NBER WORKING PAPER SERIES WHY ARE SOME IMMIGRANT GROUPS MORE SUCCESSFUL THAN OTHERS? Edward P. Lazear

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1 NBER WORKING PAPER SERIES WHY ARE SOME IMMIGRANT GROUPS MORE SUCCESSFUL THAN OTHERS? Edward P. Lazear Workng Paper NATIONAL BUREAU OF ECONOMIC RESEARCH 1050 Massachusetts Avenue Cambrdge, MA June 2017, Revsed November 2018 I am grateful to Lars Oxelhem and Charlotta Olofsson who provded the data from Sweden and to Melssa Kearney for dscussant comments at the Utah Busness Conference. My thanks also to Carolne Hoxby for extensve and thoughtful comments and to Juan Saavedra for help wth the IPUMS data. Addtonally, Enrco Morett, Robert Pollak, Kathryn Shaw and others at the NBER summer nsttute for helpful comments that are reflected n ths draft. The vews expressed heren are those of the author and do not necessarly reflect the vews of the Natonal Bureau of Economc Research. NBER workng papers are crculated for dscusson and comment purposes. They have not been peer-revewed or been subject to the revew by the NBER Board of Drectors that accompanes offcal NBER publcatons by Edward P. Lazear. All rghts reserved. Short sectons of text, not to exceed two paragraphs, may be quoted wthout explct permsson provded that full credt, ncludng notce, s gven to the source.

2 Why Are Some Immgrant Groups More Successful than Others? Edward P. Lazear NBER Workng Paper No June 2017, Revsed November 2018 JEL No. F22,J01,J15,J61,M5 ABSTRACT Success of mmgrants n the US, measured by earnngs or educaton, vares dramatcally by country of orgn. Surprsngly, mmgrants from Algera have hgher educatonal attanment than those from Israel or Japan. Another fact: The US admts few mgrants from Algera. Immgraton slots are ratoned and as a consequence, average mmgrant attanment s nversely related to the number from a source country and postvely related to ts populaton and educaton level. The formal model s three varables explan 73% of the varaton n educatonal attanment of mmgrant groups n the US. The theory and predctons are bolstered by Swedsh and Canadan data. Edward P. Lazear Graduate School of Busness Stanford Unversty Stanford, CA and Hoover Insttuton and also NBER lazear@stanford.edu

3 Algera, Israel, and Japan, along wth over one hundred other countres, are sources of mgrants to the Unted States. Try the followng thought experment: Rank those three countres mmgrants, hghest to lowest, by educatonal attanment. The rankng s Algera at the top followed by Israel and Japan. Surprsed? Consder an addtonal fact: Algerans make up.0005 of mmgrants, Israels comprse.003 of US mmgrants whereas about 1% of mmgrants are from Japan. The largest orgn country of US mmgrants s Mexco, accountng for 27% of the mmgrant populaton. Mexcan mmgrants rank 134 th out of 136 n educatonal attanment, as compared wth Algeran mmgrants who rank 25 th. Yet average educaton attanment n Mexco s hgher than that n Algera. The group wth the hghest educatonal attanment s that from the former Sovet Unon, the most under-represented group among all mmgrants n the US. The attanment of mmgrants n the US vares greatly by country of orgn. Average educatonal attanment by country of orgn ranges from a low of 9 years of schoolng to a hgh of 16 years. Smlarly, average annual earnngs by country of orgn ranges from about $16,000 to $64,000. Not surprsngly, the correlaton between these two measures of attanment s.7. Addtonally, two of the largest sources of US mmgrants are at both extremes, wth Mexco s mgrants to the US havng a mean educatonal attanment of 9 years, whereas Inda s mgrants to the US have a mean of 16 years. Contrast that wth the fact that the average educatonal level n Mexco s almost twce that of the average educatonal attanment n Inda. What explans these mmgrant attanment dfferences across orgn countres and the counterntutve patterns? Because the US admts as mmgrants only a small fracton of most orgn countres populatons, almost every country has a large enough group of hghly educated people from whch the US could draw ts mmgrants. Many of these ndvduals mght be wllng to move to the US f admtted. If so, then the average educatonal attanment of mmgrants from any orgn country depends n large part on whom the US s wllng to admt. The more selectve s mmgraton polcy, the hgher s the educatonal attanment of the group. Important s that nferences about the qualty of varous countres as sources of mmgrants are lkely to be ncorrect f they are based on the attanment of mmgrants n the US from the partcular country. The smple correlaton between an mmgrant s attaned level of educaton and the average level of educaton n hs or her orgn country does not dffer sgnfcantly from zero. 1 Mexco s not an nferor source country despte mmgrants from Mexco rankng near the bottom n educatonal attanment. That s a result of the polcy flter and selecton crteron, not the nherent qualty of Mexco s average educatonal attanment. A desrable destnaton country lke the US could lkely select hgh attanment mmgrants from almost any country f that were the goal. In general, t s not. Other consderatons such as refugee status as emphaszed by Sweden or famly reunfcaton as emphaszed n the US nfluence the admsson choce and consequent attanment of mmgrants. Most models of mmgraton treat mgrants as f they are moble labor, movng from one 1 The r-squared n a regresson of mmgrant s attaned educaton on home country educaton usng the Amercan Communtes Survey, as descrbed below, s.02. 1

4 sector to another freely, wthout any constrants on the mgrant mposed by polcy. 2 These models have served analysts well n consderng who chooses to come to the US, but they are less well-suted both theoretcally and emprcally n descrbng attanment of the mmgrant populaton when excess supply and ratonng of mmgraton slots s the rule. Instead, supply plays a dfferent and arguably more realstc role. Polcy, explct or mplct, determnes the number of mmgrants that are accepted from each source country. In the US, strong emphass on famly reunfcaton means that there are many mmgraton slots for some countres and few for others. But gven the number of slots, t s stll necessary to determne whch ndvduals come from each country. It s argued that selecton s from the top and supply consderatons may play a heavy role here. There are, therefore, two types of selecton at work. The selecton emphaszed n past lterature s personal selecton, where an ndvdual decdes whether or not to mgrate based on economc and other consderatons. Generally gnored by the earler lterature s what mght be called process selecton, where the destnaton country creates an admsson system that results n a partcular knd of selecton through an explct or mplct rule. Process selecton s more mportant n countres that have excess demand for mmgraton slots. The system n the Unted States, whch favors famly reunfcaton, s not neutral across countres and results n process selecton. Because some orgn countres are better represented among the current stock of mmgrants, a seemngly neutral rule results n a non-neutral allocaton of mmgraton slots. Ths occurs because the lkelhood of havng a relatve already resdng n the US vares by orgn country. Ratonng of mmgraton slots s clearly mportant n the Unted States. For example, between 2009 and 2014, approxmately 1 mllon ndvduals per year were granted permanent resdent status. In each of those years, there was a large number of applcants who were n the queue for resdent status, equalng about four tmes as many as the number granted permanent resdency. 3 There s excess supply of mmgrants, even by measures of those who apply. There are surely many more who would apply f they thought they would be admtted, but declne to do so because the lkelhood that ther applcaton wll succeed s too low. Each year, H-1B vsas, awarded to ndvduals who are sponsored to work at US frms, run out well before the year ends. Ratonng also has a dramatc effect on performance of mmgrants. To ncorporate the mportance of ratonng and process selecton, an extreme approach s adopted, albet a carcature of the true stuaton. A desrable destnaton country s assumed to choose the number of mmgrants that t wll admt from each of the world s source countres. Selecton s assumed to be from the top of that country s attanment dstrbuton, ether because the destnaton country uses that crteron of admsson gven the number admtted, or because those wth hgher levels of attanment are more lkely to mgrate. The latter could result from standard supply consderatons, lke the returns to mgraton beng postvely correlated wth skll, or smply 2 Models, such as the one by Roy (1951) are frequently used to descrbe the flow of mgrants to the US. See, for example, the semnal work by Borjas (1987). 3 U.S. Department of State, Bureau of Consular Affars, Annual Immgrant Vsa Watng Lst Report as of November 1, 2015, 2015, and Department of Homeland Securty, Yearbook of Immgraton Statstcs 2014,

5 because those wth hgher attanment levels are better able to learn about and secure a scarce slot. 4 As a consequence, the shape of the educaton dstrbuton n the orgn country, the country s populaton, and mportantly, the target mmgrant number from that country determne the composton and attanment of mmgrants n the US. At some level, t s obvous that polcy s a key determnant of mmgraton patterns. The large shft of mgrants to the US from source countres n Europe to those n Latn Amerca occurred after polcy changed n 1965 favorng famly reunfcaton. There was no abrupt correspondng change n supply condtons. Natves of the West Indes and Surnam a make up 3% of the populaton of the Netherlands as a consequence of Dutch polcy toward ther former colones. They account for only a tny fracton of the US populaton despte those countres beng geographcally closer to the US than to Europe. The major presence of Algerans n France and mnor presence n the US s a consequence of France allowng people from ts former colones to settle n the country. Of course, common language affects the desre to mgrate to certan countres, but ths factor does not explan tme seres changes nor the fact that the majorty of mmgrants n the US are not natve Englsh speakers. Supply consderatons, by themselves, cannot ratonalze the very dfferent dstrbutons of mmgrants by country or orgn across dfferent destnaton countres, as wll be shown by a comparson of Canada, Sweden, and the Unted States. Nor can supply consderatons alone predct performance of the varous mmgrant groups n the destnaton countres. To deal wth ether of these ssues, t s necessary to acknowledge the role that polcy and ratonng plays n the pattern of mgraton. Although the pont of ths analyss s not unque to the Unted States, the focus s the US because the assumpton that the process selecton s paramount apples n the US better than n most of the world s countres. The excess supply of potental mgrants to the US means that the ratonng rule s a key factor n determnng the nature of mmgrants n the US. However, t wll also be shown that data from Sweden, another desrable destnaton country, support the hypothess. Furthermore, a comparson of sources of mmgrants n the US and Canada, geographcally smlar countres wth almost dentcal economes, make clear that supply cannot be the only factor n explanng mmgraton patterns and attanment. The model, whch mples that three and only three varables should determne 4 Borjas and Fredberg (2009) argue that selecton rules explan the rse n wages of mmgrants that occurred between 1990 and Addtonally, Kerr and Lncoln (2010) examne the effect of the rse n H-1B vsas on nnovaton and document ts mportance. Kerr, Kerr, and Lncoln (2015) use the LEHD data and fnd that sklled mmgrant labor s an mportant determnant of the overall ncrease n the sklled workforce of Amercan frms. H-1Bs are mportant because the H-1B program s always over-subscrbed and the number of H-1Bs permtted s a polcy choce that results n selecton from the top, made by the US government. Two Hunt papers, Hunt (2011) and Hunt (2015), examne the performance of hghly sklled mmgrants n the US. Another measure of ablty to perform n the US relates to Englsh fluency, whch was explored n Lazear (1999). Lews (2013) pcks up on that theme and dscusses the ablty of mmgrants to substtute for natve-born US labor and how that relates to language sklls. Smlarly, Per, Shh and Sparber (2015) estmate the effect of STEM mmgraton on productvty and fnd t s substantal, usng cty dfferences. None of these papers speaks to the emprcal valdty of the assumpton that selecton s from the top of an orgn country s dstrbuton, but the fact that many of the orgn countres have low educatonal levels mples that the hgh sklled ones are selected from the top. 3

6 educatonal attanment does well. In the US, 73% of the varaton n mmgrant educatonal attanment s explaned by the varables of nterest n the model, namely the number of mmgrants n the US, the populaton of the orgn country, and the mean level of educatonal attanment n the orgn country. Fgure 1 llustrates the man argument. Consder two countres, 1 and 2, wth equal populaton szes and wth educatonal dstrbutons as shown. Country 2's dstrbuton s a rghtward dsplacement of country 1's dstrbuton. Suppose that the US were to decde that 3% of ts mmgrants wll come from country 1, but that 30% wll come from country 2 and suppose further that all who are offered US resdency accept. If the US also allows only the most educated mmgrants n frst from each country, or alternatvely, f the most educated n each country are most attracted to the US or most able to navgate ther way through the mmgraton process, then the upper tal of each dstrbuton wll end up mgratng to the US. In ths case, because the US targets 3% from country 1 and 30% from country 2, the mnmum cutoff level of educaton n each country s A 1 * and A 2 *, respectvely. Note that the educatonal cutoff level for country 1, the lower educaton country, s consderably above that for country 2, the hgher educaton country, because so many more are beng admtted from country 2. Gven the cutoffs and the underlyng dstrbutons, the average level of educaton among mmgrants from country 1 and country 2 are A 1 and A 2. The educatonal attanment of mmgrants from 1 exceeds that from 2,.e., A 1 > A 2, even though country 1's educaton level at home s below that of country 2 at home. Of course, ths s not a necessary outcome. It depends on the amount by whch country 2's educaton level domnates country 1 and n partcular on the number of mmgrants that the US admts from each of the two countres. But fgure 1 llustrates that other thngs equal, the smaller the proporton of mmgrants n the US who come from a country, the hgher s the expected level of educaton of mmgrants n the US who are suppled by that country. 4

7 Model The general model captures the ntuton of the fgure and dscusson. Suppose that the US chooses a selecton rule such that I of the mmgrants have orgns n country. The selecton rule that determnes I s taken to be exogenous, determned by polcy, poltcs, or consderatons outsde the model. Assume that anyone outsde the US offered mmgrant status n the US accepts t. Assume addtonally that ratonng s such that the top of the educatonal dstrbuton (or any other dmenson of mmgrant ablty) s admtted frst. Ths can ether be a result of explct US polcy or a consequence of the supply sde, where the people most lkely to come to the US from any other country are at the top of the ablty dstrbuton, the latter resultng ether because they are best able to navgate the mmgrate hurdles or because they have the hghest return from mgratng. Ths polcy-determned selecton of mmgrants fts those who come n legally wth offcal documentaton. Those who enter the country wthout documentaton are more lkely to ft a strct supply-determned mechansm because the ratonng rule chosen by the US does not bnd. 5 Let N be the populaton of country and let f (A) be the densty of educaton or some other measure of ablty or attanment, A, n country. It s not necessary to assume that anyone offered resdency n the US accepts, although that s the most straghtforward way to thnk about t. Another nterpretaton of f (A) s that t s the transformed dstrbuton that takes nto account not only attanment, but also the proporton of those n country wth attanment level A who wll mgrate to the US f permtted to do so. The necessary condton n ths case s smply that mmgrants from countres that are admtted n hgher quanttes are a lower attanment group than those from countres admtted n lower quanttes. Lmtng the quanttes of entrants has the effect of rasng the average ablty of those selected. Gven the polcy determned I, A * s the cutoff ablty level of mmgrants from country determned such that or N f ( A) da I A * (1) N [ 1 F( A*)] I 0 The expected level of educaton among those from country n the US s smply the condtonal expectaton or 5 It s possble that the polcy on nternal enforcement and border control may have an effect even on those who do not apply through legal channels. 5

8 1 (2) A Af 1 F( A*) A * ( A) da The goal s to predct the effect of the key varables on the average educatonal level or other measures of attanment of a country s mgrants to the US. Those varables are the number of mmgrant slots allocated to country, I, the populaton of country, N, and the level of educaton n country, μ, where μ s defned as the average level of educaton n orgn country. To obtan the theoretcal predctons, dfferentate (2) wth respect to I, N, and μ. In general, from (2), for any varable x, A x A * f( A*) x 2 [ 1 F( A*)] 1 1 F( A*) A * Af A * ( A) da A f ( A ) da x A * f( A*) A * 1 F( A*) x or (3) A x A * f( A*) x Af A da ( ) A * A F A * [ 1 ( *)] 1 F( A *) 1 A f ( A ) da 1 F( A*) A * x The dervaton n (3) allows the basc theoretcal predctons to be stated. Most of the mplcatons come drectly from the propertes of condtonal expectatons as nterpreted n the current context. The theory s stated n the form of propostons, the proofs of whch are contaned n the appendx. Proposton 1: A 0. I The larger s the number of mmgrants admtted from country, the lower s ther expected level of attanment, A. Proposton 2: 6

9 A 0. N For any gven number of mmgrants, I, the larger s the populaton n country, the hgher s the expected level of attanment of mmgrants A from that country. Fnally, let F (A) = F(A-μ ) so that every country s ablty dstrbuton s of the same form, but merely dsplaced by country-specfc parameter μ. Countres wth hgher μ values have hgher ablty dstrbutons. Assume further that f '(A) s negatve for all A>A *. Ths s lkely to hold emprcally under the assumpton that the most able are taken frst because there s no country that provdes so many mmgrants that the cutoff ablty, A *, would not be n the upper tal of the ablty dstrbuton, whch s expected to be negatvely sloped. Then, Proposton 3: A 0 Immgrants from countres wth hgher levels of attanment have hgher attanment n the destnaton country. It s also possble to express the concepts n propostons 1-3 n terms of the representaton rato defned as I / I R /. N / N R should be nterpreted as the over-representaton of country among mmgrants, gven the country s relatve populaton mportance. If R equals 1, the proporton of mmgrants n the US from country reflects ts weght n the overall populaton of the world. If R exceeds 1, that country s over-represented among US mmgrants. If R s less than 1, then country s underrepresented among mmgrants n the US. Note further that R s smply the rato of mmgrants from to the populaton from, I /N, tmes a scalar that measures the proporton of total mmgrants taken by the destnaton to the world populaton, I / N. Ths wll be employed later n testng functonal from and other mplcatons. The representaton rato s a useful concept for understandng some patterns that emerge. For example, Inda s hghly under-represented among mmgrants by a factor of almost four, despte the fact that Indans are the thrd largest group of mmgrants (behnd Mexcans and Flpnos). In contrast, Jamacans are hghly over-represented, makng up over forty tmes the number of mmgrants as would be expected gven Jamaca s populaton even though there are only one-thrd as many mmgrants from Jamaca as there are from Inda. It s then possble to state a corollary to propostons 1 and 2 n terms of the representaton rato: 7

10 Corollary 1: Gven a fxed number of mmgrants, A R 0 At any pont n tme, the number of mmgrants s gven. Therefore countres wth hgher representaton ratos have lower expected levels of attanment. A Addtonal theoretcal predctons can be derved. The model provdes mplcatons not only for mmgrants and ther relatve standng n the recpent country, n ths case the US, but also for ther stuaton vs à vs the general populaton of the orgn countres. For these purposes, defne A as referrng to and only to levels of attaned educaton. Let Δ / E (A A>A *) - E (A) / A - μ where E s the expected level of educaton wthn country, gven the dstrbuton of educaton f (A) n country. Then Δ s nterpreted as the dfference between the attaned educaton of mmgrants n the US from country and the average level of educaton of the overall populaton n country. Recall that Δ / A / E (A A>A *) so 1 1 F( A*) A * Af ( A) da Af ( A) da The emprcally verfable mplcatons are stated as corollares here and proved n the appendx. Corollary 2: MΔ/MI < 0. The dfference between the mean educaton of mmgrants from orgn country and the mean educaton of the populaton of that country falls n I. Corollary 3: MΔ/MN > 0. The dfference between the mean educaton of mmgrants from orgn country and the mean educaton of the populaton of that country rses n N. Corollary 4: MΔ/Mμ = 0. Under the assumptons above, a shft n the mean of the orgn country s educaton dstrbuton s neutral, havng no effect on the dfference between the mean educaton of mmgrants from that country and the mean educaton n the orgn country s overall populaton. Equvalently, f I = I j and N = N j, then the dfference between the mean level of educaton among mmgrants from country and country j equals the dfference between the 8

11 mean level of educaton n the orgn countres overall populaton. Dscusson The logc behnd the propostons and corollares fts the example n the ntroducton and the data on mmgrant background and attanment, both educaton and earnngs, n the US. Proposton 1 predcts the basc pont made at the outset. When a country s permtted to send only a small number of mmgrants and when selecton s from the top down, those who enter the US wll be hghly talented. The group wth the hghest level of educatonal attanment came from the USSR. Note that ths s USSR, not Russa, whch means that they entered before the breakup of the Sovet Unon. Among the pool of mmgrants n the sample, there were only 400 from the former Sovet Unon as compared wth over 395,000 from Mexco, the largest source of US mmgrants. The former Sovets were a rare group, needng to obtan both ext permsson from the USSR as well as entry permsson from US. A large proporton were hghly-educated poltcal dssdents, many of whom were elte academcs. The same s true perhaps to a lesser extent of other countres, lke Algera. The average level of educaton n Algera s well below the mean for orgn countres, but those who succeeded n movng to the US were not typcal Algerans. Instead, they were more educated than ther compatrots, so much so that as a orgn country, Algera s n the top 20% of mmgrant groups to the US n educatonal attanment. Algerans make up less than.0005 of US mmgrants - a tny fracton - and those who have been admtted to the US have been selected for reasons that correlate well wth educaton. The same educatonal attanment would not lkely be found of Algeran mgrants to France, where they make up a much larger fracton of the mmgrant populaton. Proposton 2 s slghtly more subtle, but almost equally ntutve. Consder selectng the most hghly educated 1 mllon people from a tny country lke Laos wth 7 mllon people versus 1 mllon from Inda wth 1.3 bllon. If the dstrbuton of underlyng ablty were the same n both countres, A* for Inda would be hgher than A* for Laos because 1 mllon people comprse a much smaller fracton of the top tal of the dstrbuton when there are 1.3 bllon than when there are 7 mllon. In fact, that s what s seen n the data. A substantal fracton of US mmgrants come from Inda, comprsng almost 5% of the sample of mmgrants. But because Inda s so large, Inda s very much under-represented (by a factor of almost four), gven ts mportance n world populaton. As such, those who come from Inda are from the top part of Inda s educatonal dstrbuton. Inda tself s not a country wth a hgh average level of educaton. Only 14 countres n the world have lower average levels of educaton than Inda has. However, because US mmgraton polcy does not select randomly from orgn countres nor from ndvduals wthn each country, Indans n the US rank second among mmgrants n educatonal attanment. Proposton 3 makes the more ntutve pont that the more hghly educated are people n the home country, the more educated are those who mmgrate from them. Consder two countres wth exactly the same populatons and that make up exactly the same proporton of US mmgrant pool. If the ablty dstrbuton from country 2 les to the rght of that from country 1, then selectng the same fracton of the upper tal from each results n a hgher average level of educaton among those selected. Ths s shown n Fgure 2. Two countres, 1 and 2, have smlarly shaped dstrbutons of talent, but country 2's dstrbuton s a rghtward shft of country 9

12 1's dstrbuton. Consequently, A 2 * exceeds A 1 * by the dfference n ther means,.e., M A / Mμ should equal 1. Furthermore, as s the subject of corollary 4, A 2, defned as the expectaton of ablty among mmgrants from 2, exceeds A 1, defned as the expectaton of ablty among mmgrants from 1, by the dfference n ther means. Ths s equvalent to the statement that A 2 exceeds the mean of dstrbuton 2 by the same amount that A 1 exceeds the mean of dstrbuton 1. Fgure 2 Corollary 1 smply states propostons 1 and 2 n another ntutve form. A country can be over- or under-represented among mmgrants. When a country s over-represented, the cutoff level of ablty from that populaton must be lower than t would be were that same country under-represented among mmgrants. Corollares 2, 3, and 4 follow drectly from the model, but emprcally, they are dfferent tests of the model s logc. The dependent varable n the corollares s Δ, whch s not the same as A. The average attanment among mmgrants from country, A could be hgh relatve to A j that from country j,, but that does not mply mechancally that A s hgh relatve to the average level of educaton n country. For example, mmgrants from the Unted Kngdom have average schoolng attanment of 15 years, above the mmgrant mean. But the average level of educaton n the UK s well above the mean educaton for other countres n the world, so the value of Δ for the UK s low. Conversely, mmgrants n the US from Yemen have only 9 years of schoolng, but the average level of educaton n Yemen s only 2.5 years, resultng n a hgh 10

13 value of Δ. Obvously, as a statstcal matter, Δ and may be related because the former A contans the latter, but they are not the same. Corollares 2-4 provde addtonal predctons that can be tested and could be rejected, even were propostons 1-3 to hold emprcally. Furthermore, note that the predcted relaton of Δ to μ s zero, not negatve as would result from pure statstcal bas. In the analyss below, attanment among mmgrants s measured by three dfferent varables, namely average educaton, hourly wages among workng mmgrants, and average earnngs among all mmgrants from a partcular country. Wthout excepton, all predctons of propostons 1 through 3 and corollary 1 are borne out for all three measures. Corollares 2-4 are found to hold wth respect to educatonal attanment, but cannot be tested for the two ncome varables because the data do not contan nformaton on ncome for the most of the 129 orgn countres used n the analyss. Specfc Dstrbutons of Ablty and Impled Structural Estmates Under more specfc assumptons, the propostons and corollares stated above can be parameterzed. Ths approach has the advantage that t allows for nterpretaton of estmates, but more mportant, t provdes addtonal checks on the credblty of the model and ts assumptons. 6 To begn, suppose that each orgn country has a normal dstrbuton of A wth a countryspecfc mean μ and country-specfc varance σ 2. Recall that I s the exogenously determned polcy varable. Let F * denote the cumulatve normal dstrbuton wth mean μ and varance σ 2. Further, let f * be the normal densty wth mean μ and varance σ 2. Then, from (1), A * can be determned as (1') N [1-F *(A *)] - I = 0 and smlarly (2') A 1 1 F *( A*) A * Af *( A) da If all the μ and σ were known, the exact A for each country would be determned, gven μ. That s, once the country s ablty dstrbuton s known precsely and once A * s gven, t s straghtforward to calculate the condtonal expectaton of those who are above A *. Then a goodness-of-ft statstc can be computed by checkng to see how well the actual A compare to those predcted based on the observed μ of the orgn country and σ. The data below provde an average attaned level of educaton for the 129 countres 6 I ask the reader to excuse my self-ndulgence for pontng out that one of (f not the) frst structural estmaton approaches n labor and appled mcroeconomcs appeared n my 1977 paper on a dfferent topc. See Lazear (1977). 11

14 studed so that μ s observable. The only mssng parameter s σ but ths can be obtaned for a subset of countres usng and addtonal dataset (IPUMS, as descrbed below). Data The prmary data on attanment of mmgrants n the US come from the Amercan Communty Survey from years 2011 through Ths s a seres of fve consecutve crosssectonal data sets. By combnng years, a larger sample s created so that more precson can be obtaned. It s straghtforward to adjust standard errors for populaton weghts and to correct wage data for nflaton to turn nomnal wages and earnngs nto real values. Gven the ndvdual data, the means of attanment varables, namely, educaton, wages, and annual earnngs can be computed by country of orgn. The varables of nterest are those that measure attanment of the mmgrants once n the US. They nclude educatonal attanment, wages, and ncome. The ndependent varables are ether nternally constructed, as s the case for I, or drawn from other data sets. UN reports provde nformaton on average educaton wthn the orgn country and populaton statststcs are taken from World Bank data. For convenence of readng the tables, I s defned as the actual number of mmgrants from country, measured n mllons as estmated by scalng up the ACS data to reflect sample sze relatve to overall populaton. Smlarly, N s defned as the populaton of country n 100 mllons. Addtonally, nformaton on GDP per capta, share n agrculture, growth rates, proporton wth tertary educaton and dstance of the orgn country from the US s obtaned. Appendx B contans the sources for each of the varables used. Addtonally, data from Sweden descrbed n a later secton s used to corroborate fndngs and dstngush the hypothess here from other explanatons. Results The man results are presented n tables 1 through 3. Table 1 tests the propostons usng the average educatonal attanment of mmgrants from country as the dependent varable. There are 129 countres wth nformaton necessary for the analyss. For each of those countres, observatons on each ndvdual n the ACS sample s used. The 129 observatons consst of orgn-country averages among those mmgrants who are n the ACS sample. Note that the country-based mmgrant weghted regressons reported n tables 1-3 are equvalent to usng the raw ndvdual-based ACS data, but the country versons are reported because the varaton n I, N, and μ are at the country, not ndvdual levels. Later, ndvdual data are used to examne cohort and age-of-arrval effects. Columns 1 through 4 of table 1 use dfferent weghtng schemes and subsamples. Column 1 s a full sample analyss where countres are weghted by the number of observatons that are used to compute the mean of the dependent varable. Ths s equvalent to usng the ndvdual data (analyzed below n table 8) from whch the country means are drawn. Column 2 presents the same analyss on the same sample, but weghts every country equally. The results are smlar, both n terms of sgn and statstcal sgnfcance. All the propostons are supported by these results. Specfcally, the average educatonal attanment of mmgrants from country declnes 12

15 n I, as predcted by proposton 1, ncreases n N, as predcted by proposton 2, and ncreases n μ as predcted by proposton 3. Furthermore, the three varable model explans 73% of the varaton n mmgrant educatonal attanment (column 1). In accordance wth proposton 1, a one standard devaton ncrease n a country s number of mmgrants decreases the predcted level of educatonal attanment n the US by about.4 years on a mean level of educaton of 13.4 years. The predcted dfference n educaton among mmgrants from the hghest mmgrant provder, Mexco, and the lowest mmgrant provder, Estona s 4.3 years. The actual dfference between mmgrants from the two countres s not far off at 5.6 years n favor of those from Estona. Proposton 2 predcts that the larger the populaton of the orgn country, the hgher s the attaned level of educaton among mmgrants. A one standard devaton ncrease n the populaton of the orgn country mples about.4 of a year ncrease n the educaton levels of the mmgrants from that country. (Concdentally, ths s the same number as a one standard devaton change n I produces.) Compare a tny country lke Cape Verde wth ½ mllon people to a large country lke Ngera wth almost 200 mllon people. Both have smlar average levels of educaton, but n accordance Proposton 2, the average level of educaton among mmgrants n the US from Cape Verde s 9.8 years versus over 15 years for those from Ngera. 7 The more ntutve predcton of proposton 3, that the educaton of mmgrants from country s postvely assocated wth educaton among natves n country, s borne out by the postve and sgnfcant coeffcents on μ n table 1. A one standard devaton ncrease n the mean level of educaton n the orgn country mples about a one year ncrease n educaton among mmgrants. Ths s not completely consstent wth the theory, however. The coeffcent should be 1, as mentoned above (see the proof n the appendx of proposton 3, whch yelds the result that M A / Mμ = 1). The coeffcent n table 1 on μ s always less than one. Some of ths may be attrbuted to an errors-n-varables ssue, where μ s ms-measured, but the coeffcent s substantally below 1, seemng to devate from the lteral predcton of the model that assumes the dstrbuton dstrbuton across countres up to a shfter n the mean. Fnally, table 1, columns 7 and 8, speak to corollary 1, where the representaton rato s used n place of I and N. Corollary 1 s supported by the results, whch yeld negatve and statstcally sgnfcant coeffcents. Recall that Inda s very much under-represented among US mmgrants, despte beng the thrd largest suppler of mmgrants. Because Inda s the second most populous country n the world, t s under-represented by a factor of 4 among US mmgrants. The mpled dfference between the educaton of mmgrants from Inda and that from, say, El Salvador, whch s hghly over-represented s about 3.5 years based on ths factor alone. The actual dfference s about 6 years. About 73% of the orgn country varaton n educatonal attanment s explaned by these three varables alone (n column 1). Importantly, almost all of ths s drven by the prmary 7 The actual dfference s much greater than that predcted from the coeffcents n table 1, but the drecton and nature of the effect s as predcted. Also, there are about 6 tmes as many mmgrants from Ngera as there are from Cape Verde, but there are 400 tmes more people n Ngera than n Cape Verde. Indeed, Cape Verde s over-represented among mmgrants by a factor of 12, whereas Ngera s underrepresented by a factor of 5. 13

16 ratonng varable, I. The r-squared n the weghted I regressons of A on I alone s.55, of A on N alone s.09, and of A on μ alone s.02. Columns 3-6 repeat the analyss, but wth dfferent sub-samples. In columns, 3 and 4, the four largest orgn countres of mmgrants are omtted to ensure that the results are not drven by a few countres. In columns 5 and 6, the smallest countres are omtted. Qualtatvely, the results are unchanged, although the magntudes do change some, especally and not surprsngly for the coeffcent on N, because the omsson of very large populaton countres changes the scale of that factor. 8 Addtonally, the conclusons are robust to weghtng and sample choce. Table 2 performs the same analyss, but defnes attanment n terms of the hourly wage receved among those workng rather than educatonal attanment. 9 Columns 1 through 7 of table 2 mrror columns 1 through 7 of table 1, wth all sgns and statstcal precson beng smlar across dependent varable defntons. A one standard devaton decrease n I mples about a $1.39 ncrease n the wage on a mean wage of $30.42 and a one standard devaton ncrease n the N mples a $2.24 ncrease. Just as was the case for educaton, the larger the number of mmgrants from an orgn country, the lower s the average wage, and the larger s the populaton of the country, the hgher s the average wage among those mmgrants. Addtonally, the hgher s the level of educaton n the orgn country, whch serves as a proxy for the average wage n the orgn country, the hgher s the mmgrant wage. Indeed, substtutng GDP per capta for educaton as a proxy for wage n the orgn country gves essentally the same results. Also, as was the case n table 1, all robustness checks on weghtngs and sub-samples confrm the ntal results of the frst column. Table 3 s analogous to table 2, but the dependent varable s average earnngs among all mmgrants from country. Ths takes nto account wage condtonal on workng, as n table 2, but also s affected by hours of work and employment rates among the mmgrant populaton. Agan, results are qualtatvely dentcal. The effects estmated n table 3 can be qute large. For example, the predcted dfference between average earnngs of those from the Phlppnes, whch supples the second largest fracton of US mmgrants and Mexco, whch supples the most, s $13,297 n favor of Phlppnes. Although Flpnos are the second largest group of US mmgrants, there are almost fve tmes as many Mexcan mmgrants n the US as Flpno. That dfference accounts for the much hgher predcted ncome for Phlppne mmgrants. The actual dfference between the two groups s about $16,300 n favor of the Phlppnes. Note that both orgn countres have average levels of educaton of around 9 years, so the orgn countres are comparable at least n ths respect. Corollary 1 has already been dscussed n the context of tables 1-3. Corollary 1 smply 8 A varable measurng populaton squared does not enter sgnfcantly n the weghted regresson, but enters postvely as predcted n the unweghted verson. 9 The dependent varable s n absolute dollars. The lnear specfcaton s approprate for country means, but not for the ndvdual-based data used below. Income dstrbutons are approxmately log normal at the ndvdual level, but should be normal for means. The actual dstrbuton of country means exhbts some postve skew. 14

17 condenses propostons 1 and 2 nto the representaton rato, whch s analyzed n columns 7 and 8 of the three tables. As dscussed earler, the data strongly support the contenton of corollary 1, namely that the lower the representaton rato, the hgher the achevement of a gven country s mmgrants n the US. Corollares 2-4 are testable n the same way that Propostons 1-3 were tested, wth two exceptons. Frst, because there s no drect measure of average wage or earnngs for all the countres n the dataset, the analyss s restrcted to estmatng only Δ defned n terms of educaton, namely the educaton of mmgrants from country mnus the average level of educaton n country. 10 Second, there s a standard statstcal problem ntroduced by regressng Δ on ndependent varables that nclude μ because μ s part of Δ. Recall that Δ s defned as A - μ, so any measurement errors n μ bas the coeffcent on μ downward. The standard soluton for ths problem s to nstrument the ndependent varable, n ths case, usng somethng that s correlated wth μ but does not have the same measurement error assocated wth t. Fortunately, there s another measure of educaton at home that s correlated wth average educaton (as s evdenced by the frst stage), but s not the same varable. The proporton of the populaton wth tertary educaton from Barro and Lee (2010) s a measure of a country s educaton level that s dfferent from μ but related to t. That varable s used as an nstrument. 11 Table 4 reports the results. Column 1 provdes the estmates from the nstrumental varables approach. As corollary 2 predcts, the sgn on I s negatve and as corollary 3 predcts, the sgn on N s postve. The larger s the group of mmgrants n the US, the smaller s the dfference between the mmgrants educatonal attanment n the US and the average educatonal attanment of the populaton n the orgn country. The larger s the populaton of the home country, the larger s the dfference between the mmgrants educatonal attanment n the US and the average educatonal attanment of the populaton n the orgn country. Fnally, as predcted, the effect of μ s not sgnfcantly dfferent from zero. Of course, the falure to fnd a sgnfcant effect of μ does not mply that corollary 4 s proved, but merely that t s not refuted and the standard error s large enough to prohbt rulng out a szeable effect of μ. The r-squared from the frst stage s.54 wth an F(1, 66) = 28.1, whch provdes some addtonal evdence on the valdty of the estmates. Column 2 reports the OLS results. They are smlar, wth the excepton of the coeffcent on μ, whch, not surprsngly, s negatve. Enterng the same varable on both sdes of the equaton results n bas, n ths case negatve. Functonal Form 10 It s mportant to use measures that are on the same scale, partcularly wth respect to proposton 4. The closest to wages or earnngs n the US would be purchasng power party GDP per capta, but ths would not be a good proxy of comparable earnngs at home f for no reason other than scalng. 11 Under the assumpton that F (A ) = F(A - μ ), t s only the mean of the dstrbuton that matters, n whch case the proporton wth tertary educaton s a vald nstrument. However, a more general specfcaton that allows the entre dstrbuton to vary mght have hgher moments of the dstrbuton ncluded and the tertary nstrument would only be vald f those other moments were ncluded. 15

18 Equatons (1) and (2) mply homogenety of degree zero n I and N. Specfcally, changng both I and N proportonately should not alter attanment among mmgrants because A *n (1) s not affected when both are multpled by any factor λ. Multplyng I and N by λ n (1) gves N [ 1 F( A*)] I 0 whch reduces to equaton (1) so A * s ndependent of the scalar. Addtonally, snce A n (2) depends only on A * and on f (A), nether of whch changes wth λ, A s not affected by λ. Ths s testable. It mples that attanment across mmgrant orgn countres should only depend on the rato of I to N and on μ, whch locates the orgn country s attanment dstrbuton, but not on the absolute levels of I and N drectly. Table 5 tests ths homogenety mplcaton and explores other functonal form ssues. Columns 1 and 2 report the results when only the rato of I to N and μ are ncluded as ndependent varables. The mean educaton n the home country should be ncluded even n the form that tests heterogenety because the dstrbuton s permtted to shft across countres. Recall that the representaton rato s merely I /N tmes a scalar relatng the world populaton to the number of mmgrants n the US. Thus, the homogenety property s equvalent to sayng that nether I nor N should affect the cutoff and therefore attanment, gven the representaton rato. In table 5, column 1 weghts by number of mmgrants from country and column 2 s the unweghted verson. In both forms, the rato enters negatvely, as predcted. Compare column 1 wth column 3 and column 2 wth column 4, the latter two allowng I and N to enter drectly. The homogenety property s clearly volated n both weghted and unweghted versons wth I contnung to enter negatvely and N enterng postvely. There are a number of possble explanatons. Recall that the assumpton was that the dstrbuton of A was dentcal across countres up to a shfter n the mean, μ. That assumpton s volated. Specfcally, large populaton countres have a hgher condtonal expectaton than would be predcted, whch suggests a thcker upper tal n larger countres. One possblty s economes of scale n educatonal producton. For example, Inda has top techncal unverstes. Smaller countres wth equal per capta GDP cannot afford to support major educatonal nsttutons. If true, there would be dsproportonately more hghly educated ndvduals n large countres than n small countres, whch would thcken the upper tal and result n a postve coeffcent on N. Ths s n fact the case. The next secton provdes structural estmates and drops the assumpton that F (A) = F(A-μ ),.e., that all source countres have the same dstrbuton of educaton (at home) up to a mean shfter. There, country-specfc educaton data from IPUMS 12 s used for a subset of countres. Those data reveal that Inda has one of the hghest standard devatons and coeffcent of varatons of wthn-country educaton levels. Despte havng a very low average level of educaton, there s a sgnfcant fracton of Indans who are hghly educated, some of whom mgrate to the US, many through the H1-B program. As mentoned at the outset, Indans are hghly under-represented n the US, but those who are 12 Internatonal Publc Use Mcrodata Seres (2018). 16

19 here tend to come from the top tal of the educatonal dstrbuton. Chna s a somewhat dfferent case, havng a hgher mean educaton than Inda, but a much lower standard devaton and coeffcent of varaton. Stll, because Chna s so large and because 10 percent of the Chnese populaton have completed the equvalent of hgh school, there are many Chnese wth hgh levels of educaton who mght be wllng to move to the US. The negatve coeffcent on I may be drven by dfferent mmgraton polcy selecton rules for countres that account for many versus few mmgrants. In the case of countres that account for only a small number of mmgrants that are under-reprensented n the US (lke the USSR or Afrcan countres that ft the Algeran example), skll rather than other factors may be a more mportant consderaton. Famly reunfcaton s lkely to play a greater role for those countres that have large numbers of mmgrants n the US. As a consequence, I enters negatvely, even holdng constant the rato of I to N, because small countres ft the selectonfrom-the-top assumpton more closely. The fnal two columns report the results when logs rather than levels are used. Unsurprsngly, the results are not affected qualtatvely. Structural Estmates The structural approach that assumes normalty of the attanment dstrbuton, outlned at the end of the model secton, can be mplemented. The detals of the estmaton are descrbed n Appendx C. Brefly, for a subset of the countres used n the tables above, IPUMS data are avalable. They provde nformaton on the actual level of educaton of ndvduals wthn the countres. The orgnal dataset had over 700 mllon observatons, but a random sample of 10,000 observatons from each of 66 countres was selected so that n addton to the mean, the standard devaton and 90 th percentle of educatonal attanment could be computed. Before engagng n structural estmaton, as a check, the reduced form regresson n column 1 of table 1 s re-estmated usng the subset of 66 countres. The coeffcents change slghtly, but are fundamentally the same as those on the sample of 129 countres. The r-squared for the table 1, column 1 regresson rses slghtly to.75 from.73 when the sample s restrcted to the 66 countres for whch IPUMS data are avalable nstead of the orgnal 129 countres. The addton of the standard devaton of the educaton n the source country enters postvely, although just below standard sgnfcance levels (t=1.89). (The coeffcent on the 90 th percentle was close to zero.) The nterpretaton makes sense. Those source countres wth the most varaton n educaton for a gven mean have a fatter upper tal, whch results n a hgher condtonal expectaton of educatonal attanment among mmgrants. The structural estmaton s performed as follows. The IPUMS data provde the mean and standard devaton of educaton n the source country. Gven those values, the actual upper tal of the educatonal dstrbuton for each country can be calculated, gettng a predcted A * based on the I/N rato for each country-specfc dstrbuton of educaton. Once A * s obtaned, a predcted average level of attaned educaton among mmgrants, namely those whose educaton exceeds A *, can be calculated for each of the countres. Goodness-of-ft of the structural model can be calculated by regressng the actual A on the estmated one. When ths s done on the subset of 66 countres for whch IPUMS data are avalable, the r-squared of actual on predcted s.62. Thus, the structural model does 83% as well n explanng the data as does the reduced form. (The rato of r-squareds n structural and 17

20 unconstraned reduced form s.62 /.75 =.83.) Addtonal Consderatons Other Explanatory Factors Table 6 allows other varables that are not explctly modeled to affect the educatonal attanment of mmgrants n the US. The ncluson of other factors rases the explanatory power by about 15 percentage ponts, from.73 to.88 n the weghted verson of column 1. In partcular, varables that measure growth and stage of development are ncluded, as s the orgn country s dstance from the US (captal cty to Washngton, DC). The varables that measure stage of development nclude GDP per capta, the last fve years growth rate, and the share of GDP that s comprsed of agrcultural output. Those varables are hghly correlated partcularly wth I and wth μ and a regresson of educatonal attanment on only the supply varables results n an r- squared that s almost the same as that for the three varables of the model. Consequently, regressons of educatonal attanment on ratonng varables as well as the addtonal varables s most nformatve to see whch drve the results. The results n table 6 show that none of the addtonal varables reman sgnfcant through all specfcatons. The opposte s true of the varables predcted by the model. Those coeffcents mantan sgn and sgnfcance throughout all specfcatons. Although the magntudes are somewhat dfferent from those found n table 1, the basc story remans the same. In the preferred specfcaton of column 1, the coeffcents on dstance, the GDP growth rate, and agrculture s share of GDP are sgnfcant. The latter two suggest that the less developed and less rapdly growng s the economy, the greater s the ncentve for hgh educaton ndvduals to seek resdency n the US. Ths seems more consstent wth a supply sde explanaton and recall that the supply sde s expected to play an mportant role n makng vald the assumpton of selecton from the top. Dstance of the orgn country from the US s also sgnfcant n column 1 and mght be assocated wth more tradtonal supply-sde explanatons. Immgrants who are further away must bear larger costs to come to the US and ths would be a barrer that mght cut most for lower sklled mgrants. Ths explanaton, whle plausble, s questonable for a few reasons. Frst, the result s drven entrely by the four largest orgn countres: Mexco, Phlppnes, Inda and Chna. When those countres are excluded or when each of those four countres s allowed to have ts own fxed effect, the mportance of dstance as an explanatory varable vanshes. Second, Inda, Chna and the Phlppnes are all dstant from the US. Immgrants from Inda have hgh levels of educaton, those from Chna are slghtly below the medan and those from the Phlppnes are slghtly above. Smlarly, Mexco and Canada each border the US. Canadan mmgrants have over fve years more educaton on average than those from Mexco. Addtonally, Mexcans are three tmes more over-represented among US mmgrants than Canadans, despte equal dstance of travel, whch suggests that dstance cannot be the prmary determnant of mgraton patterns. Thrd, the correlaton between the number of mmgrants from an orgn country and dstance s small, equalng -.11 and not statstcally sgnfcant. Ths s not surprsng because unlke n the past, n the 21 st century dstance s not much of an mpedment to movement. The 18