Gravity, Bilateral Agreements, and Trade Diversion in the Americas*

Transcription

1 Cuadernos de Economía, Vol. 46 (Mayo), pp. 3-31, 2009 Gravty, Blateral Agreements, and Trade Dverson n the Amercas* Raymond Robertson Macalester College Anton Estevadeordal Inter-Amercan Development Bank Krshna (1998) shows that a blateral agreement between two countres render a multlateral agreement less attractve f the blateral agreement s trade dvertng. Ths paper combnes Krshna s model wth the emprcal approach of Anderson and van Wncoop (2003) to show that the estmated effect of tarffs n a multple country (n>3) context over tme measures trade dverson. We apply ths measure to new asymmetrc, tme-varyng Latn Amercan trade and tarff data usng Anderson and van Wncoop s (2003) nonlnear estmaton approach and OLS. The results show an ncrease n trade dverson as sub-regonal trade agreements prolferated and enthusasm for the Free Trade Agreement of the Amercas declned. JEL: F02, F13, F15 Keywords: Gravty Models, Asymmetrc Tarffs, Trade Dverson 1. Introducton The 2005 Summt of the Amercas adourned wthout settng a date for further negotatons for the Free Trade Agreement of the Amercas (FTAA). Whle the FTAA may be resurrected, t s clear that enthusasm for the agreement has declned precptously from 1995, when the FTAA negotatons began. At the same tme, blateral agreements have prolferated throughout the Amercas, rasng the * The authors thank James Anderson, Scott Baer, Davd Hummels, and the anonymous referees for very helpful dscussons and Erc van Wncoop for sharng programs and data. The authors are solely responsble for the content of the paper, and the deas expressed heren do not necessarly reflect those of the Inter-Amercan Development Bank. The authors thank Coln Hottman for excellent research assstance. Emal: robertson@macalester.edu

2 4 Cuadernos de Economía Vol. 46 (Mayo) 2009 possblty that blateral agreements are stumblng blocks for multlateral accords 1. The queston of whether blateral agreements are buldng blocks or stumblng blocks remans at the heart of the ntegraton polcy debate, and theory suggests that one key dfference between these two outcomes s trade dverson: the degree to whch blateral agreements hnder multlateral negotatons depends on the extent of trade dverson created by the blateral agreements. Unfortunately, there are few (f any) effectve and practcal measures of trade dverson n the multcountry context. Measurng trade dverson s mportant for polcy for two reasons. Frst, as noted above, trade dverson makes multlateral agreements less attractve. Second, trade dverson s generally consdered to be a rsk of blateral agreements because t s economcally neffcent. Multlateral agreements avod ths neffcency, makng the polcy choce between blateral and multlateral agreements both relevant and dependent on beng able to measure trade dverson. Our paper makes two man contrbutons. The frst s a measure of trade dverson that can easly be appled to the mult-country context. We begn wth Krshna s (1998) theoretcal poltcal economy model, whch suggests that blateral agreements can reduce the ncentves to pursue multlateral negotatons n the presence of trade dverson. Implct n hs model s a metrc for trade dverson that can be emprcally appled to a mult-country envronment by adaptng Anderson (1979) and Anderson and van Wncoop (2003, henceforth AW). AW shows the mportance of multlateral resstance measures n emprcal studes. Trade between two countres, after controllng by sze and other varables, s decreasng n ther blateral trade barrer relatve to the average barrer of the two countres to trade wth all ther partners. Whle AW focus on the omtted varable bas that comes from gnorng multlateral resstance, we show that ncorporatng multlateral resstance can generate an alternatve emprcal metrc for trade dverson that matches Krshna s (1998) framework. Our second contrbuton s the applcaton of ths approach to a new and unque data set on tarff rates. Studes of trade dverson have tradtonally focused on dscrete events, such as the entry nto force of a trade agreement 2. Rose (2004), n partcular, fnds that the World Trade Organzaton (WTO) has had very lttle, f any, effect on trade other than that generated from tarff changes. These results suggest that focusng on tarffs s a more approprate way to focus on the effects of trade agreements. Relatvely few, however, have attempted to analyze the effects of preferental trade lberalzaton because the data requrements are consderable. To get the approprate tarff data, one must examne each preferental trade agreement and record the tarff phase-n schedule, whch s how we constructed the data used n ths paper. 1 For examples of ths debate, see Ether (1998a, 1998b) and Krueger (1995). 2 Promnent examples nclude Romals (2001), who focuses on AFTA, and Rose (2004), who focuses on the WTO.

3 Gravty, Blateral Agreements, and Trade Dverson 5 We ground our emprcal work by explctly ncorporatng asymmetrc tarff barrers nto the famlar gravty model, followng some recent emprcal attempts to drectly measure trade costs (Hummels, 2001a; Lmao and Venables, 2001). Our data allow us to take advantage of the asymmetrc nature of preferental tarffs among members of a preferental trade area n order to employ and enhance AW s non-lnear estmaton approach. Baer and Bergstrand (2005), however, suggest that the OLS estmates are suffcent. We therefore use both approaches. The AW results have a smaller varance over tme than the OLS estmates, but both approaches suggest rsng trade dverson. Combnng these theoretc advances wth a newly-constructed data set generates an approach that s ntutvely straghtforward. Fallng average tarffs, such as through pursung certan blateral agreements, ncreases the trade-reducng effect of the remanng tarffs. Ceterus parbus, a blateral agreement ncreases the dfference between a country s average tarff and the remanng tarffs. The trade dverson that drves Krshna s (1998) model emerges as an ncreasngly negatve estmated effect of remanng tarffs. That s, the remanng tarffs appear to become more effectve at blockng trade as the blateral agreement dverts trade from the pars outsde the agreements. The Latn Amercan experence between 1985 and 1997 provdes an excellent opportunty to evaluate the lnk between blateralsm and multlateralsm for two man reasons. Frst, negotatons for the Free Trade Agreement of the Amercas, expected to have been completed n 2005, have bogged down. Smultaneous negotatons for blateral agreements have been generatng what has come to be known as the spaghett bowl of blateral agreements and reductons n preferental tarff rates. In few places has the queston of whether blateral agreements hnder or help multlateral trade negotatons been as relevant for polcy as n Latn Amerca over the last 15 years. Second, concentratng on a geographcally defned regon allows us to focus on the tarff effects and abstract somewhat from the multlateral resstance effects of dstance. Fnally, havng asymmetrc tarff rates offers us the chance to make two addtonal contrbutons. Frst, whle the maorty of the lterature uses average tarff rates under the assumpton that tarff rates are bascally symmetrc, we show that, whle trade flows are generally symmetrc, tarff rates generally are not. Second, employng asymmetrc tarffs also allows us to estmate the elastcty of substtuton of goods between countres a crtcal, but rarely estmated, parameter n many theoretc trade models. Our study unfolds n sx remanng sectons. In Secton 2 we present our data, dscuss trade lberalzaton n the Amercas, and hghlght the mportance of asymmetry n tarff data. In Secton 3 we show how we combne Krshna and AW s theoretc approaches. In Secton 4 we descrbe our estmaton approach. Secton 5 contans our results and we explore robustness n Secton 6 before concludng n the fnal secton.

4 6 Cuadernos de Economía Vol. 46 (Mayo) Data and Stylzed Facts 2.1 Summary Statstcs The maor data collecton effort of ths paper nvolved constructng the preferental blateral tarff rates for all possble blateral relatons among the 29 countres ncluded n our sample from orgnal sources, n addton to the mostfavoured-natons (MF) rates that each country apples to the rest of the world. The dataset used n ths study covers the perod from 1985 to 1997 and the followng countres: Argentna, Bolva, Brazl, Colomba, Chle, Ecuador, Mexco, Paraguay, Peru, Uruguay, Venezuela, Japan, the Unted States, Canada, and the European Unon. The standard gravty varables come from standard sources n the gravty lterature, and n partcular from Andrew Rose s webste. We have complemented these data wth trade data from Unted atons COMTRADE database. All MF tarff data have been collected from offcal natonal statstcal sources and regonal ntegraton secretarats. All preferental tarff data have been collected drectly from orgnal tarff schedules from regonal and blateral trade agreements (recprocal and non-recprocal) sgned and mplemented durng the perod under study. It ncludes blateral and regonal agreements sgned under the Latn Amercan Integraton Assocaton (LAIA) framework; AFTA agreement and other non-recprocal agreements wth the Unted States and the European Unon. Table 1 contans the lst of countres ncluded n the data and some summary statstcs. Several features deserve menton. As the lst of countres shows, we focus on Latn Amerca but nclude Canada, the Unted States, Europe, and Japan. The data exhbt the typcal gravty model data characterstcs n the sense that larger and closer countres trade more. Table 1 contans the average ad-valorem tarff rate, but we use log(1+tarff), -n whch a 10% tarff would be n our estmaton. Due to our sample perod, the tarff rates European countres have for each other and mpose on non-european countres are dentcal for all countres wthn the European Unon. We dscuss the evoluton of tarffs n Latn Amerca n the next secton. 2.2 Trade Lberalzaton n the Amercas Between 1985 and 1997, blateral and sub-regonal trade agreements prolferated throughout the Amercas. Fgure 1 llustrates what s now known as the Spaghett Bowl of regonal trade agreements. These agreements were often accompaned by unlateral trade lberalzaton. Our data cover ths perod of lberalzaton and the phase-n perod. The data from our sample show fallng smple average tarff rates (Fgure 2). The declne begns n Average tarffs fall dramatcally durng the perod before levelng out around Ths declne n smple average tarffs reflects fallng MF tarff levels as well as fallng preferental tarffs ncorporated n blateral agreements. Fgure 3 shows the MF tarff rates separately from the preferental tarff rates. The prolferaton of blateral agreements and fallng average tarffs s evdent n Fgures 2 and 3.

5 Gravty, Blateral Agreements, and Trade Dverson 7 TABLE 1 SUMMARY STATISTICS Exportng Country Mean Log Trade Mean Log GDP Mean Tarff St. Dev. Tarff Mean Dstance Argentna Austra Bel-Lux Bolva Brazl Canada Chle Colomba Germany Denmark Ecuador Span Fnland France Great Brton Greece Ireland Italy Japan Mexco etherlands Peru Portugal Paraguay Sweden Uruguay Unted States Venezuela otes: Trade and Gross Domestc Product (GDP) are measured n U.S. dollars. The tarff s the average ad valorem tarff rate, and the standard devaton (St. Dev.) of the tarff rate s over tme and country. These averages are over all countres and all years Dstance s measured n klometers. Source: Inter-Amercan Development Bank based on offcal natonal sources. Blateral and sub-regonal agreements are, by defnton, exclusve. The result of these agreements that dffers from multlateral agreements s that the dfference between the maxmum tarff and the mean tarff rses wth blateral agreements. If multlateral resstance matters, then ths suggests that, effectvely, the remanng tarffs (for countres not ncluded n the agreement) effectvely rse (relatve to the mean). Ths s exactly what happened n the Amercas, as shown n Fgure 4. Fgure 4 shows both the standard devaton of mporter tarff rates and the average dfference between the mean and maxmum tarff. Both rse as the mean tarff falls. The multlateral resstance concept, as descrbed by the theory

6 8 Cuadernos de Economía Vol. 46 (Mayo) 2009 FIGURE 1 THE SPAGHETTI BOWL OF TRADE AGREEMETS I THE AMERICAS Frst-generaton agreement Second-generaton agreement Customs Unon (CU) ALADI CACM Canada-CA-4 caragua Costa Rca USA-CACM FTAA Mexco USA Canada Agreement under negotaton Recprocal agreement: CU-Country on-recprocal agreement: CU-Country Bahamas Hat USA-Chle MERCOSUR Uruguay Paraguay Brazl Argentna El Salvador Honduras Guatemala Chle Domncan Republc Panama CARICOM Trndad & Domnca Surname Tobago Jamaca St. Luca Belze St. Ktts & evs Grenada Barbados Guyana St. Vncent & Grenadnes Antgua & Barbuda Colomba Venezuela Peru Ecuador AC Bolva ALADI Source: Inter-Amercan Development Bank based on offcal natonal sources.

7 Gravty, Blateral Agreements, and Trade Dverson FIGURE 2 SIMPLE AVERAGE TARIFF RATES 0.12 Mean Tarff Year otes: Ths fgure shows the smple (unweghted) annual average of the log of the tarff rate plus one n the data used n the emprcal work. Source: Inter-Amercan Development Bank based on offcal natonal sources. 50 FIGURE 3 PREFERETIAL AD MF TARIFF RATES I LATI AMERICA (Percent) MF TARIFFS FOR ELEVE LATI AMERICA COUTRIES Preferental tarffs for eleven Latn Amercan countres wth respect to other 1 Regonal Integraton Agreements (RIA) partners n the regon ote: The countres ncluded are Argentna, Bolva, Brazl, Chle, Colomba, Ecuador, Mexco, Paraguay, Peru, Uruguay and Venezuela. Calculatons nclude only ad valorem tarffs. Source: Inter-Amercan Development Bank based on offcal natonal sources.

8 10 Cuadernos de Economía Vol. 46 (Mayo) 2009 FIGURE 4 TARIFF DISPERSIO Std. Dev. Tarff Max to Mean Tarff Rato Std. Dev. Tarff Max to Mean Tarff Rato Year otes: The standard devaton lne graphs the annual average of the standard devaton of the log of one plus the tarff rate wthn mportng countres. The Max to Mean rato graphs the annual average of the maxmum tarff dvded by the mean tarff wthn mportng countres. Source: Inter-Amercan Development Bank based on offcal natonal sources. above, suggests that the rsng dfference between average tarffs and the maxmum tarff also affects trade between an mporter and the country facng the maxmum tarff even f the maxmum tarff does not change. 2.3 Asymmetry One contrbuton of ths paper s that t ncorporates asymmetrc tarff varables. Trade patterns are generally symmetrc: countres that export a lot to a partner generally mport a lot from that partner. Ths s true for our entre sample. Fgure 5 llustrates ths pattern for 1997 wth a graph of country s exports and trade partner country s exports. The resultng coeffcent (standard error) of the mpled smple regresson s (0.025) wth an adusted R 2 of One country s exports to a gven partner explan about 80% of the varaton of partner exports to the frst country. Ths graph ndcates that total trade s a very good proxy for unlateral trade. Tarffs, n contrast, are generally not symmetrc. Fgure 6 llustrates ths pont for 1997 n whch one country s tarffs explan less than 40% of the varaton

9 Gravty, Blateral Agreements, and Trade Dverson FIGURE 5 THE SYMMETRY OF TRADE Ftted Values 45 degree lne Exports Country Log Exports Country otes: The y-axs measures the log of exports for country s tradng partner for The ftted values lne s the predcted value of an OLS regresson of the exports of country on country s exports. The resultng coeffcent (standard error) of that regresson s (0.025) wth an adusted R 2 of Source: Inter-Amercan Development Bank based on offcal natonal sources. n ther partner s tarffs towards them 3. The symmetry of tarffs ncreases over our sample. Pror to 1990, one country s tarffs explan less than 1% of the varaton n the partner s tarffs. The mplcaton of ths asymmetry s that average trade barrers ntroduce possbly sgnfcant measurement error when they are used as proxes for partnerspecfc tarffs. Ths measurement error would result n attenuaton bas, basng the estmated effects of tarffs towards zero, suggestng that the lterature that reles on average tarffs underestmates the real mpact of tarffs. Ths result also hghlghts the mportance of asymmetrc tarffs. As the theory n the next secton shows, the estmated effect of these asymmetrc tarffs measures trade dverson. 3. Theory Krshna (1998) employs a Cournot model to show that a blateral agreement between two countres can make lberalzng wth a thrd country (formng a multlateral agreement) less attractve f the blateral agreement s trade dvertng. 3 The resultng coeffcent (standard error) of the tarff regresson s (0.040) wth an adusted R 2 of

10 12 Cuadernos de Economía Vol. 46 (Mayo) FIGURE 6 THE ASYMMETRY OF TARIFFS Ftted Values 45 degree lne Tarffs Country Tarff Rate Country otes: The x-axs (y-axs) measures the log of one plus the tarff rate for country (country, country s tradng partner) for The ftted values lne s the predcted value of an OLS regresson of the log of one plus the tarff rate of country on the log of one plus country s tarff rate. The resultng coeffcent (standard error) of that regresson s (0.040) wth an adusted R 2 of Source: Inter-Amercan Development Bank based on offcal natonal sources. One of AW s man nsghts s that the concept of multlateral resstance affects trade patterns. In ths secton, we combne these contrbutons to llustrate how the multlateral resstance concept can be appled to Krshna s basc approach to generate a metrc of trade dverson. We begn wth the smplest form of a Cournot model 4. Consder three countres, 1, 2, and 3. Defnng exports from country as q and the constant margnal producton cost n country as g, assume that 2 s demand for mports s smple and lnear: P=1-Q n whch Q=q 1 +q 3. The Cournot soluton for 2 s demand for mports from each country s then 1-2g1 + g3 (1) q1 = 3 1-2g3 + g1 q3 = 3 4 Snce ths presentaton s smply llustratve, we assume homogeneous goods, zero transportaton costs, and benevolent governments, and abstract almost entrely from the consumpton sde and domestc producton.

11 Gravty, Blateral Agreements, and Trade Dverson 13 FIGURE 7 CROSS-TARIFF EFFECTS I A SIMPLE 3-COUTRY COUROT MODEL Demand for mports from Tarffs on Tarffs on otes: If country 2 mposes tarffs on countres 1 and 3 that are smply added to the producton cost from each country ( g 1 and g 3 ), the demand for mports ( P*q1 ) from 1 as a functon of tarffs on 1 and tarffs on 3. Source: Inter-Amercan Development Bank based on offcal natonal sources. Tarffs that country 2 mposes on each tradng partner can be modeled as a smple ncrease n margnal producton costs. Thus, the trade-reducng effect of a tarff that country 2 mposes on country 1, for example, s a functon of the tarff that country 2 mposes on country 3. That s, the effect of the tarff on blateral trade s a functon of the multlateral resstance that s represented here as country 2 s tarff on all other countres (whch, n ths case, ncludes ust country 3). Fgure 7 graphs the effects of country 2 s mports from country 1 as a functon of 2 s tarffs on mports from countres 1 and 3. When tarffs on mports from 3 are zero, hgher tarffs on country 1 cause mport (values) to fall, as the lne n the facng plane (n the {trade,t1} space) shows. The effect of the tarff on mports from 1, however, s affected by 2 s tarff on country 3. Hgher tarffs on mports from 3 reduce the trade-suppressng effect of tarffs on 1, whch s due to the trade dvertng effect of 2 s tarffs on 3. Hgher tarffs on country 3 dvert trade from 3 to 1, makng the tarff on 1 s exports less effectve. Krshna s (1998) nsght s that trade dverson that occurs from blateral tarff changes (e.g. through a blateral trade agreement) reduce the gans from extendng the agreement to thrd partes. Ths result s evdent n Fgure 7, and t llustrates both that the estmated effect of blateral tarffs can reflect trade dverson and the mportance of focusng on multlateral resstance measures n emprcal estmates of the effects of tarffs.

12 14 Cuadernos de Economía Vol. 46 (Mayo) 2009 The standard emprcal tool used to analyze trade volumes s the gravty model. The gravty model has a rch hstory and has recently experenced an mportant resurgence (e.g. Evenett and Keller 2002, Hanson and Xang 2004). AW show that multlateral resstance can be easly ncorporated nto the gravty model. Ther theoretc focus s on trade costs, whch, n ther emprcal work, ustfes a focus on the effects of dstance. Here we focus on tarff component of trade costs. Followng AW, a theoretcally correct representaton of the gravty model begns wth the assumpton that all goods are dfferentated by place of orgn. Ths assumpton suggests that each country produces only one good. Snce we are nterested n aggregate goods flows, ths assumpton provdes a reasonable startng pont. The second assumpton s that consumers have dentcal, homothetc preferences that can be approxmated wth a CES utlty functon. AW, for example, specfy the followng functon for consumers n country consumng goods c from country : /( 1) ( ) (2) ( 1 β σ )/ σ ( c σ 1)/ σ σ σ whch s maxmzed accordng to the budget constrant (3) pc = y Defne σ as the constant elastcty of substtuton between goods from each country, β as a postve consumpton weght (summng over to one), p as the prce of regon goods n country, and fnally y as the nomnal ncome of consumers n country. Maxmzng (2) subect to (3) generates the followng demand 5 for country goods n country : (4) z = 1 y( βp ) ( βp ) σ n whch z = pc represents country s mports from country. Snce our focus s on tarffs, we next assume that tarffs are the only factors that affect the prce (we ncorporate dstance shortly) and allow ncomplete pass through from tarffs to prces captured by the coeffcent η. (5) p = pt η 5 The complete dervaton s ncluded n the Appendx.

13 Gravty, Blateral Agreements, and Trade Dverson 15 We then follow Anderson (1979) and Deardorff (1998) who complete the dervaton by notng that market clearance mples that each country s ncome s equal to the sum of the producton shpped to each country, (6) y = z. Defnng world ncome as y leads to w = y and ncome shares as θ = y / y w (7) z = yy w y η t QP n whch 1/( ) η θ 1/( ) 1 σ ) (8) Q ( t / P ) P = ( ( βp ) = ( ) Our focus s not only on tarff levels, but the evoluton of tarffs over tme. Thus, we assume that dstance s a fxed cost that acts as a demand shfter rather than a varable that causes a movement along the demand curve. Although dfferng somewhat from the current lterature, we thnk ths s a reasonable nterpretaton of the effects of dstance n our context for several reasons. Frst, dstance s symmetrc and constant over tme 6. Second, countres that are far apart wll consstently buy less from each other regardless of temporal devatons n prce. That s, dstance s less lkely to cause a movement along the demand curve than a shft n the curve. Thrd, treatng dstance as a demand shfter allows us to focus on the effects of tarffs and to estmate the elastcty of substtuton drectly (as AW cannot do, but note s possble wth asymmetrc tarff data). We therefore defne mports as exports mnus a transportaton cost 7 (the tradtonal ceberg assumpton): 6 Shppng costs may be nether constant nor symmetrc (see Hummels 2001b). In fact, t s lkely that they have declned over the long run. We therefore allow the effect of dstance to change over tme n our emprcal work. 7 We worred about the fact that we exclude the effects of average dstance n ths specfcaton because ths was one of the key contrbutons of AW. As we show n the robustness secton, however, smlar results emerge when the average dstance varables are ncluded n OLS regressons. We beleve that ths may be due to the fact that we focus on the Amercas, whch are geographcally concentrated countres, and that we focus on the effects over tme. Our solver refused to produce estmates when average dstance was ncluded multplcatvely wth tarffs, whch dd not bother us too much because, as Hummels (2001b) ponts out, the nterpretaton of results generated by multplyng dstance and tarffs seems problematc.

14 16 Cuadernos de Economía Vol. 46 (Mayo) 2009 FIGURE 8 CROSS-TARIFF REDUCTIO EFFECTS 2.5 Flows from 1 to Country 2 tarffs on Country 2 tarffs on 3 otes: Results from a four-country smulaton of the derved demand system n (7) and (8) n whch η, y, y, and y w are set to one. A smple 3-country Cournot model, such as that postulated by Krsha (1998), exhbts smlar propertes. See Fgure 1. Source: Inter-Amercan Development Bank based on offcal natonal sources. α (9) ln z = ln x ln( d ). Combnng (7) and (9) and takng natural logs of both sdes gves us our gravty model: (10) ln x = ln y + ln y ln y + α ln d + w + ( 1 σ) ηln t ( )ln Q ( )ln P Ths specfcaton suggests that both the level and overall average of tarffs affect trade volumes. Ths multlateral resstance approach suggests that not only do blateral tarffs matter, but they matter when compared to average tarff levels. Ths result suggests an alternatve metrc for trade dverson. When two countres enter nto a trade agreement and trade between them rses whle trade between other partners falls, the tarffs that agreement countres have on thrd partes become more effectve. To llustrate ths pont, we calbrate the demand system (7)-(9) above for four countres (1,2,3,4) and examne how a reducton n 2 s tarff on 3 affects the trade between 2 and 1 for a range of 2 s tarffs on country 1 s goods. The results are shown n Fgure 8. ot surprsngly, Fgure 8 s very smlar to Fgure 7. As 2 s

15 Gravty, Blateral Agreements, and Trade Dverson 17 tarffs on 1 fall, trade between 1 and 2 ncreases, as expected. The trade-reducng effect of any gven tarff 2 mposes on 1, however, depends on the tarff 2 mposes on 3. As 2 reduces tarffs on 3, trade between 1 and 2 falls and 2 s tarffs on 1 become more effectve n the sense that, at any gven tarff level, trade s lower. The ntuton s very straghtforward. In both the AW and Krshna models, lower tarffs on 3 cause 3 s exports to 2 to rse and 1 s exports to 2 to fall: trade s dverted from 1 to 3. The real effects of tarffs are therefore dependent on average tarffs, or the multlateral resstance generated by other tarffs. The changng effect of asymmetrc specfc tarffs therefore offers a metrc of trade dverson. Ths metrc of trade dverson dffers from other recent nnovatons n the lterature. Romals (2002) examnes trade dverson by lookng at how trade between Mexco, the Unted States, and Canada changed followng the orth Amercan Free Trade Agreement (AFTA) by comparng trade between these countres and trade wth Europe. Ths s a novel approach and works well when one wants to focus on a trade agreement. In the Amercas, most blateral agreements have prolonged phase-n perods that suggest that focusng on asymmetrc tarffs s mportant. 4. Estmaton Strategy Our basc strategy begns by specfyng a stochastc form of (10): (11) ln x = k + ln y + ln y + αln d + ( 1 σ) η ln t ( )ln Q ( 1 σ)ln P + e AW suggest that the most theoretcally consstent approach to estmatng these parameters would be to fnd the η, σ, α, and a constant term k, that solve the followng nonlnear optmzaton problem 8 : (12) mn ΣΣ( ln x k ln y ln y α ln d ( 1 ση ) ln t + k, αση,, subect to (13) Q ( t / P ) P = ( t / ) + ( 1 σ)ln Q + ( ) ln P ) 2 1/( ) η θ 1/( ) η ( ) = ( ) 8 The second condton dffers from (8) because we substtute (5) and assume that goods are evenly weghted across countres (the betas are dentcal for all countres and sum to one).

16 18 Cuadernos de Economía Vol. 46 (Mayo) 2009 Baer and Bergstrand (2005) argue that the nonlnear optmzaton approach s unnecessary when usng the gravty model to resolve the border puzzle and other ssues. Ther dervaton, however, lke AW, assumes symmetrc trade costs. When tarffs are asymmetrc, as n our case, t s not clear that ther OLS approach s smlar to the nonlnear optmzaton approach. In the results secton, we begn wth results generated from solvng ths problem and then compare the solver results wth those generated by unconstraned and constraned OLS and show how the estmates of the tarff effect change when average tarffs (and other varables) are added. 5. Emprcal Results Table 2 contans the results from the mnmzaton problem descrbed n (12) and (13). Our data range from , and we calculated parameter estmates for each year by solvng (12) and (13) separately for each year. Lke AW, we do TABLE 2 SOLVER ESTIMATES Year k constant α dstance σ elast. sub. η tarffs otes: Tarff coeffcents and ther standard errors were also calculated usng bootstrappng. The coeffcents were found to ncrease over tme, rangng from to The standard errors also ncreased over tme, rangng from to Source: Own estmatons.

17 Gravty, Blateral Agreements, and Trade Dverson 19 not report standard errors for our estmates 9. Several nterestng results emerge from Table 2. The elastcty of substtuton estmates are greater than one n all years. The dstance estmates are negatve (as expected), rse (n absolute value) between 1985 and 1990, and fall (n absolute value) between 1990 and Wth the excepton of 1985, all of the estmates of the effects of tarffs are negatve. The tarff estmates are generally n the range of, albet on the hgh sde, estmates found elsewhere n the lterature. Unlke the dstance estmates, they ncrease (n absolute value) after The growng effect of tarffs over tme s consstent wth the dea of growng trade dverson. The absolute values of the tarff effect are larger after 1990, the year that many of these blateral agreements began to go nto effect, than n the years To the extent that Krshna s model apples to the Amercas, these results are consstent wth rsng trade dverson contrbutng to the fallng enthusasm for the FTAA. In addton to the annual estmates, the table also contans results from solvng the model wth pooled data. We solved the model poolng data over , , , , and 1997 to get an dea of the senstvty to changes n sample perod. Lke the earler results, the estmated tarff effect rses consstently between 1988 and 1997, whch, agan, s consstent wth rsng trade dverson. 6. Robustness Our estmaton approach follows AW, but dverges somewhat from the gravty model lterature that generally reles on cross secton and/or OLS estmaton. To explore the robustness of our estmaton approach and results, we also present cross-secton and panel OLS estmates. The gravty model that s more lkely to be found n the lterature mght look somethng lke: (14) ln x = k + β1ln y + β2ln y + β3ln d + β4 ln t + β5 Φ t + e n whch β 5 s actually a vector of parameters that reflect the effects of the varables contaned n Φ. These varables may nclude controls for common borders, languages, or other characterstcs, but has not tradtonally contaned controls for average tarff levels. One mportant dfference between ths specfcaton and equaton (11) s the nterpretaton of the coeffcent on the tarff varable. In most of the gravty model lterature that ncludes tarff estmates, the coeffcent on tarffs n equaton (14) s nterpreted as the drect effect of tarffs (that s, as η). Wthout the approprate multlateral resstance terms and correspondng theoretcal foundaton, most gravty specfcatons abstract from the elastcty of substtuton component. In the solver approach, however, t s possble to separate the two terms. In the 9 One reason the gravty model s so heavly used s that statstcal sgnfcance of the man varables s rarely an ssue. Our OLS estmates, descrbed n the next secton, show no cause for concern about statstcal sgnfcance.

18 20 Cuadernos de Economía Vol. 46 (Mayo) 2009 results that follow, we follow the conventon n the gravty lterature (for the sake of comparablty) and nterpret β 5 as η. Table 3 contans the results from 5 dfferent gravty specfcatons. All fve columns contan OLS estmates usng the log of exports as the dependent varable. For these results, we pooled data from 1985 to We begn wth the most basc, column (1), specfcaton that ncludes (natural logs of) the tarff rate (1+tarff), dstance, the GDP of each partner (mporter and exporter), and a constant term. In the second column we add dummy varables that tradtonally appear n gravty models that account for a common border, ether beng landlocked, ether beng an sland, and havng a common language. In the thrd column we exclude these dummy varables but nclude the average tarff rate of each country. In the fourth column, we nclude both the average tarff rates of each country and the tradtonal dumme varables. The fnal column excludes these tradtonal varables but adds the average dstance to the rest of the world for each country. The results n the frst column seem to suggest the mportance of the excluded multlateral resstance measures. The estmates of dstance and the GDP of each country are consstent wth pror expectatons, but the tarff effect s postve. When the tradtonal gravty model varables are ncluded n column (2), the tarff effect becomes negatve, as expected, perhaps suggestng that these varables are correlated wth the country-specfc effects of average tarffs and therefore may pck up some of ther effect. ote that ther ncluson has lttle effect on the other varables and, wth the excepton of beng an sland, they all are statstcally sgnfcant. When we replace the tradtonal varables wth the average tarff rate, we fnd an estmate of the tarff effect that s much larger (n absolute value) than our solver estmate, whle, agan, our other estmates change lttle. Includng the tradtonal gravty varables wth our average tarff rate generates a stll larger estmate of the tarff effect but has only a small effect on the average tarff effect estmates, as seen n column (4). Fnally, column (5) shows that a smlar tarff effect estmate emerges when we nclude the average dstance measures along wth the average tarff measures. The man pont from ths table s that multlateral resstance measures matter n the sense that ncludng them affects the tarff effect estmates. In addton to multlateral resstance, theory also mples several constrants. Movng closer to theory, Table 4 contans the constraned OLS estmates n four columns. In the frst column, we constran the coeffcent on the ncome terms to equal one. In the second column, we constran the coeffcents on the average tarff varables to be equal to each other. In the thrd column, we constran the ncome coeffcents to equal one and nclude country specfc (not par specfc) fxed effects 11. In the last column, we constran the ncome varables to one and the average tarff varable coeffcents to equal each other. 10 Ths perod s chosen to be comparable wth the pooled solver results. We also dscuss year-byyear results shortly. 11 We do not nclude par-specfc fxed effects for several reasons. Frst, the theory suggests that the multlateral resstance measures are country-specfc, mplyng country-specfc fxed effects. Second, perhaps not surprsngly, we do not get sgnfcant estmates when ncludng par-specfc fxed effects, snce the par-specfc fxed effects results are dentfed from purely tme-seres varaton, whch s not strctly consstent wth theory.

19 Gravty, Blateral Agreements, and Trade Dverson 21 Dependent varable: logarthm of exports TABLE 3 CROSS SECTIO ESTIMATES (1) Base (2) Common (3) Multlat. (4) Mult and Common (5) Multlat. Dst. Log(1+(Tarff/100)) (0.129)*** (0.132)** (0.792)*** (0.790)*** (0.859)*** Ln Dstance (0.013)*** (0.015)*** (0.021)*** (0.023)*** (0.024)*** Ln Real Gdp Exporter (0.007)*** (0.007)*** (0.007)*** (0.007)*** (0.007)*** Ln Real Gdp Importer (0.007)*** (0.008)*** (0.007)*** (0.007)*** (0.007)*** Common Border (0.048)*** (0.048)*** Ether Is Landlocked (0.032)*** (0.032)*** Ether Is An Island (0.030) (0.029) Common Language (0.030)*** (0.030)*** Log Avg Exp Tarff (0.353)*** (0.341)*** (0.359)*** Log Avg Imp Tarff (0.770)*** (0.759)*** (0.858)*** Ln Avg Dst Reporter World (0.067)*** Ln Avg Dst Partner World (0.075)* Constant (0.157)*** (0.181)*** (0.215)*** (0.241)*** (0.812)*** Observatons 9,709 9,709 9,709 9,709 9,709 R-squared otes: Standard errors n parentheses. *, **, *** sgnfcant at 10%, 5% and 1% respectvely. Source: Own estmatons. The results n the frst column suggest that ust constranng the ncome terms to equal one generates larger tarff effects to those generated wth the solver. The average tarff coeffcents suggest elastctes of substtuton that are close to those generated from the solver 12. Constranng the average tarff coeffcents to be equal generates a somewhat smaller tarff effect. The dstance coeffcent s not affected by the change n constrants. 12 Based on the Q and P coeffcents n equaton (10), f b s the coeffcent estmate and s s the elastcty of substtuton, then b=-(1-s), mplyng a range of estmates of the elastcty of substtuton of to

20 22 Cuadernos de Economía Vol. 46 (Mayo) 2009 TABLE 4 COSTRAIED CROSS SECTIO ESTIMATES (1) Income (2) Multlat (3) Fxed FX (4) All Cons Log(1+(Tarff/100)) (0.810)*** (0.404)*** (0.145) (0.410)*** Ln Dstance (0.021)*** (0.015)*** (0.012)*** (0.015)*** Ln Real Gdp Exporter (0.007)*** Ln Real Gdp Importer (0.007)*** Log Avg Tarff Exporter (0.360)*** (0.338)*** (0.345)*** Log Avg Tarff Importer (0.786)*** (0.338)*** (0.345)*** Constant (0.176)*** (0.183)*** (0.123)*** (0.137)*** Observatons 9,709 9,709 9,709 9,709 otes: Standard errors n parentheses. *, **, *** sgnfcant at 10%, 5% and 1% respectvely. The frst column s regresson ncluded the constrant that the ncome coeffcents equal one. The second column s regresson constraned the average tarff coeffcents to be equal. The regresson n the thrd column ncludes country-specfc fxed effects and constrans the ncome coeffcents to equal one. The last column s regresson constrans the ncome coeffcents to equal one and the average tarff coeffcents to equal each other. Source: Own estmatons. When fxed effects are ncluded, however, the tarff estmate falls dramatcally to about 6% of the estmate n column (2). To the extent that ncludng the multlateral tarff resstance measures generates smlar estmates to those generated by the solver and these are closer to the correct estmates, the results n column (3) suggest that country-specfc fxed effects are a poor substtute for multlateral resstance varables when tarffs are asymmetrc. In the fnal column, we apply all three constrants (each ncome coeffcent s equal to one and the coeffcents on the average tarff varables equal to each other). The resultng estmate of the tarff effect s the estmate n Table 4 that s most smlar to the solver estmates. Changng the constrants and/or ncludng fxed effects seems to have lttle effect on the estmate of the dstance varable. One key dfference between the estmates presented n Tables 3 and 4 and the solver estmates s that the OLS estmates are not presented year-by-year. To nvestgate changes over tme, we pool the data over tme and nclude nteracton terms for each year between 1985 and 1997 (leavng out 1988 as the reference year). These years mrror Fgure 3 by capturng the dfferent perods of trade lberalzaton n the Amercas. The estmated coeffcents on the tarff-year nteractons suggest a growng negatve effect of tarffs over tme. The coeffcent on the 1997 nteracton term shows that the tarff effect n 1997 s statstcally sgnfcantly larger (n absolute