Barriers to immigration and the dynamics of emigration

Journal of Macroeconomics 37 (2013) 41–52

Contents lists available at SciVerse ScienceDirect

Journal of Macroeconomics journal homepage: www.elsevier.com/locate/jmacro

Barriers to immigration and the dynamics of emigration Slobodan Djajic´ ⇑ The Graduate Institute, Geneva, Switzerland

a r t i c l e

i n f o

Article history: Received 16 February 2012 Accepted 1 June 2013 Available online 18 June 2013 JEL classification: F22 Keywords: Emigration Migration costs Remittances Capital accumulation

a b s t r a c t In a dynamic model of emigration and return migration I examine the role of migration costs in the process of capital accumulation of the source country. Every migration attempt reduces the amount of savings available for capital accumulation. It contributes, however, to an increase in the per-capita capital stock of the source country if the migrants leave some of their capital behind or decide to return and repatriate accumulated savings. The interaction among these flows governs the evolution of the economy’s capital stock and factor rewards, which in turn affects the decisions to emigrate and return migrate. Both the quantitative and qualitative effects of host-country policies and other disturbances on the key macroeconomic variables of the source country are found to depend on the level of migration costs. Ó 2013 Elsevier Inc. All rights reserved.

1. Introduction The 20th century was one of fundamental change with respect to immigration policies of the host countries. A relatively open system of international migration has been steadily modified with layers of new restrictions applying primarily to unskilled immigrants from the developing countries. For workers from parts of Africa, Latin America and Asia, legal access to the labor markets of many of the advanced countries has become practically impossible. This has resulted in rapid growth of illegal immigration, smuggling of humans, unfounded asylum applications, and the use of a wide range of legal loopholes as well as illegal methods of getting to and staying in an advanced country. The cost of coming illegally to the USA or Canada from an overseas location is now in the tens of thousands of dollars. Expenses faced by illegal immigrants and asylum seekers arriving to the European Union are only slightly lower.1 In many cases, entire families pool their savings to contribute to the cost of passage of a single family member. For migrants from very poor developing countries, even partial, up-front payment for the journey is often larger than the economy’s average amount of capital per head. Emigration can then potentially lower the economy’s capital-labor ratio, push down wages and contribute to an expansion of migration pressures.

⇑ Tel.: +41 22 908 5934. E-mail address: [email protected] According to Hajdinjak (2002), immigrants from Central Asia coming to Western Europe have to pay between $9000 and $14,000, while immigrants from China pay up to $24,000. For someone from Sri Lanka trying to reach Canada, the UK or Germany without proper documentation in 2008–2009, the cost was $40,000, $25,000, and $20,000, respectively (see Van Hear (2010), p.15). Petros (2005) uses over 500 secondary sources to compile data on the amounts paid by smuggled migrants for a wide range of origin and destination points. The payments are found to depend on the mode of transport, the distance traveled and the services provided by the smuggling organization. 1

0164-0704/$ - see front matter Ó 2013 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.jmacro.2013.06.001

42

S. Djajic´ / Journal of Macroeconomics 37 (2013) 41–52

Legal migration of unskilled workers, where that is possible, also imposes a heavy financial burden on the migrants. The cost of a visa and the fee charged by a recruiting agent can be more than a year’s earnings in a developing country.2 Accordingly, every migration attempt by a low-skilled worker, whether legal or illegal, chips away at the savings of the source country, reducing capital accumulation and employment expansion that is needed to stem the tide of emigration. The other side of the coin is that emigration generates a stock of migrants abroad. This gives rise to flows of remittances, return migration, and repatriated savings, which tend to improve welfare of the source country. Repatriated savings play a particularly important role in the creation and expansion of small businesses. According to Woodruff and Zenteno (2007), in regions of Mexico that experienced significant emigration to the USA, over one third of new small businesses are started by returning migrants with savings accumulated abroad. The role of return migration and repatriated savings in the process of capital accumulation is well documented in the literature.3 The present study introduces these features of contemporary international migration into a simple dynamic model of emigration and return migration. The focus is on the process of capital accumulation in the source country and how it relates to the outflows and return flows of migrants in the presence of high and rising barriers to immigration imposed by a host country. Three channels through which migration affects the per-capita capital stock of the source country are modeled explicitly. First, every migration attempt diverts savings of the source country to cover migration costs at the expense of other projects such as physical investment. If, however, the cost of a successful migration attempt is smaller than the economy’s per-capita capital stock, emigration increases the economy’s capital intensity, assuming that emigrants leave their capital behind. Finally, a certain proportion of workers employed abroad will eventually return to their country of origin. This generates a flow of returnees who typically repatriate their accumulated savings and contribute to capital accumulation in the source country. The interaction among these flows that are triggered by emigration and possible return migration has non-trivial implications for the dynamics of the capital stock and the stock of labor employed in the source country. Relative supplies of productive factors influence, in turn, the factor rewards that govern the evolution of emigration and return migration in the short run and the long run. Within this framework of analysis, it is shown that while a high cost of entering the host country serves to deter migration attempts, it also has an indirect effect that operates in the opposite direction. Migration costs lower the source country’s net benefit of emigration, which manifests itself in a lower rate of capital accumulation. Paradoxically, as a result of this indirect effect, disturbances that stimulate emigration, such as an increase in the foreign wage or political instability at home, generate a larger steady-state flow of migrants when the cost of migration is relatively higher. The paper goes further to examine the consequences of a change in the level of immigration barriers, as reflected in the cost of a migration attempt and the probability of successful arrival in the host country. While a lower probability of success is found to reduce emigration flows, an increase in migration costs, for a given probability of success, may actually stimulate emigration under certain conditions. In particular, when an increase in migration costs gives rise to decumulation of capital, the stock of migrants in the new steady state is shown to increase, provided the responsiveness of migration flows to migration costs is sufficiently low. Such low responsiveness is likely to be observed only in very exceptional situations where political instability or armed conflict is pushing migrants out of the source country. Earlier models of international migration and capital accumulation have focussed on the role of differences in the savings propensities of migrants and non-migrants in influencing the economy’s steady-state stock of capital per head (see, e.g., Berry and Soligo (1969), Rodriguez (1975a,b), Galor (1986), and Hazari and Sgro (2003)). The more recent contributions to the literature on migration and growth focus, instead, on various aspects of the brain-drain problem. They analyze the implications of international mobility of skilled workers and how it affects the growth process or the stock of human capital in the sending or receiving countries.4 Most of these contributions assume that international mobility is costless. In the current environment, characterized by high and rising barriers to international migration, it is increasingly important to take migration costs into account. This is especially the case when examining the source-country effects of international mobility of unskilled workers, which is the focus of the present study. The remainder of the paper is organized as follows. A model of an economy experiencing emigration and return migration is developed in Section 2. Both phenomena affect the rate of capital accumulation, while the economy’s capital stock, in turn, has an impact on the propensity of labor to emigrate and return migrate. Section 3 looks at the short- and long-run implications of changes in the economic environment facing the migrants, including the immigration policies of the host country that affect the cost and the probability of successful emigration. Finally, Section 4 concludes the paper with a summary of the main results.

2 Shah (1998) reports that for unskilled migrants who worked in Kuwait in 1995, the average cost of a visa was $1733 for workers from Bangladesh, $1116 for Indians, $1294 for Pakistanis and $645 for Sri Lankans. Other fees charged by recruiting agents plus travel expenses come on top. For temporary migrants from Thailand, Jones and Pardthaisong (1999) find the average cost of migration to be two year’s worth of an unskilled worker’s wages at home, with large variations across destination countries. For example, the fees charged by Thai recruitment agencies in 1995–1996 were $1600 for Brunei, $2200 for Israel, $1800 for Singapore and $3400 for Taiwan. 3 See Rivera-Batiz (1986), Singer et al. (1995), Durand et al. (1996), Escobar-Patapi et al. (1991), Taylor (1987), Ilahi (1999), Lucas (1987), Massey and Parrado (1998), and McCormick and Wahba (2001). 4 See, e.g., Beine et al. (2001), Benhabib and Jovanovic (2012), Chen (2006, 2008), Di Maria and Stryszowski (2008), Miyagiwa (1991), Mountford (1997), Vidal (1998), and Wong and Yip (1999).

S. Djajic´ / Journal of Macroeconomics 37 (2013) 41–52

43

2. Migration and the source country Let us assume that the world consists of the source country (S) and the host country (H). A single commodity is produced in this world under constant returns to scale with the aid of capital and labor. Output can be either consumed or used as capital. There is perfect competition and full employment of factors. H has a more advanced technology, more developed institutions, more capital per head, and hence a higher wage rate w. This attracts immigrants. Of those who successfully migrate, some eventually return to S for economic or other reasons. When they do, they bring with them accumulated savings. We shall assume that H is large in relation to S, so that its wage w can be taken as given. The wage prevailing in country S at time t, wt(kt), is an increasing function (with the usual properties) of the capital-labor ratio, kt, employed in production. For notational simplicity, we shall drop all time subscripts in the discussion below and use subscripts to indicate partial derivatives. It should be clear that the endogenous variables are functions of time. 2.1. Emigration International migration is assumed to be costly, with the cost directly related to the level of barriers to immigration imposed by the authorities of H in an effort to limit immigration from S. Let us suppose that each potential migrant is obliged to pay or use up w units of output when attempting to enter H. The attempt is successful with the probability p 2 (0, 1), allowing the migrant to settle and work at the destination. For simplicity, we treat both w and p as exogenous variables, determined by the immigration policies of H.5 Both w and p have an impact on the proportion of the labor force of S that will attempt to migrate. The relationship between w and w is also important, as is the quality of the political and institutional environment, x, of the source country. When the young generation has confidence that economic, social, and political stability will improve in the years to come, due to improved institutional structures, they are less likely to emigrate. The total flow of emigrants, E, can be expressed as the product of the following three variables: L, the current stock of labor in the source country, m, the proportion of the labor force attempting to migrate, and p, the probability that the attempt is successful. We thus write E as

E ¼ Lpm½wðkÞ; w ; w; p; x;

ð1Þ

where m1, m3, m5 < 0, m2, m4 > 0 for reasons given above. If migration costs are lower than k, we shall assume that the migrants leave whatever remains of their capital at the disposal and for the benefit of family members in S.6 Alternatively, if migration costs exceed k, it is the rest of the family that pools its savings to help cover the costs. 2.2. Return migration Emigration from S need not be permanent. Over the 20th century, roughly one third of immigrants to the advanced countries ended up choosing to return to their country of origin or to move on to a third country within a decade or more after arrival [see Borjas and Bratsberg (1996) and Mulder et al. (2002)]. From the perspective of the source countries, return migration has been an important source of capital, contributing to economic development. Let us therefore assume that a proportion q of the stock of emigrants return per unit of time, each bringing a constant amount, /, of saved output to contribute to capital formation in S.7 It is natural to assume that the returning migrants are relatively rich in comparison with the source-country population in the sense that / > k (see, e.g., Jones and Pardthaisong (1999) and Sobieszczyk (2000)). The flow, R, of returning migrants is

R ¼ ðL  LÞqðk; xÞ;

ð2Þ

where q1 < 0,under the assumption that return migration is discouraged by an increase in k, which lowers the rental rate on savings repatriated to the source country.8 In addition, q2 > 0 on the assumption that a higher quality of the political and institutional environment in S attracts migrants to come back. L  L is the stock of migrants abroad, L being the original level of the labor force of S and L its current stock. For simplicity we assume that households are infinitely lived and there is no population growth. 5 In general, immigration barriers, along with optimizing behavior of migrants, determine jointly p and w. Policies that enhance border controls will clearly have a direct negative effect on p, but also contribute to an increase in w, as migrants find it optimal to expand more resources in order to overcome the higher obstacles. Other policies, such as that of confiscating vehicles used to transport illegal aliens have a relatively greater impact on w than they do on p. We therefore treat w and p as separate variables, capturing a range of immigration barriers and enforcement measures used by the host country. Endogenous determination of w and p through optimizing behavior of migrants is a topic for another paper. For the seminal work on illegal immigration, see Ethier (1986). 6 This is typically the case for low-skilled migrants and particularly for those who have intentions to return to their country of origin. 7 For simplicity, I assume that savings of migrants are repatriated at the time of return, rather than being sent back gradually in the form of remittances. 8 Djajic´ (2010) shows that an increase in the expected rate of return on capital in the source country encourages utility-maximizing migrants to return (if they otherwise intended to remain permanently in the host country) and return sooner (if they planned to stay abroad temporarily).

S. Djajic´ / Journal of Macroeconomics 37 (2013) 41–52

44

2.3. The dynamic system With the proportion m of the labor force emigrating and the proportion q of the emigrant stock returning to the source country, the rate of change of L is given by dL=dt ¼ ðL  LÞqðk; xÞ  Lpm½wðkÞ; w ; w; p; x. Using b L to represent the proportional rate of change of the labor force, we have

b L ¼ kqðk; xÞ  pm½wðkÞ; w ; w; p; x;

ð3Þ

where k ¼ ðL  LÞ=L is the stock of emigrants as a proportion of the source country’s current labor force. To keep the model relatively simple, let us assume that a constant proportion, s, of per capita income, y(k), is saved, where y(k) is the standard neoclassical production function, with the usual properties, written in its intensive form. A part of the savings, wm(.), is used to finance emigration attempts and the rest is invested in physical capital formation. Capital accumulation is also supported by the savings of returning migrants, /kq(k, x), while a constant proportion d of the capital stock K ^K b b L, the rate of change of the per-capita capital stock, dk/dt, is therefore depreciates per unit of time. Since k

k_ ¼ syðkÞ  wm½wðkÞ; w ; w; p; x þ /kqðk; xÞ  dk  kb L:

ð4Þ

Eqs. (3) and (4) constitute a system of two differential equations in k and L, which govern the dynamics of capital accuL ¼ 0 and k_ ¼ 0. We thus have mulation and the labor force of S. In the steady state, both b

kqðk; xÞ  pm½wðkÞ; w ; w; p; x ¼ 0; 

syðkÞ þ /kqðk; xÞ  dk  wm½wðkÞ; w ; w; p; x ¼ 0:

ð5Þ ð6Þ

In what follows, we suppress the arguments of the functions to express the steady-state conditions simply as kq = pm and sy  dk = wm  /kq. To examine the stability properties of our dynamic system, consider the partial derivatives of (3) and (4) with respect to k and L.

@b kq L pm ¼ g  gqk 70; k mk @k k @b L L ¼  2 q < 0; @L L L @ k_ sy wm /kq @b ¼ gyk þ gmk  d  gqk  k 70; @k @k k k k @ k_ L ¼ qðk  /Þ < 0; @L L2

ð7Þ ð8Þ ð9Þ ð10Þ

where gmk = (@m/@k)(k/m) > 0, gqk = (@ q/@k)(k/q) > 0, and gyk = (@ y/@k)(k/y) 2 (0, 1). From (7)–(10), we find that the slopes L ¼ 0 and k_ ¼ 0 schedules in the neighborhood of the steady-state are given by of the b

 . L dL pm  ¼ gmk  gqk q:  dk bL¼0 k L2    dL sy mðpk  wÞ pmð/  kÞ mðp/  wÞ Lð/  kÞq ¼ ð g  1Þ  g  g  : mk qk dkk¼0 k yk k k k _ L2

ð11Þ ð12Þ

In the discussion below, we shall focus on the case in which gmk > gqk (i.e., the emigration propensity, m(.), is more elastic than the return propensity, q(.), with respect to changes in the economic conditions of the source country associated with an L=@k > 0 in Eq. (7) and the b L ¼ 0 schedule is positively sloped, as shown in Figs. 1a and increase in k).9 Under this assumption, @ b 1b. The k_ ¼ 0 schedule may be either positively or negatively sloped, depending on the environment facing the migrants. The condition that w < pk is sufficient to guarantee that k_ ¼ 0 is negatively sloped, as in Fig. 1a. This is the case of ‘‘low’’ migration costs, where the average expenditure required for successful emigration, w/p, is smaller than k, the average amount of capital available per unit of labor in S. For higher values of w, the k_ ¼ 0 schedule may be positively sloped as in Fig. 1b. In fact if w > /p + [sy(1  gyk)/m(1 + gmk)], the k_ ¼ 0 schedule is not just positively sloped, but it is steeper than the bL ¼ 0 schedule. In that case, however, our dynamic system exhibits saddlepoint instability.10 In what follows we shall focus on the stable case by assuming that

w < /p þ ½syð1  gyk Þ=mð1 þ gmk Þ;

ð13Þ

9 In relation to emigrants living abroad, potential migrants are much more aware of and directly affected by economic developments in S. Their behavior, therefore, is likely to be more responsive to changes in k. The interested reader can easily work through the opposite case where gmk < gqk. 10 The determinant of the matrix of partial derivatives (7)–(10) is then negative, implying that the two characteristic roots of the system are of opposite sign.

S. Djajic´ / Journal of Macroeconomics 37 (2013) 41–52

45

Fig. 1a. Dynamics of adjustment in the presence of ‘‘low’’ barriers to migration.

Fig. 1b. Dynamics of adjustment in the presence of ‘‘high’’ barriers to migration.

and hence consider only the two configurations of the dynamic system which are presented in Figs. 1a and 1b. The arrows and the examples of the adjustment paths in the diagrams reflect the signs of the partial derivatives (7)–(10). Total differentiation of (5) and (6) in the neighborhood of the steady state yields

"

#

q  dk  sy ðgyk  1Þ þ g þ 1Þ  /pkm ðgqk þ 1Þ q/ dk k " #  p m  x ðgmx þ gqx Þdx þ mð1 þ gmp Þdp þ pwm gmw dw  pwm gmw dw ; ¼  wm  mx ðwgmx þ /pgqx Þdx þ wgmp m p dp þ w gmw dw þ mð1  gmw Þdw  pmd/ pm ðg

mk k wm ð mk k

 gqk Þ

ð14Þ

where gmx = (@m/@x)(x/m) > 0, gqx = (@ q/@x)(x/q) > 0, gmw ¼ ð@m=@w Þðw =mÞ > 0, gmw = (@m/@ w)(w/m) > 0, and gmp = (@m/@ p)(p/m) > 0. All elasticities are assumed to be constant. The determinant of the coefficient matrix, h i D ¼ pkm ðgmk  gqk Þq/  syk ðgyk  1Þ þ wm ðgmk þ 1Þ  /pkm ðgqk þ 1Þ q, is positive when the stability condition (13) is satisfied. k The system (14) can be solved for the long-run effects of changes in the exogenous variables w, x, p, w, and / on the key endogenous variables k and k. Once we know k and k, the implications for y, L, m, and q follow immediately. We shall examine these results as well as the paths of adjustment to the steady-state in the next section. 3. Dynamics of migration and the capital stock Let us consider the short- and long-run effects of changes in the environment facing the migrants. 3.1. An increase in the foreign wage L ¼ 0 schedule down to ðb L ¼ 0Þ0 , as illustrated in Figs. 2a and 2b. The magnitude of the shift is A rise in w shifts the b

S. Djajic´ / Journal of Macroeconomics 37 (2013) 41–52

46

Fig. 2a. Effects of an increase in w with a negatively sloped k_ ¼ 0 schedule.

Fig. 2b. Effects of an increase in w with a positively sloped k_ ¼ 0 schedule.

 .L dL  pm ¼   gmw q < 0;  w dw bL¼0 L2

ð15Þ

while the vertical shift of the k_ ¼ 0 schedule is given by

 . dL  m L ¼ ðw  kpÞ  gmw ðk  /Þ 2 q?0:  w dw k¼0 _ L

ð16Þ

Thus with / > k, as assumed in Section 2, the k_ ¼ 0 schedule shifts up if migration costs are relatively ‘‘low’’ (i.e., w < kp) and down if they are relatively ‘‘high’’ (i.e., w > kp). The downward shift of the k_ ¼ 0 schedule can be even larger than that of L ¼ 0 schedule. This occurs if w > p/, so that the cost of a migration attempt exceeds the associated benefit of return the b migration from the perspective of capital accumulation in the steady state.11 Emigration and the consequent return migration then have a net adverse effect on capital accumulation, resulting in a lower steady-state value of k. By contrast, when migration costs are lower than the steady-state benefits (i.e., w < p/), an increase in w raises k in the long run. This is confirmed by solving the system (14) for dk/dw.

 h i dk 1 mq ¼ gmw ðp/  wÞ ?0; as   D w dw

p/?w:

ð17Þ

11 In the steady state, the per-capita flow of emigrants pm is equal to the flow of returnees, kq. If each successful emigrant drains w/p units of the economy’s savings, while each returnee brings / units back for capital formation, then the per-capita inflow of savings, /kq, is smaller than the per-capita emigration cost, wm, when w > p/.

S. Djajic´ / Journal of Macroeconomics 37 (2013) 41–52

47

To get a rough idea of how these results relate to what is observed in developing countries where international migration plays an important role in the society and where migration costs represent a heavy burden on a migrant’s household, let us consider the case of Thailand. The average monetary costs of migration for officially recruited guest workers and clandestine migrants surveyed by Sobieszczyk (2000) were $2334 and $4173, respectively, in the 1990s. For the same period, Jones and Pardthaisong (1999) estimate the costs to be around 2 years worth of unskilled wages in Thailand. If we take a capital-output ration of 2.5, which was roughly the average for developing Asian economies at the time [see Nehru and Dhareshwar (1993)], back of the envelope calculations indicate that w < pk.12 We also know that returnees were bringing back 10, 20 and even up to 50 thousand US dollars of accumulated savings, depending on the destination country, occupation, and the duration of stay. With more than 95% of migrants successfully migrating and eventually returning to their villages,13 it is clear that in the case of Thailand, p/ > w. This implies that an increase in emigration from that country in response to higher demand for foreign labor in the Middle East or the rapidly growing East Asian economies can be expected to raise the economy’s capital-labor ratio in the long run. By contrast, in a country like Somalia, where k is much lower and emigrants face rising barriers to entry and progressively narrower opportunities for asylum in the advanced countries, it is safe to assume that w > pk. Nonetheless, it is difficult to say whether in the steady state, if one is attained, the amount of savings absorbed by the cost of emigration would exceed or fall short of the inflow of savings coming from abroad.14 Turning back to our theoretical model, note that when the stability condition is satisfied,

dk  ¼ dw

 h i 1 pm sy gmw ð/p  wÞðgqk þ 1Þ þ ð1  gyk Þ > 0;  D wk k

ð18Þ

meaning that dL/dw < 0. We thus have Proposition 1. In the long run, an increase in w raises the stock of migrants abroad and may either lower or raise k, depending on whether the cost of a migration attempt is larger or smaller than the eventual inflow of repatriated savings stemming from that attempt. Let us consider next the dynamics of adjustment to the steady state. An immediate effect of an increase in w is to encourage emigration. As this is costly, it draws source-country capital away from productive activity. If w/p < k, then every attempted departure, on the average, leaves the remaining population with a higher k. As can be seen in (16), this is the case in which the k_ ¼ 0 schedule shifts up to ðk_ ¼ 0Þ0 in Fig. 2a. Emigration is then initially accompanied by an expansion of k, as along the adjustment path from A towards B1. By contrast, with a somewhat higher w in relation to other variables (i.e., pk < w < p/), the k_ ¼ 0 schedule shifts down to ðk_ ¼ 0Þ00 in Figs. 2a and 2b. Expansion of emigration now contributes to an initial decline in k. Over time, however, the increase in the stock of migrants abroad, along with a lower k, stimulates return migration and repatriation of savings from abroad. This contributes to capital accumulation and eventually brings about an increase in k, as shown by the adjustment paths AB2 in Figs. 2a and 2b.15 The long-term effect on k of an increase in emigration may therefore be the opposite of that observed in the short run. L ¼ 0 locus, setting the economy on Finally, when w > p/, the downward shift of the k_ ¼ 0 schedule exceeds that of the b the adjustment path AB3 in Figs. 2a and 2b.16 Decumulation of capital in the initial phase is now more pronounced, as is the decline in w, which encourages larger outflows of labor. As the stock of migrants abroad increases and k declines, the flow of return migration expands. This helps to partly rebuild k and stabilize L along the path to the new steady state at B3. Nonetheless, in contrast to the cases corresponding to relatively smaller migration costs, k is lower in the steady state, as are w and L. We thus have Proposition 2. In response to an increase in w, the stock of immigrants in H increases more when the cost of migration is high than it does when it is low. The same is true for the flow of migrants. This can be seen in Eq. (5), which shows the steady-state flow of migrants, Lpm equal to the flow of returnees, ðL  LÞq, which is unambiguously higher when both L and k are lower. The intuition behind this somewhat paradoxical result is simple to grasp. When a disturbance such as a rise in w triggers an outflow of labor, the higher is w, the more of the economy’s savings are absorbed by emigration, reducing its capacity to accumulate capital. A lower k contributes to greater emigration pressures in the long run and results in a larger stock and flow of migrants. 12 Consider a Cobb–Douglas production function where annual output Y = AKaL1a. It follows that Y/K = Aka1 and annual earnings of a worker, oY/ oL = (1  a)AKa. With K/Y = 2.5 and a = 1/3, we have annual earnings of labor equal to (4/15)k. Since the cost of migration, w, in the case of Thailand is twice that amount and the migrants are primarily contract workers with p close to unity, it follows that w < pk. 13 A very small proportion of overseas workers from Thailand fail to return to their villages. Jones and Pardthaisong (1999) report that in only 2 of the 63 surveyed villages was this proportion over 5%. 14 The one-million-strong Somali diaspora sends roughly a billion U.S. dollars per year to support consumption and investment spending back home. In some of the communities where calm has been restored, bombed-out housing has been reconstructed and new enterprizes are emerging in the services sectors such as transport and commerce, showing signs of growth in k. As we shall see below, this does not necessarily provide an indication as to the sign of w  p/, as an expansion of k along the adjustment path is consistent with both w > p/ and w < p/. 15 Note that in the range of w such that pk < w < p/, the k_ ¼ 0 schedule may be either positively or negatively sloped, hence both Figs. 2a and 2b are relevant. 16 Once again the k_ ¼ 0 schedule can be either positively or negatively sloped. In the borderline case of w = p/, the sign of the slope of the k_ ¼ 0 locus is the same as that of /  k  [sy(1  gyk)/pm(gmk  gqk)], which may be either positive or negative.

S. Djajic´ / Journal of Macroeconomics 37 (2013) 41–52

48

Fig. 3. Effects of an increase in p.

3.2. An increase in the probability of successful migration Since we treat w and p as separate variables, let us first examine the implications of a change in p while holding w constant. An increase in p stimulates emigration, causing the b L ¼ 0 locus to shift down by

  dL  L ¼ mð1 þ gmp Þ q < 0;  dp bL¼0 L2

ð19Þ

while the k_ ¼ 0 schedule may shift either up or down.

 dL  L ¼ m½wgmp  kpð1 þ gmp Þ=pðk  /Þ 2 q?0: dpk¼0 _ L

ð20Þ

To understand the conflicting forces that affect the shift of the k_ ¼ 0 schedule, note that as the flow of migrants increases with an increase in p, this has both a positive and a negative immediate impact on capital accumulation. On the one hand, departing emigrants leave their capital behind, which helps increase the amount of capital available to the remaining residents. On the other hand, emigration is costly, absorbing some of the economy’s capital stock. When migration costs are sufficiently low relative to k, the first effect dominates, so that an increase in p triggers an initial expansion in k. More precisely, this occurs when (w/p) gmp < k(1 + gmp), in which case the k_ ¼ 0 schedule in Fig. 3 shifts up to ðk_ ¼ 0Þ0 . Capital accumulation then continues along the adjustment path from A to B1, where the economy ends up with a larger k and a smaller L in relation to the initial values at A. For relatively higher migration costs, (w/p) gmp > k(1 + gmp), implying that the k_ ¼ 0 schedule shifts down. The magnitude of the shift may be either greater or smaller than that of the b L ¼ 0 locus, depending on whether the per-capita cost of the larger emigration flow, wgmp, is greater or smaller than the per-capita inflow of repatriated savings, p/(1 + gmp). That is, depending on whether an increase in p generates in the long run a negative or a positive net contribution to capital accumulation. As shown in Fig. 3, with a downward shift of the k_ ¼ 0 schedule, the increase in emigration induced by an increase in p initially causes k to contract. Growth in the stock of migrants abroad and the increase in the return on capital in S stimulates return migration to eventually reverse the process of capital decumulation. In the end, depending on whether wgmp is smaller or greater than p/(1 + gmp), the economy may end up with either a higher or a lower k in the new steady state. This is illustrated in Fig. 3 by the points B2 and B3, respectively.17 Our diagrammatic analysis of the steady state can be confirmed by solving (14) for the long-run change in k and k.

 dk 1 mq ¼ ½ð1 þ gmp Þ/p  wgmp ; dp D p 

  dk 1 pm sy wm /pm ¼ ðgmk  gqk Þwgmp  mð1 þ gmp Þ ðgyk  1Þ þ ð1 þ gmk Þ  ð1 þ gqk Þ : dp k k k k D

ð21Þ ð22Þ

17 The dynamics of adjustment are very similar when the k_ ¼ 0 schedule is positively sloped. To save space, we depict and discuss only the case of a negatively sloped k_ ¼ 0 locus in Fig. 3. The same is done for the analysis of an increase in w in Fig. 4.

S. Djajic´ / Journal of Macroeconomics 37 (2013) 41–52

49

Fig. 4. Effects of an increase in migration costs.

Note that dk/dp > 0 when the stability condition (13) is satisfied. Proposition 3. An increase in the probability of successful migration generates a larger stock of migrants abroad and may either raise or lower k in the long run, depending on whether the per-capita cost of the larger emigration flow is smaller or greater than the increase in the per-capita inflow of repatriated savings. What the various equilibria in Fig. 3 illustrate, in addition, is that the higher the cost of migration, the larger the steadystate stock of migrants and the lower the value of k. A lower k and a larger k imply that the steady-state flow of returnees (and hence outflow of emigrants) is also higher when w is larger. We recall that similar findings were obtained in our analysis of an increase in w. That is, the higher the level of migration costs, the greater the long-run stock and flow of migrants as a result of a change in the environment that increases the attractiveness of international migration. 3.3. An increase in the cost of migration While an increase in w, for a given p, tends to discourage emigration, it has a rather complex influence on both k and k. On the basis of (14), the long-run effects of an increase in w on k and k are given by

    dk 1 p/ mq gmw 1  1 : ¼ dw w D 

  dk 1 pm2 p/ sy ¼ gmk  gqk þ gmw ð1  Þð1 þ gqk Þ  ðgyk  1Þ : dw w wm D k

ð23Þ ð24Þ

Both of these expressions are of ambiguous sign. To understand the source of ambiguity, we turn to Fig. 4, where an increase in w shifts the b L ¼ 0 locus up by

  dL  pm L ¼ g q > 0: dwbL¼0 w mw L2

ð25Þ

L ¼ 0 locus is smaller, the higher Note that for any given gmw and other parameters of the model, the upward shift of the b the initial level of w. The k_ ¼ 0 schedule may shift either up or down:

   dL  pk L ð/  kÞ 2 q?0: ¼ m gmw ð1  Þ  1  dw k¼0 w _ L

ð26Þ

As the denominator of this expression is positive, its sign hinges on the sign of the numerator, which consists of two potentially conflicting terms. There is the direct negative impact on capital accumulation as an increase in w raises the burden of any given emigration flow. This corresponds to 1 in the bracketed expression. The increase in w also discourages emigration, which has either a positive or negative indirect effect on capital accumulation in the short run, depending on whether w is greater or smaller than pk. This indirect effect is captured by the first term in the brackets of expression (26). If w > pk and the propensity to migrate is sufficiently sensitive to w (i.e., a large enough gmw), we can have   gmw 1  pwk > 1. This is the case in which the indirect deterrent effect of higher migration costs dominates the direct effect. Capital accumulation is then initially stimulated by an increase in w and the k_ ¼ 0 schedule shifts up in Fig. 4. The shift can

S. Djajic´ / Journal of Macroeconomics 37 (2013) 41–52

50

  be either larger or smaller than that of the b L ¼ 0 locus, depending on whether gmw 1  pw/ ?1. In either case, adjustment to the new steady state begins with capital accumulation, as illustrated along the paths AB1 and AB2 in Fig. 4.18 The initial increase in w and the expansion of k along the adjustment path discourages emigration, causing L to rise. Along with an expansion of k, this reduces the flow of return migration and repatriated savings, eventually producing a reversal in the process of capital   accumulation. In the end, the economy settles at B2 with a lower k when gmw 1  pw/ < 1, and B1 with a higher k when   by Eq. (23). gmw 1  pw/ > 1. This isconfirmed  Alternatively, if gmw 1  pwk < 1, either because migration is not very responsive to an increase in w or because w < pk, the k_ ¼ 0 schedule shifts down to ðk_ ¼ 0Þ000 . The economy then decumulates capital in response to an increase in w, as shown along the trajectory AB3. Proposition 4. An increase in the cost of migration tends to lower k in the long run, except if the cost of migration is high in relation to the inflow of repatriated savings and the propensity to migrate is sufficiently responsive to migration costs. Note that steady states at B1, B2, and B3 feature an increase in L, implying that an increase in migration costs lowers the stock of migrants in the new steady state. An increase in the stock of migrants, however, is also possible. As may be seen in Fig. 4, a necessary condition for this outcome is that the k_ ¼ 0 schedule shifts down. The intersection point between the k_ ¼ 0 and b L ¼ 0 schedules may then be at a lower level of L in relation to the initial value L0. This is clearly the outcome if gmw = 0, L ¼ 0 schedules does not shift in response to an increase in w. When migration is not at all responsive to an in which case the b increase in migration costs, there is only the direct effect of an increase in w on capital accumulation, causing a downward shift of the k_ ¼ 0 schedule to produce a new steady state at B4. Similar outcomes that generate a long-run decline in L (and hence a larger stock of immigrants in H) emerge as long as gmw is sufficiently small, as may be seen in Eq. (24). This scenario can be relevant in situations where a conflict in S is the principal cause of emigration. Migrants and refugees in such cases try to reach a desired destination almost at any cost, even if the attempt may result in the loss of life. Policies that increase migration costs to H in an effort to reduce the inflows can then fail to have a sufficient deterrent effect and prove to be counterproductive. By draining a larger volume of savings of the source country, they can increase migration pressures without effectively preventing the inflows. 3.4. Effects of a positive institutional change An increase in x has a wide-ranging impact on the economy. Focusing here only on the direct impact of institutional change on emigration and return migration, we find that it may have either a positive or a negative effect on the longrun value of k.19 By deterring costly emigration, positive institutional change enables the economy to use more of its savings for capital accumulation. In steady state, however, less emigration is associated with an equal reduction in the flow of return migration and repatriated savings, which has a negative impact on the long-run value of k. If w > p/, the fall in expenditure on emigration exceeds the loss of repatriated savings, causing the steady-state value of k to increase. Alternatively, when w < p/, k declines in the long run. This can be confirmed by solving (14) for dk/dx.

dk ¼ dx

 1 qm g ðw  p/Þ?0: D x mx

ð27Þ

Proposition 5. Positive institutional change is relatively more effective in promoting capital accumulation in the source country when the cost of successful emigration (w/p) is high, the amount of savings (/) brought back by each returning migrant is relatively small, and the flow of emigration is very responsive to institutional change (gmx is large). The long-run effect on L is always positive, provided the stability condition (13) is satisfied.20 3.5. An increase in / An increase in the amount of savings, /, repatriated by returning migrants has an unambiguous positive impact on capital L ¼ 0 locus unaffected. Both k and L are therefore higher and accumulation. It shifts the k_ ¼ 0 schedule up, while leaving the b the stock of migrants lower in the long run. The steady-state flow of return migration, ðL  LÞq, is also smaller, as must be the outflow of emigrants. 18 The only difference between the steady states at B1 and B2 is assumed to be the initial value of w, which is relatively higher at B1, while all other parameters of the model are the same. 19 In general, the social and political dimensions of institutional change may affect the marginal productivity of capital and labor as well as the propensity to save of residents. Allowing for such effects would obviously contribute to a positive impact of institutional change on the steady-state capital stock. 20 Short and long-run effects of an increase in x are examined in detail in a longer version of this paper, Djajic´ (2009).

S. Djajic´ / Journal of Macroeconomics 37 (2013) 41–52

51

Proposition 6. By contributing to capital accumulation and higher wages in the source country, an increase in the amount of repatriated savings per returning migrant reduces both the stock and flow of migrants in the new steady state. Policies that help raise /, such as a return subsidy, would have a similar impact. 4. Conclusions Over the last two or three decades, due to tightening of immigration restrictions in the advanced countries, migration costs facing low-skilled workers and asylum seekers have risen in real terms to levels that have not been seen for centuries. These costs affect not only the migrants and their families, but also the pace of capital accumulation and the evolution of migration pressures in the source countries. The present study examines the implications of migration costs for the process of capital accumulation and the dynamics of emigration and return migration. Disturbances that stimulate emigration, such as an increase in the foreign wage or political instability at home, are found to entail larger flows of migrants when the level of migration costs is higher. These costs drain resources of the source country, leaving less savings available for capital accumulation. Less capital per head means lower wages, which makes it less attractive for potential migrants to stay at home. An increase in migration costs is found to have very different effects on both the steady-state flow of migrants and the stock of capital per head, depending on the values of the model’s parameters.21 Expansion of the capital stock is more likely, the larger the costs relative to benefits of emigration and the greater the elasticity of the propensity to migrate with respect to migration costs. By deterring emigration, an increase in costs can under these circumstances reduce emigration flows and contribute to capital accumulation in the source country. In contrast, if an increase in costs gives rise to decumulation of capital, the stock of migrants in the new steady state may actually increase, provided the responsiveness of migration flows to migration costs is sufficiently low. Such low responsiveness is likely to be observed in very exceptional situations where political instability or armed conflict is pushing migrants out of the source country. Host-country efforts to reduce the inflows by raising immigration costs can then prove to be counterproductive. Our analysis also suggests that policies that encourage return by means of supporting political, economic and social stability in the source country or increasing the flow of repatriated savings (either by facilitating such flows or by providing return subsidies to migrants willing to return) are likely to be more effective than immigration barriers in reducing migration pressures. They have an indirect effect of stimulating capital accumulation in the source country, while barriers to immigration, by increasing migration costs, lower capital accumulation and contribute to an increase in the desire to emigrate. Reducing migration pressures by supporting positive institutional change, is found to be most effective when the cost of migration is high, the savings repatriated by returning migrants are small, and the flow of migrants is very sensitive to institutional change. Our comparative statics results are supported by an analysis of the adjustment process to the steady state. The adjustment paths illustrate that the direction of change in the capital stock in the short run may be the opposite of that in the long run. This stems from the fact that the burden of emigration costs comes first, while the benefits of return migration and repatriated savings are enjoyed by the source country only after having built a stock of migrants abroad. References Beine, M., Docquier, F., Rapoport, H., 2001. Brain drain and economic growth: theory and evidence. Journal of Development Economics 64, 275–289. Benhabib, J., Jovanovic, B. 2012. Optimal Migration: A World Perspective. International Economic Review 53, 321–348. Berry, R., Soligo, R., 1969. Some welfare aspects of international migration. Journal of Political Economy 77, 778–794. Borjas, G., Bratsberg, B., 1996. Who leaves? The outmigration of the foreign-born. Review of Economics and Statistics 78, 165–176. Chen, H.-J., 2006. International migration and economic growth: a source country perspective. Journal of Population Economics 19, 724–748. Chen, H.-J., 2008. The endogenous probability of migration and economic growth. Economic Modeling (forthcoming). Di Maria, C., Stryszowski, P., 2008. Migration, human capital accumulation and economic development. Journal of Development Economics (forthcoming). Djajic´, S., 1989. Migrants in a guest-worker system: a utility maximizing approach. Journal of Development Economics 31, 327–339. 21 Indeed, our model shows a wide range of possible outcomes for a given disturbance, depending on the environment facing potential emigrants. This raises the question as to whether some of the outcomes could be ruled out by using a model based on more solid micro foundations. My original intention was to rely on the results of my earlier work on optimal behavior of temporary migrants [Djajic´ and Milbourne (1988) and Djajic´ (1989, 2013, 2010)] in developing a dynamic model of emigration, return, and capital accumulation. The problem with that approach is that, as the wage and the rate of return on capital in the source country vary over time, each cohort of emigrants has a different optimal duration of stay and time path of consumption, as well as a different stock of assets to repatriate and invest in the source country upon return [see Djajic´ (2010)]. This makes dynamic analysis extremely complex and analytically intractable. There remains the possibility of comparing steady states, with the outcomes determined by what one assumes with respect to preferences and other parameters of the model. This does not help us, however, in narrowing down the range of possible outcomes. For example, in a model of temporary migration (Djajic´ (2010)), if the degree of concavity of the utility function is constant and equal to 0.85, a utility-maximizing migrant with a time horizon of 50 years will stay abroad for 10.64 years and accumulate $19,200 of savings when the rates of interest and time preference are both 3%, the annual wage abroad is $3000, while the domestic wage is $1000 and he is assumed to get 20% more utility by consuming a given bundle of goods at home rather than abroad. If we increase the assumed degree of concavity of the utility function from 0.85 to 0.90, he will stay abroad 2.56 years and repatriate only $5350 back to the source country. This example illustrates how a small change in the value of one parameter of the utility function can have a very large effect on the optimal duration of stay abroad and the amount of repatriated savings. Since we know very little about the degree of concavity of a migrant’s utility function, much less whether it takes on a value of 0.85, 0.90 or, for that matter, 0.95, (in which case the worker would not want to migrate at all in the context of the environment described above), a macro model of migration and capital accumulation based on solid micro foundations would not allow us to narrow down the range of empirically relevant macro outcomes.

52

S. Djajic´ / Journal of Macroeconomics 37 (2013) 41–52

Djajic´, S. 2009. Barriers to Immigration and the Dynamics of Emigration, mimeo. Graduate Institute, Geneva, Switzerland. Djajic´, S. 2013. Temporary Migration and the Flow of Savings to the Source Country, forthcoming, Review of Development Economics. Djajic´, S., 2010. Investment opportunities in the source country and temporary migration. Canadian Journal of Economics 43, 663–682. Djajic´, S., Milbourne, R., 1988. A general-equilibrium model of guest-worker migration: the source country perspective. Journal of International Economics 25, 335–351. Durand, J., Kandel, W., Parrado, E.A., Massey, D.S., 1996. International migration and development in mexican communities. Demography 33, 249–264. Escobar-Patapi, A., de la, M., Martinez-Castellanos, O., 1991. Small scale industry and international migration in Guadalajara. In: Diaz-Briquets, S., Weintraub, S. (Eds.), Migration, Remittances, and Small Business Development: Mexico and Caribbean Basin Countries. Westview, Boulder. Ethier, W.J., 1986. Illegal immigration: the host-country problem. American Economic Review 76, 56–71. Galor, O., 1986. Time preference and international labor migration. Journal of Economic Theory 38, 1–20. Hajdinjak, M., 2002. Smuggling in Southeast Europe. CDS Report no. 10, Center for the Study of Democracy, Sofia. Hazari, B.R., Sgro, P.M., 2003. The simple analytics of optimal growth with illegal migrants. Journal of Economic Dynamics and Control 28, 141–151. Ilahi, N., 1999. Return migration and occupational change. Review of Development Economics 3, 170–186. Jones, H., Pardthaisong, T., 1999. The impact of overseas labour migration on rural thailand: regional, community and individual dimensions. Journal of Rural Studies 15 (1), 35–47. Lucas, R.E.B., 1987. Emigration to South Africa’s mines. American Economic Review 77, 313–330. Massey, D.S., Parrado, E.A., 1998. International migration and business formation in Mexico. Social Sciences Quarterly 79, 1–20. McCormick, B., Wahba, J., 2001. Overseas work experience, savings and entrepreneurship amongst return migrants to LDCs. Scottish Journal of Political Economy 48, 164–178. Miyagiwa, K., 1991. Scale economies in education and the brain drain problem. International Economic Review 32, 743–759. Mountford, A., 1997. Can a brain drain be good for economic growth in the source country? Journal of Development Economics 53, 287–303. Mulder, T., Guzman, J.B., Brittingham, A. 2002. Evaluating Components of International Migration: Foreign-Born Emigrants. Population Division Working Paper no. 62, U.S. Census aBureau. Nehru, V., Dhareshwar, A., 1993. A new database on physical capital stock: sources, methodology and results. Revista de Analisis Economico 8, 37–59. Petros, M., 2005. The Cost of Human Smuggling and Trafficking. Global Migration Perspective, Report no. 31, Global Commission on International Migration. Rivera-Batiz, F., 1986. International migration, remittances and economic welfare in the source country. Journal of Economic Studies 13, 3–19. Rodriguez, C.A., 1975a. Brain drain and economic growth. Journal of Development Economics 2, 227–247. Rodriguez, C.A., 1975b. On the welfare aspects of international migration. Journal of Political Economy 83, 1065–1072. Shah, N.M., 1998. The role of social networks among South Asian male migrants in Kuwait. In: Appleyard, R. (Ed.), Emigration Dynamics in Developing Countries, Vol. II. Ashgate Publishing, South Asia, Adershot. Singer, A., Durand, J., Massey, D.S. 1995. Coming into the Country: The Social Process of Border Crossing among Undocumented Mexican Migrants. Working paper, Population Studies Center, University of Pennsylvania. Sobieszczyk, T., 2000. Pathways abroad: gender and internatinal migration recruitment choices in northern thailand. Asian and Pacific Migration Journal 9 (4), 391–428. Taylor, J.E., 1987. Undocumented Mexico-U.S. migration and the returns to households in rural Mexico. American Journal of Agricultural Economics 69, 616–638. Van Hear, N., 2010. In the Mix: The Growing Salience of Mixed Migration as an Analytical and Policy Concept, paper presented at the Conference on The Concept of Mixed Migration, Geneva, 8–9 April, 2010. Vidal, J.-P., 1998. The effect of migration on human capital formation. Journal of Population Economics 11, 589–600. Wong, K.-Y., Yip, C.K., 1999. Education, growth and brain drain. Journal of Economic Dynamics and Control 23, 699–726. Woodruff, C., Zenteno, R., 2007. Migration networks and microenterprises in Mexico. Journal of Development Economics 82, 509–528.