Technological Superiority and the Losses From Migration

Transcription

1 Technologcal Superorty and the Losses From Mgraton by Donald R. Davs and Davd E. Wensten Columba Unversty and NBER May 21, 2002 Abstract Two facts motvate ths study. (1) The Unted States s the world s most productve economy. (2) The US s the destnaton for a broad range of net factor nflows: unsklled labor, sklled labor, and captal. Indeed, these two facts may be strongly related: All factors seek to enter the US because of the US technologcal superorty. The lterature on nternatonal factor flows rarely lnks these two phenomena, nstead consderng one-at-atme analyses that stress ssues of relatve factor abundance. Ths s unfortunate, snce the welfare calculatons dffer markedly. In a smple Rcardan framework, a country that experences mmgraton of factors motvated by technologcal dfferences always loses from ths mgraton relatve to a free trade baselne, whle the other country gans. We provde smple calculatons suggestng that the magntude of the losses for US natves may be qute large $72 bllon dollars per year or 0.8 percent of GDP. We are grateful to Alan Deardorff and James Harrgan for helpful comments, to Joshua Greenfeld for research assstance, and to the Center for Japanese Economy and Busness for support.

2 Technologcal Superorty and the Losses From Mgraton I. Technology, Factor Flows, and Income Losses Arguably the dstnctve feature of the Unted States economy n a global context s the hgh level of ts technology. Whether measured n the aggregate or at the level of the ndustry, US technology frequently fgures as the most productve n the world, often by a consderable margn. Ths productvty, naturally, not only delvers hgh ncome to natves of the Unted States, but also nfluences decsons over the nternatonal flow of productve factors to the US economy. A strkng fact s the breadth of productve factors wth net nflows to the Unted States. One mght expect, on smple factor abundance grounds, that unsklled labor mght fnd advantage n enterng the Unted States. And so t does. Yet hghly sklled labor also fnds t advantageous to enter the Unted States. And the US has been a net captal mporter for decades. 1 One magnes that f land were free to mgrate, a great deal of t mght seek to move to the US as well. The study of these nternatonal factor flows s almost always consdered case by case. There are very good reasons for dong so, snce the relevant agents, objectves and constrants vary consderably across these problems. However, the remarkable fact that such a broad array of productve resources desres to locate n the Unted States suggests that the logc s deeper than may be captured n the one-at-a-tme approaches. The superorty of US technology provdes a parsmonous and plausble hypothess to account for the attracton of the US locaton to such a broad array of factors. However, t s mportant to recognze that when factor movements are motvated 1 For all the talk of the twn defcts, net captal nflows contnued nto the Unted States even as the US government budget moved nto surplus n the late 1990s. 2

3 by technologcal dfferences, both the postve and normatve dmensons of these flows may dffer sgnfcantly from more conventonal approaches. The conventonal approach consders dscrete nflows of a sngle factor to an economy. It then calculates an mmgraton surplus as the economy moves down the margnal product curve for the mgrant factor. Much of the dscusson concerns the magntude of ths surplus and whether fscal consderatons offset or reverse the sgn of the net surplus. 2 The conventonal approach does not always make explct the orgns of factor prce dfferences that motvate mgraton. When these are made explct, the bass s usually dfferences n relatve factor abundance. However, ths mmedately runs nto a problem. In such a framework, f one factor receves a hgher return n the US economy (say unsklled labor), then some other factor (e.g. sklled labor) must receve less so want to leave the US economy. Ths s at odds wth the observaton that all factors seek to enter the US. Ths puzzle has an obvous fx. Ths s to allow nternatonal productvty dfferences that lead all factors to be more productve n the US, and so lead all factors to desre to enter such a hghly productve economy. 3 As a frst pass of analyss, ths suggests some economy from treatng the multple factors as a sngle composte factor. And ths leads drectly to a varant of the standard Rcardan trade model, now amended to allow for mgraton, as a settng n whch to examne the consequences for a country of mmgraton when ths s motvated by technologcal advantage. 2 For example, see Borjas (1995), Fgure 1; Lalonde and Topel (1997), Fgure 1; or Razn and Sadka (2001) Fgure 1. 3 Indeed, recent research by Lutz Hendrcks (2002) strongly supports the hypothess that natonal TFP dfferences matter for the wage dfferences motvatng labor mgraton. 3

4 The key analytc nsght can be stated smply. When mmgraton s motvated by technologcal advantages, natves n the country that receves mmgrants always lose relatve to a baselne wth free trade. Ths s very much at odds wth the presumpton n the lterature that consders nflows one factor at a tme. Nonetheless, the logc of the result s qute smple. Even n autarky, a country enjoys the fruts of ts own hghly productve technology. When the country opens to trade, havng a monopoly on ts own technology s a crucal element of comparatve advantage and gves rse to gans for ths economy. Immgraton, n ths context, amounts to an eroson of ths monopoly power. Although mmgraton motvated by technologcal advantage shfts out the world producton opportuntes set, the country experencng the mmgraton always loses. Trade arsng due to technologcal dfferences s a source of mutual gan. However, when free trade s n place, mgraton due to technologcal dfferences s not a source of mutual gan. World ncome rses, but more than all of ths s captured by natves of the country of emgraton. Natves of the country experencng mmgraton lose. Gven the smplcty of these analytc results, and the plausblty of the underlyng assumptons, t s surprsng that ths approach has prevously fgured almost not at all n the dscussons of factor flows. Although the Rcardan model s nearly always the frst model of trade that we teach students, t s almost never used to dscuss mgraton ssues. We have found only two references. Fndlay (1982) dscusses the possblty of natve losses from mgraton n a paper on Internatonal Dstrbutve Justce, and Danel Trefler (1997) does lkewse amdst a catalog of models that mght be used to thnk about these ssues. Both solve the model and recognze that mmgraton creates a loss for the recevng country. We go beyond ther work n several respects. The 4

5 frst s smply to grasp that coordnated nflows of a wde range of productve factors unsklled labor, sklled labor, and captal would make an nterpretaton of labor n the Rcardan model as a composte factor qute reasonable. The second s to see that ths s n fact a good descrpton of the US experence n recent decades. The thrd s to use these nsghts to develop emprcal applcatons that allow us to quantfy the losses for US natves. 4 Trade theorsts have a long tradton of dscussng the possblty of losses from factor accumulaton or nternatonal factor movements, as n Jagdsh N. Bhagwat (1958), or Gene M. Grossman (1984). Even a graduate textbook treatment of the nteracton of trade and factor moblty has been developed n Kar-Yu Wong (1995). Yet there seems not to have been a recognton n the feld that the Rcardan model mght be the rght framework for thnkng about the consequences of such factor nflows to the US economy. Ths mght reflect the avalablty of what appear to be more general models of factor flows, a tendency to thnk about these flows one at a tme, and the fact that untl recently emprcal analyss played a relatvely small role n the feld. Emprcal consderaton of the nternatonal movement of labor has attracted some of the top talent among labor economsts. Ths ncludes outstandng work by Borjas (1995, 2001), who s one of the frst to take serously the task of quantfyng the aggregate mpact of mmgraton on US ncome. It also ncludes a wealth of work surveyed by Lalonde and Topel (1997) and Fredberg and Hunt (1995). There are two 4 Trefler (1997, p. 11) seems to have on hs mnd only nflows of low-sklled labor, wrtng Snce mmgrant and natve labor compete head on for the same jobs at the same wages, the home country can only absorb the mmgrants n low productvty ndustres that sprng up n response to mmgraton. One should thnk of these ndustres as garments or ctrus frut whch would dsappear n the absence of mgrant workers. By contrast, we thnk of the nflow of a broad range of factors as potentally expandng output n many or all sectors. 5

6 factors that have tended to dstract labor economsts from the results we hghlght. The frst s smply that they have focused on labor flows, not all factor flows. 5 The second s that dstnct methodologcal tradtons have acted as barrers between the labor economsts who have thought hardest about the emprcs and the theoretcal tradtons n nternatonal trade that are a key part of the approach developed here. In any case, the labor economsts must be gven great credt for beng the frst to quantfy the mpact of labor flows. Fnally, those who thnk about nternatonal captal flows have lkewse neglected the ssue. The classc model of MacDougall (1960) on the consequences of captal nflows delvers precsely the type of mmgraton surplus featured n the labor lterature, n ths case wth captal nflows takng the place of labor nflows. Agan, one reason for neglect of the ssues we rase s specalzaton by feld, so that those economsts who thnk about captal flows rarely concern themselves wth labor flows. 6 In sum, our approach to analyzng these factor flows seems not to have been carred out prevously n large part because the analytc and methodologcal elements key to these effects have been dvded across felds that have too lttle communcaton. Ths paper sets out a smple framework for explorng these ssues. Secton II consders the gans and losses from mmgraton wthn the classc model of Dornbusch, Fscher, and Samuelson (1977). Secton III extends ths to consder the case n whch labor qualty dffers across countres. Secton IV establshes our ratonale for usng the 5 In ths case, the exceptons tend to prove the rule. For example, Lalonde and Topel (1997) do brefly dscuss what would happen f captal moved nto the US n the same proporton as labor, but conclude that t would then leave ncomes unchanged due to constant returns to scale, gnorng the possblty of terms of trade losses that we dentfy. 6 A rare excepton s Razn and Sadka (2001), who do dscuss both Labor and Captal Flows. Nonetheless, havng taken advantage of the symmetry of the problems n analytcs when consdered one at a tme, they then move to dscuss the ssues wholly separately. 6

7 Rcardan model as a framework for analyzng factor mmgraton to the US, documentng the dmensons and magntude of US technologcal superorty and of the nflows themselves. Secton V provdes emprcal exercses that establsh baselne quantfcaton of the losses to US natves of these factor nflows. These exercses buld most mportantly on Acemoglu and Ventura (2002) and on Harrgan (1997). We also consder some robustness checks. Secton VI concludes. II. Mgraton n the Dornbusch-Fscher-Samuelson Model We consder a world wth two countres, home and foregn (wth foregn varables ndcated by an astersk). The world labor force home and foregn countres so that: W L s fxed and dstrbuted among the (1) W L+ L = L For the moment, we assume there are no possbltes of mgraton. There exsts a contnuum of goods ndexed by z [ 0,1]. Let output of z at home be yz ( ) and output of z abroad be are: (2) yz ( ) = AzLz ( ) ( ) y ( z ). Then the correspondng producton functons (3) y z = A z L z ( ) ( ) ( ) ( ) and ( ) Az A z are the respectve productvtes. We order the goods accordng to decreasng degree of home comparatve advantage and for smplcty assume ths orderng s strct. Hence Az ( ) Az ( ) (4) If z < z, then > A ( z) A ( z ) 7

8 Goods and factor markets are perfectly compettve. Free entry excludes the possblty of economc profts, so that for any good z, the wage equals the value margnal product n the market where t s produced: w= A( z) p( z) f z s produced at home. (5) w = A ( z) p( z) f z s produced n foregn. For any good z, the relatve productvtes n the goods establsh the relatve wage at whch the good could be compettvely produced n both countres. Ths defnes a functonal relaton over z between relatve wages and relatve productvtes that s derved by takng the rato of the equatons n (5). We assume the goods are traded freely, so that pz ( ) s the common goods prce. Ths yelds the functon: Az ( ) (6) ρ( z) A ( z) Note that ρ ( z) < 0, ndcatng decreasng home comparatve advantage. w If we knew the equlbrum relatve wage w then we could dentfy whch goods are produced n whch country. Suppose for a moment that the equlbrum relatve wage s such that some good z can be proftably produced n both locatons. Then, snce home s comparatve advantage s strongest n low ndex goods, t must be the case that goods produced at home, for whch z < z, Az ( ) w (7) > A ( z) w Correspondngly, snce foregn s comparatve advantage s strongest n hgh ndex goods, t must be the case that goods produced n foregn, for whch z Az ( ) w (8) < A ( z) w > z, 8

9 Equatons (7) and (8) wll be very mportant when we derve the welfare consequences of mgraton. But frst we show how the equlbrum relatve wage s establshed. We assume that consumers n each country have dentcal log lnear preferences, so that expendture shares on each good are fxed and common across countres. Let ths share for good z be gven by bz ( ). We requre that share of spendng on goods n the range [ 0, z ] to be gven by: 1 0 bzdz= ( ) 1. We can also defne the (9) z θ ( z) = b( z ) dz 0 Ths allows us to defne a market clearng equaton. Assume for a moment that good z defnes a boundary between goods produced at home (low ndex goods n whch home has comparatve advantage) and those produced abroad. Then θ ( z) s the share of consumer spendng fallng on goods produced n the home country. Home and foregn ncome (hence spendng) are wl and w L respectvely. Here market clearng can be expressed as a balanced trade condton: (10) [ ] 1 θ( z) wl= θ( z) w L Ths can also be expressed as a relaton between the relatve wage and the boundary good consstent wth market clearng: (11) ω( z) θ ( z) [ 1 θ ( z) ] L L Note that ω ( z) > 0. The relatons ρ( z) and ω ( z) can be plotted n the space of relatve wages and z. Ther ntersecton defnes the boundary good z and share of spendng on products 9

10 produced n the home country θ ( z ) consstent wth trade accordng to comparatve advantage and market clearng. Absent mgraton, ths determnes equlbrum, as n Fgure 1. We now turn to consder the equlbrum when costless mgraton s allowed n addton to trade. The frst observaton s that costless mgraton wll nsure that nferor technologes are never employed. Producton wll be accordng to absolute advantage. Moreover, labor moves to equate wages. By equaton (11), adjustment n the dstrbuton of the world labor force across countres wll shft ω ( z) to acheve equal wages. It s worth pausng for a moment to note that allowng labor to mgrate freely expands the feasble world producton set any tme, as here, that technologes across countres are not dentcal. Wth perfect competton n all markets and an expanded feasble world producton set, we can be assured that world ncome wll go up (at least weakly) wth the possblty of mgraton. Ths framework gves us two cases to consder. The frst s one n whch each country has an absolute advantage n an nterval of goods. Ths s depcted n Fgure 2, and wthout loss of generalty, we assume that the ntal dstrbuton of world labor led country 1 to have a hgher relatve wage. Then enough foregn labor moves to the home economy to nsure that ω ( z) and ρ ( z) cross where the wages are equated. The key queston to resolve s who gans or loses from ths mgraton. Note that wth an expanded world ncome, t s feasble for both to gan. If lump sum taxes were avalable and employed, both could gan agan. Unfortunately, snce they are n practce nfeasble ether admnstratvely or poltcally, we look only at gans and losses through the market. 10

11 In the Rcardan framework, t s convenent to derve a real wage separately n terms of the prce of typcal goods produced at home and abroad. These allow us to make the approprate nferences about welfare. For a good produced at home, equaton (5) tells us that the wage equals the value margnal product, or w= p( z) A( z). It s very useful to rearrange ths to defne a real wage n terms of such a good: w (12) Az ( ) f zs produced at home. pz ( ) = That s, the real wage n terms of z for a good produced at home s just gven by the home productvty n z. Moreover, snce producng a good oneself s always an opton, the home productvty Az ( ) s also a lower bound on the home real wage n terms of ths good. If a good z s produced abroad, then w = p( z) A ( z). The home real wage n terms of such a good s: (13) w w = A z z pz ( ) w ( ) f s produced n foregn. Equaton (13) reveals that for a good produced n foregn, the home real wage depends on w the factoral terms of trade, w, and the foregn productvty A ( z ). The pattern of producton and trade n the Rcardan model depends on a comparson of relatve productvtes and relatve wages. From equaton (7) above, a Az ( ) w good wll be produced at home just n case >. In the reverse case t wll be A ( z) w produced n foregn. It s convenent to rearrange ths equaton to lnk the pattern of 11

12 producton and trade to the real wages for the respectve goods. Multplyng through, we have that a good s produced at home just n case: (14) Az w w ( ) > A( z) These terms compare precsely the real wages developed n equatons (12) and (13) above. That s, a good s produced at home just when the real product wage offered there exceeds that avalable through trade. Ths also makes t very easy to understand the mpact of mgraton on home real wages relatve to the free trade baselne. By hypothess, the ntal relatve wage of home w0 was 1 w > and wth free mgraton, ths factoral terms of trade falls to w1 1 w =. Wth 0 nflows of labor to the home economy, we showed above that the range of goods produced at home expands. Hence there are at most three types of goods. () If good z s produced at home before and after mgraton, then w Az ( ) s unchanged pz ( ) = () If good z s ntally produced n foregn, but swtches to home after the mgraton, and recallng that A(z) s a lower bound for a home product wage, 1 w pz ( ) w falls from A( z) to A( z). w 0 0 () If good z s produced n foregn both before and after mgraton, and recallng w0 that ntally 1 w >, whle w1 1 w, 0 1 w pz ( ) w falls from A( z) to A( z). w

13 In short, the home country that experences mmgraton loses for sure. Its wage s unchanged n terms of the type () goods that t produced both before and after mgraton. But ts real wage falls n terms of both type () and type () goods, those newly produced n home due to the mgraton and those goods produced by the foregn workers who reman n foregn. The foregn country that provdes the mmgrants gans for sure. The smplest way to see ths s smply to recall that mgraton leads world ncome to rse and ths must accrue to someone. If the home labor lost, t must be because the foregn labor reaped more than all of the world ncome gans. We could also do the good-by-good analyss as before. Ths would reveal that foregn labor nether gans nor loses n terms of the type () goods t produced before and after. Yet t experenced real ncome gans n terms of both goods that t prevously mported and those newly produced n the home country. Havng consdered the case n whch each country had techncal superorty n an nterval of goods, we now can very easly analyze the case n whch one country (say home) has technologcal superorty n all goods. When mgraton s not possble, the two countres trade accordng to comparatve advantage. When mgraton s possble, the nferor foregn technologes smply cease to be employed. Agan, we could analyze the movement of wages n terms of the prces of goods ntally produced n each of the two countres. However, a shortcut provdes the desred answers more quckly. Note that when foregn labor has access to the superor home technology, the relatve prces of all goods are determned smply by the relatve productvtes of home technology, exactly as n the home autarky equlbrum. In fact the equlbrum wth mgraton effectvely returns home labor to the autarky equlbrum. Snce home labor 13

14 ntally enjoyed gans from tradng wth the foregn country due to comparatve advantage, ths return to effectve autarky means that home labor loses for sure. Foregn lkewse may be thought of as havng returned to a type of autarky, but t s an autarky wth the superor home technology, so that foregn labor experences substantal gans from mgraton. Agan, mgraton shfts out world producton possbltes and wth perfect factor markets rases world ncome. But, relatve to the tradng equlbrum, more than all of the ncremental world ncome from mgraton accrues to foregn labor. Home labor loses. 7 III. Non-Homogeneous Labor The foregong has assumed that home and foregn labor are dentcal provded they have access to the same naton-specfc technology. However, we know that n the Unted States, mmgrant labor has nether the same geographcal nor occupatonal dstrbuton as natves. 8 Moreover, mmgrants on average do not earn as much as natves when controllng for other relevant characterstcs. Snce the emprcal exercses to follow must confront these non-homogenetes, we need an analytc framework to determne an approprate way to do so. 7 These results have been developed wthn the context of the Dornbusch-Fscher-Samuelson model, wth ts restrctve assumptons on demand, the exstence of a contnuum of goods, and that the degree of comparatve advantage s tself contnuous. These assumptons are convenent for the transparency of the analyss. However, by analogy wth the results developed here, t would be straghtforward to demonstrate that none of these restrctons s necessary. 8 In what follows we gnore the ssue of the geographcal concentraton of mmgrant labor. However, we wll note that an extensve dscusson among labor economsts has already consdered the mportance of ths, notng that the opportuntes of other potental nternal mgrants to alter plans and of producers to shft producton mx to adjust to nternatonal mgrant settlement patterns suggests that the geographcal mpact may be qute lmted. Ths seems sensble n an approprate long run. Borjas (1994, p. 1700) notes that the puzzlng fact s that ths equlbraton n the case of nternatonal mgrants seems to happen extremely rapdly. 14

15 exercse, let The essental analytc ponts can be set out n a very smple framework. For ths F L be the equlbrum quantty of foregn labor that enters the home economy. Let ϕ( z) 1 be the productvty of foregn labor relatve to home labor when t has access to the home technology. In other words, allow for the possblty that foregn labor s less productve than home labor at producng a good z even when t has access to the home technology. Hence, for foregn labor employed n the home country, F (15) yz ( ) = ϕ( zazl ) ( ) ( z) Output for home labor remans as n Equaton (2). For smplcty, dvde the goods produced n the home country nto two groups + Z and Z dstngushed by the relatve productvty of foregn labor, where ϕ ( z) s + assumed constant wthn each group and ϕ( z) > ϕ( z ) f z Z and z Z. For the moment, we can smplfy further by assumng ϕ ( z) = 1 for z Z + (so home and foregn labor are equally productve n these goods). For our purposes, the nterestng case to consder s one n whch, n equlbrum, home labor s actve n producng both types of goods. In ths case, mmgrant labor wll be actve only n producng Z + -type goods, snce the wage on offer to t there wll be equvalent to the natve wage whle t would be lower were they to be employed n Z - type goods. Ths case has two features that are especally mportant for us. Frst, mmgrant labor s hghly concentrated, producng only Z + -type goods. Second, ths concentraton s wholly nconsequental for the equlbrum of the real economy. Snce wages of natve and mmgrant labor are already equalzed, there would be no ncentve for ether type to change sectors even f there were no productvty gap n the remanng goods. In ths type 15

16 of equlbrum n whch natve labor remans actve n all sectors and mmgrant labor only n some, one can treat the two as dentcal even f there are productvty dfferences that prevent the mmgrant labor from movng nto other sectors. Ths can be readly extended to the case n whch home labor has a productvty advantage n both types of goods. In that case, ϕ ( z) < 1 for z Z +. So long as the productvty gap remans smaller n Z + -type goods and natve labor remans actve n both sectors, mmgrant labor wll be concentrated n the Z + -type goods. Changes n mmgrant labor that do not shft us from ths equlbrum can be treated as f each mmgrant delvers ϕ ( z) unts of labor when measured n natve equvalents. Ths ratonalzes a world n whch mmgrant labor s concentrated by productve sector and n whch there exsts a wage gap between mmgrants and natves. Nonetheless, t says that we can treat mmgrant and natve labor as equvalents provded we make the approprate converson to effcency unts. IV. The US Productvty Advantage and Factor Inflows The emprcal segment of ths paper has two objectves. The frst s to establsh on a pror bass the reasonableness of our use of the Rcardan model as a framework for analyzng factor nflows to the US economy. The second s then to use ths framework, and smple varants, to calculate the mpact of these flows on the US. The Rcardan framework s specal n two dmensons. The frst s that technologcal dfferences are the foundaton for observed factor flows. The second s that the Rcardan model reles on a sngle composte factor labor. For ths to be a reasonable framework for our exercse, we would lke to verfy the plausblty of these 16

17 assumptons. For the frst, we would lke to confrm that the US has productvty advantages that could be the orgn of these flows. For the analytcs based on a composte factor, we would lke to see that the entry patterns to the US of moble factors are at least broadly smlar across dfferent types of factors. Measurng these factor nflows wll also then serve as an nput to our calculaton of the mpact on the US. A. US Productvty Advantages The US enjoys a large productvty advantage over vrtually all other countres n the world. Table 1 presents estmates from Islam (1995 and 2001) of total factor productvty (TFP) for a large sample of countres. As the data reveal, many developng countres have TFP levels less than 20 percent of the US level. In some extreme cases, productvty n developng countres s less than 5 percent that of the US. In these data only Hong Kong and Canada have TFP levels hgher than that of the US. Whle there s a rch TFP lterature that has produced a varety of pont estmates for ndvdual countres [see e.g. recent work by Hall and Jones (1996)], all studes conclude that TFP n the US s among the hghest n the world. 9 Hendrcks (2002) provdes an alternatve approach that arrves at a smlar concluson. He draws on observatons of the earnngs of mmgrants to the US from varous countres as one nput n a decomposton of the sources of cross-country ncome dfferences. If dfferences n the qualty of human captal were to explan the vast cross- 9 Whle dfferences n aggregate TFP suffce to establsh a motve for mgraton and would be fully adequate to the story we tell here, trade accordng to comparatve advantage requres as well that there be varaton at the product level n the TFP gap. The best exstng evdence s the work of Jorgenson and varous co-authors, as for example n Jorgenson and Kuroda (1990), whch shows substantal varaton n relatve TFP at the ndustry level even for relatvely rch countres. Moreover, Harrgan (1997) shows that ths ndustry varaton n TFP also affects patterns of nternatonal specalzaton. 17

18 country dfferences n ncome, then there would need to be very large gaps n wages between mmgrants and US natves of a magntude that we do not observe. He concludes that to make sense of the much smaller actual gaps, even after accountng for other cross-country dfferences, one must rely on large dfferences n TFP precsely the mechansm that we rely on n ths paper as the motvaton for factor mgraton. B. Contrbuton of Immgraton to the US Labor Force The US census provdes the most accurate numbers on the percent of the US labor force that was born abroad. The Census Bureau tres hard to make adjustments for undercountng of llegal mmgrants. The Census Bureau reports that the proporton of foregn born as a share of the US populaton n 1998 was 9.8 percent [OECD (2001)]. As t turns out, the contrbuton of the foregn born to the US labor force s even greater than ts contrbuton to US populaton because mmgrants have hgher labor force partcpaton rates than natves. As a result, n 1998 fully 11.7 percent of the US labor force was comprsed of people born outsde of the US. Ths s the pont estmate that we wll use throughout the remander of the paper. Although census data s superor to INS (2002) data n terms of understandng what share of the US labor force comes from abroad, INS data s useful n understandng the tmng and sources of mmgrant nflows. 10 The US mmgrant populaton s largely the result of a dramatc ncrease n mmgraton to the US n recent decades. As we can 10 One must be careful n comparng the INS data wth the census data because gross legal mmgrant nflows nto the US are not the same thng as net flows of mmgrants. The INS dentfes two man sources of error. Frst the census bureau estmates that n the 1990 s approxmately 220,000 foregn-born resdents and 48,000 natve-born resdents emgrated from the US each year. On the other hand, the INS estmates that 275,000 entered the US llegally each year. Surprsngly, these numbers are qute smlar, suggestng net nflows n the last decade were qute smlar n magntude to the level of legal mmgraton. 18

19 see from Table 2, legal mmgraton rose from approxmately 250,000 per year n the 1950 s to close to one mllon per year n recent decades. In addton to the large absolute nflows, mmgrants have accounted for an ncreasng share of US populaton growth. Between 1950 and 1998, the US populaton rose approxmately 80 percent, growng from 152 mllon to 271 mllon. Usng legal flows of mmgrants as a proxy for net flows, the share of mgrants n US populaton growth rose from approxmately 9 percent n the 1950 s to around 37 percent snce Much of ths reflects the fact that legal mmgrant nflows as a share of the exstng populaton rose from around 0.1 percent to 0.3 percent per year. Ths, coupled wth declnng fertlty n the natve populaton, accounts for the growng relatve mportance of mmgraton n US populaton growth. A second strkng feature of the INS data s the sources of mmgraton. Only 5.5 percent of the legal mmgrants to the US n 1999 came from countres whose TFP as measured by Islam (2001) was at least 70 percent as hgh as that of the US. Moreover, over half of the legal mmgrants to the US between 1991 and 1995 came from the Carbbean, Central and South Amerca countres wth typcally less than one-thrd the US TFP level. Other major source countres, such as the Phlppnes, the Sovet Unon, Chna, Inda, and Vetnam, have low TFP levels as well. Taken together, the data reveal that mmgraton from countres wth low TFP levels account for the vast majorty of mmgraton nto the US. Moreover, ths mmgraton from low TFP countres accounts for a substantal share of the growth n the US populaton and labor supply. These facts underscore the Rcardan motvatons for mgraton. 19

20 C. Composton of Immgrants to the US The foregong has consdered the contrbuton of the foregn born to the US labor force, yet t has not taken account of possble dfferences n the skll composton of natve and foregn born workers. Untl 1994, the Current Populaton Survey contaned a queston regardng whether or not a worker was born abroad. Based on ths, t s possble to examne dfferences between natve and foregn-born educatonal attanment (see Table 3). The CPS data ndcate that mmgrants have lower levels of educatonal attanment. But the dfferences are not as substantal as one mght thnk. In 1994, 29 percent of foregn-born workers had at least a college degree (16 or more years of educaton) whle 32 percent of US born workers dd. At the hgh skll end, there s a gap, but t s small. There s a greater dfference between mmgrants and natves among the lower ters of educatonal attanment. Whle 33 percent of mmgrants had less than 12 years of educaton only 13 percent of natve-born people dd. Ths suggests the nflux of mmgrants s lkely to have ts bggest relatve mpact on the factor supply of low sklled workers n the US. D. Contrbuton of Net Captal Inflows to the US Captal Stock Factor nflows to the Unted States have not been lmted to labor. In recent decades, the US has experenced large and persstent net captal nflows. These captal nflows have assumed an mportant and growng role as a share of US gross captal formaton. Fgure 4 reveals that whle there was a small captal outflow from the US n the 1970 s, ths was reversed n the early eghtes. Indeed, for the last two decades, net 20

21 foregn captal nflows fnanced between 5 and 21 percent of US gross captal formaton. 11 We would lke to emphasze that n makng ths calculaton we do not mean to mply that technologcal advantage s the sole determnant of net captal flows. Rather, we look on natonal technologcal advantage as one determnant of the level of nvestment, whch along wth other determnants of savng and nvestment works through the natonal ncome accountng to determne the net captal flows. Here we are able only to calculate the mpact of actual nflows, not to separate the motvatons for these nflows. Ths notwthstandng, we beleve that natonal technologcal advantage, per the dscusson above, s almost certanly an mportant component n the jont determnaton of these net flows. We can obtan some sense of the mportance of these net flows by lookng at how much of the US captal stock has been fnanced from abroad. Captal n year t can be defned as K = I / P + 1 δ K (16) t t t ( ) t 1 where K t s the captal stock, I t s gross fxed captal formaton, P t s the prce of captal equpment and δ s the deprecaton rate. We defne a counterfactual domestcally fnanced captal stock n year t as, K I NK / P 1 K d d (17) = ( ) + ( δ ) 1 t t t t t where NK t s the net flow of captal nto the US. d Kt can be ether larger or smaller than the actual captal stock dependng on the sgn of NK t. If t s smaller, then t represents 11 Indeed, by the year 2000 these net captal nflows accounted for one-fourth of US gross captal formaton. 21

22 the amount of captal that was fnanced by domestc savers. If t s larger, then t represents how much the US captal stock would have been f net flows of nvestment funds had not flowed out of the US but rather had been nvested domestcally. Fnally, we defne the foregn fnanced captal stock as (18) K K K. f d t t t Implctly, ths decomposton of the actual captal stock nto foregn and domestc components assumes that the path of domestcally fnanced nvestments would have been no dfferent had the US closed ts borders to captal nflows. To go beyond ths requres a model of ths counterfactual, an exercse we do not perform n ths paper. Here we assume that domestc nvestment s unaffected by net foregn captal nflows and vew our calculatons as a benchmark. Usng data on nvestment and the prce of captal goods from the IMF, we set the captal stock n 1947 equal to zero and calculate the US captal stock usng the same deprecaton rate (13.3 percent) as n Bowen, Leamer and Svekauskas (1987) and Harrgan (1997). We then set the domestc captal stock n 1970 equal to our estmate of the US captal stock n that year and calculate the domestc captal stock accordng to equaton (17) and the foregn captal stock accordng to equaton (18). Ths procedure yelds an estmate of the foregn-fnanced captal stock n 1998 equal to 11.8 percent of the total US captal stock. E. Reasonableness of the Rcardan Framework We stated two crtera at the outset for the reasonableness of our use of the Rcardan framework for examnng the consequences of the nflow of factors to the US 22

23 economy. The frst crteron s that the US has a productvty advantage that s plausbly a motvaton for these factor movements. We saw that ths s strongly confrmed by the evdence above on US TFP advantages, whch are partcularly strong relatve to countres that are the man sources for mmgraton to the US. The second crteron s that t s plausble to treat the factor nflows as f they were a composte factor as per the Rcardan model. Ths n turn requres that the magntude of the nflows across factors not have been too dfferent. We saw above that the contrbuton of the foregn born as a share of the US labor force s 11.7 percent. Under our assumptons, ths number s strkngly close to the 11.8 percent estmate of the share of the US captal stock fnanced by net nflows of foregn captal. If ths were the whole story, then our treatment of the factors as a composte would be strongly confrmed. Of course, we also saw that when we dsaggregate labor nto dfferent types, there are some dfferences n composton, especally among the least sklled. We wll address ths ssue of composton more drectly below when we turn to a mult-sector account of the mpact of these factor flows on output composton and our terms of trade. Nonetheless, the fact that, n broad terms, the nflows of captal and labor are so smlar n magntude seems to us strong reason for takng serously our Rcardan approach to the consequences of factor nflows as an alternatve to the standard approach, whch consders nflows only of one factor at a tme. V. How Factor Mgraton Affects the Income of US Natves In ths secton we calculate the mpact of these factor nflows on the US economy. In prncple, we could generate as many estmates of ths mpact as there are potental 23

24 models of the US and world economes. Our core results are developed n two steps. The frst step focuses purely on the rse of the US scale n the world economy due to mmgraton and s closest to the macroeconomc lterature, as exemplfed by Acemoglu and Ventura (2002). The second step supplements ths by allowng for greater heterogenety n labor nflows and output composton, and s closer to the nternatonal trade lterature, as n Harrgan (1997). We also dscuss robustness to alternatve assumptons. 12 A. Macroeconomc Approach A frst step n estmatng the mpact of factor mgraton to the US would merge a smple varant of our Rcardan model above wth the AK approach of Acemoglu and Ventura (2002). We can smplfy our Rcardan model so that there s a sngle good produced n each of the US and the rest of the world, but whch dffer from one another. 13 As n both our model and that of Acemoglu and Ventura, we wll thnk of only a sngle composte factor ( captal for them, labor for us). The US technologcal advantage then gves rse to factor movements that rase output of the US good and contract output of the good produced n the rest of the world. Ths shft n relatve outputs then wll have 12 The smulatons we develop are n the same analytc sprt as those of Borjas, Freeman, and Katz (1997). Borjas (1999, p. 48) argues n support of ths approach, notng that although the factor proportons approach reles on theory, so must any appled economc analyss that wshes to do more than smply calculate correlatons. In the end, any nterpretaton of economc data and partcularly any use of these data to predct the outcomes of shfts n mmgraton polcy requres a story. 13 The central results we developed above n Secton II are robust to a restrcton that the margn of goods produced n each country does not change, as we assume here. Unfortunately, the emprcal researcher does not drectly observe a change n the margn of goods produced, as the theoretcal model of Secton II would requre. No doubt, some of ths change n the margn may be captured by the changng composton of output consdered n Secton V.B. below. 24

25 terms of trade effects and we wll use the elastctes estmated n Acemoglu and Ventura to evaluate these. As noted earler, our treatment of the factor nflows as a composte s motvated by the fact that the contrbuton of foregn labor nflows to the US labor force and the contrbuton of foregn net captal nflows to the US captal stock come n at almost the same level (11.7 vs percent). If we multply the US labor share by 11.7 percent and the captal share by 11.8 percent, then, we wll then translate ths nto an equvalent proportonal ncrease of 11.8 percent n output of the US good. At ntal prces, ths would translate nto an equvalent proporton excess supply of US goods n world markets. Adjustment wll occur through a deteroraton n the US terms of trade. For our calculaton, we wll use the preferred estmate from Acemoglu and Ventura, n whch the elastcty of the terms of trade wth respect to GDP s The consequent deteroraton n the US terms of trade as a result of the growth mpled by these factor nflows s then 7.0 percent. Before we can calculate the cost to the US economy of ths, we need to resolve an ambguty here. Whether the change n the terms of trade comes through a declne of export prces or a rse n mport prces would be mmateral f trade were balanced. However, snce the IMF reports that exports were 8 percent and mports 11 percent of US GDP, ths could make a dfference. Our approach s smply to splt the dfference, assumng that the change n the terms of trade comes half n the form of a fall n US export prces and half n the form of a rse n US mport prces. Hence our calculaton of the lost ncome va the terms of trade deteroraton s of the form: 25

26 (19) GDP T 1 M + E ε GDP 2 GDP where the frst term n parentheses s the change n GDP due to factor nflows, ε T s the Acemoglu-Ventura estmate of how much GDP growth causes the terms of trade to deterorate, M s mports and E s exports. Ths yelds an mpact n 1998 of 0.7 percent of US GDP or $58.4 bllon dollars. So far, we have focused on the consequences of the expanson of US output of these factor flows. However, we also need to recognze that ther movement leads to a contracton of output of the rest of the world, makng foregn output scarcer relatve to US output, causng addtonal deteroraton n the US terms of trade. These ncremental effects are lkely to be smaller than those calculated above precsely because of the lower productvty of factors n the rest of the world. Of the 28 mllon foregn-born resdents of the US, only 16 mllon are actually n the labor force. Gven that the World Bank (1999 WDR) puts the global labor force outsde of the US at 2.6 bllon workers, ths probably only represents a 0.6 percent declne n the number of avalable workers. In terms of captal we get slghtly larger effects. Davs and Wensten (2002) estmate that 23 percent of the world s captal stock s n the US. Snce 11.8 percent of the US captal stock was fnanced from abroad, the flows mply a 3.5 percent reducton n the captal stock of the rest of the world. Multplyng these numbers by the US labor and captal shares, we estmate that factor flows from the rest of the world to the US decreased output n the ROW by 1.9 percent. Ths mples an addtonal deteroraton n the US terms of trade of 1.1 percent, whch would cost the US an addtonal 9.2 bllon dollars. Taken together ths frst step 26

27 n our exercse generates a net ncome loss to the US from factor mgraton of 68 bllon dollars n 1998 or 0.8 percent of US GDP n that year. B. Heterogeneous Labor n Mult-Sector Model Approach We now supplement ths macro approach wth elements focused on composton effects. There are two key departures. The frst s that we dsaggregate our labor varable accordng to skll class. The second s that we move to a mult-sector model of the US economy. These departures allow us to develop a smple model that bulds on Harrgan (1997) to descrbe the mpact on the US net offer to the rest of the world at the ntal prces. We then apply terms of trade elastctes at a sectoral level, whch we draw from Deardorff and Stern (1986). Agan these wll allow us to calculate the mpact on US ncomes of the mmgraton of these factors, now takng account both of scale and composton effects. In ths exercse, we dsaggregate the labor force nto three classes, those wth a college degree, hgh school graduates, and hgh school dropouts. As we noted earler, the proporton of foregn born n the hgh educatonal bracket mrrors reasonably closely that proporton n the natve populaton. However, ths s less true at lower educatonal levels, where natves are more lkely to have completed hgh school and the foregn born to have dropped out. These dfferences are at least potentally mportant n our framework because n a mult-sector model they wll have a non-unform effect on the composton of output. In prncple ths could even mprove the US terms of trade f the composton works to prncpally expand mport-competng sectors. By usng a mult-sector model and employng the estmates of Harrgan (1997), we can take drect account of these output 27

28 composton effects. Fnally, the mult-sector model also allows us to move away from applyng a sngle terms of trade elastcty for composte exports, but rather to allow for dfferent elastctes by sector. We now dscuss our mplementaton. Let T be net trade, absorpton n sector. Then, (20) T = X D X be output and D be.e. our net offer s just output less absorpton n that sector. We now need to see how that net offer wll change at the ntal prces f a non-unform nflow of factors changes sectoral output, GDP, and absorpton. For smplcty, we assume that absorpton s homothetc, so that at ntal prces, the nflow of factors affects the scale of absorpton, but not ts composton. Keepng n mnd that we are lookng at dscrete changes, we need only take dfferences n our net offer equaton. Let s X GDP be defned to be the rato of output n sector to GDP, and a crcumflex, ^, represent a proportonal change. In Appendx A, we show that the change can be examned as follows: (21) T = X sˆ + T GDP + X sˆgdp Ths dfferenced equaton has three terms. The frst s a Composton Effect reflectng the fact that even at the orgnal GDP, there s a change n the share of output n sector. The second s a Sze Effect reflectng the fact that even f the nflow of factors had no mpact on the composton of output, the smple scalng-up of output would rase our net offer. Fnally, because of the dscrete changes, there s also an nteracton between the scale and composton changes that need not be small. 28

29 The startng pont for the emprcal mplementaton of ths equaton s the excellent work of Harrgan (1997). Harrgan bulds a full general equlbrum Heckscher- Ohln-Rcardo model of global producton and then obtans precse estmates of the effects of productvty and endowments on the producton of the varous manufacturng sectors. The parameter estmates that Harrgan derves are exactly what we need n order to understand how changes n captal and low, medum, and hgh-skll labor wll affect US exports. Harrgan s pont estmates tell us how much a gven percentage change n a partcular factor wll change the value-added share of a partcular sector n GDP. By multplyng Harrgan s coeffcent estmates (from Table 5 of hs paper) by the changes n US factor supples mpled by mgraton, we obtan estmates for how much each sector s value added share of GDP should change as a result of mgraton. The only remanng ssue s that trade s the dfference between producton and absorpton, not value added and absorpton. We wll assume that the percentage change n a sector s share of value added s the same as ts percentage change n output. Thus, we can use Harrgan s coeffcents to calculate s ˆ and so to mplement the model of the change n the US net offer emboded n equaton (21). 14 Snce the last CPS data on the composton of foregn-born workers s from 1994, we wll have to assume that ths dd not change apprecably by Performng ths calculaton for the US reveals that the nflows of factors nto the US caused the bggest expansons n US net offers n processed food, apparel, and ndustral machnery and contractons n paper, chemcals, and metals. We then calculate T by summng the varous terms of equaton (21). 14 In calculatng the terms of trade changes, we are lmted to usng the sectors employed by Harrgan. Ths s less than the full unverse of sectors (cf. Harrgan 1997). Implctly we are oblged to assume that terms of trade effects n excluded sectors match the average for ncluded sectors. 29

30 Assessng the mpacts of these changes n net offers on prces requres some addtonal assumptons and modelng. T must be accommodated by adjustments n the prces of exports and mports. We model ths as follows. Assume that prce changes n US goods map nto export and mport prces accordng to the followng equatons: (22) E E = ε E p p (23) M M = ε M p p E M where E and M are US exports and mports n sector, ε ( ε ) s the elastcty of US exports (mports), and p s the relatve prce of US to foregn goods n the sector. 15 We can then wrte the mpact of a change n the US net offer on prces as, E M p T E M E M p (24) = = ( ε ε ) or (25) T E M ( ε E ε M) p = p Equaton (25) gves us a mappng between changes n net offers and changes n US export prces. Usng data on sectoral export and mport elastctes taken from Deardorff and Stern (1986) we can estmate the mpact of these changes n net offers on prces. Once agan we are faced wth the ambguty of whether a certan percentage change n the relatve prce of US exports s due to export or mport prces changes. Here agan we 15 US Import demand elastctes were taken from Table 3.2 pp of Deardorff and Stern (1986). US export elastctes were based on Table 3.2 and recalculated accordng to Deardorff and Stern's methodology (equatons A.1.25 and A.1.32) wth 1994 data. 30

31 assume that half of the change s due to export prce movements and half due to mport prce movements. We calculate the change n the terms of trade as (26) Change n Terms of Trade 1 p E M = 2 p + E M where E and M denote aggregate US exports and mports. Usng equaton (26), we fnd that factor composton effects mply that the US terms of trade deterorated by an addtonal 1.5%. Ths mples an addtonal loss for the US of 12.5 bllon dollars, whch brngs the aggregate ncome loss up to 80 bllon or 0.9 percent of GDP. 16 C. Magntude of Losses We have now provded an approach to calculatng the mpact of mgraton on the ncome of US natves n two steps. The frst step focuses on pure scale effects n a world n whch US output s a functon of the captal stock and aggregate labor and then apples the trade elastcty estmates of Acemoglu and Ventura (2002). The second step supplements ths by consderng a world n whch output s dvded nto multple ndustres and labor s dsaggregated accordng to educatonal attanment. The mpact of factors on output levels and composton s based on Harrgan (1997) and the sectoral trade elastctes are drawn from Deardorff and Stern (1986). It s worth notng that the latter experment, n whch some sectors expand and others contract n relatve terms, could n prncple have led to mprovements n the US terms of trade. The results from these experments suggest that the resultng terms of trade losses are approxmately $80 bllon n Of ths, approxmately 90 percent of the loss 16 Ideally, we would lke to have calculated the mpact of changng factor ratos on output n the rest of the world. Unfortunately, we don t have consstent data on value added by ndustry that matched the export data, so we dd not do ths calculaton. 31