Trade Wars and Trade Talks with Data

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1 Trade War and Trade Talk with Data Ralph Oa y Univerity of Chicago and NBER July 11, 2011 Abtract What are the optimal tari of the US? What tari would prevail in a worldwide trade war? What are the gain from international trade policy cooperation? And what gain can be expected from future reciprocal trade negotiation? I addre thee and other quetion uing a uni ed framework which net traditional, new trade, and political economy motive for protection. I nd that US optimal tari average 66 percent, world trade war tari average 63 percent, the welfare gain from international trade policy cooperation average 4.4 percent, and there i almot no cope for future reciprocal trade negotiation. JEL clai cation: F11, F12, F13 Keyword: Optimal tari, trade war, GATT/WTO negotiation I am grateful to Kyle Bagwell, Chang-Tai Hieh, Bob Staiger, and eminar participant at Stanford Univerity and the Univerity of Chicago for very helpful comment and uggetion. I alo thank John Romali for haring hi tari data. The uual diclaimer applie. y Univerity of Chicago, Booth School of Buine, 5807 South Woodlawn Avenue, Chicago, IL 60637, United State; ralph.oa@chicagobooth.edu. 1

2 1 Introduction I propoe a exible framework for the quantitative analyi of unilateral and multilateral trade policy. It i baed on a multi-country multi-indutry general equilibrium model of international trade featuring inter-indutry trade a in Ricardo (1817), intra-indutry trade a in Krugman (1980), and pecial interet politic a in Groman and Helpman (1994). By combining thee element, it take a uni ed view of trade policy which net traditional, new trade, and political economy motive for protection. Speci cally, it feature import tari which erve to manipulate the term-of-trade, hift pro t away from other countrie, and channel pro t toward politically in uential indutrie. I ue thi framework to addre ome natural quetion emerging from the qualitative trade policy literature. To thi end, I calibrate it to perfectly match indutry-level trade and tari of the main player in recent GATT/WTO negotiation. I begin with an invetigation of unilateral trade policy: What are the optimal tari of the US and what would they imply for welfare, trade, production, and pro t around the world? How powerful are the traditional, new trade, and political economy motive for protection? I then turn to an examination of multilateral trade policy: What tari would prevail in a worldwide trade war and what are the implied gain from international trade policy cooperation? What tari change correpond to the GATT/WTO principle of reciprocity and what gain can be expected from future reciprocal trade negotiation? 1 With repect to unilateral trade policy, I nd that US optimal tari vary widely acro indutrie and trading partner and average 66 percent. They would increae real income in the US by 2.6 percent and decreae real income in the other countrie by 1.6 percent on average. In the US, import would fall by 27 percent on average and a reallocation of reource to more pro table indutrie would increae pro t by 4.2 percent on average. In the other countrie, import would fall by 12 percent on average and a reallocation of reource to le 1 The principle of reciprocity i one of the central pillar of the GATT/WTO ytem which I explain in detail later on. 2

3 pro table indutrie would decreae pro t by 1.8 percent on average. Traditional termof-trade e ect and new trade pro t-hifting e ect are the key driving force behind thee reult. Political economy e ect are only of limited quantitative importance. With regard to multilateral trade policy, I nd that the world trade war tari vary widely acro indutrie, countrie, and trading partner and average 63 percent. Thi i roughly in line with the noncooperative tari oberved following the Smoot-Hawley Tari Act of They would ubtantially decreae real income in all countrie with the average lo amounting to 4.1 percent. I alo nd that tari change which correpond to the GATT/WTO principle of reciprocity can be characterized by a imple formula which i eay to implement in practice. While thi formula identi e a number of indutrie in which there i till cope for future reciprocal trade negotiation, it alo ugget that the overall gain from uch negotiation would be quite mall. I am unaware of any quantitative analyi of unilateral and multilateral trade policy which i of imilar cope a the one provided here. I believe that thi i the rt quantitative framework which net traditional, new trade, and political economy motive for protection. I alo believe that thi i the rt tudy which provide etimate of optimal and noncooperative tari at the indutry level for the major player in recent GATT/WTO negotiation. The urpriing lack of comparable work i mot likely rooted in long-binding methodological and computational contraint. In particular, widely accepted calibration technique of general equilibrium trade model have only become available quite recently following the eminal work of Eaton and Kortum (2002). Alo, the calculation of diaggregated optimal and noncooperative tari i very demanding computationally and wa imply not feaible without preent-day computer. The mot immediate predeceor are Perroni and Whalley (2000), Broda et al (2008), and Oa (2011). Perroni and Whalley (2000) provide quantitative etimate of optimal and noncooperative tari in a imple Armington model which feature only traditional term-oftrade e ect. Oa (2011) provide uch etimate in a imple Krugman (1980) model which 3

4 feature only new trade production relocation e ect. Both contribution allow trade policy to operate only at the mot aggregate level o that a ingle tari i aumed to apply againt all import from any given country. 2 Broda et al (2008) provide detailed tatitical etimate of the invere export upply elaticitie faced by a number of non-wto member countrie. The idea i to tet the traditional optimal tari formula which tate that a country optimal tari i equal to the invere export upply elaticity it face in equilibrium. 3 The paper further relate to an extenive body of theoretical and quantitative work. The traditional, new trade, and political economy motive for protection are borrowed from the theoretical trade policy literature including Johnon ( ), Venable (1987), and Groman and Helpman (1994). 4 The analyi of the GATT/WTO principle of reciprocity build on the pioneering work of Bagwell and Staiger (1999). My calibration technique i imilar to the one ued in recent quantitative work baed on the Eaton and Kortum (2002) model uch a Caliendo and Parro (2011). However, my analyi di er from thi line of work in term of framework and quetion. In particular, I take a uni ed view of trade policy by neting traditional, new trade, and political economy e ect. Alo, I go beyond an invetigation of exogenou trade policy change by emphaizing optimal and noncooperative tari. 5 My application focue on 7 region and 26 manufacturing indutrie in the year The region are Brazil, China, the EU, India, Japan, the US, and a reidual Ret of the World and are choen to comprie the main player in recent GATT/WTO negotiation. I need data 2 The work of Perroni and Whalley (2000) i in the computable general equilibrium tradition and extend an earlier contribution by Hamilton and Whalley (1983). It predict implauibly high noncooperative tari of up to 1000 percent. 3 Thi approach i not uitable for etimating the optimal tari of WTO member countrie. Thi i becaue uch countrie impoe cooperative tari o that the factual invere export upply elaticitie they face are not informative of the counterfactual invere export upply elaticitie they would face if they impoed optimal tari under all but the mot retrictive aumption. 4 The analyzed pro t hifting e ect i more cloely related to the production relocation e ect in Venable (1987) than the claic pro t hifting e ect in Brander and Spencer (1981). Thi i explained in more detail in footnote 12. See Mrazova (2010) for a recent treatment of claic pro t hifting e ect in the context of GATT/WTO negotiation. 5 Exiting work typically focue on quantifying the e ect of exogenou tari change. Caliendo and Parro (2011), for example, analyze the e ect of the North American Free Trade Agreement. One exception can be found in the work of Alvarez and Luca (2007) which include a hort dicuion of optimal tari in mall open economie. 4

5 on trade ow and tari a well a etimate of two et of tructural parameter. I contruct the matrix of international and dometic trade ow from United Nation trade data, NBER production data, and World Bank production data. I take the matrix of tari from an extenion of United Nation tari data. I ue etimate of the elaticitie of ubtitution by Broda and Weintein (2006) and etimate of the in uence of lobbie a well a the lobbying tatu of indutrie from Goldberg and Maggi (1999). A detailed dicuion of the data including the applied aggregation, extrapolation, and matching procedure can be found in the appendix. The remainder of the paper i organized a follow. In the next ection, I lay out the baic etup, characterize the equilibrium for given tari change, demontrate how to compute the general equilibrium e ect of tari change, and dicu the welfare e ect of tari change. I then turn to US optimal tari, world Nah tari, and GATT/WTO negotiation. 2 Analyi 2.1 Baic etup There are N countrie indexed by i or j and S indutrie indexed by. Conumer have acce to a continuum of di erentiated varietie. Preference over thee varietie are given by the following utility function: U j = Q X i Z Mi 0 x ij ( i ) 1 1 j d i (1) where x ij i the quantity of an indutry variety from country i conumed in country j, M i i the ma of indutry varietie produced in country i, > 1 i the elaticity of ubtitution between indutry varietie, and j i the fraction of country j income pent on indutry varietie. Each variety i uniquely aociated with an individual rm. Firm are homogeneou 5

6 within indutrie and their technologie are ummarized by the following invere production function: l i = ij x ij ' i (2) where l i i the labor requirement of an indutry rm in country i featuring iceberg trade barrier ij and a productivity parameter ' i. Each rm ha monopoly power with repect to it own variety and the number of rm i given exogenouly. 6 Government can impoe import tari but do not have acce to other policy intrument. 7 I denote the ad valorem tari impoed by country j againt import from country i in indutry by t ij and make frequent ue of the horthand ij t ij + 1 throughout. Government preference are given by the following objective function: G j = V j + X j j (3) P j where V j P j i the welfare of country j, i total expenditure or income in country j, P j i the ideal price index in country j, j 0 i the political economy weight of indutry in country j, and j are the pro t of indutry in country j. 8 Notice that government imply maximize welfare if the political economy weight are zero. The interpretation of the political economy weight i that one dollar of pro t in indutry of country j count 1 + j a much a one dollar of wage income or tari revenue in the government objective function. Thi formulation of government preference can be viewed a a reduced form repreentation of the "protection for ale" theory of Groman and Helpman 6 The model can alo be olved and calibrated with free entry and xed cot of production. I focu on a verion without free entry for two main reaon. Firt, becaue it feature poitive pro t and therefore lend itelf more naturally to an analyi of political economy conideration. Second, becaue it rule out corner olution with zero production in ome ector o that it can be implemented uing a much impler algorithm. See footnote 12 for a further dicuion of the model with free entry. 7 Thi retriction i motivated by the fact that import tari have alway been by far the mot important trade policy intrument in practice. However, it would be eay to extend the framework to alo include export ubidie, import quota, or voluntary export retraint. See Bagwell and Staiger (2009a, 2009b) for a dicuion of the importance of thi retriction for the theory of trade agreement in a range of imple new trade model. 8 A in mot trade model, welfare i the ame a real income if nominal income i de ated by the ideal price index. Thi i becaue the ideal price index i a unit expenditure function and utility only depend on conumption. Nominal income conit of labor income, pro t, and tari revenue. 6

7 (1994). I compute the political economy weight baed on the etimate of Goldberg and Maggi (1999) uing a procedure which I explain in detail in the appendix Equilibrium for given tari Utility maximization implie that rm in indutry of country i face demand x ij = (p i ij ij ) j (4) P 1 j where p i i the ex-factory price of an indutry variety from country i and P j i the ideal price index of indutry varietie in country j. Alo, pro t maximization require that rm in indutry of country i charge a contant mark-up over marginal cot p i = w i (5) 1 ' i where w i i the wage rate in country i. It i ueful to characterize the equilibrium for given tari with four condened equilibrium condition. The rt condition follow from ubtituting equation (2), (4), and (5) into the relationhip de ning indutry pro t i = M i P j p i ij x ij w i l i : i = 1 Xj M i ij ij 1 ' i w i P j 1 j (6) The econd condition combine equation (2), (4), and (5) with the requirement for labor market clearing L i = P M il i : w i L i = X i ( 1) (7) 9 In order to clearly expoe the novel feature of my framework, I deliberately abtract from many bell and whitle which can be found in other quantitative work. For example, I do not allow for intermediate good or nontraded good which i in line with much of the theoretical trade policy literature. The idea i that intermediate good tend to magnify the e ect of trade policy while nontraded good tend to dampen the e ect of trade policy o that omitting both eem like a reaonable rt pa. 7

8 The third condition reult from ubtituting equation (5) into the formula for the ideal price P index P j = i M i (p i ij ij ) : P j = X i M i 1! 1 w i ij 1 1 ij ' i (8) And the nal condition combine equation (4) and (5) with the budget contraint equating total expenditure to labor income, plu tari revenue, plu aggregate pro t, minu aggregate net export which are treated a a parameter in thi tatic environment: 10 = w j L j + X i X t ijm i ij 1 ' i w 1 i P j ij j + X j N (9) Condition (6) - (9) repreent a ytem of 2N (S + 1) equation in the 2N (S + 1) unknown w i, X i, P i, and i. It can be olved given a numeraire and I normalize P j w jl j = 1 throughout. 2.3 General equilibrium e ect of tari change An advantage of thi characterization i that the general equilibrium e ect of counterfactual tari change can now be computed uing a method inpired by Dekle at al (2007). In particular, condition (6) - (9) can be rewritten in change a X j ij (b ij ) bpj 1 bxj = b i ( bw i ) 1 (10) bw i = X ib i (11) 10 Treating the aggregate trade balance a a parameter i tandard in the quantitative trade literature. The idea i that it i determined by intertemporal aving and invetment deciion which do not repond to trade policy. One problem i that thi dichotomy cannot hold in the limit a tari approach prohibitive level becaue the aggregate trade balance then alo ha to go to zero. A a reult, a more realitic peci cation may involve a negative relationhip between the abolute value of the aggregate trade balance and tari. Since the detail of thi relationhip are far from clear, it would be ideal to explore a number of alternative peci cation. Unfortunately, thi i very di cult in practice ince it take about two month until all algorithm converge. I therefore tick to the tandard aumption and point out where and how it a ect my reult. 8

9 b = w jl j bw j + X i X bp j = Xi ij ( bw i b ij ) t ij T ij bt ij ( bw i ) 1 1 bpj (b ij ) Xj b + X j b j (12) N (13) where a "hat" denote the ratio between the counterfactual and the factual value, ij T ij / P n T in, ij ij T ij / P m mjt mj, i P. P j 1 T ij t M ij i 1 ' i 1 w i P j country j evaluated at world price. Pn t 1 t T int, and T ij ij j i the value of indutry trade owing from country i to Equation (10) - (13) repreent a ytem of 2N (S + 1) equation in the 2N (S + 1) unknown bw i, b Xi, b Pi, b i. Crucially, their coe cient depend on and obervable only o that the full general equilibrium repone to counterfactual tari change can be computed without further information on any of the remaining model parameter. Moreover, all required obervable can be inferred directly from widely available trade and tari data ince the model require = P i P P ijt ij, w j L j = i P t P ijt ij j, and NX i = P j P (T ij T ji ), where j = 1 Pj T ij in thi contant markup environment. Notice that thi procedure enure that the model perfectly matche all oberved trade ow and tari by default. 11 A an illutration, the upper panel of Table 1a ummarize the key general equilibrium e ect of a counterfactual 25 percentage point increae in the US tari on pharmaceutical or cometic. Pharmaceutical product have a relatively low elaticity of ubtitution of 1.98 while cometic product have a relatively high elaticity of ubtitution of The US tari i low in both indutrie, averaging cloe to 0 percent in pharmaceutical and cloe to 1 percent in cometic. The rt column give the predicted percentage change in the US wage relative to the numeraire. A can be een, the US wage i predicted to increae by 0.20 percent if the tari increae occur in pharmaceutical and i predicted to increae by 0.18 percent if the tari increae occur in cometic. 11 Eentially, the calibration technique impoe a retriction on the et of parameter fm i; ij; ' i g uch that the predicted T ij perfectly match the oberved T ij given the oberved ij and the etimated. 9

10 The econd column preent the predicted percentage change in the quantity of US output in the protected indutry and the third column the imple average of the predicted percentage change in the quantity of US output in the other indutrie. Hence, US output i predicted to increae by 4.13 percent in pharmaceutical and decreae by an average 0.12 percent in all other indutrie if the tari increae occur in pharmaceutical. Similarly, US output i predicted to increae by 9.27 percent in cometic and decreae by an average 0.29 percent in all other indutrie if the tari increae occur in cometic. Intuitively, a US import tari make imported good relatively more expenive in the US market o that US conumer hift expenditure toward US good. Thi then incentivize US rm in the protected indutry to expand which bid up US wage and thereby force US rm in other indutrie to contract. 2.4 Welfare e ect of tari change Given the general equilibrium e ect of counterfactual tari change, the implied welfare e ect can be computed from b V j = b = b P j, where b P j = bpj j i the change in the aggregate price index. Thi framework feature both traditional a well a new trade welfare e ect of trade policy. Thi can be een mot clearly from a log-linear approximation around factual with aggregate net export et to zero. A I explain in detail in the appendix, it yield the following relationhip for the welfare change induced by tari change where V j V j i the percentage change in country j welfare and o on: V j V j t X i X T ij pj p j p i + X p i j j j p j + X p j i X t ij T ij Tij T ij p i p i (14) The rt term i a traditional term-of-trade e ect which capture change in country j real income due to di erential change in the world price of country j production and conumption bundle. Country j bene t from an increae in the world price of it conumption bundle relative to the world price of it production bundle becaue it export then command more import in world market. The term-of-trade e ect can alo be viewed a a relative 10

11 wage e ect ince world price are proportional to wage given the pricing formula (5). The econd term i a new trade pro t hifting e ect which capture change in country j real income due to change in country j aggregate pro t originating from change in indutry output. It take change in indutry pro t, net out change in indutry price, and then aggregate the remaining change over all indutrie uing pro t hare a weight. Thee remaining change are change in indutry pro t originating from change in indutry output ince indutry pro t are proportional to indutry ale in thi contant markup environment. 12 The lat term i a combined tari revenue e ect which capture change in country j real income due to change in country j tari revenue originating from change in import volume. It take change in import value, net out change in import price, and then aggregate the remaining change over all countrie and indutrie uing tari revenue hare a weight. Thee remaining change are change in import volume ince change in import value can be decompoed into change in import price and import volume. A an illutration, the lower panel of Table 1a report the welfare e ect of the counterfactual 25 percentage point increae in the US tari on pharmaceutical or cometic dicued above and decompoe them into term-of-trade and pro t hifting component along the line of equation (14). A can be een, US welfare increae by 0.07 percent if the tari increae occur in pharmaceutical but decreae by 0.03 percent if the tari increae occur in cometic. The di erential welfare e ect are due to di erential pro t hifting e ect. While the term-of-trade e ect i poitive in both cae, the pro t hifting e ect i poitive if the tari increae occur in pharmaceutical and negative if the pro t increae occur in cometic. The poitive term-of-trade e ect are a direct conequence of the increae in the US 12 Thi pro t hifting e ect i more cloely related to the production relocation e ect from Venable (1987) than the claic pro t hifting e ect from Brander and Spencer (1981). It can be hown that in a verion of the model with free entry and xed cot of production, the equivalent of equation (14) would be V j t P i P T ij pj p j p i p i + P i P ij T ij 1 1 M i M i + P i P t ij T ij Tij T ij V j p i p i, where the econd term can now be interpreted a a production relocation e ect. Eentially, tari lead to change in indutry output at the intenive margin without free entry and at the extenive margin with free entry. 11

12 relative wage identi ed above. The di erential pro t hifting e ect are the reult of croindutry di erence in markup which are brought about by cro-indutry di erence in the elaticity of ubtitution. Since the quantity of US output alway increae in the protected indutry but decreae in other indutrie, the change in pro t which i due to change in indutry output i alway poitive in the protected indutry but negative in other indutrie. The overall pro t hifting e ect depend on the net e ect which i poitive if the tari increae occur in a high pro tability indutry uch a pharmaceutical and negative if it occur in a low pro tability indutry uch a cometic. 13 Notice that the overall welfare e ect are maller than the um of the term-of-trade and pro t hifting e ect in both example. One miing factor i, of coure, the tari revenue e ect from equation (14). However, thi e ect i approximately zero in both example ince the lo in tari revenue due to a decreae in import volume in the protected indutry i approximately o et by the gain in tari revenue due to an increae in import volume in other indutrie. 14 The dicrepancy therefore largely re ect the fact that equation (14) only provide a rough approximation if tari change are a large a 25 percentage point ince it i obtained from a linearization around factual US optimal tari The above dicuion ugget that government have incentive to ue import tari to increae relative wage generating a poitive term-of-trade e ect and induce entry into highpro tability indutrie generating a poitive pro t hifting e ect. However, thee incentive combine with political economy conideration a government alo eek to protect high i j j p j p j = 0 if = for all o 13 A i eay to verify, equation (5) and (11) imply that P j that there i then no pro t hifting e ect. 14 The volume of overall US import fall a a conequence of the higher tari in pharmaceutical and cometic. The reaon that tari revenue till remain largely unchanged i that US tari on pharmaceutical and cometic are relatively mall compared to US tari in other indutrie. 15 In particular, the overall reduction in import aociated with the increae in tari alo reduce the import hare which leverage the improvement in relative world price. Thi e ect doe not appear in equation (14) ince change in import hare are econd order e ect. 12

13 indutrie to channel pro t to politically in uential lobbie. The optimal tari of a government maximize that government objective function (3) ubject to condition (10) - (13). They can be computed uing a imple iterative algorithm which I dicu in detail in the appendix. Figure 1a ummarize the optimal tari of the US taking a given all other countrie factual tari. It rank all indutrie by elaticity of ubtitution and plot the optimal tari of the US with repect to all trading partner againt the indutry rank. A can be een, optimal tari vary widely acro indutrie and are trongly decreaing in the elaticity of ubtitution a one would expect given the pro t hifting motive for protection. There i alo ome variation acro trading partner although it i much le pronounced. At 62 percent, the average US optimal tari impoed againt Brazil i the lowet. At 69 percent, the average US optimal tari impoed againt Japan i the highet. The average US optimal tari impoed againt all trading partner combined i 66 percent. The quantitative e ect of political economy force i very limited. In particular, the imple average of the di erence between the optimal tari ummarized in Figure 1a and the optimal tari obtained by etting all political economy weight equal to zero i only 0.35 percentage point with the maximum di erence being only 1.15 percentage point. Thi i mainly due to the mall political economy weight which are contructed baed on etimate by Maggi and Goldberg (1999) uing a procedure which I dicu in detail in the appendix. An apparent alternative would have been to recalibrate the political economy weight given the trade and tari data at hand. However, the di culty i that mot countrie et tari cooperatively in GATT/WTO negotiation o that factual tari are not informative of optimal tari without trong aumption on the nature of the negotiation proce. 16 Figure 2a illutrate the change in the value of US import correponding to US optimal tari. It rank all indutrie by elaticity of ubtitution and plot the predicted change in US 16 Of coure, one could follow Broda et al (2006) and retrict attention to non-wto member countrie only. However, thee countrie tend to be rather pecial politically o that identifying political economy weight from them eem problematic. For intance, Ruia and Iran are currently the bigget non-wto member countrie. 13

14 import with repect to all trading partner againt the indutry rank. A a conequence of the tilted tari chedule, US import fall in mot indutrie but increae harply in the highet elaticity indutrie. US relative wage rie fater than US tari in the highet elaticity indutrie o that importing e ectively become more attractive in thee indutrie. There i again relatively little variation acro trading partner. At -33 percent, US import from the Ret of the World fall the mot. At -14 percent, US import from Brazil fall the leat. Overall, US import fall by 27 percent. 17 Figure 3a highlight the change in the quantity of US production correponding to US optimal tari. It rank all indutrie by elaticity of ubtitution and plot the predicted change in US hipment with repect to all trading partner againt the indutry rank. It alo include change in US dometic hipment a well a change in US total hipment by indutry. US hipment to trading partner fall acro the board mirroring the decline in US import. Thi decline i particularly pronounced in high elaticity indutrie. US total hipment increae in low elaticity indutrie but decreae in high elaticity indutrie a one would expect given the pro t hifting motive for protection. Overall, the reallocation of reource toward high pro tability indutrie increae total US pro t by 4.2 percent. 18 The rt column of Table 2a lit the welfare e ect correponding to US optimal tari. A can be een, US real income i predicted to increae by 2.6 percent at the expene of all other countrie. The US can gain at the expene of other countrie becaue the term-of-trade and pro t hifting e ect have a beggar-thy-neighbor character. Thi can be een from the econd and third column of Table 2a. While US wage are predicted to rie by 21.9 percent relative to the numeraire, the wage of the other countrie are predicted to fall by an average 5.6 percent relative to the numeraire. And while total US pro t are predicted to increae by 4.2 percent due to the reallocation of reource toward high pro tability indutrie, total pro t 17 Change in the value of import can be computed at variou level of aggregation from b T ij = (b! i) 1 1 bpj (b ij) X b j, T b ij = P P T ij bt t T ijt ij, and o on. 18 Shipment are de ned a Q ij = T ij p i. Change in hipment can be computed from Q b T ij = b ij b! i. Change in total pro t induced by the reallocation of reource acro ector can be computed from b i b! i = P P ij j bq ij. P n P t int 14

15 in the other countrie are predicted to fall by an average 1.8 percent due to the reallocation of reource toward low pro tability indutrie. China and Japan are predicted to u er mot everely from US optimal tari. Chinee export account for 36 percent of Chinee ale which make China by far the mot open economy in the ample. Thi implie that US optimal tari hit China particularly hard which explain the large advere relative wage and pro t hifting e ect. The Japanee aggregate trade urplu account for 14 percent of Japanee ale which make Japan by far the larget net exporter in the ample. The percentage drop in Japanee import mut therefore far exceed the percentage drop in Japanee export in order to keep Japanee net export unchanged. A a conequence, Japanee import mut become much more expenive relative to Japanee export which explain the large drop in Japanee relative wage. 19; World Nah tari The above dicuion of US optimal tari aume that other countrie do not retaliate which allow the US to bene t coniderably at their expene. I now turn to an analyi of the Nah equilibrium in which all countrie retaliate optimally. The Nah tari are uch that each government chooe it tari to maximize it objective function (3) given the tari of all other government a well a condition (10) - (13). They can be computed uing a imple iterative algorithm which I dicu in detail in the appendix. I refer to optimal tari without retaliation a optimal tari and optimal tari with retaliation a Nah tari throughout. Figure 4a and 4b provide a ummary of the world Nah tari. Figure 4a rank all indutrie by elaticity of ubtitution and plot the average Nah tari impoed by each country againt the indutry rank. Figure 4b rank all indutrie by elaticity of ubtitution and plot the average Nah tari faced by each country againt the indutry rank. A can 19 Of coure, thi depend crucially on the aumption that aggregate trade balance are exogenou. If they were allowed to be decreaing in the tari, the Japanee wage adjutment would be le pronounced. See footnote 10 for a detailed dicuion of the aumption of contant aggregate trade balance. 20 The percentage change in the value of import and export are reported in the lat two column of Table 2a. The percentage drop in import exceed the percentage drop in export whenever a country run an aggregate trade urplu and vice vera. Overall, world trade i predicted to fall by 17 percent. 15

16 be een, the average Nah tari are quite imilar acro countrie. 21 The average acro all Nah tari i 63 percent which i remarkably cloe to the average tari of 50 percent typically reported for the trade war following the Smoot-Hawley tari Act of Thi trade war i the only full- edged trade war in economic hitory and therefore the only benchmark available to me. Of coure, it can only erve a a rough reference point given the di erence in the et of player and the timing of the experiment. In order to compare thee world Nah tari to the US optimal tari dicued above, I now again focu on the US and preent the Nah equilibrium analog to Figure 1a - 3a. Figure 1b i the Nah equilibrium analog to Figure 1a. It rank all indutrie by elaticity of ubtitution and plot the US Nah tari with repect to all trading partner againt the indutry rank. A can be een, the pattern of US Nah tari i very imilar to the pattern of US optimal tari. However, each US Nah tari exceed the correponding US optimal tari a one might intuitively expect. At 75 percent, the average US Nah tari impoed againt Brazil i the lowet. At 92 percent, the average US Nah tari impoed againt Japan i the highet. The average acro all US Nah tari i 82 percent and therefore exceed the average acro all US optimal tari by 16 percentage point. Figure 2b i the Nah equilibrium analog to Figure 2a. It illutrate the change in the value of US import correponding to world Nah tari. It rank all indutrie by elaticity of ubtitution and plot the predicted change in US import with repect to all trading partner againt the indutry rank. A can be een, the US import repone to world Nah tari ummarized in Figure 2b are largely a magni ed verion of the US import repone to US optimal tari ummarized in Figure 2a. At -64 percent, US import from the Ret of the World fall the mot. At -19 percent, US import from Japan fall the leat. Overall, US import fall by 48 percent a a conequence of world Nah tari which i almot twice the 21 The EU impoe the lowet average Nah tari (56 percent) and the US impoe the highet average Nah tari (82 percent). At the ame time, the US face the lowet average Nah tari (58 percent) and Japan face the highet average Nah tari (70 percent). 22 See, for example, Bagwell and Staiger (2002: 43). There i a mall number of zero in the matrix of trade ow. Since the correponding Nah tari can be et to arbitrary value, I do not include them in the calculation of any average. 16

17 repone predicted a a conequence of US optimal tari. Figure 3b i the Nah equilibrium analog to Figure 3a. It highlight the change in the quantity of US production correponding to world Nah tari. It rank all indutrie by elaticity of ubtitution and plot the predicted change in US hipment with repect to all trading partner againt the indutry rank. It alo include the change in US dometic hipment a well a change in US total hipment by indutry. A can be een, the repone of US hipment exhibit le cro-indutry diperion under world Nah tari than under US optimal tari. Since thi i particularly true with regard to US total hipment, the US i le ucceful at reallocating reource toward high pro tability indutrie in the Nah equilibrium. Thi re ect the fact that all countrie attempt to promote their high pro tability indutrie at the ame time. Overall, the reallocation of reource toward high pro tability indutrie increae total US pro t by 1.2 percent under world Nah tari which i le than one third of the e ect under US optimal tari. The rt column of Table 2b lit the welfare e ect of world Nah tari. A can be een, the US i no longer able to gain at the expene of other countrie and welfare fall acro the board. Intuitively, each country now increae it import tari in an attempt to induce favorable term-of-trade, pro t hifting, and political economy e ect. The end reult i a large drop in trade volume which leave all countrie wore o. However, there are till ubtantial adjutment in wage and pro t a can be een from column 2 and 3 of Table 2b. A a conequence, there are izeable di erence in the overall welfare e ect acro countrie. At -0.5 percent, the US loe the leat. At -8.6 percent and -9.1 percent, China and Japan loe the mot. On average, welfare fall by 4.1 percent. The reaon why China and Japan are predicted to u er o everely from protectionim are the ame a before. China i by far the mot open economy in the ample o that world Nah tari induce large advere relative wage and pro t hifting e ect. Japan i by far the larget net exporter in the ample o that the large contraction in trade volume require a large reduction in Japanee relative wage to keep Japanee net export unchanged. The 17

18 tory for the US i the mirror image of the tory for Japan. The US aggregate trade de cit account for 33 percent of US import making the US by far the larget net importer in the ample. The percentage drop in US export mut therefore far exceed the percentage drop in US import to keep US net import unchanged. A a conequence, US export mut become much more expenive relative to US import which explain the large increae in US relative wage. 23; GATT/WTO negotiation The welfare loe from world Nah tari can be viewed a the welfare gain from international trade policy cooperation. 25 The primary forum for international trade policy cooperation i the GATT/WTO. In a nuthell, GATT/WTO regulation require countrie to impoe tari according to the principle of nondicrimination and change tari according to the principle of reciprocity. While the principle of nondicrimination imply prohibit impoing di erent tari againt di erent trading partner, the principle of reciprocity i much more looely de ned. In particular, countrie are encouraged to liberalize reciprocally in trade negotiation in the ene that they make tari conceion of equal value. Similarly, countrie are entitled to retaliate reciprocally in trade dipute in the ene that they remove tari conceion of equal value. 26 I interpret thi de nition of the principle of reciprocity a referring to an ideal of mutual tari change which have no term-of-trade and pro t hifting e ect. Formally, uch tari change can be found by impoing the retriction P i P T ij pj p j p i p i = 0 and 23 Again, thi depend crucially on the aumption that aggregate trade balance are exogenou. If they were allowed to be decreaing in the tari, the Japanee and US wage adjutment would be le pronounced. See footnote 10 for a detailed dicuion of the aumption of contant aggregate trade balance. 24 The percentage change in the value of import and export are reported in the lat two column of Table 2b. The percentage drop in import exceed the percentage drop in export whenever a country run an aggregate trade urplu and vice vera. Overall, world trade i predicted to fall by 57 percent. 25 Of coure, the welfare gain are the invere of the welfare loe trictly peaking. They amount to 3.4% for Brazil, 9.4% for China, 2.4% for the European Union, 2.8% for India, 10.1% for Japan, 2.3% for the Ret of the World, 0.5% for the US, and 4.4% on average. 26 Thee principle a well a their numerou exception are dicued in detail in Bagwell and Staiger (2002). One particularly important exception i that GATT/WTO member are allowed to ign free trade agreement in pite of the principle of nondicrimination. 18

19 P j j j p j p j = 0 on the equilibrium condition (10) - (13). I view thi a a natural extenion of the interpretation adopted by Bagwell and Staiger (1999) which implie that reciprocal tari change have no term-of-trade e ect. 27 By precluding countrie from gaining at the expene of one another through term-of-trade and pro t hifting e ect, the principle of reciprocity repreent a force toward international trade policy cooperation. In particular, it tend to incentivize countrie to o er tari conceion and deter countrie from withdrawing tari conceion in anticipation of the reulting trade volume e ect. Notice that there are at leat a many tari a retriction even if the principle of nondicrimination i impoed o that the et of reciprocal tari change i typically not unique. A particularly intuitive formula characterizing nondicriminatory and reciprocal tari change can be obtained by impoing p i p i = i i = 0 in a verion of the model in which tari are treated a a component of iceberg trade barrier. A I explain in detail in the appendix, thi yield v v 6=v! P T P vj n6=v T! vn Tjj / P n6=v T P m T mj vn m6=v T mv T vv / P j m T (15) mv j where j denote the nondicriminatory tari impoed by country j in indutry. Thi i a ytem of N equation in N tari change whoe coe cient are in term of obervable trade ow only. Given one country tari change in a particular indutry, it uniquely pin down the neceary repone of all other countrie in the ame indutry ince one of the equation i alway linearly dependent. The rt term capture that country v need to repond more to a tari change by country j the larger i the hare of country v export going to country j. The econd term capture that country v need to repond more to a tari change by any country the larger are country 27 Bagwell and Staiger (1999) interpret the principle of reciprocity a referring to an ideal of mutual tari change which bring about change in the volume of each country import that are of equal value to change in the volume of it export. They demontrate that thi ideal can eliminate all term-of-trade e ect which i alo true in the environment dicued here. In particular, their interpretation implie P P P P P j6=i pjdqji = P i pidqij. Alo, di erentiating the trade balance condition yield P i (pjdqji P + Qjidpj) = (pidqij + Qijdpi). If aggregate trade imbalance are et equal to zero, thee relationhip combine j6=i to P i P T ij dpj p j dp i p i = 0. 19

20 v export relative to country v import overall. The nal term capture that country v need to repond more to a tari change by country j the more open country v i relative to country j. Thi term i a meaure of how open country v i relative to country j ince the numerator i the hare of country j purchae from itelf and the denominator i the hare of country v purchae from itelf. While thi formula i derived in a verion of the model in which tari are treated a a component of iceberg trade barrier, it perform well in the full model featuring tari revenue. Thi i illutrated in Table 1b which reviit the e ect of a counterfactual 25 percentage point increae in the US tari on pharmaceutical or cometic dicued above. The key di erence i that the US trading partner are now aumed to repond reciprocally to the US tari increae according to formula (15). 28 A can be een, the US i now predicted to loe from the tari increae in both indutrie ince the term-of-trade and pro t hifting e ect are all but eliminated. Thi i becaue US wage and US production repond much le to the US tari increae given the retaliatory repone of the US trading partner. Table 3a report the combined e ect of the larget poible tari cut in all indutrie which are conitent with formula (15). It i baed on the aumption that countrie do not impoe import ubidie o that the larget poible tari cut in a given indutry are alway uch that one country completely eliminate it tari in that indutry. A can be een, the predicted welfare gain and trade repone are mall uggeting that there i little cope for future reciprocal trade liberalization. The reaon i that the EU, Japan, and the US already impoe low tari in mot indutrie o that there i little room for further reciprocal tari cut. The larget reciprocal tari cut are poible in textile but alo only average to 3.29 percent. No tari cut at all are poible, for example, in road vehicle ince Japan tari i already at 0.00 percent in that indutry The peci c tari increae in pharmaceutical and cometic required by formula (15) are 4% and 23% for Brazil, 11% and 24% for China, 31% and 59% for the EU, 71% and 51% for India, 13% and 12% for Japan, and 7% and 10% for the Ret of the World. 29 Complete trade liberalization in all countrie and indutrie i not a likely outcome of multilateral trade negotiation becaue it doe not lead to Pareto gain. At -1.3%, India i predicted to loe the mot becaue it average factual tari i the highet in the ample (27.0%). At 0.6%, Japan i predicted to gain the mot 20

21 3 Concluion I propoed a exible framework for the quantitative analyi of unilateral and multilateral trade policy which net traditional, new trade, and political economy motive for protection. I ued thi framework to addre ome natural quetion emerging from the qualitative trade policy literature. I began with an invetigation of unilateral trade policy: What are the optimal tari of the US and what would they imply for welfare, trade, production, and pro t around the world? How powerful are the traditional, new trade, and political economy motive for protection? I then turned to an examination of multilateral trade policy: What tari would prevail in a worldwide trade war and what are the implied gain from international trade policy cooperation? What tari change correpond to the GATT/WTO principle of reciprocity and what gain can be expected from future reciprocal trade negotiation? The interpretation of my reult depend on whether the framework i taken a a maintained or teted hypothei. In the former cae, they can be viewed a anwer to quetion of immediate policy relevance: for example, a revealing what would have happened if a trade war had broken out in the wake of the recent nancial crii; or a uggeting how the GATT/WTO could implement the principle of reciprocity in future trade dipute. In the latter cae, they can be interpreted a uggetive of the plauibility of ome of the leading model of trade policy making: for example, a demontrating that the predicted tari are roughly in line with the noncooperative tari oberved following the Smoot-Hawley Tari Act of 1930; or a howing that the underlying trade policy externalitie can be u ciently trong to plauibly jutify a lengthy proce of multilateral trade negotiation. A direct tet of the framework quantitative prediction i challenging given that mot countrie now impoe cooperative tari a a reult of GATT/WTO negotiation. One approach would be to collect detailed hitoric trade and tari data and ee if the framework can not only match the average but alo the ditribution of tari oberved during the trade becaue it average factual tari i the lowet in the ample (1.5%). The intereted reader can nd a ummary of all aociated e ect in Table 3b. 21

22 war following the Smoot-Hawley Tari Act of Another approach would be to focu on non-tari barrier like Goldberg and Maggi (1999) or non-wto member countrie like Broda et al (2006) and aume that they are not ubject to the contraint impoed by international trade policy cooperation. Yet another approach would be to impoe more tructure on the nature of GATT/WTO negotiation uch a Bagwell and Staiger (2011) and focu on the tari change reulting from WTO-acceion. Thee approache could be the bai of rewarding future work. Beide, the framework could alo be extended in many way and ued to addre a whole hot of related quetion emerging from the large qualitative literature on GATT/WTO negotiation. A one of many example, GATT/WTO member are allowed to ign free trade agreement a an important exception to the principle of nondicrimination. Bagwell and Staiger (1999) have pointed out that thi can limit the e ectivene of the principle of reciprocity a a force toward international trade policy cooperation ince inider can then gain at the expene of outider through trade diverion e ect. The framework could be ued to quantify the e ciency cot free trade agreement impoe through uch e ect. 22

23 4 Appendix 4.1 Data The data on international trade ow i from the UN-Comtrade databae which cover mot countrie in the world. It i originally at the HS 6-digit level and I convert it to the SITC- Rev2 4-digit level uing an NBER concordance which I downloaded from Jon Haveman webite at Macleter College. I then aggregate it to the 2-digit level by umming over all relevant indutrie. I impute dometic trade ow uing US hipment data from the NBER- CES manufacturing indutry databae which i originally at the SIC 4-digit level a well a worldwide value added data from the World Bank-WDI databae which i at the country level. The NBER-CES manufacturing data i only available until the year 2005 which i why I chooe thi year for my analyi. I ue the following procedure to impute dometic trade ow: Firt, I convert the US hipment data to the SITC-Rev2 4-digit level uing a concordance between SIC 4-digit code and SITC-Rev2 4-digit code contructed by matching concordance from Feentra (1996) and Pierce and Schott (2010). Second, I merge the US hipment data with the US trade data and compute the US indutry expenditure hare which I ubequently apply to all other countrie. Third, I compute total expenditure for all countrie from total hipment, minu total export, plu total import. I impute total hipment for all countrie other than the US by dividing value added by which i the number for value added reported by Dekle et al (2007). Fourth, I compute dometic trade ow for all countrie other than the US by multiplying the expenditure hare with total expenditure and ubtracting indutry import. Finally, I aggregate the dometic trade ow to the 2-digit level by umming over all relevant indutrie. The tari data wa generouly provided to me by John Romali. It i a carefully cleaned verion of the TRAINS-UN data which give applied tari in ad valorem term. Applied tari are either the mot-favored nation tari or preferential tari if exception uch a 23

24 free trade agreement apply. It i originally at the SITC-Rev2 4-digit level and I aggregate it to the 2-digit level by averaging over all relevant tari uing trade weight. Becaue the data give applied tari and thee tari are aggregated uing trade weight, the reulting tari matrix i inconitent with the GATT/WTO principle of nondicrimination. I therefore further average thee tari acro trading partner for the calculation hown in Table 1b, 3a, and 3b. Omitting thi tep would only lightly alter the reult preented in thee table. The elaticitie are taken from Broda and Weintein (2006). I ue the SITC-Rev3 3-digit level elaticitie computed for the period for the US. I aggregate thee elaticitie to the 2-digit level by averaging over all relevant indutrie. The SITC-Rev2 and SITC- Rev3 code are very imilar at the 2-digit level. Since elaticitie tend to decreae with the level of aggregation, thi procedure i likely to generate elaticitie which are omewhat too high. I have therefore alo experimented with the elaticity etimation technique uggeted by Caliendo and Parro (2011). However, my tari data doe not contain enough variation for thi technique to deliver igni cant reult. The political economy weight are contructed baed on the etimate of Goldberg and Maggi (1999) for the US. Their Table B1 provide a lit of unorganized indutrie at the SIC 3- digit level which I aggregate to the SITC-Rev2 2-digit level uing the ame concordance I ued for the US hipment data. I then rank the SITC-Rev2 2-digit level indutrie by how many unorganized SIC 3-digit level indutrie they contain and impoe the hare of unorganized indutrie from Table B1. I nally et i = 1 = in all organized indutrie and i = 0 in all unorganized indutrie, where = 0:9837 i the average "implied " from their Table 1. I apply the ame political economy weight in all countrie. I focu on 7 region and 26 manufacturing indutrie. The 7 region are Brazil, China, the EU, India, Japan, the US, and a reidual Ret of the World and are choen to comprie the main player in recent GATT/WTO negotiation. The 26 manufacturing indutrie are all SITC-Rev2 2-digit manufacturing indutrie other than thoe from ection 8 ("Micellaneou manufactured article"). I drop the manufacturing indutrie from ection 8 only to omewhat 24