FREE TRADE AGREEMENTS IN A MODEL OF TRADE, MIGRATION AND POLITICS. May 22, 2016

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1 Prelmnary Comments Welcome FREE TRADE AGREEMENTS IN A MODEL OF TRADE, MIGRATION AND POLITICS by John Douglas Wlson Department of Economcs Mchgan State Unversty East Lansng, MI USA Ilkay Ylmaz Department of Economcs Mersn Unversty Cftlkkoy, Meztl 33342, Mersn Turkey May 22, 2016 ABSTRACT: Ths paper usng a probablstc votng model to nvestgate votng for a free-trade agreement between a labor-abundant country and a captal-abundant country. Immgraton from the labor-abundant country to the captal-abundant country ncreases the probablty of a freetrade agreement, wth lower mgraton costs leadng to more mmgraton and a hgher free-trade probablty. On the other hand, f a lower probablty of free trade s caused by an ncreased voter bas aganst free-trade canddates, then there s less mmgraton. A dynamc extenson of the model s also nvestgated. Acknowledgements: We thank semnar partcpants at the Unversty of Kentucky and Tulane Unversty for helpful comments and dscusson that led to the probablstc votng framework used n the current paper. Emal addresses: Wlson: wlsonjd@msu.edu; Ylmaz: lkay_y1240@yahoo.com

2 1 1. Introducton The purpose of ths paper s to use a poltcal economy approach to nvestgate a classc queston n nternatonal trade: Are goods and factor trade complements or substtutes? The modern lterature on ths queston starts wth Mundell (1957), who extends the Heckscher-Ohln trade model to nclude captal moblty and concludes that goods trade and factor moblty are substtutes. In partcular, Samuelson s factor prce equalzaton theorem mples that costless trade equalzes factor prces, whch elmnates ncentves for captal to relocate from one country to another. Mundell s contrbuton led to an outpourng of research that sought to endogenze captal moblty n the standard trade models, and Rchard Brecher has been a leader n ths area, wth mportant contrbutons ncludng Brecher (1983), Brecher and Feenstra (1983) and Brecher and Fndlay (1983). Markusen (1983) consders specfcally Mundell s clam that goods and factor trade are substtutes and argues that there can be a complementary relaton, partcularly n settngs where trade s based on scale economes or dfferences n producton technologes, rather than factor-endowment dfferences. Wong (1995) provdes an extended dscusson of the lterature on ths ssue, and Neary (1995) uses a specfc-factors framework to argue that goods and factor trade are lkely to be substtutes gven that nternatonally moble captal s used n a country s mport competng sector (p. S20), though the results are reversed when captal s used n the export sector. 1 More recently, Antras and Caballero (2009) modfy a North-South Heckscher-Ohln model by assumng that captal nvestment n one of the goods s lmted n the South by fnancal frctons. Internatonal trade 1 See also Svensson (1984) and Markusen and Svensson (1985), and Wong (1986). Wong (1995) descrbes the dfferent meanngs of substtutablty and complementarty. Throughout ths paper, we use these terms n a volume-of-trade sense.

3 2 allows the South to mport the good from the North. As a result, the return on captal rses n the South, mplyng a complementary relaton between trade and net captal flows. The analyss n the current paper also uncovers a complementary relaton between goods trade and factor moblty, but the model also produces a type of substtute relatonshp, dependng on what causes varatons n goods trade and factor movements. Unlke the lterature revewed above, ths relaton s not dependent on modfyng or replacng the Heckscher-Ohln model. Rather, we supplement ths model wth a poltcal economy model, n whch ctzens vote on whether to allow free trade. 2 The model uses the 2-country, Heckscher-Ohln framework developed by Levy (1997) to study the poltcal economy of free-trade agreements (FTAs). In hs model, a trade agreement s mplemented when a majorty of the ctzens vote to approve t. The assumptons of the medan voter theorem hold, so the polcy most preferred by the medan voter receves the majorty of votes. We nstead use a probablstc votng model. 3 Indeed, once we ntroduce factor moblty nto the model, uncertan decsons on free trade agreements become a crtcal aspect of the model. 4 The partcular factor moblty analyzed n ths paper s mmgraton from a lowwage, labor-abundant country to a hgh-wage, captal-abundant country. Ths mmgraton s costly, and can be nterpreted as llegal mmgraton, snce t s not subject to mmgraton 2 See Concon (2012) for a recent emprcal analyss of the poltcs of trade and mgraton. Facchn (2004) surveys the theory on the poltcal economy of trade and factor moblty. 3 The model s a smplfed verson of the probablstc votng model descrbed n Perrson and Tabelln 4 Our paper bulds on Ylmaz (2005, 2006), whch s based on hs Ph.D. thess. But he uses a medan voter model. Ths framework s not entrely satsfactory, because an equlbrum requres uncertanty n the outcome of the vote. The medan voter wll vote randomly f he s ndfferent between the polcy alternatves, but t s dffcult to justfy why hs votng probabltes are those that satsfy the equlbrum condtons for the model. The probablstc votng model provdes a mechansm by whch the equlbrum votng probabltes are acheved.

4 3 restrctons. As a result, there must be a postve beneft to offset ths cost. We lnk the decsons of voters n the captal-abundant country to mmgraton from the labor-abundant country (whch always prefers an FTA). The basc argument s that ths mmgraton hurts enough voters under autarky to ncrease the probablty that free trade wns the vote. Moreover, free trade causes mmgraton to stop, snce t leads to the equalzaton of factor prces between countres. The analyss demonstrates that more mmgraton, modeled as the result of reduced mgraton costs, causes more goods trade, suggestng a complementary relaton between goods trade and mmgraton. A smlar result s obtaned by Magg and Rodrguez-Clare (2007), but they use a model wth lobbyng, and factor moblty n the form of captal movements occurs only after the trade agreement has been approved. The basc dea s that captal moblty affects ncentves to lobby. Votng s not explctly modeled. 5 We also show, however, that a lower probablty of free trade, caused by an ncreased bas among voters for canddates who are opposed by free trade, leads to more mmgraton. The reason s that mmgrants decde that t s more lkely that the factorprce-equalzng effects of free trade wll occur. Ths result suggests a substtute relaton between goods trade and factor moblty: less trade leads to more factor moblty. Thus, the relaton between goods and factor trade depends on what s causng them to vary. Our analyss sheds lght on some mportant polcy questons. For example, f the Mexcan mmgraton had not occurred over the years before NAFTA, and f there were no threat of further (llegal) mmgraton, would NAFTA get enough support n the Unted 5 Facchn and Testa (2009) uses a medan voter framework to model why countres jon a free trade area, and they also emphasze the mportance of factor flows n FTA decsons, but these flows also occur only after the agreement.

5 4 States? In the European Unon context, could the possblty of possble further unwanted mgraton from Eastern Europe be one of the reasons some of these countres have joned the EU and others reman canddates for membershp? Our model suggests that mmgraton at least helps facltate these free trade agreements. The plan of ths paper s as follows. In the next secton, we descrbe the basc model. Secton 3 contans the man results. Secton 4 extends the model to nclude dynamc consderatons, and shows how mmgraton affects the tme lag before free trade occurs. Secton 5 provdes conclusons and dscusses other extensons. 2. The Model The model conssts of two countres, hgh-ncome and low-ncome, denoted by symbols H and L. Each country has fxed captal and labor endowments. The hgh-ncome country s captal-abundant and the low-ncome-country s labor-abundant, where abundance s measured by relatve factor endowments. Followng the Heckscher-Ohln model, compettve frms n each country use captal and labor to produce two goods, a labor-ntensve good, X, and a captal-ntensve good, Y. The producton technology for each good exhbts constant returns to scale n labor and captal, and ths technology s dentcal between countres. Both countres are ncompletely specalzed n the producton of X and Y. Consumer utlty functons contan X and Y as arguments, and are homothetc and dentcal between countres. Good Y s the numerare. The relatve prce of X s ph n the hgh-ncome country and pl n the low-ncome country. Under an autarky equlbrum, ph exceeds pl, snce the labor-abundant, low-ncome country produces more

6 5 X relatve to Y. As a result, the Stolper-Samuelson theorem mples that the real wage n the hgh-ncome country exceeds the real wage n the low-ncome country. Followng Levy (1997), we assume that there s no trade n the absence of a freetrade agreement. In other words, effectve tarff rates are prohbtve n the absence of free trade. Wth an agreement, the factor-prce equalzaton theorem mples that free trade equalzes not only product prces, but also factor prces. By the Heckscher-Ohln theorem, the low-ncome country mports Y from the hgh-ncome country and exports X to the hghncome country. We shall sometmes refer to free trade n goods as economc ntegraton, but the equalzaton of factor prces mples that free factor moblty would have no real effects followng a free-trade agreement. Indvduals n each country possess dfferent endowments of labor and captal and therefore have dfferent vews about the desrablty of free trade. For smplcty, assume that all ndvduals supply one unt of labor but dffers n ther ownershp of captal. The utlty of an ndvdual wth a captal endowment k s a functon of ncome, w + rk, and the relatve product prce p: V(w + rk, p). However, factor prces are determned by p n the Heckscher-Ohln model (assumng no factor-ntensty reversals), and the equlbrum p s determned by the economy s captal-labor rato, k, where the relevant economy s ether the country of resdence n the case of autarky or the ntegrated economy n the case of free trade. The resultng utlty functon can therefore be defned, v(k, k) = V(w(k) + r(k)k, p(k)). Levy (1997) proves that ths functon s strctly quas-convex n k and has a unque mnmum where k = k (see Fgure 1). In other words, an ndvdual benefts from beng n an economy wth a captal-labor rato further from hs captal endowment.

7 6 Before consderng mmgraton, let us ntroduce the probablstc votng model. The vote s between canddate (or party) F, who supports free trade and canddate A, who desres autarky. Under free trade, factor and product prces wll be determned by the captal-labor rato for the entre free trade area, whch we call the ntegrated economy. Let ki denote ths rato. Thus, ndvdual wll obtan utlty v(k, ki) from hs consumpton of X and Y under free trade, regardless of where he resdes. Agan, we are applyng the factor-prce equalzaton theorem: free trade n goods equalzes factor prces. Let kh and kl denote the captal-labor ratos for the low-ncome and hgh-ncome countres, respectvely. Under autarky, ndvdual obtans utlty v(k, kh) f he resdes n the hghncome country, and v(k, kl) f he resdes n the low-ncome country. Voters not only have preferences between free trade and autarky, but they also have preferences between the two canddates that are unrelated to trade. Normalze these preferences so that v(k, ki) s the utlty f the free-trade canddate s elected, but v(k, kj) + ε s the utlty n country j f the autarky canddate s elected. Consequently, ndvdual votes for the free-trade canddate only f v(k, ki) v(k, kj) + ε. (1) Votng s probablstc because ε s a random varable and ts realzed value s determned only when votng occurs. For smplcty, assume that ε s unformly dstrbuted wth mean zero over the nterval [-δ/2, δ/2]. In ths case, the probablty that ndvdual n country j wll vote for a free trade agreement s

8 7 β = 0 f β = 1 f v(k, k f ) - v(k, k j) v(k, k f ) - v(k, k j ) - ½ < 0; (2a) - ½ > 1; (2b) β = v(k, k f ) - v(k, k j ) - ½ otherwse. (2c) As δ goes to zero, the votes become determnstc, as descrbed by (2a) and (2b). Under determnstc votng, the medan voter theorem apples, snce preferences are snglepeaked. We later dscuss a bas aganst free trade. Usng ths model, we wll show how mmgraton affects the probabltes that a free-trade agreement passes. Events unfold n three stages. Frst, countres vote for free trade. If free trade passes n both countres, then a free-trade agreement s mplemented, causng factor prces to equalze, and no mgraton occurs. But to solate the postve effects of mgraton on free trade, we assume that free trade loses the vote n the hghncome country, although t s favored n the low-ncome country. We therefore have a second stage, n whch workers mgrate. In the thrd stage, countres vote for free trade agan. In equlbrum, potental mmgrants correctly antcpate the probablty of a freetrade agreement, and the number of actual mmgrants depends on ths probablty. Consder the frst-stage vote for free trade n the low-ncome country. Fgure 1 depcts the medan voter s utlty,,,, as a functon of the economy s captal-labor rato, k. Let kl,0 denote the low-ncome country s captal-labor rato pror to any mmgraton. We assume that, < kl,0, reflectng the skewed dstrbutons of ncome that are observed n practce. As shown n Fgure 1, the medan voter prefers free trade over autarky. If we now ntroduce uncertanty n the outcome of the vote, then the vote wll stll

9 8 be n favor of free trade wth certanty, f the parameter δ s not too large. The reason s that each voter s choce becomes certan as δ goes to zero, except for voters who are ndfferent between free trade and autarky. These voters form a set of measure zero, wth a captal endowment k between kl,0 and ki. All voters wth k less than k prefer free trade. Wth, less than k, t follows that free trade wns wth 100 percent probablty f δ s suffcently small. We make ths assumpton, whle notng that uncertan voter outcomes wll later emerge when there s mgraton, regardless of the postve value of δ. utlty kl,0 ki economy s K/L Fgure 1: The relaton between the utlty for the medan voter n the low-ncome country and the relevant economy s captal-labor rato. We are nterested n the case where the hgh-ncome country turns down free trade n the absence of mgraton. Ths stuaton s llustrated n Fgure 2 below, whch depcts the utlty functon for the medan voter n the hgh-ncome country. Ths voter s captallabor rato s,, kh,0 s the hgh-ncome country s ntal captal-labor rato, and ki agan denotes the captal-labor rato for the ntegrated economy. In addton, k ~ H now represents

10 9 the captal-labor rato that would have to exst n the hgh-ncome country for ts medan voter to be ndfferent between autarky and free-trade. As shown, k I M ~ k k k. (3) H H H,0 utlty economy s K/L Fgure 2: Utlty of the medan voter n the hgh-ncome country when. For the frst nequalty, we make the reasonable assumpton that the hgh-ncome country s medan voter has more captal than the average captal possessed by ndvduals n both countres combned. 6 The frst nequalty then mples the second equalty, snce the utlty functon s u-shaped. For the last nequalty, we assume that the medan voter prefers autarky over free trade n the absence of mgraton. Followng the prevous arguments, we may agan ensure that the free-trade canddate s defeated wth certanty by assumng a 6 Despte the relatve captal abundance of the hgh-ncome country, ths assumpton could be volated f ths abundance was the resulted from the captal holdngs from only a small number of wealthy resdents there.

11 10 suffcently small value of δ. Wth ths setup, we wll demonstrate that mgraton changes ths vote so that the free-trade canddate now has a postve probablty of wnnng. Consder now the mgraton stage. Wth no free trade agreement, resdents of the low-ncome country may now have an ncentve to mmgrate to the hgh-ncome country to take advantage of the hgher real wage there. Ths ncentve depends on the cost of mmgraton, whch we denote by C. Let us nterpret ths cost as a payment to smugglers or facltators n H. 7 By treatng the cost as an ncome transfer, we avod unnecessary complcatons nvolvng the wthdrawal of real resources from productve uses. 8 Moreover, t seems approprate to nterpret mgraton as llegal for two reasons. Frst, the majorty of voters n the hgh-ncome country do not want mmgraton. Second, we assume that mmgrants from the low-ncome country do not posses votng rghts n the hgh-ncome country. An alternatve nterpretaton would be to allow costly legal mgraton but assume that votng rghts are granted only after a lengthy delay. For smplcty, assume also that all potental mgrants are endowed only ther unt of labor but no captal. Immgraton reduces the captal-labor rato n the hgh-ncome country from kh,0 to a lower level denoted kh,1. Smlarly, the captal-labor rato n the low-ncome country rses from kl,0 to a hgher level, kl,1. Thus, mgraton rases the real wage n the mgrant s home country and lowers the real wage n the foregn country, assumng no goods trade. 7 Naturally, the level of C would depend on the enforcement actvtes that the hgh-ncome country uses to detect and prevent mgraton. For models of border and nternal enforcement polces, see Ether (1986), Bond and Chen (1987), Bucc and Tenoro (1996) and Yoshda (2000). Snce we are not nterested n the welfare effects of varous enforcement polces, we work wth ths reduced-form specfcaton of llegal mmgraton. 8 An alternatve nterpretaton of C would be that t represents a psychc cost of mgraton, as n Sjaastad (1962).

12 11 But mgraton can never equalze factor prces, because then there would be no beneft of mgraton to offset the cost C. In partcular, kl,1 stays below ki. For ths reason, the medan voter n the low-ncome country wll contnue to favor free trade, as llustrated n Fgure 1, and the low-ncome country wll then vote wth certanty for free trade f δ s suffcently low. Consder now the fnal vote n the hgh-ncome country. If free trade were mplemented wth certanty, then factor prces would be equalzed. Mgrants would have ncurred the cost of mgratng, but wth no gan. On the other hand, f autarky were mplemented wth certanty, then factor prces would reman unequal. We then see that mgraton ether does not occur, due to hgh mgraton costs, or C s low enough for mgraton to occur to the pont where the vote for free trade generates a probablty of free trade that leaves mgrants ndfferent about mgratng. Thus, for low enough C, the vote wll be uncertan, regardless of how close δ s to zero. We now derve the equlbrum level of mgraton and probablty of a favorable free-trade vote. Lettng β denote ths probablty, mgraton occurs unt expected utltes are equated between the two countres: (1 ) V( w( k L,1 (1 ) V( w( k ), p( k H,1 L,1 ) C, p( k )) V( w( k H,1 I ), p( k )) V( w( k I I )) ) C, p( k I )) (4) Ths equlbrum level of mgraton s declnng n the probablty of free trade, gven that there s no beneft from mgraton under free trade. We therefore have the downwardslopng mgrant supply curve, labeled T(β) n Fgure 3. To summarze, as the probablty of free trade falls, the beneft of mgraton rses, thereby ncreasng the number of mgrants untl the expected utltes at home and abroad

13 12 are equated. At the vertcal ntercept for the mgrant supply curve, there s no mgraton, because the probablty of free trade s 100 percent, mplyng factor-prce equalzaton. At the horzontal ntercept, autarky occurs wth certanty, and mgraton brngs the captallabor ratos for the two countres close enough to equate the mgrants expected utltes. β 1 T(β) β(t) Fgure 3: Mgrant supply and votng curves. Number of mgrants (T) We can also derve an votng curve, labeled β(t) n Fgure 3. In the medan voter model wth no uncertanty, the mddle porton of ths curve would be vertcal. Referrng to Fgure 2, mgraton would occur untl the captal-labor rato dropped to, at whch pont the medan voter would be ndfferent between free trade and autarky, mplyng that the outcome of the vote would be determned by te-breakng rules. In the probablstc votng model, ths dscontnuous jump n the free-trade probablty from zero to one becomes contnuous. Before mgraton rses to the pont where the medan voter becomes

14 13 completely ndfferent between free trade and autarky, he frst starts to vote randomly, as do some of the other voters, gven ther random preferences between the two canddates. Thus, the probablty rses smoothly, and t reaches 100 percent wth the captal-labor rato between and n the hgh-ncome country, assumng agan that δ s suffcently small (see Fgure 2). But once the number of mgrants reaches the level where β =1, addtonal ncreases n ths number wll cause factor-prce equalzaton to be approached. Thus, β(t) must eventually fall (not shown), snce the vote between free trade and autarky would be random under factor prce equalzaton, regardless of δ. We can therefore not rule out addtonal equlbra, where the votng curve falls below the mgrant supply curve. Such equlbra wll not occur, however, for low values of δ, whch s the case consdered here. 3. The Relaton Between Mgraton and Trade We now consder varatons n mgraton and trade created by changes n ether mgraton costs or preferences towards the free-trade and autarky canddates. Once C falls below the maxmum level consstent wth mgraton, further reductons n C shft up the mgrant supply curve n Fgure 3, ncreasng the probablty of free trade. Note that as C converges to zero, the horzontal ntercept of the mgrant supply curve, T(β), converges to the level of mgraton that produces factor-prce equalzaton. But the curve stll slopes down, and β = 1 stll mples no mgraton, as long as C s postve. Thus, a reducton n C shfts rght the horzontal ntercept, but not the vertcal ntercept, Lett β(c) denote the equlbrum probablty of free trade. We have proved:

15 14 Proposton 1. There exsts a C* > 0, such that (C) s postve and decreasng n C for 0 < C < C*, (C) = 0 for C > C*, and (C) converges to 1 as C goes to zero. Wth ths proposton, we have establshed a poltcal connecton between free trade and mgraton: The lower the cost of mgraton, the more lkely s a free trade agreement. In ths sense, mgraton and free trade are complements. But can we go n the reverse drecton, where less free trade mples less mgraton, once agan representng a complementary relaton? In partcular, suppose that nstead of varyng mgraton costs, we vary preferences for the free-trade and autarky canddates, ndependently of mgraton. Ths can be done by changng shftng the dstrbuton of preferences for the free-trade canddate from [-δ/2, δ/2] to [b - δ/2, b + δ/2]. Then (2) becomes β = 0 f β = 1 f v(k, k v(k, k f f ) - v(k ) - v(k, k, k j j ) - b ) - b - ½ < 0; (2a ) - ½ > 1; (2b ) β = v(k, k f ) - v(k, k j ) - b - ½ otherwse. (2c ) Then a postve b ndcates a bas aganst free trade. In partcular, f a voter s free-trade and autarky utltes are equal, the voter wll vote for the free-trade canddate wth a probablty less than one-half. In terms of Fgure 3, a small bas aganst free trade shfts down the votng curve where β s between zero and one, causng the equlbrum probablty of free trade to declne, but also causng the amount of mgraton to ncrease. Ths suggest

16 15 a substtute relaton between free trade and mgraton: less free trade, brought on by an ncreased bas aganst free trade, leads to more mgraton: Proposton 2. Assume that mgraton cost C s suffcently low for mgraton to occur n equlbrum when there s no bas for or aganst free trade. Then ntroducng a bas aganst free trade rases the equlbrum level of mgraton. Ths result can be smply explaned. At any gven level of mgraton, the bas aganst free trade makes t less lkely that voters wll elect the free-trade canddate. But then the expected beneft of mgraton rses, snce t s more lkely that the economy remans n autarky, where factor prces fal to equalze. As can be seen by shftng the votng curve n Fgure 3, mgraton ncreases, whch reduces, but does not elmnate, the bas-nduced fall n the probablty of a free-trade agreement. 4. A Dynamc Extenson In the prevous model, free trade s never certan because there would then be no ncentve to mgrate. But another way to restore such ncentves would be through an ncrease n the tme needed to obtan a postve vote. Buldng on the prevous model, we now present ths analyss. The settng of ths dynamc model s smlar to the one on the prevous model. The man dfference s the modelng of mgraton costs. Now t s assumed that they are ncreasng n the amount of mgraton that occurs n any gven tme perod: C = C(M(t)), dc/dm > 0, where M(t) s the total number of mmgrants enterng the hgh-ncome country at tme t, where tme s treated as a contnuous varable. Wth C agan treated as an ncome

17 16 transfer, the nterpretaton here s that as the number of mgrants rses, hgher payments are requred to get across the border. In other words, there s an upward-slopng supply of smugglng servces n any gven tme perod. One nterpretaton s that more mgraton requres more smugglers, whch requres hgher payments to smugglers. Alternatvely, more mgraton ncreases the rsks of beng caught, and exstng smugglers demand hgher payments as compensaton. 9 In ths contnuous-tme model, there s also the ssue of when these mgraton costs are pad. We could model mgrants as savng funds for the purpose of fnancng ther mgraton, but ths needlessly complcates the algebra. Instead, we rather artfcally assume that the funds are effectvely borrowed and then a constant fracton, C, s pad back each perod once the mgrant reaches the hgh-ncome country. The descrpton of autarky remans unchanged, and once agan, free trade requres an affrmatve vote n both countres. But now mgraton occurs over tme. As before, the medan voter n the hgh-ncome country prefers autarky over free trade n the ntal tme perod, t = 0. For a low enough value of C(0), some postve number of workers then moves from the low-ncome country to the hgh-ncome country, wth M(t) set so that the cost of movng, C(M(t)), equals the present value of ther expected benefts from mmgraton, where future benefts are dscounted at a fxed rate of tme preference. As t rses contnuously above zero, votng occurs n each nstant of tme. We agan use the probablstc votng setup from the prevous model. If and when a majorty of the 9 In Ylmaz (2005), t s assumed that the costs of mgraton are psychc costs. The nterpretaton of rsng costs s that more llegal mmgrants n the host country mght cause locals to have more racst-xenophobcantagonstc feelngs towards these newcomers. Wth ths nterpretaton, we would need to assume that these psychc costs are felt prmarly at the tme of mmgraton, before mmgrants wll get used to the host country.

18 17 populaton votes for free trade, the agreement s mmedately establshed, equalzng product and factor prces between the two countres. As before, we consder the case where the parameter δ n (2) s small enough to ensure that the hgh-ncome country rejects free trade wth certanty when mgraton s zero or small, whereas the low-ncome country votes n favor of free trade wth certanty. The equlbrum may be descrbed as follows. Startng at tme t = 0, mgraton occurs n each tme perod to equate the cost C(M(t)) to the expected dscounted benefts of mmgraton. Untl tme t = t*, the probablty of free trade s zero. However, M(t) must declne wth t between t = 0 and t = t* because the expected tme untl free trade s mplemented gets shorter. After t = t*, the number of mmgrants moves nto the range where the hgh-ncome country moves up the votng curve depcted n Fgure 3. However, the level of mgraton at any gven tme, M(t), contnues to declne, so that C(M(t)) can declne and stay equated to the dmnshng expected benefts of mgraton. If the freetrade canddate wns at any gven tme, mgraton ceases because factor prces are equalzed. Otherwse, mgraton contnues to occur at a dmnshng rate over tme, ether untl t reaches zero, or the free-trade canddate wns. If mgraton ceases, then we have reached the pont where any further mmgraton would rase the probablty of free trade occurrng n each future tme perod beyond the pont where the expected dscounted benefts of mgraton are equal or exceed the cost C(0). The equlbrum condton for M(t) can be stated n symbols by ntroducng as the dscount factor and then wrtng the dynamc equvalent to the condton for equlbrum mgraton gven by (4):

19 18 1,, 1,, (5) In words, mgraton M(s) at each tme perod s > t mples a mgraton cost C(M(t)) such that a mgrant s expected dscounted welfare from remanng n the low-ncome country from perod t onward equals hs expected dscounted welfare from movng to the hghncome country n perod t. As prevously explaned, the probablty of a free trade agreement passng at any gven tme s,, starts at zero but becomes postve when enough mmgrants are resdng n the hgh-ncome country, and contnues to rse untl M(s) drops to zero. Comparatve statcs are more complcated because the tmng of mgraton depends on the propertes of the mgraton functon C(M), rather than a sngle cost parameter, C. However, we may parameterze the functon by re-wrtng t as γc(m) for the parameter γ > 0. Gven the functon C(M), mgraton requres that γ be suffcently low, and further drops n γ can be expected to result n hgher levels of mgraton at each perod t where M(t) s postve, thereby reducng the expected tme to free trade. In ths sense, mgraton and trade agan appear to be complements: reduced mgraton costs shorten expected tme to free trade. On the other hand, ntroducng a bas aganst free trade (.e., varable b n eq. (2 )) can be expected to reduce the amount of mgraton n any gven perod where t s postve, whle also lengthenng the expected tme to free trade.

20 19 5. Concludng Remarks To conclude, ntroducng poltcs nto a standard Heckscher-Ohln trade model wth factor moblty produces a complex relaton between factor movements and free trade. Lower mgraton costs facltate free trade agreements, suggestng that more mgraton s assocated wth a greater probablty of free trade. But a bas aganst canddates who support free trade leads a lower probablty of free trade but more mgraton. On the one hand, more mgraton appears to cause more free trade. On the other hand, less free trade appears to cause more mgraton. Clearly, the relaton between trade and mgraton s senstve to what s causng the levels of trade and mgraton to vary. A useful extenson would be to model a world wth more than two countres, allowng us to nvestgate whch countres are more lkely to form free trade agreements n a world wth lmted amounts of mgraton. We could also revst Levy s (1997) queston of whether blateral agreements nhbt multlateral agreements. Another extenson would be to allow mmgrants to send remttances back to the home country. Intutvely, remttances mght ncrease the wage dfferences needed to offset the cost of mgraton, f those ndvduals left behnd n the low-ncome country beneft anyway through the recept of these remttances. 10 As a result, t mght be less lkely that enough mgraton would occur to produce a favorable free-trade vote n the hghncome country. A dynamc model that ncluded delays n adjustments to a long-run equlbrum would also be useful. In the current model, a free trade agreement leads mmedately to 10 The fnal effect would depend on how we specfy mmgrant preferences for gvng remttances. Note, also, that mpedments to trade n the absence of a free-trade agreement would also mpede the transfer of remttances.

21 20 factor-prce equalzaton, elmnatng ncentves to mgrate. If, however, factor prces reman unequal for some perod of tme after the agreement, then ts passage mght occur more quckly. In partcular, ncentves to mgrate mght be mantaned wthout the need for a tme delay between the entrance of the last mmgrant and the passage of an agreement, snce the mmgrant could now receve wage gans after the agreement. The experence wth NAFTA has shown that ncentves to mgrate have remaned hgh. Martn (2001) draws attenton to ths ncrease n mgraton after the free trade agreement, notng that loosenng the assumpton that the adjustment to changes n nternatonal markets s nstantaneous can produce a mgraton hump, meanng that, when mgraton flows are charted over tme, mgraton frst ncreases wth closer economc ntegraton and then decreases. Addng populaton growth to the model would also rase some nterestng possbltes. For example, f the llegal mmgrants grow faster than the natve populaton n the captal-abundant country, ths ncreases the rate at whch the captal-labor rato decreases n the captal-abundant country and consequently hastens the tme to economc ntegraton. On the other hand, f mmgrants are gven votng rghts, they wll vote aganst economc ntegraton n order to further enjoy hgh wages n the captal- abundant country. Ths mght cause economc ntegraton to occur at a later tme or even prevent t altogether. However, f we assume that the mmgrants and ther descendants vote natonalstcally (.e. for economc ntegraton wth ther orgnal country), rather than economcally (.e. aganst economc ntegraton wth ther orgnal country), then the tme of economc ntegraton would be sooner.

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