# Emigration, Immigration, and Skill Formation: The Case of a Midstream Country

Authors: Kenji Kondoh
Journal: International Journal of Population Research
 (2014)

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## Abstract

This study theoretically investigates the economy of a small country that exports skilled labor to higher developed countries and simultaneously imports unskilled labor from lower developed countries. Compared with the free immigration case, if this country adopts an optimally controlled immigration policy by imposing income tax on immigrants to maximize national income, skills formation is negatively affected and the number of domestic unskilled workers increases. Moreover, under certain conditions, we can assert the counter-intuitive possibility that the wage rate of domestic unskilled workers may decrease but that of skilled workers may increase owing to the restriction of foreign unskilled workers.


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## Body

## 1. Introduction

The word “international migration” usually refers to labor inflows for higher developed countries (HDCs) such as Germany, Japan, and the United States. For lower developed countries (LDCs) such as Bangladesh, Cambodia, and most African countries, migration implies an outflow of labor. Most of the economic literature has focused on mutual relationships between the source and host countries and studied the effects of international migration on the economies of those countries. However, globalization in the more recent past has resulted in several new types of international migration. In observing the recent expansion of multilateral economic integration between countries at various phases of development, we recognize that several medium developed countries (MDCs) are playing a new role in the international labor market. These MDCs export labor to HDCs and, simultaneously, import labor from LDCs. In other words, these countries are coincidentally host as well as source countries and are at the midstream of international labor flows.For example, the Romanian economy is placed almost precisely between those of HDCs such as Belgium, Germany, and the Netherlands and LDCs such as Albania, Moldova, and Ukraine1. Until 2007, Romania was excluded from a large economic bloc of developed countries, the European Union (EU), and thus, free mobility of goods and factors was not permitted. Hence before 2007, despite of relatively lower wage rates and limited job opportunities, high levels of migration from Romania to the EU did not occur. When the EU expanded in 2007, Romania was permitted to join the bloc and its local economy was successfully integrated into the EU. Romania started to enjoy rapid economic progress by attracting foreign investment and exporting workers to Germany, Italy, and Spain. Remittances enable those left behind to consume several types of modern manufactured goods produced only in the developed countries2. The labor market of the country has undergone drastic changes owing to FDI inflows, which create job opportunities, as well as the outflow of domestic workers. A key problem of this new economic wave is that quick changes have caused serious labor shortages in Romanian urban areas. To maintain its economic performance, Romania started to introduce Chinese workers from the spring of 2008, although their employment is limited to permitted firms. As of 2013, more than 3,000 Chinese workers are still employed in Romania, although several workers returned to China because of the 2008 global recession sparked by the collapse of Lehman Brothers.Another example of an MDC in the international labor market is Thailand3. In 2009, about 150,000 relatively skilled Thai workers went to Taiwan and countries in the Middle East for job opportunities, while the country had a large inflow of lower skilled workers, amounting to 1300 thousand from Cambodia, Laos, and Myanmar. As seen by this substantial labor inflow, the government of Thailand has been ineffective in controlling the number of foreign workers. The government took the only option available and decided to approve numerous illegal workers by permitting their employment. Since 2006, immigration policy of Thailand has changed. Now immigrants are required to submit documents issued in their home countries that establish their nationalities. This new immigration policy still includes several points but Thailand has nevertheless started to introduce an optimally controlled immigration policy, which is regarded as the most important and urgent issue in the country4.A similar case is seen in Mexico. More than 25 million workers migrate from Mexico to the United States, while southern Mexico is simultaneously faced with immigration from Central American countries such as Guatemala. Those immigrants’ final destinations are often the United States or Canada. Thus, to them, Mexico serves as a transit country until they find good opportunities elsewhere5.Numerous theoretical studies on the economic effects of international migration employ two-country models or small-country models. However, no studies consider the economies of midstream countries that face both outflows and inflows of workers and need to introduce immigration and emigration policies simultaneously.One pioneering study is that by MacDougall [1], who studies the gains from free factor movement by means of a simple two-factor, two-country, one-good model. He finds that, even though free factor movement might be best for the global economy, most countries adopt several types of policies restricting such movement to maximize domestic welfare. The choice between an optimally controlled labor import policy and a capital export policy is investigated by Ramaswami [2] in his seminal study that is an extension of MacDougall [1]; several studies follow as extensions to Ramaswami [2]6.With regard to immigration policies, Djajic [3] studies the economic effects of qualitative restriction policies on legal immigration, while Kondoh [4] studies illegal immigrants, in which illegal workers optimally choose not to legalize their employment status despite having the option to do so in due course, which is a minor extension of Djajic’s study. Applying a three-country model—two developed countries and one developing country—Coniglio and Kondoh [5] studied the effects of economic integration between countries with heterogeneous immigration policies—one country adopts a qualitative restriction policy while another adopts a quantitative restriction policy. However, no studies consider the economies of midstream countries that face both outflows and inflows of workers and need to introduce immigration and emigration policies simultaneously.As the case of Thailand demonstrates, the most important issues for such midstream countries affected by international migration are to control brain drain caused by outflow of skilled workers as well as the immigration of LDCs’ unskilled workers. Well-controlled unskilled workers’ immigration may result in positive effects on the economic welfare of the midstream country even though it may cause negative effects on the wage gap between domestic skilled and unskilled workers. This study adopts a two-factor, three-country model with one good, following MacDougall [1]. As only one good is produced in each country, there is no trade between countries. The two factors are skilled and unskilled labor and their endowments are flexibly changeable by skill formation. The three countries comprise an HDC, LDC, and MDC. Using this framework, we investigate the economic effects of immigration restriction policies on the number of domestic skilled/unskilled workers, the number of foreign unskilled workers, and economic welfare (as measured by national income). We compare two different cases: free immigration (or out of control immigration) and optimally controlled unskilled workers’ immigration.The main findings are as follows. Compared with the case where free immigration is allowed, if the MDC adopts an optimally controlled immigration policy and imposes income tax on immigrants to maximize national income, skill formation is negatively affected and the number of domestic unskilled workers increases. Moreover, under certain conditions, we can assert the counter-intuitive possibility that the wage rates of domestic unskilled workers may decrease but that of skilled workers may increase owing to the restriction of foreign unskilled workers. This result occurs in case that the decreasing number of domestic skilled workers caused by skill formation effect dominates the decreasing number of unskilled workers which is the sum of decreasing unskilled immigrants and increasing domestic unskilled workers.The remainder of this paper is organized as follows. In Section2, we present the model. Comparative static analyses are performed in Section 3, while Section 4 presents concluding remarks.


## 2. A Simple Three-Country Model of International Migration

### 2.1. Production and Wage Rates

We assume the manufacturing industry of countryB, a medium developed country (MDC), is labor intensive. We assume a relatively scarce role for capital in the production of this country, with capital being completely substituted by skilled workers. Therefore, similar to, for example, Chao and Yu [6], the primary factors of production in countryB are two types of labor: skilled workers (S) and unskilled workers (U). For full employment, the following condition needs to be satisfied:
(1)LBU+LBS=L-B,
where L-B denotes fixed labor endowment in countryB. However, note that the distribution of the two types of workers is determined endogenously by solving the individual’s lifelong income maximization problem; thus, the two factors are substitutable in production, as ordinarily in the case of capital and labor. To simplify our analysis, let us specify the production function as follows:
(2)XB=LBULBS-a2(LBU)2-b2(LBS)2,
where LBU and LBS are the number of domestic unskilled and skilled workers, respectively, in countryB7. We assume that the following conditions are satisfied before and after international migration: 0<a<LBS/LBU and 0<b<LBU/LBS, which are necessary to obtain positive marginal products of labor in both sectors. Now we have the following properties under perfect competition in both factor markets: ∂XB/∂LBS=LBU-bLBS=wBS>0, ∂XB/∂LBU=LBS-aLBU=wBU>0, ∂2XB/∂(LBS)2=-b<0, ∂2XB/∂(LBU)2=-a<0, and ∂2XB/∂LBS∂LBU=1>0, where wBS and wBU denote the wage rates of skilled and unskilled workers, respectively, in countryB, while the price of the products is taken as a numeraire. Without loss of generality, we assume
(3)LBU>1+b1+aLBS,
which implies wBS>wBU in equilibrium.In contrast, we assume that in the highly developed country (HDC), countryA, the manufacturing industry is capital intensive, with the primary factors of this country being capital and skilled workers. Here, we emphasize a difference from the case of the MDC, in the existence of fixed legal minimum wage rates for workers employed in countryA: w-AS(>wBS)8. Those workers are treated equally to domestic workers in countryA.Finally, in a lower developed country (LDC), countryC, the main industry is agriculture. The primary factors of production are land and labor, while all workers are unskilled. Similar to the case of countryB, we specify the production function as follows:
(4)XC=TCLCU-a′2(LCU)2-b′2TC2,
where LCU and TC denote the number of unskilled workers and fixed endowment of land, respectively, in countryC. We also assume perfect competition and full employment in this country. Under the assumption of a sufficiently large fixed labor endowment, L-CU, we can assert wBU>wCU in autarky, where wCU is the competitive wage rate of countryC.


### 2.2. Brain-Drain Migration from CountryB toA

Assume that each individual in countryB is identical and survives for the period T. The wage rate of an unskilled worker in countryB, wBU, is low and, for simplicity, we assume that income is spent entirely on consumption and not saved for sustaining future consumption. In other words, the desired minimum level of consumption is, by assumption, lower or equal to wBU. On the other hand, the income of a skilled worker is higher than that of an unskilled worker; moreover, some skilled workers have the opportunity to migrate to countryA legally for employment at a fixed higher wage rate. Thus, each individual in countryB intends to be a skilled worker at the beginning, but this requires spending for the education cost of a specific human capital, μ. At age τ(0<τ<T), the individual finishes accumulating the required level of skills and will then be employed as a skilled worker. The following condition should be satisfied in equilibrium in which nobody has an incentive to invest in human capital in order to be a skilled worker anymore:
(5)[p(w-AS-γ1)+(1-p)wBS-wBU][T-τ]-μ=0,
where γ1 is the fixed trip cost fromB toA and p is the rate of countryB’s skilled workers being employed in countryA, which satisfies the following relationship, p=LABS/LBS9. For simplicity, we assume no intertemporal discount factor.


### 2.3. Unskilled Workers’ Migration from CountryC toB

Assume that countryB confronts the inflow of unskilled foreign workers from countryC, the neighboring LDC. Following the case of Thailand, we assume free immigration. We call this benchmark case as Case 1. After several immigration challenges faced by the government, countryB succeeds in controlling the optimal number of immigrants to maximize its national income. We call this Case 210.First, we consider Case 1. As there are no restrictions on migration, workers migrate from countryC to countryB until there is no income gap between the two countries. Then, the number of immigrants, LBCU, should satisfy the following condition:
(6)(1-p)LBS-a(LBU+LBCU)=TC-a′(L-CU-LBCU).In Figure1, which is frequently applied to explain MacDougall’s model,O andO* denote the origin point of countryB and countryC, respectively. The vertical line shows the value of marginal products of labor in countriesB andC, while the horizontal line shows labor inputs. The distancesOR andRO* denote LBU and L-CU, respectively; therefore, the distance betweenO andO* equals the total endowment of unskilled workers of both countries.Figure 1
Unskilled workers’ immigration to countryB.In Case 1, because of the arbitrage condition between countries, the number of immigrants fromC toB is equal to the distanceRN. Then, considering that the national income (NI) of countryB is equal to GDP minus immigrants’ income, NI can be expressed by the areaOGEDR:
(7)NIB1=a2(LBU+LBCU)2+LBU[(1-p)LBS-a(LBU+LBCU)],
and by applying (1) and (6), NIB1 can be expressed as a function of LBS11.Second, in Case 2, immigrants confront restriction policies imposed by the government of the host country. We assume that individuals are risk-neutral when they decide to migrate illegally. Considering that developed countries usually accept the entry of sightseeing travelers and a considerable number of illegal workers camouflage themselves as such at borders, we assume no restriction of entry into countryB. Illegal immigrants are assumed to be well-disguised as domestic workers but the government ofB makes a political effort to reduce illegal residency via internal enforcement policies. This means that an illegal worker, if detected while working, is fired and deported. We let ρ∈[0,1] denote the probability of detection in every period and let LBCU denote the number of succeeded illegal immigrants. The probability of detection is known to potential illegal migrants and is negatively related to the total number of aggregate illegal immigrants (both succeeded and failed) from countryC, LBCU/(1-ρ). As the government’s efforts to reduce illegal immigrants remain constant, the probability of detection for an illegal worker is not only a decreasing function of the total number of aggregate illegal workers but also a decreasing function of succeeded illegal immigrants12. Let the penalty cost that an illegal immigrant should pay in the case of detection, θ, be constant. In equilibrium, in each period, the expected income of illegal migrants should be equal to that of those left behind:
(8)(1-ρ(LBCU))wBU+ρ(LBCU)(wC-θ)-γ2=wC,
where γ2 denotes the fixed trip cost fromC toB and we assume, for simplicity, that the travel cost of migration (and return) is null13.We consider a situation in which, given the skills accumulation of domestic workers, the number of illegal workers is determined endogenously by the government of countryB in order to maximize the economic welfare of its native population, the sum of domestic skilled workers’ income, unskilled workers’ income, and government income14. Government income consists of penalty charges paid by illegal workers who are detected. In Figure 1, this implies the optimal choice ofRM, the number of illegal workers, to maximize the areaOGABFR. This area can be expressed numerically as(9)NIB2=-(a′+a2)(LBCU)2+LBCU[(1-p)LBS-a(LB-LBS)-TC+a′LCU],
and the first order condition of the national income maximizing problem is
(10)∂NIB∂LBCU=-(2a′+a)LBCU+[(1-p)LBS-a(LB-LBS)-TC+a′LCU]=0.Making use ofwBS=wBS(LBS),wBU=wBU(LBS,LBCU), in Case 1, two endogenous variables LBS and LBCU are determined from the two equations (5) and (6), while in Case 2, these two variables are determined from (5) and (10), whilst the optimal level of θ is determined from (8). This completes the setup of the model.


## 2.1. Production and Wage Rates

We assume the manufacturing industry of countryB, a medium developed country (MDC), is labor intensive. We assume a relatively scarce role for capital in the production of this country, with capital being completely substituted by skilled workers. Therefore, similar to, for example, Chao and Yu [6], the primary factors of production in countryB are two types of labor: skilled workers (S) and unskilled workers (U). For full employment, the following condition needs to be satisfied:
(1)LBU+LBS=L-B,
where L-B denotes fixed labor endowment in countryB. However, note that the distribution of the two types of workers is determined endogenously by solving the individual’s lifelong income maximization problem; thus, the two factors are substitutable in production, as ordinarily in the case of capital and labor. To simplify our analysis, let us specify the production function as follows:
(2)XB=LBULBS-a2(LBU)2-b2(LBS)2,
where LBU and LBS are the number of domestic unskilled and skilled workers, respectively, in countryB7. We assume that the following conditions are satisfied before and after international migration: 0<a<LBS/LBU and 0<b<LBU/LBS, which are necessary to obtain positive marginal products of labor in both sectors. Now we have the following properties under perfect competition in both factor markets: ∂XB/∂LBS=LBU-bLBS=wBS>0, ∂XB/∂LBU=LBS-aLBU=wBU>0, ∂2XB/∂(LBS)2=-b<0, ∂2XB/∂(LBU)2=-a<0, and ∂2XB/∂LBS∂LBU=1>0, where wBS and wBU denote the wage rates of skilled and unskilled workers, respectively, in countryB, while the price of the products is taken as a numeraire. Without loss of generality, we assume
(3)LBU>1+b1+aLBS,
which implies wBS>wBU in equilibrium.In contrast, we assume that in the highly developed country (HDC), countryA, the manufacturing industry is capital intensive, with the primary factors of this country being capital and skilled workers. Here, we emphasize a difference from the case of the MDC, in the existence of fixed legal minimum wage rates for workers employed in countryA: w-AS(>wBS)8. Those workers are treated equally to domestic workers in countryA.Finally, in a lower developed country (LDC), countryC, the main industry is agriculture. The primary factors of production are land and labor, while all workers are unskilled. Similar to the case of countryB, we specify the production function as follows:
(4)XC=TCLCU-a′2(LCU)2-b′2TC2,
where LCU and TC denote the number of unskilled workers and fixed endowment of land, respectively, in countryC. We also assume perfect competition and full employment in this country. Under the assumption of a sufficiently large fixed labor endowment, L-CU, we can assert wBU>wCU in autarky, where wCU is the competitive wage rate of countryC.


## 2.2. Brain-Drain Migration from CountryB toA

Assume that each individual in countryB is identical and survives for the period T. The wage rate of an unskilled worker in countryB, wBU, is low and, for simplicity, we assume that income is spent entirely on consumption and not saved for sustaining future consumption. In other words, the desired minimum level of consumption is, by assumption, lower or equal to wBU. On the other hand, the income of a skilled worker is higher than that of an unskilled worker; moreover, some skilled workers have the opportunity to migrate to countryA legally for employment at a fixed higher wage rate. Thus, each individual in countryB intends to be a skilled worker at the beginning, but this requires spending for the education cost of a specific human capital, μ. At age τ(0<τ<T), the individual finishes accumulating the required level of skills and will then be employed as a skilled worker. The following condition should be satisfied in equilibrium in which nobody has an incentive to invest in human capital in order to be a skilled worker anymore:
(5)[p(w-AS-γ1)+(1-p)wBS-wBU][T-τ]-μ=0,
where γ1 is the fixed trip cost fromB toA and p is the rate of countryB’s skilled workers being employed in countryA, which satisfies the following relationship, p=LABS/LBS9. For simplicity, we assume no intertemporal discount factor.


## 2.3. Unskilled Workers’ Migration from CountryC toB

Assume that countryB confronts the inflow of unskilled foreign workers from countryC, the neighboring LDC. Following the case of Thailand, we assume free immigration. We call this benchmark case as Case 1. After several immigration challenges faced by the government, countryB succeeds in controlling the optimal number of immigrants to maximize its national income. We call this Case 210.First, we consider Case 1. As there are no restrictions on migration, workers migrate from countryC to countryB until there is no income gap between the two countries. Then, the number of immigrants, LBCU, should satisfy the following condition:
(6)(1-p)LBS-a(LBU+LBCU)=TC-a′(L-CU-LBCU).In Figure1, which is frequently applied to explain MacDougall’s model,O andO* denote the origin point of countryB and countryC, respectively. The vertical line shows the value of marginal products of labor in countriesB andC, while the horizontal line shows labor inputs. The distancesOR andRO* denote LBU and L-CU, respectively; therefore, the distance betweenO andO* equals the total endowment of unskilled workers of both countries.Figure 1
Unskilled workers’ immigration to countryB.In Case 1, because of the arbitrage condition between countries, the number of immigrants fromC toB is equal to the distanceRN. Then, considering that the national income (NI) of countryB is equal to GDP minus immigrants’ income, NI can be expressed by the areaOGEDR:
(7)NIB1=a2(LBU+LBCU)2+LBU[(1-p)LBS-a(LBU+LBCU)],
and by applying (1) and (6), NIB1 can be expressed as a function of LBS11.Second, in Case 2, immigrants confront restriction policies imposed by the government of the host country. We assume that individuals are risk-neutral when they decide to migrate illegally. Considering that developed countries usually accept the entry of sightseeing travelers and a considerable number of illegal workers camouflage themselves as such at borders, we assume no restriction of entry into countryB. Illegal immigrants are assumed to be well-disguised as domestic workers but the government ofB makes a political effort to reduce illegal residency via internal enforcement policies. This means that an illegal worker, if detected while working, is fired and deported. We let ρ∈[0,1] denote the probability of detection in every period and let LBCU denote the number of succeeded illegal immigrants. The probability of detection is known to potential illegal migrants and is negatively related to the total number of aggregate illegal immigrants (both succeeded and failed) from countryC, LBCU/(1-ρ). As the government’s efforts to reduce illegal immigrants remain constant, the probability of detection for an illegal worker is not only a decreasing function of the total number of aggregate illegal workers but also a decreasing function of succeeded illegal immigrants12. Let the penalty cost that an illegal immigrant should pay in the case of detection, θ, be constant. In equilibrium, in each period, the expected income of illegal migrants should be equal to that of those left behind:
(8)(1-ρ(LBCU))wBU+ρ(LBCU)(wC-θ)-γ2=wC,
where γ2 denotes the fixed trip cost fromC toB and we assume, for simplicity, that the travel cost of migration (and return) is null13.We consider a situation in which, given the skills accumulation of domestic workers, the number of illegal workers is determined endogenously by the government of countryB in order to maximize the economic welfare of its native population, the sum of domestic skilled workers’ income, unskilled workers’ income, and government income14. Government income consists of penalty charges paid by illegal workers who are detected. In Figure 1, this implies the optimal choice ofRM, the number of illegal workers, to maximize the areaOGABFR. This area can be expressed numerically as(9)NIB2=-(a′+a2)(LBCU)2+LBCU[(1-p)LBS-a(LB-LBS)-TC+a′LCU],
and the first order condition of the national income maximizing problem is
(10)∂NIB∂LBCU=-(2a′+a)LBCU+[(1-p)LBS-a(LB-LBS)-TC+a′LCU]=0.Making use ofwBS=wBS(LBS),wBU=wBU(LBS,LBCU), in Case 1, two endogenous variables LBS and LBCU are determined from the two equations (5) and (6), while in Case 2, these two variables are determined from (5) and (10), whilst the optimal level of θ is determined from (8). This completes the setup of the model.


## 3. Multilateral Economic Integration

First, we consider Case 1. By differentiating (5) and (6) and considering that LBU+LBS=LB and that therefore dLBU also implies -dLBS, we derive the following equation:
(11)[ΨΦ1-p+a-(a+a′)][dLBSdLBCU]=[10]dμ+[-p0]dw-A+[-W0]dτ,
where λi≡(w-AS-wBS)(dp/dLBS)=(w-AS-wBS)LABS(LBS)-2>0, i=1,2,
(12)Ψ={(1-p)∂wBS∂LBS-∂wBU∂LBS+(w-AS-wBS)dpdLBS}(T-τ)={-(w-AS-wBS)LABS(LBS)-2}-(1-p)(1+b)-(1+a)-(w-AS-wBS)LABS(LBS)-2}(T-τ)<0,Φ={-∂wBU∂LBCU}(T-τ)=a(T-τ)>0,W=pw-AS+(1-p)wBS-wBU.The determinant of the matrix of the LHS of (11) is
(13)Δ1=(T-τ){(a+a′)[(1-p)(1+b)+(1+a)+λ1]iiiiiiiiiiii-a(1-p+a){(a+a′)[(1-p)(1+b)+(1+a)+λ1]}>0.Similarly, for Case 2, from (5) and (10) we obtain
(14)[ΨΦ1-p+a-(a+2a′)][dLBSdLBCU]=[10]dμ+[-p0]dw-AS+[-W0]dτ.The determinant of the LHS of (14) can be expressed as
(15)Δ2=(T-τ){(a+2a′)[(1-p)(1+b)iiiiiiiiiiiiiiiiiiiiiiiiiiiii+(1+a)+λ2]-a(1-p+a){(a+2a′)[(1-p)(1+b)}>0.Under given parametersw-AS,μ,τ, and γ1, we can numerically express Figure 2 that shows the schedules in (LBS,LBCU) dimension15. Considering that dp/dLBS=-LABS(LBS)-2<0, we can ascertain that line G6 corresponds to (6) in Case 1 and that line G10 corresponds to (10) in Case 2, respectively, as convex functions of LBS. In addition, considering that dλ/dLBS=-LABS(LBS)-2{2(w-AS-wBS)(LBS)-1+(1+b)}<0, we can ascertain that line F corresponds to (5) and, in Case 1 as well as Case 2, is a concave function of dLBS. Thus, in equilibrium, in Case 2, we can conclude smaller LBS and LBCU with larger LBU. That is, in the case where countryB enacts an immigration restriction policy, there will be less domestic skilled labor, less unskilled labor from countryC, and more domestic unskilled labor. Again, as both equilibrium points in Figure 2, E1 and E2, are on line F, the slope of which is dLBCU/dLBS=((1-p)(1+b)+(1+a)+λi)/a>1 and d{(1-p)LBS}/dLBS=1, we can conclude that both the number of skilled workers and unskilled workers in countryB are smaller in Case 2 than that in Case 1. This implies that an immigration restriction policy adopted by countryB will have negative effects on skill formation in that country.Figure 2
The determination ofLBS and LBCU.Furthermore, ifa<LBS/LBU<1, which implies that the number of domestic skilled workers is less than domestic unskilled workers, because of dLBCU/dLBS>2 which implies d[LBCU+LBU]/dLBS>1, we can conclude that the marginal product of skilled workers—equal to the wage rate of those workers in countryB—is smaller in Case 2 than that in Case 1. By contrast, the wage rate of unskilled workers in countryB is larger in Case 2 than that of Case 1. Thus, under an optimally controlled restriction policy, the wage rate of skilled workers is lower than that under free migration.On the other hand, if conditiondLBCU/dLBS<2 which implies d[LBCU+LBU]/dLBS<1 is satisfied, as we have dwBS=(dLBU+dLBCU)-bdLBS=[d(LBU+LBCU)/dLBS-b]dLBS and dwBU=dLBS-a(dLBU+dLBCU)=[1-a(d(LBU+LBCU)/dLBS)]dLBS from (2), depending on the magnitude of parameters, the wage rates of skilled workers might be larger than those under free migration while those of unskilled workers might be smaller under an optimally controlled restriction policy16.This counter-intuitive result, which implies that a restriction of the inflow of unskilled foreign workers results in wage reduction for domestic unskilled workers, could be caused by a change in domestic workers’ optimal choices in skills formation. In any case, by restriction, the number of illegal unskilled workers decrease and that dominates both the numbers of increasing domestic unskilled workers and decreasing domestic skilled workers. Thus in total, unskilled workers in countryB should decrease. But in case that the dominated skill formation effect is sufficiently not so small, decreased number of skilled workers could be larger than that of unskilled workers which is the sum of decreased foreign immigrants and increased domestic unskilled workers. This concludes that unskilled/skilled ratio of workers in countryB could increase after restriction17. Figure 3 shows this case. Finally, we find that as countryB optimally controls the number of immigrants—free immigration remains an option—by imposing taxes, its economic welfare is larger in Case 2; national income of this case equals the area O′G′A′B′F′R more than that in Case 1, areaOGEDR in Figure 3.Figure 3
The counter-intuitive case considering skill formation.With regard to comparative statics analysis, we obtainΔi(dLBS/dμ)<0, Δi(dLBCU/dμ)<0,Δi(dLBS/dw-AS)>0, Δi(dLBCU/dw-AS)>0, Δi(dLBS/dγ1)<0, Δi(dLBCU/dγ1)<0, Δi(dLBS/dτ)>0, and Δi(dLBCU/dτ)>0, in line with our ordinary intuition. Although the signs of changes in endogenous variables caused by increases in parameters are identical in both cases, the magnitudes of the effects should differ depending on the parameters.


## 4. Concluding Remarks

This study investigated the economy of a small country that exports skilled labor to higher developed countries and simultaneously imports unskilled labor from lower developed countries. Analysis results revealed that compared with the case of free immigration, if this country adopts an optimally controlled immigration policy by imposing income tax on immigrants to maximize national income, skill formation is negatively affected and the number of domestic unskilled workers increases. Moreover, under certain conditions, we can assert the counter-intuitive possibility that the wage rate of domestic unskilled workers may decrease but that of skilled workers may increase owing to the restriction of foreign unskilled workers. Therefore, the policy implication of this study is that, even though it yields lower national income, free immigration of unskilled workers might be better if the host country stresses skill formation of domestic workers.This study is based on a simple model that excludes international trade, FDI, and definite dynamic skill formation systems, in line with Djajic [3]. We also consider other types of immigration restriction policies such as quotas or permission for short period stays. Furthermore, we assume the source country to be somewhat passive, and we did not consider any interactions with countryC. Incorporating these issues could change our simple results; this remains a topic for future studies.



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