Trade and search generated unemployment

Transcription

1 Journal of Internatonal Economcs 48 (1999) Trade and search generated unemployment * Carl Davdson, Lawrence Martn, Steven Matusz Department of Economcs The El Broad College of Busness, Mchgan State Unversty, 101 Marshall Hall, East Lansng, MI 48824, USA Receved 10 September 1996; receved n revsed form 13 February 1998; accepted 5 March 1998 Abstract We argue that trade economsts should begn to serously consder envronments n whch unemployment s carefully modeled. We ntroduce such a model, derve several results, and compare them to results derved n full employment models. We argue that some tradtonal results are probably too narrow (the determnants of comparatve advantage) and that some results do not generalze to models wth unemployment (the lnk between trade and ncome dstrbuton for employed factors). We also show that n some mportant cases results do generalze (there s an extended Stolper Samuelson Theorem that lnks trade to the dstrbuton of ncome for searchng factors) and that our model allows us to address ssues that tradtonal models cannot handle (the mpact of trade on unemployment and the welfare of the unemployed) Elsever Scence B.V. All rghts reserved. Keywords: Internatonal trade; Search; Unemployment JEL classfcaton: F10; F11 1. Introducton The vast majorty of publc debate concernng trade polcy centers on the mpact of trade on employment. Those opposed to free trade argue that lower producton costs and fewer regulatons n other countres allow foregn frms to out-compete domestc producers. Ths, they argue, results n less domestc output and fewer * Correspondng author. Tel.: ; fax: E-mal address: davdso4@plot.msu.edu (C. Davdson) / 99/ $ see front matter 1999 Elsever Scence B.V. All rghts reserved. PII: S (98)

2 272 C. Davdson et al. / Journal of Internatonal Economcs 48 (1999) domestc jobs. On the other hand, proponents of free trade argue that free trade expands our export markets, resultng n a greater demand for our products, greater domestc producton, and more jobs. The vast majorty of economsts vew both of these arguments as msguded and fundamentally ncorrect. In fact, the debate about trade polcy among economsts almost always gnores the mpact of trade on employment. There are at least two reasons for ths dchotomy. Frst, most nternatonal trade economsts vew trade as a mcroeconomc ssue that focuses on the dstrbuton of resources wthn an economc envronment whle they vew unemployment as a macroeconomc concern related to the overall level of economc actvty and other aggregate 1 measures of economc performance. Second, the feld of nternatonal trade has been, snce ncepton, predomnately a mcro-based theoretcal feld relyng on nsghts from mathematcal models to draw conclusons about the mpact of trade polces on real world economes. Snce, untl recently, economsts have been unable to produce convncng mcroeconomc models of unemployment, trade economsts have largely gnored the role of unemployment n the debate about 2 trade polcy. In fact, the manstream vew among economsts s that trade has lttle, f any, mpact on unemployment. Ths s true n spte of the fact that there s lttle evdence to support or contradct ths vew. Almost all models of trade, and certanly those that have served as the area s workhorses, are full employment models. In addton, although there s some emprcal work on the mpact of trade on employment n partcular sectors of an economy, there s very lttle emprcal work on the aggregate employment effects of trade polces (see Baldwn, 1995, for a recent survey). Recently, the obstacles to the development of trade models wth unemployment have slowly been removed. Over the past 20 years economsts have made great progress n developng mcro-based models of unemployment. In these models, the frctons that obstruct labor market clearng are explctly modeled and the rate of unemployment arses endogenously as an equlbrum outcome. These theores nclude, but are not restrcted to, effcency wages, search, mplct contracts, and nsder outsder models of the labor market (for a revew, see Davdson, 1990). 1 See, for example, the artcles of Krugman (1993) and Mussa (1993) n the Amercan Economc Revew n whch they argue that t should be possble to emphasze to students that the level of employment s a macroeconomc ssue... dependng n the long run on the natural rate of unemployment, wth mcroeconomc polces lke tarffs havng lttle net effect (Krugman), and that economsts... understand that the effect of protectonst polces s not on the overall employment of domestc resources, but rather on the allocaton of resources across productve actvtes (Mussa). 2 Of course, there are some exceptons. In partcular, n the 1970s there were several attempts to nvestgate the mpact of trade polcy n economes wth mperfect labor markets. Ths lterature, known prmarly as the labor-market dstortons lterature, eventually fell out of favor due to the nablty of the authors to draw general conclusons (see, for example, Magee, 1976). Ths falure was largely a result of nadequate mcro-based models of unemployment.

3 C. Davdson et al. / Journal of Internatonal Economcs 48 (1999) Snce the equlbrum unemployment rate generated n these models s generally ntertwned wth the equlbrum allocaton of resources, anythng that results n resource reallocaton (e.g., trade polcy) must affect the rate of unemployment and ts composton across sectors of the economy. As a result, some economsts have begun to emphasze the mportance of generalzng the analyss of nternatonal trade to nclude consderatons of unemployment (see, for example, the Ely Lecture of Blnder (1988) n the Amercan Economc Revew). Extendng standard trade models to allow for equlbrum unemployment s mportant for at least two reasons. Frst, there s the ssue of whether trade creates net job opportuntes. Whle we provde some prelmnary answers to ths queston n ths paper, we vew ths as largely an emprcal queston. Second, and we beleve more mportant, there s the ssue of whether or not results obtaned n tradtonal, full employment trade models extend to settngs n whch unemployment s carefully modeled. Ths ssue s partcularly mportant for those results that have not held up well to emprcal scrutny. The purpose of ths paper s to use a smple general equlbrum model of nternatonal trade that ncludes an equlbrum rate of unemployment to address these two ssues. That s, our goal s to try to determne the extent to whch some of the classc results of trade theory must be modfed when unemployment s a concern. In addton, we show that some questons that cannot be addressed n full employment models can be answered n our smple framework. The plan of the paper s as follows. In the next secton, we ntroduce a smple general equlbrum search model of trade between two countres. In ths model, t takes tme for unemployed factors to fnd each other and start a productve partnershp. Whle searchng for a partner both factors are unemployed. In Secton 3 we determne the pattern of trade and show that the tradtonal lst of the determnants of comparatve advantage must be broadened to nclude features of the labor market (.e., turnover rates) when unemployment s present. In Secton 4 we nvestgate the lnk between trade and the dstrbuton of ncome. We show that there s an extended Stolper Samuelson Theorem that descrbes the mpact of trade on searchng factors. The mpact on employed factors s more complcated, ncludng Stolper Samuelson forces as well as those at work n a tradtonal Specfc Factors model. Whle Sectons 3 and 4 deal wth ssues that have been addressed prevously n full employment models, Secton 5 deals wth an ssue that full employment models cannot handle the mpact of trade on the unemployed. Our man fndng s that when a relatvely captal-abundant large country begns to trade wth a small, relatvely labor-abundant country, unemployed workers n the large country unambguously suffer welfare losses. In addton, we fnd that such trade ncreases the aggregate unemployment rate n the large country. We close the paper n Secton 6 where we dscuss the generalty of our results and suggest future avenues for research.

4 274 C. Davdson et al. / Journal of Internatonal Economcs 48 (1999) The model 2.1. The basc structure We consder a contnuous tme model of a world consstng of two countres, Home and Foregn, wth all foregn country varables desgnated by an astersk. Each economy conssts of two sectors (X and Y) and two types of agents, workers and entrepreneurs. Each nfntely lved worker s endowed at each nstant wth one (ndvsble) unt of lesure that s sold as labor (L). Each nfntely lved entrepreneur s endowed at each nstant wth one (ndvsble) unt of captal (K) that s rented for producton. At each nstant, workers are ether employed or unemployed and captal s ether actve or dle. Both factors are assumed to be moble across sectors and thus when unemployed (dle), workers (captal) must 3 choose a sector n whch to seek a job (rental opportunty). We use Ish to represent the number of type- factors searchng n sector h and Ieh to denote the number of type- factors employed n that sector ( 5 L,K; h 5 X,Y). Therefore, I 5 I 1 I h sh eh s the number of type- factors attached to sector h at any pont n tme and I 5 Ix1 Iy s the number of type- factors n the economy. In order to focus on the mplcatons of factor market frctons, we assume that both countres have the same factor endowments and that the producton technology, shared by both countres, s the same n both sectors. In each sector, t takes one unt of each factor to produce a unt of output. Accordngly, an unemployed worker s searchng for an entrepreneur wth dle captal. Once that captal s found, a match s created that lasts untl an exogenous shock causes the partners to separate. Upon separaton, both partners must reenter the factor market n search of a new match. In order to allow the duraton of a match to vary across sectors and countres, we assume that the break-up rate s both sector and country specfc wth b denotng the break-up rate n sector h. The producton technology h mples that the output produced n a sector s equal to the number of agents of each type employed (matched): h 5 Leh 5 Keh for h 5 X,Y. (1) We also assume that n one sector matches mght be relatvely harder to fnd. We use eh to denote the arrval rate of employment prospects for a type- factor searchng n sector h, and assume that l e 5 (1 2 s )E for h 5 X,Y, (2) h h h 3 Ths s not to say that we requre factors to commt to a sector. In fact, they may swtch sectors at any tme. However, at any nstant a worker (or captalst) can only search n one sector. Therefore, although unemployed ndvduals may feel no partcular attachment to ether sector, at any pont n tme ther search decson dentfes the sector to whch they belong.

5 C. Davdson et al. / Journal of Internatonal Economcs 48 (1999) k e 5 se, h h h where E h. 0 s a constant and sh denotes the proporton of the sector h 4 unemployment pool that s made up of labor [.e., sh 5 L sh /(Lsh 1 K sh)]. From (2), t becomes more dffcult for an unemployed worker to fnd a match as the labor ntensty of the searchng populaton ncreases. In addton, as ths labor ntensty ncreases t becomes easer for an entrepreneur wth dle captal to fnd a match. In (2), the constant term Eh can be nterpreted as an ndex of aggregate arrval rates 5 or employment probabltes n sector h. In what follows, we shall sometmes use h e to represent the arrval rate, and sometmes use the specfc functonal form, dependng upon whch s more notatonally convenent. Fnally, although we assume that search s requred to fnd employment, product markets are assumed to be frctonless and compettve Factor returns Our rsk neutral searchng agents seek matches n the sector that offers the hghest expected lfetme utlty. Agents can expect to spend a fracton of ther lfetme searchng (unemployed or dle) and a fracton matched. No agent receves ncome whle searchng. When employed, each partner earns a share of the revenue generated by the sale of the output they produce. We denote the share of revenue obtaned by a type- partner n sector h by a h and use Ph to denote the unt prce l k of good h. Therefore, a type- sector h partner earns a hp h. Of course, a h1 a h5 1. We are now n a poston to derve the expected lfetme utlty for a typcal agent. Let V sh denote the expected lfetme utlty for a sector h type- searcher and V eh the expected lfetme utlty for a sector h type- agent who s currently matched. For a type- searcher we have the asset value equaton rv 5 e (V 2V ), (3) sh h eh sh where r s the dscount rate. In (3) the term (V 2V ) represents the captal gan that would be earned f the agent became matched. Ths term s weghted by the probablty of the captal gan occurrng gven that the agent s currently searchng. eh sh 4 In earler work (Davdson et al., 1987) we examned the mplcatons of a more general search technology for a closed economy. We use ths lnear form, whch s a specal case of a constant returns to scale matchng technology, so that we may focus on the mplcatons of dfferental turnover rates across natonal and nternatonal labor markets wth as few dstractons as possble. Emprcal support for the assumpton of constant returns to scale can be found n Pssardes (1990). The mportance of ths assumpton for an open economy s dscussed n footnote 7 below. 5 Over a small perod of tme (D t), the probablty of success for a type- worker who s lookng for a job n sector h can be approxmated as ehd t. The mean probablty of employment for sector h k l searchers s then sed1(1 h h t 2 s h)ehd t. Substtutng from (2) allows us to show that the probablty that a searcher fnds a job n sector X relatve to the probablty of fndng a job n sector Y equals E x/e y.

6 276 C. Davdson et al. / Journal of Internatonal Economcs 48 (1999) Smlarly, the asset value equaton for an agent who s currently matched can be expressed as rv 5 a P 2 b (V 2V ). (4) eh h h h eh sh The frst term on the rght-hand sde of (4) represents the nstantaneous utlty of an agent who s currently matched whle the second term represents the captal loss that accompanes sudden separaton of the partners. As before, the latter term s weghted by the probablty of the captal loss occurrng. Eqs. (3) and (4) can be solved to obtan rv 5 e a P /D, (5) sh h h h h rv 5 (r 1 e )a P /D, (6) eh h h h h h h h where D 5r 1 b 1 e. To complete the descrpton of our model we must explan how the revenue shares are determned. For most of our results, t does not matter what assumpton we make at ths pont. The excepton can be found n the secton on the mpact of trade on ncome dstrbuton. We therefore delay a detaled dscusson of ths ssue 6 untl then. The assumpton that we use, whch s common n the search lterature, s that the revenue shares are determned by the Nash Cooperatve Barganng Soluton. Ths soluton evenly splts the surplus created by the match. Whenever a sh l l k k eh eh sh eh sh match occurs, the expected lfetme utlty for the type- partner rses from V to V. Therefore, the total surplus generated by a match s (V 2V ) 1 (V 2V ). Splttng the surplus evenly yelds a h5d h/h2(r 1 b h) 1 Ehj. (7) Note that ncreasng eh mproves the barganng poston of a type- agent and ncreases her share Autarkc equlbrum We close ths secton wth a descrpton of the autarkc equlbrum. In ths paper, we focus only on steady-state equlbra. To ensure that the composton of each sector s statonary over tme, we need to guarantee that the flows nto and out of employment are balanced for each type of agent n each sector. In other words, the number of matches that are dssolved by separaton must equal the number of new matches that are created. Ths condton s gven by h sh bi 5 ei for h 5 X,Y and 5 L,K. (8) h eh 6 See, for example, Damond (1982), Mortensen (1982) or Pssardes (1990).

7 C. Davdson et al. / Journal of Internatonal Economcs 48 (1999) On the left-hand sde we have the number of matches that dssolve due to the exogenous break-up rate. The rght-hand sde represents the number of new matches formed by factor n sector h. In addton to the steady-state condtons represented by (8), an equlbrum for ths economy s characterzed by utlty maxmzaton by all agents and zero excess demand n both product markets. Indvdual utlty maxmzaton requres that moble factors search for matches n the sector that offers the hghest expected lfetme utlty. If both goods are to be produced n equlbrum, moble factors must dstrbute themselves such that the expected lfetme return from search s equal across sectors; or, f factor s moble t must be the case that sx sy V 5V. (9) If we substtute (7) nto (5) to obtan V, we then fnd that factor earns the same expected lfetme utlty from searchng n ether sector f sh x x x y y y ep/[2(r 1 b ) 1 E ] 5 e /[2(r 1 b ) 1 E ], (10) where P ; P x/p y. Eq. (10) s the fundamental equlbrum condton n our model. For both goods to be produced (10) must hold for all moble factors n the economy. Otherwse, one sector, say, for example, sector X, wll offer searchers a hgher expected lfetme reward and wll attract all such searchers to that sector. Over tme, as the establshed matches n sector Y break-up, the newly separated factors wll swtch sectors and start lookng for sector-x matches. Eventually, producton of Y wll cease. To complete our background dscusson of the autarkc equlbrum, we must now dscuss product market demand. Utlty maxmzaton requres workers to purchase the optmal mx of goods for consumpton purposes. Indvduals are not allowed to save and goods cannot be stored. We assume that all agents have the same homothetc utlty functon. As such, relatve demands for the two goods are ndependent of the dstrbuton of ncome, the economy s factor mx, as well as the level of unemployment. Gven these assumptons about preferences, the relatve demand for (X/Y) s smply a functon of relatve prces (P x/p y). We are now n a poston to characterze the autarkc equlbrum. Snce labor and captal are moble, (10) must hold for both factors. We can then use (10) to prove the followng result. Lemma 1. The equlbrum composton of the searchng populaton s ndependent of the sector. That s, sx5 sy5 s. Proof. Dvdng the ndfference condton for labor by that for captal reveals that l k l k e /e 5 e /e. Substtuton from (2) then yelds the desred result. j x x y y

8 278 C. Davdson et al. / Journal of Internatonal Economcs 48 (1999) We can solve (10) to fnd the relatve output prce that would cause all factors to be ndfferent when choosng a sector n whch to search for a match. Upon dong so, we obtan the followng result. Lemma 2. There exsts a unque value of P (denoted as P) consstent wth the factor ndfference condton. Furthermore, P depends only on exogenous varables. In partcular, P s ndependent of s, the fracton of all searchers who are workers. Proof. We frst rearrange (10) to yeld 2(r 1 b ) 1 E e x x y P 5 ]]]]]. (11) 2(r 1 b ) 1 E e From (2) and Lemma 1, e /e 5 E /E. Therefore, P s ndependent of endogen- ous varables. j y y x y x y x If P. P, sector X offers searchers a hgher expected lfetme utlty than they could expect to receve n sector Y. In ths case, only X s produced. If P, P, the reverse s true, wth the economy specalzed n the producton of Y. Based on ths reasonng, we can nfer that the economy s relatve supply curve s horzontal at P, 7 as shown n Fg. 1. Gven our assumptons about preferences, we can also draw the relatve demand curve n Fg. 1 to determne equlbrum relatve outputs. As Fg. 1 and Lemma 2 make clear, our model wth unemployment has a decdedly Rcardan nature. The job dssoluton and job creaton technologes determne the (unque) relatve prce that s consstent wth a dversfed supply-sde equlbrum and then preferences determne the relatve outputs. Ths s summarzed n Proposton 1. Proposton 1. Autarkc equlbrum exsts and s unque. 3. Comparatve advantage We now turn to the determnants of the pattern of trade. In standard trade models the prmary determnants of comparatve advantage are producton 7 If we had assumed a more general matchng technology (such that eh s not lnear n s), the rght-hand sde of (11) would depend on s. As such, changes n s would result n changes n P and the relatve supply curve would not be horzontal. In fact, we demonstrated n Davdson et al. (1991) that there exsts the possblty of U-shaped relatve supply curves when only one sector s characterzed by unemployment. By choosng ths search technology we are able to focus clearly on the mpact of dfferences n the search technology as a bass for comparatve advantage. In partcular, ths form of the search technology assures that dfferences n relatve factor endowments have no ndependent role n determnng the pattern of trade.

9 C. Davdson et al. / Journal of Internatonal Economcs 48 (1999) Fg. 1. Autarkc Equlbrum. technologes and endowments. We have removed these factors from consderaton by assumng that they are dentcal across countres. Therefore, the only factors that could cause nternatonal trade n our model are ted to the structure of the labor markets. How would we expect the structure of the labor market to matter for trade patterns? In our model, t s clear that labor market turnover rates nfluence the autarkc prces that are requred to nduce factors to search for matches n a sector. If sector-h jobs are easy to fnd (Eh s hgh) or long lastng (bh low), then the compensaton needed to attract factors to that sector (P ) s relatvely low. h Thngs get more complcated when turnover rates vary across countres but not across sectors. Suppose, for example, that one country has a more effcent search technology n all sectors. Whch good would ths country be lkely to export? Alternatvely, suppose that one country has a more dynamc labor market n that the flows nto and out of employment are hgher n that country than n the labor market of ther tradng partner? How wll ths affect the pattern of trade? We begn by notng that from the analyss of autarkc equlbrum, our model possesses Rcardan propertes. From Lemma 2, the autarkc relatve supply curve s horzontal at a relatve prce that s determned strctly by parameters assocated wth the job search and job dssoluton technologes. As such, the offer curves of

10 280 C. Davdson et al. / Journal of Internatonal Economcs 48 (1999) Fg. 2. Offer curves depctng a tradng equlbrum for a small home country. the two countres appear as n Fg. 2. The lnear portons of the offer curves have slopes of P and P *. As drawn, the home country has the comparatve advantage n Y. We have also drawn Fg. 2 such that the home country s small, n the sense that dfferental shfts of ts offer curve due to polcy changes have no effect on ts terms of trade. As noted above, there are two ways n whch the search technology can contrbute to systematc dfferences n relatve autarkc prces. Frst, parameters that vary across sectors mght also vary across countres. Proposton 2 below summarzes the determnants of comparatve advantage n ths case. Second, t s possble that nter-country varaton n parameters leads to dfferent relatve autarky prces even when there are no ntersectoral dfferences. Propostons 3 and 4 below deal wth ths case. For smplcty, we llustrate the combned effects of nter-sectoral and ntercountry varaton by assumng that both countres possess the same job search/ job dssoluton technologes n sector X, but dfferent job search/ job dssoluton technologes n sector Y. We then have the followng result. Proposton 2. Assume that bx5 b* x and Ex5 E x*. Then the home country has a comparatve advantage n the producton of Y f and only f the followng relaton s satsfed:

11 C. Davdson et al. / Journal of Internatonal Economcs 48 (1999) r 1 by r 1 b* y ]],]]. (12) E E* y y Proof. Follows mmedately from (2), (11), and Lemma 1. j For low dscount rates the expresson (r 1 b h)/eh s the rato of the factor market turnover rates n sector h. To see ths, note that snce bh s the break-up rate, 1/bh s the expected duraton of a job n sector h. In addton, snce Eh s the average rate at whch jobs are found n sector h (see footnote 5), the nverse s the average duraton of unemployment. The nequalty n (12) s vald f, all else equal, the expected job duraton n sector Y s hgher n the home country than n the foregn country, or f the expected duraton of unemployment n sector Y s lower n the home country than n the foregn country. In ether case, searchng for a Y-sector job n the home country s more attractve than comparable job search n the foregn country, so, compared wth ther foregn counterparts, home factors need less compensaton to nduce them nto sector Y. Comparatve advantage can also derve from nter-country dfferences n parameters that do not vary across sectors. Suppose, for example, that Ex5 Ey5 E, E* x 5 E y* 5 E *, and E ± E *. Further assume that the break-up rates dffer between sectors, but not between countres. We then have Lemma 3. Suppose that there are nter-country but not nter-sectoral dfferences n aggregate search effcency and that there are nter-sectoral but not ntercountry dfferences n break-up rates. Then the country wth the more effcent search technology (.e., hgher value of E) has a comparatve advantage n the good produced n the sector wth the hgh break-up rate. The proof of ths lemma follows the same logc as the proof of Proposton 2 and s therefore omtted. Intutvely, the sector wth the hgher break-up rate requres a hgher prce to compensate workers. Ths follows snce job acquston rates are the same n both sectors. The hgher the average rate of job acquston (.e., the larger the value of E), the smaller the amount of compensaton needed to nduce factors to enter the sector. In the lmt, as E rses and the duraton of unemployment goes to zero, any fnte dfferences n the sector-specfc breakup rates wll be swamped by the fact that new employment s always obtaned nstantly, so relatve prce tends toward unty. Although Lemma 3 lnks cross-country dfferences n search technologes to the pattern of trade, t does not lnk the pattern of trade drectly to unemployment rates. The followng lemma, along wth Lemma 3, allows us to do just that. Lemma 4. Suppose that there are no nter-sectoral dfferences n aggregate

12 282 C. Davdson et al. / Journal of Internatonal Economcs 48 (1999) search effcency and that there are nter-sectoral dfferences n break-up rates. Then the sector wth the hgh break-up rate s also the sector wth the hgh unemployment rate and vacancy rate. That s, f E 5 E then b. b m $ x y x y x m n $ n where m 5 L /(L 1 H) s the sector h unemployment rate and y x y h sh sh n 5 K /(K 1 H) s the sector h vacancy rate for h 5 X,Y. h sh sh Proof. Recognzng that Leh 5 Keh 5 H, we can use the steady-state condtons n 8 (8) to show that mh5 b h/[bh1 (1 2 s)e] and nh5 b h/[bh1se]. It follows that f b x. by then m x. my and n x. n y. Thus, the hgh-unemployment sector s also the hgh-vacancy sector. j Combnng Lemmas 3 and 4, we arrve at the followng result. Proposton 3. The country wth the more effcent search technology has a comparatve advantage n the good produced n the hgh-unemployment/hghvacancy sector. Proposton 3 lnks dfferences n search technologes across countres to the pattern of trade and tells us that, wth all else equal, the country wth a more effcent matchng process wll have a comparatve advantage n the hgh-un- 9 employment/ hgh-vacancy good. As we dscuss below, there s reason to beleve that the U.S. labor market s characterzed by a more effcent matchng process than ether Europe or Japan. However, there s also evdence to suggest that break-up rates may be hgher n the U.S. than elsewhere (see below). In other words, the U.S. has a more dynamc labor market than Europe and Japan n that flows nto and out of unemployment are both hgher n the U.S. Thus, before dscussng the practcal mplcatons of our results, we provde one last result. Proposton 4. Suppose that Ex 5 Ey 5 E, E x* 5 E y* 5 E *, and that E 5 be *. Suppose further that bh5 bb* h for h 5 X,Y and that b. 1. Then the home country has a comparatve advantage n the good produced n the low-unemployment/lowvacancy rate sector. Proof. Suppose that b x. by so that Y s the low-unemployment/low vacancy rate sector. Then, snce 8 Note that these results make use of Lemma 1 whch states that sx5 sy5 s. 9 Note that Proposton 3 lnks the pattern of trade to dfferences n search technologes usng sectoral unemployment and vacancy rates evaluated n the autarkc equlbrum. Thus, t appears at frst that to test Proposton 3 we would need to know autarkc unemployment and vacancy rates. However, snce s does not vary across sectors (Lemma 1), the rankng of sectors n terms of unemployment and vacancy rates does not change when trade s allowed that s, there are no unemployment rate or vacancy rate reversals caused by trade. Thus, free trade rates are suffcent to test Proposton 3.

13 C. Davdson et al. / Journal of Internatonal Economcs 48 (1999) (r 1 b x) 1 E P 5]]]] 2(r 1 b y ) 1 E t follows that ncreasng b x, b y, and E by a factor of b ncreases the autarkc relatve prce of X. j Accordng to Proposton 4, f the home country has more turnover n ts labor market (through job creaton and destructon) than the foregn country, then t wll have a comparatve advantage n the good produced n low-unemployment/ lowvacancy sector. Ths result contrasts sharply wth Proposton 3 and can best be understood by consderng the prospects of an unemployed worker tryng to decde 10 where to search for a job. Wth Ex5 Ey5 E, the expected duraton of unemploy- ment s the same n both sectors whle wth b x. b y, a job found n sector Y wll last longer (on average) than a job found n sector X. Now, consder the ncome that ths worker can expect to earn up to tme T where T 5 1/E 1 1/b. Durng the x spell of unemployment (whch lasts, on average, 1/E perods) the worker earns nothng. Once a job s found, t lasts, on average 1/bh perods f t s n sector H. Thus, up to tme T the expected ncome earned by a worker searchng n sector X l l x x x y y y s a P /b whle the same worker can expect to earn (T 2 1/E)a P /b f employed n sector Y. Now assume that there s a margnal ncrease n b x, b y, and E wth all ncreasng proportonately. The ncrease n E shortens the expected duraton of unemployment n both sectors. The ncrease n bx also shortens the expected duraton of a sector-x job, and therefore reduces the amount of ncome expected to be earned n that sector up to T. On the other hand, the amount of ncome expected to be earned n sector Y up to T actually rses even though the duraton of a job s now shorter, employment begns earler and s not expected to end untl after T. It follows that even though there s no change n the relatve ncomes from the two jobs, ncome earned n Y s pushed forward n tme. Wth dscountng, ths tme-shftng of ncome makes sector Y (the low-unemployment/ low-vacancy sector) more attractve and allows that sector to offer less compensaton to searchng factors. As a result, the autarkc relatve prce of that good falls. Our results to ths pont suggest that the structure of the labor market can play a role n determnng the pattern of trade wth the key features beng the job creaton and job destructon technologes. Snce t takes tme and effort for dle factors to meet, the longer t takes to meet n a sector, the hgher the compensaton must be for factors to seek employment n that sector. Smlarly, the longer a partnershp lasts n a sector, the lower the compensaton can be and stll attract workers to that sector. In practcal terms, ths suggests that labor market turnover costs may play a role n determnng comparatve advantage. Moreover, n a more elaborate model 10 The argument works equally well for an entrepreneur wth dle captal.

14 284 C. Davdson et al. / Journal of Internatonal Economcs 48 (1999) of unemployment, other turnover costs (e.g., tranng and recrutment costs) would surely nfluence equlbrum prces. Are turnover costs sgnfcant enough to matter? Do they vary across sectors and across countres enough to make a sgnfcant dfference? Whle a detaled answer to these questons s beyond the scope of ths paper, a casual revew of the labor economcs lterature suggests that the answer s probably yes. A revew of turnover costs n Hamermesh (1993) ndcates that n many sectors the turnover costs ncurred by frms tryng to fll vacances are qute hgh. For example, one large pharmaceutcal company estmated the present value of the cost of replacng a worker at roughly twce that worker s annual salary. A second study pegs the cost of replacng a truck drver at slghtly less than half of that worker s annual pay. There are, of course, some sectors where these costs are qute low (the lowest of the hrng cost estmates reported by Hamermesh appears to be about three weeks worth of pay). It s also well known that there are sgnfcant dfferences n the turnover rates across countres. The average duraton of a job s much hgher n Europe and Japan than t s n the U.S. n a typcal month n 1988 about 2% of Amercans became unemployed whle n Europe and Japan the rate was much lower at 0.4% (Freeman, 1994). In addton, workers fnd reemployment much more rapdly n the U.S. than they do n Europe for example, n 1988 almost half (46%) of the Amercans who were unemployed n a gven month were no longer unemployed n the next month, whle n Europe the rate of reemployment was only 5% (Freeman, 1994). Labor economsts conclude that U.S. labor markets are much more flexble than ther European counterparts. They have recognzed for qute some tme now that ths dfference n flexblty has mportant mplcatons for a varety of ssues ncludng job tranng and macroeconomc performance (see, for example, Layard et al., 1991). It s not at all hard to magne that there are mportant mplcatons for the pattern of trade as well. 4. Trade and the dstrbuton of ncome One of the most debated ssues concernng trade polcy both publcly and n the professon s the mpact of trade on the dstrbuton of ncome. Ths has been a partcularly hot topc recently wth publc debate about the welfare mplcatons of NAFTA and the Uruguay round of GATT and debate wthn the professon as to whether or not nternatonal trade has played a sgnfcant role n the recent 11 dramatc changes n the dstrbuton of ncome n the Unted States. If we turn to the textbook explanatons of how trade affects ncome dstrbuton there are two competng theores. In the tradtonal full employment two-factor 11 See, for example, the artcles on ncome nequalty and trade n the Summer 1995 Journal of Economc Perspectves.

15 C. Davdson et al. / Journal of Internatonal Economcs 48 (1999) two-good Heckscher Ohln model the mpact of trade on ncome dstrbuton s summarzed by the Stolper Samuelson Theorem. Ths theorem states that protectng an ndustry ncreases the real return to the factor that s used relatvely ntensvely n that sector and lowers the real return to the other factor. In contrast, the tradtonal full employment Rcardo Vner model predcts that free trade benefts the factor specfc to the export sector, harms the factor specfc to the mport sector, and has an ambguous mpact on the welfare of the moble factor. In ths secton we ask whether the nsghts from the Heckscher Ohln model 12 generalze to models wth unemployment. Ths s one queston concernng trade and unemployment that has recently receved some serous attenton n the lterature. Two papers, Davdson et al. (1988) and Hosos (1990), both provde partal answers to ths queston n an HO-settng. Thus, we begn ths secton by summarzng ther fndngs. We then extend ther results to provde a more complete pcture of the lnk between welfare and trade n a Heckscher Ohln settng wth unemployment. Whle the analyses offered n Davdson et al. (1988) and Hosos (1990) are very smlar, for our purposes, there s one key dfference the manner n whch the surplus s splt once a partnershp s formed. In our earler artcle, we followed the search lterature tradton n usng the Nash Cooperatve Barganng Soluton whch splts the surplus created by a match evenly between the partners. As s well known (see, for example, Damond, 1982) ths sharng rule leads to sub-optmal equlbra. In fact, we showed n our paper that wth ths sharng rule the factor mx attracted to each sector wll not, n general, be optmal. Hosos, on the other hand, assumed effcent barganng so that the factor mx attracted to each sector would, n fact, maxmze the value of steady-state output. To see why ths matters, consder the standard Stolper Samuelson argument. In the Heckscher Ohln model of trade the cost of producng a unt of output equals the prce of that output, or P 5 a w 1 a w, (13) h lh l kh k where ah s the cost mnmzng amount of factor used to produce one unt of good h and w s the payment to factor. Totally dfferentatng ths expresson for each sector, translatng the terms nto percentage changes and then subtractng across sectors leads to the famlar expresson (Pˆ 2 P ˆ ) 5u *(wˆ 2 w ˆ ), (14) x y l k where u * ranks the sectors n terms of ther value factor ntenstes (u *. 0 mples that the X sector s relatvely labor-ntensve n value terms) and a crcumflex above a varable represents a percentage change n that varable. Thus, 12 For the lnk between trade and ncome dstrbuton n the Rcardo Vner model, see Davdson (1997).

16 286 C. Davdson et al. / Journal of Internatonal Economcs 48 (1999) an ncrease n P x/py leads to an ncrease n w l/w k. Ths argument leads drectly to the Stolper Samuelson Theorem. However, t s mportant to note that n dervng (14) t s necessary to make use of the fact that, due to cost mnmzaton, wl dalh1 wk dakh5 0. That s, snce factors are chosen to mnmze the cost of producng output, small changes n the factor mx result n only second-order changes n the cost of producton. Now, turn to models wth unemployment. Hosos shows that n a model qute smlar to ours n whch both factors are moble an expresson smlar to (13) holds. In partcular, he shows that l k h lh sh kh sh P 5 a rv 1 a rv, (15) where ah 5 (Ieh 1 I sh)/h measures the total number of type-i workers attached to sector h (both employed and searchng) per unt of output. Totally dfferentatng (15) and followng the same procedure outlned above, Hosos derves an extenson of the Stolper Samuelson Theorem for models wth unemployment. Ths theorem states that f a sector s protected the steady-state real return to the unemployed factor used relatvely ntensvely n that sector rses and the steadystate real return to the other factor falls. However, n calculatng factor ntenstes those who are searchng n each sector must be ncluded n the calculatons. Moreover, the theorem tells us how the steady-state returns to searchng factors are affected (.e., V ). It says nothng of the mpact of protecton on the steady-state sh eh return to employed factors (.e., V ). We return to ths ssue below and extend Hoso s analyss to see how the steady-state returns to employed factors are affected by trade. In dervng ths extended Stolper Samuelson Theorem Hosos makes use of the fact that the equlbrum factor ntenstes n hs sectors are optmal [and, thus, l k sh lh sh kh rv (da ) 1 rv (da ) 5 0]. Ths follows from hs assumpton of effcent barganng. In our artcle (Davdson et al., 1988) we showed that wth the barganng shares determned by the Nash Cooperatve Barganng Soluton the Stolper Samuelson Theorem could be overturned snce changes n the (neffcent) factor mx exerts a second mpact on steady-state factor rewards that may swamp the Stolper Samuelson effects. It follows that the mpact of trade on the dstrbuton of ncome depends crucally on whether sectoral factor mxes are effcent. Whch assumpton concernng barganng s most realstc? Whle the answer to ths queston s beyond the scope of ths paper there are a few comments that can be made. Frst, there s a sold non-cooperatve foundaton for the Nash Cooperatve Barganng Soluton n that t has been shown to be the equlbrum outcome of a well defned, sensble barganng process (e.g., Bnmore et al., 1986). We know of no smlar non-cooperatve foundaton for effcent barganng. On the other hand, we know of no emprcal evdence that search externaltes cause sgnfcant neffcences n factor mxes. Although such externaltes are easy to

17 C. Davdson et al. / Journal of Internatonal Economcs 48 (1999) analyze theoretcally, t s extremely dffcult, f not mpossble, to measure them. Our own vew s that t s unlkely that factor ntenstes are ndeed optmal; but, t s also unlkely that changes n those factor ntenstes could generate secondary effects strong enough to overturn the extended Stolper Samuelson Theorem descrbed above. Now, as noted above, the extended Stolper Samuelson Theorem of Hosos (1990) holds for searchng factors t says nothng about how trade affects the steady-state welfare of employed factors. However, t s straghtforward to % generalze hs results to employed factors. To see ths, let P denote the prce ndex that s used to turn nomnal values nto real values. Then, from (5) (7) we have eh sh r h % % % 2(r 1 b h) 1 Eh rv rv P ]] 5]] 1 ]]]]]]. (16) P P P As (16) makes clear, the mpact of trade on the steady-state return to employed factors s determned by two forces. The frst term on the rght-hand sde of (16) s the steady-state return to searchng factors and, as we have seen above, changes n ths term are governed by Stolper Samuelson forces. The second term on the rght-hand sde of (16) rses for factors employed n the export sector and falls for those employed n the mport sector. Ths term captures the beneft (loss) to employed factors for beng fortunate (unfortunate) enough to be already matched n the sector that benefts (suffers) from free trade. It follows that f a factor s employed and used ntensvely n the export sector, then t gans from trade. If a factor s employed and used ntensvely n the mport sector, then t s harmed by free trade. The mpact on the other two types of employed factors s ambguous. A factor that s employed n the export sector but used relatvely ntensvely n the mport sector gans from beng matched n the export sector but suffers from the Stolper Samuelson forces. A factor that s employed n the mport sector but used relatvely ntensvely n the export sector gans from the Stolper Samuelson effects but suffers from beng matched n the mport sector. Thus, we have Proposton 5. If barganng between matched factors s effcent, then the steady-state real return to searchng factors vares accordng to the Stolper Samuelson Theorem. For matched factors t s somewhat more complcated. For the factor that s used relatvely ntensvely n the export (mport) sector, ts steady-state real return vares accordng to the Stolper Samuelson Theorem f t s matched n the export (mport) sector. The effect of trade on the steady-state real return to the remanng matched factors s ambguous. The ntuton behnd Proposton 5 s that when tme and effort are requred to fnd employment, an exstng job creates a sectoral attachment snce employed

18 288 C. Davdson et al. / Journal of Internatonal Economcs 48 (1999) agents are reluctant to qut ther jobs n order to search for new employment elsewhere. Matched factors n ths model are therefore analogous to the mmoble factors n a Rcaro Vner model. By contrast, unemployed factors have no attachments to any sector and are therefore completely moble. As a result, the gans and loses from trade that accrue to searchng factors are precsely what would be found n a Heckscher Ohln model. On the other hand, the mpact of trade on employed factors combnes Specfc Factor effects (through sectoral attachments) wth Heckscher Ohln effects (snce they wll someday become unemployed agan). It s clear from (16) that the Specfc Factor effects are more lkely to be domnant f employed factors have strong attachments to ther sector. Ths occurs when bh and Eh are low so that jobs are long lastng and dffcult to fnd. Ths proposton has mplcatons for the emprcal lterature that has attempted to dstngush between the predctons of the Stolper Samuelson Theorem and the Rcardo Vner model. Magee (1980) tested the predctons of these two theores by examnng whether labor and captal wthn a gven ndustry tended to oppose each other on the ssue of protecton for that ndustry. One of the mplcatons of the Stolper Samuelson Theorem s that a factor s poston wth respect to free trade does not depend on the sector n whch t s employed all that matters s whether the factor s relatvely scarce or abundant. Thus, dfferent factors employed n the same ndustry should oppose each other on ths ssue. The Rcardo Vner model suggests just the opposte. By examnng the postons taken by labor and captal n 27 ndustres durng ther Congressonal testmony wth respect to the Trade Reform Act of 1973, Magee fnds strong evdence that factors wthn an ndustry tend to be on the same sde of the protecton/ free trade 13 argument. Of the 27 ndustres studed, 15 are clearly consstent wth the Rcardo Vner model, three others lean heavly n that drecton, sx are ambguous, and only two are consstent wth the Stolper Samuelson Theorem. He concludes that ths test, along wth the results of two others, support the Rcardo Vner model at the expense of the Stolper Samuelson Theorem. Our results ndcate that dstngushng between these two models s not qute so easy when search s requred to fnd a job a sectoral attachment s created by employment that muddles the dstncton between these two theores. Industres n whch job attachments are strong (.e., the duraton of a job and the duraton of unemployment are both relatvely long) should behave more lke the Rcardo Vner model snce employment creates a strong te to the ndustry and makes employed factors behave as s they were specfc to the ndustry. In contrast, f jobs are relatvely transtory or easy to fnd n an ndustry, then job attachments 13 Magee actually provdes data on 33 ndustres. However, for sx of the ndustres the data s ncomplete.

19 C. Davdson et al. / Journal of Internatonal Economcs 48 (1999) Table 1 Expected duraton of a job n 12 of the ndustres consdered by Magee (1980) Industry SIC code Data consstent wth Average job duraton (months) Plastcs 2821 Rcardo Vner Paper 26 Rcardo Vner Machne tools 3541 Ambguous Machnery 35 Rcardo Vner Textles 22 Rcardo Vner Avaton 3720 Rcardo Vner Electrcal 36 Ambguous Bearngs 3562 Rcardo Vner (weakly) Stone 32 Rcardo Vner Rubber 30 Ambguous Trucks 3713 Rcardo Vner Apparel 23 Rcardo Vner Leather 31 Rcardo Vner Tobacco 21 Stolper Samuelson Note: average job duraton s the nverse of average monthly nvoluntary separatons (per 100 workers). Data on nvoluntary separatons (total separatons less quts) s taken from Employment and Earnngs (Unted States Government Prntng Offce, 1970, 1971, 1972, 1973, 1974). wll be weak and ndustry behavor s more lkely to be consstent wth the Stolper Samuelson Theorem. Although a careful emprcal analyss of ths clam s beyond the scope of ths paper, a quck look at some prelmnary data suggests that ths mght be an avenue worth pursung. In Table 1 we lst the expected duraton of a job n 12 of the ndustres that Magee consdered. These are the only ndustres for whch we could fnd labor market turnover data at the same SIC level that Magee reports n hs Table 1. These expected duratons were based upon the average monthly rate of nvoluntary separaton (total separatons less quts) n each ndustry over the perod (the data s taken from the March ssue of Earnngs and Employment for each year). Expected job duraton s then the nverse of ths separaton rate. Table 1 lsts the ndustres accordng to expected job duraton wth the ndustry wth the longest duraton lsted frst. Note that the only ndustry consstent wth the Stolper Samuelson Theorem (tobacco) also turns out 14,15 to be the ndustry wth the weakest job attachment! 14 In terms of our model, Table 1 reports data on 1/b h. Unfortunately, snce data on ndustry-specfc average duratons of unemployment are not avalable, we could not derve estmates of E h. 15 We were unable to fnd nvoluntary separaton rates for Petroleum, the other ndustry consstent wth the Stolper Samuelson Theorem n Magee s Table 1, at the same SIC level as Magee (2911). However, we were able to fnd data at a dfferent SIC level (291) that ndcates relatvely strong job attachment n that sector, contrary to what our model predcts.

20 290 C. Davdson et al. / Journal of Internatonal Economcs 48 (1999) Trade and the unemployed The most heated debates concernng trade and unemployment typcally arse durng dscussons about trade agreements between developed countres and ther less developed counterparts. Arguments that reduced trade barrers would lead to job losses n the U.S. were central n the debate leadng up to the establshment of NAFTA. In fact, careful scrutny of the debate precedng the vote on NAFTA n the U.S. House of Representatves and the U.S. Senate reveals that of the 141 ant-nafta statements made, 112 were of the form NAFTA wll destroy jobs whle of the 219 pro-nafta statements made, 199 were of the form NAFTA 16 wll create jobs. Smlar fears and dscussons can be found n Europe where there s concern about the admsson of Turkey to the EC and n Asa where Japan rsks ncreases n unemployment f t were to reduce trade barrers wth ts ndustralzng neghbors. Whle tradtonal full employment models cannot drectly address such ssues, our model wth unemployment offers an deal settng to begn an examnaton of 17 these concerns. Thus, n ths secton, we nvestgate the mpact of free trade on unemployment and the steady-state welfare of the unemployed when a large, relatvely captal-abundant country trades wth a small, less developed, relatvely labor-abundant neghbor. We assume that the large country has a more effcent labor market n the sense that t has a lower aggregate unemployment rate than ts tradng partner (these assumptons are made precse below). We consder the mpact of free trade between these countres n two steps. We begn by consderng the mpact of trade n goods, holdng factor allocatons fxed. We then move on to nvestgate the consequences of an ntegrated captal market for the flow of captal that such trade may nduce and the ultmate mpact of such flows on unemployment. To capture the essence of the stuaton, we assume that the break-up rates are dentcal n the two countres, but dffer across sectors, and that the large country has a more effcent search technology. Ths leaves us wth a settng smlar to the one used to derve Propostons 3 and 4 n Secton 3 we have bx5 b * x. by5 b* y and Ex 5 Ey 5 E. E* 5 E* x 5 E * y. Ths mples that sector X s the hgh-un- employment sector and that the home country (whch we take to be the large country) has the more effcent search technology. We also assume that after trade s lberalzed, the small country ends up specalzed whle the large country remans dversfed. Thus, from Lemma 2, free trade between these two countres does not affect the relatve prce level n the large country. From Proposton 3 we know that n ths settng the large country has a comparatve advantage n the hgh-unemployment good and wll therefore export 16 These data were collected by Robert Baldwn and Chrstopher Magee whle preparng Baldwn and Magee (1997) and was reported to us by Magee. 17 For a dfferent approach to these ssues see Davdson et al. (1988) and Matusz (1996).