Abstract
Ability drain’s (AD) impact seems economically significant, with 30% of US Nobel laureates since 1906 being immigrants, and immigrants or their children founding 40% of Fortune 500 companies. Nonetheless, while brain drain (BD) and gain (BG) have been studied extensively, AD has not. I examine migration’s impact on ability (a), education (h), and productive human capital or “skill” s =s(a, h), for source country residents and migrants under (a) the points system (PS) which accounts for h and (b) the “vetting” system (VS) which accounts for s (e.g., US H1B program). The findings are as follows: (i) Migration reduces (raises) residents’ (migrants’) average ability, with an ambiguous (positive) impact on average education and skill, and net skill drain, SD, likelier than net BD; (ii) these effects increase with ability’s inequality or variance, are greater under VS than PS, and hurt source countries; (iii) the model and two empirical studies suggest average AD ≥ BD for educated US immigrants, with real income about twice the home country income; and (iv) SD holds for any BD and for a very small AD (7.4% of our estimate). Policy implications are provided.
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Notes
 1.
Bhagwati and Rodriguez (1975) provide an overview of a collection of studies dealing with pre1970s’ and 1970s’ brain drain theory, evidence, and policy.
 2.
Some innate ability might be further developed later in life, though at a cost (which may well be prohibitive for those poorly endowed with it or with complementary ones). I abstract from this possibility to provide a sharp contrast between this study and previous ones which have typically excluded heterogeneous ability.
 3.
 4.
 5.
I selected as simple a model as possible in order to obtain results that are clear and make intuitive sense. For instance, with s _{ i } = a _{ i } + h _{ i }, there are no interaction effects between ability and education. Nevertheless, the optimal value of h _{ i } rises with a _{ i }, with the exact relationship depending on the host country’s immigration policy (see Sections 3 to 5). One could also specify s _{ i } as s _{ i } = a _{ i } h _{ i }. This would complicate the model without affecting the qualitative results—though it would lead to a greater negative (positive) impact on home country residents’ (migrants’) average ability and education.
 6.
A large number of empirical studies show that investment in education exhibits diminishing returns. Given that income is a linear function of education in (1), assuming a quadratic education cost function results in diminishing returns to education (with a negative second derivative of c_i with respect to education).
 7.
Of the 42 sample countries in the empirical analysis (provided in Section 6 and the Appendix), 55% are either lowincome or lowermiddleincome countries (defined by the World Bank for 2017 as countries with a per capita income below US $4036 in 2015) and about two thirds of the sample countries had a per capita income of US $5000 or less in 2015. A quadratic education cost seems reasonable for those countries as a constraint is likely to prevail on the number and qualifications of individuals teaching students who are completing a bachelor’s degree or more—which is the level of education for which the relationship between ability drain and brain drain is derived (as shown in the Appendix).
 8.
Thus, average education and skill levels are higher for migrants than for residents, i.e., migrants are positively selected for both ability a _{ i } and education h _{ i }. As Docquier and Marfouk (2006) show for education, the share of the highly educated in SouthNorth migrants is three times that among the South’s residents, and the ratio is larger for poor, landlocked and island countries (e.g., 15 for subSaharan Africa).
 9.
This assumes a wellfunctioning visa program, which is not necessarily the case. See Section 8 for more on this issue.
 10.
Proof that \( \lambda \le \frac{1}{2} \): Residents’ actual (as opposed to expected) consumption under the vetting system is \( {c}_{iv}^A={\alpha}_0{s}_{iv}\frac{h_{iv}^2}{2} \) \( ={\alpha}_0\left(\frac{\alpha_0}{2}+{a}_i\right)2{\lambda}^2{\left({\alpha}_0+{a}_i\right)}^2\ge 0 \), and thus, λ ^{2} ≤ ψ \( =\frac{{\alpha_0}^2+2{a}_i{\alpha}_0}{4{\left({a}_i+{\alpha}_0\right)}^2}= \) \( \frac{1}{4}\frac{{a_i}^2}{{4\left({a}_i+{\alpha}_0\right)}^2} \), which reaches a maximum, \( {\psi}_M=\frac{1}{4} \) at a _{ i } = 0, so that \( \psi \le \frac{1}{4} \) and \( {\lambda}^2\le \psi \le \frac{1}{4} \), i.e., \( \lambda \le \frac{1}{2\ } \). QED.
 11.
In addition to generating a direct benefit for migrants’ home country, such interaction would also likely raise bilateral trade and investment over and above the increases found in existing studies because of further reductions in information and transactions costs, thereby benefiting both countries (see Parsons and Winters’ (2014) excellent survey on migration’s impact on bilateral trade and Javorcik et al. (2011) and Kugler and Rapoport (2007) on migration’s impact on bilateral investment).
 12.
As for agreements on expanded market access commitments for services, such as those delivered through the temporary crossborder movement of natural persons (a.k.a. mode IV), would benefit both source and host countries—with the former supplying labor services in, say, construction, cleaning, and hospitality, and the latter supplying, say, banking, insurance, and ICT. Such arrangements would reduce some of the concerns related to the brain and ability drain associated with permanent migration. So far, though, both sets of countries have limited the access to this mode of trading services.
 13.
Haque (2007) argues that human capital should be thought of exactly as financial capital, where the return of flight capital depends in large measure on the policies implemented by the country of origin.
 14.
A notable example is Southern California Edison, which replaced its IT employees with younger ones brought in through the H1B program, with the original employees forced to train their replacements and sign nondisclosure agreements and gag orders. Salaries fell from $110,000 to $70,000 a year on average or by 36% (based on depositions in a Senate Judiciary Committee hearing spurred by complaints of the practice).
 15.
Migrants’ average ability “gain” is \( \frac{\pi}{\phi P} V\left({a}_i\right)=\left[\left(1 P\right)/ P\right] \)*AD, and their average education “gain” \( \Delta {H}^M=\left({H}^G{H}_0\right)+\frac{2\pi \lambda}{\phi P} V\left({a}_i\right)=2\lambda \left({\alpha_0+ A}^G\right)+\left[\left(1 P\right)/ P\right] \)*BD.
 16.
This is consistent with their finding that H1B visa holders earned on average 13.5% more than US nativeborn workers with a bachelor’s degree.
 17.
Given that prices are typically lower in the home country, US immigrants gain more than 100% of the income earned back home if part of their income is transferred back home—say, through remittances—and consumed by family members there.
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Acknowledgements
Thanks are due to Lant Pritchett, Hillel Rapoport, two anonymous referees, and participants at the 2016 Western Economic Association International meetings, the 2016 Conference of the Society of Government Economists, and a World Bank seminar for their comments.
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Appendix
Appendix
Clemens, Montenegro, and Pritchett (2009)—referred to as CMP—use data on 41 developing source countries j and the USA, and examine various income ratios (denoted here by lowercase letters), where the denominator is the average income of source country residents, Y _{0} = α _{0} S = α _{0}(A + H), where A is unobservable ability and H is observable education. CMP’s objective is to obtain the average income ratio, \( {y}_d^{\prime \prime }={Y}_d^{\prime \prime }/{Y}_0 \), of migrants living in the USA who were educated in their home country, relative to the income of home country residents with the same A and H levels, i.e., \( {y}_d^{\prime \prime }={Y}_d^{\prime \prime }/{Y}_0={\alpha}_d\left( A+ H\right)/{\alpha}_0\left( A+ H\right)={\alpha}_d/{\alpha}_0 \). The problem with such comparisons is of course that migrants selfselect on both ability and education, whose levels are denoted by A ^{M} and H ^{M}, respectively, and that their observed income is Y _{ d } = α _{ d } S ^{M} = α _{ d }(A ^{M} + H ^{M}) rather than \( {Y}_d^{\prime \prime } \).
CMP find that for the 42 source countries, migrants’ average income ratio \( {y}_d=\frac{\alpha_d{S}^M}{\alpha_0 S}=\frac{\alpha_d\left({A}^M+{H}^M\right)}{\alpha_0\left( A+ H\right)}=7.99 \), i.e., migrants’ average income is 7.99 times that of source country residents. They first correct y _{ d } for migrants’ selfselection with respect to observable H in order to obtain \( {y}_d^{\prime }={\alpha_d{S}^{M\prime }/{\alpha}_0 S=\alpha}_d\left({A}^M+ H\right)/{\alpha}_0\left( A+ H\right) \) where, from Eq. (14), \( \Delta H\equiv {H}^M H=\left[2\pi \lambda \phi P\left(1 P\right)\right] Vai \). They find that \( {y}_d^{\prime }=5.11=0.64{y}_d \) for the 42 countries. Thus, correcting for selection on observables (i.e., education) reduces migrants’ income by\( \frac{\alpha_d\Delta H}{Y_0}=2.88=0.36{y}_d \) or a reduction in migrants’ relative income of 36%.
US immigrants and home country residents may also differ in terms of nonobservable characteristics associated with migrants’ selfselection on ability. CMP correct for migrants’ selfselection on ability, replacing \( {y}_d^{\prime }={\alpha}_d\left({A}^M+ H\right)/{Y}_0 \) by\( {y}_d^{\prime \prime }={\alpha}_d\left( A+ H\right)/{Y}_0 \), where ΔA ≡ A ^{M} − A= \( \frac{\pi}{\phi P\left(1 P\right)} V\left({a}_i\right) \), and\( {\ y}_d^{\prime }{y}_d^{\prime \prime }={\alpha}_d\Delta A/{Y}_0 \).
Two conditions make it possible to obtain the value of the ability drain, AD; brain drain, BD; and their relative size, AD/BD, from the relationship between \( {y}_d{y}_d^{\prime } \) and \( {\ y}_d^{\prime }{y}_d^{\prime \prime } \):

(i)
The relationship between AD and BD is identical to that between ΔA and ΔH. From Eq. (14), \( {\Delta A\equiv A}^M A=\frac{\pi}{\phi \left(1 P\right)} V\left({a}_i\right)+\frac{\pi}{\phi P} V\left({a}_i\right)=\frac{\pi}{\phi P\left(1 P\right)} V\left({a}_i\right) \), so that \( \mathrm{AD}=\frac{\pi}{\phi \left(1 P\right)} V\left({a}_i\right)= P\ast \Delta A \).^{Footnote 15} Similarly, BD = P*ΔH. Thus, AD/BD = ΔA/ΔH.

(ii)
ΔA and ΔH are multiplied by the same parameter, α _{ d }, to obtain the income changes associated with the vetting system, so that AD/BD can be obtained from the difference between relative incomes \( {\ y}_d^{\prime } \) and \( {y}_d^{\prime \prime } \).
CMP use various methods, based on both macroeconomic and microeconomic evidence, to obtain an estimate of the impact on migrants’ average income of selection on (nonobservable) ability, η, in \( {y}_d^{\prime \prime }= \) \( {y}_d^{\prime }/\eta \), where η ≥ 1. They conclude that the degree of positive selection on unobserved wage determinants results in a bias, η, between 1.0 (no bias) and 1.45 in the case of Peru, i.e., η ϵ [1.0, 1.45]. The average ability drain obtained over these η values is AD = 1.0742BD, as shown below.
CMP obtained the range of η values for workers with 9 years of education and state that selection on ability for lesseducated workers is likely to be attenuated by the fact that they tend to work in occupations without plausibly high returns to unobserved skill, a result confirmed by the model.
Recalling that h _{ i } = 1 represents 20 years of education, it follows that h _{ i } = 0.45 for 9 years of education. From Eq. (12), we have \( {h}_i=\frac{\alpha_0}{\phi}+2\lambda {a}_i \), or \( {a}_i=\frac{1}{2\lambda \phi}\left(\phi {h}_i{\alpha}_0\right) \). For individuals with 9 years of education, we have \( {a}_i=\frac{1}{2\lambda \phi}\left(0.45\phi {\alpha}_0\right) \). Migrants who enter the USA via the H1B visa program must have at least a bachelor’s degree or a minimum of 16 years of education, i.e., a level of h _{ i } equal to 0.8 or higher, and the equation for a _{ i } and the correction for selection on ability must take the difference in education levels into account. Rothwell and Ruiz (2013) report that 90% of US companies’ H1B applications are for occupations that require highlevel STEM (i.e., highlevel science, technology, engineering, and math) knowledge. These typically require a graduate degree or equivalent, which takes at least 1 year and often 2 years to complete.^{Footnote 16} Thus, it seems reasonable to assume that H1B immigrants average one to two more years of education. Assuming conservatively that they have one more year of education implies that h _{ i } = 0.85. Then, \( {a}_i=\frac{1}{2\lambda \phi}\left(0.85\phi {\alpha}_0\right) \), and the correction for selection on ability, η, becomes \( {\eta}^{\prime }=\eta \left(\frac{0.85\phi  {\alpha}_0}{0.45\phi {\alpha}_0}\right) \). Thus, for these individuals, \( {y}_d^{\prime \prime }={y}_d^{\prime }/{\eta}^{\prime } \) and ability drain’s impact is \( {y}_d^{\prime }{y}_d^{\prime \prime }={y}_d^{\prime}\left[\left({\eta}^{\prime }1\right)/{\eta}^{\prime}\right]=0.64{y}_d\left[\left({\eta}^{\prime }1\right)/{\eta}^{\prime}\right] \).
With the correction for selfselection on education equal to 0.36y _{ d }, we have
Probability p _{ i } = π(a _{ i } + h _{ i }) ≤ 1, with \( \pi \le \frac{1}{a_i+{h}_i} \), ∀a _{ i } ϵ [0, a _{ M }] , h _{ i } ϵ [0, 1], implying that \( \pi \le \frac{1}{1+{a}_M}. \) Individual education is \( {h}_i=\frac{\alpha_0}{\phi}+2\lambda {a}_i=\frac{\alpha_0+2\pi \left({\alpha}_d{\alpha}_0\right){a}_i\ }{12\pi \left({\alpha}_d{\alpha}_0\right)}\le 1 \). Define x ≡ α _{ d } − α _{0} > 0, so that \( {h}_i=\frac{\alpha_0+2\pi x{a}_i\ }{12\pi x}\le 1 \), or α _{0} ≤ 1 − 2πx(1 + a _{ i }), \( \forall \pi \left(0,\frac{1}{1+{a}_M}\right] \), i.e., \( {\alpha}_0\le 12 x\frac{\left(1+{a}_i\right)}{\left(1+{a}_M\right)} \). With h _{ i }(a _{ M }) = 1, we have α _{0} = 1 − 2x = 1 − 2(α _{ d } − α _{0}). Thus, \( {\alpha}_d=\frac{1{\alpha}_0}{2} \).
I proceed now to “guess” a solution for α _{ d }/α _{0}, namely α _{ d }/α _{0} = 2 (this is verified below). Then, from \( {\alpha}_d=\frac{1{\alpha}_0}{2} \), it follows that α _{0} = 0.2 and α _{ d } = 0.4. Thus, α _{ d } − α _{0} = 0.2 and ϕ = 1 − 2π(α _{ d } − α _{0}) = 1 − 0.4π. From \( \lambda \le \frac{1}{2} \) and h _{ i }(a _{ M }) = 1, we have π ≤ 0.8 or π ϵ (0, 0.8].
I verify now whether the guess that α _{ d }/α _{0} = 2 is correct. The average ability drain relative to the brain drain, AD/BD, is obtained by averaging the AD/BD values obtained for η ϵ [1, 1.45] and π ϵ (0 , 0.8]. For instance, take π = 0.2 and η = 1.25. Then, ϕ = 1 − 0.2^{∗}0.4 = 0.92. Substituting the values for ϕ and η into Eq.(A.1), the ratio AD/BD = 1.0301, which means that the ability drain is 3% larger than the average brain drain.
The average value is AD/BD = 1.0742. Thus, AD = 1.0742BD = 0.3867y _{ d } = 3.09, and the impact of selection on unobservable traits is to reduce \( {y}_d^{\prime }=5.11 \) by 3.09, so that \( {y}_d^{\prime \prime }=2.02 \) (or 1% above 2). Thus, developing country natives with a bachelor’s degree (or more) who migrate to the USA would be expected to earn on average about twice the real income they earned in their country of origin.^{Footnote 17}
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Schiff, M. Ability drain: size, impact, and comparison with brain drain under alternative immigration policies. J Popul Econ 30, 1337–1354 (2017). https://doi.org/10.1007/s0014801706441
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Keywords
 Migration
 Points system
 Vetting system
 Ability drain
 Brain drain
 Brain gain
JEL code
 F22
 J24
 J61
 O15