Iigration and ocial Justice (Translated fro the French original published in Revue Econoique, vol. 48, o. 5, epteber 1997, pages 1291-1309.) Thoas Piketty 1 ABTRACT Can the opening of the borders in the orth be harful to the unskilled workers of the outh, who are the ost disadvantaged people in the world? With two production factors, igration between outh and orth is always beneficial to outhern unskilled workers since they are the ost abundant factor. However, with three factors (three skill levels, or two levels and one iperfectly obile capital input), opening the borders ay lead to a decrease in the wage of the outhern unskilled if their copleentarity with high-skill labor or capital in the orth is sufficiently low copared to the lesser skilled workers of the outh. everal recent studies suggest that the elasticity of copleentarity falls sharply beyond a certain skill gap. However, nothing proves that these effects are sufficiently high to copare the optial policy of opening the borders fro the viewpoint of Rawlsian distributive social justice with the policy of closing the borders ipleented recently in Europe, a fortiori with an open border policy beneficial to highly skilled workers of the outh. ITRODUCTIO The political econoy of igration is paradoxical fro the point of view of pure econoic logic. On the one hand, the lowest skilled workers are generally the ost hostile towards igrant workers, which is consistent with their econoic interest since any skill group in general benefits fro its relative scarcity. 2 On the other hand, left-wing parties though they 1 Paris chool of Econoics.Thanks to Michael Kreer, Coen Teulings and Yves Younes for stiulating discussions. 2 During the first round of the presidential election in France in 1995, 27% of blue collar workers voted for Jean- Marie Le Pen, against 19% of white collar workers, 10% of id-level professionals and 6% of executives (Le Monde, April 25, 1995). 1
support and are supported in their ajority by the popular classes 3 hold political views that, copared to right-wing parties, are ore favorable to igrant workers. These tensions, which see strange if political actors pursue the rational self-interest eerging fro public choice odels in the odern econoic literature, becoe understandable once we take into account the fact that political actors generally try to hold a coherent views (at least in appearance) about a just society and social justice. For exaple, left-wing parties support igrant workers by focusing on the equal capacity of individuals to be integrated in the social life of the host country regardless of their country or cultural background, and therefore on equal opportunity. By contrast, right-wing parties would insist on the inertia of individual sociocultural roots, on the unavoidable inequality in the capacity to assiilate and therefore on the liits of a global society and on the benefits of national preference. 4 Left-wing parties rarely suggest opening borders in order to give these persons right to the sae range of opportunities regardless of their birthplace. Actually the periods of high iigration in rich countries are far fro systeatically coinciding with periods when the left is in power the latter often requests a ore huane treatent of the iigrants who are already established on the territory, without necessarily advocating an increase in their size. One arguent often used by the left to justify the liited attention given to potential igrants fro poor countries is that a coplete open border policy would not necessarily be a good thing for those sae countries: it would benefit ostly the high-skill workers fro poor countries and the 3 During the second round of the presidential elections in 1995, 57% of blue collar workers voted for Lionel Jospin, against 55% of white collar workers, 51% id-level professional, and 41% of executives (Le Monde, May 10, 1995) 4 For exaple, according to alt et al. ([1994], table 7.5., p. 179) and Friedberg et Hunt [1995], fig. 1), the average nuber of igrants settling in France was about 50,000 per year between 1980 and 1992, a period during which the governent was essentially socialist whereas, during the sae period, the corresponding figure was approxiately 300,000 per year in Gerany, 150,000 per year in the United Kingdo, and between 800,000 and 1,000,000 per year in the United tates, three countries with right-wing governents. On the political origins of the 1980s and 1990s in the United tates, which was a period of high iigration siilar to the 1880-1914 period. ee for exaple Younes [1994]. 2
low-skill workers would not be able to seize the opportunity and would reain in a persistent state of underdevelopent. Another traditional arguent is that given the actual state of public opinion on this atter, opening the borders would risk provoking violent tensions that would end up being harful for the very igrants whose existence one clais to iprove. The first arguent is essential: it actually plays a key role in the political discourse, to the extent that it iplies that opening the borders is not the just ideal policy 5 and therefore that it is useless to attept to find convincing arguents about the advantages of opening the borders. The objective of the paper is to analyze and evaluate the conditions that validate such view: under which conditions would it be accurate to say that the ost disadvantaged workers in poor countries, and hence in the world, would suffer fro a coplete opening by rich countries of their borders? In other words, what is the optial level of iigration fro the perspective of Rawlsian distributive justice? The analysis is conducted using a basic odel with two distributions of workers by skill level initially living in two countries, the orth and the outh. The sae production function with constant returns of scale allows the production of a good that is hoogenous in the two countries with inelastic quantities of capital and labor available at various skill levels. The assuption of a hoogeneous good iplies that international trade in good and services does not play any role in that odel and allow us to focus on the question of the igration of the labor force. 6 5 That is, the just policy in a world in which we would have the tie and an infinite ability to convince every one of what a just policy actually is. 6 In a ore general odel where both the orth and outh would produce and exchange different goods by using different cobinations of production inputs, the results we arrive at would be valid for international trade and not only for igration. But the free trade of coodities between countries endowed with different distributions of workers by skill levels is erely a very iperfect substitute for the international igration of the labor force, due to copleentarities between production inputs existing within a sae country and within a sae production space, and to the fact that several good and services are not internationally tradable. Because Bangladesh is able to export 3
To begin with, we reind the reader that, in such a odel, the coplete opening of the borders between orth and outh leads to the ost efficient allocation of huan resources and hence to the highest average wage at world level (section 2). By ignoring the possibility of copensatory fiscal transfers between losers and winners resulting fro opening the borders which in practice are always costly and liited we then ask under what conditions the opening of the borders would also lead to an increase in the iniu wage at world level. First we show that, if there are only two skill levels, 7 opening the borders leads the outhern unskilled to igrate to the orth until their relative weight in the orth reaches that of the outh and until the unskilled wage in both countries reaches the sae level a level that is higher than the one existing initially in the outh (section 3). But this not necessarily the case if there are at least three levels of skills (section 4). For exaple, assue that low-skill (illiterate) workers, skilled workers (literate), and a sall inority of high-skill workers live in the outh while a very sall quantity of low-skill workers and a substantial quantity of skilled and highly skilled workers live in the orth. The opening of the borders would lead the outhern literate workers to work with (or for) the orthern high-skill workers and not anyore with the outhern low-skill, hence their wage would decrease as copared to their initial position. We specify the conditions under which such a phenoenon can occur and show that it is necessary for the relationship between the copleentarity elasticity of two skill levels and the distance separating the two skill levels to have an inverted U ( ) shape. We show that the sae phenoenon can occur with two levels of its rice and textiles does not change the fact that the quantity available of land, equipent, and literate workers by resident is very low copared to that in western countries a fact which only igration could change. Free capital oveent would only perfectly substitute for the free igration of people if each country were endowed with the sae distribution of workforce by level of skills. (see section 2). 7 iilarly if only one level of skill exists (one hoogenous labor input) and one iperfectly obile capital input (see section 3). 4
skill and iperfectly obile capital concentrated in the orth if copleentarity between the outhern low-skill and orthern capital is sufficiently low as copared to the copleentarity between outhern skilled and orthern capital. In other words, the opening of borders can be harful for outhern low-skill workers if their skill level is too low to be able to benefit fro production inputs available in the orth whereas other inputs available in the outh take advantage of this opportunity. Finally, we exaine several recent epirical estiates of this elasticity of copleentarity: it appears that the effects described above are qualitatively realistic but it is not proven that they could be sufficiently strong quantitatively for the opening of the borders to be harful to outhern low-skill workers (section 5). ection 6 concludes. EFFECT OF MIGRATIO O AVERAGE ICOME Let us consider two countries, orth and outh, with populations I and I. Each agent i is characterized by a skill level q i) { 1;...; Q} ( where Q 2 is the nuber of different level of skills. The orthern population (resp. the outhern) is characterized by skill distribution ( q)) 1 q Q ( resp.( ( q)) q Q )) : in the orth there are (q) workers with skill q ( 1 (resp. ( q workers in the outh). The world stock of physical capital is denoted k, and )) 1 q Q fixed capital in the orth is denoted k (resp. k in the outh), with k = k + k. Each country has access to the sae technology, represented by an aggregate production function F ( 1), (2);...; ( Q); k) ( which transfors the quantities ( 1), (2),..., ( Q) of skill level Q and one quantity k of capital into a quantity of hoogenous good 5
( (1);...; ( Q k ) Y = F );. We assue that it is a constant returns to scale technology with respect to Q + 1 production inputs: ( 0, F ( λ(1), λ(2);...; λ( Q); λk) ) λf( (1), (2);...; ( Q); k) λ f = In other words, one country twice as large as another but rigorously identical in ters of the distribution of its production inputs yields twice as uch. The absence of increasing returns to scale enables us to abstract fro country size effects and to focus our attention on the coposition effects. 8 Consider,..., F F 1 Q k the first derivatives of function F (arginal F, productivities), and ( F qq F qk ) qq Q properties. 9 ', the second derivatives of F, which satisfy all traditional 1 ' Finally let us assue that labor supply is inelastic: workers supply one labor unit corresponding to their skill q, regardless of the wage w (q) that is offered for that skill in their own country. The labor arket is copetitive as long as, in each country, the wage w (q) is equal to the arginal productivity of the skill q in that country. 8 Clearly, introducing increasing returns to scale would reinforce the advantage of opening the borders, ceteris paribus. Borjas [1995] notes that using a production function with increasing returns to scale at the aggregate level, is often used in growth theory and international trade theory but is not sufficiently well founded epirically to include it in our analysis of the effects of igration. 9 i.e., F,..., F, F 0, F 0 q { 1;...; Q}, F 0. 1 Q k > qq kk 6
Let us assue first that the border between the orth and the outh is closed. In the orth, wages are established at a level such that, at equilibriu, all available inputs are utilized, so that the national incoe in the orth Y is given by: ( (1);...; ( Q k ) Y = F ); The equilibriu wages in the orth ( w (1);...; w ( Q)) for the range of skills, as well as the rate of return on capital r (interest rate, rate of return), are given by their respective arginal productivities: { 1 ;...; Q}, w ( q) = Fq ( (1);...; ( Q k q ); r = Fk ( (1);...; ( Q); k ) iilarly, in the outh, national incoey, equilibriu wages ( w (1);...; w ( Q)) and the rate of return on capital r are given by: ( (1);...; ( Q k ) Y = F ); { 1 ;...; Q}, w ( q) = Fq ( (1);...; ( Q k q ); r = Fk ( (1);...; ( Q); k ) If we assue that the border between orth and outh is open for capital flows (but not for the labor force) and that the capital arket is perfectly efficient, the world stock of capital k will be distributed between both countries so that rates of return are equalized at the world level, i.e., r = r r. In practice, international capital obility is constrained by a range of incentive = probles (liited coitent capacity of a country not to expropriate foreign investors, high 7
costs of financial interediation, etc) or siply by the fact that capital that is already located in one country (land, infrastructure, real estate) cannot be easily relocated: typically, the apparent arginal productivity of capital in the outh r could be higher than in the orth for a long period of tie. 10 Whatever the case ay be, as long as the border reains closed for the labor force, the equilibriu wages ( w ( 1);... w ( Q) ) and ( w ( 1);... w ( Q) ) in the orth and outh will be generically different as long as the initial distributions ( ( q) ) and ( ) 1 q Q q) 1 q Q ( of which both countries are endowed are not strictly identical. The fact that the arginal productivity of the sae production input takes different values in different production locations violates the traditional productive efficiency condition at the world level: typically, if a low skill q is ore abundant in the outh than in the orth, its arginal productivity in the outh w (q) will be lower than its level in the orth w (q). This eans that a transfer of one unit of low skill fro outh to orth would increase production in the orth by an aount greater than the decrease in production in the outh. Let us now assue that the border is copletely opened to the flow of labor and that transportation costs between orth and outh are negligible. 11 The igratory equilibriu would 10 There are liits to this type of arguent. As noted by Lucas [1990], if the difference in national incoe between India and United-tates were siply explained by the inequality of the stock of physical capital of those two countries, this would iply that the arginal productivity of capital is 58 ties greater in India than in the United- tates. It is difficult to conceive that incentives issues could bring this ratio down to 1. It suggests that inequality between skill distributions plays a key role. 11 The existence of high transport costs could explain why low-skill workers fro the outh whose onetary gain resulting fro igration is lower than that of skilled workers, and who generally cannot borrow oney, could be the victi of an opening of the border. But such an arguent is not decisive: transport costs are declining and are now 8
reach a level such that nobody has an incentive to igrate, i.e., wages for different skill levels take the sae value in the orth as well as in the outh, which we note ( w ( 1);... w ( Q) ) + +. Given that labor supply is inelastic and that technology exhibits constants returns to scale, these wages are equal to the arginal productivity of inputs as long as all available skills are fully eployed at the world level. { 1 ;...; Q}, w ( q) = F ( (1) + (1);...; ( Q) + ( Q k k ) q + ); + q ( ( 1) + (1);...; ( Q) + ( Q k k ) r + + = Fk ); The world incoe Y + is then given by: ( ( 1) + (1);...; ( Q) + ( Q k k ) Y + + = F ); This world incoe Y +, which corresponds to the free arket equilibriu at world level, is the axiu world incoe that can be obtained given technology and available production inputs. 12 It cannot be inferior to the world incoe Y + Y corresponding to the closed border regie and, generically, it is strictly superior as long as wages were not rigorously identical in the orth and in the outh in the closed border regie. Proposition 1. Opening the borders leads to a higher world incoe, and thus to a higher average incoe Y + > Y + Y uch lower than the onetary gain resulting fro igration to the orth; and there are now several echaniss and networks through which credit can be obtained in advance. 12 This equivalence between free arket equilibriu and axiization of total incoe siply results fro the axiization of firs profit, which iplies that we will always be on the efficiency frontier of the production area. Thus it is equivalent to axiizing total incoe since all inputs are inelastically available and are fully used up, and there is only one consuption good. This equivalence would not be verified if the labor supply elasticities were positives: for exaple, if the elasticity of the low-skill labor supply in the orth is greater than the other elasticities, then subsiding the orthern low-skilled labor (which could be done indirectly by closing the borders) could lead to a greater total incoe. More generally, this equivalence would not be valid if several goods of consuption related to different levels of incoe: the concept total incoe could not be separated anyore fro distributive considerations. 9
Let us reeber that, in the presence of constant returns of scale vis-à-vis Q + 1 production inputs, the international obility of Q inputs would be sufficient to reach the sae world production optiu Y + only if Q + 1 production inputs are obile: if the borders are opened to flows of Q types of labor but closed to capital flows, the igration equilibriu which equalizes the prices of Q labor inputs would also lead to the equalization of the rates of returns on capital both in the orth and outh, so that capital flows would be unnecessary. iilarly, the international obility of capital would be a perfect substitute for international igration if only one skill existed (Q =1). ot so in the case we are interested in, which is Q 2. EFFECT OF MIGRATIO O MIIMUM ICOME WITH TWO KILL The fact that the average incoe is greater in an opened border regie does not iply that all individual wages are greater: the free arket equilibriu at world level does not guarantee a Pareto iproveent of the arket equilibriu with closed borders. The fact that total incoe is greater would, however, generate a distribution of wealth, once borders are opened, such that everyone would benefit fro the openness. everal reasons explained why such transfers are liited in practice. (i) The tate always observes iperfectly the characteristics of individuals on the basis of which it would like to condition its transfers (negatives or positives), so that adinistrative and disincentive costs could be substantial on a larger scale. 13 13 In the odel described above, it would be sufficient to know the technology, the distribution by skills and observe the individual incoes to be able to redistribute wealth at zero cost given the inelasticity of labor supply. The result would have been different if we introduced the (ore realistic) possibility for workers to transit between skills, under specific conditions and then let their incoe vary within a given skill group. 10
(ii) Copetitions between governents to attract fiscal benefits (that is to say the fact that both orth and outh are not hoogenous political entities) strongly reduce their capacity to redistribute: a orthern country cannot decide alone to tax heavily those who benefit the ost fro igration. (iii) Totally copensating orthern low-skill workers for the costs that igration iposes would require that a large nuber of workers with siilar skills be treated differently on a sae territory depending on whether they are born and bred ortherners or igrants. This raises a nuber of substantial probles (for exaple, how should the intergenerational transission of these differences be handled in that case?) (iv) Independently of these practical difficulties, public opinion has not yet clearly aditted that it could be legitiate to have a fiscal redistribution aong workers after having freely allowed the labor arket to play its allocative role. Indeed quite aside fro the igration issue odern governents rarely ipleent explicit redistributions aong wage earners. 14 One should not exaggerate the iportance of these liits to fiscal copensation but, given these liits, we ask the following: assuing that these transfers are inexistent or insignificant which is often the case in practice under which conditions does opening the border lead to an increase in ean incoe and in the iniu wage? That is to say, if we call 14 Moreover, it is because of this that the net budgetary ipact of igration is clearly positive in all Western countries: the ain solidarity efforts in the odern welfare state being directed toward the elderly (health and retireent benefits) and not toward low wage earers, the social security contributions by low-wage igrant workers are significantly larger than the public expenditures directed at the even if they have any children and igrate to a country with generous faily allocations (see toresletten [1996] for a coplete estiation in witzerland). This could be changing, however, as indicated by transfer systes directed at low-wages recently developed in the United tates. 11
w the wage of the ost disadvantaged in a closed border regie ( w Min{ w ( 1);...; w ( Q); w (1);...; w ( Q) }) = and workers under an open border regie w Min{ w ( 1);...; w ( Q) } w the wage of the ost disadvantaged ( ) =, under which conditions + + does w > w? What is the optial quantity of igration fro the point of view of the ost disadvantaged and, hence, of Rawlsian distributive justice? A transparent answer can be provided using an often-used fraework with two types of skills, the unskilled and the skilled. Abstracting for the oent fro the existence of capital input k, assue that = 2 Q and consider any production function F( ( 1), (2) ) exhibiting constant returns of scale vis-à-vis production factors (1) and (2). Let us note q = 1 the lowest skill (the one with the lowest arginal productivity) and q = 2 the highest skill. By definition, the outh is the country with the greatest aount of unskilled workers with respect to the nuber of skilled workers: ( 1 ) ( 2 ) > ( 1 ) ( 2 ) In the closed border regie, the wage w (1) of the outhern unskilled is given by ( (1); (1) ) w ( 1) = F1 or, given the constant returns of scale assuption, by ( (1) / (2);1) w ( 1) = F1. iilarly, the wage w (1) of the orthern unskilled is given by ( (1) / (2);1) w ( 1) = F1. ince F 0 the unskilled wage is a diinishing function of the ratio between the nuber of 11 unskilled and the nuber OF skilled workers, and therefore we have w 1) w (1) : the outhern ( unskilled pay for their relative abundance as copared to the orth so that the iniu wage w at world level in a closed border regie is equal to w (1). 12
ow, if we open the borders so that the outhern unskilled decide to igrate assively to the orth until they reach the point where the ratio of the nuber of unskilled workers and of the nuber of skilled workers becoes equal, both in the orth and in the outh, to the world ratio ( 1) (1) / (2) + (2)) ( +. The unskilled wage will be given by: (( (1) + (1)) /( (2) (2));1) w + ( 1) = F1 + ince ( 1) (1) / (2) + (2)) ] (1) / (2); (1) / (2)[ ( + and F 0, we infer that ] w (1); w (1) [ 11 w + ( 1) the iniu wage w = w + (1) under an open border regie is greater than the iniu wage w = (1) under a closed border regie. 15 w The sae reasoning would apply to the case where there is only one type of labor ( Q = 1) and one capital input k: starting fro an initial condition where capital is only iperfectly obile internationally, and hence where the outh is abundant in labor and the orth is abundant in capital, thus leading to wages that are lower in the outh than in the orth, the opening up of the borders to the labor force leads to a assive igration fro outh to orth and hence to an increase in the iniu wage at the world level, in addition to an increase in total incoe. However, this reasoning could not apply to the case where there are two skill levels and one iperfectly obile capital input, as we will deonstrate in the next section. 16 To suarize, we have: 15 w is strictly greater than w provided that there is a positive copleentarity between the two skill levels, i.e. as long as the elasticity of substitution between the two skill levels of the function F ( ( 1), (2) ) is not infinite. 16 However, we can deonstrate that the reasoning would be valid in the case of the production function F ( ( 1), (2); k) if we assue that capital is perfectly obile internationally, including in a closed border regie. 13
Proposition 2: In presence of two iobile production factors (two levels of skills, or one level of skill and one capital input), opening the borders also leads to an increase in the iniu wage: w > w The fact that opening the borders leads to a greater iniu wage at world level, obviously, does not solve all our probles: the orthern unskilled experienced a decrease in their incoe (and the uneployent rate would increase if we were to introduce uneployent) and it would doubtlessly be difficult to copensate the entirely for the reasons cited above. evertheless, if the world were as transparent as the bipolar world described in this section that is to say if igration fro outh to orth always unabiguously benefited the outhern ost disadvantaged workers the political discourse which cast doubts on the benefits of igration for the outhern countries would not have uch weight, and would consequently affect iigration policies. In fact, the world is ore coplex and does not easily lead to unabiguous conclusions. EFFECT O THE MIIMUM ICOME WITH n > 3 KILL The reasoning discussed above in which outh-orth igration is an opportunity for the outhern ost disadvantaged workers to exit fro the relative abundance fro which low-skill workers suffer fro does not apply as long as at least three distinct skill levels (or two skill levels and one iperfectly obile capital input, which is siilar see below). Intuitively, the reason is siple: as soon as we leave the bipolar world (unskilled vs. skilled, labor vs. capital) by introducing interediate categories, opening the borders between two worlds that are uneven in ters of their distributions could benefit first those whose skills are not too far fro the average 14
in the orth and not siply those whose skills are abundant in the outh, and therefore could leave the latter worse off than before. Let us start with an exaple. Exaple 1. Three kill Levels Let us assue three skill levels ( Q = 3) and abstract, to siplify, fro the capital input. To clarify ideas, let us call skill q = 1 the group of illiterate workers, who represent a sall inority of the population in orthern countries but can typically account for 50-60% of the labor force in the poorest countries in the outh (Indian subcontinent, ub-aharan Africa), 17 q = 2 the group of literate workers who did not have access to higher education and who account for an iportant part of the population (ore than 50% in the orth, and slightly less in the outh), and q = 3 the group of highly skilled workers (sall inority in the outh, and large inority in the orth). Consider technologies F( ( 1), (2), (3) ) with constant returns of scale as described in Kreer and Maskin (1996): each production unit requires two workers, one playing the role of anager and the other of assistant ; if the anager s level of huan capital is h M and that of the assistant is h A, then production is y = h h 2 A M. In other words, the level of huan capital of the anager counts ore in total production than that of the assistant. The anager-assistant etaphor can obviously be interpreted in a broader sense: copleentarity between the illiterate farer and the literate technician in a village, the craftsan and the engineer, the secretary and the executive, etc. ote h ( 1) < h (2) < h (3) the three huan capital levels corresponding to the three skill levels. The key issue is to know who is going to work with who in equilibriu: either the ore skilled workers will function as anager in the sae production units where low- 17 ee for exaple Drèze and en [1995] 15
skill workers would function as assistant, or the ore skilled workers will work aong theselves, and so will the low-skill workers. To siplify, assue that there are no workers with skill q = 3 in the outh and no workers with skill = 2 q in the orth: ( ( 3) (1) = 0) =. We can easily show that, as long as the ratios h ( 2) / h (1) and h ( 3) / h (2) are below a specific threshold λ > 1, literate workers will work with outhern illiterate workers and high-skill workers will work with orthern literate workers. Conversely, if the ratios h ( 2) / h (1) and h ( 3) / h (2) are greater than λ then it would be efficient for high-skill workers in both countries to work together and allow the low-skill workers to do so as well. 18 Assuing that h ( 2) / h (1) and h ( 3) / h (2) are actually inferior than λ, and assuing that ( 2) < (3) and 1) < (2) in such a way that, both in the orth ( and in the outh, there would be excess deand for low-skill workers in a closed border regie. In the orth, there would be (2) production units involving a highly skilled anager and a literate assistant, with individual production 2 h ( 2) h(3), 19 whereas the reaining highly skilled workers 3) (2) will create ( 3) (2))/ 2 ( production units in which both anager ( and assistant are highly skilled, hence the individual production would be 2 3 h ( 3) h(3) = h(3) ; the equilibriu wage w (3) of high-skill workers would be equal to their arginal productivity 3 h (3) / 2, and the equilibriu wage of the literate would be equal to their arginal productivity 18 Because of the equivalence between the arket equilibriu and axiization of total incoe in such odel (see 3 3 above), there is separation if the associated production, i.e. h ( 2) + h(1), is greater than the production obtained 2 if both skill groups act together, hence 2h (1) h(2). Denoting λ = h( 2) / h(1), this condition is equivalent to λ = production function 3 2 + 1 2λ, therefore λ > λ = ( 1+ 5) / 2 α β y = h h, with β > λ A M. A siilar property would be valid in the ore general case of a 19 This last hypothesis is not entirely consistent with the nuerical approxiation given above on the skill distribution in the orth and in the outh, but things would work out if we assue that each production unit involves one anager and n assistants. 16
2 3 3 h(2) h(3) h(3) / 2. iilarly, in outh, the wage w (2) would be equal to h (2) / 2 and the 2 3 wage w (1) would be equal to h(1) h(2) h(2) / 2. The iniu wage at world level is given 2 3 by w = w (1) = h(1) h(2) h(2) / 2. Let us now assue now that borders are open to labor force flows. outhern literate workers now have the opportunity to work with (or for) orthern high-skill workers. Assue that 1) > (2) + (2) so that, potentially, all literate workers in the world could work with (or ( for) orthern high-skill workers. If we assue that the skill gap h ( 2) / h(1) between illiterate and literate is sufficiently high copared to the gap h ( 3) / h(2) between literate and high-skill, then this is exactly what will happen: 20 in equilibriu, there will be 2) + (2) production units ( that involve a high-skill anager and a literate assistant, in which the wage w + (3) of the high- 3 skill workers would be h (3) / h(2) and the wage w + (2) of the literate would 2 3 be h(2) h(3) h(3) / h(2), whereas the outhern illiterate (1) would yield (1) / 2 production units with anager and assistant being both illiterate and the wage w + (1) equal 3 3 to h (1) / 2. The iniu wage is now w w (1) h(1) / 2, which is lower than the = + = 2 3 iniu wage = h(1) h(2) h(2) / 2 prior to the opening of the border. The wage of the w 20 The exact condition for a arket equilibriu is that the wage loss experienced by outhern low-skill workers when they work alone ( 2 3 3 h (1) h ( 2 ) h ( 2 ) / 2 h (1) / 2 ) be inferior to the wage increase 2 2 3 h ( 2 ) h (3) h (3) / 2 h ( 2 ) / 2 earned by the outhern illiterate workers when working as assistant to orthern high-skill workers rather than being anager of a outhern low-skill worker. If we write λ = h( 2) / h(1) and λ ' = h(3) / h(2), it is sufficient for λ to be sufficiently high copared with λ ' for the condition h (1) h ( 2 ) 2 3 3 2 2 3 h ( 2 ) / 2 h (1) / 2 < h ( 2 ) h ( 3 ) h ( 3 ) / 2 h ( 2 ) / 2 to hold: for exaple if λ = λ and λ' < λ, then the first ter is zero and the second is positive (see footnote 18), and the inequality would reain valid if λ is close to λ by continuity. 17
literate and of the high-skill workers in the orth has not changed the orthern literate workers have captured all the benefits of econoic integration. Intuitively, this is consistent with a situation in which Indian peasants are too illiterate to be able to do any kind of work in the orth, and where the opening the borders with the orth siply prevents the fro having the benefit of working with literate peasants who, previously, allowed the to soewhat increase their productivity (by reading the user s guide of the tractor, or whatever) but now igrate orth to work for Westerners. The conditions described in this first exaple show that the opening of the borders can be harful to outhern low-skill workers: what is required is that the copleentarity between two skill levels decrease sufficiently rapidly when the gap between both skills increases such that the gap between illiterate and literate is greater than the gap between literate and very literate (high-skill) to such an extent that the opening of borders dispossesses outhern illiterate workers fro the copleentarity they previously enjoyed with their literate workers. For a general technology F ( ( 1);...; ( Q) ), we define the elasticity of copleentarity c between two level of skills q and q as the percentage wage increase of skill qq' q generated by an increase in the nuber of workers with skill q corresponding to one percent of the labor force. c qq' is equal to Fqq' F 21. For q=q, we always have c qq < 0 Fq Fq ' : the arginal productivity of a group with a given skill decreases as its relative abundance increases. The specific technology introduced by Kreer and Maskin (1996) iplies that, at an aggregate level, 21 ee Haeresh [1993] 18
the elasticity of copleentarity c 13 between illiterate and high-skill would also be negative: by attracting the literate workers with who they are strongly copleentary, a rise in the nuber of high-skill workers can reduce the arginal productivity of illiterate workers. This property illustrates a ore general and extreely intuitive hypothesis: the elasticity of copleentarity c is axiu and positive for an interediate level of skill gap q q', qq' though it ay be lower and even negative at very low or very high levels of this gap. That is to say, the curve linking the elasticity of copleentarity and skill gap has a shape which increases first then decreases. 22 In order for the opening of the borders to be harful to low-skill workers, a necessary and sufficient condition is that this -shaped curve decrease sufficiently rapidly at the skill gap level which separates outhern low-skill workers fro high-skill workers in the orth (the ost abundant). 23 We suarize these observations in the following proposition: Proposition 3. With Q 3 skill levels, opening the borders leads to a decrease of the iniu wage if the elasticity of copleentarity between outhern low-skill workers and orthern skilled workers is sufficiently negative. If these conditions are present, the socially optial iigration policy fro the point of view of Rawlsian distributive justice is not the coplete opening of the borders. The socially optial borders, i.e., the borders axiizing the iniu wage at the world level, would be the 22 It is consistent with a curve linking the elasticity of substitution between two skill groups and the distance between these two skill groups. 23 In the first order approxiation, opening the borders would lead to a saller iniu wage if c q ( q) 0, i.e. if c 1 q is sufficiently negative for skills q where (q) is high. 1 < 1 q Q 19
borders that link the low-skill workers with the greatest nuber of workers with interediate skills but carefully leaves high-skill workers on the other side of the border. It would be equivalent to sending outh all the orthern interediate-skill workers! o iigration policy see to succeed in achieving such a social optiu. In particular, a orthern policy that would only allow outhern low-skill workers assuing that skills are sufficiently observable to ake such a policy feasible (which sees unlikely) would in no way iprove things. Purely and siply closing the borders could then becoe the least worse policy. Another consequence of the -shaped curve of the elasticities of copleentary is that, in such world, only the oderately skilled are able to help the low-skill workers while the best thing that the high-skill workers can do is to pay taxes whenever that is possible A siilar phenoenon would occur with two skill groups and iperfectly obile capital the latter playing the sae role as high-skill labor in the orth in our previous exaple. Consider the following circustance. Exaple 2. Two kill Levels and One Iperfectly Mobile Capital Input Assue two skill levels ( = 2) Q where q = 1 is the illiterate labor force abundant in the outh and issing in the orth, and q = 2 literate labor force, and an iperfectly obile capital input k distributed exogenously between stock k and stock constant returns of scale technology F ( 1); (2); k ) ( ( 1); (2); k) G( (1) k; (2) ) k << k in the outh. Consider the ( so that we have F = + where G is a production function with constant returns of scale vis-à-vis its two production inputs. Capital and unskilled labor-force are then perfectly 20
substitutable (we can use either a achine or a craftsan) whereas the skilled labor-force is copleentary to the. In a closed border regie, the wage w (1) of outhern illiterate workers is given by: (( (1) k ) / (2);1) w ( 1) = F1 ( (1); (2); k ) = G + In an open border regie, the wage w + (1) of outhern illiterate workers is given by: (( (1) + k + k ) /( (2) (2));1) w + ( 1) = F ( (1); (2); (2); k + k ) = G1 + 1 uppose that k is sufficiently high relative to k and to (1) such that k / (2) is greater than k + ( 1) / (2). Then w + ( 1) < w (1) : by giving outhern skilled workers the opportunity to work with capital in the orth, opening the borders creates a deterioration in the status of outhern unskilled workers. Proposition 4. With two levels of skills and one capital factor iperfectly obile, opening the borders lead to a decrease in the iniu wage if the elasticity of copleentarity between unskilled labor and capital is sufficiently negative. Which Paraeters for a Just Iigration? We have identified siple conditions for the copleentarity elasticities of production function and the skill dispersion in the orth and in the outh under which the opening of the borders can be harful to low-skill workers in the outh. Are epirical estiates available for these paraeters? 21
The forces at play identified here are qualitatively realistic and are well docuented in the literature. everal recent studies have shown that copleentarity elasticities between different inputs production vary considerably if the different skill level are sufficiently disaggregated. Teulings (1996) estiate the copleentarity elasticities between skill deciles using U data and finds that they shift fro about -3 for the workers in the first decile to approxiately +2.5 when the skill gap is ore iportant. 24 Kreer and Maskin (1996) test the epirical prediction central to their technology odel [see exaple 1 above] knowing that high-skill workers increasingly work aong theselves as the skill gap between the and low-skill workers increases. They show that in the United tates, in France and in the UK, the segregation between different skill levels in various types of firs has considerably increased over the last twenty years: for exaple, in France, the correlation between wage levels of workers fro the sae fir has increased by ore than 20% (fro 0.36 to 0.44) between 1986 and 1992. As noted by Kreer and Maskin (1996), econoic activity tend to shift fro firs such as General Motors, which eploy skilled and unskilled workers, to firs such as Microsoft and McDonald s which only eploy one skill level. Even if it is possible that a greater part of this effect is due to a technology shift rather than to an increase of the skill gap for any given technology, it is astonishing that an increase of the correlation has occurred in all econoic sectors so that it is not siply a anifestation of the transition toward services. It has been particularly high in the United tates where the dispersion of skills has increased the ost. Everything supports the notion that, beyond a certain skill gap threshold, 24 ee Teulings ([1996], table 5. The technology and econoetric specification considered by Teulings [1996] prevent hi fro detecting a possibly decrease in the elasticities of copleentarity beyond a given skill gap. Therefore this study does not docuent the idea of a -curve but it tells us that the rising part of the curve has an extreely steep slope. 22
copleentarity ay becoe so sall that workers fro different skill levels would essentially evolve in essentially separate econoies. The idea of the curve sees epirically valid, at least qualitatively. Krussel et al. (1996) also validate the idea that capital is ore copleentary with skilled work than with unskilled work: using U data, they estiate that skilled work and capital are highly copleentary (with an elasticity of substitution of 0.3) whereas low-skill labor and capital are highly substitutable (with an elasticity of substitution of 2.5). These epirical estiates indicate that it is plausible that opening the borders could be harful to low-skill workers of the outh because they have too few skills to benefit fro highskill work or capital in the orth, which attract outhern skilled workers by separating the fro outhern unskilled workers. The notion that outhern low-skill workers are rarely the ones who take advantage of the opening of the borders is also supported by the fact that igrant workers are rarely illiterate though 50% of the population of several outhern countries is illiterate. For instance, the United tates practices a relatively open border policy while Canada uses a point-syste that allows it to attract ore high-skill igrants than if it had a less open policy as in Europe (particularly in France). Despite the rapid evolution of the coposition of iigration in the United tates over the last 20 years, the average nuber of recent educated igrants (less than 5 years) in the United tates in 1990 was 11.9 years against 13.2 for the reaining Aerican population. 25 In other words, even though recent igrants into the United 25 ee Borjas ([1995], Table 1). In 1990, ore than 80% of recent igrants in the United tates were fro Asia and Latin Aerica, whereas in the 1950s and 1960s ore than 50% were fro Europe (ee Friedberg and Hunt ([1995], Table 2). This low difference between the average skill of iigrants and of the native population ay explain why the estiated effects of igration on average incoe have a odest size (Borjas, Freean and Katz [1992] estiate that about 25% of the increasing wage gap between skills over the 1980s in the United tates is explained by igration.) 23
tates have sensibly lower skills than U-born citizens, these igrants are ostly literate (as in category q=2 of exaple 1) and not illiterate. evertheless, the fact that it is plausible that opening the borders could be harful to outhern low-skill workers does not iply that the forces at work are sufficiently large quantitatively to ake it happen. The fact that outhern low-skill workers are, in fact, less present aong workers who have igrated orth does not iply necessarily that they are not skilled enough to take advantage of a link with the orth: indeed, even in a country which does not attept explicitly to attract highly skilled igrants by using a syste of points or quota, several aspects of the visa policy show that, in practice, it is uch ore difficult for low-skill worker to find work in the orth (for instance, in order to obtain a professional visa for the igrant worker, the eployer often has to prove that the igrant is endowed with specific skills that are in short supply aong the U born population) Let us return then to the nuerical estiates of the copleentarity elasticities. The studies entioned above provide evidence that the elasticity of copleentarity between the low-skill in the outh and the skilled and/or capital in the orth are sufficiently low, no study has yet established that they are negative. For instance, the values estiated by Krussel et al. (1996) of the elasticity of substitution between capital, skilled labor and unskilled labor, although ore extree than standard estiations, are not sufficient to generate the negative elasticity of copleentarity between capital and unskilled labor. 26 Intuitively, a low but positive elasticity 26 F Krussel et al. [1996] estiate a production function of the type α ( σ 1) / σ ( ρ 1) / ρ ( ρ / ( / ( 1) /( 1) ( (1); (2); ; ) [ (1) ( (2) ] 1) ρ ρ σ ) 1) σ ρ σ σ k k = k + + k eq st eq in the for of buildings and elasticity of copleentarity st, where kst is capital k eq is capital in the for of equipent. They found α =0.12, σ =2.47, ρ =0.35. The c 1) k ( between skilled work of type 1 and equipent is the sign of [( 1 α ) σ /( σ 1)] 1 thus +0.49 (with α =0.12, the elasticity σ ust be greater than 8.2 for c 1) k ( to be negative). 24
eans that rickshaw drivers in Calcutta would lose their clients as the orthern borders open but they would also benefit fro orthern capital and infrastructure by becoing anual laborer, craftsan in the orth so that the global effect on their wage would be, on average, slightly positive. Regarding the negative elasticity of copleentarity between the outhern unskilled and the orthern highly skilled, it is worth rearking that the trend docuented by Kreer and Maskin (1996) would tend to increase the value of this elasticity: the fact that the gap between the high-skilled and literate workers in the orth becoes so high that orthern high-skill workers start working aong theselves reduces the risks for outhern illiterate workers to loose their literate copanions as well, in the case of border opening. This notion is reinforced by the fact that the low skill level of the orthern unskilled workers is in constant progression: the gap between the unskilled and the fairly skilled tends to narrow copared to the gap between the fairly skilled and the highly skilled, and this reduces the accuracy of a negative elasticity of copleentarity between outhern low-skill workers and orthern highly skilled workers. Intuitively, this iplies that since the fairly skilled in the orth tend to work increasingly aong theselves in order to serve haburgers to the highly skilled, opening the borders would not isolate the outhern under-skilled but conversely would enable the to participate in the ary of service providers for the highly skilled on the orth and then slightly increase their wage. COCLUIO International igration has always played a inor role in the discourse and doctrine of left-wing parties. Yesterday, international igration played a sall role because, according to the doinant discourse, all one had to do to ake poverty disappear was to put an end to capitalist ote however that it is an estiation of the elasticity of substitution between capital and low-skill Aerican work and not with low-skill outhern work. 25
exploitation in the world. Today, a ore odest arguent plays a siilar role. It iplies that opening the borders ay not be the best solution to reduce poverty in the outh because it could benefit only highly skilled workers fro the outh and be harful to low-skill workers. In this paper, we took this arguent seriously and derived the conditions under which the opening of borders would be harful to outhern low-skill workers. Existing estiates suggest that the iportant paraeters of our odel do not take sufficiently extree values to indicate that the outhern low-skilled would not benefit at all fro the opening of borders in the orth. But these paraeters erit further epirical study. Explaining such conditions would also explain why it is difficult to accept the alost-coplete closed border policy of countries like France in the 1980s and 1990s. REFERECE BORJA G. [1995], The Econoic Benefits fro Iigration, Journal of Econoic Perspectives 9 (2), p. 3-22. BORJA G., FREEMA R. et KATZ L. [1992], On the Labor Market Effects of Iigration and Trade ", in G. BORJA et R. FREEMA (eds), Iigration and the Work Force: Econoic Consequences for the United tates and ource Areas, Chicago, University of Chicago Press. DRÈZE J., E A. [1995], India: Econoic Developent and ocial Opportunity, Oxford, Oxford University Press. FRIEOBERG R., HUT J. [1995], «The Ipact of Iigrants on Host Country Wages, Eployent and Growth ", Journal of Econoic Perspectives 9 (2), p. 23-44. HAMMERMEH D. [1993], Labor Deand, Princeton: Princeton University Press. KREMER M., MAKI E. [1996], egregation by kill and the Rise in Inequality Mieo, MIT et Harvard. KRUEL P., OHAIA L., RIO-RULL J. V. et VIOLATE G. [1996], Capital-kill Copleentarity and Inequality ", Mieo, University of Rochester. 26