. This, together with wages in ountry and pries of omposite goods given by P, determines the unit ost of produing an intermediate good ω in ountry. If we use the prodution funtion above, the unit ost of produing variety ω in ountry is given by ψ/a ω ), where ψ = χ w 1 t ) ) χ k ) γ Pk k. 12) γk Finally, following Eaton and Kortum 2002), the optimal deision to import intermediate goods from the lowest ost origin implies that the share of good expenditure in ountry that is imported from ountry is given by π, = A A 24 ) ν d, ψ d, ) ν. 13) ψ

25 Moreover, the prie of the omposite good in ountry is given by P = Γ ρ ) [ ] ρ ) ν ν A d, ψ. 14) ν Finally, we assume that workers are perfetly mobile within setors aross the ontinuum of varieties), while their setoral hoie is desribed by the Roy model in setion 2, where the produtivity of a worker of type θ in setor is given by a θ) ɛ, where ɛ is drawn from a Frehét distribution with shape parameter σ, as desribed in setion 2. Additionally, workers utility funtion is given by U x) = xα. 5.2 Calibration and the China Shok In this setion, we desribe the alibration of the baseline model and the China shok. We follow Caliendo et al. 2017) and Galle et al. 2017) and model the China shok as an inrease in setor speifi TFP, i.e., by hanging A China. Here, we briefly desribe the alibration of the model ingredients and relegate the alibration details to the Appendix. Data and Benhmark Calibration. We alibrate the model in Setion 5 by taking a laissezfaire version of this eonomy one without government poliies to the data. As a robustness hek, in Setion 5 we allow for the presene of redistributive taxes in our benhmark alibration. 15 We hoose some of the parameters of the model similar to those hosen in the literature. In line with many estimates of the intensive elastiity of labor supply, we hoose ε = 0.5; see Chetty et al. 2011) for an extensive disussion. We hoose the dispersion of produtivity to be ν = 5. This is based on estimated trade elastiities in Head and Mayer 2014). The elastiity of substitution in the final goods prodution funtion is ρ = 4. Moreover, we hoose σ = 1.6 whih is lose to the benhmark used in Galle et al. 2017). 16 Finally, we assume that the elastiity of substitution aross different onsumption goods is 1. The parameters of tehnology, produtivities, and prodution funtions are hosen to math the following data. We use the data on bilateral trade and employment by setor from the World Input-Output Database WIOD) in year 2000 and We restrit our analysis to the U.S. and the following nine ountries: Australia, Canada, China, Denmark, Finland, Frane, Germany, Japan, and Spain. Our setors are listed in Table 1 and onsist of 13 manufaturing setors and one nonmanufaturing setor. Our manufaturing setors roughly orrespond to two-digit ISIC Rev. 3 odes. We use these data to alulate bilateral trade shares and alibrate the share of labor and intermediate goods in the prodution funtion in 12). We follow Autor et al. 2013) and Galle et al. 2017) and define workers types or groups assoiated with θ in the model based on their geographi loation and eduation in the United States. More speifially, we use ommuting zones CZs) to define loal labor markets. We split 15 We do this mainly beause finding omprehensive data on government poliies is diffiult, and it is in line with the rest of the international trade literature. 16 Galle et al. 2017) estimate a range of values for this parameter. They hoose 1.5 as their preferred values. Sine we have elasti labor supply within eah setor we have to hoose a value that is larger than 1 + ε. Notably, our results are not sensitive to hanges in the value of σ in the range of See Timmer et al. 2015) for a detailed desription of the data. 25

26 a) Perentage hanges in employment by setor b) Distribution of welfare gains Figure 1: Employment and welfare effet of the China shok. Panel a) shows the perentage hanges in employment by setor after the China shok. Panel b) shows the distribution of welfare gains aross different types. The rise of China leads to aggregate inome weighted) welfare gain of 0.59%. Mean welfare gains aross types is 0.67% with oeffiient of variation of The minimum gain is -1.70% and maximum gain is 1.74%. Overall, 2.5 perent of all types experiene a welfare loss. eah ommuting zone into two eduation groups based on whether workers hold at least an Assoiate degree or not. This implies that there are a total of 1,444 types 722 CZs 2 skills). All other ountries have only a single type. 18 In eah ommuting zone we use the data on wages and setoral employment shares by eduation from the 2000 Census. 19 Finally, we use the data on relative pries in eah setor and ountry from the Groningen Growth and Development Centre GGDC) Produtivity Level Database. 20 We use these data to alibrate the setoral TFP parameters in the benhmark. For more details on the alibration proedure, refer to the Appendix B. Calibration of the China Shok. We alibrate the China shok as the rise in the setorspeifi TFP parameter A China in year 2011 relative to the alibrated values in year Our alibration proedure losely follows that of Autor et al. 2013) and Galle et al. 2017). In order to alibrate the hange in TFP in China, we use the hange in trade shares between the U.S. and China as a target. In partiular, in order to determine how muh of the hange in expenditure shares on Chinese goods in the U.S. is driven by the China shok, we first run the following 18 Note our definition of types based on loation and eduation implies no mobility aross loal labor markets and eduation ategories. As Galle et al. 2017) argue, there is little evidene of trade exposure ausing population shifts aross loal labor markets. 19 We use the rosswalk provided by David Dorn to map Census Publi Use Miro-data Areas PUMAs) into ommuting zones. See 20 See Inklaar and Timmer 2014) for a detailed desription of these data. 26

27 a) Low skilled workers b) High skilled workers Figure 2: Changes in welfare aross ommuting zones in the United States in response to China shok. Panel a) depits the perentage hange in welfare for the less-eduated workers those with eduation less than an Assoiate degree. Panel b) depited the perentage hange in welfare for eduated workers. For the less-eduated workers, 13 ommuting zones experiene a welfare loss. For the eduated workers, 23 ommuting zones experiene a welfare loss. regression π U S,China = β0 + β1 π Others,China + where π U S,China = πu S,China in year 2011 πu S,China in year 2000 and π Others,China P = P {Other} π,china in year 2011 {Other} π,china in year This regres- sion, inspired by Autor et al. 2013), is aimed at isolating the portion of the hanges in U.S. expenditure share on Chinese goods that is only due to the rise of China. The π Others,China is alulated using the following ountries: Australia, Denmark, Finland, Germany, Spain, and Japan. The regression oeffiient is 1.32, with R2 of These estimates are lose to those of Autor et al. 2013) and Caliendo et al. 2017). We then use the predited values from this regression as the target for alibration of the hange in TFP. These predited values are reported in the third olumn of Table 1. To better understand the results of our quantitative exerise, it is useful to disuss the welfare and employment hanges implied by the model. The left panel in Figure 1 shows the perentage hange in employment within eah setor. The setors that are most negatively affeted are Textile and Leather Produts, Eletrial Equipments, and Other Manufaturing, as they suffer the largest loss from the China shok. In terms of employment share, Textile and Leather Produts and Other Manufaturing are very small, with only about 0.5% perent of total employment. However, Eletrial Equipment employs more than 2.2% of workers in our sample. The right panel of Figure 1 shows the distribution of welfare gains aross types. The gains range from -1.70% to 1.74%, with about 2.5% of all types experiening a welfare loss about 4.1% of population in our sample). The aggregate inome weighted) welfare gain is 0.59% and the mean welfare gain is 0.67%. These values are higher than those reported in Galle et al. 2017), mainly beause we allow for an elasti intensive margin of labor supply. This alone sales all welfare hanges by a fator of 1 + ε 1.5 in our alibration). Finally, Figure 2 depits the geographi distribution of welfare gains aross the U.S. In line with Galle et al. 2017), the main area that experienes welfare losses is the southeastern United 27

28 Figure 3: Employment share aross setors. Comparing types who lose from the China shok to the rest. Notie that the types who lose from the rise of China are disproportionately employed in Textile & Leather, Eletrial Equipments and Other Manufaturing. States. As Figure 3 shows, this is mainly beause this area has employment onentrated in setors that are hit the most: Textile and Leather, Eletrial Equipment, and Other Manufaturing. Note that as equation 4) states, the sign of the hange in welfare for a group is determined by its employment distributions aross setors. 5.3 Pareto Optimal Poliies In this setion, we solve for optimal redistributive poliies in the environment desribed above. Our main assumption on the obetive funtion is that poliies must be Pareto improving with respet to the welfare of workers before the China shok. More speifially, we assume that the world eonomy faes the rise of TFP in China, yet all groups of workers in the United States must be as well off as they were prior to the China shok. To do so, we solve a planning problem that maximizes a weighted average of utility of all ountries other than the United States, while we impose that worker groups in the United States must reeive a utility at least as high as that of the laissez-faire eonomy prior to the China shok. Note that the question of how to redistribute the gains from trade whih depends on the institutional and politial details in eah ountry is beyond the sope of this paper. Our riterion is in line with that used by Werning 2007) and Hosseini and Shourideh 2018). In Setion 5.4.2, we disuss another riterion for the determination of the optimal poliy that ensures that all groups ahieve at least a fration of the total gains from the trade shok. As disussed above, our optimal poliy obetive is to maximize a weighted average of welfare in all ountries other than the United States. In partiular, we hoose a welfare funtion of the 28

29 Figure 4: Optimal VAT taxes in the United States form U.S. ψ û, where û is the utility of the representative onsumer in ountry. We assume that ψ is proportional to the population of ountry in This, assumption implies that the distribution of welfare aross other ountries is not pinned down and hene transfers are indeterminate. In other words, we intentionally hoose the weights so that transfers are not pinned down and rossountry redistributive motives are absent among ountries other than the U.S.). This implies that our poliies do not arise beause we are differentially about workers in the ountries other than the United States. As for workers in the U.S., the goal is to make sure that their welfare does not fall below its level before the China shok. Therefore, we maximize this obetive subet to equilibrium onstraints, as desribed in Proposition 2, together with a onstraint of the form û US θ) û US,pre θ), where û US θ) is the utility of workers in group θ in the U.S and û US,pre θ) is its value in the laissez-faire eonomy above before the China shok. Note that solving this problem is equivalent to solving the problem studied in setions 2 4 where the welfare weights ψ g θ) for U.S. workers are determined by the Lagrange multipliers on onstraint û US θ) û US,pre θ). Therefore, the same formulas govern the behavior of optimal VAT taxes and those of inome taxes. Optimal VAT Taxes Figure 4 depits optimal VAT taxes in the United States. In line with signifiant employment drops in Textile & Leather, Eletrial Equipment, and Other Manufaturing, these setors reeive signifiant subsidies. In fat, Textile & Leather has the largest drop in employment around 18%; see Figure 1), and it reeives approximately 18.6% in VAT subsidies. Note that despite this relatively large subsidy, the employment share of the workers in this setor 29

30 Figure 5: Breakdown of optimal VAT taxes into welfare effet and the rest: fisal externality on inome taxes and the reloation effet. is fairly small and around 0.6% of employment. An important observation is that the magnitude of the welfare hanges ranging from -1.70% to 1.74%) is muh smaller than that of the VAT tax and subsidies ranging from -18.6% to 5.3%). The key to this observation an be understood from the term apturing the welfare effet in equation 10, the term W. The main determinant of this effet is the welfare weights, g θ), whih are the Lagrange multipliers on the onstraint û US θ) û US,pre θ). Therefore, they are negatively orrelated with welfare losses from the China shok.this effet, together with differenes between the setoral employment of different groups of workers, implies a higher degree of variation in VAT taxes. Note that, as Figure 5 depits, the main fore that shapes optimal VAT taxes is the welfare effet, while the reloation effets and externality effets are onstant and insignifiant aross setors. To gain insight on what determines the differenes between these welfare effets aross different setors, we plot the distribution of welfare gains/loses from China shok for two different setors in Figure 6. The blue bars show the distribution of welfare gains/loses in Eletrial Equipment setor. Note the onentration of the mass at the bottom of the distribution. Approximately, 10 perent of workers in this setor experiene very large losses. These large losses resulting from the China shok in this setor implies that to ompensate these workers large subsidies are required. Indeed this setor reeived seond highest subsidy rate of 7.4%). The red bars in 6 show the distribution of welfare gains/loses in Paper and Print setor. In this setor, very few workers experiene big loses or any loses). Moreover, the distribution is almost symmetri around its mean. Therefore, there is very little motive to ompensate loses for these workers if any). In fat, this setor pays value added taxes of 3.5%) that are used to ompensate losers in many other setors suh as Eletrial equipment ). At the heart of these results is the pattern of speialization of the labor fore. As Figure 3 shows, groups that experienes losses are the groups who have higher employment ratio in se- 30

31 Figure 6: Distribution of welfare gains with Eletrial Equipment and Paper and Print Setor. tors that experiene highest employment losses. This is partiularly apprent when onsidering their employment share in Eletrial Equipments and Textile & Leather ; they have an employment share of 4% and 7.3% respetively, ompared to the national employment shares of 0.5% and 2%. In other words, these groups produtivity in these setors is high and they annot respond to the China shok by swithing to other setors sine they speialize. Providing the VAT subsidy to these setors transfers resoures to these groups of workers. Optimal Inome Taxes Our simulations imply that optimal inome taxes are largely zero, exept at the very bottom of the inome distribution. The optimal nonlinear) inome tax rates are shown in Figure 7, where we plot marginal tax rates and average tax rates as a funtion of individual inome normalized by inome per apita). To highlight the pattern of inome tax rates at the very bottom of the inome distribution, we have split the figure into two. The left panel shows the tax rates for those at the bottom 1 or 2% of the distribution. The right panel shows the tax rate for the rest of the inome distribution. As we see, aside from extremely low inome levels, optimal inome taxes are zero. This feature of the optimal poliy is surprising, as inome taxes an be potentially useful in redistributing the gains from the China shok. However, the main fore that explains this result is the fat that the average inome and welfare gains or losses are not highly orrelated among different groups. We show this in Figure 8) by plotting eah group s welfare gains or losses from the China shok against the average inome relative to per apital inome). The orrelation between the two is positive but very small about 0.19). 5.4 Robustness In this setion we study two extensions of our main quantitative exerise. First, we onsider an eonomy where the status quo inludes a redistributive inome tax. Seond, we onsider an 31

32 Figure 7: Optimal inome taxes alternative welfare riterion that guarantees a minimum level of welfare gain for all groups of workers in response to the China shok Redistributive Tax in Status Quo Reall that our benhmark alibration was performed under the assumption of no government poliy. In this setion, we relax this assumption and assume there is an affine inome tax and transfer is in plae in the U.S. for the other ountries we ontinue with the assumption of no government poliy). More preisely, let y be the before-tax labor inome. Then, eah worker pays the following taxes on their labor inome T US y) = τ US y T US. For this exerise we assume a tax rate τ US = 0.1 and the transfer T US is suh that all tax revenues are rebated to workers. These parameters are hosen so that we roughly math the level of transfers in the United States. The rest of the parameters and the China shok) are alibrated exatly as desribed in Setion 5.2. Using this model, we first repeat the China shok exerise. Figure 9 shows the distribution of welfare gains panel a)) and employment hanges panel b)) after the rise of China. As the figures demonstrate, inlusion of redistributive inome taxes has a minimal effet on the outome of the China shok in our baseline eonomy. Indeed, the distribution of welfare gains is very similar to the one reported for the benhmark exerise. The gains range from -1.54% to 1.73%. The aggregate inome weighted) welfare gain is 0.63%, and the mean welfare gain is 0.70%. The slightly higher minimum and high average welfare are due to the fat that the redistributive tax and transfer partially mitigate the negative employment effets. Indeed, the fration of groups with negative gain also falls to 1.5% from 2.5%). 32

33 Figure 8: Welfare gains and average inome aross groups in the United States Figure 10 shows the hanges in welfare aross ommuting zones. These graphs also demonstrate the same patterns of gains and loses aross ommuting zones as the ones reported for the benhmark model in Setion 5.2. Using the baseline eonomy with redistributive inome taxes, we an alulate the optimal poliy response to the China shok. As Figure 11 demonstrates, the presene of the redistributive inome tax has very little effet on the pattern and magnitude of taxes and subsidies aross setors. As disussed in Setion 5.3, the main fore behind these taxes and subsidies is welfare effets. This an be learly seen in Figure 12, whih shows the breakdown of these optimal taxes into welfare effets and reloation effets. Note that the presene of inome tax generates a fisal externality. In other words, the hanges in value-added taxes and employment in a setor affet the inome tax olleted from workers in that setor. For this reason, the reloation effet and welfare effets have been shifted in the opposite diretion) in Figure 12 relative to Figure 5. The main insight remains the same. The pattern and magnitude of taxes and subsidies are driven by the welfare effets. The reloation terms show very little variability aross setors, and they are not an important determinant of optimal value-added taxes. Finally, Figure 13 shows the optimal inome taxes. This figure onforms to our earlier finding that a Pareto improving poliy response aimed at redistributing gains from the China shok does not involve a reform or response of the inome tax. As we see in Figure 13, the optimal marginal inome tax is 10%, whih is idential to the one assumed in the alibration. This result resembles that in Werning 2007) and Hosseini and Shourideh 2018), namely, that many inome tax funtions an be Pareto effiient. Therefore, a Pareto improving poliy reform does not neessarily require a reform of the inome tax funtion. 33

34 a) Perentage hanges in employment by setor b) Distribution of welfare gain Figure 9: Employment and Welfare Effet of the Rise of China in eonomy with redistributed taxes. Panel a) shows the perentage hanges in employment by setor after the China shok. Panel b) shows the distribution of welfare gains aross different types. The rise of China leads to aggregate inome weighted) welfare gain of 0.63%. Mean welfare gains aross types is 0.70% with oeffiient of variation of The minimum gain is -1.54% and maximum gain is 1.73%. Overall, 1.6 perent of all types experiene a welfare loss a) Low skilled workers b) High skilled workers Figure 10: Change in welfare aross ommuting zones in the United States in response to China shok in eonomy with redistributive tax and transfer. Panel a) depits the perentage hange in welfare for the less-eduated workers those with eduation less than an Assoiate degree. Panel b) depited the perentage hange in welfare for eduated workers. For the less-eduated workers, 9 ommuting zones experiene a welfare loss. For the eduated workers, 13 ommuting zones experiene a welfare loss. 34

35 Figure 11: Optimal VAT taxes in the United States Figure 12: Breakdown of optimal VAT taxes into welfare effet and the rest: fisal externality on inome taxes and the reloation effet. 35

36 Figure 13: Optimal inome tax Alternative Welfare Criterion So far, our poliy experiments have foused on Pareto improvement relative to the status quo before the rise of China. By onstrution, this poliy response transfers all the potential aggregate) gains from the rise of China to the rest of the world. In this setion we report the results of an optimal poliy experiment that guarantees no one is worse off relative to the status quo prior to the China shok and yet the aggregate welfare rises to the level of the post-china shok. To this end, we repeat our main exerise with a small modifiation. We sale up the status quo welfare prior to the China shok) so that the average saled up) welfare mathes the average welfare after the China shok. Reall that in Setion 5.2 we reported that the rise of China results in a 0.67% rise in the average welfare. This exerise guarantees that under optimal poliies the average welfare from the rise of China is realized and at the same time no group is harmed. The resulting optimal taxes are shown in Figure 14. The optimal value- added taxes fall and subsidies rise) relative to those in the main exerise by about 1 or 2 perentage points). The aggregate gains, however, are larger beause under these poliies there are larger transfers from the rest of the world to the U.S. or smaller transfers from the U.S. to the rest of the world). Finally, Figure 15 ompares the distribution of welfare gains aross groups for three senarios: 1) rise of China and no poliy response, 2) Pareto improving poliy response that guarantees the status quo welfare, and 3) Pareto improving poliy response that guarantees the status quo welfare and delivers the aggregate welfare from the rise of China. The poliies that deliver only the status welfare green bar) have lower aggregate welfare gains. On the other hand, the poliies that deliver the status quo and the aggregate welfare from the rise of China red bar) have higher average welfare gains that math the average welfare gains from the rise of China in the absene of a poliy response. 36

37 Figure 14: Optimal VAT taxes in the United States for Pareto improving poliies that maintain the aggregate gain from the rise of China Figure 15: Distribution of welfare for three senarios. The blue bar is the histogram of the welfare gains from the rise of China in the absene of a poliy response. The green bar is the histogram of the welfare gains from the rise of China under poliies that guarantee no loss relative to the status quo prior to the rise of China). The red bar is the histogram of the welfare gains from the rise of China under poliies that guarantee no loss relative to the status quo prior to the rise of China) and deliver average welfare gains from the rise of China. 37

38 6 Conlusion In this paper, we have provided a theoretial and quantitative analysis of optimal poliies when international trade reates winners and losers and when inome taxes annot target winners and losers i.e., lump-sum tax and transfers are unavailable). We show that for a large lass of prodution funtions, prodution must be effiient and, as a result, trade poliy should be designed to respet that. Consequently, tariffs and other distortionary trade poliies are not optimal. We show theoretially and quantitatively that produer taxes in the form of value-added taxes play an important role in redistributing the gains from trade. In ontrast, inome taxes are not an integral part of redistributing the gains from trade. While our analysis provides a foundation for optimal government response to trade shoks and potentially other tehnologial hanges), some issues remain unexplored. For example, in our model we have treated the skill deomposition of eah ountry as given. While suh an assumption might be suitable in the short-run, in the long-run workers skills respond to hanges in international trade and tehnology. This implies that dynami and transitional onsiderations an potentially be an important determinant of optimal poliies. Moreover, we have foused on tax and transfer poliies, while a potentially important aspet of poliy response to tehnologial hanges is training poliies. These are important extensions of our framework that we leave for future work. In our analysis, we have assumed that poliies are determined under ooperation in order to fous on the design of trade agreements. Muh of trade between ountries is organized using a form of trade agreements: WTO, European Union, NAFTA, et. are all examples of situations where ountries negotiate trade poliies. Evidently, a ountry has inentives to unilaterally deviate and hoose different set of prodution and onsumption taxes. The impliation of domesti redistributive motives on unilaterally optimal poliy is an important diretion of future researh. Referenes Akerlof, G. A. 1978): The eonomis of" tagging" as applied to the optimal inome tax, welfare programs, and manpower planning, The Amerian eonomi review, 68, Ales, L. and C. Sleet 2017): Spatial Attration: Optimal Geographi Soial Insurane, Working Paper, Carnegie Mellon University. Artuç, E., S. Chaudhuri, and J. MLaren 2010): Trade shoks and labor adustment: A strutural empirial approah, Amerian eonomi review, 100, Atkinson, A. B. and J. E. Stiglitz 1976): The design of tax struture: diret versus indiret taxation, Journal of publi Eonomis, 6, Autor, D. H., D. Dorn, and G. H. Hanson 2013): The China Syndrome: Loal Labor Market Effets of Import Competition in the United States, The Amerian Eonomi Review, 103, Bagwell, K. and R. W. Staiger 1999): An eonomi theory of GATT, Amerian Eonomi Review, 89,

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42 Appendix A Proofs A.1 Derivation of the Distribution of Labor Produtivity Suppose that wages are given by w = { w }. Then the distribution of labor produtivity for workers of type θ an be drived as follows Pr z ẑ) = = = = = = N =1 N =1 N =1 N =1 R N [ w a θ) ɛ w i a i θ) ɛ i, i ] 1 [ ẑ w a θ) ɛ ] dh ɛ) ẑ w a θ) ẑ w a θ) ẑ w a θ) i w e a θ)ɛ w i a i θ) ) σ e w a θ)) σ ɛ σ w a θ) ) σ i w i a i θ))σ d N w a θ) ) σ d i w i a i θ))σ =1 N =1 w a θ) ) σ i w i a i θ))σ e ẑ σ = e ẑ σ iwi a i θ))σ σ ɛ σ 1 e ɛ σ dɛ iw i a i θ))σ σɛ σ 1 e w a θ)) σ e w a θ)) σ iw i a i θ))σ ɛ σ ) σ ẑ w a θ) dɛ iw i a i θ))σ ) iw i a i θ))σ This implies that labor produtivity of workers of type θ has a Frehét distribution with shape parameter σ and mean of Γ ) [ 1 1 σ i w i a i θ)) σ] 1 σ. This shows that λ z, θ; w ) = iw z e z σ i a i θ))σ = σ z σ 1 i wi a i θ)) σ e z σ iwi a i θ))σ 42

43 Additionally, the fration of type θ workers that work in setor is given by Λ θ) = 1 [ wa θ) ɛ wi a i θ) ɛ i, i ] dh ɛ) = = R N + 0 w a θ) ) σ i w i a i θ))σ d w a θ) ) σ i w i a i θ))σ e w a θ)) σ ɛ σ iw i a i θ))σ ) A similar derivation as above establishes that λ z, θ; w ) = Λ θ) λ z, θ; w ). A.2 Proof of Lemma 1 Proof. The welfare of a worker of type θ is given by û θ) = = 0 = 0 0 u z) λ z, θ; w ) dz [ ] ) u z) d e a θ)w ) σ z σ u z) d = u z) 1 e + 0 = u 0) e 1 e 1 e [ a [ a [ a [ a θ)w ) σ ] z σ ) θ)w ) σ ] z σ ) θ)w ) σ ] z σ ) θ)w ) σ ] z σ ) 0 u ) z) dz u ) z) dz 43

44 where in the above we have used integration by parts. Differentiating both sides with respet to wages implies that δû θ) = δu 0) + σ N =1 0 z σ a θ) w N = δu 0) + σ a θ) w) σ δw =1 = δu 0) + σ N =1 = δu 0) + σ N whih proves the laim. =1 w ) σ δw [ ] e a θ)w ) σ z σ u ) z) dz w a θ) w) σ δw i a i θ) w )σ w i Λ θ) δw w A.3 Proof of Proposition [ ] z σ e a θ)w ) σ z σ u ) z) dz 0 z u ) z) d z u ) z) λ z, θ; w ) dz [ e a θ)w ) σ ] z σ ) Proof. That any alloations and onsumer and produer prie vetors must satisfy the onstraints in problem P) is straightforward from the definition of indiret utility funtion, demand funtion, and optimality ondtion by firms for their hoie of intermediate goods. Now suppose that alloations { I z), l z), λ z, θ; w ), Λ θ), u z) } z R +, {1,,C}, and {{ Q i }, L i } {1,,N C },i {1,,N} together with onsumer pries and wage {q, w } {1,,NC } satisfy the onstraints in P). We onstrut a set of ommodity taxes and show that under these poliies the resulting alloations and pries are a ompetive equilibrium. Using the alloation, we an simply onstrut produer pries aording to p i = L G i w i L i, { Q i}) Consider an arbitrary vetor of international pries ˆp = ˆp 1,, ˆp N ) where ˆp i > 0. For eah good i and ountry, we an define and t p, i t p, i t x, i = p i ˆp i 1 = q i ˆp i 1 = p i ˆp G i Q i { Q i }, L i ) 1 Obviously, at pries given by ˆp and taxes as defined above the firms first order onditions are satisfied. Sine the prodution funtions are assumed to be onave, then we must have that firms optimality onditions are satisfied. Moreover, by definition of the demand funtion and indiret value funtion, the workers optimality onditions are also satisfied. This implies that we only 44

45 need to hek that government budget onstraints are satisfied. Sine all workers budget onstraints hold - given the definition of the demand funtion, all feasibility onstraints are satisfied - the first onstraint in problem P), and transfers between governments are allowed, Walras law implies that government budget onstraints are satisfied. This ompletes the proof. A.4 Proof of Lemma 2 Proof. If { } Q i solves the optimization in the statement for some positive vetor ρ i,, i, then } whih inreases final onsumption of all goods obviously there annot exist an alternative { ˆQ i sine this suh an alloation would improve the obetive of the optimization 8). To show the reverse onsider an alloation { Qi} that is pseduo-effiient. Define the following two sets: A = B = { { x 1,, x N ) ; x 1,, x N ) ; { } ˆQ i, x i C =1 G i C =1 G i L i, { Q i}) C { }) L i, ˆQ i =1 C =1 } N Q i x i By definition of psuedo-effiieny, A B = {X 1,, X N )} where X i is the total onsumption of good i under the alloation { Q i}. Moreover, sine G i is onave, the sets A and B are onvex. Therefore, by the separating hyperplane theorem, there must exists a non-zero vetor ρ = ρ 1,, ρ N ) suh that x A, y B, N ρ i x i i=1 =1 N ρ i y i Note that for all i, X 1,, X i 1, X i + ε, X i+1,, X N ) B, sine X 1,, X N ) A, the above inequality implies that ρ i 0. Moreover, sine X 1,, X N ) B, for all x 1,, x N ) A, we must have N N ρ i x i ρ i X i This onludes the proof. A.5 Proof of Proposition 5 i=1 Proof. Consider the optimization P) and let ρ i be the multiplier on the resoure onstraint for good i, ζ i be the lagrange multiplier on labor market learing for setor i ountry and let γ z) be the lagrange multiplier on the seond onstraint in program P). We, first, show that there must exist a onstant ρ suh that qi = ρ 1 ρ i. This proof losely follows Deaton 1981). Moreover, let V I; q) = I + ν q) ϑ q). Note that under this assumption, Roy s identity implies that x i I; q) = s i q) I + b i q) where s i q) = Note that by budget onstraint, we must have that i q is i q) = 1 and i q ib i q) = i=1 i=1 q i ν q) ν q) N =1 ˆQ i } and b i q) = ν q) q i ϑ q).

46 Now, if we take first order ondition with respet to qi, we have [ s ] [ ] ρ Ī + b + γ q z) i ν q) q i q i ν q) 2 I z) + ϑ q) dz = 0 q i where Ī = Θ I z) λ z, θ; w ) dzdµ. Moreover, the first order ondition with respet to I z) gives us ρ s λ z, θ; w ) dµ + γ z) Θ ν q) = 0 This implies that γ z) dz = ν q) ρ s q) 15) Now, if we set q i = 1 ρ ρ i for some ρ, we have s ρ = ρ q i ρ s = ρ b ρ = ρ q i s q = ρs i = ρ q i q s = ρ q i ν q) ν q) b q = ρb i = ρν q) ϑ q) q i q i Therefore, we have ρ s q i Ī q i ν q) ν q) 2 ρs iī γ z) I z) dz = q i ν q) ν q) ρī = 0 and ρ b q i + ϑ q i γ z) dz = ρb i + q i ϑ ν q) ρ = 0 In other words, the FOC is satisfied when q i = 1 ρ ρ i. We refer the reader to Deaton 1981) for the proof of why this must be satisfies at every solution of the FOC. Now, onsider the FOC with respet to L. It is given by ζ i + ρ i L G i = 0 46

47 Finally, the FOC with respet to w is given by ψ i g θ) ρ i s i u z) I z) ζ w w 1 ) w 2 λ z, θ; w ) dzdµ λ z, θ; w ) dzdµ Λ y λ dzµ + ζi Λ i zl λ z, θ; w ) dzdµ w i + Λ ζi i zl λ dzdµ = 0 w i Note that sine λ z, θ; w ) = e d ) z σ a θ)w ) σ, therefore dz w λ z, θ; w ) = 2 z w = σ a θ) w w e z σ a θ)w ) σ ) Therefore, for any differentiable funtion ϕ z), we have ϕ z) w λ z, θ; w ) dz = σ a θ) w w = σ a θ) w w = σ a θ) w w ) σ ) σ ) σ + σ a θ) w w ) σ z σ e ) z σ a θ)w ) σ z ϕ z) d z σ e ) z σ a θ)w ) σ ϕ z) d z σ e ) z σ a θ)w ) σ [ ϕ z) z σ e z σ a θ)w ) σ ] ) σ ϕ z) z σ e z σ a θ)w ) σ dz = σ a θ) w σ ) w i a i θ) ϕ z) z σ a w i θ))σ i θ) wi θ)) σ e z σ a θ)w ) σ dz i = 1 a θ) w σ ) w i a i θ) w i θ)) zϕ z) σz 1 σ a i θ) wi θ)) σ e z σ a θ)w ) σ dz i = 1 Λ w θ) zϕ z) λ z, θ; w ) dz 0 47

48 We an therefore write the FOC for w as Note that ψ g θ) Λ θ) z u ) z) λ z, θ; w ) dzdµ ρ i s i Λ θ) z I ) z) λ z, θ; w ) dzdµ i 1 ζ Λ w y λ dzdµ + ζ i Λ w iλ z y ) λ z, θ; w ) dzdµ i i +σ ζ i Λ w i θ) [ 1 [i = ] Λ θ) ] y λ dzdµ = 0 i i I z) = y z) T y z)) I ) z) = y ) z) [1 τ l z)] ) y z 1 τ l z)) ν = v z) z 1 z τ l z) 1 τ l z) = v y ) ) z) y z) v z z 2 1 z τ l z) 1 τ l z) = v y /z y ) 1 ) v y z 1 z τ l z) 1 τ l z) = 1 y ) 1 ) ε z) y z 1 + ε ε τ l = y ) z 1 τ l y [ ] 1 + ε y 1 τ l ) ε τ l = I ) z 1 τ l 1 τ l ) l = u ) ν q) 48

49 Therefore, the above FOC beomes y ψ g θ) Λ 1 τl θ) ) λ z, θ; w ) dzdµ ν q ) [ ] ρ Λ θ) y 1 τ l ) 1 + ε ε zτ l λ z, θ; w ) dzdµ 1 τ l ρ G 1,L Λ w y λ dzdµ + ρ i G [ ] i,l Λ w iλ y 1 + ε ε zτ l λ z, θ; w ) dzdµ i i 1 τ l +σ ρ i G i,l Λ w i θ) [ 1 [i = ] Λ θ) ] y λ dzdµ = 0 i i Note that if we hoose world pries to be ˆp i = ρ i /ρ = q i, then Thus, we an write the above as ρ Λ +ρ Λ iλ 1 t i ρ i G i,l w i = ρ ˆp ig i,l w i = ρ 1 t i 16) 1 ρ σ 1) Λ 1 t y λ dzdµ 17) ψ g + Λ ν y 1 τl ) λ dzdµ [ ] y 1 τl ) 1 + ε ε zτ l λ dzdµ 1 τ l [ ] y 1 + ε σ ε zτ l λ dzdµ = 0 1 τ l Moreover, a uniform inrease in u z) implies the following ondition: ψ g θ) dµ = γ z) dz = ν ρ i s i = ν ρ 18) i where in the above we have used 15). Dividing 17) by ρ and using the above, we an write Λ + Λ iλ 1 t i 1 σ 1) Y 1 t g Λ y 1 τl + ) λ dzdµ g dµ [ ] y 1 τl ) 1 + ε ε zτ l λ dzdµ 1 τ l [ y 1 + ε σ ε zτ l 1 τ l ] λ dzdµ = 0 The above equation leads to the equation in the statement of the proposition. 49

50 A.6 Proof of Proposition 6 Proof. Given the disussion in the text, it is suffiient to show that under absolute advantage, W is the same for all setors. From its definition, we have W = g Λ y 1 τl ) λ dzdµ g dµ. Λ y λ dzdµ Absolute advantage implies that Λ θ) is independent of θ. As a result, we an write the above as W = g Λ y 1 τl ) λ dzdµ g dµ Λ y λ dzdµ = Λ Λ = g y 1 τl ) λ dzdµ g dµ y λ dzdµ g y 1 τ l ) λ dzdµ g dµ y λ dzdµ whih is independent of. This onludes the proof. A.7 Proof of Proposition 7 Proof. Consider the optimization P) and suppose that ξ θ) is the ostate variable assoiated with the inentive onstraint 7). Then optimality requires the following ondition to hold ψ g θ) λ z, θ; { w }) dµ γ z) + ξ ) z) = 0 together with the limit ondition From setion A.5, we know that ν q) ρ Θ lim z ξ z) = 0 λ z, θ; w ) dµ = γ z) We an replae this in the above optimality ondition and use integration to arrive at ξ z) = [ψ g θ) ρν q)] λ z, θ; w ) dµ dz z Using the definition of f, we an write the above as [ ] ψ ξ z) = ρν g θ) q) ρν q) 1 λ z, θ; w ) dµ dz = ρν q) z z [W z) 1] f z) dz 50

51 where W z) = = = = ψ g θ) ρν q) λ z, θ; w ) dµ f z) ψ g θ) λ z, θ; w ) dµ ρν q) f z) ψ g θ) λ z, θ; w ) dµ ψ g θ) dµ f z) g θ) λ z, θ; w ) dµ g θ) dµ f z) where in the above we have used 18). Next, onsider the optimality ondition for l z). We have ζ { }) z, θ; w dµ γ z) v l z)) + ξ z) 1 z v l z)) 1 + 1ε ) = 0 w zλ Using the fat that γ z) = ν q ) ρf z) and ζ = ρ i L G i and equation 16), we an write the above as zρ 1 { }) λ 1 t z, θ; w dµ ν q ) ρv l z)) +ρν q) [W z) 1] f z) dz 1 z v l z)) 1 + 1ε ) = 0 z We an divide the above by ρν q ) v ) l z)) and we have z 1 { }) ν q ) v ) λ l z)) 1 t z, θ; w dµ ε ) [W z) 1] f z) dz = 0 z From the definition of labor wedge τ l z), we know that z [1 τ l z)] Therefore, the above equation an be written as z ν q ) = v l z)) 1 1 τl z) f z) 1 t 1 = ε ) [1 W z)] f z) dz z z This implies the equation in the statement of proposition 7. 51

52 A.8 Proof of Proposition 4 Proof. If p i = ˆp i 1 t p, i ) is the after tax prie faed by firms in setor i ountry, then optimality ondition with respet to labor of type θ is given by p i G i L θ) = w i θ) where w i θ) is the wage of workers of type θ in setor i ountry and w = { w θ) },θ. As a result, the setoral hoie of workers is given by θ, ɛ) arg max w θ) a θ) ɛ. In equilibrium, the distribution of labor produtivity among workers of type θ is given by λ z, θ; w ) = d ) e w θ)a θ))σ z σ dz with λ z, θ; w ) = w θ) a θ) ) σ i w i θ) a i θ))σ λ z, θ; w ) = Λ θ) λ z, θ; w ). Therefore, the optimal taxation problem beomes ψ subet to Θ 0 max q,w,p,{l z),u z),i z)} Θ x q; I z)) λ z, θ; w ) dzdµ + Λ i θ) 0 u z) λ z, θ; w ) dzdµ Q i = i G i V q; I z)) v l z)) = u z) 0 G p i i l z) v ) l z)) z = u ) z) zl z) λ z, θ; w ) dz = L i θ) {L i θ)}, { Qi}) L θ) Now, onsider a perturbation of Q i by ε. We know that = w i θ) {L i θ)}, { Q i}) Therefore Q i 2 G i Q i Lθ) G i Lθ) G i Lθ) G i Lθ ) = 0 2 G i Q i Lθ ) G i Lθ ) = 0. 52

53 This implies that if we perturb p i by p i 2 G i Q i Lθ) G i Lθ) G i ε for some θ, then p i = Lθ ) w i θ ) is satisfied for all θ. Therefore, that the optimality ondition with respet to this perturbation is ρ i G i Q i where ρ i is the lagrange multiplier on the resoure onstraint for good i. The above is the ondition that is equivalent to pseudo-effiieny of prodution. This onludes the proof. = ρ B Data and Calibration We alibrate the model in Setion 5 by taking a laissez-faire version of this eonomy i.e., one without government poliies) to the data. We hoose some of the parameters of the model similar to those hosen in the literature; these are mostly parameters related to the behavioral responses: elastiities of labor supply intensive and extensive margin), trade elastiities, et. The parameters of tehnology, produtivities, as well as prodution funtions are hosen to math the data. 21 Data. The data we use to alibrate the model ome from the following two soures: 1) World Input-Output Database WIOD), whih inludes the World Input-Output Tables WIOT) and Soio Eonomi Aounts SEA), 22 and 2) Groningen Growth and Development Centre GGDC) Produtivity Level Database, whih inludes data on relative pries and labor produtivity aross ountries for 42 maor eonomies and up to 35 industries in We use the World Input-Output Tables to onstrut bilateral trade shares, and intermediate input and labor shares for eah setor and ountry. The data for employment by setor ome from the Soio Eonomi Aounts. Finally, we use prie data from the GGDC together with data from the WIOT to bak out the parameters of preferenes and tehnology. Setors and Countries. We alibrate the model to a sample of 10 ountries and 14 aggregated setors. Our setors onsist of 13 manufaturing industries lassified aording to the International Standard Industrial Classifiation ISIC Rev. 3.1), with Textile and Leather produts ombined. We also inlude an aggregated non-manufaturing setor. Table 1 lists the 14 setors we use. We inlude the following 10 ountries in our sample: Australia, Canada, China, Denmark, Finland, Frane, Germany, Japan, Spain, and the United States. Parameters Chosen Independently. In line with many estimates of the intensive elastiity of the labor supply, we hoose ε = 0.5; see Chetty et al. 2011) for an extensive disussion. We hoose the dispersion of produtivity to be ν = 5, based on estimated trade elastiities in Head and Mayer 2014). The elastiity of substitution in the final goods prodution funtion is ρ = 4. Moreover, we hoose σ = 2 as estimated by Galle et al. 2017). Finally, we assume that the elastiity of substitution aross different onsumption goods is We do this mainly beause finding omprehensive data on government poliies is diffiult, and it is in line with the rest of the international trade literature

54 ISIC rev.3 ode Setor Desription Predited πus,china in year 2011 π US,China in year Food, Beverage & Tobao Textile, Textile Produts & Leather Produts Wood & Produts of Wood and Cork Pulp, Paper, Printing & Publishing Coke, Refined Petroleum & Nulear Fuel Chemials & Chemial Produts Rubber & Plastis Other Non-Metalli Mineral Produts Basi & Fabriated Metal Mahinery ne) Eletrial & Optial Equipment Transport Equipment Manufaturing ne) & Reyling 3.95 Non-Manufaturing 4.65 Table 1: List of 14 aggregated setors. The last olumn shows the predited hanges in U.S. expenditure shares on Chinese goods between 2011 and Bilateral Trade Shares, Labor Shares, and Intermediate Input Shares. We use the World Input-Output Tables in 2000 to onstrut bilateral trade flows, X, ; gross output, X ; and bilateral trade shares, π,. These quantities are used in alibrating onsumption shares and trade osts, as we desribe below. We also use the WIOD to onstrut the share of value added in gross output, χ, and the intermediate input shares, γk, aross ountries and setors using data on value added, gross output, and intermediate onsumption. Final Consumption Shares. Using value-added data from the WIOD together with setoral employment data in SEA, we ompute the value added per worker in eah setor and eah ountry. We assume that the national inome in eah ountry is equal to the sum of all value added. We also assume the trade balane at the ountry level. 24 With these two assumptions, we an use the equation market learing ondition for good in ountry to bak out the final onsumption shares as α = X N J k=1 γ N, k, =1 X k, I where I is a the sum of all value added in ountry. Setoral hoie parameters. Setoral Choie Parameters. 24 Note that this alulation assumes that trade balanes are 0. An alternative approah is to inlude the trade defiit and rebate it to workers in a lump-sum fashion, as in Caliendo and Parro 2015). The resulting parameters are very lose to what we ompute under the balaned trade assumption and, as a result, we have deided to proeed with balaned trade. 54

55 Let µ θ) be the share of population in ountry who are in group/type θ. Sine for all ountries other than the U.S. we have only one group, µ θ) = 1 for all USA. As we desribed in Setion 5, for the U.S. we define group/types based on geographi loations. In other words, we use ommuting zones CZs) to define loal labor markets. We split eah ommuting zone into two eduation groups based on whether workers hold at least an Assoiate degree or not. This implies that there are a total of 1,444 types 722 CZs 2 skills). We use the rosswalk provided by David Dorn to map Census Publi Use Miro-data Areas PUMAs) into ommuting zones. 25 Using Census data, we an alulate the distribution of workers aross different groups, µ USA θ). Moreover, using Census data, we an alulate the share of workers of eah group in eah setor Λ US θ), whih, in the model, is given by the following formula: Λ θ) = w a θ) ) σ i w i a i θ))σ. In ountries other than the U.S. the share of workers in eah setor is given by the Soio Eonomi Aounts SEA), whih is part of the World Input-Output Database WIOD). To alibrate the model, we need to bak out the wage rate in eah setor, w, and produtivity shifter a θ). To do this, we need data on labor inome in eah setor and, in the ase of U.S., eah group. We get this information from value added data in the WIOD. For the U.S. we have inome data for workers in eah setor and group Y USA,Census θ). We split the value added in setor from SEA aross U.S. groups so that the distribution of inome of eah setor aross different groups is onsistent with Census data and the aggregate inome in eah setor is onsistent with value-added data in the WIOD. In other words, we use the following as a measure of labor inome in setor and group θ USA,W IOD θ) = Y USA,Census θ) θ Y USA,Census θ) Y USA,W IOD Y USA, where Y is the value added in setor in the U.S. from the WIOD data. Using the properties of the Fréhet distribution in the model, we an derive the equation for labor inome per worker in ountry and setor as wl = P ) ε Γ ε ) µ θ) Λ θ) Φ θ)) 1+ε, 19) σ θ where and Φ θ) = P = i w i a i θ)) σ ) 1 σ N P ) α. =1 α 25 See 55

56 Food & B. Textile & L. Wood & Cork Paper & Print Coke & Petrol Chemials Rubber & Plasti Mineral Prod. Metal Mahinery Eletrial Equip. Transport Equip. Other Manu. Non-Manu. AUS CAN CHN DEU DNK ESP FIN FRA JPN USA 1e+03 1e+02 1e+01 1e+00 Figure 16: Log of setor TFPs for all setors and ountries of the sample. Lighter shades represent higher TFP. We an alulate the aggregate prie P for eah ountry using data on relative setoral pries, P, in GGDC s Produtivity Level Database. Finally, we make the following normalization with respet to the produtivity shifter a θ) in eah ountry µ θ) a θ) = 1 for all and. θ Using normalization, we an solve the equation 19) for w and a θ) noting that the left hand side of the equation is given in the data from the WIOD and Census). Trade Costs and Effiieny Parameter. The last set of parameters to be alulated are trade osts, d,, and setoral produtivities, A. 26 To alulate these values, we use the prie data and omputed wages to alulate the unit ost ψ assuming value-added taxes are zero in the benhmark). The ieberg trade osts an be alulated using the equation for expenditure shares. In partiular, we have ) ν A τ, ψ π, = P ) ν Γ ρ ν ) ν, 1 ρ where in the above we have used the definition of P in 14. Therefore, π, π, = d, ) ) ν P ν, P 26 Our alibration proedure losely follows that of Lewis et al. 2018). 56

57 AUS CAN CHN DEU DNK ESP FIN FRA JPN USA AUS CAN CHN DEU DNK ESP FIN FRA JPN USA AUS AUS CAN CAN CHN CHN DEU DEU DNK DNK ESP 5.00 ESP 5.00 FIN FIN FRA FRA JPN 2.00 JPN 2.00 USA USA a) Agriulture, forestry & fishing b) Manufaturing Figure 17: Ieberg trade ost. Left panel shows trade osts for non manufaturing setor. Right panel shows the average over all manufaturing setors. Row y-axis) ountries represent origin. Column x-axis) represent destination. sine d, = 1. Given our assumed value for ν, the equation above an be solved to bak out the trade ost d,. Finally, note that we an ombine the equations above and 14) to arrive at the following equation: π, ) P ν ) = A ψ ν Γ ρ ) ν 1 ρ. ν We an then use this equation to solve for setoral TFP parameters, A. This onludes the alibration. Figure 16 shows the heat map of the logarithm of setoral TFPs in eah ounty. Lighter shades represent higher TFP. Figure 17 shows the heat map of trade osts in the non-manufaturing setor and average over all manufaturing setors. The rows y-axis) represent origin ountries, and the olumns x-axis) represent destinations. Here, white ells represent no trade osts or very small trade osts, and darker ells represent higher trade osts. Note that the U.S. and many other advaned ountries fae lower trade osts when exporting goods in all setors. This is onsistent with findings in Waugh 2010), among others. 57