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BY 4.0 license Open Access Published by De Gruyter Open Access March 29, 2022

Highly Skilled International Migration, STEM Workers, and Innovation

  • Anelí Bongers , Carmen Díaz-Roldán and José L. Torres EMAIL logo
From the journal Economics

Abstract

This article studies the implications of highly skilled labor international migration in a two-country dynamic stochastic general equilibrium model. The model considers three types of workers: Science, Technology, Engineering, or Mathematics (STEM) workers, non-STEM college educated workers, and non-college educated workers. Aggregate productivity in each economy is a function of innovations, which can be produced only by STEM workers. The model predicts (i) the existence of a wage premium of STEM workers relative to non-STEM college educated workers, (ii) the skill wage premium is higher in the destination country and increases with positive technological shocks, (iii) a reduction in migration costs increases output, wages, and total labor in the destination country, with opposite effects in the country of origin, and (iv) high skilled immigrants reduce skilled native labor and do not affect unskilled labor. Finally, a migration policy designed to attract STEM workers generates similar effects to a positive aggregate productivity shock.

JEL Classification: F43; J61; O31

1 Introduction

Human capital and skill acquisition investment are accepted to be fundamental variables for productivity growth (Jones, 1995, 2002; Lucas, 1988). In a context of international labor mobility, the stock of human capital in any economy does not only depend on investment in skill acquisition by natives but is also affected by the skill embodied in the flows of workers to/from abroad. Moreover, human capital and educational attainment by immigrants have not only direct consequences for productivity in the hosting country through increasing the stock of human capital for production, but they also have important implications for the generation of ideas and innovations, which is an additional source of productivity growth. At the same time, these movements of skilled workers could lead to a “brain drain” problem in the countries of origin. Recent trends in international labor mobility flows, influenced by the design of migration policies of high-income countries, suggest that migration of some types of high-skilled workers (as scientist and engineer) can be an important factor to promote research, development, and innovation activities. Koser and Salt (1997) pointed the importance of a highly skilled, specialized elite of migrants as a crucial element of the spread of expertise. They also addressed that highly skilled migrant labor would transfer expertise through using new technologies and international networking. In this line, Regets (2007) provided a broad overview of research and policy issues related to international mobility of high skilled migrants, paying special attention to scientists and engineers.

In recent years, the interest of studying the contribution of high-skilled workers to economic growth has been concentrated on those high-skilled workers related to R&D and innovation generating occupations. Namely, workers with an educational background in Science, Technology, Engineering, or Mathematics, the so-called STEM workers. In some high-income countries, such as the US, immigrants represent a significant fraction of these occupations. According to Hanson and Slaughter (2017), in 2013 in the US, foreign-born workers accounted for 19.2% of STEM workers with a bachelor’s degree, 40.7% of those with a master’s degree, and more than half (54.5%) of those with a PhD. As evidence of the interest of some countries in welcoming foreign STEM workers, specific migration policies have been designed. Examples are the H-1B visa program and the Optional Practical Training (OPT) program in the US (see Peri, Shih, & Sparber, 2015).

Several papers study the effects of STEM migration on the labor market in the hosting country. Empirical evidence shows mixed results but in general little displacement effect of native STEM workers by high-skilled immigrants is observed. For instance, Lowell (2010) found that there is no evidence of the displacement of natives. Similarly, Peri and Sparber (2011) argued that highly educated immigrants and natives are imperfect substitutes. However, Kerr and Kerr (2013) found that job transition for STEM workers is more difficult during period of high immigration. Jaimovich and Siu (2017) found that high-skilled immigration has an important role in the decline of wage inequality in the US. Hanson and Slaughter (2017) studied wage differences between native and foreign-born STEM workers and found that wage difference is smaller for STEM than for non-STEM workers. Similar results are found by Picot and Hou (2013) for Canada. Turner (2022) estimated that immigration during the period 1990–2010 reduced STEM worker wages relative to non-STEM in the US between 4 and 12%. Gunadi (2019) studied the impact of STEM immigration on the wage structure of the US and found that the elasticity of substitution between US and foreign-born STEM workers with similar skills is high but finite, which implies that STEM immigration does not displace US-born STEM workers.

More scarce is the literature on the effects of STEM immigrants on innovation. These works analyze the contribution of STEM educated immigrants to innovation in the hosting country, highlighting the positive contribution of high-skilled to innovation and inventions, especially by scientist and engineer immigrant. Chellaraj, Maskus, and Mattoo (2008) studied the impact of foreign graduate students on the US innovation system during the period 1963–2001. They found a positive impact on future patent applications and patent awarded in university and non-university institutions and quantified that a 10% increase in foreign graduate students would raise patent applications by 4.5%. Hunt and Gauthier-Loiselle (2010) analyzed the contribution of college graduated immigrants to patents, where immigrants account for 24% of the patents, and estimated that a 1% point increase in high-skilled immigrants share increases in patents per capital by 6% and accounting for positive spillovers the estimated increase in patents is in the range 9–18%. Kerr and Lincoln (2010) concentrated in Indian and Chinese STEM workers and their contribution to inventing patenting and found a limited displacement effect on natives and that higher admissions of science and engineering immigrants have a positive contribution to innovation. Stuen, Mobarak, and Maskus (2012) analyzed the contribution of foreign doctoral students to innovation in American science and engineering departments and argued that visa restrictions limiting entry of high-quality foreign students pose an obstacle for academic innovation. Peri et al. (2015) used changes in the H-1B visa program to study the effects of high-skilled immigrant in the innovation process. Jaimovich and Siu (2017) highlighted the role played by high-skilled immigrants in STEM occupations, and their contribution to economic growth through higher productivity steaming from research and innovation areas in the US Demirci (2019) illustrated the importance of the OPT program for increasing the probability that STEM foreign students would remain in the US.

This article proposes a theoretical framework to analyze the dynamics of highly skilled international migration on both the origin and the receiving countries, in a unified two-country dynamic general equilibrium model.[1] We assume that only high skilled workers can move internationally from the low productivity (origin) country to the high productivity (host) country. In one hand, following Peri et al. (2015), the model considers three types of workers: STEM workers, non-STEM college educated workers, and non- college educated workers. The first two types of workers are high-skill workers, whereas the last one is classified as low-skill. High-skill and low-skill workers are imperfectly substitutable and innovations are only produced by STEM workers. Accordingly, the TFP in each economy is a function of innovations, which can be produced only by STEM workers. On the other hand, the model considers two types of capital assets: structures and equipment. Equipment capital assets and skill workers are complements but equipment and low-skilled workers capital are substitutes. The model also introduces the skill-bias technological hypothesis in which skill workers foster the adoption of skill complementary technologies. In this theoretical framework, the contribution of high-skill workers to economic growth is analyzed from different perspectives. First, STEM workers are modelled as a productive factor that contributes exogenously to aggregate productivity by producing innovations (a greater number of STEM lead to higher productivity) with positive effects on growth in the short term, since they are a key factor for the development of new technologies and, in this sense, comparable to capital assets in structures. But, in addition, STEM workers also contribute endogenously to the increase of TFP, because they are the only workers able to generate ideas and promote the innovative process (a greater number of STEM means an increase of innovation), with positive effects on long-term growth. And, second, the model also allows for an additional mechanism contributing to economic growth, i.e., the complementarity of the high-skill workers (including non-STEM college educated) with equipment.

The model developed here offers several new dimensions to be explored. First, we study the effects of a positive idiosyncratic aggregate productivity shock to both sending and receiving countries. This shock increases wages for all types of workers, increasing the number of skilled workers and reducing the number of unskilled workers. In the sending country, this shock also provokes a reduction of the incentives to migrate to the destination country. Additionally, the productivity shock increases the wage differential of STEM workers related to non-STEM college educated workers. We found the existence of a wage premium to skilled workers related to unskilled workers, but also a wage premium from STEM workers related to non-STEM workers, consistently with the empirical evidence. Additionally, when aggregate productivity differential between the receiving country and the sending country is large enough, it is possible to find situations in which wage for unskilled workers in the destination country is larger than the wage for skilled workers in the sending country. Finally, the model is used to simulate a change in the migration policy implemented by the destination country. A relaxation of the migration policy to allow a larger number of skilled workers increases output in the destination country but has a negative effect on the sending country’s output. Total skilled workers increase in the destination country, but there is a partial substitution of native skilled workers, without any effects on the quantity of unskilled workers. Finally, a more specific migration policy to attract foreign STEM workers has similar effects to a positive aggregate productivity shock, in addition to the effects on productivity due to the rise in human capital.

The structure of the rest of the article is as follows. Section 2 introduces a two-country general equilibrium model as a unified theoretical framework to study the effects of several shocks affecting international migration of skilled workers on both sending and hosting countries. Section 3 presents the calibration of the model. In Section 4, the dynamic properties of the model are analyzed by simulating a positive idiosyncratic TFP shock in each country. Section 5 presents the prediction of the model for the wage premium of STEM workers relative to non-STEM college educated workers. Section 6 simulates the effects of changes in the migration policy implemented by the destination country. Finally, Section 7 summarizes the main conclusions.

2 The Model

In this section, we develop a two-country dynamic stochastic general equilibrium (DSGE) model with imperfect international labor mobility. The model is based on previous DSGE models with the possibility of migration developed by Canova and Ravn (2000), Djajic (1989), Hauser (2014), Klein and Ventura (2009), and Mandelman and Zlate (2012). The model considers a world composed of two countries: A country of origin and a destination high-income country. Following Peri et al. (2015) the model considers three types of workers: STEM workers, non-STEM college educated workers, and non-college educated workers. These three types of workers are aggregated into low-skilled workers (non-college educated workers) and high-skilled workers (STEM and non-STEM college educated workers). The difference between STEM and non-STEM college educated workers is not in the level of skill but in the occupation. The economy is populated by an infinitely lived representative agent who maximizes the expected value of her lifetime utility. Given a migration policy implemented by the destination country, it is assumed that only high-skill workers are allowed to migrate from the low-income country to the high-income country. It is assumed that productivity in the destination country is higher than in the sending country, and hence, a wage premium exists. That difference can be explained by TFP differentials (see, for instance, Hall & Jones, 1999; Klenow & Rodriguez-Clare, 1997, etc.), or by differences in the stock of human capital (as in Klenow and Rodriguez-Clare, 1997).

A key point of the model economy is the introduction of a positive externality in the production process, reflecting R&D, and innovation activities, which are connected with the number of STEM workers (Peri et al., 2015; Pyo, 2005). The importance of STEM workers on economic growth has been highlighted by Griliches (1992) and Jones (1995, 2002), among others. These authors consider that STEM workers are the main input in the idea-production function and that innovation is the main factor behind productivity growth in the long run. In our model, the innovation process is based on the production of ideas by STEM workers. The model assumes that aggregate productivity is driven by innovations and that innovations depend on the number of STEM workers. Additionally to the labor inputs, the aggregate production function considers two types of capital assets: structures and equipment, with capital equipment-skill complementarity in the production process.

2.1 Population

We consider a world composed of two countries with imperfect international labor mobility: A (relative) low-income country, denoted by o (the country of origin), and a high-income country, denoted by d (the destination country). In both countries, there exists three types of workers: Low-skilled workers (NS), STEM workers (ST), and non-STEM (NST) college educated workers. Let s t j j denotes the proportion of STEM college educated workers born in each economy, j = d , o , n s t j j , the proportion of non-STEM college educated workers, and n s j j the proportion of unskilled workers. The total population born in each country is the sum of both skilled and unskilled country born, which is normalized to 1, s t j j + n s t j j + n s j j = 1 . World population is assumed constant, but population in each country can change due to emigration. In particular, population increases in the destination country and reduces in the sending country in the presence of migration. We assume that, given a migration policy implemented by the destination country, only skilled workers, both STEM and non-STEM college educated, can migrate. Therefore, unskilled workers are forced to remain in the born country. Agents are born at time zero and acquire their respective skill endowments, i , at birth, where i = n s , s t , n s t .

With the possibility of migration of skilled workers, population in the destination country, N d , is defined as:

(1) N d = n s d d + s t d d + n s t d d + s t o d + n s t o d ,

where s t o d is the proportion of STEM workers born in the country of origin that emigrate to the destination country, and n s t o d is the equivalent for non-STEM college educated workers.[2] By symmetry, population in the origin country, N o , is defined as:

(2) N o = n s o o + s t o o + n s t o o s t o d n s t o d .

Migration changes the relative proportion of each type of worker over total labor, increasing the proportion of high-skilled workers in the destination country and reducing their proportion in the sending country.

2.2 Innovation Process

An important characteristic of the proposed model economy is the introduction of a positive externality in the production process, revealing research, development, and innovations activities. In the literature on economic growth, there are several contributions showing the extent to which TFP trend depends on the innovation process. Griliches (1992) and Jones (1995) studied the relationship between economic growth and ideas production, finding that growth is generated endogenously through R&D spillovers, and economic growth is tied to the growth of productivity. On the other hand, Acemoglu and Angrist (2000), Iranzo and Peri (2009), Moretti (2004a), and Peri et al. (2015) emphasize the role of human capital externalities associated with innovation. Factors like the number of college graduates, immigration of highly educated workers, and the adoption of new technology, among other factors promoting high-skill abilities, generate positive spillover effects on productivity. As addressed by Peri et al. (2015), STEM workers are the fundamental inputs for innovation, and the main drivers of productivity growth.[3]

Having those considerations in mind, we assume that the aggregate production function of the economies includes an additional factor to neutral technology (TFP) representing innovation, which in turn is a function of the number of STEM workers. Following Peri et al. (2015) and Pyo (2005), we will assume that aggregate productivity is an increasing function of the number of STEM workers who are the only workers capable of generating ideas and, consequently, innovation. Hence, innovations are considered as a positive externality in the production process given by,

(3) e η j L j , ST , t ,

where L j , ST , t is the number of STEM workers in country j at time t , and η j determines the elasticity of output with respect to the innovations generated by the STEM workers. The other component of technology, representing neutral technical change, A j , t , is assumed to be exogenously determined, following an autoregressive process of order 1:

(4) log A j , t = ( 1 ρ A , j ) A ¯ j + ρ A , j log A j , t 1 + ε j , t A ,

where A ¯ j is the steady-state TFP in country j , ρ A , j < 1 , and ε j , t A N ( 0 , σ A 2 ) .

2.3 The Technology

The model considers a five-factor aggregate production function: Three types of labor (STEM, non-STEM college educated, and non-college educated) and two types of capital assets (structures and equipment). STEM workers are the key inputs in developing new technologies, whereas all high-skill workers, including non-STEM college educated, are key inputs in the adoption of those new technologies given their complementarity with capital equipment.

We assume the following aggregate production function:

(5) Y j , t = A j , t e η j L j , ST , t K j , s , t α j × μ j L j , NS , t ϕ j + ( 1 μ j ) ( θ j K j , e , t ρ j + ( 1 θ j ) L j , H , t ρ j ) ϕ j ρ j ( 1 α j ) ϕ j ,

where Y j , t is the final output in country j at time t , A j , t is the TFP, K j , s , t is the capital stock in structures, K j , e , t is the capital stock in equipment, L j , NS , t is the non-college educated labor, L j , H , t is the high-skilled labor, which is a combination of STEM labor, L j , ST , t , and non-STEM college educated labor, L j , NST , t . The parameter α j indicates the elasticity of output with respect to structures. The parameters ρ j and ϕ j capture the elasticity of substitution between unskilled labor, capital equipment, and skilled labor. The elasticity of substitution between equipment or skilled labor and unskilled labor is 1 / ( 1 ϕ j ) , whereas the elasticity of substitution between equipment and skilled labor is 1 / ( 1 ρ j ) . Capital skill complementarity requires that ϕ j > ρ j . Finally, μ j and θ j are distribution technological parameters that govern income shares.

The skilled labor is an Armington aggregator of STEM and non-STEM college educated labor,

(6) L j , H , t = ω j L j , ST , t ( σ j 1 ) σ j + ( 1 ω j ) L j , NST , t ( σ j 1 ) σ j σ j σ j 1 ,

where the parameter σ j > 1 is the elasticity of substitution between STEM and non-STEM college educated workers. Both types of workers are similar in education skills but not in occupation.

The objective of the firms is profit maximization, where profits are defined as:

(7) Π j , t = Y j , t W j , i , t L j , i , t R j , e , t K j , e , t R j , s , t K j , s , t ,

where W j , i , t is the wage for i = { NS , ST , NST } , R j , e , t is returns to equipment, and R j , s , t is returns to structures.

From the profit maximization problem first-order conditions we obtain the following input prices:

(8) W j , NS , t = μ j ( 1 α j ) Y j , t L j , NS , t ϕ j 1 X j , t ,

(9) W j , ST , t = η j Y j , t + ( 1 α j ) ( 1 θ j ) ( 1 μ j ) ω j L j , NT , t 1 σ j Y j , t Z j , t L j , H , t ρ j 1 X t ,

(10) W j , NST , t = ( 1 α j ) ( 1 θ j ) ( 1 μ j ) ( 1 ω j ) L j , NST , t 1 σ j Y j , t Z j , t L j , H , t ρ j 1 X t ,

(11) R j , s , t = α j Y j , t K j , s , t ,

(12) R j , e , t = ( 1 α j ) ( 1 μ j ) θ j K j , e , t ρ j 1 Z j , t Y j , t X j , t ,

where

X j , t = μ j L j , NS , t ϕ j + ( 1 μ j ) [ θ j K j , e , t ρ j + ( 1 θ j ) L j , H , t ρ j ] ϕ j ρ j

and

Z j , t = [ θ j K j , e , t ρ j + ( 1 θ j ) L j , H , t ρ j ] ϕ j ρ j 1 .

As we can observe, the model produces two wage premia: one between STEM and non-STEM college educated workers, and another between college and non-college workers. First, there is a wage premium of skilled workers relative to unskilled workers, as it is standard in the literature. Second, we find the existence of a wage premium of STEM workers relative to non-STEM college educated workers, a result supported by the empirical evidence. Therefore, wage inequality is not only generated by the education attainment but also by the occupation. Even in the case in which both college educated workers are perfect substitutes, a wage premium exists, as STEM workers are contributing more to final productivity. STEM workers produce innovations which is an additional source of productivity to their skills in addition to that of non-STEM college educated workers, which explains the wage premium between these two types of skilled workers.

Without considering the effects of STEM workers on innovation, the relative wage for STEM workers versus college non-STEM would be given by:

(13) W j , ST , t W j , NST , t = ω j ( 1 ω j ) L j , NST , t L j , ST , t 1 σ j ,

depending on the relative supply of both types of workers and the elasticity of substitution.

2.4 Destination Country Households

Each economy is populated by an infinity lived representative agent who maximizes the expected value of her lifetime utility. Agents derive utility from consumption and leisure by taking optimal consumption-saving and labor supply decisions. Utility function for the destination country households is given by:

(14) U d , i , t ( C d , i , t , L d , i , t ) = γ d log C d , i , t + ( 1 γ d ) log ( 1 L d , i , t ) ,

where C d , i , t is the consumption by agents born in the destination country, L d , i , t indicates the working hours, and γ d ( 0 < γ d < 1 ) is a parameter determining the weight of consumption in the household’s utility. Total available discretionary time has been normalized to one. The household’s budget constraint is given by:

(15) C d , i , t + I d , i , t = W d , i , t L d , i , t + K d , s , i , t R d , s , t + K d , e , i , t R d , e , t ,

where I d , i , t is the investment by agents born in the destination country, W d , i , t is the wage, K d , e , t is the stock of capital equipment, K d , s , t is the stock of structures held by agents born in the destination country, and R d , s , t and R d , e , t are the rental rate of structures and equipment, respectively. Total investment by agents born in the destination country is the sum of investment in structures plus investment in equipment.

(16) I d , i , t = I d , s , i , t + I d , e , i , t .

Accumulation equations for each capital asset is given by:

(17) K d , e , i , t + 1 = ( 1 δ d , e ) K d , e , i , t + I d , e , i , t ,

(18) K d , s , i , t + 1 = ( 1 δ d , s ) K d , s , i , t + I d , s , i , t ,

where δ d , e and δ d , s are the depreciation rates for equipment and structures, respectively.

The corresponding Lagrange’s auxiliary function is given by:

(19) d = t = 0 β d t [ γ d log C d , i , t + ( 1 γ d ) log ( 1 L d , i , t ) ] λ d , i , t C d , i , t + K d , e , i , t + 1 ( 1 δ d , e ) K d , e , i , t + K d , s , i , t + 1 ( 1 δ d , s ) K d , s , i , t W d , i , t L d , i , t + K d , s , i , t R d , s , t + K d , e , i , t R d , e , t ,

where β d is the discount factor. From first-order conditions, we obtain the following equilibrium condition for destination country natives labor supply:

(20) ( 1 γ d ) ( 1 L d , i , t ) = W d , i , t γ d C d , i , t for i = NS , ST , NST .

The optimal consumption path (investment decisions) is given by the following two equilibrium conditions for equipment and structures, respectively:

(21) C d , i , t + 1 C d , i , t = β d ( R d , e , t + 1 + 1 δ d , e ) ,

(22) C d , i , t + 1 C d , i , t = β d ( R d , s , t + 1 + 1 δ d , s ) .

2.5 Sending Country Households

Sending country households’ utility function presents some differences, as they can decide to migrate depending on the migration policy implemented by the destination country. Similar to Borjas (1987), in our model, the resulting emigration rate is (i) a negative function of mean income in the sending country; (ii) a positive function of mean income in the hosting country; and (iii) a negative function of the costs of emigrating to the hosting country. The utility function for the sending country is given by:

(23) U o , i , t ( C o , t , L o , i , t , L o s , i , t ) = γ o log C o , i , t + ( 1 γ o ) log ( 1 L o , i , t L o d , i , t ) ,

where C o , i , t is the consumption of agents born in the country of origin, L o , i , t is the working time in the country of origin and L o d , i , t is the working time in the destination country, representing the fraction of workers who emigrate to the destination country. The budget constraint is given by

(24) C o , i , t + I o , i , t = W o , i , t L o , i , t + ( W d , i , t M i , t ) L o d , i , t + K o , s , i , t R o , s , t + K o , e , i , t R o , e , t ,

where I o , i , t is the total investment by agents born in the origin country, K o , s , i , t and K o , e , i , t are the stock of structures and equipment, respectively, R o , s , t and R o , e , t are the rental rate of structures and equipment capital assets, respectively, W o , i , t is the wage in the country of origin, and W d , i , t is the wage in the destination country. M i , t represents the cost of emigration including both monetary and non-monetary costs incurred by migrant workers seeking jobs abroad. This migration cost is supposed to reflect a heterogeneous set of factors, such as travel and installing costs, adjustment to a new lifestyle and cultural adaptation, cost of searching for employment, family constraints, geographical location of countries, etc., including migration policy. In our context, we assume that migration cost reflects migration policy, which can be specific to foreign worker type.

Capital stock accumulation for equipment and structures is given by:

(25) K o , e , i , t + 1 = ( 1 δ o , e ) K o , e , i , t + I o , e , i , t ,

(26) K o , s , i , t + 1 = ( 1 δ o , s ) K o , s , i , t + I o , s , i , t ,

where I o , e , i , t is the investment in equipment and I o , s , i , t is the investment in structures by agents born in the country of origin.

By incorporating the capital accumulation equations into the budget constraint, the corresponding Lagrange’s auxiliary function is given by:

(27) o = t = 0 β o t [ γ o log C o , i , t + ( 1 γ o ) log ( 1 L o , i , t L o d , i , t ) ] λ o , i , t C o , i , t + K o , e , i , t + 1 ( 1 δ o , e ) K o , e , i , t + K o , s , i , t + 1 ( 1 δ o , s ) K o , s , i , t W o , i , t L o , i , t ( W d , i , t M i , t ) L o d , i , t K o , s , i , t R o , s , t K o , e , i , t R o , e , t ,

where β o is the discount factor. Equilibrium condition for labor supply in the country of origin is given by:

(28) ( 1 γ o ) ( 1 L o , i , t L o d , i , t ) = W o , i , t γ o C o , i , t for i = NS , ST , NST ,

whereas the equilibrium condition for labor supply in the destination country (emigration) is given by:

(29) ( 1 γ o ) ( 1 L o , i , t L o d , i , t ) = ( W d , i , t M i , t ) γ o C o , i , t for i = NS , ST , NST .

Note that due to assumed migration policy by the destination countries L o d , NS , t = 0 .

By combining the above two expressions we obtain the equilibrium condition for emigration, given by

(30) ( W d , i , t M i , t ) = W o , i , t .

Equilibrium conditions for investment in equipment and structures are given by:

(31) C o , i , t + 1 C o , i , t = β o ( R o , e , t + 1 + 1 δ o , e ) ,

(32) C o , i , t + 1 C o , i , t = β o ( R o , s , t + 1 + 1 δ o , s ) .

Aggregate values for consumption, investment, and capital assets in each country are obtained by assuming that consumption and investment of immigrants are equal to the corresponding values for native in the destination country in per capita terms. That is, we add to the variables of native households in the hosting country the corresponding value from immigrants, and subtract those values for the country of origin.

2.6 Migration Policy

A key element of the model is the migration policy. In practice, each country chooses a particular migration policy. However, in our model economy we assume that only the receiving country implements a migration policy by imposing some restrictions to immigration.[4] These restrictions can be qualitative (depending on the characteristics of immigrants) or quantitative (number of immigrants). We assume that the destination country implements both restrictions: international mobility of low-skill workers is not allowed. Additionally, there is a quantitative restriction by the destination country to the number of high-skill workers that can migrate. Djajic (1989) studied the implications of emigration restrictions. The results vary depending on whether immigration policies limit the quality, or both the quality and the quantity of migrants, but it is shown that qualitative restrictions lower the welfare of the host country, as well as that of the rest of the world.

Migration decision depends on the difference in wages between the origin and the destination countries compared to the cost of migration, as defined above. According to that, the condition for emigrating would be

(33) W d , i , t M i , t W o , i , t > 1 .

The positive wage gap induces movements of workers from the low-income country to the high-income country. However, this migration process is dampened by the existence of a migration cost. In our theoretical framework, M i , t > 0 represents the cost of migration, and changes in this value are assumed to reflect changes in migration policy, by assuming that all other factors affecting the cost of migration are constant. Migration policy is defined as:

(34) M i , t = ε M , i , t M ¯ ,

where M ¯ is the steady-state value for M i , t , and ε M , i , t is a shock to the migration policy affecting the value of the emigration cost. As low-skill worker migration is not allowed, this implies that M NS , t W d , NS , t W o , NS , t .

3 Calibration

The model is calibrated for two artificial economies representing one high-income destination country, and an origin country that can be a developed economy or a developing economy. This choice is supported by the empirical evidence. Only a few countries are net receptors of migration, including the US, Canada, Australia, and the UK. These are high-income countries in which there exists a wage premium with respect to that of the potential sending countries. In absolute terms, the first destination country of workers migration in the world is the US. A larger variety is found in the case of sending countries, which includes both developed and developing countries. Therefore, calibration of the model for the country of origin can be done using either a developing or developed country as the reference economy. However, to isolate the effects of emigration of high skilled workers in the innovation process, we consider that all parameters of the model are the same for both countries, except the steady-state value for aggregate productivity. We assume that the steady-state value for TFP is larger in the destination country with respect to the sending country. In particular, we assume that TFP in the destination country is A ¯ D = 1.50 , and that TFP in the sending country is A ¯ S = 1.00 .[5] This ensures the existence of a wage premium and an incentive to emigrate from the origin country to the destination country.

Calibrated parameter values are shown in Table 1. The discount factor is fixed to be 0.99 (using a quarterly basin), as it is standard in the literature. Depreciation rates for structures and equipment are taken from Greenwood, Hercowitz, and Krusell (1997) and Krusell, Ohanian, Ríos-Rull, and Violante (2000). Values are 0.05 for structures and 0.125 for equipment, using annual data. For quarterly data, the corresponding values are 0.014 for structures and 0.031 for equipment. The preference parameter representing the weight of consumption in the utility function is fixed to be 0.45.

Table 1

Calibration of the model

Parameter Definition Country D Country S
β Discount factor 0.990 0.990
δ e Equipment depreciation rate 0.031 0.031
δ s Structures depreciation rate 0.014 0.014
γ Consumption/leisure weight 0.450 0.450
α Elasticity of output to structures 0.120 0.120
ϕ Equipment/unskilled substitution 0.401 0.401
ρ Equipment/skilled substitution −0.495 −0.495
μ Unskilled share 0.413 0.413
θ Equipment share 0.553 0.553
η Innovation productivity 0.800 0.800
ω Proportion of STEM workers 0.117 0.117
σ STEM/non-STEM substitution 1.750 1.750
A ¯ Steady-state TFP 1.500 1.000
ρ A Autoregressive parameter TFP 0.950 0.950
σ A Standard deviation TFP 0.010 0.010

Technological parameters of the production function are taken mainly from Krusell et al. (2000). The elasticity of output with respect to structures is estimated to be 0.117 by Krusell et al. (2000) and 0.12 by Greenwood et al. (1997). Substitution of low-skill workers by new capital is argued to explain the low demand of non-college educated workers (Acemoglu, 1998, 2002; Autor, Katz, & Krueger, 1998; Autor, Katz, & Kearney, 2006; Beaudry & Green, 2005; Krusell et al., 2000; among others). Johnson (1997) estimated an elasticity of substitution between unskilled and skilled labor of 1.5. Hamermesh (1997) presented similar estimations. Krusell et al. (2000) reported estimates of 1.67 for the elasticity of substitution between unskilled and skilled labor (or, similarly between unskilled labor and equipment), and an estimated substitution elasticity between skilled labor and equipment of 0.67. These estimates imply that ρ = 0.495 and that ϕ = 0.401 .

The weight μ and θ in the CES nestings of the production function are taken from Lindquist (2004), who calibrate these parameters to be μ = 0.413 , and θ = 0.553 . Peri et al. (2015) estimated an elasticity of TFP to the number of STEM workers of 2.75. Based on that estimation, the innovation productivity parameter is fixed to be 0.8. The proportion of STEM workers over total employment is around 6.2% for the US, and the total skilled workers represents around 52% of total employment. Combining both figures we obtain that the proportion of STEM workers with respect to skilled workers is 0.117. Finally, the elasticity of substitution between STEM and non-STEM college educated workers, following Peri et al. (2015) is fixed to be 1.75, with estimates values in the literature between 1.5 and 2.5.[6]

4 TFP Shock

In this section, we present some simulations to show the dynamics of the model economies via impulse-response functions to an aggregate productivity shock. This first exercise considers the case of an exogenous idiosyncratic positive neutral shock to each economy, represented by an increase in TFP, A t . This standard technological shock is studied in most real business cycle models and so it is used as a benchmark to test the dynamic properties of the model economy. When studying the dynamics of the response of the economies to technological shocks, we assume that the immigration rate remains constant and that the migration policy is endogenously determined. In this context, a change in the migration cost reflects the pressure of immigration. This is justified by the fact that the number of (legal) immigrants is not endogenous determined by the model, but it is a variable determined by the migration policy.

We assume that TFP increases by one standard deviation on impact. As expected, this shock raises output on impact, as more output is produced for given factor inputs. When the shock occurs, private investment also increases in the period, given that the shock reduces the marginal cost of capital accumulation. As a consequence, capital stock also increases in response to the rise in its productivity, increasing the persistence of output to the shock. These changes in output and physical capital lead to a gradual increase in consumption above its steady-state. Thus, the overall effects of this shock in our theoretical framework are the same (from a qualitative point of view) than in the standard real business cycle model, in which a rise in output, investment, consumption, and capital stock (both structures and equipment) in response to the shock is observed. Additionally, to the standard results, the model indicates that the demand for unskilled workers reduces and increases the demand for skilled workers in the country hit by the productivity shock. This would justify a relaxation of the migration policy to attract high-skilled workers from abroad.

When looking at the migration’s decision, additional effects are observed. A positive productivity shock in the sending country reduces the number of native workers that want to emigrate to the destination country. The most important implications can be found in the response of wages, which are assumed to represent labor productivity. The positive aggregate productivity shock has a positive effect on the number of skill workers but reduces the number of unskilled workers. This is due to the assumption of capital-skill complementarity used to model the production function. In this context, there is a reallocation of investment between structures and equipment, which increases the demand of skilled workers and reduces the demand of unskilled workers. On the other hand, the effects of this shock on wages are positive for all types of workers. Finally, the model’s dynamic shows that the cost of migration must be increased to maintain constant the proportion of immigrants. This means that migration policy should be reinforced in the case of a rise in productivity, as this shock generates more incentives to emigrate for workers in the origin country.

Figures 1 and 2 plot the effects of a positive productivity shock in the destination country (for the sending country, results are similar, except for migration pressure which moves in the opposite direction). We observe how this positive shock increases skilled labor, both STEM and non-STEM college educated labor. Change in the unskilled labor is not significant. Given the rise in aggregate productivity, all wages for the three types of workers increase in response to the shock, increasing the wage premia of both skilled relative to unskilled labor and for STEM relative to non-STEM college educated labor. Finally, we obtain a measure of migration pressure, by calculating the change in migration cost required to maintain the number of immigrants.

Figure 1 
               Impulse-responses to a positive aggregate productivity shock (I).
Figure 1

Impulse-responses to a positive aggregate productivity shock (I).

Figure 2 
               Impulse-responses to a positive aggregate productivity shock (II).
Figure 2

Impulse-responses to a positive aggregate productivity shock (II).

5 STEM versus Non-STEM Wage Premium

An important issue widely studied by the literature related to the effects of immigration is its impact on wages and employment conditions for native workers in the destination country. The model presented in this article produces several results regarding the effects of emigration on labor markets in both, destination and sending countries, in terms of changes in factor inputs and wage inequality.

First, as expected, all three types of wages (those for STEM, non-STEM college educated, and non-college educated workers) are higher in the destination country compared to wages for the three types of workers in the country of origin. Since the model assumes that aggregate productivity is higher in the destination country, this also implies that wages in this country are higher than the equivalent wage for each type of worker in the country of origin. This creates an incentive for all types of workers to emigrate from their countries to higher productivity countries. Nevertheless, as it is assumed by the model, the number and the type of immigrants will depend on the cost of migration, which includes the migration policy implemented by the destination country. In the benchmark calibration of the model, wages for unskilled workers in the destination country are lower than wages for the skilled workers in the sending country. However, depending on the calibration of the model it is possible to produce situations in which wages for unskilled workers in the destination country are higher than the wage for skilled workers (both STEM and non-STEM college educated) in the origin country.

Second, the model produces a wage premium for skilled workers with respect to unskilled workers. This is a standard result obtained in the literature, reinforced by the assumption of capital-skill complementarity. As it is pointed out by Krusell et al. (2000), skill-biased technological change is the main factor explaining the rise in the skill premium of skilled workers relative to that of unskilled workers. Katz and Murphy (1992), analyzed changes in the US wage structure from 1963 to 1987 and they found that part of the divergence in wage structure changes across countries was due to skill-biased technological changes, since skilled workers become a key factor of technological revolution. Acemoglu (1998) considered that new technologies are not complementary to skills by nature, but by design. In this context, the rise in the supply of skills reduces the skill premium in the short run, but then it induces skill-biased technological change, which leads to a rise in the skill premium in the long run. Our model is consistent with those findings when there is a rise in the number of skilled immigrants, as we will show in the next section.

Third, a novel result obtained from the model is that the wage premium for skilled workers relative to unskilled workers is larger in the destination country than in the sending country. This implies that wages inequality is a factor mainly driven by aggregate productivity, and hence, productivity growth will increase the skill premium across countries. This result has important implications for the emigration process at a global level, as that implies the existence of more monetary incentives to migrate for STEM workers compared to that of non-STEM college educated workers.

Fourth, we obtain that the existence of a wage premium of STEM workers relative to non-STEM college educated workers. This wage premium is given by expression (13), where the wage differential depends on the relative quantity of each type of labor and on the technological parameter of the innovation process and on the parameter representing the elasticity of substitution between STEM and non-STEM college educated workers. That result is consistent with the empirical evidence, where the average wage for STEM workers is larger compared with that of non-STEM workers with similar levels of education.[7]

Finally, a major finding is that wage premium for STEM workers relative to non-STEM college educated workers is higher in the destination country than in the country of origin. This result means that the difference in aggregate productivity across countries is an additional factor explaining the wage premium for STEM versus non-STEM college educated workers. This is consistent with the results obtained previously, indicating that the incentives to emigrate to high productivity countries is larger for STEM workers than for non-STEM college educated workers. These findings are of particular interest to be considered when designing migration policies in both the hosting and the origin countries.

6 Migration Policy Shocks

Finally, we study the effects of changes in the migration policy implemented by the destination country where only skilled workers are allowed to migrate. We consider that modifications in migration policy are represented by changes in the migration cost, M t . The migration cost would capture both a quantitative migration policy that limits the number of immigrants, and a qualitative migration policy allowing only some types of skilled workers to migrate. Having those in mind, migration costs are assumed to be exogenously determined, and two types of migration policies can be considered. First, we consider a relaxation of migration policy that allows the entrance of a great number of high skilled workers, both STEM and non-STEM (i.e., a quantitative migration policy). Second, we study the effects of a migration policy designed to attracting only STEM workers (i.e., qualitative migration policy). The calibrated model can be used to assess the extent to which the changes in the migration policy affect labor markets and productivity in both countries.

We start by studying a relaxation of migration policy for all skilled workers. This will increase the number of skilled immigrant labor force in the destination country, reducing the number of skilled workers (both STEM and non-STEM college educated) in the country of origin. As a first result, we observe a positive effect on final output in the destination country and a negative effect on output in the origin country. This is a direct consequence on the rise in labor inputs in the destination country, and to the reduction in skilled labor inputs in the sending country. Figures 3 and 4 plot the transition dynamics for the selected variables to a relaxation in the immigration policy implemented by the destination country. As we can observe, there is a sudden drop in output in the sending country and a sudden rise in output in the destination country as the model assumes that migration is an instantaneous process. After this initial adjustment, output converge (increasing in the destination country and reducing in the sending country) to the new steady-state. In quantitative terms, the relative gain in output in the destination country is lower than in the origin country. However, the final effect is a net world gain, given that output in the destination country is higher than in the origin country. Therefore, international labor mobility of highly skilled workers increases total world output but at the cost of a reduction of output in the sending country. Nevertheless, this result must be interpreted with caution, as the theoretical framework developed here does not consider other factors, such as remittances, circular migration, and knowledge transfers, which are expected to have a positive effect on production in the country of origin.

Figure 3 
               Transition dynamics to a relaxation in migration policy (I).
Figure 3

Transition dynamics to a relaxation in migration policy (I).

Figure 4 
               Transition dynamics to a relaxation in migration policy (II).
Figure 4

Transition dynamics to a relaxation in migration policy (II).

As a rule, wages increase in the destination country and reduce in the sending country. This is true for all three types of workers and implies that international labor mobility of highly skilled workers also affects wages for unskilled workers. Interestingly, wages for skilled workers reduce in impact in the destination country and increase in impact in the country of origin just reflecting changes in productivity. However, after the initial negative effects, we observe a recovery in wages, increasing in the long run with respect to the initial steady-state in the destination country. In the country of origin, we observe the opposite response. After an initial positive impact, as the supply of skilled labor is reduced, the response is negative, producing a reduction in wages in the long run as productivity decreases. An important result is that wages for STEM workers increase more than that of non-STEM college educated workers, enhancing the wage premium between both types of occupations in the destination country. The opposite result is observed in the country of origin. This result indicates that the higher the number of STEM workers, the higher the level of innovations, which in turn implies higher wages for STEM workers. Therefore, the model predicts not only an increase in the wage premium of skilled workers related to unskilled workers, as shown by the literature, but also an increase in the wage premium of STEM workers related to non-STEM college educated workers, as innovation is one of the key factors fostering productivity.

On the other hand, total skilled labor in the destination country increases with the relaxation of the migration policy. This is expected, as immigrants are high skilled workers. However, we observe that the response is positive in impact given the instantaneous entry of new workers, but negative subsequently. Nevertheless, the long run impact is a rise in skilled labor. The negative response of skilled labor after the initial positive impact is related to the response of native skilled labor to the entry of skilled immigrants. In fact, the model predicts a reduction in the working hours by native workers, an effect also found in some empirical works. By contrast, unskilled labor is not affected in any country. This means that migration of skilled workers does not have consequences, on the quantity of unskilled labor, although unskilled wages are affected depending on changes in aggregate productivity. Therefore, in this case the model predicts a loss of skilled labor as native skilled workers in the destination country are partially substituted by skilled immigrants from the country of origin.

Finally, we simulate the effects of a migration policy designed to attract only STEM workers from abroad. In this case, the relaxation in migration policy only affects foreign STEM workers. This is intended to represent, for example, the H-1B visa program specifically designed to allow access to the US of foreign STEM workers. Results are qualitatively similar to the case of a migration policy change affecting all skilled workers, but the quantitative effects are reinforced as this migration policy generates additional gains in productivity, sharing similar effects to a positive TFP shock. Transition dynamics are not shown for this experiment, as they resemble the previous case. However, two important differences can be observed. First, the quantitative impact on all variables is larger than when the migration policy allows both STEM and non-STEM college educated workers to emigrate. This is a direct consequence of the higher impact of this type of workers on aggregate productivity through the production of innovations. Second, the negative impact on native STEM workers is of similar magnitude to the previous case. This result can be explained by the fact that STEM workers contribute to increase productivity through two channels: a direct channel by increasing the level of skills for production and another channel through the production of innovations, which is an additional factor of aggregate productivity. A conclusion that arises from this result is that a specific migration policy designed to attract STEM workers, does not crowing-out native employment in these occupations in a greater extent than a more general migration policy to attract skilled workers.

7 Conclusion

This article has studied the implications of high skilled worker migration for both receiving and sending countries, focusing on the role of STEM workers. For this goal, we have developed a two-country DSGE model. Our main concern has not directly focused on the (potentially negative) effects of STEM migration in the sending countries (the so-called “brain drain”), neither in the (potentially positive) effects of STEM migration in the hosting countries (the “brain gain”), but on the integrated and global effects on economic growth provoked by a significant increase in international skilled worker movements. In our experiments, the number of STEM migrants allowed by a particular immigration policy, should be understood as a proxy of the cumulative effect of an appropriate set of policies (affecting educational, social, and inclusion policies, together with labor measures) aimed to encourage the incorporation of high-skilled workers to STEM-oriented tasks.

The main contribution of the article is that specific migration policies to attract foreign STEM workers, not only increase output by increasing the level of human capital, as for non-STEM workers, but also has effects similar to a positive aggregate productivity shock by increasing innovation. Our results show that specific productivity shocks to each country provok a change in the incentives to migrate. A positive aggregate shock in the destination country increases the incentive to migrate from the origin country, whereas a positive productivity shock in the origin country reduces those incentives. Additionally, the productivity shock increases the wage differential of STEM workers related to non-STEM college educated workers. We found the existence of a wage premium to skilled workers related to unskilled workers, but also a wage premium from STEM workers related to non-STEM workers. This result can be interpreted as the existence of more incentives for migration of STEM workers than for non-STEM workers. One important property of the model economy developed in the article is that it can be used to simulate a change in the migration policy implemented by the destination country. A relaxation of the migration policy to allow a larger number of skilled workers increases output in the destination country but has a negative effect on the sending country’s output. Total skilled workers increase in the destination country, but there is a partial substitution of native skilled workers, without any effects on the quantity of unskilled workers.

As the most obvious policy implications, we could say that our results would support economic policy recommendations suggesting the promotion of new technologies oriented to favor technological intensive educational policies, immigration policies attracting STEM workers, and a proper combination of investment in equipment and structures compatible with the social capability of population.

Acknowledgements

We would like to thank three anonymous reviewers for very useful comments and suggestions on a previous version of the manuscript. Part of this project were developed while Anelí Bongers was visiting the Department of Economics at the Universidad de Castilla-La Mancha, whose hospitality she gratefully acknowledges. Anelí Bongers and José L. Torres acknowledge financial support from the Spanish Ministry of Science, Innovation and Universities through grants ECO-2016-76818-C3-2-P and PID2019-107161GB-C33. Carmen Díaz-Roldán acknowledges financial support from the Spanish Ministry of Science, Innovation and Universities through grant ECO-2016-78422-R. Anelí Bongers acknowledges financial support from Junta de Andalucía through grant UMA2018-FEDERJA-135.

  1. Conflict of interest: Authors state no conflict of interest.

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Received: 2021-09-30
Revised: 2021-12-23
Accepted: 2022-01-06
Published Online: 2022-03-29

© 2022 Anelí Bongers et al., published by De Gruyter

This work is licensed under the Creative Commons Attribution 4.0 International License.

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