The empirical contribution of this work is the first country-specific bounds on the price equivalent of migration barriers using data on nationally representative samples of individual workers from the same country working on both sides of the border. 2 The methodological contribution is to propose new measures of selection bias in these estimates—derived from the theory of migrant self-selection and predicting patterns in the estimates by country of origin, skill group, and labor-market outcomes in the destination country.

We cannot separately estimate for each country the relative contributions of natural and policy barriers. That said, we note that spatially integrated labor markets in the absence of policy barriers rarely sustain real wage ratios above 1.5—even in the presence of important cultural and geographic barriers. This suggests a plausible prior that policy barriers to labor mobility account for at least as much of the observed gap in wages of fully equivalent workers as do natural barriers to movement, such as psychic costs or transportation costs.

Our focus is on prime-age, low-skill males educated abroad (35–39 years old, nine to twelve years of education acquired in the home country), though we present estimates for other demographic categories as well. We calculate lower bounds on the ratio of real wages in the United States to real wages of an identical worker in each home country. This lower bound varies greatly across countries, from a high of 16.4 for Yemen to a low of 1.7 for Morocco. Weighted by the working-age (15–49) population of the home countries, the average lower bound on this wage ratio is 5.65. For the median country, the lower bound is 3.95, and for the eightieth percentile country, the lower bound is 6.14. The working-age population weighted average of the lower bound on the absolute wage gain is PPP$13,710 per year across 1.5 billion working-age people from the 42 countries. The lower-bound absolute gain for workers from the median country is PPP$13,600, and for the 80th percentile country it is PPP$15,600.

We use a unique collection of data sets on individuals' wages from 42 developing countries and the United States to place lower bounds on the price equivalent of barriers to labor mobility into the U.S. market. We estimate the real (purchasing power parity, PPP) wage gaps between immigrants in the United States and their observably equivalent national counterparts in the 42 home labor markets. We then use theory and evidence on migrant self-selection to bound the real wage gap for fully equivalent workers, adjusted for both observable and unobservable characteristics. We call this wage gap a place premium because it does not arise from portable individual traits. We then use these bounds on the place premium to discuss what fraction of this price wedge might plausibly be attributed to natural barriers and what fraction to policy barriers.

ECONOMISTS often study the costs of frictions in international commerce by estimating their ad valorem equivalent. Such estimates are made for frictions that include trade quotas (e.g., Anderson & van Wincoop, 2004 ), transportation costs (e.g., Hummels, 2007 ), and capital controls (Edwards, 1999 ). But there are no systematic estimates of the price equivalent of barriers to the international movement of labor. Both the simple Harberger triangle intuition that welfare losses rise with the square of the price distortion and calibrated models of the world economy suggest that if the price equivalent of migration barriers is high, the annual global costs are trillions of dollars. 1

The ratios are quite precisely estimated. For the ratios R c , the t -statistic is above 10 in 38 out of 42 countries. Standard errors on R ^ c are bootstrapped with 500 draws to avoid the retransformation problem. The appendix presents robustness checks for other ages, recently arrived workers, and men only and discusses the potential for reporting bias. All of these PPP-dollar wage ratios presume that wages are spent at U.S. prices and are thus a conservative estimate of the gain to the extent that migrants remit a portion of wages to their (lower-price) home country. 6

The estimated wage ratios are very large. For the working-age population, weighted average country of birth is R c = 6 . 84 , while for the median country of birth, R c = 4 . 5 (five of the six largest countries in our sample—India, Indonesia, Bangladesh, Pakistan, and Nigeria—have estimates above the median). These ratios represent the difference in purchasing-power-adjusted wages between immigrants to the United States who received their education in the home country and observably equivalent workers in their country of origin: 35- to 39-year-old male workers with nine to twelve years of education who were born and educated in that home country.

Table 1 presents estimates of R u and R c where wages are measured in PPP U.S. dollars. The first column shows β ^ without any controls for education, age, and sex; the second column shows β ^ + ζ ^ edu 9--12 + ζ ^ age 35--39 with controls included. 5 The third column repeats the regressions with controls but drops all U.S.-resident workers who were younger than 20 years old when they arrived in the country. This eliminates most workers who received U.S. education, since domestic education and foreign education can have markedly different returns (Friedberg, 2000 ). These last results are converted to the wage ratio R ^ c for the final column, and countries are sorted in decreasing values of this ratio.

We use a unique standardized collection of individual-level data sets on wage earners compiled by the World Bank, combined with the U.S. Census Public Use Microdata Sample (PUMS) 5 percent file. 4 The unified database describes 2,015,411 individual wage earners, ages 15 to 65, residing in 43 countries close to the year 2000. This comprises 891,158 individuals residing in 42 developing countries, 623,934 individuals born in those same 42 developing countries but residing in the United States, and 500,319 individuals born in the United States and residing in the United States. Wages are measured in 1999 U.S. dollars at purchasing power parity (PPP).

whereis the monthly wage in U.S. dollars andis equal to 1 if the person lives in the United States and 0 otherwise.andare vectors of indicator variables for different groupings of years of education and quinquennial age, andis an indicator for female. 3 To be estimated are the parametersand, and the parameter vectors, whileis an error term. This specification allows all observable traits to have different returns in the two countries and assumes less about functional form than a model linear in traits. The key parameters areand the vectors

To begin to estimate these ratios, for each country of birth we run a separate regression for each country (other than the United States) where the sample includes all workers born in that country, whether they reside in the home country or the United States:

The ratios R u , R c , and R compactly summarize migrant selection on observed and unobserved wage determinants. R u / R c > 1 if and only if there is positive selection of migrants on observables, since ln ( R / R c ) = γ 0 ( E US [ s ] - E 0 [ s ] ) > 0 ⇔ E US [ s ] > E 0 [ s ] . Likewise, R c / R > 1 if and only if there is positive selection of migrants on unobservables, since ln ( R c / R ) = γ ˜ 0 ( E US [ s ˜ ] - E 0 [ s ˜ ] ) > 0 ⇔ E US [ s ˜ ] > E 0 [ s ˜ ] .

whereanddenote expectations—across residents of the home country and residents of the United States, respectively—for people born in the home country. The ratiois the place premium, that is, the real wage premium that a worker earns by working in the United States rather than home country.

Formally, suppose that a worker born and educated in a foreign country would earn w 0 in that home country and earn w US in the United States and that w 0 and w US are determined by

R u is the unconditional ratio of migrants' wages in the United States to wages in the home country, without adjustment for observable or unobservable differences between average migrants and average nonmigrants. R c is the ratio conditional on observable inherent differences like age and education. Finally, R accounts for all inherent differences, both observable and unobservable. That is, ratio R measures the real wage gain that the same person could expect in the United States relative to the home country.

III. Bounding Selection Bias Section: Choose Top of page Abstract I.Introduction II.Wage Ratios for Observ... III.Bounding Selection Bi... << IV.Discussion: Policy Bar... V.Conclusion REFERENCES CITING ARTICLES

The principal objection to the use of R c to estimate the wage of equivalent labor in two different labor markets is that migrants are self-selected. For U.S. migrants negatively selected on unobserved determinants of earnings, such as Mexicans (Fernández-Huertas, 2011), the estimates R c form a lower bound on the wage ratio for fully equivalent workers R . Under positive selection, R c can overstate R .

The rich microdata we use allow informative bounds on the bias from such self-selection in three ways. The first uses coefficent stability tests to bound the bias, comparing the results to existing empirical estimates of selection on unobservables. The second is to derive tests for selection bias under Roy (1951) selection. The third tests predictions about positive selection arising from capital constraints.

A. Lower Bounds from Coefficient Stability The first approach is to estimate the degree of bias that would arise from different degrees of selection on unobservables and compares this to selection estimates from the literature. Altonji, Elder, and Taber (2005) propose a method for bounding treatment effects under unobserved self-selection into treatment. They suggest that in many empirical settings, the degree of selection on unobservables can be bounded from above by the degree of selection on observables. In rough terms, this is because if the included (observed) covariates were chosen at random from the set of possible (observed or unobserved) covariates, then the degree of selection on observables would equal the degree of selection on unobservables. Researchers typically do not choose included covariates at random but specifically to reduce bias guided by theory; thus, the degree of selection explained by deliberately chosen covariates must exceed the degree explained by omitted covariates. This suggests an avenue for bounding the degree of migrant selection on unobserved determinants of earnings, given that variables like education, age, and gender are chosen not at random but specifically to reduce selection bias: all are known to be first-order determinants of both earnings and migration. Recently, Oster (forthcoming) observed that this method may not be sufficiently conservative and extended it. She shows that plausible bounds on selection must take account of the fraction of covariance in outcomes and treatment that is explained by observables. In other words, researchers must not only assert that they chose observables to reduce selection bias but show that those observables do have the explanatory power to reduce selection bias. Oster derives a simple approximation of the consistent estimator for a treatment effect β , β ^ ^ = β ^ - δ ( β ˚ - β ^ ) R ¯ - R ^ R ^ - R ˚ , (7) where β ^ and R ^ are the estimated treatment effect and the coefficient of determination ( R 2 ) from the regression, including observed controls; β ˚ and R ˚ are the estimate and the coefficient of determination without any controls; δ is the ratio of the degree of selection on unobservables to the degree of selection on observables; and R ¯ ≡ Π R ^ is the coefficient of determination from a hypothetical regression that includes all important observed and unobserved controls ( Π > 1 ). With conservative choices for δ and Π , equation ( β ^ ^ = 0 in equation ( δ allows estimation of how large selection on unobservables must be, relative to selection on observables, for the true treatment effect to be 0. Oster proposes a stringent standard for reporting results of δ = 1 and Π = 1 . 3 , the level of stability typically demonstrated by studies in the literature where treatment is randomized. whereandare the estimated treatment effect and the coefficient of determination () from the regression, including observed controls;andare the estimate and the coefficient of determination without any controls;is the ratio of the degree of selection on unobservables to the degree of selection on observables; andis the coefficient of determination from a hypothetical regression that includes all important observed and unobserved controls (). With conservative choices forand, equation ( 7 ) can bound the true treatment effect. 7 Alternatively, settingin equation ( 7 ) and solving forallows estimation of how large selection on unobservables must be, relative to selection on observables, for the true treatment effect to be 0. Oster proposes a stringent standard for reporting results ofand, the level of stability typically demonstrated by studies in the literature where treatment is randomized. We can apply these standards to compute a lower bound on R for each country. Table 2 carries out this bounding exercise for the wage ratios at PPP for a 35- to 39-year-old man with nine to twelve years of education. The first column reproduces R ^ c from table 1. The second column estimates lower bounds on R using equation (7), under the robustness standard for quasi-random treatment assignment: Π = 1 . 3 and δ = 1 . All of these bounds remain above a treatment effect of 0 ( R = 1 ), and most remain very large. The lower bound on R exceeds 5.0 in 17 countries and exceeds 3.0 in 29 out of 42 countries. The third column adopts the even more conservative standard of Π = 2 . The lower bound on R is still above 1.0 for 40 out of 42 countries and above 3.0 for 22 countries.8 Table 2. Lower Bounds on R from Coefficient Stability Test In column 4 we report the relative degree of selection on unobservables to observables ( δ ) that would be necessary in order for the estimated ratio R c to be consistent with R = 1 ) using Π = 1 . 3 . The selection on unobservables would typically need to be an order of magnitude larger than selection on observables (median δ | R = 1 = 12 . 2 , 80th percentile 23.5) for R to be unity given the observed R c . Column 5 reports the ratio R u / R c , showing generally positive selection on observables, with a median of 1.17. The median ratio of the estimates of the coefficient-stability lower bound on R is 1.12. The median ratio of the lower bounds on R in the third column ( Π = 2 ) to R c is 1.44. Is it plausible that selection on unobservables is an order of magnitude greater than selection on observables? Several studies of migrant self-selection have recently been done, in a variety of settings, that allow calculation of the relevant parameters. Table 3 presents all estimates of which we are aware. Eleven of these use panel data to compare nonmigrants with subsequent migrants prior to migration. These eleven results come from a variety of settings: origin areas both rich (Finland) and poor (Tonga); policy barriers both absent (Poland) and present (Mexico); distance both short (Lithuania) and long (Micronesia); time both contemporary (Israel) and historical (Norway). None of these settings records positive selection on unobservables with δ exceeding 0.89. In six cases, there is positive selection on unobserved determinants of earnings, but the highest R c / R ever recorded is 1.36. In three cases, there is no appreciable selection on unobservables despite selection on observables; thus δ ≈ 0 . In two of the cases, there is negative selection on unobservables ( R c / R < 1 ), so that R c serves as a lower bound on R . Both are studies of Mexico–U.S. migration; in one of these, δ < 1 and in the other, δ reaches + 2.25. One study has used retrospectively reported premigration wages for recent U.S. immigrants to estimate δ < 1 3 for a group of home countries comprising 36 of the 42 we study, and δ ≈ 1 in the rest.9 In all of these cases of positive selection on unobservables where it is possible to estimate δ given the published results, δ is approximately equal to or much less than 1. Table 3. Selection in the Literature These studies support the interpretation of column 2 of table 2 as conservative lower bounds on R (not as unbiased or consistent estimates of R ). The working-age population-weighted average of the lower bounds on R is 5.65. The lower bound for the median country (the Philippines) is 3.48, and for the 80th percentile country (India), it is 5.93. The final column of table 2 shows the dollar-value difference in PPP annual wages implied by R | δ = 1 , Π = 1 . 3 . These are best interpreted as lower bounds on the price equivalent for observably and unobservably equivalent low-skill, male, prime-age workers between the home country and the United States.

B. Testing Predictions of Roy Model Self-Selection We can gain more insight into the plausibility of large, positive selection on unobservables by testing necessary conditions implied by theory. Here we follow Hanson's (2006) nonstochastic extension of the Roy (1951)--Borjas (1991) model of migrant self-selection and consider selection on unobservables within observed skill groups as in Ambrosini and Peri (2012). Suppose a worker with observed skill s will migrate if U.S. wages exceed the forgone foreign wage plus migration costs: ln w US - ln ( w 0 + C ) > 0 . Expressing migration cost in time-equivalent form ( π ≡ C / w 0 ), then by equations (1) and (2), workers migrate if their unobserved skill satisfies s ˜ > π - ( μ US ' ( s ) - μ 0 ' ( s ) ) γ ˜ US - γ ˜ 0 ≡ s ̲ ( s ) . (8) This standard result implies that migrants will exhibit positive selection on unobservables if the return to unobservables at the destination exceeds the return at the origin ( γ ˜ US > γ ˜ 0 ). But because we have data from numerous countries, we can derive a necessary condition for bias in R c due to Roy selection on unobservables. From equations ( ∂ ln ( R c ( s ) / R ) ∂ γ ˜ US | γ ˜ 0 = γ ˜ 0 · ∂ E [ s ^ | s ^ > s ̲ ( s ) ] ∂ γ ˜ US | γ ˜ 0 > 0 . (9) That is, if R c is biased upward by positive selection on unobservables, Roy selection predicts that this bias will be greatest when the relative return to unobserved skill is higher in the destination country relative to the origin country. This standard result implies that migrants will exhibit positive selection on unobservables if the return to unobservables at the destination exceeds the return at the origin (). But because we have data from numerous countries, we can derive a necessary condition for bias indue to Roy selection on unobservables. From equations ( 4 ), ( 5 ), and ( 8 ),That is, ifis biased upward by positive selection on unobservables, Roy selection predicts that this bias will be greatest when the relative return to unobserved skill is higher in the destination country relative to the origin country. We can test condition (9) by following the literature since Juhn, Murphy, and Pierce (1993) and considering the dispersion of s ˜ for workers of a given country of birth, in each country of residence ( σ 0 and σ US ), to proxy for the corresponding returns to unobserved skill. Let σ US ( s ) be the standard deviation of ln wage conditional on observables, from regression (6), for workers born in each country and resident in the United States. Let σ 0 ( s ) be the same conditional standard deviation for workers resident in the country of birth. Thus, σ US ( s ) - σ 0 ( s ) proxies for γ ˜ US ( s ) - γ ˜ 0 ( s ) , the returns to unobserved skill in the United States relative to the country of birth, specific to each observed skill group. Figure 1 tests for the relationship, equation (9), by graphing R c against σ US ( s ) - σ 0 ( s ) , by country, separately for each of three observed skill groups.10 For example, figure 1a plots R c against σ ^ US ( s ) - σ ^ 0 ( s ) for workers with five to eight years of education only, across all countries. There is no positive correlation between the estimates of R c and the relative returns to unobserved skill, contrary to what theory predicts if positive selection is an important source of bias. If anything, the relationship is negative. This suggests that positive selection on unobservables predicted by the Roy model could not be a first-order determinant of the magnitude of the estimates R c . Egypt and Yemen are slight outliers. The gray line shows local linear regression, Epanechnikov kernel, bandwidth 0.5.

C. Testing for Self-Selection Due to Borrowing Constraints Theory predicts another reason that migrants might exhibit positive self-selection on unobserved determinants of wages. While migrant selection theory has traditionally focused on Roy selection, recent literature has stressed borrowing constraints as an important determinant of selection.11 Workers with low earnings for unobservable reasons may simply be unable to afford the costs of migration, broadly considered, so that migrants have levels of unobserved skill that exceed the average in the origin country. Again extending Hanson (2006) to the case of selection on unobservables within observed skill groups, suppose that income y 0 of a worker in the origin country is a function of unobserved skill. For workers of observed skill s , y 0 ( s ) = ξ ˜ 0 ( s ) + ν ˜ 0 ( s ) s ^ , where ξ ˜ 0 , ν ˜ 0 > 0 . Some workers cannot pay the migration cost C ( s ) , which is a function of observed skill, but they can borrow it if they hold collateral ψ C ( s ) , ψ > 0 . The condition for migration becomes s ^ > ψ C ( s ) - ξ ˜ 0 ( s ) ν ˜ 0 ( s ) ≡ s ̲ ̲ ( s ) . (10) That is, positive selection on unobservables arises within observed skill groups because those with the highest unobserved determinants of earnings are the ones most likely to be able to acquire the necessary assets. This force for positive selection can act independent of Roy selection, equation ( That is, positive selection on unobservables arises within observed skill groups because those with the highest unobserved determinants of earnings are the ones most likely to be able to acquire the necessary assets. This force for positive selection can act independent of Roy selection, equation ( 8 ). We can use condition (10), as we used condition (8), to make predictions about patterns the data should contain if selection of this kind is driving the results. Suppose that migration costs are lower for high-observed-skill workers ∂ C ∂ s < 0 and that wealth and the wealth returns to unobserved skill are greater for workers with higher observed skill ∂ ξ ˜ 0 ∂ s > 0 , ∂ ν ˜ 0 ∂ s > 0 . Both of these are plausible: many countries actively encourage high (observed) skill migration while obstructing low (observed) skill migration. And workers in developing countries with higher observed skill typically have greater wealth and work in complex occupations with higher returns to unobserved skill than menial occupations. Suppose, furthermore, that credit constraints bind for workers without any observed skill ψ > ξ ˜ 0 ( s ) C ( s ) . Together, these imply ∂ ln R c ( s ) / R ∂ s = ∂ E [ s ^ | s ^ > s ̲ ̲ ( s ) ] ∂ s < 0 . (11) That is, if the estimates of R c are systematically biased upward from R because of self-selection on unobservables arising from poverty constraints, then we should see estimates of R c decline when higher and higher levels of observed skill are considered separately. That is, if the estimates ofare systematically biased upward frombecause of self-selection on unobservables arising from poverty constraints, then we should see estimates ofdecline when higher and higher levels of observed skill are considered separately. This test is possible with the information already discussed previously: separate estimates of R c for each education group: five to eight years, nine to twelve years, and 13 or more years.12 In 8 countries, R c is higher for workers with thirteen or more years of education than for workers with five to eight years of education, which is incompatible with equation (11). In the other 34 countries, R c falls somewhat at higher levels of observed skill, which is compatible with equation (11). The median ratio R c (5–8 years)/ R c (13 or more years) is 1.38. Collectively, this evidence is compatible with modest positive selection on unobservables that induces upward bias in R c as an estimate of R to a degree comparable to the independent estimates of this bias from table 2. In other words, to the extent that marginal workers who can afford university education can also afford migration, R c for workers with thirteen or more years of education can serve as a lower bound on R for that category of worker. A second test uses the fact that in the credit-constraint theory of positive selection, unlike in Roy selection, selection on observables and unobservables must go in the same direction. In this theory, the poor do not migrate because they do not have the money, and from the standpoint of theory, it does not matter whether the reason they do not have money is due to observable or unobservable traits. Take Hanson's (2006) observable counterpart to the wealth equation above and suppose that wealth is also positively correlated with observed skill: y 0 ( s ) = ξ 0 + ν 0 s , where ξ 0 , ν 0 > 0 . Migrants are positively selected on observed skill analogous to equation (10), and just as above, we can derive an observable counterpart to condition (11), ∂ ln R / R c ( s ) ∂ ln w 0 < 0 , (12) with the innocuous assumption that income correlates positively with wealth. That is, if positive self-selection on observables arises due to poverty constraints, the degree of positive self-selection should fall as average wages rise. with the innocuous assumption that income correlates positively with wealth. That is, if positive self-selection on observables arises due to poverty constraints, the degree of positive self-selection should fall as average wages rise. Figure 2 carries out this test, plotting the degree of selection on observables ( ln R u / R c ) against E [ w 0 ] for all countries of birth and each observed skill group. The pattern predicted by equation (12) is not present across all the countries at any level of observed skill. For workers of five to eight years of education, this is perhaps no surprise, since there is less scope for positive selection on education. For higher levels of observed skill, the pattern is more informative. For workers with nine to twelve years of education, the degree of positive selection on observables is roughly the same in Costa Rica and Argentina as it is in Vietnam and Sierra Leone, despite a fourfold difference in average wages. The conditional mean does fall slightly, from about 1.4 to 1.2, as the average wage ranges over an order of magnitude. This is consistent with a modest upward bias on R u as an estimate of R c due to selection on observables arising from credit constraints. For the most educated workers (thirteen or more years of education), the conditional mean changes little between the average wage of PPP$300/month and PPP$1,200/month. It does fall by roughly 0.3 log points over the range PPP$600–1,200/month. This too is compatible with modest upward bias arising from positive selection on observables due to credit constraints.13 The simple theory presented here does not suggest a reason why income that reflects observables should affect credit constraints differently from income that reflects unobservables.14 The gray line shows local linear regression, Epanechnikov kernel, bandwidth 100 (panels a,b) or 175 (c). A third and separate test for bias due to positive selection of this kind takes advantage of information contained in the relative performance of migrants and natives in the U.S. labor market. Suppose that U.S. natives' wages, analogous to equations (1) and (2), are determined by w * ( s ) = μ 0 * + γ 0 * s + γ ˜ 0 * s ˜ and natives' unobserved skill has mean 0. Migrants' skill is only partially transferable, as in the model advanced by Gould and Moav (2016). Observed skill is transferable from the migrant-origin country to the United States in the proportion γ US / γ 0 , and unobserved skill is transferable in the proportion γ ˜ US / γ ˜ 0 . We can express the wages of a migrant in the United States as E US [ ln w US ] = E [ ln w * ] - 1 - γ US γ 0 E [ ln w * - ln w ̲ ] + γ ˜ US E US [ s ^ ] , (13) where w ̲ * is the wage of a U.S. worker with no observable skill (no education, no experience) and E US denotes expectations for migrant workers in the United States. The identity equation ( γ US / γ 0 = 0 and migrants are neutrally selected on unobservables E US [ s ^ ] = 0 , all migrants regardless of observed or unobserved skill have the earnings of a U.S. teenager with no schooling. From equations ( ln R c R = γ ˜ 0 E US [ s ^ ] , into which we substitute equation ( E US [ ln w US ] - E [ ln w * ] = γ ˜ US γ ˜ 0 ( ln R c - ln R ) - 1 - γ US γ 0 E [ ln w * - ln w ̲ * ] . (14) whereis the wage of a U.S. worker with no observable skill (no education, no experience) anddenotes expectations for migrant workers in the United States. The identity equation ( 13 ) states that the average wage of a migrant worker in the United States equals the average wage of an observably equivalent U.S. worker, minus the portion of migrant workers' observable wage determinants that do not transfer from the origin country to the United States, plus the U.S. returns to migrants' unobservable skill. In the limiting case where none of migrants' observable skills are valued in the U.S. marketand migrants are neutrally selected on unobservables, all migrants regardless of observed or unobserved skill have the earnings of a U.S. teenager with no schooling. From equations ( 4 ) and ( 5 ), we have, into which we substitute equation ( 13 ) to get Intuitively, migrants who are more positively selected on unobserved skill ( R c > R ) should earn more relative to natives of the same observable skill, to the extent that their unobserved skill is transferable ( γ ˜ US / γ ˜ 0 ). If there are 0 returns to migration ( R = 1 ), a regression of R c on the native-immigrant wage gap within an observed skill group should have slope representing the transferability of unobserved skill. If that slope is 0, then either unobserved skill is completely untransferable—it does not represent IQ, energy, risk tolerance, or anything else that comes with migrants and has returns in the United States—or R c ≈ R . We calculate E US [ w US ] - E [ w * ] for each country of birth and three observed education groups, always for 35- to 39-year-old men.15 This allows us to run the regression (14) nonparametrically in figure 3. The gray line shows local linear regression, Epanechnikov kernel, bandwidth 0.3 log points. The slope is generally indistinguishable from 0 across most of the support of R c for all three observed skill groups. Two exceptions, in workers with five to eight years of education, are Cameroon and Morocco. This suggests that either unobserved skill exhibits near-0 transferability to the U.S. labor market or that estimates of R c do not greatly exceed R . Research that compares U.S. immigrants' earnings to their premigration earnings estimates that the transferability of foreign unobserved skill is 0.34 shortly after arrival (Jasso, Rosenzweig, & Smith, 2002), a lower bound on γ ˜ US / γ ˜ 0 since the returns to migrants' unobserved skill rise in the years following arrival (Chiswick & Miller, 2012). This suggests that the gap between R and R c is not large. We can use this information to estimate a rough bound on the selection bias R c / R . For the observed skill group with the most positive slope in figure 3 (five to eight years of schooling), a linear regression of E US [ w US ] - E [ w * ] on ln R c gives the slope 0.144 (standard error 0.061). If a lower bound on the transferability of unobserved skill for those who have chosen to migrate is 0.34, this puts an upper bound on R c / R of e ( 0 . 144 / 0 . 34 ) = 1 . 53 for workers with five to eight years of education. For the group with thirteen or more years of schooling, the linear regression slope is 0.031 (standard error, 0.043), and the corresponding upper bound on R c / R is e ( 0 . 031 / 0 . 34 ) = 1 . 10 . These estimates independently corroborate the approximate magnitude of bias estimated above. The declining bias at higher observed skill also agrees with the prediction of equation (11). These results are consistent with modest systematic bias in R c as an estimator of R due to positive selection on unobservables arising from credit constraints. Incidentally, these results also have implications for the discussion of Roy selection in section IIIB. The slopes in figure 3 further suggest that Roy selection is unlikely to create a large upward bias on R c as an estimate of R . A well-known prediction of Roy selection is that positive selection on unobservables cannot occur without positive returns to unobservables in the destination country.16 The flat slopes in the figure imply either that almost none of migrants' unobserved skill is transferable to the destination country or that R c ≈ R . But if migrants' unobserved skill is not transferable, the Roy model predicts negative selection on unobservables. In that case, the estimates of R c would generally serve as a lower bound on R . A final and intuitive robustness check, presented in the appendix, is to simply truncate the very poorest workers from the analysis. The findings are robust to this change. After dropping workers below PPP$4/day, the median ratio of R c to the original result in table 1 is 1.07.