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A model for liberalizing nursing and trade
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Japan and the World Economy xxx (2018) xxx–xxx
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Japan and the World Economy journal homepage: www.elsevier.com/locate/jwe
A model for liberalizing nursing and trade Masao Oda* , Masayuki Okawa Department of Economics, Ritsumeikan University, Japan
A R T I C L E I N F O
Article history: Received 1 November 2016 Received in revised form 26 October 2017 Accepted 1 March 2018 Available online xxx JEL classifications: F13 F22
A B S T R A C T
This paper proposes a model for liberalizing nursing and trade and analyses the welfare effects of nurse and trade liberalizations. We show that the welfare effects of nurse liberalization depend on the income enhancing (I-E) and tariff revenue (TR) effects and that contrary to the conventional (Heckscher-Ohlin) model of capital imports the former is not always zero and the latter is not always negative and then provide sufficient conditions for nurse liberalization welfare enhancing. We also provide a necessary and sufficient condition for trade liberalization welfare enhancing. © 2018 Elsevier B.V. All rights reserved.
Keywords: Nurse liberalization Trade liberalization I-E effect TR effect
1. Introduction As a result of the Economic Partnership Agreements (EPAs), Japan started to accept foreign nurses. It started in 2008 accepting 104 nurses from Indonesia. At the end of 2014, the total number of nurses from Indonesia was 481 and that from the Philippines was 337. Further, we accepted 21 nurses from Vietnam in 2014.1 As the acceptance of foreign nurses began recently, the number of foreign nurses in Japan is still small. However, other OECD countries have already accepted many foreign nurses and the
* Corresponding author. E-mail addresses: [email protected] (M. Oda), [email protected] (M. Okawa). 1 Based on the programs of EPAs, these nurses are working at the medical facilities and preparing for the qualifying examination. They must pass it within three years and if not they must return to their countries. Some problems in the examination and the terms of stay have been solved. But one defect of the programs was that it does not require the understanding of Japanese beforehand. Accordingly, all candidates from Vietnam are required to pass the examination of Japanese, N3, before coming to Japan.
importance of nurse immigration has been recognized.2 Yet the economic analysis is scarce. The only work is Rutten (2009) and it deals with the output effects of medical immigration by the use of the Rybczynski theorem. No literature exists on the welfare effects of nurse liberalization.3 Today, international agreements on factor mobility including nurses are nested within the EPAs and the liberalization of nurse and trade is proceeding along with the EPAs. Is nurse liberalization welfare enhancing? If enhancing, by what factors and under what conditions? The purpose of this paper is to address these issues and provide an answer to these questions. Proposing a model for liberalizing nursing and trade, we show that the welfare effects of nurse liberalization depend on the income enhancing (I-E) and tariff revenue (TR) effects and that contrary to the conventional (Heckscher-Ohlin) model of capital imports the former is not always zero and the latter is not always
2 See a report of OECD, The Looming Crisis in the Health Workforce: How can OECD countries respond? (2008). 3 In contrast, many papers have been written on capital imports and welfare including seminal works such as Bhagwati (1973), Brecher and Diaz Alejandro (1977), Hamada (1971), and Uzawa (1969), among others. By the use of the conventional model they produced a wisdom; “Capital import under a tariff is always immiserizing”. But this wisdom is too pessimistic and far from the realities. A model that justifies the acceptance of foreign capital in a multi-dimensional framework was provided by Oda and Shimomura (2012).
https://doi.org/10.1016/j.japwor.2018.03.003 0922-1425/© 2018 Elsevier B.V. All rights reserved.
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negative and then provide sufficient conditions for nurse liberalization welfare enhancing. We also provide a necessary and sufficient condition for trade liberalization welfare enhancing. It will be shown that our model produces more general and optimistic results than the conventional one. Our study is related to the theory of distortions in growth and welfare literature. This theory says that when a distortion such as a tariff exists in an economy an increase in factors of production is not always welfare enhancing. A pioneering work within the realm of trade theory would be Bhagwati (1971). Based on this theory, the conventional model says that trade must be liberalized (a distortion must be removed) before the acceptance of foreign capital. In contrast, in our model, an increase in foreign nurse could be welfare enhancing under a tariff, so that trade need not always be liberalized before the acceptance of foreign nurse. The rest of the paper is as follows. In Section 2, we point out some stylized facts about nurse inflow in Japan and then set up a model for liberalizing nursing and trade. In Section 3, we consider the factors and conditions for welfare enhancement of nurse and trade liberalizations. Section 4 concludes. The Appendix confirms the stability condition of the model. 2. The model 2.1. Stylized facts We start by pointing out some stylized facts about nurse, nurse inflow, and nurse markets in Japan. First, nurse is an indispensable skilled labor specifically used in the medical care sector and the medical care service is a nontraded good. Therefore, it is necessary to provide a specific factor model with a non-traded good. The specific factor model was developed by Jones (1971) and has been used in many aspects of trade theory including factor mobility. Second, Japan has been negative to labor inflow, accepting only skilled labor in exceptional cases.4 This is the same in nurse inflow and we care about the benefits of Japanese nurses. As Giordani and Ruta (2011), we do not choose complete open or complete ban in nurse liberalization. Third, we have two types of nurses and two nurse markets; the Japanese nurses and foreign ones, and the markets for the Japanese nurses and for foreign ones. Two nurses are considered different in skills and two markets are separated. The market for the Japanese nurses is organized only by the Japanese and protected by the Japanese Nursing Association. Fourth, at the negotiations of EPAs, Indonesia and the Philippines required the emigration of nurses. In order to start EPAs, Japan decided to accept their nurses. A feature of this nurse inflow is that the Japanese government is paying a training (or education) subsidy. Fifth, there are labor abundant developing countries that supply nurses to Japan with low rate of returns. We regard them as a foreign country. Thus we totally have three kinds of nurses, three
4 In order to level up the competitiveness of the economy, the Japanese government decided, in 2011, to relax the conditions for the permanent stay of foreign skilled labors in science and technology sectors.
kinds of markets, and three rates of returns, where two nurses and markets are in Japan and one nurse and market are in the foreign country.5 2.2. Model setup We set up a model of nurse inflow and trade that reflects above facts. Assume two countries, host (domestic) and home (foreign). Let the country in question be the host country and assume that as a result of an EPA it liberalizes nurse and trade. It is a small open economy with three sectors; export (X), import (Y), and non-traded medical care (Z). We assume four factors; capital (K), unskilled labor (L), host nurse (Nh), and foreign nurse (Nf), where capital, unskilled labor, and host nurse are supplied domestically. Capital is a general factor used in all three sectors and unskilled labor is also a general factor used in both traded sectors. Domestic nurse is a skilled labor educated in the domestic country and used in the medical care sector.6 Foreign nurse is a semi-skilled labor used in the medical care sector. Thus the medical care is produced by capital and two types of nurses. The production functions are; X = X (Kx, Lx), Y = Y(Ky, Ly), and Z = Z(Kz, Nh, dNf), where d is a multiplicative parameter that captures the effects of training subsidy. Two nurses are assumed different in skills and two nurse markets are separated. Perfect competition and full employment are assumed. Choosing export good as the numeraire, denote the domestic relative price of imports by p. Also let q be the relative price of medical care determined in the domestic market. Under perfect competition, we have 1 ¼ cx ðr; wÞ;
ð1Þ
p ¼ cy ðr; wÞ;
ð2Þ
q ¼ cz ðr; nh ; nf Þ;
ð3Þ
where r is the rental rate of capital, w the wage rate of unskilled labor, nh the rate of returns to domestic nurse, and nf the rate of returns to foreign nurse. The right side of (1), (2), and (3) stands for the unit cost function of each good. Assume the domestic country imports Y under a tariff. Then, we have p ¼ p þ t;
ð4Þ
where p* is the fixed foreign relative price of imports and t the specific tariff rate. Given the supply of capital, unskilled labor, domestic nurse, and foreign nurse, the assumption of full employment produces cxr ðr; wÞX þ cyr ðr; wÞY þ czr ðr; nh ; nf ÞZ ¼ K;
ð5Þ
5 EPAs require that the rate of returns to foreign nurses in Japan must be equal to that of the Japanese nurses. But the reports of the Japanese Nursing Association and the Ministry of Health, Labor, and Welfare indicate that, at 2014, the average rate of returns to a Japanese nurse per month was about 330,000 yen, whereas that of Indonesian nurse in Japan was about 150,000 yen and that of Indonesian nurse in Indonesia was about 30,000 yen. The difference between former two is about two times while the difference between latter two is just five times. We have another difference; the difference in the passing rate of the qualifying examination. From 2010 to 2014, the average rate of passing of Japanese nurse was 90.1% while that of foreign nurse was just 7.3%. 6 We assume that the decision of an unskilled labor to be skilled or unskilled has been made in the previous stage. Skill formation has been taken up by Behrens and Sato (2010), Kar and Beladi (2004), and Stark and Zakharenko (2012). Recently, Sato and Yamamoto (2012) provided a model to explain how trade induces skill formation.
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cxw ðr; wÞX
þ
cyw ðr; wÞY
¼ L;
ð6Þ
cznh ðr; nh ; nf ÞZ ¼ Nh ;
ð7Þ
cznf ðr; nh ; nf ÞZ ¼ Nf ;
ð8Þ
where cxr ð¼ @cx =@rÞ is, for example, the unit demand for capital in X. To complete the model, we will introduce the revenue and expenditure functions. The revenue function is; R(1, p, q, Nh, dNf) = max XðK x ; Lx Þ þ pYðK y ; Ly Þ þ qZððK z ; Nh ; dNf Þ with respect to X, Y, and Z subject to full employment. R(1, p, q, Nh, dNf) is twice continuously differentiable, homogeneous of degree one and convex in prices and concave in factor supply. From this function, using the envelop theorem, we obtain: Rp = Y, Rq = Z, RNh ¼ nh , and RdNf ¼ nf with Rpp > 0, Rqq > 0, RNh Nh < 0, and RdNf dNf < 0. The cross partial derivatives Rpq and Rqp are continuous and Rpq = Rqp < 0. The signs of RNh dNf and RdNf Nh depend on whether two nurses are substitute or complement but our results are not affected by the relationships between two nurses. The expenditure function is; E(1, p, q, u) = min C x þ pC y þ qC z with respect to Cj subject to uðC x ; C y ; C z Þ ¼ u, where u() is a homothetic utility function of a representative resident in the domestic country assuming that the utility of foreign nurses is the same as that of the native residents, Cj the consumption of j th good (j = x, y, z), and u a target level of utility. E(1, p, q, u) is twice continuously differentiable, homogeneous of degree one and concave in prices and increasing in utility. From this function, using the envelop theorem, we obtain: Ep = Cy, and Eq = Cz with Epp < 0, and Eqq < 0. The cross partial derivatives Epq and Eqp are continuous and Epq = Eqp > 0. From these functions, we obtain Eð1; p; q; uÞ ¼ Rð1; p; q; Nh ; dNf Þ pNf t Nf þ tM;
ð9Þ
M ¼ Ep ð1; p; q; uÞ Rp ð1; p; q; Nh ; dNf Þ;
ð10Þ
Eq ð1; p; q; uÞ ¼ Rq ð1; p; q; Nh ; dNf Þ;
ð11Þ
where p is the rate of remittance, pNf the amount of remittance, t the rate of training subsidy, and t Nf the cost of training subsidy. The foreign nurses require both incentives to move to the host country and incomes to live there. Let n* be the rate of returns to nurses in the home country. Then, if p is greater than n* and less than nf, these requirements are satisfied. M is the quantity of imports and tM the tariff revenue. Eq. (9) is the budget equation that implies that the expenditure is equal to the sum of net income and tariff revenue.7 Eq. (10) shows that the quantity of imports is the excess demand for that product and (11) gives the equilibrium condition of the medical care sector. These three equations are added with the same number of variables; u, M, and q. We are paying a training subsidy. This subsidy is indispensable in nurse inflow and it works to increase foreign nurse through skill enhancement. To consider these facts, we specify d as a function of t . We assume that it (i) is linear in t , (ii) is 1 initially, and (iii) increases when t increases. Under these specifications, it could be
dðt Þ ¼ 1 þ at ;
3
where a is a parameter that captures the effectiveness of a training subsidy. A lapse of time is necessary to make the subsidy effective. We divide time into two: (i) short run (a = 0), and (ii) long run (a > 0). In (12), when a or t is zero, d = 1 and when both a and t are positive, d > 1. Eqs. (1) to (12) make up our model. It has twelve equations with the same number of variables. Given the exogenous variables; p*, p, t , t, Nh, Nf, K,L, and a the model determines twelve variables; p, r, w, nh, nf, X, Y, Z, u, M, q, and d.8 2.3. Equations of change The condensed version of the model consists of (9), (10), and (11) with variables u, M, and q. From these, by the use of (10), (11), and (12), we obtain Eu du ¼ nh dNh þ ðnf p t ÞdNf Nf dp þ Nf ðanf 1Þdt þ tdM;
ð13Þ
dM ¼ Epu du þ Adt þ Bdq RpNh dNh RpNf dNf aNf RpNf dt ;
ð14Þ
dq ¼ ðRqNh dNh þ RqNf dNf Equ du Bdt þ aNf RqNf dt ÞD1 ;
ð15Þ
where A = (Epp Rpp) < 0, B = (Epq Rpq) > 0, and D = (Eqq Rqq) < 0. These will play key roles on the welfare effects of nurse and trade liberalization. We also have: Eu > 0, Epu>0, and Equ > 0 if the utility function is homothetic. It is reasonable that RpNh < 0, RpNf < 0, RqNh > 0, and RqNf > 0. From (13), (14), and (15), we obtain ðnh tRpNh Þ ðEu tEpu Þ tB du ¼ dNh RqNh Equ D dq ðnf p t tRpNf Þ þ dNf RqNf Nf þ dp 0 Nf ðanf atRpNf 1Þ þ dt aNf RqNf tA þ ð16Þ dt: B Let the determinant of the coefficient matrix of the left side of (16) be D. Then it is: ðEu tEpu ÞD þ tBEqu . As proved in the appendix, D < 0. 3. The analysis 3.1. Nurse liberalization 3.1.1. I-E and TR effects Consider nurse liberalization first.9 Nurse inflow is a temporary immigration with following features that are not found in capital mobility. First, it is carried out exogenously to attain some noneconomic objectives such as the realization of EPAs. Second, the owners of nurse services have to move to the host country. Comparing with the conventional model, we will explore the factors and conditions for nurse liberalization welfare enhancing. Suppose the host country liberalizes nurse inflow at a given tariff rate. As native residents and foreign nurses live in the host country, a representative resident is a representative of both
ð12Þ
7 Since the rate of remittance is less than the returns to foreign nurses the expenditure includes the consumption of both native residents and foreign nurses.
8 By nature, p is an endogenous variable determined by the foreign nurses. But as we are interested in the effects of a change in the rate, we treat it here as an exogenous one. 9 The Japanese government is trying to increase the supply of Japanese nurses. Our model can analyze the welfare effects of an increase in domestic nurses.
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residents. Thus if the welfare of a representative resident increases it implies the welfare of both residents increases. From (16), we obtain i h @u=@Nf ¼ ðnf p t ÞD þ tðBRqNf DRpNf Þ D1 : ð17Þ In (17), the first term is the income enhancing (I-E) effect and the second term the tariff revenue (TR) effect. Consider the former first. This paper is the first to clarify the implications of this effect. We argue followings. First, it shows how the national income increases as a result of an increase in nurse inflow, so that we will name it as the income enhancing (I-E) effect. Second, it is necessary to revive this effect. This effect has been neglected in the conventional model of capital imports. Extant many papers including Brecher and Diaz Alejandro (1977) and Komiya and Amano (1972) used that model but they neglected it because it is zero. It is zero because that model assumes the maximum remittance and there exists no training subsidy. However, such remittance is a special case that does not occur in nurse inflow. In contrast, in our model this effect could take any signs. The implications of remittance and training subsidy will be taken up separately. Next, consider the TR effect. This shows how TR changes when the host country accepts foreign nurses. In the conventional model, it is negative. Why is it negative? This is due to the facts that it uses the Heckscher-Ohlin model and assumes that the host country imports a capital intensive good. Thus by the Rybczynski theorem, an increase in capital by a capital inflow increases the output of the capital intensive good, which in turn reduces imports, TR, and thus welfare. In contrast, in our model this effect is not always negative, so that trade need not always be liberalized first. Below, we show why the second term of (17) is the TR effect and takes any signs. From (14) and (15), setting du = dNh = dp = dt = dt = 0, we obtain dM ¼ Bdq RpNf dNf ;
dq ¼ ðRqNf dNf ÞD1 :
ð15aÞ
ð18Þ
From (18), we obtain
@M=@Nf ju¼const ¼ ðBRqNf DRpNf ÞD1 :
ð19Þ
When (19) is multiplied by t, it denotes the effects of an increase in Nf on TR under fixed utility.10 Therefore, the second term of (17) is the TR effect. Moreover, as D < 0, from (19), we obtain signðBRqNf DRpNf Þ ¼ signð@M=@Nf ju¼const Þ:
Lemma 1. The welfare effects of nurse liberalization depend on the I-E and TR effects. Proposition 1. (i) Under free trade, (nf p t ) > 0 is a sufficient condition for nurse liberalization welfare enhancing, (ii) if t > 0 and (nf p t ) > 0, then ðBRqNf DRpNf Þ < 0 is a sufficient condition for nurse liberalization welfare enhancing, and (iii) if t > 0, (nf p t ) > 0, and ðBRqNf DRpNf Þ > 0, then nurse liberalization is not always welfare enhancing. Following remarks are in order. Remark 1. We must consider cases where the I-E effect is not positive. When it is negative, under free trade nurse liberalization is always welfare reducing and under a tariff if the TR effect is positive and large enough nurse liberalization could be welfare enhancing. When it is zero, only the TR effect exists, so that it is a case of the conventional model. Here if the TR effect is positive (negative), nurse liberalization is always welfare enhancing (reducing).
ð14aÞ
Eqs. (14a) and (15a) yield dMju¼const ¼ ðBRqNf dNf ÞD1 RpNf dNf :
Our next task is to divide the term ðBRqNf DRpNf Þ into three parts and investigate the implications. First, B = Epq Rpq indicates the complementarity and substitutability between the imported good and nursing service in consumption and production. Second, D = Eqq Rqq indicates the responses of consumption and production of nursing service to the price of its product. Third, RqNf and RpNf indicate the effects of an increase in foreign nurse on the outputs of the nursing service and imported good. Among them, the conventional model is related to the third one because it just focuses on the output effects of an increase in factors of production. In contrast, in our model these three work and we see that the welfare effects of nurse liberalization depend on the natures of the revenue and expenditure functions. From above, we obtain a lemma and proposition on the factors and conditions for nurse liberalization welfare enhancing:
ð20Þ
From (20), if ðBRqNf DRpNf Þ < 0, then ð@M=@Nf ju¼const Þ > 0. In such a case, the TR effect is positive and an increase in foreign nurse increases imports, TR, and welfare. If ðBRqNf DRpNf Þ > 0, then it is negative and an increase in foreign nurse reduces imports, TR, and welfare. Further, if ðBRqNf DRpNf Þ ¼ 0, then an increase in foreign nurse does not affect welfare. Thus, in our model the TR effect could be positive. This is a novel contribution of this paper.
10 Note that (19) could also be written as: @M=@Nf ju¼const ¼ @M=@qjNf ¼const @q=@Nf þ@M=@Nf jq¼const , where @M=@qjNf ¼const ¼ B>0, @q/@Nf¼ RqNf =D < 0, and @M=@Nf jq¼const ¼ RpNf > 0.
Remark 2. On nurse inflow, we have a wisdom that an increase in foreign nurses is against to host nurses. This wisdom is concerned with the long run effect. Two aspects must be divided; (i) in the short run when two nurses are different in skills host nurses gain by accepting foreign nurses, but the host country will be obliged to pay a training subsidy, and (ii) in the long run when the skill difference disappears by the subsidy and two nurses become substitute, their interests will be opposed. 3.1.2. Remittance Foreign nurses make remittance from their returns. They will determine the rate by considering the costs of living in the host country, the moving costs, and the incomes of their family in the home country.11 Our concern here is to show that the rate must be medium and that an increase in the rate is welfare reducing. Depending on the rate, the remittance is divided into three. As noted, the rate of returns to nurse in the home country is n*. Thus if p = n*, it is minimum and is the lower bound. If n* < p < nf, it is medium, and if p = nf, it is maximum and is the upper bound. A feature of nurse inflow is that the owners of nurse services move to the host country and stay there. In the case of minimum, there exists no incentive to move. In the case of maximum, a foreign nurse cannot afford the costs of living in the host country. Thus the
11 The rate of remittance can be calculated from the balance of payment of the home countries. But we can guess the mode of the rate as the average of the returns to foreign nurses in the host and home countries. If this is applied to the case of Indonesian nurses in 2014, from the numerical values of footnote 5, the rate could be about 90,000 yen per month.
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rate must be medium and is bounded within this range. In contrast, in capital mobility, the maximum remittance is realized. This is due to a fact that the owners of capital need not move to the host country. If they do not move, the costs of living in the host country are not an issue, so that the maximum remittance is made. The conventional model always assumes this case. From (16), we obtain
@u/@p = NfDD1.
(21)
This shows that an increase in the rate is welfare reducing. This is due to a fact that the remittance is a cost to the host country, so that its increase reduces the incomes left for the foreign nurses in the host country. These are summarized as a lemma: Lemma 2. In nurse inflow, (i) the rate of remittance is medium, and (ii) an increase in the rate is welfare reducing. 3.1.3. Training subsidy A feature of our model is the existence of a training subsidy. Different from the remittance, the subsidy has welfare enhancing aspect and is a policy variable of the host government. We first show that the rate of training subsidy also has the bounds. The I-E effect must be nonnegative in the long run. This produces the upper bound and it is the incomes left for the foreign nurses in the host country. The lower bound is zero. Hence, the host government chooses the rate within this range.12 From (16), we obtain h i @u=@t ¼ Nf ðanf 1ÞD þ taNf ðBRqNf DRpNf Þ D1 : ð22Þ The first term of (22) is the welfare enhancing effect and the second term the TR effect and the former consists of two aspects; welfare enhancing and cost aspects. To see the effects of training subsidy, in addition to time, we divide trade policy into two: (i) free trade (t = 0), and (ii) under a tariff (t > 0). Thus we have case 1. a = 0 and t = 0. Here, (22) is NfDD1, which is the same as (21), so that only the cost aspect exists. case 2. a = 0 and t > 0. Here, (22) is also NfDD1, so that only the cost aspect exists. 1 case 3. a > 0 and t = 0. Here, (22) is Nf ðanf 1ÞD D and the sign of this term depends on (anf 1), which could be positive, zero, and negative. Here, a is fixed but nf is a variable that depends on t . An increase in t enhances d which affects nf. If anf is greater than 1, it is positive. In this case, an import subsidy works to increase welfare. If it is zero, the welfare enhancing effect is zero. If it is negative and if an increase in t reduces nf, the negative effect will be intensified. case 4. a > 0 and t > 0. Here, both terms of (22) take either sign, so that the welfare effects of training subsidy are no longer determinate. From these, we obtain a lemma: Lemma 3. A training subsidy is a cost in the short run and the welfare enhancing aspect occurs in the long run. These hold irrespective of trade policy.
12
The rate of training subsidy is calculated from the budget of the host country. According to the budget of the Ministry of Health, Labor, and Welfare of Japan in 2014, it was about 120,000 yen per month. Japan is paying a high rate of subsidy.
5
3.2. Trade liberalization Trade liberalization is also proceeding along with the EPAs. From (16), we obtain
@u/@t = t(AD B2)D1.
(23)
This shows that the welfare effects depend on (AD B2). Following proposition is immediate: Proposition 2. Under t > 0, a necessary and sufficient condition for trade liberalization welfare enhancing is (AD B2) > 0. This is a newness of our analysis of trade liberalization. Next task is to find out the situations where this condition is realized. We will show that it is realized in two probable situations. Situation 1. the expenditure function is strictly concave and the revenue function is strictly convex. We assumed that the expenditure function is concave and revenue function is convex. This implies (Epp Rpp)(Eqq Rqq) (Epq Rpq)2 0.
(24)
2
which is the same as (AD B ) 0. Thus if the expenditure function is strictly concave and revenue function is strictly convex, then we obtain (AD B2) > 0. This situation is probable because it implies that the product of the two direct effects of price change is greater than the square of the indirect effects of price change.13 Situation 2: the tariff and imports is negatively related under fixed utility. Let du =dNh =dNf =dp =dt = 0 in (14) and (15). From these we obtain: dM/dt=(AD B2)D1. Thus if dM/dt < 0, then we have (AD B2) > 0. This situation is also probable because dM/ dt = Epp Rpp = A < 0. Following corollary is immediate: Corollary 1. Under t > 0, (i) if the expenditure function is strictly concave and the revenue function is strictly convex, or (ii) if dM/ dt < 0 under fixed utility, then trade liberalization is welfare enhancing. The above analyses show that the welfare effects of trade liberalization depend on the natures of the revenue and expenditure functions. This could be another novel contribution of this paper. Lastly, suppose the host country liberalizes nurse and trade at the same time. From Proposition 1 (ii) and Proposition 2, a sufficient condition for such liberalization welfare enhancing is; t > 0, (nf p t ) > 0, ðBRqNf DRpNf Þ < 0, and (AD B2) > 0. 4. Conclusions Proposing a model for liberalizing nursing and trade, we explored the factors and conditions for these liberalizations welfare enhancing. To conclude, it is in order to provide some remarks on our model and results. First, we assumed the utility of foreign nurses is the same as that of the native residents. This may be very strong and it is desirable to separate them, for example, by assuming two representatives, one for the native residents and the other for the foreign nurses, and consider the effects of nurse inflow on the welfare of native residents. Second, we assumed the host country is small. A justification is that we can compare our results with that of
13 Define the net expenditure function as the expenditure function minus the revenue function. Then it is concave in price and its Hessian matrix is negative semidefinite. But if the expenditure function is strictly concave and the revenue function is strictly convex, then its Hessian matrix is negative definite.
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the conventional model of capital imports. It is desirable to consider a case of large country, especially in the case of Japan. Third, we assumed two nurses are different in skill and two nurse markets are separated. In the long run, however, the differences in skill will be contracted and two markets will be integrated. Lastly, our model is based on the stylized facts in Japan. But it is general and the results are applicable to other developed countries. Nonetheless, this study is the first to provide a model for nurse inflow and trade and examine the welfare effects of nurse and trade liberalization. We revived the I-E effect, justified the medium remittance, and provided a new condition for trade liberalization welfare enhancing. We showed that our model produces more general and optimistic results than the conventional model of capital imports. Acknowledgements We would like to thank the editor, Yasushi Hamano, and two anonymous referees for valuable comments and suggestions which were very useful in revising the paper. This paper benefited from the presentations at the Japanese Economic Association, the JSIE, Nanzan University, and Tezukayama University. We are grateful to Nicola Coniglio, Noritsugu Nakanishi, and Hiroshi Ohta for constructive comments. Thanks are due to Taiji Furusawa, Katsuhiko Hori, Tatsuro Iwaisako, Naoto Jinji, Isao Kamata, Yasushi Kawabata, Ngo Van Long, Tadashi Morita, Yasuhiro Sato, Keiko Shimono, Makoto Tawada, and Shigemi Yabuuchi for useful comments on the earlier version of this paper. We also thank Ichiro Daito, Yasukazu Ichino, Hiroshi Kurata, Kaz Miyagiwa, Takao Ohkawa, and Takanori Shimizu for useful discussions during the various stages of this paper. Appendix In this appendix, we first show that (Eu tEpu) > 0 and then
D < 0 by the use of the stability condition.
To show (Eu tEpu) > 0, let E(1, p, q, u)= E and differentiate it with respect to u holding p and q constant. Then we obtain: Eudu = dE. As noted above Cy = Ep, so that dCy = Epudu. From these we obtain: dCy/dE =Epu/Eu. Let the marginal propensity to consume imports be my. Then it is: my =p(dCy/dE) =pEpu/Eu. It is reasonable to assume: 0 < my < 1. Thus we obtain: (Eu tEpu) =Eu 1 tðEpu =Eu Þ ¼Eu 1 ðtmy =pÞ ¼ ð1=pÞEu p þ tð1 my Þ > 0. Next, we show that D < 0 by the use of the stability condition. Assume that the price of medical care adjusts: q_ ¼ ’V, where the dot denotes the time derivative, ’ is a positive constant, and V the
excess demand for medical care: V = Eq(1, p, q, u)Rq(1, p, q, Nh, dNf). Then the Walrasian stability requires: dV/dq < 0. Differentiation of V with respect to q and u holding other variables constant yields dV = (Eqq Rqq)dq + Equdu.
(A1)
From (13), assuming exogenous variables constant, we obtain Eudu = tdM.
(A2)
Also from (14), assuming exogenous variables constant, we obtain dM = Epudu + Bdq.
(A3)
Substituting (A3) into (A2), we obtain du ¼ tB=ðEu tEpu Þ dq:
ðA4Þ
We know already that (Eu tEpu) > 0. Substitute (A4) into (A1). Then the stability condition requires: (Eu tEpu)(dV/ dq) = (Eu tEpu)(Eqq Rqq) + tBEqu=(Eu tEpu)D + tBEqu < 0. Thus D < 0. References Behrens, K., Sato, Y., 2010. Migration, skill formation, and the wage structure. J. Region. Sci. 20 (no. 10), 1–26. Bhagwati, J., et al., 1971. The generalized theory of distortions and welfare. In: Bhagwati, J. (Ed.), Trade, Balance of Payments, and Growth, , pp. 69–90 Chap. 4, Amsterdam North-Holland. Bhagwati, J., 1973. The theory of immiserizing growth: further applications. In: Connolly, M., Swoboda, A. (Eds.), International Trade and Money. University of Toronto Press, pp. 45–54. Brecher, R., Diaz Alejandro, C., 1977. Tariffs, foreign capital and immiserizing growth. J. Int. Econ. 7, 317–322. Giordani, P.E., Ruta, M., 2011. The immigration policy puzzle. Rev. Int. Econ. 19 (issue 5), 922–935. Hamada, K., 1971. International Trade and the Theory of Direct Investment. Toyo Keizai, pp. 110–116 Special Issue (in Japanese). Jones, R., et al., 1971. A three factor model in theory, trade and history. In: Bhagwati, J. (Ed.), Trade, Balance of Payments, and Growth, , pp. 1–21 Chap.1, Amsterdam North-Holland. Kar, S., Beladi, H., 2004. Skill Formation and International Migration: welfare perspective of developing countries. Jpn. World Econ. 16, 35–54. Komiya, R., Amano, A., 1972. International Economics. Modern Economics, 8. Iwanami Shoten, pp. 424–428 Chap. 16 (in Japanese). Oda, M., Shimomura, K., 2012. A model of welfare enhancing capital imports. Rev. Int. Econ. 40 (issue 4), 758–766. Rutten, M., 2009. The economic impact of medical migration: a receiving country’s perspective. Rev. Int. Econ. 17 (issue 1), 156–171. Sato, Y., Yamamoto, K., 2012. Trade impacts on skill acquisition via variety expansion. Jpn. Econ. Rev. 63 (no. 4), 451–466. Stark, O., Zakharenko, R., 2012. Differential migration prospects, skill formation, and welfare. Rev. Int. Econ. 20 (issue 4), 657–673. Uzawa, H., 1969. Liberalization of foreign investment and national economy. Econ. Dec. 23, 106–122 (in Japanese).
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Japan and the World Economy xxx (2018) xxx–xxx
Contents lists available at ScienceDirect
Japan and the World Economy journal homepage: www.elsevier.com/locate/jwe
A model for liberalizing nursing and trade Masao Oda* , Masayuki Okawa Department of Economics, Ritsumeikan University, Japan
A R T I C L E I N F O
Article history: Received 1 November 2016 Received in revised form 26 October 2017 Accepted 1 March 2018 Available online xxx JEL classifications: F13 F22
A B S T R A C T
This paper proposes a model for liberalizing nursing and trade and analyses the welfare effects of nurse and trade liberalizations. We show that the welfare effects of nurse liberalization depend on the income enhancing (I-E) and tariff revenue (TR) effects and that contrary to the conventional (Heckscher-Ohlin) model of capital imports the former is not always zero and the latter is not always negative and then provide sufficient conditions for nurse liberalization welfare enhancing. We also provide a necessary and sufficient condition for trade liberalization welfare enhancing. © 2018 Elsevier B.V. All rights reserved.
Keywords: Nurse liberalization Trade liberalization I-E effect TR effect
1. Introduction As a result of the Economic Partnership Agreements (EPAs), Japan started to accept foreign nurses. It started in 2008 accepting 104 nurses from Indonesia. At the end of 2014, the total number of nurses from Indonesia was 481 and that from the Philippines was 337. Further, we accepted 21 nurses from Vietnam in 2014.1 As the acceptance of foreign nurses began recently, the number of foreign nurses in Japan is still small. However, other OECD countries have already accepted many foreign nurses and the
* Corresponding author. E-mail addresses: [email protected] (M. Oda), [email protected] (M. Okawa). 1 Based on the programs of EPAs, these nurses are working at the medical facilities and preparing for the qualifying examination. They must pass it within three years and if not they must return to their countries. Some problems in the examination and the terms of stay have been solved. But one defect of the programs was that it does not require the understanding of Japanese beforehand. Accordingly, all candidates from Vietnam are required to pass the examination of Japanese, N3, before coming to Japan.
importance of nurse immigration has been recognized.2 Yet the economic analysis is scarce. The only work is Rutten (2009) and it deals with the output effects of medical immigration by the use of the Rybczynski theorem. No literature exists on the welfare effects of nurse liberalization.3 Today, international agreements on factor mobility including nurses are nested within the EPAs and the liberalization of nurse and trade is proceeding along with the EPAs. Is nurse liberalization welfare enhancing? If enhancing, by what factors and under what conditions? The purpose of this paper is to address these issues and provide an answer to these questions. Proposing a model for liberalizing nursing and trade, we show that the welfare effects of nurse liberalization depend on the income enhancing (I-E) and tariff revenue (TR) effects and that contrary to the conventional (Heckscher-Ohlin) model of capital imports the former is not always zero and the latter is not always
2 See a report of OECD, The Looming Crisis in the Health Workforce: How can OECD countries respond? (2008). 3 In contrast, many papers have been written on capital imports and welfare including seminal works such as Bhagwati (1973), Brecher and Diaz Alejandro (1977), Hamada (1971), and Uzawa (1969), among others. By the use of the conventional model they produced a wisdom; “Capital import under a tariff is always immiserizing”. But this wisdom is too pessimistic and far from the realities. A model that justifies the acceptance of foreign capital in a multi-dimensional framework was provided by Oda and Shimomura (2012).
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negative and then provide sufficient conditions for nurse liberalization welfare enhancing. We also provide a necessary and sufficient condition for trade liberalization welfare enhancing. It will be shown that our model produces more general and optimistic results than the conventional one. Our study is related to the theory of distortions in growth and welfare literature. This theory says that when a distortion such as a tariff exists in an economy an increase in factors of production is not always welfare enhancing. A pioneering work within the realm of trade theory would be Bhagwati (1971). Based on this theory, the conventional model says that trade must be liberalized (a distortion must be removed) before the acceptance of foreign capital. In contrast, in our model, an increase in foreign nurse could be welfare enhancing under a tariff, so that trade need not always be liberalized before the acceptance of foreign nurse. The rest of the paper is as follows. In Section 2, we point out some stylized facts about nurse inflow in Japan and then set up a model for liberalizing nursing and trade. In Section 3, we consider the factors and conditions for welfare enhancement of nurse and trade liberalizations. Section 4 concludes. The Appendix confirms the stability condition of the model. 2. The model 2.1. Stylized facts We start by pointing out some stylized facts about nurse, nurse inflow, and nurse markets in Japan. First, nurse is an indispensable skilled labor specifically used in the medical care sector and the medical care service is a nontraded good. Therefore, it is necessary to provide a specific factor model with a non-traded good. The specific factor model was developed by Jones (1971) and has been used in many aspects of trade theory including factor mobility. Second, Japan has been negative to labor inflow, accepting only skilled labor in exceptional cases.4 This is the same in nurse inflow and we care about the benefits of Japanese nurses. As Giordani and Ruta (2011), we do not choose complete open or complete ban in nurse liberalization. Third, we have two types of nurses and two nurse markets; the Japanese nurses and foreign ones, and the markets for the Japanese nurses and for foreign ones. Two nurses are considered different in skills and two markets are separated. The market for the Japanese nurses is organized only by the Japanese and protected by the Japanese Nursing Association. Fourth, at the negotiations of EPAs, Indonesia and the Philippines required the emigration of nurses. In order to start EPAs, Japan decided to accept their nurses. A feature of this nurse inflow is that the Japanese government is paying a training (or education) subsidy. Fifth, there are labor abundant developing countries that supply nurses to Japan with low rate of returns. We regard them as a foreign country. Thus we totally have three kinds of nurses, three
4 In order to level up the competitiveness of the economy, the Japanese government decided, in 2011, to relax the conditions for the permanent stay of foreign skilled labors in science and technology sectors.
kinds of markets, and three rates of returns, where two nurses and markets are in Japan and one nurse and market are in the foreign country.5 2.2. Model setup We set up a model of nurse inflow and trade that reflects above facts. Assume two countries, host (domestic) and home (foreign). Let the country in question be the host country and assume that as a result of an EPA it liberalizes nurse and trade. It is a small open economy with three sectors; export (X), import (Y), and non-traded medical care (Z). We assume four factors; capital (K), unskilled labor (L), host nurse (Nh), and foreign nurse (Nf), where capital, unskilled labor, and host nurse are supplied domestically. Capital is a general factor used in all three sectors and unskilled labor is also a general factor used in both traded sectors. Domestic nurse is a skilled labor educated in the domestic country and used in the medical care sector.6 Foreign nurse is a semi-skilled labor used in the medical care sector. Thus the medical care is produced by capital and two types of nurses. The production functions are; X = X (Kx, Lx), Y = Y(Ky, Ly), and Z = Z(Kz, Nh, dNf), where d is a multiplicative parameter that captures the effects of training subsidy. Two nurses are assumed different in skills and two nurse markets are separated. Perfect competition and full employment are assumed. Choosing export good as the numeraire, denote the domestic relative price of imports by p. Also let q be the relative price of medical care determined in the domestic market. Under perfect competition, we have 1 ¼ cx ðr; wÞ;
ð1Þ
p ¼ cy ðr; wÞ;
ð2Þ
q ¼ cz ðr; nh ; nf Þ;
ð3Þ
where r is the rental rate of capital, w the wage rate of unskilled labor, nh the rate of returns to domestic nurse, and nf the rate of returns to foreign nurse. The right side of (1), (2), and (3) stands for the unit cost function of each good. Assume the domestic country imports Y under a tariff. Then, we have p ¼ p þ t;
ð4Þ
where p* is the fixed foreign relative price of imports and t the specific tariff rate. Given the supply of capital, unskilled labor, domestic nurse, and foreign nurse, the assumption of full employment produces cxr ðr; wÞX þ cyr ðr; wÞY þ czr ðr; nh ; nf ÞZ ¼ K;
ð5Þ
5 EPAs require that the rate of returns to foreign nurses in Japan must be equal to that of the Japanese nurses. But the reports of the Japanese Nursing Association and the Ministry of Health, Labor, and Welfare indicate that, at 2014, the average rate of returns to a Japanese nurse per month was about 330,000 yen, whereas that of Indonesian nurse in Japan was about 150,000 yen and that of Indonesian nurse in Indonesia was about 30,000 yen. The difference between former two is about two times while the difference between latter two is just five times. We have another difference; the difference in the passing rate of the qualifying examination. From 2010 to 2014, the average rate of passing of Japanese nurse was 90.1% while that of foreign nurse was just 7.3%. 6 We assume that the decision of an unskilled labor to be skilled or unskilled has been made in the previous stage. Skill formation has been taken up by Behrens and Sato (2010), Kar and Beladi (2004), and Stark and Zakharenko (2012). Recently, Sato and Yamamoto (2012) provided a model to explain how trade induces skill formation.
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cxw ðr; wÞX
þ
cyw ðr; wÞY
¼ L;
ð6Þ
cznh ðr; nh ; nf ÞZ ¼ Nh ;
ð7Þ
cznf ðr; nh ; nf ÞZ ¼ Nf ;
ð8Þ
where cxr ð¼ @cx =@rÞ is, for example, the unit demand for capital in X. To complete the model, we will introduce the revenue and expenditure functions. The revenue function is; R(1, p, q, Nh, dNf) = max XðK x ; Lx Þ þ pYðK y ; Ly Þ þ qZððK z ; Nh ; dNf Þ with respect to X, Y, and Z subject to full employment. R(1, p, q, Nh, dNf) is twice continuously differentiable, homogeneous of degree one and convex in prices and concave in factor supply. From this function, using the envelop theorem, we obtain: Rp = Y, Rq = Z, RNh ¼ nh , and RdNf ¼ nf with Rpp > 0, Rqq > 0, RNh Nh < 0, and RdNf dNf < 0. The cross partial derivatives Rpq and Rqp are continuous and Rpq = Rqp < 0. The signs of RNh dNf and RdNf Nh depend on whether two nurses are substitute or complement but our results are not affected by the relationships between two nurses. The expenditure function is; E(1, p, q, u) = min C x þ pC y þ qC z with respect to Cj subject to uðC x ; C y ; C z Þ ¼ u, where u() is a homothetic utility function of a representative resident in the domestic country assuming that the utility of foreign nurses is the same as that of the native residents, Cj the consumption of j th good (j = x, y, z), and u a target level of utility. E(1, p, q, u) is twice continuously differentiable, homogeneous of degree one and concave in prices and increasing in utility. From this function, using the envelop theorem, we obtain: Ep = Cy, and Eq = Cz with Epp < 0, and Eqq < 0. The cross partial derivatives Epq and Eqp are continuous and Epq = Eqp > 0. From these functions, we obtain Eð1; p; q; uÞ ¼ Rð1; p; q; Nh ; dNf Þ pNf t Nf þ tM;
ð9Þ
M ¼ Ep ð1; p; q; uÞ Rp ð1; p; q; Nh ; dNf Þ;
ð10Þ
Eq ð1; p; q; uÞ ¼ Rq ð1; p; q; Nh ; dNf Þ;
ð11Þ
where p is the rate of remittance, pNf the amount of remittance, t the rate of training subsidy, and t Nf the cost of training subsidy. The foreign nurses require both incentives to move to the host country and incomes to live there. Let n* be the rate of returns to nurses in the home country. Then, if p is greater than n* and less than nf, these requirements are satisfied. M is the quantity of imports and tM the tariff revenue. Eq. (9) is the budget equation that implies that the expenditure is equal to the sum of net income and tariff revenue.7 Eq. (10) shows that the quantity of imports is the excess demand for that product and (11) gives the equilibrium condition of the medical care sector. These three equations are added with the same number of variables; u, M, and q. We are paying a training subsidy. This subsidy is indispensable in nurse inflow and it works to increase foreign nurse through skill enhancement. To consider these facts, we specify d as a function of t . We assume that it (i) is linear in t , (ii) is 1 initially, and (iii) increases when t increases. Under these specifications, it could be
dðt Þ ¼ 1 þ at ;
3
where a is a parameter that captures the effectiveness of a training subsidy. A lapse of time is necessary to make the subsidy effective. We divide time into two: (i) short run (a = 0), and (ii) long run (a > 0). In (12), when a or t is zero, d = 1 and when both a and t are positive, d > 1. Eqs. (1) to (12) make up our model. It has twelve equations with the same number of variables. Given the exogenous variables; p*, p, t , t, Nh, Nf, K,L, and a the model determines twelve variables; p, r, w, nh, nf, X, Y, Z, u, M, q, and d.8 2.3. Equations of change The condensed version of the model consists of (9), (10), and (11) with variables u, M, and q. From these, by the use of (10), (11), and (12), we obtain Eu du ¼ nh dNh þ ðnf p t ÞdNf Nf dp þ Nf ðanf 1Þdt þ tdM;
ð13Þ
dM ¼ Epu du þ Adt þ Bdq RpNh dNh RpNf dNf aNf RpNf dt ;
ð14Þ
dq ¼ ðRqNh dNh þ RqNf dNf Equ du Bdt þ aNf RqNf dt ÞD1 ;
ð15Þ
where A = (Epp Rpp) < 0, B = (Epq Rpq) > 0, and D = (Eqq Rqq) < 0. These will play key roles on the welfare effects of nurse and trade liberalization. We also have: Eu > 0, Epu>0, and Equ > 0 if the utility function is homothetic. It is reasonable that RpNh < 0, RpNf < 0, RqNh > 0, and RqNf > 0. From (13), (14), and (15), we obtain ðnh tRpNh Þ ðEu tEpu Þ tB du ¼ dNh RqNh Equ D dq ðnf p t tRpNf Þ þ dNf RqNf Nf þ dp 0 Nf ðanf atRpNf 1Þ þ dt aNf RqNf tA þ ð16Þ dt: B Let the determinant of the coefficient matrix of the left side of (16) be D. Then it is: ðEu tEpu ÞD þ tBEqu . As proved in the appendix, D < 0. 3. The analysis 3.1. Nurse liberalization 3.1.1. I-E and TR effects Consider nurse liberalization first.9 Nurse inflow is a temporary immigration with following features that are not found in capital mobility. First, it is carried out exogenously to attain some noneconomic objectives such as the realization of EPAs. Second, the owners of nurse services have to move to the host country. Comparing with the conventional model, we will explore the factors and conditions for nurse liberalization welfare enhancing. Suppose the host country liberalizes nurse inflow at a given tariff rate. As native residents and foreign nurses live in the host country, a representative resident is a representative of both
ð12Þ
7 Since the rate of remittance is less than the returns to foreign nurses the expenditure includes the consumption of both native residents and foreign nurses.
8 By nature, p is an endogenous variable determined by the foreign nurses. But as we are interested in the effects of a change in the rate, we treat it here as an exogenous one. 9 The Japanese government is trying to increase the supply of Japanese nurses. Our model can analyze the welfare effects of an increase in domestic nurses.
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residents. Thus if the welfare of a representative resident increases it implies the welfare of both residents increases. From (16), we obtain i h @u=@Nf ¼ ðnf p t ÞD þ tðBRqNf DRpNf Þ D1 : ð17Þ In (17), the first term is the income enhancing (I-E) effect and the second term the tariff revenue (TR) effect. Consider the former first. This paper is the first to clarify the implications of this effect. We argue followings. First, it shows how the national income increases as a result of an increase in nurse inflow, so that we will name it as the income enhancing (I-E) effect. Second, it is necessary to revive this effect. This effect has been neglected in the conventional model of capital imports. Extant many papers including Brecher and Diaz Alejandro (1977) and Komiya and Amano (1972) used that model but they neglected it because it is zero. It is zero because that model assumes the maximum remittance and there exists no training subsidy. However, such remittance is a special case that does not occur in nurse inflow. In contrast, in our model this effect could take any signs. The implications of remittance and training subsidy will be taken up separately. Next, consider the TR effect. This shows how TR changes when the host country accepts foreign nurses. In the conventional model, it is negative. Why is it negative? This is due to the facts that it uses the Heckscher-Ohlin model and assumes that the host country imports a capital intensive good. Thus by the Rybczynski theorem, an increase in capital by a capital inflow increases the output of the capital intensive good, which in turn reduces imports, TR, and thus welfare. In contrast, in our model this effect is not always negative, so that trade need not always be liberalized first. Below, we show why the second term of (17) is the TR effect and takes any signs. From (14) and (15), setting du = dNh = dp = dt = dt = 0, we obtain dM ¼ Bdq RpNf dNf ;
dq ¼ ðRqNf dNf ÞD1 :
ð15aÞ
ð18Þ
From (18), we obtain
@M=@Nf ju¼const ¼ ðBRqNf DRpNf ÞD1 :
ð19Þ
When (19) is multiplied by t, it denotes the effects of an increase in Nf on TR under fixed utility.10 Therefore, the second term of (17) is the TR effect. Moreover, as D < 0, from (19), we obtain signðBRqNf DRpNf Þ ¼ signð@M=@Nf ju¼const Þ:
Lemma 1. The welfare effects of nurse liberalization depend on the I-E and TR effects. Proposition 1. (i) Under free trade, (nf p t ) > 0 is a sufficient condition for nurse liberalization welfare enhancing, (ii) if t > 0 and (nf p t ) > 0, then ðBRqNf DRpNf Þ < 0 is a sufficient condition for nurse liberalization welfare enhancing, and (iii) if t > 0, (nf p t ) > 0, and ðBRqNf DRpNf Þ > 0, then nurse liberalization is not always welfare enhancing. Following remarks are in order. Remark 1. We must consider cases where the I-E effect is not positive. When it is negative, under free trade nurse liberalization is always welfare reducing and under a tariff if the TR effect is positive and large enough nurse liberalization could be welfare enhancing. When it is zero, only the TR effect exists, so that it is a case of the conventional model. Here if the TR effect is positive (negative), nurse liberalization is always welfare enhancing (reducing).
ð14aÞ
Eqs. (14a) and (15a) yield dMju¼const ¼ ðBRqNf dNf ÞD1 RpNf dNf :
Our next task is to divide the term ðBRqNf DRpNf Þ into three parts and investigate the implications. First, B = Epq Rpq indicates the complementarity and substitutability between the imported good and nursing service in consumption and production. Second, D = Eqq Rqq indicates the responses of consumption and production of nursing service to the price of its product. Third, RqNf and RpNf indicate the effects of an increase in foreign nurse on the outputs of the nursing service and imported good. Among them, the conventional model is related to the third one because it just focuses on the output effects of an increase in factors of production. In contrast, in our model these three work and we see that the welfare effects of nurse liberalization depend on the natures of the revenue and expenditure functions. From above, we obtain a lemma and proposition on the factors and conditions for nurse liberalization welfare enhancing:
ð20Þ
From (20), if ðBRqNf DRpNf Þ < 0, then ð@M=@Nf ju¼const Þ > 0. In such a case, the TR effect is positive and an increase in foreign nurse increases imports, TR, and welfare. If ðBRqNf DRpNf Þ > 0, then it is negative and an increase in foreign nurse reduces imports, TR, and welfare. Further, if ðBRqNf DRpNf Þ ¼ 0, then an increase in foreign nurse does not affect welfare. Thus, in our model the TR effect could be positive. This is a novel contribution of this paper.
10 Note that (19) could also be written as: @M=@Nf ju¼const ¼ @M=@qjNf ¼const @q=@Nf þ@M=@Nf jq¼const , where @M=@qjNf ¼const ¼ B>0, @q/@Nf¼ RqNf =D < 0, and @M=@Nf jq¼const ¼ RpNf > 0.
Remark 2. On nurse inflow, we have a wisdom that an increase in foreign nurses is against to host nurses. This wisdom is concerned with the long run effect. Two aspects must be divided; (i) in the short run when two nurses are different in skills host nurses gain by accepting foreign nurses, but the host country will be obliged to pay a training subsidy, and (ii) in the long run when the skill difference disappears by the subsidy and two nurses become substitute, their interests will be opposed. 3.1.2. Remittance Foreign nurses make remittance from their returns. They will determine the rate by considering the costs of living in the host country, the moving costs, and the incomes of their family in the home country.11 Our concern here is to show that the rate must be medium and that an increase in the rate is welfare reducing. Depending on the rate, the remittance is divided into three. As noted, the rate of returns to nurse in the home country is n*. Thus if p = n*, it is minimum and is the lower bound. If n* < p < nf, it is medium, and if p = nf, it is maximum and is the upper bound. A feature of nurse inflow is that the owners of nurse services move to the host country and stay there. In the case of minimum, there exists no incentive to move. In the case of maximum, a foreign nurse cannot afford the costs of living in the host country. Thus the
11 The rate of remittance can be calculated from the balance of payment of the home countries. But we can guess the mode of the rate as the average of the returns to foreign nurses in the host and home countries. If this is applied to the case of Indonesian nurses in 2014, from the numerical values of footnote 5, the rate could be about 90,000 yen per month.
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rate must be medium and is bounded within this range. In contrast, in capital mobility, the maximum remittance is realized. This is due to a fact that the owners of capital need not move to the host country. If they do not move, the costs of living in the host country are not an issue, so that the maximum remittance is made. The conventional model always assumes this case. From (16), we obtain
@u/@p = NfDD1.
(21)
This shows that an increase in the rate is welfare reducing. This is due to a fact that the remittance is a cost to the host country, so that its increase reduces the incomes left for the foreign nurses in the host country. These are summarized as a lemma: Lemma 2. In nurse inflow, (i) the rate of remittance is medium, and (ii) an increase in the rate is welfare reducing. 3.1.3. Training subsidy A feature of our model is the existence of a training subsidy. Different from the remittance, the subsidy has welfare enhancing aspect and is a policy variable of the host government. We first show that the rate of training subsidy also has the bounds. The I-E effect must be nonnegative in the long run. This produces the upper bound and it is the incomes left for the foreign nurses in the host country. The lower bound is zero. Hence, the host government chooses the rate within this range.12 From (16), we obtain h i @u=@t ¼ Nf ðanf 1ÞD þ taNf ðBRqNf DRpNf Þ D1 : ð22Þ The first term of (22) is the welfare enhancing effect and the second term the TR effect and the former consists of two aspects; welfare enhancing and cost aspects. To see the effects of training subsidy, in addition to time, we divide trade policy into two: (i) free trade (t = 0), and (ii) under a tariff (t > 0). Thus we have case 1. a = 0 and t = 0. Here, (22) is NfDD1, which is the same as (21), so that only the cost aspect exists. case 2. a = 0 and t > 0. Here, (22) is also NfDD1, so that only the cost aspect exists. 1 case 3. a > 0 and t = 0. Here, (22) is Nf ðanf 1ÞD D and the sign of this term depends on (anf 1), which could be positive, zero, and negative. Here, a is fixed but nf is a variable that depends on t . An increase in t enhances d which affects nf. If anf is greater than 1, it is positive. In this case, an import subsidy works to increase welfare. If it is zero, the welfare enhancing effect is zero. If it is negative and if an increase in t reduces nf, the negative effect will be intensified. case 4. a > 0 and t > 0. Here, both terms of (22) take either sign, so that the welfare effects of training subsidy are no longer determinate. From these, we obtain a lemma: Lemma 3. A training subsidy is a cost in the short run and the welfare enhancing aspect occurs in the long run. These hold irrespective of trade policy.
12
The rate of training subsidy is calculated from the budget of the host country. According to the budget of the Ministry of Health, Labor, and Welfare of Japan in 2014, it was about 120,000 yen per month. Japan is paying a high rate of subsidy.
5
3.2. Trade liberalization Trade liberalization is also proceeding along with the EPAs. From (16), we obtain
@u/@t = t(AD B2)D1.
(23)
This shows that the welfare effects depend on (AD B2). Following proposition is immediate: Proposition 2. Under t > 0, a necessary and sufficient condition for trade liberalization welfare enhancing is (AD B2) > 0. This is a newness of our analysis of trade liberalization. Next task is to find out the situations where this condition is realized. We will show that it is realized in two probable situations. Situation 1. the expenditure function is strictly concave and the revenue function is strictly convex. We assumed that the expenditure function is concave and revenue function is convex. This implies (Epp Rpp)(Eqq Rqq) (Epq Rpq)2 0.
(24)
2
which is the same as (AD B ) 0. Thus if the expenditure function is strictly concave and revenue function is strictly convex, then we obtain (AD B2) > 0. This situation is probable because it implies that the product of the two direct effects of price change is greater than the square of the indirect effects of price change.13 Situation 2: the tariff and imports is negatively related under fixed utility. Let du =dNh =dNf =dp =dt = 0 in (14) and (15). From these we obtain: dM/dt=(AD B2)D1. Thus if dM/dt < 0, then we have (AD B2) > 0. This situation is also probable because dM/ dt = Epp Rpp = A < 0. Following corollary is immediate: Corollary 1. Under t > 0, (i) if the expenditure function is strictly concave and the revenue function is strictly convex, or (ii) if dM/ dt < 0 under fixed utility, then trade liberalization is welfare enhancing. The above analyses show that the welfare effects of trade liberalization depend on the natures of the revenue and expenditure functions. This could be another novel contribution of this paper. Lastly, suppose the host country liberalizes nurse and trade at the same time. From Proposition 1 (ii) and Proposition 2, a sufficient condition for such liberalization welfare enhancing is; t > 0, (nf p t ) > 0, ðBRqNf DRpNf Þ < 0, and (AD B2) > 0. 4. Conclusions Proposing a model for liberalizing nursing and trade, we explored the factors and conditions for these liberalizations welfare enhancing. To conclude, it is in order to provide some remarks on our model and results. First, we assumed the utility of foreign nurses is the same as that of the native residents. This may be very strong and it is desirable to separate them, for example, by assuming two representatives, one for the native residents and the other for the foreign nurses, and consider the effects of nurse inflow on the welfare of native residents. Second, we assumed the host country is small. A justification is that we can compare our results with that of
13 Define the net expenditure function as the expenditure function minus the revenue function. Then it is concave in price and its Hessian matrix is negative semidefinite. But if the expenditure function is strictly concave and the revenue function is strictly convex, then its Hessian matrix is negative definite.
Please cite this article in press as: M. Oda, M. Okawa, A model for liberalizing nursing and trade, Japan World Econ. (2018), https://doi.org/ 10.1016/j.japwor.2018.03.003
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the conventional model of capital imports. It is desirable to consider a case of large country, especially in the case of Japan. Third, we assumed two nurses are different in skill and two nurse markets are separated. In the long run, however, the differences in skill will be contracted and two markets will be integrated. Lastly, our model is based on the stylized facts in Japan. But it is general and the results are applicable to other developed countries. Nonetheless, this study is the first to provide a model for nurse inflow and trade and examine the welfare effects of nurse and trade liberalization. We revived the I-E effect, justified the medium remittance, and provided a new condition for trade liberalization welfare enhancing. We showed that our model produces more general and optimistic results than the conventional model of capital imports. Acknowledgements We would like to thank the editor, Yasushi Hamano, and two anonymous referees for valuable comments and suggestions which were very useful in revising the paper. This paper benefited from the presentations at the Japanese Economic Association, the JSIE, Nanzan University, and Tezukayama University. We are grateful to Nicola Coniglio, Noritsugu Nakanishi, and Hiroshi Ohta for constructive comments. Thanks are due to Taiji Furusawa, Katsuhiko Hori, Tatsuro Iwaisako, Naoto Jinji, Isao Kamata, Yasushi Kawabata, Ngo Van Long, Tadashi Morita, Yasuhiro Sato, Keiko Shimono, Makoto Tawada, and Shigemi Yabuuchi for useful comments on the earlier version of this paper. We also thank Ichiro Daito, Yasukazu Ichino, Hiroshi Kurata, Kaz Miyagiwa, Takao Ohkawa, and Takanori Shimizu for useful discussions during the various stages of this paper. Appendix In this appendix, we first show that (Eu tEpu) > 0 and then
D < 0 by the use of the stability condition.
To show (Eu tEpu) > 0, let E(1, p, q, u)= E and differentiate it with respect to u holding p and q constant. Then we obtain: Eudu = dE. As noted above Cy = Ep, so that dCy = Epudu. From these we obtain: dCy/dE =Epu/Eu. Let the marginal propensity to consume imports be my. Then it is: my =p(dCy/dE) =pEpu/Eu. It is reasonable to assume: 0 < my < 1. Thus we obtain: (Eu tEpu) =Eu 1 tðEpu =Eu Þ ¼Eu 1 ðtmy =pÞ ¼ ð1=pÞEu p þ tð1 my Þ > 0. Next, we show that D < 0 by the use of the stability condition. Assume that the price of medical care adjusts: q_ ¼ ’V, where the dot denotes the time derivative, ’ is a positive constant, and V the
excess demand for medical care: V = Eq(1, p, q, u)Rq(1, p, q, Nh, dNf). Then the Walrasian stability requires: dV/dq < 0. Differentiation of V with respect to q and u holding other variables constant yields dV = (Eqq Rqq)dq + Equdu.
(A1)
From (13), assuming exogenous variables constant, we obtain Eudu = tdM.
(A2)
Also from (14), assuming exogenous variables constant, we obtain dM = Epudu + Bdq.
(A3)
Substituting (A3) into (A2), we obtain du ¼ tB=ðEu tEpu Þ dq:
ðA4Þ
We know already that (Eu tEpu) > 0. Substitute (A4) into (A1). Then the stability condition requires: (Eu tEpu)(dV/ dq) = (Eu tEpu)(Eqq Rqq) + tBEqu=(Eu tEpu)D + tBEqu < 0. Thus D < 0. References Behrens, K., Sato, Y., 2010. Migration, skill formation, and the wage structure. J. Region. Sci. 20 (no. 10), 1–26. Bhagwati, J., et al., 1971. The generalized theory of distortions and welfare. In: Bhagwati, J. (Ed.), Trade, Balance of Payments, and Growth, , pp. 69–90 Chap. 4, Amsterdam North-Holland. Bhagwati, J., 1973. The theory of immiserizing growth: further applications. In: Connolly, M., Swoboda, A. (Eds.), International Trade and Money. University of Toronto Press, pp. 45–54. Brecher, R., Diaz Alejandro, C., 1977. Tariffs, foreign capital and immiserizing growth. J. Int. Econ. 7, 317–322. Giordani, P.E., Ruta, M., 2011. The immigration policy puzzle. Rev. Int. Econ. 19 (issue 5), 922–935. Hamada, K., 1971. International Trade and the Theory of Direct Investment. Toyo Keizai, pp. 110–116 Special Issue (in Japanese). Jones, R., et al., 1971. A three factor model in theory, trade and history. In: Bhagwati, J. (Ed.), Trade, Balance of Payments, and Growth, , pp. 1–21 Chap.1, Amsterdam North-Holland. Kar, S., Beladi, H., 2004. Skill Formation and International Migration: welfare perspective of developing countries. Jpn. World Econ. 16, 35–54. Komiya, R., Amano, A., 1972. International Economics. Modern Economics, 8. Iwanami Shoten, pp. 424–428 Chap. 16 (in Japanese). Oda, M., Shimomura, K., 2012. A model of welfare enhancing capital imports. Rev. Int. Econ. 40 (issue 4), 758–766. Rutten, M., 2009. The economic impact of medical migration: a receiving country’s perspective. Rev. Int. Econ. 17 (issue 1), 156–171. Sato, Y., Yamamoto, K., 2012. Trade impacts on skill acquisition via variety expansion. Jpn. Econ. Rev. 63 (no. 4), 451–466. Stark, O., Zakharenko, R., 2012. Differential migration prospects, skill formation, and welfare. Rev. Int. Econ. 20 (issue 4), 657–673. Uzawa, H., 1969. Liberalization of foreign investment and national economy. Econ. Dec. 23, 106–122 (in Japanese).
Please cite this article in press as: M. Oda, M. Okawa, A model for liberalizing nursing and trade, Japan World Econ. (2018), https://doi.org/ 10.1016/j.japwor.2018.03.003