Review of Economic Dynamics

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1 Revie of Economic Dynamic 16 (201) L1 L1 Content lit available at SciVere ScienceDirect Revie of Economic Dynamic.elevier.com/locate/red Open border John Kennan a,b,,1 a Department of Economic, Univerity of Wiconin-Madion, 1180 Obervatory Drive, Madion, WI 5706, United State b NBER, United State article info abtract Article hitory: Received 6 January 2012 Revied 20 Augut 2012 Available online 17 October 2012 JEL claification: F16 F22 F66 J61 O15 Keyord: Immigration Factor price equalization There i a large body of evidence indicating that cro-country difference in income level are aociated ith difference in productivity. If orker are much more productive in one country than in another, retriction on immigration lead to large efficiency loe. The paper quantifie thee loe, uing a model in hich efficiency difference are laboraugmenting, and free trade in product market lead to factor price equalization, o that age are equal acro countrie hen meaured in efficiency unit of labor. The etimated gain from removing immigration retriction are huge. Uing a imple tatic model of migration cot, the etimated net gain from open border are about the ame a the gain from a groth miracle that more than double the income level in le-developed countrie Elevier Inc. All right reerved. 1. Introduction Imagine there no countrie It in t hard to do [John Lennon] Citizen of Zimbabe or Somalia ho ould prefer to repond to the enormou problem in their home countrie by imply moving to a country that doe not have uch problem are generally prohibited from doing o by the government of thee detination countrie. One could ell argue that prohibition of thi kind contitute a very eriou violation of human right. 2 More proaically, one can ak hat ould happen if uch prohibition ere eliminated. Before proceeding to analyze a orld economy ith open border, the firt quetion that mut be anered i hether retriction on factor mobility have any real effect. If product price are the ame acro countrie (becaue there i free trade and tranportation i not cotly, for example), and if there are to good that are produced in to different countrie, and if the production technologie (for thee to good) are the ame acro the to countrie, then the factor price equalization theorem applie. That i, real age and other factor price are equalized acro countrie even though factor are immobile, becaue difference in factor price are implicitly arbitraged through the product market. The theoretical * Correpondence to: Department of Economic, Univerity of Wiconin, 1180 Obervatory Drive, Madion, WI 5706, United State. addre: kennan@c.ic.edu. 1 A verion of thi paper a preented a a plenary talk at the SED meeting in Gent, July I thank Michael Clemen, Eric French, Rebecca Leem, to anonymou referee and many eminar participant for helpful comment. Xiaodong Fan provided valuable reearch aitance. 2 See Hanon (2010) /$ ee front matter 2012 Elevier Inc. All right reerved.

2 L2 J. Kennan / Revie of Economic Dynamic 16 (201) L1 L1 argument i beautiful, but of coure the fact are otherie. For example, age in the U.S. are about 2.5 time the Mexican age, for comparable orker. Empirical tudie that attempt to account for the oberved difference in average income acro countrie have repeatedly hon that large difference remain after aduting for difference in phyical and human capital endoment. In other ord, there are large difference in productivity. 4 Thi paper conider a model ith labor-augmenting difference in productivity acro countrie. In thi model, the factor price equalization theorem hold (under the uual aumption) if age are meaured in term of efficiency unit of labor. Thi mean that the rental rate of capital i equalized acro countrie, but a Mexican orker in the U.S. ha more efficiency unit of labor (and therefore higher earning) than the ame orker in Mexico. In the tandard (Heckcher Ohlin) model, factor price equalization mean that there i no economic incentive to migrate from one country to another. But hen the model i extended to allo for labor-augmenting productivity difference, there are potentially large gain from migration, becaue a orker ho move to a more productive place acquire more efficiency unit of labor. There are alo potentially large cot, ince people tend to be trongly attached to the place here they ere born and raied. 5 Uing a very imple pecification of migration cot, the net gain from open border can be roughly etimated. The main concluion of the paper i that thee gain are huge. Given that immigration i heavily retricted in developed countrie, it i clear that the gain accruing to immigrant are offet to ome extent by perceived loe impoed on the reident of thee countrie. Thee loe may be aociated ith change in the age tructure, or ith the cot of including immigrant in ocial inurance cheme (net of the additional tax revenue collected), or ith the dilution of a country cultural identity. The effect of immigration on age are analyzed belo, but no attempt i made to quantify the public finance implication of open border, and of coure the cultural implication are far beyond the cope of the paper. 6 The gain from open border have alo been treed in recent ork by Freeman (2006), Klein and Ventura (2007, 2009) and Clemen (2011). In the Klein Ventura model, cro-country income difference are attributed to difference in total factor productivity, and there are large gain hen capital and labor are moved to more productive countrie. The main novelty in thi paper i that the gain from open border are analyzed in an environment in hich income difference are attributed to difference in labor productivity, and the factor price equalization theorem hold, a in Trefler (199). In contrat to the Klein Ventura model, the gain have nothing to do ith reallocating capital acro countrie, becaue it i aumed, in line ith the evidence preented by Caelli and Feyrer (2007), that there are no difference in the productivity of capital, and factor price equalization implie that the return to capital i the ame in all countrie. 2. Data Clemen et al. (2008) compare the age of foreign-born, foreign-educated orker in the 2000 U.S. Cenu ith the age of imilar orker in 42 home countrie. The relative age data are hon in Fig. 1, along ith data on GDP per peron from the Penn World Table. 7 Thee relative age are ued belo to meaure cro-country difference in labor efficiency that i, difference in the productivity of a given tock of human capital, hen moved from one country to another. For example, the age of a Mexican orker in Mexico i about 40% of the age of a orker ith the ame education and experience ho a born and educated in Mexico but ho a orking in the U.S. in the 2000 Cenu. Thi i taken to mean that Mexican orker have 0.4 efficiency unit of labor (per unit of human capital), o that a Mexican orker ho croe the U.S. border become a productive a 2.5 Mexican orker ho tayed at home. The aumption here i that the variable that reduce labor productivity in Mexico (hatever they might be) are pecific to the location, and not to the people ho ork in that location. Thi i obviouly a trong aumption, given that there i no theory of hat the relevant variable are. The main concern i that the orker ho migrate are elected from the upper tail of the individual-pecific productivity ditribution (conditional on obervable). Clemen et al. (2008) revieed the empirical literature on migrant election, and concluded that although the typical migrant i probably omehat more productive than the typical non-migrant (conditional on obervable), it i quite unlikely that the typical migrant i dran from a point above the 70th percentile of the individual-pecific productivity ditribution (in the home country). In Fig. 2, the age at the 70th percentile in the ending country relative to the mean U.S. age (for See Clemen et al. (2008). 4 See Hall and Jone (1999), Hendrick (2002) and Caelli (2005), forexample.schoellman (2011) ho that cro-country difference in the quality of education are important, but even after accounting for thee difference, the remaining difference in labor productivity are very large. 5 For empirical evidence on the importance of attachment to place ee Kennan and Walker (2011) (for migration ithin the U.S.), and Leem (2011) (for migration beteen Mexico and the U.S.). 6 See Storeletten (2000) for a detailed analyi of the fical effect of immigration, hoing that, at leat in ome realitic cae, the preent value of the additional retirement benefit paid to immigrant i actually more than offet by the preent value of the additional tax revenue. Freeman (2006) dicue ay of tranferring ome of the gain from immigration to reident of the hot country, including the idea of imply elling entry permit, a uggeted by Becker and Becker (1998). 7 The GDP data are from PWT verion 7.1; ee Heton et al. (2012). The relative age etimate for Puerto Rico i taken from Table 9 in Clemen et al. (2008). A relative age etimate for China ha been added, uing data from Shi (2009). In the figure, countrie are identified by internet domain name.

3 J. Kennan / Revie of Economic Dynamic 16 (201) L1 L1 L Fig. 1. Cro-country difference in age relative to age of imilar orker in the U.S., uing data from Clemen et al. (2008), and difference in income per orker from the Penn World Table. Fig. 2. Wage at the 70th percentile and at the mean of the dometic ditribution, both relative to mean U.S. age; data from Clemen et al. (2008). a orker ith the ame obervable), i plotted againt the relative age at the mean. The reult i that the election effect i not large. Income per orker varie acro countrie not only becaue of difference in labor efficiency, but alo becaue of difference in human capital endoment. Income per orker can be computed from data on GDP per orker and labor hare. The labor hare in country can be ritten a λ = a h N Y here i the real age, a repreent efficiency unit of labor per orker in country, h i the human capital of the average orker, N i the labor force, and Y i total GDP. So if data are available on λ and Y, income per orker can be computed a y = a h = λ Y N Bernanke and Gurkaynak (2002) and Gollin (2002) report labor hare for 20 countrie that are alo in the Clemen et al. (2008) data. The relationhip beteen relative income and relative age i illutrated in Fig.. A country that ha the ame level of human capital per orker a the U.S. hould lie on the 45-degree line in thi plot. For mot countrie, the data lie ell belo the 45-degree line, indicating that the average orker in thee countrie ha coniderably le human capital than the average orker in the U.S. But the data for Egypt and Venezuela are implauible: for example, the average orker in Egypt urely doe not have more human capital than the average orker in the U.S. Fig. 4 ho factor price data for 17 countrie. The vertical axi ho meaure of the marginal product of capital, taken from Caelli and Feyrer (2007). The horizontal axi ho the relative age data from Clemen et al. (2008). There are big

4 L4 J. Kennan / Revie of Economic Dynamic 16 (201) L1 L1 Fig.. Relative age from Clemen et al. (2008) and real GDP per orker from Penn World Table, multiplied by labor hare from Bernanke and Gurkaynak (2002) and Gollin (2002). Fig. 4. Marginal product of capital, from Caelli and Feyrer (2007), compared ith relative age. age difference, but the return on capital i roughly equal acro countrie, a Caelli and Feyrer (2007) point out. Thi i conitent ith factor price equalization, given labor-augmenting technology difference acro countrie.. Model.1. The Heckcher Ohlin model The Heckcher Ohlin theorem ay that each country export factor in hich it i abundant. Trefler (199) ho that data on import and export can alay be made to atify the Heckcher Ohlin theorem if uitable productivity adutment are made. Let Ω f = a fω f be the effective endoment of factor f in country, here Ω denote phyical unit, and a repreent factor-augmenting productivity difference, o that Ω i meaured in efficiency unit. Then f i abundant in if Ω f Ω f τ > 0 τ here i hare in orld conumption. If there are I produced good, and T i the vector of net export of thee good, then F = A T i the factor content of trade, here A i the matrix of cot-minimizing factor quantitie for each good (at a given factor price vector), and it i aumed that thi matrix i the ame for all countrie. That i, it i aumed that technology difference acro countrie

5 J. Kennan / Revie of Economic Dynamic 16 (201) L1 L1 L5 are confined to factor-augmenting productivity difference (a oppoed to difference in elaticitie of ubtitution beteen factor, for example). Then the (modified) Heckcher Ohlin theorem i F fc = Ω fc c Ω f There are a lot of free parameter in thi model. The iue i hether the productivity adutment match the data on relative factor price acro countrie hether the adutment needed to match the trade flo data are conitent ith factor price equalization. For capital and labor, and for a ample of countrie, Trefler (199) ho that the match i quite good; moreover, the labor adutment are bigger than the capital adutment. The next ection develop a verion of thi model in hich cro-country difference in technology are purely labor-augmenting. Thi model i ued in the ubequent ection to analyze the implication of open border..2. Factor price equalization ith labor-augmenting technology difference Suppoe there are J countrie, ith different productivity level. If the productivity difference are labor-augmenting (i.e. Harrod-neutral), then the technology for product in country can be pecified a Q ( = F K, a L ) here a repreent efficiency unit of labor per orker in country. Let c 0 be the unit cot function for product hen the labor input i meaured in efficiency unit, o that the production function i Q = F (K, L ). Then it i eay to ee that the cot function for product in country i c(v, ) = c 0 (v, a ) here i the age per efficiency unit of labor, and v i the price of capital. If there i free trade in the product market, ith no tranportation cot, then the zero-profit condition implie ( p = c 0 v, ) a If to product r and are produced in country, then ( v, ) = p r c 0 r c 0 ( a v, a ) = p Thee equation determine the factor price in country. If the marginal rate of technical ubtitution atify a inglecroing condition, the factor price are uniquely determined. Then if country l alo produce thee ame to product, the ame equation determine factor price in country l, itha l in place of a.thiimpliev = v l, and a Thu = l a l = a 0 here 0 i a reference age level that can be normalized to 1. In thi model, migration ha no effect on relative age. Thu if 0 million orker move from Mexico to the U.S., it ill till be true that the age in the U.S. i 2.5 time the age in Mexico. In particular, it i not the cae that migration reduce the age in the receiving country hile increaing the age in the ending country, a ould be the cae in a ingleproduct model here migration involve oppoing movement along the marginal product of labor curve. But migration affect age level (thi i analyzed in Section.4 belo). 8 8 See Bora (2009) for an analyi of the effect of immigration on age in a etting here the dometic and foreign economie produce ditinct good, o that the factor price equalization theorem doen t apply.

6 L6 J. Kennan / Revie of Economic Dynamic 16 (201) L1 L1.. General equilibrium Given the factor price, the price of conumer good are determined by the cot function. Then the quantitie are determined by thee good price, and by preference and total income (here income depend on factor price). Given the quantitie to be produced, and the factor price, producer determine the profit-maximizing factor quantitie. Thi give demand curve for the factor, and factor price are determined o a to clear the factor market. For implicity, it i aumed that: (1) preference are identical in all countrie, and are decribed by a loglinear utility function ith expenditure hare parameter θ ; and (2) the production function for each good i a CES, and i the ame in all countrie, ith an elaticity of ubtitution σ that i the ame for all good (and ith the undertanding that the labor input i meaured in efficiency unit). It i alo aumed that each orker upplie one time-unit of labor (inelatically). Thi time-unit implie different amount of effective labor in different countrie, for to reaon: human capital endoment h may differ acro countrie, and each unit of human capital in country mean a efficiency unit of labor. 9 Given that the production function for each good i a CES, the price of good i given by p 1 σ = α ( v α ) 1 σ + β ( β ) 1 σ here i the age in efficiency unit, and here α + β = 1. The quantitie to be produced are determined by the expenditure hare θ applied to total income p Q = θ ( L + v K ) here L i the aggregate amount of labor in the orld (in efficiency unit), and K itheaggregateamountofcapital. The conditional factor demand function are the derivative of the cot function, by Shephard lemma. The derivative are determined by c σ c σ ( ) σ c v v = α ( ) σ c = β Thu the factor demand are given by ( ) σ v α K = Q c σ ( ) σ L = Q c σ β Finally, the factor market clearing equation are ( ) σ Q c σ v = K α ( ) σ Q c σ = L β One of thee equation i redundant, by Walra La. Write the capital market equation a p Q c σ 1 ( v α ) σ = K and define ξ a the capital hare for good : vk ξ = vk + L ( α vα ) 1 σ = ( α vα ) 1 σ ( + β ) 1 σ β 9 Thee are obviouly trong aumption. When there are more than to factor of production, ith variable elaticitie of ubtitution (for different pair of factor, or for different good), the analyi become much more complicated. But there i no reaon to believe that thee complication ould eriouly undermine the main argument regarding the gain from open border, o it i ueful to develop the argument in the context of a imple and relatively tranparent model.

7 J. Kennan / Revie of Economic Dynamic 16 (201) L1 L1 L7 Then the market-clearing equation for capital can be expreed a ( ) 1 1 v K θ ξ = α α L + v K hich reduce to v K θ ξ = v K + L The point here i that ξ i the capital hare for product, and θ i the hare of product in total conumer expenditure, o the equilibrium condition i that the eighted average of the capital hare ha to match the capital hare of total income (implying that the correponding equality hold for labor). Note that ξ may be an increaing or decreaing function of the factor price ratio, depending on the elaticity of ubtitution. But in the cae of Cobb Dougla production function (σ = 1), ξ = α i ut a technological parameter, and the equilibrium factor price ratio i then determined by 1 θ α = 1 + L v K implying that the elaticity of the factor price ratio ith repect to the capital labor ratio i unity...1. Good price The price ratio beteen any to conumer good i given by p 1 σ ( p 1 σ = ασ v ) 1 σ + β σ t α σ ( v ) 1 σ t + β σ t Thu an increae in the price of capital relative to labor implie an increae in the relative price of capital-intenive good. For example, in the limit, hen σ approache 1, ( ) ( ) p v log = (α α t ) log p t.4. Immigration and age The effective total upply of labor aggregated over countrie i L = a h N here N i the labor force in country. When orker move to countrie here labor i more efficient, the effective upply of labor increae, and if the orld capital tock i taken a fixed, thi reduce the capital labor ratio. Thu if M k orker migrate from to k, the change in the effective labor upply i L = (a k h k a h )M k k The amount of effective labor time needed to earn enough to buy one unit of good i p. Thi i determined by ( ) 1 σ ( ) 1 σ p = α σ v + β σ and in the Cobb Dougla cae thi reduce to ( ) ( ) p v log = α log α log(α ) β log(β ) When immigration retriction are relaxed, the capital labor ratio K L fall, o the factor price ratio v rie, and thi lead to a fall in the real age,, meaured in term of good. 10 The reduction in the real age i the ame in all countrie p 10 In the CES cae, the elaticity of the real age ith repect to the factor price ratio i α ( p v )σ 1.

8 L8 J. Kennan / Revie of Economic Dynamic 16 (201) L1 L1 (regardle of hether they are ending or receiving countrie). Factor price equalization hold both before and after the migration of labor, but migration reduce the age per efficiency unit of labor (and therefore alo reduce the age of all orker ho do not migrate). Even though migration reduce the price of labor-intenive good relative to capital-intenive good, there i a reduction in the real age regardle of hether the real age i defined in term of labor-intenive or capital-intenive good. But the magnitude of the effect depend on the compoition of the conumption bundle. For example, in the Cobb Dougla cae, the elaticity of the factor price ratio ith repect to the capital labor ratio i unity, o if the effective labor upply double, the factor price ratio i cut in half. Then if the capital hare for good i α = 1, the real age fall by about 20% hen meaured in term of good..5. Wage in the long run Migration increae the return on capital, ince the effective capital labor ratio decreae. In teady tate equilibrium ith a contant return technology f ( k ) = ρ + δ here f i the marginal product of capital, ρ i the rate of time preference, δ i the depreciation rate and k i the effective capital labor ratio. In the hort run, migration increae the effective labor upply, o the capital labor ratio fall belo k, and the marginal product of capital rie above ρ + δ. The invetment rate therefore increae, and thi continue until the effective capital labor ratio return to k, and the real age return to it original level. Thu migration doe not reduce age in the long run. And if immigration retriction are removed gradually, in uch a ay that the effective labor upply gro at the ame rate a the capital tock, then age do not fall even in the hort run..6. Migration deciion One might initially expect that in a orld ith open border, everyone ould move to the mot productive location. But thi ignore the trong attachment to home location that i evident in the data. 11 Let a = y y 0 1 be the level of income in the home location (y ), relative to the highet income available elehere (y 0 ), and aume that migration involve a utility cot δ, hich i dran from a ditribution F. Since the utility function i loglinear, the indirect utility function can be expreed a log(y). Then it i optimal to tay in the home location if log(y 0 ) δ log(y ) If the ditribution of δ i the unit exponential, F (t) = 1 e t, then the probability of taying i 12 ( ( )) y0 Prob δ log = e log( y 0 y ) = a y Thi model i of coure overimplified in many repect. 1 But it i conitent ith the data on migration beteen Puerto Rico and the U.S. According to Clemen et al. (2008), the relative age in Puerto Rico i approximately 2 of the U.S. age, and according to the 2000 Cenu, the proportion of adult born in Puerto Rico ho ere living in Puerto Rico i alo approximately 2.Moreover,Leem (2011) etimate that a 10% increae in the Mexican/U.S. age ratio ould decreae migration by 11.6%, hich i roughly conitent ith the unit elaticity of the migration rate predicted by the imple model. 11 For example, Kennan and Walker (2011) ho that attachment to home i an important determinant of internal migration deciion in the U.S. 12 Klein and Ventura (2009) ue a imilar pecification of the diutility of living aay from home. More generally, it i reaonable to uppoe that thi diutility varie from one country to another. For example, if δ i exponentially ditributed ith cale parameter ν in country, F (t) = 1 e ν t, then the probability of taying i ( ( )) y0 Prob δ log = a ν y 1 For example, if killed and unkilled labor are not perfect ubtitute, intereting quetion arie. Are the difference in efficiency more important for killed labor or for unkilled labor? Internal migration data for the U.S. ho much higher migration rate for killed orker, uggeting that the attachment to home may be eaker for killed orker. Thu if the efficiency difference are imilar, one might expect that the flo of killed orker ould be larger ith open border. Open border alo affect the incentive to invet in human capital; in a more general treatment, one ould not take the number of killed and unkilled orker a given.

9 J. Kennan / Revie of Economic Dynamic 16 (201) L1 L1 L9 Fig. 5. Cro-country difference in real GDP per peron (Penn World Table, 7.1). 4. Labor upply and age ith open border: magnitude 4.1. The effective upply of labor Given that each peron tart ith ah unit of effective labor, and that the proportion of tayer i a, the average upply of effective labor after migration (to the mot productive location, here the efficiency level i normalized to 1) i a ah + (1 a) h = ( 1 a + a 2) h Thu the increae in effective labor per peron i (1 a + a 2 a)h = (1 a) 2 h, and the aggregate increae in effective labor due to migration i L = J (1 a ) 2 h N =1 The increae in the upply of labor i proportional to the increae in gro income (ince income i ut effective labor multiplied by the age, and the age i the ame everyhere). Since total labor income can be ritten a a h N = λ Y, the proportional increae in effective labor can be retated in term of income a J (1 a ) 2 L L = =1 a λ Y 0 J =1 λ Y In order to etimate thi increae in the effective labor upply, it i neceary to have data on labor income and relative age for all countrie. The available data include meaure of real GDP per capita for almot all countrie (i.e. all 189 countrie in the Penn World Table), real GDP per orker for all but 11 of thee countrie, together ith labor hare and relative age etimate for a limited et of countrie. The firt tep i to define a et of countrie at the productivity frontier. Thi involve chooing a cutoff productivity level above hich the gain from migration are negligible. The mot recent data on GDP per peron in PWT7.1 are for Thee data are diplayed in Fig. 5, ith a propoed cutoff point at $25,000. Thi cutoff i of coure arbitrary to ome extent, but the reult are not enitive to the precie number choen. The $25,000 cutoff give a reaonable claification: the frontier et contain 8 countrie, including all of Wetern Europe except for Portugal, a ell a Japan and South Korea (hich i ut above the cutoff). The et i then expanded to include countrie that already hare open border ith the frontier countrie. Thi add 12 relatively poor countrie that are in the European Union (hich ha open border); Puerto Rico i alo added, ince the border beteen the U.S. and Puerto Rico i open. Thu defined, the frontier et include 51 countrie in all Labor income and relative age Gollin (2002) analyzed the available data on labor hare and concluded that the variation acro countrie i quite limited, and in particular that labor hare do not vary ytematically ith the level of income. Baed on thi, labor hare i taken to be a contant for countrie not included in Gollin (2002) data, or in the data analyzed by Bernanke and

10 L10 J. Kennan / Revie of Economic Dynamic 16 (201) L1 L1 Gurkaynak (2002); thuλ = 2 for thee countrie, thi value being very cloe to the average labor hare reported in both paper (0.675 and 0.650). There remain the problem of etimating a for countrie ithout relative age data. Thi i done by regreing relative age in 1999 on real GDP per orker in 1999, for the 40 countrie for hich the relevant data are available, and uing the etimated regreion function to predict the miing relative age data. 14 The reult are aduted for change in real GDP per orker beteen 1999 and Effective orld labor upply etimate Uing the above approximation, the effective orld labor upply, before alloing for migration, i etimated a million orker, taking one U.S. orker a the efficiency unit; thi i ut total orld labor income divided by income per orker in the U.S. 16 With open border, the upply increae to million. Thu the effective labor upply double. The number of orker in frontier countrie increae by much more than 100%, but thi greatly overtate the increae in the effective labor upply, ince the labor upplied by each orker ho migrate i proportional to the amount of human capital the orker ha, and the relative age and income data imply that human capital level in the ending countrie are much loer than in the frontier countrie. A urpriing concluion from thi analyi i that the effect of open border on real age rate i mall (even in the hort run, ith capital held fixed). For example (a a mentioned in Section.4), if the technology i Cobb Dougla, and the real age i computed in term of good for hich the capital hare i 1, the real age ould fall by only about 20% if everyone moved immediately, ith no time for adutment of the capital tock. In a dynamic model, the effect on real age ould be very much attenuated, even in the hort run. For example, in the Kennan and Walker (2011) model of internal migration ithin the U.S., it take about 10 year before the repone to a imulated (permanent) increae in the real age in one location i more or le complete. 5. Net gain from migration Given factor price equalization, average income per orker in country i y = a h, here h i the human capital of the average orker. 17 Both h and a are meaured in efficiency unit of labor; the difference beteen them i that h i embodied in the orker, and i carried from one country to another hen the orker migrate, hile a i embodied in the country. Thu hen a orker move from to a frontier country (here a = 1), the (gro) income gain i y = (1 a )h = 1 a a y The net gain from migration differ from one individual to another. The net gain for the marginal migrant i zero, and of coure there i no gain for thoe ho do not migrate. If the loet migration cot i zero then the firt peron ho 1 a move gain the full income difference, y a. For the average migrant, the gain i roughly the average of thee: 1 a y 2a. 18 The proportion of people ho do not migrate i a (according to the imple model of migration deciion decribed in Section.6), o the income gain for the average peron (including non-migrant) i ḡ = 1 (1 a ) 2 2 a y 14 For mot countrie, the mot recent data on GDP per orker in PWT7.1 refer to There are 11 (mall, non-frontier) countrie ith miing obervation on GDP per orker in Prediction for thee countrie are made by uing real GDP per peron in place of real GDP per orker. 15 In the cae of countrie that are included in the regreion, â (t + ) = a (t) +[Y (t + ) Y (t)] ˆβ; for the countrie that do not have relative age data, â (t + ) = ˆα + Y (t + ) ˆβ. HereY denote real GDP per orker, ˆα, ˆβ are etimated regreion coefficient, t = 1999 and t + = An even impler calculation, auming equal labor hare for all countrie, divide total orld GDP by GDP per orker in the U.S.; the reult of thi calculation i 81 million orker (uing data for 2010). Since the U.S. labor force i million, thi mean that the U.S. upplie about 20% of the (effective) labor in the orld market. Thi illutrate the Leontief (195) explanation for hy the U.S. export labor-intenive good in exchange for capital-intenive good: hen difference in labor productivity are taken into account, the U.S. ha a relative abundance of labor. 17 Note that a country endoment of phyical capital ha no effect on income per orker. Factor price equalization mean that endoment do not change factor price, o lo age cannot be explained by lo phyical capital endoment. On the other hand, to countrie ith the ame (countrypecific) productivity level can have quite different level of income per orker (a i evident from Fig. ), if the average level of human capital per orker are different. 18 Thi i not exact for the exponential cot ditribution aumed in Section.6, but it i not far off.

11 J. Kennan / Revie of Economic Dynamic 16 (201) L1 L1 L11 Fig. 6. Net gain per orker; computed uing imple migration model. After deleting three countrie (Egypt, Yemen and Venezuela) ith anomalou relative age data, net gain from migration (ḡ ) can be etimated for a ample of 40 countrie. Thi include 18 countrie for hich labor hare etimate are available either from Bernanke and Gurkaynak (2002) or from Gollin (2002), ith income per orker computed a y = λ Y, and 22 countrie for hich labor hare i fixed at N λ = 2, ith income per orker com- puted a y = λy N. The reult of thi calculation are hon in Fig. 6; ome detail are hon in Table 1 and 2 in Appendix A. 19 The average net gain over all countrie i given by ḡ = N ḡ N For the 40 countrie in Fig. 6 thi give an etimate of $10,798, per orker (including non-migrant), per year (in 2012 dollar, aduted for purchaing poer parity). Thi i a very large number: the average income per orker in thee countrie i $86, o the gain in (net) income i 125%. For all of the countrie in the Penn World Table that are not at the productivity frontier (a defined above), uing GDP data to etimate relative age, the etimated gain i $10,15, relative to an average income of $9079, o the gain i 112%. Thee are of coure ut rough etimate, relying on a number of trong implifying aumption. But unle thee aumption are extremely far off the mark, the reult indicate that the gain from open border ould be enormou. 6. Concluion Liberal immigration policie are politically unpopular. To a large extent, thi i becaue the beneficiarie of thee policie are not alloed to vote. It i alo true, hoever, that the enormou benefit aociated ith open border have not received much attention in the economic literature. 20 Economit are generally enthuiatic about free trade. But if free movement of good i important, then urely free movement of people i even more important. One concluion of thi paper i that open border could yield huge elfare gain: more than $10,000 a year for a randomly elected orker from a le-developed country (including non-migrant). Another i that thee gain are aociated ith a relatively mall reduction in the real age in developed countrie, and even thi effect diappear a the capital labor ratio adut over time; indeed if immigration retriction are relaxed gradually, alloing time for invetment in phyical capital to keep pace, there i no implied reduction in real age. 19 Although the reult are noiy, Fig. 6 ho a hump-haped relationhip beteen income and migration gain acro countrie. In the cae of very poor countrie, the gain are mall becaue h i lo; for relatively rich countrie, the gain are mall becaue a i relatively high. 20 See Clemen (2011) for a recent revie of the relevant literature.

12 L12 J. Kennan / Revie of Economic Dynamic 16 (201) L1 L1 Appendix A. Migration gain Table 1 Migration gain, uing labor hare data. Country Code Labor hare Relative age Worker million GDP per orker Income per orker Gain per orker Bolivia bo ,099 Chile cl ,499 17,994 14,944 Colombia co ,176 11, Cota Rica cr ,16 20, Ecuador ec , ,07 India in , ,791 Jamaica m ,828 1,097 14,108 Jordan o ,184 1,558 20,22 Sri Lanka lk , ,061 Morocco ma , Mexico mx ,795 17, Panama pa ,470 19,2 11,069 Peru pe , Philippine ph Paraguay py Uruguay uy ,458 15, Vietnam vn South Africa za ,17 14, Total Average ,145 11, Average (eighted) , ,729 Note: The code in the econd column are the domain name ued in the figure. The labor hare data are from Bernanke and Gurkaynak (2002) and Gollin (2002). The relative age etimate for 1999 are from Clemen et al. (2008); the etimate for 2010 are etimated uing change in GDP per orker. Labor force and GDP data are from the Penn World Table (v.7.1). Net gain are computed uing the imple migration model decribed in the text. The average in the lat ro ue labor force eight. Table 2 Migration gain, uing fixed labor hare. Country Code Relative age Worker million GDP per orker Income per orker Gain per orker Argentina ar ,7 20, Bangladeh bd Brazil br ,274 12,18 11,694 Belize bz ,542 16, Cameroon cm China cn , ,25 Dominican Republic do ,205 18, Ethiopia et Ghana gh Guatemala gt ,481 11, Guyana gy , Haiti ht ,64 Indoneia id ,696 Cambodia kh Nigeria ng ,155 Nicaragua ni Nepal np Pakitan pk ,97 Sierra Leone l Thailand th ,275 10, Turkey tr ,974 25, Uganda ug Total Average , Average (eighted) , ,4 Note: Labor hare data not being available, the labor hare for thee countrie i fixed at 2, a dicued in the text. Reference Becker, G.S., Becker, G.N., The Economic of Life: From Baeball to Affirmative Action to Immigration, Ho Real-World Iue Affect Our Everyday Life. McGra Hill, Ne York. Bernanke, B.S., Gurkaynak, R.S., I groth exogenou? Taking Manki, Romer, and Weil eriouly. In: NBER Macroeconomic Annual, pp

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