High-Skilled Migration and Global Innovation

Transcription

1 High-Skilled Migration and Global nnovation Rui Xu Practice Talk Series 2 Aug 14,

2 Motivation Significant contribution of immigrants to innovation in the US 25% of US S&E workforce (50% of doctorates) in % of tech startups in Kauffman Report 20% of inventors (WPO) nventors 2

3 Motivation Significant contribution of immigrants to innovation in the US 25% of US S&E workforce (50% of doctorates) in % of tech startups in Kauffman Report 20% of inventors (WPO) nventors Most (80%) skilled immigrants are from non-oecd countries ndia and China are top origins H1B visa %ofustotal S&E workers Startups Patents ndia 7.2% 6.5% 5.4% China 3.5% 1.8% 8.5% 2

4 Benefit and Cost of Skilled Migration Benefits: US: contribution to innovation Source country: technology diffusion back home (Kerr et al. 2008) and Remittances World: better allocation of talent and higher growth? 3

5 Benefit and Cost of Skilled Migration Benefits: US: contribution to innovation Source country: technology diffusion back home (Kerr et al. 2008) and Remittances World: better allocation of talent and higher growth? Potential costs US: crowding out local talent (Borjas 2006) Source country: brain drain (Docquier and Rapoport 2011) 3

6 Benefit and Cost of Skilled Migration Benefits: US: contribution to innovation Source country: technology diffusion back home (Kerr et al. 2008) and Remittances World: better allocation of talent and higher growth? Potential costs US: crowding out local talent (Borjas 2006) Source country: brain drain (Docquier and Rapoport 2011) Net effects? 3

7 My Research Questions What s the net impact of high-skilled migration on the US economy: F F F innovation and growth welfare of low-skilled and high-skilled native workers aggregate welfare source countries (e.g. ndia): F F F technology diffusion and research intensity welfare of remaining workers and skilled emigrants aggregate welfare 4

8 Contributions study high-skilled migration in a multi-country GE model with endogenous growth through innovation and imitation international knowledge diffusion heterogeneous research talent within countries 5

9 Contributions study high-skilled migration in a multi-country GE model with endogenous growth through innovation and imitation international knowledge diffusion heterogeneous research talent within countries Three contributions: 1 A new channel of brain gain through enhanced global innovation is introduced and quantified 2 General-equilibrium effects and transition dynamics are considered in welfare analysis 3 The paper provides estimates of net GE effects of migration in a model which matches many relevant micro facts 5

10 Preview of Results Counterfactual: double the stock of skilled immigrants in the US TFP growth would increase from 1% to 1.15% 6

11 Preview of Results Counterfactual: double the stock of skilled immigrants in the US TFP growth would increase from 1% to 1.15% US: Aggregate welfare: " 3.9% F low-skilled: " 4.2%, high-skilled:# 3.4% 6

12 Preview of Results Counterfactual: double the stock of skilled immigrants in the US TFP growth would increase from 1% to 1.15% US: Aggregate welfare: " 3.9% ndia: F low-skilled: " 4.2%, high-skilled:# 3.4% Aggregate welfare: " 1.3% F remaining low-skilled: " 1.1%; high-skilled: " 3.9% F emigrants (high-skilled): " >100% 6

13 Outline 1 Literature Review 2 Micro Facts 3 Model Without Migration ntroduce High-skilled Migration 4 Quantitative Results 5 Conclusion 7

14 Outline 1 Literature Review 2 Micro Facts 3 Model Without Migration ntroduce High-skilled Migration 4 Quantitative Results 5 Conclusion 8

15 Related Empirical Literature For the US: nnovation: Kerr (2008, 2010, 2013), Hunt (2010, 2014), Peri et al. (2013), Moser et al. (2014) Native-born workers: Borjas (2003, 2005, 2011), Ottaviano and Peri (2008, 2012), Peri et al. (2010, 2013, 2015), Kerr et al. (2013), Doran et al. (2015) 9

16 Related Empirical Literature For the US: nnovation: Kerr (2008, 2010, 2013), Hunt (2010, 2014), Peri et al. (2013), Moser et al. (2014) Native-born workers: Borjas (2003, 2005, 2011), Ottaviano and Peri (2008, 2012), Peri et al. (2010, 2013, 2015), Kerr et al. (2013), Doran et al. (2015) mpact on source countries: Brain drain: see Docquier and Rapoport (2012) for a review Remittances: Docquier and Rapoport (2005), Bollard et al. (2011) Network externalities of diaspora: Rauch and Trindade (2002), Kerr (2008), Nanda and Khanna (2010) and Agrawal et al. (2011), Aleksynska and Peri (2012), Ortega and Peri (2013) mpact on migrants: Clemens (2010, 2011) Net effects: Docquier and Rapoport (2009) 9

17 Related Theoretical Literature Migration: Bhagwati and Hamada (1982), Beine et al. (2001), Benhabib and Jovanovic (2012) Research-driven endogenous growth: Aghion and Howitt (1992), Howitt (2000), Bloom et al. (2014) Technology diffusion: Barro and Sala-i-Martin (1997), Eaton and Kortum (1999), Keller (2001), Comin and Hobjin (2010), Benhabib et al. (2014), Perla and Tonetti (2014) Human capital and growth: Lucas (1988), Acemoglu et al. (2006), Jaimovich and Rebelo (2014), Grossman and Helpman (2014) 10

18 Outline 1 Literature Review 2 Micro Facts 3 Model Without Migration ntroduce High-skilled Migration 4 Quantitative Results 5 Conclusion 11

19 Researchers in the US Data: American Community Survey (ACS)

20 Researchers in the US Data: American Community Survey (ACS) % of employed workers are researchers S&E workers: those in S&E occupations with bachelor s degree in S&E fields S&E Occupations S&E Degrees S&E workers, researchers, and skilled workers will be used interchangeably 12

21 Researchers in the US Data: American Community Survey (ACS) % of employed workers are researchers S&E workers: those in S&E occupations with bachelor s degree in S&E fields S&E Occupations S&E Degrees S&E workers, researchers, and skilled workers will be used interchangeably Among researchers, 22% are immigrants from non-oecd countries They earn more on average than native researchers Regressions ndia Selection of immigrants by origin can be proxied by wage differentials Wage Differentials 12

22 Researchers in ndia Data: National Sample Survey (NSS) of ndia from

23 Researchers in ndia Data: National Sample Survey (NSS) of ndia from % of the employed are S&E workers in 2009 S&E workers: college graduates working in S&E occupations 13

24 Researchers in ndia Data: National Sample Survey (NSS) of ndia from % of the employed are S&E workers in 2009 S&E workers: college graduates working in S&E occupations Share of S&E workers has more than doubled since 1987: 13

25 Outline 1 Literature Review 2 Micro Facts 3 Model Without Migration ntroduce High-skilled Migration 4 Quantitative Results 5 Conclusion 14

26 Outline 1 Literature Review 2 Micro Facts 3 Model Without Migration ntroduce High-skilled Migration 4 Quantitative Results 5 Conclusion 15

27 General Setup GE with 1 + M countries: the US and M non-oecd countries The US innovates Non-OECD countries learn from the US Use ndia as an example non-oecd country 16

28 General Setup GE with 1 + M countries: the US and M non-oecd countries The US innovates Non-OECD countries learn from the US Use ndia as an example non-oecd country Endogenous growth achieved through quality improvement Both innovation and imitation require research effort mitation is easier when further away from the frontier 16

29 General Setup GE with 1 + M countries: the US and M non-oecd countries The US innovates Non-OECD countries learn from the US Use ndia as an example non-oecd country Endogenous growth achieved through quality improvement Both innovation and imitation require research effort mitation is easier when further away from the frontier New products are protected by patents Perfect patent enforcement in the US Costly patent enforcement in non-oecd countries 16

30 Standard Household Problem Preferences : U( ) = Z 1 0 exp( t) c(,t)1 1 dt where research talent 2 [1, 1) Pareto(1, ) Talent labor supply is constant and inelastic (no population growth) 17

31 Standard Household Problem Preferences : U( ) = Z 1 0 exp( t) c(,t)1 1 dt where research talent 2 [1, 1) Pareto(1, ) Talent labor supply is constant and inelastic (no population growth) Agent s budget constraint: ȧ(, t)+c(, t) = a(, t)r(t)+w(, t) 17

32 Standard Household Problem Preferences : U( ) = Z 1 0 exp( t) c(,t)1 1 dt where research talent 2 [1, 1) Pareto(1, ) Talent labor supply is constant and inelastic (no population growth) Agent s budget constraint: ȧ(, t)+c(, t) = a(, t)r(t)+w(, t) Transversality condition: apple exp lim t!1 Z t 0 r(s)ds a(,t) = 0, 8 17

33 Production Final good producers : max L Y (t),x(i,t) R 1 0 A(i, t)x(i, t) di L Y (t) 1 R 1 0 p(i, t)x(i, t)di w Y (t)l Y (t) where A(i, t) is the quality of variety i 2 [0, 1] at time t. 18

34 Production Final good producers : max L Y (t),x(i,t) R 1 0 A(i, t)x(i, t) di L Y (t) 1 R 1 0 p(i, t)x(i, t)di w Y (t)l Y (t) where A(i, t) is the quality of variety i 2 [0, 1] at time t. ntermediate good producer for each i: max x(i,t) (i, t) = p(i, t)x(i, t) A(i, t) x(i, t) {z } MC 18

35 Production Final good producers : max L Y (t),x(i,t) R 1 0 A(i, t)x(i, t) di L Y (t) 1 R 1 0 p(i, t)x(i, t)di w Y (t)l Y (t) where A(i, t) is the quality of variety i 2 [0, 1] at time t. ntermediate good producer for each i: max x(i,t) FOC (normalize ): (i, t) = p(i, t)x(i, t) A(i, t) x(i, t) {z } MC p(i, t) = A(i, t) w Y (t) = (1 ) 1 Z 1 0 A(i, t)di 18

36 R&D: nnovation (US) nnovation process: 1 unit of research talent generates a flow rate us of success for inventing a new machine of quality A us (i, t) for some i. 19

37 R&D: nnovation (US) nnovation process: 1 unit of research talent generates a flow rate us of success for inventing a new machine of quality A us (i, t) for some i. The arrival rate of ideas (replacement rate): z us (t) = us H us (t) = us Z 1 us(t) f ( )d! L us 19

38 R&D: nnovation (US) nnovation process: 1 unit of research talent generates a flow rate us of success for inventing a new machine of quality A us (i, t) for some i. The arrival rate of ideas (replacement rate): z us (t) = us H us (t) = us Z 1 Growth is driven by US innovation: us(t) f ( )d A us (t) = ( 1)A us (t)z us (t)! L us >1: step size 19

39 R&D: nnovation (US) nnovation process: 1 unit of research talent generates a flow rate us of success for inventing a new machine of quality A us (i, t) for some i. The arrival rate of ideas (replacement rate): z us (t) = us H us (t) = us Z 1 Growth is driven by US innovation: us(t) f ( )d A us (t) = ( 1)A us (t)z us (t)! L us >1: step size The value of each new idea (in steady state): V us (i, t) = us(i, t) z ss us + r ss 19

40 R&D: mitation (ndia) mitation process: 1 unit of research talent generates a flow rate ind (A us (t) A ind (t)) /A ind (t) of success for reverse engineering a machine of quality A ind (i, t) for some i. 20

41 R&D: mitation (ndia) mitation process: 1 unit of research talent generates a flow rate ind (A us (t) A ind (t)) /A ind (t) of success for reverse engineering a machine of quality A ind (i, t) for some i. The arrival rate of ideas: z ind (t) = ind a ind (t) 1 1 H ind (t) 20

42 R&D: mitation (ndia) mitation process: 1 unit of research talent generates a flow rate ind (A us (t) A ind (t)) /A ind (t) of success for reverse engineering a machine of quality A ind (i, t) for some i. The arrival rate of ideas: z ind (t) = ind a ind (t) 1 1 H ind (t) Growth in ndia: g ind (t) = ( 1)z ind (t) 20

43 R&D: mitation (ndia) mitation process: 1 unit of research talent generates a flow rate ind (A us (t) A ind (t)) /A ind (t) of success for reverse engineering a machine of quality A ind (i, t) for some i. The arrival rate of ideas: z ind (t) = ind a ind (t) 1 1 H ind (t) Growth in ndia: g ind (t) = ( 1)z ind (t) The value of each successful imitation (in steady state): V ind (i, t) = ind(i, t) z ss (1 + r ss apple) ind apple is the flow cost to enforce patent (lobbying or bribery by incumbents) 20

44 Free Entry Condition Free entry for intermediate firm: w us,r (t) = us E (V us (i, t)) = us E ( us (i, t)) z ss us + r ss w ind,r (t) = ind E (V ind (i, t)) = ind E ( ind (i, t)) z ss ind + r ss (1 apple) 21

45 Free Entry Condition Free entry for intermediate firm: w us,r (t) = us E (V us (i, t)) = us E ( us (i, t)) z ss us + r ss w ind,r (t) = ind E (V ind (i, t)) = ind E ( ind (i, t)) z ss ind + r ss (1 apple) Talent cutoff is pinned down by: w us,y (t) = us w us,r (t) w ind,y (t)(1 + s ind ) = ind w ind,r(t) where subsidy to workers sind comes from patent enforcement fee: s ind w ind,y (t)l ind,y = apple ) s ind = apple Z 1 0 (i, t)di 21

46 General Equilibrium Definition For any country, an equilibrium can be represented as time paths of prices [{p(i, t)} i2[0, 1], r(t), w Y (t), w R (t)] 1 t=0,quantities {x(i, t)}i2[0, 1], L Y (t), {c(, t)} 2[1,1), Y (t), A(t) 1 t=0,andtalentcutoff [ (t)] 1 t=0 for researchers such that: households maximize utility; producers maximize profit; free entry for intermediate firms; marginal agent is indifferent between two occupations; labor market clears: L(t) =L Y (t)+l R (t), where L R (t) = R 1 (t) f ( )d ; goods market clears: Y (t) = R 1 1 c(, t)f ( )d 22

47 Balanced Growth BGP: an equilibrium path where Y (t), A(t) and c(, t) grow at the same constant rate. 23

48 Balanced Growth BGP: an equilibrium path where Y (t), A(t) and c(, t) grow at the same constant rate. Growth is driven by innovation in the US: g ss = ( 1) us Z 1 ss us f ( )d! L us {z } zus ss 23

49 Balanced Growth BGP: an equilibrium path where Y (t), A(t) and c(, t) grow at the same constant rate. Growth is driven by innovation in the US: g ss = ( 1) us Z 1 ss us f ( )d! L us {z } zus ss Steady state technology in ndia relative to the US: g ss = ( 1) ind aind ss 1 1 H ind ) aind ss A ind(t) A us (t) = ( 1) ind H ind ( 1) ind H ind + g ss 23

50 Steady State Comparative Statics () US: us L us,r g ss Parameters (talent cutoff) (researchers) (growth rate) us " (research efficiency ) " (step size ) # (talent dispersion) # " " " or # " or # " " " " 24

51 Steady State Comparative Statics () ndia: ind L ss ind,r a ss ind Parameters (talent cutoff) (researchers) (rel. tech) ind " (research efficiency ) apple " (patent enforcement cost) " # # " 25

52 Outline 1 Literature Review 2 Micro Facts 3 Model Without Migration ntroduce High-skilled Migration 4 Quantitative Results 5 Conclusion 26

53 Assumptions Only consider high-skilled migration (H1-B visa) Agents in country m with talent m migrate with probability p m mmigrants enjoy research efficiency of us Perfect substitution between native and immigrant researchers 27

54 Effect of Migration New arrival rates of ideas are: z us = us z m = m Z 1 f ( )d L us + X m us m Z 1 m f ( )d L m p m Z 1 where m =(1 + WageDi erential m ) us Z! 1 p m f ( )d L m max{ m, m } f ( )d L m! 28

55 Effect of Migration New arrival rates of ideas are: z us = us z m = m Z 1 f ( )d L us + X m us m Z 1 m f ( )d L m p m Z 1 where m =(1 + WageDi erential m ) us Benefit: US: the technology frontier grows faster (g ss ") ndia: grows faster too because of diffusion F Z! 1 p m f ( )d L m max{ m, m } f ( )d L m Chinese immigrants have positive externality on ndia Talent allocation improves Cutoff converges! 28

56 Effect of Migration New arrival rates of ideas are: z us = us z m = m Z 1 f ( )d L us + X m us m Z 1 m f ( )d L m p m Z 1 where m =(1 + WageDi erential m ) us Benefit: US: the technology frontier grows faster (g ss ") ndia: grows faster too because of diffusion Cost: F Z! 1 p m f ( )d L m max{ m, m } f ( )d L m Chinese immigrants have positive externality on ndia Talent allocation improves Cutoff converges US: relative wage and employment of native researchers decrease ndia: average talent among researchers decreases (brain drain) 28!

57 Transition Dynamics for ndia US is always on the Balanced Growth Path 29

58 Transition Dynamics for ndia US is always on the Balanced Growth Path ndia is going through transition Growing faster than the US Liberalization in the 1990s (a drop in apple in the model) Transition paths need to be computed for welfare analysis 29

59 Transition Dynamics for ndia US is always on the Balanced Growth Path ndia is going through transition Growing faster than the US Liberalization in the 1990s (a drop in apple in the model) Transition paths need to be computed for welfare analysis Solving for rational expectations equilibrium during transition: Discretize the model Start from some initial talent cutoffs and update them until the talent cutoff sequence converges (Lee, 2005) Transition paths Baseline vs. Counterfactual 1 Researchers 29

60 Outline 1 Literature Review 2 Micro Facts 3 Model Without Migration ntroduce High-skilled Migration 4 Quantitative Results 5 Conclusion 30

61 Calibration of Parameters () Outside Calibration: Parameter Explanation Source / Target Value Capital share NPA 1/3 CRRA Hall (2009) 2 Discount rate nterest rate 4% 0.02 L us Employment in the US Normalization 1 31

62 Calibration of Parameters () One-to-one moment matching Parameter Explanation Source / Target Value Pareto shape ES and ACS 2.5 m Average immigrant talent ACS Wage Differentials L ind Employment in ndia NSS 2 p ind mplied migration prob. ACS 0.07 Micro-based estimate for talent dispersion : Essential Science ndicators (ES): F Number of citation-weighted publications by top 200 academics in 21 fields F ˆ 2 [1.58 (CS), 3.74 (SocSci)], ˆ pooled 2.58 American Community Survey (ACS): F ˆ 2 [2.5, 4] from hourly wage income of native S&E workers 32

63 Calibration of Parameters () Joint calibration: Parameter Targeted Moment, Value Source us = 0.03 % of S&E workers in the US, 7.8% ACS (2010) = 1.80 US TFP growth rate (Hicks-neutral), 1% PWT 8.1 ind = % of S&E workers in ndia, 1.56% NSS (2009) apple = ndia s TFP growth rate since 1990, 1.4% PWT 8.1 Model Fit 33

64 Main Results : Double Migration (US) Counterfactual 1: doubletheobservedstockofimmigrants Growth and labor allocation in the US: g ss s us,r s dom us,r E ( > us) Actual 1.00% 7.8% 6.1% 5.1 Double 1.15% 8.3% 5.0%

65 Main Results : Double Migration (US) Counterfactual 1: doubletheobservedstockofimmigrants Growth and labor allocation in the US: g ss s us,r s dom us,r E ( > us) Actual 1.00% 7.8% 6.1% 5.1 Double 1.15% 8.3% 5.0% 5.4 Consumption equivalent welfare changes in the US (%): W R R!W Aggregate % [-3.4, 4.2] 3.9 F F Native workers benefit from higher productivity Native researchers are hurt by crowding-out effect 34

66 Main Results : Double Migration (ndia) Counterfactual 1: doubletheobservedstockofimmigrants Steady state growth and labor allocation in ndia: g ss s ss ind,r a ss ind E ( > ss ind) Actual 1.00% 1.3% Double 1.15% 1.4%

67 Main Results : Double Migration (ndia) Counterfactual 1: doubletheobservedstockofimmigrants Steady state growth and labor allocation in ndia: g ss s ss ind,r a ss ind E ( > ss ind) Actual 1.00% 1.3% Double 1.15% 1.4% Welfare changes in ndia (%): Aggregate F W R W!R New emig Excl. emig All % [1.1,3.9] [108, 205] ndia benefits from innovation by non-ndian immigrants (positive externality) 35

68 Main Results : Remove mmigrants Counterfactual 2 & 3: sendalloronlyndianimmigrantsback Steady state growth and labor allocation in ndia: g ss l ss ind,r a ss ind E ( > ss ind) 2. Send all imm back 0.86% 1.21% Send ndian imm back 0.95% 1.26% Baseline (actual) 1.00% 1.28%

69 Main Results : Remove mmigrants Counterfactual 2 & 3: sendalloronlyndianimmigrantsback Steady state growth and labor allocation in ndia: g ss l ss ind,r a ss ind E ( > ss ind) 2. Send all imm back 0.86% 1.21% Send ndian imm back 0.95% 1.26% Baseline (actual) 1.00% 1.28% Welfare changes in ndia (%): Aggregate Case W R W!R New emig Excl. emig All [-3.6, -1.1] [-70, -54] [-2.3, 0.14] [-69, -54]

70 Robustness Checks 1 mperfect substitution between immigrants and native researchers CES 2 10% research subsidy in the US Subsidy 3 Optimal research subsidy in the US Optimal Subsidy 4 Alternative Pareto shape parameter Pareto Shape 5 Alternative discount rate Discount rate 6 Diaspora network effect Network 37

71 Outline 1 Literature Review 2 Micro Facts 3 Model Without Migration ntroduce High-skilled Migration 4 Quantitative Results 5 Conclusion 38

72 Conclusion High-skilled migration from developing countries to the US is a significant phenomenon with potential impact on global innovation and welfare. 39

73 Conclusion High-skilled migration from developing countries to the US is a significant phenomenon with potential impact on global innovation and welfare. proposeanendogenousgrowthmodelwithheterogeneoustalentand international knowledge diffusion to study GE effects on the US and ndia. Research intensity is enhanced in both countries. Both countries benefit from observed level of migration. Welfare impact differs by talent. 39

74 Conclusion High-skilled migration from developing countries to the US is a significant phenomenon with potential impact on global innovation and welfare. proposeanendogenousgrowthmodelwithheterogeneoustalentand international knowledge diffusion to study GE effects on the US and ndia. Research intensity is enhanced in both countries. Both countries benefit from observed level of migration. Welfare impact differs by talent. Future work: ntroduce education choices and quality into the model. 39

75 Remittances as % of GDP in ndia Back 40

76 mmigrant entrepreneurs account for 1/4 of tech start-ups Back 41

77 H1B Visa by Origin Back 42

78 mmigrant nventors Back 43

79 US Utility Patent Applications and Grants Back 44

80 S&E Occupations S&E occupations Biological, agricultural and environmental life scientists Computer and mathematical scientists Physical scientists Social scientists Engineers S&E postsecondary teachers Notes: classification provided by NSF S&E related occupations Health-related occupations S&E managers S&E pre-college teachers S&E technicians and technologists Architects Actuaries Back 45

81 S&E Degree Fields S&E degree fields Biological, agricultural and environmental life sciences Computer and mathematical sciences Physical sciences Social sciences Engineering Notes: classification provided by NSF S&E related fields Health fields Science and math teacher education Technology and technical fields Actuarial science Architects Back 46

82 Native-immigrant Wage Differentials log(hourly wage) = (imm) + 2 1(OECD) + controls (1) (2) (3) (4) (imm) (OECD) Education X X X Enter before 25 X X Age X X Gender X X Field of Study X Note: all estimates are significant at p<0.01. Back 47

83 Kernel Density Back 48

84 Research Talent Each person is born with units of research talent drawn from a Pareto distribution with CDF=1 the same talent of 1 to be a worker Education is not modeled n equilibrium, researchers earn higher income than workers On average: S&E workers earn 80% more than non S&E workers Exceptions: high-income non-s&e occupations, such as bankers, lawyers and managers Back 49

85 Skilled migration improves talent allocation Back 50

86 Research nput during Transition Back 51

87 Transition Paths for ndia Back 52

88 Wage Differentials by Origin Mean wage of immigrants from country m is 1 m. m =(1 + m ) us where m is estimated by running the following regression: log(wage) = 0 + m country dummies m estimates for the top 10 origins are plotted below: Back 53

89 Wage Differentials by Origin Back 54

90 Model Fit Untargeted Moments Model Data US ndia ncome share by S&E workers 12.8% 13.2% Wage ratio of S&E vs. non S&E workers ncome share by S&E workers 2.8% 9.3% Wage ratio of S&E vs. non S&E workers n the model, wage ratio is mainly governed by the talent distribution t captures income distribution in the US quite well t is unable to explain the high inequality in ndia. Under-estimation of income by self-employed? Back 55

91 Robustness Checks (CES) n the CES specification: 2 z us = us 4 Z 1 us f ( )d l us! 1 Z f ( )d pl m 5 m 1 Counterfactual 1: doubletheobservedstockofimmigrants Welfare changes in the US (%): g W R R!W Agg % [-3.4, 4.2] % [-2.3, 4.5] 4.2 Effects of considering imperfect substitution: Benefit of doubling migration is bigger for the US Back 56

92 Robustness Checks (Actual Subsidy) Counterfactual 1: doubletheobservedstockofimmigrants Welfare changes in the US (%): subsidy g W R R!W Agg 0% 1.15% [-3.37, 4.23] % 1.15% [-3.06, 4.25] 3.94 Effects of a 10% research subsidy: Benefit of doubling migration is slightly bigger for the US Back 57

93 Robustness Checks (Optimal Subsidy) Counterfactual 1: doubletheobservedstockofimmigrants Welfare changes in the US (%): g subs tax W R R!W Agg Actual 1.48% 42% 12% Double 1.56% 40% 11% [-5.0, 3.1] 2.3 AplannerintheUSchoosestheoptimalresearchsubsidytomaximize agg. welfare (excluding immigrants) Not enough research is done in DE Optimal research subsidy decreases with more immigrants Benefit of migration is smaller than in DE F n DE: immigrants help push the equilibrium closer to socially optimal Back 58

94 Robustness Checks (Pareto Shape) Counterfactual 1: doubletheobservedstockofimmigrants Welfare changes in the US (%): g W R R!W Agg % [-3.4, 4.2] % [-1.8, 3.4] 3.2 Thinner Pareto tail: us and re-calibrated to fit growth rate and R&D intensity in the US More modest effects on growth and welfare Back 59

95 Robustness Checks (Discount Rate) Counterfactual 1: doubletheobservedstockofimmigrants Welfare changes in the US (%): g W R R!W Agg % [-3.4, 4.2] % [-2.0, 6.5] 6.1 Counterfactual 3: send ndian immigrants back Welfare changes in ndia (%): Aggregate W R W!R New emig Excl. emig All [-2.3, 0.14] [-69, -54] [-2.6, -0.21] [-70, -53] Back 60

96 Robustness Checks (Network) ndian diaspora helps facilitate knowledge diffusion (Kerr 2008): Aus(t) A ind (t)! z ind = ind 1 + H diaspora ind H dom ind A ind (t) Counterfactual 3: sendallndianimmigrantsbacktondia Welfare changes in ndia (%): Aggregate! W R W!R New emig Excl. emig All [-2.3, 0.14] [-69, -54] [-2.7, -0.14] [-69, -54] Sending ndian immigrants back is bad for everyone in ndia! Back 61