High-Skilled Migration and Global Innovation

Transcription

1 High-Skilled Migration and Global Innovation Rui Xu August 5, 205 Preliminary Abstract This paper evaluates the net impact of high-skilled migration on global technological progress and welfare in the US and in the source countries. I construct a multi-country endogenous growth model where the US has a comparative advantage in doing innovative research over the source countries. As a result, increasing the number of immigrants can enhance global innovation and indirectly benefit origin countries through knowledge diffusion. I quantify the model using micro and macro moments and perform counterfactual analysis to estimate the net impact of skilled migration. My results suggest that high-skilled migration can improve productivity growth and welfare in both the US and source countries like India. (JEL: F22, J24, O30, O40) Keywords: High-Skilled Migration, Innovation, Imitation, Heterogeneous Agents, Endogenous Growth, International Knowledge Diffusion, Consumption-Equivalent Welfare ruix@stanford.edu. Mailing Address: Stanford University, Department of Economics, 579 Serra Mall, Stanford, CA The paper has benefited from advice from Pete Klenow, Chad Jones, Pablo Kurlat, Bob Hall, Chris Tonetti, Melanie Morten, Caroline Hoxby, Petra Persson, Kalina Manova, Martí Mestieri, Ran Abramitzky, Andres Pablo Drenik and other seminar participants at Stanford.

2 Introduction High-skilled immigrants contribute significantly to innovation and entrepreneurship in the US. They account for roughly a quarter of the US workers in Science and Engineering (S&E) occupations and have a similar contribution in terms of output measures like patents (Kerr (2008a)) or firm starts (Wadhwa et al. (2007)). The quantity and quality of immigrants have been rapidly growing over the last three decades thanks to the establishment of certain visas permitting the entry of high-skilled workers. Immigrants from developing countries, especially those from India and China, benefited most from temporary work visas and over time they made up the majority of high-skilled immigrants in the US (Kerr (203)). Their welfare improved substantially due to the large wage premium in the US (Clemens (200), Clemens (20)). Nevertheless, how immigrants affect native workers in the US and remaining workers in source countries is still under debate. For the US, the literature has not agreed on whether immigration has a significant adverse impact on the earnings of native-born workers 2.Forsourcecountries,recent literature shows that remittances, the network externalities of diaspora, increased incentives to invest in human capital, and induced trade and FDI may compensate the sending countries for their loss of human capital 3,buttheneteffectremainstobequantifiedmorerigorouslyina general equilibrium framework 4. These include temporary work visas, such as the H-B specialty occupation visas and the L- intra-company transferees visas for managers and specialty workers, and certain classes of employment-based green cards. 2 For example, Borjas (2003) and Aydemir and Borjas (2007) assumed perfect substitution between immigrants and native workers of similar education background and experience, and estimated a 3 to 4 percent drop in the wage of native workers as a result of a 0 percent increase in the supply of immigrants. The perfect substitution assumption was later substantiated in Borjas et al. (20) using data from US decennial Censuses and American Community Survey. The same adverse effect on high-skilled native workers was identified in Borjas (2005) by studying immigration-induced shifts in the supply of students entering particular doctoral fields at particular times. On the other hand, Ottaviano and Peri (202) found evidence of imperfect substitution between similarly skilled immigrants and natives in the United States, estimating an elasticity of substitution of around 20. Highlyeducated native and foreign-born workers are also shown to be imperfect substitutes in Peri and Sparber (200) since native-workers with graduate degrees respond to an increased presence of highly-educated foreign-born workers by choosing new occupations with different skill content. With the recent availability of administrative data, empirical studies are able to achieve better identification by exploiting the exogenous variation in H-B visa lotteries. Doran et al. (205) compared winning and losing firms in 2006 and 2007 H-B visa lotteries and found evidence that additional H-Bs lead to lower average wages, whereas Peri et al. (205) exploited random H-B variation across U.S. cities and found evidence to support complementarity between native and foreignborn H-B computer workers. Kerr et al. (203) used matched employer-employee data and found rising overall employment of skilled workers with increased immigrant employment, where younger natives experience more employment expansion than their older counterparts. 3 Papers that discuss each channel include: Rapoport and Docquier (2005) and Bollard et al. (20) on remittances, Kerr (2008b), Nanda and Khanna (200) and Agrawal et al. (20) on the network externalities of diaspora, Mountford (997), Beine et al. (200) and Beine et al. (20) on increased incentives to invest in human capital, and Gould (994), Rauch and Trindade (2002), Aleksynska and Peri (202) and Ortega and Peri (203) on induced trade and FDI. For a review of the literature on brain drain, see Docquier and Rapoport (202). 4 Docquier and Rapoport (2009) was the only paper (that I know of) that brought together various channels of costs and benefits of brain drain and quantified its net effects. The simple partial equilibrium model they adopted is stylized and simple to implement, but it fails to consider general-equilibrium effects and dynamic responses of the economy. 2

3 The objective of this paper is to evaluate the net impact of skilled migration on global innovation and on welfare, both in the US and in non-oecd source countries. To quantify the effects, I propose a multi-country endogenous growth model that enriches the standard quality ladder model (Aghion and Howitt (992)) by introducing heterogeneity in agent s research talent 5 and cross-country knowledge diffusion 6.Ifocusmyattentiononimmigrantsfromdevelopingcountries for three reasons. First, they account for the majority of innovative activities conducted by immigrants. In terms of research input, more than 80% of foreign-born S&E workers come from non-oecd countries according to the American Community Survey in In terms of research output, 60%oftheimmigrantinventorsintheUS 7 are nationals of non-oecd countries. Second, the US is much more productive in conducting scientific research than countries with low income per capita, but not productive more than those with high income per capita (Kahn and MacGarvie (Forthcoming)). Therefore, allowing skilled immigrants from developing countries can improve talent allocation and increase total innovation. Last but not the least, less developed countries are more prone to brain drain (as documented by Docquier and Rapoport (202)) and the possibility of widening the existing income gap signifies the need to carefully evaluate the net effect. This paper builds on and contributes to several strands of literature. The major contribution is the introduction and quantification of a new brain gain channel for source countries. The mechanism can be best illustrated with a system of three countries: the US as a host for skilled immigrants, and India and China as origin countries. Skilled immigrants contribute to frontier knowledge creation in the US 8, which can later diffuse to India and China and enhance long-run growth. This frontier growth effect has been overlooked in previous studies for two reasons. First, it is empirically difficult to estimate the growth effect because the counterfactual scenario (i.e. a world without migration) is rarely observed. Second, if we only consider the shortrun interaction between India and the US, one may argue that the frontier innovation will 5 Previous theoretical work, including Lucas (988), Jaimovich and Rebelo (202) and Grossman and Helpman (204), also introduced heterogeneous labor to endogenous growth models. 6 Similar to Barro and i Martin (997), the world growth rate is driven by discoveries in the technologically leading economies like the US. Followers learn from the leaders and converge toward the leaders because imitation is cheaper than innovation over some range. Followers will not catch-up to the technology frontier as they would optimally choose to fall-back to take advantage of easier imitation, as is in Benhabib et al. (204). 7 The statistics cited here are based on a new database mapping migratory patterns of inventors (Miguelez and Fink (203)), which are extracted from information included in patent applications filed under the Patent Cooperation Treaty. Note that immigrants here refers to US residents who are foreign nationals, which is a subset of foreign-born immigrant inventors. 8 See Hunt and Gauthier-Loiselle (200), Kerr (2008a), Kerr (203), Peri et al. (203), Moser et al. (204) and Kahn and MacGarvie (Forthcoming). 3

4 typically be of second-order importance for growth in poor countries (Agrawal et al. (20)). In this paper, I capture the frontier growth effect by constructing an endogenous growth model with knowledge diffusion to both India and China. The net impact of migration is quantified by comparing the baseline model to a counterfactual environment. How much the frontier innovation matters for growth in India or China would be a quantitative question. Based on my results, frontier growth is of first-order importance to welfare in India. There are two explanations for why frontier growth matters in my model. First, there is positive externality of Chinese immigrants on India, because India can learn from knowledge created by Chinese diaspora in the US. In a two-country model with only India and the US, the benefit of having immigrants from Chinese cannot be captured. Second, even if we ignore the positive externality, the long-run effects of frontier innovation can be much larger than the short-run effects because knowledge diffusion takes time (Comin and Hobjin (200); Comin and Mestieri (200)). In terms of quantitative analysis, this paper takes advantage of the rich empirical literature on migration and quantified the model with existing findings. Parameters in the baseline model are disciplined by key micro and macro moments, such as immigrant s wage premium, elasticity of substitution between immigrant and native workers (Borjas et al. (20) and Ottaviano and Peri (202)), share of S&E workers in the US and in India (Ruggles et al. (200)), India s technology level relative to the US, and growth rates of total factor productivity in the US and in India (Feenstra et al. (forthcoming)). Counterfactual analyses are then conducted to provide estimates for the impact on growth and welfare, which is difficult, if not impossible, to obtain from empirical studies. Another contribution of the paper is to solve for the transition dynamics in emerging economies. In my model with one technological leader and multiple countries, each follower economy will go through transitions when parameters change or workers move. Take India for instance. The growth rate of the Indian economy has been well above that of the US since 990. To correctly evaluate welfare changes for India, it is necessary to take the transition paths into consideration. My main quantitative results in the paper compare the baseline environment with a counterfactual scenario where the stock of skilled immigrants 9 in the US from each source economy 9 As you will see later in the model quantification, probability of migrating to the US from each country is usually smaller than 0.5. When we double the stock of immigrants, we double the migration probability instead of lowering the selection criteria. 4

5 is doubled. I choose India as a representative for the source countries in the quantitative analysis as it is the top origin for foreign-born S&E workers. My quantitative results suggest that long-run TFP growth in the US would rise to.5% if we double the skilled immigrant population,. Aggregate consumption-equivalent welfare for US native workers would increase 3.9% compared to the baseline environment, but workers with different skill levels are affected differentially: lower-skilled workers would experience a welfare gain of 4.23%, whereas high-skilled workers welfare would decrease by 3.37%. The marginal skilled native workers would be replaced by immigrants and their welfare changes would range from -3.37% to 4.23 depending on skill levels. For India, the largest origin of skilled workers in the US, aggregate welfare (including Indian diaspora in the US) would be.25% higher 0 in the counterfactual environment. More specifically, remaining low-skilled workers welfare would increase by.07%, high-skilled workers would gain by 3.89%, and new emigrants welfare would increase by more than 00%. Note that the increase in welfare of Indian workers in the counterfactual environment partly comes from the positive externality of increased migration from other countries. To disentangle the bilateral brain drain effect from the externality effect (i.e. China s brain drain will be India s brain gain), I compare the baseline model with two other counterfactual scenarios: sending all skilled immigrants in the US back to their home countries, or sending only Indian immigrants back to India. The difference between the two counterfactual scenarios will indicate the size of the externality. The quantitative results suggest that, even for large origins like India, the externality channel is an order of magnitude more important than the bilateral brain drain channel. The rest of the paper proceeds as follows. In Section 2, I lay out the model. In Section 3, IdocumentthemicrofactsofskilledimmigrantsintheUSandlabormarketcompositioninthe US and in India. In Section 4, Iparametrizethemodelandconductcounterfactualanalysis to quantify the growth and welfare impact of immigrants on the US and India. In Section 5, I test robustness of the baseline model to alternative assumptions and parameter values. Section 6 concludes. 2 Theoretical Framework 0 The aggregate welfare gain for remaining workers in India would be.%, which is smaller because large welfare gains of migrants are not considered. 5

6 2. The Basic Model without Migration Consider a world economy with +M countries, and they grow endogenously through creating frontier knowledge or learning from the frontier. Assume only one country (referred to as the US henceforth) has access to the technology frontier and the other M countries (referred to as non-oecd countries henceforward) learn from the frontier and try to catch up. The innovation process follows the standard quality ladder model (Aghion and Howitt (992)), but with an additional technology diffusion term from the US to non-oecd countries. In addition to their innovation capability, countries also differ in their ability to enforce intellectual property rights, which is reflected by a flow cost to keep out imitators in the model. The detailed construction of the general equilibrium model without migration is presented below. To simplify notation, I omit country subscripts whenever possible. 2.. Demand and supply for consumption goods An economy is populated by a mass L of individuals (no population growth) indexed by their talent in doing research. Agent s innate talent of doing research is randomly drawn from a Pareto distribution whose cumulative density function is.eachindividualmaximizes her present discounted utility U(, t) = ˆ t e ( t) c(, ) d where c(, ) is consumption of agent with talent at time t in terms of consumption goods. Inasmuch as talent varies across individuals, so does income and consumption. The consumption good serves as numeraire and its price at every moment is normalized to one. It follows from the individual s intertemporal optimization problem that ċ(, t) c(, t) = (r(t) ) () where r(t) is the interest rate at time t in terms of consumption goods. The consumption goods are produced under perfect competition by labor and a continuum > is the shape parameter of the Pareto distribution, and is assumed to be the same across countries. The scale parameter is normalized to. 6

7 of intermediate products of measure according to the production function Y (t) = ˆ 0 A(i, t)x(i, t) di L Y (t) (2) where A(i, t) and x(i, t) are the quality and quantity of intermediate good i. L Y (t) is the amount of labor used in consumption goods production. Wage for workers and price for intermediate goods are given by the marginal product w Y (t) = ( ) ˆ 0 A(i, t)x(i, t) di L Y (t) x(i, t) = ( A(i, t)/p(i, t)) (3) 2..2 Supply, pricing, and profits of intermediate goods There are mass one of varieties in the intermediate goods market. In equilibrium, each intermediate good is only produced by one monopolistically-competitive firm, until an improved version is invented. Marginal cost of producing intermediate goods is proportional to the quality. Each intermediate good producer chooses unconstrained monopolistic price 2 to maximize profit max (i, t) = p(i, t)x(i, t) A(i, t)x(i, t) (4) p(i,t) where x(i, t) is the demand for intermediate good i given p(i, t) and A(i, t) is the marginal cost. Normalize = and substitute in 3, one can get the profit maximizing price for each intermediate good to be simply A(i, t). Profitofeachintermediategoodproducerisproportional to the quality A(i, t) and labor used in producing consumption goods The R&D Processes Endogenous growth comes from creative destruction and quality upgrades result from R&D efforts by new intermediate firms. Guided by the empirical fact that OECD countries file the vast majority of patents in the trilateral co-operation, i.e. the European Patent Office (EPO), the Japan Patent Office (JPO), and the United States Patent and Trademark Office (USPTO), 2 I rationalize unconstrained monopolistic pricing (instead of limit pricing) by introducing an infinitely small overhead cost to produce each period. Once an improved version of a product is invented, the incumbent won t pay the overhead cost to produce in equilibrium as the new entrant can always threat to charge a low enough price to take over the whole market. 7

8 I assume only the US (as a representative of OECD countries in the model) can forward the world technology frontier through creative destruction and the other M countries try to catch up to the frontier. To emphasize on the role of human capital, I abstract away from capital input and assume labor to be the only input in the R&D process, as well as in production. In the US, unit of research talent generates a flow rate us of success for inventing a new machine of quality A us (i, t) for some variety i 3.Aggregatingallresearchtalent,thePoisson arrival rate of innovation in each variety is z us (i, t) = us H us,r (i, t), where us is a parameter indicating the productivity of innovative research, and H us,r (i, t) is the amount of research talent devoted to R&D in each variety 4. A researcher is paid the value of her inventions, which is proportional to her research talent. Workersinfinalgoodsproductionarepaidaflatratew Y regardless of their research talent. Each agent will compare the payoff from being a researcher to the flat wage w Y and decide which occupation to choose. In equilibrium, those with talent higher than some threshold us will be researchers, and the total amount of research talent utilized in the US can be expressed as the integral of talent for all researchers: H us,r (t) = ˆ us f( )d L us Define average technology level as A(t) 0 A(i, t)di, and then we can write the law of motion for the technology frontier as A us (t) = = ˆ 0 ˆ 0 A us (i, t)di ( )z us (i, t)a us (i, t)di ˆ = ( ) us f( )d L us A us (t) (5) us In the model, innovation in the US is not affected follower economies, and hence we can solve for its competitive equilibrium as if it were a stand-alone economy. As in most endogenous growth models, the US is always on the balanced growth path, and its growth determines the long-run growth in all countries. From the law of motion in (5), we can derive the steady state growth rate as g ss Ȧus A us =( ) us f( )d L us, where A us (t) is the technology frontier defined us as the average quality of machines in the US: A us (t) = 0 A us(i, t)di. 3 The standard assumption of undirected research is made here. 4 H us,r (i, t) is the same across varieties because of symmetry. 8

9 In a follower economy m 2 {, 2,...,M}, unit of research talent generates a flow rate Aus(t) A m(t) m of success for reverse engineering a machine of quality A m (i, t) for some A m(t) variety i. Note that the learning process differs from the innovation process in that country m s research efficiency depends on its distance to the frontier 5. The Poisson arrival rate of new machines in each variety is z m (i, t) = Aus(t) A m(t) m H m,r (i, t), where m is a parameter A m(t) indicating the country-specific efficiency of imitative research, and H m,r (i, t) = f( )d L m m is the amount of research talent devoted to R&D in each variety. Long-term growth in all follower economies is exogenously determined by innovation in the US, which equals to g ss in steady state. Nevertheless, technology levels relative to the frontier will be different across countries depending on their research efficiency m : g ss = A m (t) A m (t) =( ) a ss m = 2..4 Free entry condition ˆ ) Aus (t) A m (t) m f( )d L m A m (t) ( ) m H ss m,r ( ) m H ss m,r + gss (6) Each intermediate firm can make flow profits 6 until it is replaced by an entrant with better quality. In steady state, the value of each intermediate firm can be written as m V (i, t) = (i, t) z ss + r ss (7) where z ss is the arrival rate of quality upgrades in each variety and r ss is the steady state real interest rate. Free entry condition for intermediate firms requires the expected value of new inventions net of patent enforcement cost to be the same as the cost of innovation, i.e. w R,us (t) = E ( us V us (i, t)) w R,m (t) = E ( m V m (i, t)) ( apple m ) (8) where w R (t) is the payoff for each unit of research talent, and apple m is the cost to enforce the patent. You may think of apple m taking the form of lobbying, bribery or other frictions that reduce 5 Note that the catch-up function for technology diffusion takes the form of confined exponential as in Nelson and Phelps (966), where knowledge diffusion is faster when the follower economy is further behind the frontier. 6 Aus(t) A Note that the newly invented variety has quality A us(i, t) in the US and quality m(t) A! Am(i, t) m(t) in country m. 9

10 firm s incentive to conduct research in developing countries. Note that the country subscript suggests that the enforcement cost is country-specific and is normalized to zero in the US Determining talent cutoff Agents with research talent above will choose to be researchers as they can earn higher salary. The talent cutoff can be derived from the marginal agent, who is indifferent between being a worker and being a researcher: w Y (t) = w R (t) (9) where w Y (t) is the flat wage rate for workers specified in (3) and w R (t) is the wage rate for each unit of research talent as in (8) Equilibrium and balanced growth path An equilibrium can be represented as time paths of [c(, t), Y(t), g(t), A(t), (t)] t=0, such that (), (2), (5), (6), (9) are satisfied in each country; [p(i, t), x(i, t)] t=0,suchthat(3)issatisfiedand(4)isoptimizedineachcountry; [r(t), w Y (t), w R (t)] t=0 such that (), (3), (7), (8) and (9) hold in each country; Goods market clears: Y (t) = c(, t)f( )d Labor market clears: L(t) =L Y (t)+l R (t) in each country. A balanced growth path (BGP) is an equilibrium path where Y (t), c(, t) and A(t) grow at a constant rate. Such an equilibrium can alternatively be referred to as a steady state since it is a steady state in detrended variables. On the balanced growth path, talent cutoff and real interest rate r are constant and consumption c(, t) grows at a constant rate g ss = ( ) us H R,us L us. 0

11 2..7 Steady State Comparative Statics The key variable for a balanced growth path is the talent cutoff in each country. The steady state allocation can be solved analytically, but may not have an explicit solution depending on the Pareto shape parameter. Instead of presenting the implicit solutions for,iperform the following comparative statics analysis 7. For the US, higher research efficiency us leads to lower talent cutoff us, which means more people doing research and faster steady state growth. Similarly, bigger step size of quality improvement yields higher growth rate. Talent distribution also matters for labor allocation and growth rate. As talent distribution gets more dispersed (lower ), the Pareto tail becomes denser, which will lead to more people doing research and higher growth rate. For a follower economy m, therearetwokeyparameters:researchefficiency m and patent enforcement cost apple m. m only affects the relative technology level a ss m in steady state. 8. The patent enforcement cost apple m governs the distortion on research efforts and hence pins down the talent cutoff m in steady state. As the enforcement becomes more costly, i.e. apple m increases, talent cutoff will be higher, leading to fewer researchers and lower relative technology level. 2.2 Introduce High-Skilled Migration Here we introduce high-skilled migration from non-oecd countries to the US in the model. Based on the model and macroeconomic data (Feenstra et al. (forthcoming)), production technology is more advanced in the US than in non-oecd countries. As a result, wages in the US are higher and everyone in developing countries would want to migrate to the US in a frictionless world. In reality, migration to the US is highly controlled and sometimes selected. For the purpose of this paper, I will restrict my attention to high-skilled migration Assumptions In the baseline model, I make three assumptions about the migration process. First, I abstract away from any cost associated with migration and consider a simple probabilistic migration process: people with talent above a country-specific cutoff m can migrate to the US with a 7 The detailed derivations are included in Appendix A 8 The steady state talent cutoff m does not vary with m. This can be easily shown by combining (6) and (9) 9 Low-skilled migration is definitely an interesting and equally important topic, but it is beyond the scope of this paper.

12 country specific probability p 20 m.valuesfor m and p m of each source country will be estimated with information on immigrants income in Section 3. Second, immigrants will take up the same research efficiency us as native researchers after they migrate to the US. This assumption can be partly justified by the fact that many of them received their highest degrees in the US based on the National Survey of College Graduates. Lastly I assume immigrant researchers are perfect substitutes for native researchers. As I mentioned in Introduction, there is a large literature on the substitutability between immigrants and native-born workers. For the purpose of my analysis, I do not take a stand on that issue. To test if the baseline results are robust to the assumption of perfect substitution, I will resolve the model with imperfect substitution as a robustness check in Section 5. Note that the model would predict no return migration as wages are higher in the US New arrival rates of ideas After introducing migration from non-oecd countries to the US, talent distribution will change in all countries, which affects the expression for arrival rates of ideas. In the US, skilled immigrants will lead to a discontinuous jump in the density of talent in the right tail. This change in talent distribution is analogous to a smaller in the comparative statics, and so the arrival rate of ideas will increase and the endogenous talent cutoff for researchers will rise. In a non-oecd country m, the loss of talent will reduce the idea arrival rate and lower the talent cutoff. Mathematically, the new arrival rate of ideas for the US and country m can be rewritten as follows. ˆ z us = us f( )d L us + X ˆ! p m f( )d L m us m m z m (t) = m f( )d L m m (t) ˆ p m ˆ max{ m (t), m} f( )d L m! (0) () 20 The country-specific selection reflects the empirical fact that origins differ in their socio-economic status and US immigration policy towards them. 2 Empirically, return rates among skilled professionals tend to increase with home country skill prices and growth prospects. Because of the high skill premium in the US, skilled immigrants from non-oecd countries rarely go back and the return migrant flow is composed of the least skilled immigrants (Borjas and Bratsberg (996)). The high stay rate is especially true for foreign doctorate recipients in the US based on a study by Finn (204). Among all doctorates, 65% of them remain in the US 0 years after they graduated. The stay rates are highest (more than 80%) among doctorates from China and India. 2

13 where us and m(t) 22 are the new talent cutoffs after migration, and m is the talent cutoff for migrants from country m Effects of high-skilled migration After adding high-skilled migration to the general equilibrium framework, the model captures key benefits and costs of high-skilled migration for the US and source countries. Taken to the data, the calibrated model can be used to perform counterfactual analysis and provide quantitative estimates of the net effects. A major benefit of skilled migration is the faster growth of frontier knowledge. This frontier growth effects have been ignored in the literature due to the absence of a general equilibrium framework. A key contribution of this paper is to introduce and quantify of this new channel of brain gain. Skilled migration leads to more innovation because migrants would not have been able to contribute to world technology frontier had they not migrated. As the technology frontier grows faster, non-oecd countries can benefit from it through knowledge diffusion. This frontier growth effect can be small if we only consider one source country in the model (Agrawal et al. (20)). However, once we include multiple source countries in the framework, immigrants from one origin can push up the frontier and benefit research in other source countries through knowledge diffusion. This positive externality aggregated across all source countries will make the frontier growth effect quantitatively important. The presence of externality also suggests that the socially optimal migration rate could be higher than the observed level, which has important implications on countries migration policies. Migration of skilled workers can also encourage research activities in both the US and the source countries. In the US, immigrant researchers earn higher wages than native researchers 23, indicating that they are more talented on average. Since immigrants and native-born researchers are assumed to be perfect substitutes, some marginal native researchers will be displaced by more talented immigrants. Both the quality and quantity of the researcher pool will improve in the US. For source countries like India, the observed low research intensity indicates a high cost to enforce patent or other frictions on R&D investment 24. Those frictions make the allocation of research 22 Note that us and z us are not functions of time, because the US, as the leading economy, is always on the balanced growth path. On the other hand, m (t) and zm(t) depend on where they are on the transition path. 23 This is based on a simple analysis of earnings by S&E workers in the American Community Survey. The details are discussed in Section Examples for other frictions include high entry cost, fixed cost and financial constraint. 3

14 talent less efficient than in the competitive equilibrium 25. Skilled migration may improve the talent allocation by encouraging talented agents, who would not have been researchers in their home countries due to frictions, to become researchers in the US. My quantitative results show that the talent cutoffs in the US and in India converge with more skilled migration, suggesting an improvement in the allocation of research talent. Despite the potential benefit mentioned above, skilled migration may have negative impact on the US and the source countries. In the US, immigrants may reduce the wage of researchers and crowd out marginal native researchers. Source countries may suffer from lower technology adoption rates due to the direct brain drain effect. Whether the cost of migration outweighs the benefit is an important question to be answered with a quantified model and counterfactual analysis in Section Transition paths As discussed in research processes, the US is always on the balanced growth path. However, that is not the case for non-oecd countries as follower economies. Because of knowledge diffusion from the US, they will go through transitions as long as they are growing at a different rate than the US. According to the latest Penn World Table (Feenstra et al. (forthcoming)), most non-oecd countries have been growing at a faster rate than the US in the past two decades, suggesting that they are in a transition phase. To match this important observation, I solve for transition paths of source countries and incorporate them in the welfare analysis. IfollowtheiterativeprocedureinLee(2005)tocalculatetherationalexpectationsequilibrium during transition 26. The idea is to start from a constant talent cutoff and update it until the talent cutoff sequence on the transition path converges. In the first iteration, we solve the talent cutoff at period t assuming that future talent cutoffs will be the same as current ones, n o T from which we get a sequence of talent cutoffs E () = () m,t 27. Notice that E () is an equilibrium but it is not a rational expectations equilibrium because () m,t is not constant over time as was assumed in solving for the cutoff at time t. The rational expectations equilibrium, E = m,t T t= Therefore, finding E =, is one that is consistent with people s expectations of future talent cutoffs. m,t T t= t= is equivalent to finding the fixed point talent cutoff sequence 25 As I will show in one of the robustness checks, the competitive equilibrium is not socially optimal either. 26 The model is discretized to calculate the transition paths. 27 Note that we don t know ex ante how long it takes for the source country to converge to its new steady state, and so we need to choose a T that s large enough. 4

15 in the model. After obtaining the first iteration equilibrium, E (),wegototheseconditerationandassume the ratio of talent cutoff series is the one obtained from the first iteration: (2) m,t+ (2) m,t = () m,t+ () m,t, 8t (2) This assumed relationship yields a sequence of talent cutoffs that can be written solely in terms of (2) m, and we can solve for the equilibrium level of (2) m,. Similarly (2) m,2 can be calculated by writing all talent cutoffs from t =2on as a function of (2) m,2 and we can solve for the equilibrium level of (2) m,2. Repeat this procedure to the final period T and we get a sequence of talent n o T cutoffs that clears the labor market in each period, denoted by E (2) = (2) m,t. Compare E (2) with E (),ifthedistancebetweenthetwoiterationsisnotcloseenough,theassumptionin (2) would be hold and we continue on to the third iteration. This process is continued to get t= iterations of the talent cutoff sequences until a sequence E (n) is close enough to E (n ) under some criterion 28. The converged talent cutoff sequence E (n) would be the rational expectations equilibrium where people s expectation about future replacement rate (as a function of talent cutoffs) is realized as the equilibrium replacement rate Welfare analysis As in Lucas (987), I use consumption-equivalent welfare changes to evaluate the effect of highskilled migration on different agents in the US and in source countries. Use! to denote welfare changes. Specifically,! us ( ) and! m ( ) represent individual welfare changes in the US and in origin m;! us and! m represent aggregate welfare changes in the US and in origin m. The welfare gains (or losses) can be solved from the following equations. X t=0 X t=0 t t ( +!us( )) c old us,t( ) ( +! m( )) c old m,t( ) = = X t=0 X t=0 t cnew us,t( ) t cnew m,t ( ) (3) (4) X t=0 ˆ t ( +!us) c old us,t( ) f( )d = X t=0 ˆ t c new us,t( ) f( )d (5) 28 The convergence criterion used here is: E (n) E (n ) < 0 6 5

16 X t=0 ˆ t ( +!m) c old m,t( ) f( )d = X t=0 ˆ t c new m,t ( ) f( )d (6) where = + is the discrete-time discount factor29. 3 Micro Facts In this section, I analyze national survey data in the US and in India to obtain key micro moments to quantify the model. The moments of interest include ) the Pareto shape parameter in the distribution of research talent; 2) immigrant s talent relative to native researchers in the US; 3) probability of migration; 4) research intensity in the US; and 5) research intensity in India. 3. Skilled Labor Market in the US 3.. Data My main data source for the US is the IPUMS micro-data of the American Community Surveys (ACS) in (Ruggles et al. (200)) 30. Following Hunt (forthcoming), I adopt a more restrictive definition of employment by only including respondents aged who are fulltime workers 3. I define S&E workers as people who work in broadly defined Science and Engineering (S&E) occupations with bachelor s degrees in Science and Engineering fields 32. They can be labeled as researchers in the model, as most innovative activities in the US are conducted by S&E workers. The ACS suits basic need of my quantitative analysis as the sample is large enough to allow a focus on S&E workers and distinctions by immigrant origin 33. For robustness checks that require additional information such as education, I will use the National Survey of College Graduates (NSCG) The model is discretized for both the US and the source country m to ensure comparability of welfare changes 30 The weighted three-year sample is used to have a large enough sample. 3 Respondents who worked for more than 30 hours per week for wage last year are classified as full-time workers. Those currently enrolled and those who worked for less than 48 weeks are dropped from employment. Self-employed workers are included. 32 The lists of S&E occupations and S&E fields are included in Appendix B. 33 Note that I define immigrants as those born abroad, except those born in US territories and born abroad as US citizens. 34 The National Survey of College Graduates ( isalongitudinal biennial survey conducted since the 970s that provides data on the nation s college graduates, with particular focus on those in the science and engineering workforce. The public-use micro data contains useful information on respondent s education history, entry visa type and patenting activities that is unavailable elsewhere. 6

17 3..2 Immigrant researchers from non-oecd countries Using my definition of S&E workers, 7.8% of employment in the US works as researchers. Among the sample of S&E workers, 22% are immigrants from non-oecd countries and 5% are born in OECD countries. To focus on immigrants from non-oecd countries, I treat the 5% researchers from advanced economies as native-born researchers in the US. ACS has detailed information on income, which can be used to imply the research talent of immigrants compared to native researchers in the US. First, I compare immigrants from non-oecd countries with those from OECD countries and native-born researchers with the following least squares log wage regression: log w i = + I F i + 2 I OECD i + 3 I T i + 4 A i + t + i where w i represents the hourly wage of worker i; I F i dummy for immigrants from OECD countries; I T i is a dummy for the foreign-born; I OECD i is a is a dummy for workers born in US territories; A represents polynomials of age; and t captures time fixed effect. I did not control for other observable characteristics such as education and occupation, as they reflect worker s talent which is what I intend to capture with the foreign-born dummies. Age is controlled because experience may affect wages and it s arguably orthogonal to worker s inherent talent. The coefficient of interest is, which measures the average wage premium for immigrants from non- OECD countries. Based on the simple least squares analysis (Column, Table ), immigrant researchers from non-oecd countries earn 5.4% higher wages than native researchers Immigrants by country of origin The selection of immigrants, namely m and p m in the model, vary by origins due to different migration cost, visa and green card quotas, etc. To correctly quantify the effects of migration using equation (0), we need to estimate the selection criterion m and the migration probability p m for each country 36. I use least squares log wage regressions to estimate country-specific Note that using the wage premium to proxy for talent uremia may lead to downward biases because immigrants (especially new immigrants) may be paid less than native counterparts with the same talent (Doran et al. (205), Bartolucci (204)). However, it is hard to correct for the bias empirically due to unobserved characteristics and selection in the census data. Therefore, I do not correct for this potential bias for now. 36 Using the wage premium of immigrants from all non-oecd countries estimated above will under-estimate the total research talent of immigrants based on Jensen s inequality. 37 We group some countries, such as Central American Countries and Countries in West Indies, to get reasonable sample sizes 7

18 Table : Regression Results for Wage Differentials Variables () (2) (3) log(hourly wage) I F i 0.054*** 0.040*** *** ( ) ( ) ( ) I OECD i *** *** *** (0.000) (0.000) (0.000) Ii T X X X Year FE X X X Age, Age 2 X X X Degree FE X X Degree field FE X Observations 6,698,350 6,698,350 6,698,350 Robust standard errors in parentheses *** p<0.0, ** p<0.05, * p<0. wage premium: log w i = + I i + 2 A i + t + i (7) where I i are dummy variables for all origin countries/areas. The coefficients ˆ give us a vector of estimated wage-premia for all origins, from which we can derive the selection criterion for immigrants from each origin: m = + ˆ,m us (8) where us is the endogenous talent cutoff in the US. Using m and the number of immigrant researchers from each origin, we can back out the migration probability p m as p m = L m us,r L m m f( )d (9) 8

19 Figure : Wage Premium by Origin Note: CAm refers to Central American Countries, SAm refers to South American Countries and WInd refers to West Indies Countries. where L m us,r is the number of immigrant researchers from country m in the US and L m is the size of labor force in country m. The estimates for ˆ of the top 0 origins are plotted in Figure Immigrants from India In my main quantitative results, I will choose India as a representative source country to perform counterfactual analysis. To explain my choice of India and to provide the context for the quantitative results, I present a few facts about Indian immigrants in the US. First, India is the top origin of foreign-born S&E workers in the US. In my ACS sample, Indian immigrants make up 7.2% of all S&E workers in the US. In addition to supplying skilled workers to the US labor market, immigrants from India also create jobs for skilled workers in the US as founders of technology firms. According to Wadhwa et al. (2007), 6.5% of the new technology firms founded during have at least one Indian immigrants as key founders. In terms of research output in the US, Indian ethnic researchers account for more than 5% of domestic patent applications every year in the US since 2000 (Kerr (2008a)). It is evident that Indian immigrants play an important role in US innovation, but all their contribution may 9

20 Figure 2: Share of US S&E Workers from India come at a cost to India. Whether the brain drain effects will dominate is not only an intellectual curiosity, but also a concern of the Indian government. Second, the rise of high-skilled immigrants from India is a recent phenomenon thanks to the establishment of the H-B visa in Since then, the share of S&E workers 39 from India has increased from about one percent to more than six percent in recent years (see Figure 3). During the same period, share of labor force working in S&E occupations has also being increasing steadily, partly due to the increasing number of high-skilled immigrants (Kerr and Lincoln (200)). The (changing) share of S&E workers from India and the share of workers in S&E occupations are key moments to match in the quantitative analysis. Third, Indian immigrant researchers earn higher unconditional hourly wage than their native counterparts as indicated by the kernel density plot (Figure 4). Assuming all talent is transferable and immigrants can pick up the US research efficiency us immediately after migration, the observed wage premium can proxy the inherent talent selection as shown in equation (8). However, the estimated ind obtained from the observed wage premium may be biased downward if the two assumptions do not hold. In fact, previous literature suggests some skills are country-specific due to cultural and language barriers. and some immigrants may not be able 38 H-B visas were introduced by the Immigration Act of Note that S&E workers are defined as people working in S&E occupations (not including S&E related occupations). This definition is slightly different from S&E workers in the main specification above. We cannot use the definition from main specification because the Current Population Survey data do not have information on fields of bachelor s degree. The figures here just indicate the trend. 20

21 Figure 3: Kernel Density of Hourly Wage to enjoy the higher research efficiency in the US if part of us comes from better university education in the US. To test the two assumptions empirically or to estimate the size of bias empirically is extremely challenging. In one of the robustness checks, I will consider a polar case where all immigrants above a certain threshold migrated to the US and try to bound the impact of migration on India. 3.2 Skilled Labor Market in India 3.2. Data The micro-data of current labor market in India come from the 66th Round of the National Sample Survey (NSS) in Historical data on employment in India are also available in the IPUMS-International micro-data (Ruggles et al. (200)), which is used to get an idea of the trend in research intensity S&E workers in India I cleaned the data following the same procedure as I did for the ACS. S&E workers are defined as college graduates working in S&E occupations 4 and they account for.56% of total employment in India in Low as it may seem, the share of researchers has actually been increasing since 40 The data are provided by Pete Klenow through the NBER server. 4 Note that I did not require college degrees in S&E fields because that information is not available in NSS. 2

22 Figure 4: Share of S&E Workers in India 983 from less than 0.7% to.56% in 2009 (Figure 4). The increase is an interesting observation and may be related to the liberalization starting in 99 in India. Given that the focus of the paper is on skilled migration, I will not try to explain the increasing trend. Instead, I will only match the share of researchers in 2009 and assume no policy changes after that in the quantitative analysis. 4 Quantitative Results To evaluate the impact of migration on growth and welfare, I quantify the baseline model by matching key micro and macro moments, and conduct counterfactual analysis. I consider three counterfactual scenarios. The main one is to double the observed stock of immigrants in the US from each non-oecd country. In the other two scenarios, I send either all immigrants back their home countries, or only Indian immigrants back to India. The last two scenarios are necessary if we want to disentangle the direct effect of emigration from the positive externality effects. 4. Calibration First, I externally calibrate some of the parameters involving common quantities from the macroeconomics literature. Table 2 reports the values of these parameters. After that, I cal- 22

23 Table 2: Outside Calibration of Common Parameters Parameter Explanation Source, Value Capital share NIPA, /3 Discount rate Annual interest rate 4%, 0.02 CRRA Hall (2009), 2.0 L us US employment Normalization, Table 3: Parameters Calibrated Independently Parameter Explanation Source, Value Pareto shape ESI and ACS, 2.5 m Average immigrant talent ACS L ind Employment in India NSS, 2 p ind Implied migration prob. ACS, 0.07 ibrate four independent parameters using micro data described in Section 3 (Table 3). Two of the moments, i.e. talent dispersion and country-specific talent cutoff m,arediscussedin detail below, as they are essential to quantifying the model. 4.. Talent dispersion Imeasureresearchtalentusingtwodifferentmetrics: citation-weightedpublicationsbyscientists and wage rate of S&E workers. The publication and citation data are downloaded from the InCites: Essential Science Indicators 42 My sample includes the top 200 researchers in each of the 2 fields defined by a unique grouping of Thomson-indexed journals 43. Assuming the distribution of publication count is the same as the distribution of research talent, we can obtain the maximum likelihood estimator for the Pareto shape parameter. Ipoolresearchersinall 2 fields (4200 scientists in total) and estimate for all scientists using ˆ = P 2 f= h P i P 2 f= N f ln x f i ln ˆx f m i (20) 42 I thank Tian Qin, a student at University of Southern California, for her help with access to the InCites platform. 43 Researchers are ranked by their citation-weighted publication counts during the decade of The 2 fields include Agricultural Sciences, Biology and Biochemistry, Chemistry, Clinical Medicine, Computer Science, Economics and Business, Engineering, Environment/Ecology, Geosciences, Immunology, Materials Science, Mathematics, Microbiology, Molecular Biology and Genetics, Neuroscience and Behavior, Pharmacology and Toxicology, Physics, Plant and Animal Science, Psychiatry/Psychology, General Social Sciences and Space Science. 23