Reversing the Brain Drain: Is it Beneficial?

World Development Vol. 67, pp. 310–322, 2015 0305-750X/Ó 2014 Elsevier Ltd. All rights reserved. www.elsevier.com/locate/worlddev

http://dx.doi.org/10.1016/j.worlddev.2014.10.023

Reversing the Brain Drain: Is it Beneficial? SYED MUHAMMAD HUSSAIN* Lahore University of Management Sciences, Pakistan Summary. — This paper investigates costs and benefits of calling back expatriates of a developing country. I employ a life cycle model with a rich and poor country with endogenous migration and return migration. Cost of bringing back a worker is the compensation that is paid to him while the benefit is the increased output because of his higher skill level and positive externalities, which are empirically estimated, from him resulting in higher skill levels for local workers. Results show that welfare gains are maximized when workers with skill levels 1.28 standard deviations above the domestic mean skill level are called back. Ó 2014 Elsevier Ltd. All rights reserved. Key words — brain drain, spillovers, life cycle model, return migration, developing countries, Pakistan

1. INTRODUCTION

other words, it is quite possible for two expatriates of the same skill level to have different preferences when it comes to quality of life and other factors mentioned above. Second, the model built in this paper is a problem that a policy maker is solving. It is unreasonable to believe that the policy maker will be able to observe all these preferences. Therefore it is assumed that the policy maker is only able to observe the skill level of the worker. Furthermore, the model considered in this paper is not an attempt at modeling the migration and return migration decisions at an individual level. Rather, it assesses return migration which class of workers, in terms of skill level, will bring the highest net benefit to the home country. Third, even if it is assumed that preferences about quality of life vary perfectly by skill level and that the policy maker is able to observe these preferences, the modification required in the model will be minimal since only the cost paid by the government will have to be scaled up or down which will leave the qualitative nature of the results unchanged since the utility function that is used in the model is linear (like most labor search models). I will focus on the case of Pakistan but the model developed in this paper is general enough to be applied to any country. Developing countries, like Pakistan, suffer from brain drain since they are unable to offer suitable opportunities to highly educated workers. There are different estimates for the number of Pakistanis in the USA ranging between 250,000 and 700,000. Recent years have seen an increase in the number of Pakistanis who emigrate to the USA. Figure 1 plots the number of Pakistani immigrants to the USA in each year for the 1992–2009 time period. The figure shows that the number of Pakistani immigrants to the USA have been steadily growing over the last two decades. The only exception was the 2002–03 period when the number of immigrants admitted to the USA fell because of the 9/11 events. However, increasing trend of Pakistani immigration resumed soon after and it has

This paper analyzes the effect of return migration on the macroeconomic performance of a developing country; and particularly on the incomes of the residents and nationals of the country. One of the leading engines of growth in capitalscarce countries is human capital accumulation. A major factor that acts as a detriment to human capital accumulation in developing countries is brain drain. A considerable proportion of immigrants settle in resource rich countries and it is hard for the home country to provide them with the right incentives to return to their homeland. This paper seeks to formalize this issue through a theoretical model of migration, skill growth, skill spillovers, and government incentives to call back the emigrants. It further takes data on the Pakistani population to calibrate the model and suggest policy implications. The basic idea is grounded in making the worker indifferent between migrating and staying abroad. In the model, workers that migrate for better financial and economic opportunities abroad can only be attracted back by the government through a compensation mechanism that gives them a greater lifetime utility than staying in the rich country. To illustrate the key findings of the model two countries are considered; one termed as rich and the other denoted poor. The migration decision is endogenous to the model. For the government, the direct benefit to the poor country from calling a migrant back is the increase in output. The cost is the higher compensation that the worker will have to be paid to come back and work in the poor country. The more interesting and novel contribution of the paper to the literature is the empirical estimation of the benefit that the migrant brings in the form of positive spillovers; skill based externalities that extend to the entire labor force working around him. The respective costs and benefits vary by the skill of the migrant. It can reasonably be argued that return migration decision of expatriates do not depend just on the income that they earn. Several other factors play a role as well. These factors include asset holdings, preference for being near to their family if it resides in the home country, preference for having a superior lifestyle, and preference about education quality for their children, and security. While all these factors, and possibly more, play an important role in decision of an expatriate to return to his or her home country, the model of this paper abstracts away from these preferences for three reasons. First, it is not clear how these preferences will vary by skill level. In

* I would like to thank Ryan Michaels, William Hawkins, Mark Bils, Joshua Kinsler, and two anonymous referees for providing me with valuable comments and feedback. I would also like to thank seminar participants at University of Rochester, NY who provided me with useful comments. Thanks also to Abid Burki of Lahore University of Management Sciences for providing me with the data used in this paper. This paper appeared as the third chapter of my Ph.D. thesis at University of Rochester, NY. All mistakes are my own. Final revision accepted: October 22, 2014. 310

Number of Pakistani Immigrants to the USA

22000

20000

18000

16000

14000

12000

10000

0 1992

1994

1996

1998

2000 2002 Year

2004

2006

2008

2010

Remittances from the USA to Pakistan (in millions of dollars)

REVERSING THE BRAIN DRAIN: IS IT BENEFICIAL?

311

200 180 160 140 120 100 80 60 40 20 0

Jul97

Jan00

Jul02

Jan05 Time

Jul07

Jan10

Figure 1. Pakistan to the USA Migration. Source: Yearbook of Immigration Statistics, DHS, USA.

Figure 2. Remittances from the USA to Pakistan. Source: State Bank of Pakistan.

been climbing ever since. These numbers only include Pakistanis who become naturalized citizens and do not include workers who come to the USA on a temporary basis. Data show that Pakistani Americans 1 tend to be more prosperous than average Americans. The 2002 US census showed that the average yearly income of a US household was $57,852 whereas that of an average Pakistani American household was $70,047. There are no current estimates for the average education level of Pakistani Americans. However, Carrington and Detragiache (1998) estimated that there were 52,717 Pakistani immigrants in the US in 1990 and out of these, 36,097 (68%) had 12 years or more of education. This shows that most of the Pakistanis who emigrate to the USA have high levels of education. On the other hand, literacy rates in Pakistan remain extremely low. According to the Federal Bureau of Statistics, Pakistan, only 3.28% of Pakistani population has 12 or more years or education. The migration of such high-skilled workers to the USA and other western countries causes the economy to suffer especially in a country like Pakistan where high skilled workers are in scarce supply. Apart from the direct contribution to the income of the economy, these high skilled workers also create positive externalities for their coworkers and other people who interact with them. Apart from this immediate impact on the country’s economy, such migration can have long-term effects as well. Well-educated workers affect the economy in at least two ways (other than directly contributing to the overall output) (1) They create positive externalities for other individuals working with them and (2) They are more likely to educate their children as well hence benefiting the country’s economy in the future as well. However, having more expatriates is also beneficial for a country’s economy. Some of the migrants return home after getting valuable experience and/or education abroad. They then apply their newly acquired skills in the home country. Furthermore, these expatriates, while abroad, earn higher wages and send remittances back to the country. For a developing country, these remittances can represent a significant proportion of the GDP. 2 Figure 2 plots the remittances (in nominal dollar terms) that have been sent to Pakistan from the USA since 1996 on a monthly basis. The plot shows that the remittances sent home have been growing over time. There was a sharp increase in remittances sent to Pakistan after the 9/11 events. After that event, fearing for the confiscation of their assets, Pakistani Americans started shifting their assets to Pakistan. Ahmed and Jha (2010) showed that reducing

remittances by 50% would increase the poverty rate by 6.35%. Hence, although there are benefits from calling back expatriates to work in Pakistan, they must be weighed against the prospect of forgone remittances which form an important part of the foreign exchange. Another channel through which expatriates can prove to beneficial to the economy of the country is return migration. Expatriates gain skills while working in the developed countries which impact the economy of the home positively if they choose to return migrate. There have been a number of theoretical and empirical models built to explain the migration and return migration decisions. One of the strongest theoretical models about return migration was by Dustmann, Fadlon, and Weiss (2011) in which they model migration as decisions that respond to where human capital can be acquired most efficiently. They showed that return migration of workers can lead to brain gain since the return migrants will be more productive at home. Borjas and Bratsberg (1996) used the 1980 census data to show that return migration occurs because workers can sometimes find better opportunities for working back home. Dustmann and Weiss (2007) used a dynamic Roy model with worker who possessed two different skill levels which had different prices in different countries. They showed that return migration may be planned when making the initial migration decision. Workers may temporarily migrate to a rich country to boost their skill which in turn would enhance their earning potential back home. Mayr and Peri (2008) used an overlapping generations model to show that workers in a poor country may get higher education to increase their chances of landing a job abroad. However, if migration process is not deterministic, some of these highly educated workers will not be able to move to the rich country and work in their home country which would lead to brain gain. Beine, Docquier, and Rapoport (2001) also showed that individuals in a developing country invest in human capital and education to maximize their chances of moving to a richer country. The home country then benefits from the skills of those who are not able to migrate. None of these papers focus on evaluating the costs and benefits of calling some workers to migrate back to the home country. This paper fills this void by employing a simple model to quantify the costs and benefits of enforced return migration. Furthermore, to my knowledge, there is no paper that attempts to estimate the spillovers from returning migrants to a country. This paper also attempts to fill this gap in the literature. The results show that an extra return migrants leads

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to a 0.88% increase in the income of workers that are in the same occupation–location pair as the return migrant. The simulation results of the model show that for the government to maximize the income earned by workers working in the home (developing) country, it will be optimal for it to call back a worker from abroad whose skill level is 1.28 standard deviations above the mean skill level of workers at home. Since skill is a combination of education and experience, this skill level can either correspond to highly skilled young professionals or highly experienced professional or a combination of both. Calling back workers of lower skill levels will lower the gain since their experience in the rich country would not be high and hence the superior skill accumulation would be lower. Calling back workers of higher skill levels will lower the gain since the cost of calling them back would be too high. The model considered in this chapter is a simple model that does not include savings or labor supply decisions. It simplifies the computation exercise greatly and allows for the model to be tractable. However, the cost of having a simple specification is that it abstracts away from some real life phenomenon, such as labor supply decisions depending on asset levels of return migrants: a returning migrant with high level of savings may not supply the same amount of labor as other workers. In that case, the benefits of bringing that worker back will be lower. The benefits may also go up for bringing back a worker with high assets because investment of those savings would create more jobs. 3 A solution to this problem is that the government can require the return migrants to work full time and monitor their work behavior. This monitoring would increase the cost that the government needs to pay for bringing a worker back but this monitoring cost would be small in comparison to the compensation that the government would pay in form for forgone wages to the return migrant. Furthermore, the government cannot observe the asset levels of the expatriates and thus cannot include it in their decision mechanism. Thus, even without incorporating level of savings, this paper provides a useful framework to evaluate such a policy experiment and future research can build on this model to allow for richer specifications that take care of some of the mechanisms not considered here. The rest of the paper is organized as follows: Section 2 describes the model, Section 3 describes the data, Section 4 describes calibration and estimation of parameters used in the mode, Section 5 reports the results, Section 6 discusses the policy implications and directions for future research, and Section 7 concludes the paper. 2. MODEL There are two countries named Poor and Rich (abbreviated to P and R hereafter). N number of workers are born in R at the beginning of period 1 and they live for T periods. All age 1 agents have identical preferences over consumption paths ct , t ¼ 1; . . . ; T . All agents are risk neutral and discount the future with discount factor b, and therefore have utility function 4 " # T X t U ¼E b ct : t¼1

Workers start off with different levels of skill. The skill level of worker i in at time t in country j, where j 2 P ; R is denoted by xi ðj; tÞ. The skill level of a worker is the same as his marginal product. The skill level for age 1 workers is drawn from a distribution Gp ð:Þ. xi ðP ; 1Þ ¼ mi ; mi  N ðlG ; rG Þ

Since negative skill levels are not possible, the distribution is truncated at 0. At t = 1, every newborn starts working in P. Labor markets in P are competitive so that a worker in P earns his marginal product. While working in P each worker earns his marginal product. At the same time he searches for jobs in R. Jobs from R arrive at a rate kðxðÞÞ which depends on the skill level of the worker. The wage offers that workers in P looking for jobs in R get are drawn from a normal distribution W ðÞ with mean lW and variance rW . Once a worker finds a job in R, his wage grows at rate g. Jobs in R get destroyed at a rate d; if his job is destroyed, worker returns to P and works there for the remaining periods. Denote the number of workers in P and R by P t and Rt respectively. In each country the skill level of workers grows over time. In R the skill growth is at an exogenous rate gR . xi ðR; t þ 1Þ ¼ xi ðR; tÞð1 þ gR Þ In P, the skill growth depends both on an exogenous rate gP and the overall skill level of return migrants. 5 Since return migrants only form a small fraction of the total population, it is assumed that only their average skill level is what matters in the growth rate of skill. This specification rules out scale effects: the number of returning migrants does not affect the growth of skill. In future work, it will be interesting to generalize this to allow for a scale effect. In this model, however, a simpler functional form is considered to preserve tractability. 6 The growth rate of skill of a return migrant is gRM which may be different from gP which is the growth rate of skill of workers of P who never migrated to R. Denote the number of return migrants by RM. That is, P j2RM xj ðÞ xi ðP ; t þ 1Þ ¼ xi ðP ; tÞð1 þ gP þ 1IRM ðgRM  gP ÞÞ þ j RM ð1Þ where  1IRM ¼

1

if agent i is a return migrant

0

otherwise

Given these details, the Bellman equations for workers can now be written. The Bellman equation for a worker working in P is, for t < T , V Pt ðxi ðP ;tÞÞ ¼ ðxi ðP ;tÞ  cÞ þ bkðxi ðÞÞ

Z

 w wi

V Rtþ1 ðxi ðR; t þ 1Þ;wÞdW ðwÞ

þ bð1  kðxi ð:ÞÞV Ptþ1 ðxi ðP ; t þ 1ÞÞ

ð2Þ

The first term on the R.H.S. is the current payoff for a worker of skill level xðP ; tÞ working in P (recall that the labor market in P is considered to be competitive i.e., workers earn their marginal product). c is the average cost that every worker in P will have to pay in case the government calls some of the expatriates back. This term will be discussed in detail later once the model has been set up for worker in both countries. The second term represents the continuation value for the worker when he gets a job in R. wi is the wage offer which makes the worker indifferent between moving to R and staying  is the highest wage offer that any worker can get. The in P. w third term represents the continuation value when the worker stays in P. For t ¼ T , the worker earns his marginal product only, so that

REVERSING THE BRAIN DRAIN: IS IT BENEFICIAL?

V Pt ðxi ðP ; tÞÞ ¼ xi ðP ; tÞ  c The Bellman equation for a worker of skill level xðR; tÞ and wage w working in R is, for t < T  V Rt ðxi ðR;tÞ;wÞ ¼ max V Pt ðxi ðP ;tÞÞ;wð1  sÞ þ bdV Ptþ1 ðxi ðP ;t þ 1ÞÞ  þbð1  dÞV Rtþ1 ðxi ðR;t þ 1ÞÞ For t ¼ T , V Rt ðxi ðR; tÞ; wÞ ¼ wð1  sÞ The second term in the max operator shows the value of staying in R. If V Pt ðxi ðp; tÞÞ > wð1  sÞ þ bdV Ptþ1 ðxi ðP ; t þ 1ÞÞ þ bð1  dÞV Rtþ1 ðxi ðR; t þ 1ÞÞ then the worker will not work in R and instead return to P. If instead wð1  sÞ þ bdV Ptþ1 ðxi ðP ; t þ 1ÞÞ þ bð1  dÞV Rtþ1 ðxi ðR; t þ 1ÞÞ > V Pt ðxi ðp; tÞÞ then the worker will stay in R and his value would be the equation on the left side of previous inequality. The first term in the equation is the current payoff which is equal to the wage that the worker earns in that period reduced by a factor s. ws represents the amount that the worker working in R will send back to P (in form of remittances). In the baseline model, it is assumed that workers working in R do not get any utility from the remittances sent home. Later this assumption will be changed and workers in R will get utility from remittances sent home too. The second term is the continuation value of the worker when his job is exogenously destroyed. In that case the worker returns to P. The final term is the continuation value of the worker whose job is not destroyed and he continues to work in R. In this case his wage grows at a rate g. wtþ1 ¼ wt ð1 þ gÞ When a worker of skill level xðP ; tÞ working in P receives a job offer that pays w, he chooses to migrate to R if V Rt ðxi ðR; tÞ; wÞ > V Pt ðxi ðp; tÞÞ The cost c that every worker in P would pay in case the government decides to call some of the migrants back can now be defined. These workers will be referred to as call backs to differentiate them from other return migrants who choose to migrate back either endogenously or because of exogenous ~ job destruction, denote the number of callbacks as RM. Assume that the government decides to call exactly one migrant back to P at time t. Further assume that the call back is of skill level xð:; tÞ and works at a wage rate w in R. Because the call back is risk neutral, to make him indifferent between working in R and coming back and working in P, he will have to be paid the difference in between what he would have earned in R and what he would actually earn in P. Since the worker is risk neutral, he does not care about when the cost is paid to him. He can be paid the full cost in the first period of his returning back, or he could be paid the difference in earnings each period. The cost c is defined as ci ¼

wt ð1sÞð1bð1þgÞðT tþ1Þ Þ 1bð1þgÞ

ðT tþ1Þ

RM Þ  xðP ;tÞð1bð1þg 1bð1þgRM Þ

Þ

Pt

Finally, two measures of welfare are defined. The first one is the IR (Income of Residents) of P and the second one is the IN (Income of Nationals) of P. It is not clear whether the cost

313

that each worker has to pay in case of call back should be or should not included in the welfare functions. The cost that is paid in form of compensation to the call backs is part of the overall output (GDP) of the country. Since, the welfare is measured at the macroeconomic level, it just means that the higher compensation is being transferred from the locals to the returning migrants. Based on this line of reasoning, the compensation paid to the returning migrants should not be considered a cost. On the other hand, it can be argued that since every local worker is losing some part of his income, and that the government is not able to spend the amount that government pays as compensation to return migrants elsewhere in the economy, the higher compensation should be considered a cost. The two measures of welfare consider both these possibilities. IR treats the higher compensation paid to returning migrants as a cost where IN does not. P P s j2R wj X i2P xi ðP ; tÞ IRt ¼ þ  ck Pt Rt ~ k2RM P P i2P xi ðP ; tÞ þ j2R wj IN t ¼ P t þ Rt This concludes the description of the model. 3. DATA This paper uses data from two sources. The first is the Labor Force Survey of Pakistan which is conducted every year. I use the data from the surveys of 2007 and 2008. Although the total of observations in both surveys combined was 301,961, some of them had to be discarded because of various reasons. The main reason for discarding most of the observations was the absence of wage data which is central to this study. Some other observations that were missing relevant information, like occupation, location, age etc, were also discarded. The sample dropped those occupations which require very low or no skills at all. Examples would include manual laborers, daily wagers, domestic workers etc. Observations that were about unemployed or self employed workers were also omitted. This ensured that the analysis would involve only those professions where spillovers from returning migrants actually matter. Including unskilled professions in the analysis would definitely lower the estimated spillover parameters since the wages of workers in unskilled professions only depends on the supply and demand of labor and returning migrants would increase the supply of labor thereby reducing the wage rate. This would make the benefits from return migration look less attractive then they really are. Also, a government will never consider financing the return of unskilled workers to home country since their return will bring no benefits to the local workers. A final filter was used to drop observations where the age was below 18. Eventually the sample used for this analysis had 51,149 observations. Table 1 gives a break down of reasons because of which observations were dropped. Out of these, 919 people were return migrants i.e., were employed abroad in the previous period. The second data set used is the IPUMS-USA (Integrated Public Use Microdata Series-USA). IPUMS, housed at the Minnesota Population Center, consists of microdata samples from the US census records. This paper uses data from eight consecutive censuses starting from 2000. Respondents who report their ancestry as Pakistani are separated. The total sample size of those who reported their ancestry as Pakistani was 11,987. This sample included both citizens and those who were not citizens of the United States at the time of

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WORLD DEVELOPMENT

Table 1. A breakdown of observations dropped from the Labor Force Survey Total number of observations Number of observations dropped Number of observations dropped Number of observations dropped Number of observations dropped Number of observations dropped not involve skill

301,961 due to missing wages 173,241 due to low education level 51,851 due to age < 18 8,463 due to missing information 6,209 where occupation does 11,048

Total number of observation used in the analysis

51,149

collection of data. About 54% of the sample consisted of naturalized citizen of Pakistani ancestry whereas the rest were those who were not citizens of the United States. The Appendix to this paper describes the profile of Pakistanis in the United States in more detail. 4. CALIBRATION The Appendix to this paper describes the parameter values used for the model. Most of the parameters are standard or could be computed easily from available data. However, the most important parameter to enter the model was the spillover parameter, estimation of which is described next. (a) The spillover effects The most important parameter, to be estimated is the spillover effect from returning migrants. This is the main channel through which the benefits from a return migrant (or a call back) would be realized. If there were no spillovers then the only benefit to the economy from the call back would be his direct contribution to the income which will not be more than the cost that will have to be paid to bring him back. The reason is that the cost to bring an expatriate back is the difference between what he actually earns and what he would have earned. Since his earnings would be higher in R, this implies that he will be earning more than what a worker, who never migrated to R, of same skill level would be. This extra earning would be paid by everyone else making them worse off. However, these positive externalities make sure that the skill level of others also go up thereby making them better off too. There are no estimates of such spillovers from returning migrants. The basic equation that needs to be estimated is lnwageijl ¼ b0 þ b1 Educi þ b2 Expi þ b3 Exp2i þ b4 Abroad i þ jAbroad jl þ ijl

ð3Þ

In this equation, the dependent variable is the log of wages of worker i of occupation j working in location l. Educi is the education level (number of years), Expi and Exp2i are the experience and the square of experience of the worker. Since experience was not reported in the data, potential experience was implicitly calculated as Expi ¼ Agei  Educi  5 Abroad i is a dummy variable which takes a value of 1 if worker i is a return migrant. Abroad jl is the fraction of occupation j workers that are return migrants among all occupation j workers in location l. The coefficient on this will give the spillover effects. In absence of any endogeneity and/or reverse causality issues, this coefficient will represent the increase in

log wages of workers of a particular occupation–location pair attributable to the number of return migrants. However, it is unlikely that workers randomly sort into different locations when returning to the home country. Attractiveness of a particular location or occupation may result in the problem of reverse causality. The coefficient on Abroad ij can only be interpreted as the increase in wages from returning migrants if those workers choose their locations randomly. It is possible that the returning migrants choose those locations where they know they will earn higher wages. Hence, it then would be the wages driving their decisions of migrating back rather than the return migration being responsible for the increase in wages. To tackle this problem, the Abroad ij variable was split into two variables namely Abroad Famij and Abroad Econij . Each individual in the data was asked about the reason of migration. These reasons could be put into two broad categories namely family related reasons and economic reasons. Abroad Famij represents the proportion of people who migrated back for mainly family reasons. Abroad Econij represents those who migrated back for economic (job or business related) reasons. It is reasonable to assume that workers who migrate back for family reasons choose the location they settle in less because of the economic conditions there than do those who migrate for economic reasons. Hence the coefficient on this variable will be a better estimate of the true increase in wages in a particular occupation–location pair because of returning migrants. To further isolate the economic effects particular to a location, another variable Dom Migjl is included in the regression. This variable represent the proportion of workers in that occupation–location pair that migrated from within the country. It is assumed that domestic migration takes place only because of economic reasons. 7 The regression now becomes lnwageijl ¼ b0 þ b1 Educi þ b2 Expi þ b3 Exp2i þ b4 Abroad i þ b5 Dom Migjl þ jAbroad jl þ j1 Abroad Econij þ j2 Abroad Famij þ ijl

ð4Þ

The results of this regression are in Table 2. The first column reports the results of this equation when the Abroad jl variable is not split. The results show that coefficients on education and experience are unchanged and the coefficient on Abroad jl (which is the coefficient of interest) is reduced in magnitude but is still positive and significant. The coefficient on the new variable, Dom Migjl is positive and significant. The second column in Table 2 reports the result of Eqn. (4) when Abroad kl is split into Abroad Econij and Abroad Famij . The coefficients on education, experience, and the domestic migrants are virtually unchanged. The coefficient on Abroad Econij is 4.15% and is significant. This suggests that the suspected reverse causality may indeed be present and wages drive the return migration decisions. The coefficient on Abroad Famij , which is now the true measure of spillovers, is 0.65 % which implies an increase of 1 point in returning workers leads to a 0.65% increase in wages of workers in the occupation–location pair. Using the average incomes,this implies an increase of around 600 PKR or $7 in yearly incomes. The coefficient on Abroad is still negative and insignificant which is confusing. A final regression with an interaction term between experience and the abroad dummy was run because it may be possible that every return migrant does not earn significantly more than the locals and thus the average impact of return migration may seem to be insignificant.

REVERSING THE BRAIN DRAIN: IS IT BENEFICIAL?

315

Table 2. Estimation of spillover parameter

Educ Exp Exp2 Abroad Abroad Dom_Mig

(1) ln_wage

(2) ln_wage

(3) ln_wage

(4) ln_wage

0.0726*** (123.22) 0.0539*** (71.47) 0.000698*** (50.72) 0.00777 (0.22) 0.829*** (4.39) 0.372*** (15.35)

0.0726*** (123.30) 0.0538*** (71.46) 0.000698*** (50.69) 0.00784 (0.22)

0.0726*** (123.22) 0.0537*** (71.05) 0.000694*** (50.06) 0.180* (2.13) 0.811*** (4.29) 0.371*** (15.33)

0.0726*** (123.30) 0.0537*** (71.03) 0.000694*** (50.04) 0.182* (2.16)

Abroad Econ Abroad Fam Abroad*Exp _cons N

0.369*** (15.21) 4.151*** (4.67) 0.646*** (3.32)

9.669*** (875.08)

9.668*** (875.16)

0.00516* (-2.46) 9.670*** (874.68)

51,149

51,149

51,149

0.368*** (15.19) 4.153*** (4.68) 0.627** (3.22) 0.00524* (-2.50) 9.669*** (874.77) 51,149

t statistics in parenthesis. * p < 0.05. ** p < 0.01. *** p < 0.001.

lnwageijl ¼ b0 þ b1 Educi þ b2 Expi þ b3 Exp2i þ b4 Abroad i þ b5 Dom Migjl þ jAbroad jl þ j1 Abroad Econij þ j2 Abroad Famij þ cExpi  Abroad i þ ijl

ð5Þ

The results of this equation are in columns 3 and 4 of Table 2. The results are not different from the previous regression, however now the coefficient on Abroad becomes positive and significant. Workers who return from abroad, on average, earn 0.2% more than other workers. Interestingly, the coefficient on the interaction term between experience and abroad dummy is negative and significant. This implies that within the group of returning migrants, young workers earn more than the older ones. This can be the case if the older workers returning have already exhausted their skills and are not returning for work related reasons. It is common for workers to return to Pakistan and spend their post retirement life there. 8 Data show that people returning for non economic reasons are on average 8 years older than those returning for economic reasons. Further, 23% of workers returning from abroad for family reasons are of age 60 or more whereas none of those returning for economic reasons are age 57 or more. The Appendix to this paper presents the results for this regression when those returning for family reasons who are above the age of 55 are excluded from the fraction of return migrants since these workers are likely to either not work at all, or work less than full time. The results show that the spillover parameter in that case becomes numerically bigger and remains highly significant. At the end of the analysis, the value chosen for j for the baseline model was 0.0088 which lies in the middle of the various estimates obtained from the regressions. 9 Two other values, namely 0.0068 and 0.0108 were used to check for robustness of results. The Appendix to this paper presents an alternative computation of benefits to local economy of returning migrants based on works of Kapur, McHale, and McHale (2005) and Borjas (1995).

The parameters for initial skill distribution and the wage distribution are set to match the data. The fitted values from Eqn. (4) give the skill level of workers in P. The mean and standard deviation of these fitted values were used as the parameters of initial skill distribution. Similarly the mean and standard deviation of the wages of Pakistani Americans were used as the parameters of the wage distribution. It is assumed that all wage offers are drawn from the same distribution which is set to match the existing wage distribution of Pakistani workers in the USA. 10 The wages of both countries were converted to real terms using the purchasing power parity. Table 3 summarizes the values of the parameters chosen. 5. RESULTS The model was solved in the following way: wages from the data were used to find the parameters of skill distribution (ls and rs ). These parameters are used to form an interval ðls  3rs ; ls þ 3rs Þ. This interval is then discretized into N equally spaced points. The Bellman equations are then solved using backward induction. These equations are then used to simulate the migration and return migration decisions of a model economy with M workers. Figures 3 and 4 plot the simulated distributions of wage and age of migrants against their data counterparts. This exercise was done to check for the goodness of fit of the model. Figure 3 plots the observed distribution of wages and the simulated distribution that comes from the model. The model does a good job in matching this distribution. The norm of distance between these two distributions is 0.11. Figure 4 does the same job for the distribution of age of migrants. 11 The model again does a reasonable job in matching the age distribution from the data. The norm of distance between these two distributions is 0.052.

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WORLD DEVELOPMENT Table 3. Parameter values

Variable

Description

Value

Source

T b d s j gP gR g gM

No. of periods an agent lives for Discount factor Return migration rate Fraction of income sent home as remittances Spillover effect Growth rate of skill in P Growth rate of skill in R Growth rate of wages in R Growth rate of skill of return migrants

42 0.9709 0.018 0.18 0.0068–0.0108 0.0012 0.0125 0.0213 0.0101

Corresponds to working age of Pakistanis Corresponds to real interest rate of 3% (World Bank) United Nations, FBS Calculated Estimated Estimated Estimated Various sources Estimated

Age Distribution of Migrants

0.14 0.12 0.1 0.08

DIN t ¼ IN ct  IN nc t

0.06

This change in IR and IN is calculated for each period for every skill level that is located abroad. These differences are plotted in Figures 5 and 6 for a few skill levels. There were 60 different skill levels and in the model and 49 get job offers to move to R. The lowest skill level to move to R was 3 and highest was 58. 13 Figure 5 plots DIRt resulting from calling back workers of different skill levels. The x-axis has the time and y-axis has the change in income of the residents of P DIRt . The first plot shows that when a worker of the lowest skill level (skill level 3) is called back, there is a decline in the fifth period in the per capita income of workers of P. Recall that it is the average skill level of return migrants which affects the growth rate of skill of workers of P. When a worker of very low skill level is called back, the average skill level of return migrants (denoted by the last term in Eqn. (1) goes down because of which the growth rate of skill levels of workers is lower then it would be in absence of this call back. Further reducing the income of workers of P is the cost that has to be paid to

0.04

0.16 Data Model

0.14 0.12

0

1

2

3

4 5 Age Groups

6

7

8

Figure 4. Age distribution of migrants from P.

x 10

−8

Skill Level 3

Change in total income of Residents, Δ IRt

Change in total income of Residents, Δ IRt

−7

0

−0.5

−1

−1.5

10 −8

10

x 10

20 30 Time Skill Level 41

40

0

10

20 Time

30

x 10

40

Skill Level 26

0

−5

10 −8

5

−5

5

15

x 10

20 30 Time Skill Level 56

40

20 Time

40

10 5 0 −5

10

30

Figure 5. Effect of calling back workers of various skill levels on income per capita of nationals of P over time.

0.1 Frequency

0.02

Change in total income of Residents, Δ IRt

Wage Distribution of Migrants

Data Model

0.16

Change in total income of Residents, Δ IRt

DIRt ¼ IRct  IRnc t

0.18

Frequency

To calculate the change in income of workers in P (IR) and income of all nationals of P (IN) that results from calling one worker back from R, the model was first solved without any nc call backs. Both the IRnc t and IN t were calculated for each period. The model was then solved again but this time one worker of a particular skill level was called back. 12 Denote the total incomes in this model economy as IRct and IN ct . The change in per capita IR and IN is calculated as

0.08 0.06 0.04 0.02 0

1

2

3

4

5 Wages

6

7

Figure 3. Wage distribution of migrants from P.

8

9

the call back. The same phenomenon can be observed in the second plot of Figure 5 which plots DIRt for skill level 26. In this case there is initially an increase in income of residents of P when the returning migrants arrives. However, the increase is small and quickly starts to dissipate over time. However, the residents still have to pay the cost to the returning migrant and hence the change in welfare becomes negative after a few periods and continues to decline after that. There are two effects that take place over time after the initial impact

REVERSING THE BRAIN DRAIN: IS IT BENEFICIAL?

−4 −6 −8

10

1.5

x 10

20 Time

30

40

Skill Level 41

0.5

10

20 Time

30

x 10

40

Skill Level 26

5

0

−5

10 −7

1

0

10

3

x 10

20 Time

30

40

be seen that the effect on incomes of workers of P, when a worker of skill level 26 is called back, is mostly positive. Unlike DIRt ; DIN t for this skill level does not dissipate very quickly and does not become negative because there is no cost that is paid by the workers of P in this case. The last two plots also show that the increase in income using this measure is more than before (again because of an absence of cost). The next two figures plot the sum of gains or losses accumulated over one cycle of model. Define

Skill Level 56

Dwelfare1 ¼

2

T X

DIRt

t¼1

1

Dwelfare2 ¼

T X

DIN t

t¼1 0

10

20 Time

30

40

Figure 6. Effect of calling back workers of various skill levels on income per capita of nationals of P over time.

of the call back. (1) Each period, one generation which was impacted by the call back dies and is replaced by a new generation which had never been directly affected by the call. This effect causes the impact of call back to dissipate over time. (2) Apart from changing the growth rate of skill for one period, the initial impact also changes the skill profile for subsequent periods despite the growth rate returning to its original value. 14 Hence, changing the growth rate for one period changes the skill profile over time for all the periods to come. This effect also alters the mix of migrants who move to R and that in turn changes the skill profile of return migrants. This implies that the workers who are born after the call back was brought back to P will also be affected. This effect will cause the initial change in income to persist, increase, or decrease over time. In the first case when a worker of skill level 3 is brought back, the second effect out weighs the first effect for some periods and thus the income of residents continues to fall (relative to the income they would have earned without the call back) before rising again. The third plot of Figure 5 is for skill level 41. The plot shows that the arrival of a call back of this skill level increases the income of workers of P. If this increase is applied to the GDP of Pakistan, it would translate into an increase of $17,000 for one year. The gain then tapers off in the subsequent periods as the first effect described in the previous section diminishes the initial gain. The second effect is still present is this case which can be seen from the fact the increase in income for residents does not become 0 after 42 periods. In absence of any spillovers and cost that has to be paid to the returning migrant, the increase in income would become 0 after exactly 42 periods (because by then every generation that experienced the increased skill growth would have died). However, the initial increase in income means that higher skilled workers go to R and some of them later come back which then increase the skill level of even those generation which were not born when the call back arrived. The fourth plot of Figure 5 shows the same phenomenon for skill level 56. The initial increase in incomes is now higher because of higher spillovers. Figure 6 plots DIN t for the same skill levels. The plots show the same pattern but numerically they are different. In case of call backs of skill levels 3 and 26, arrival of whom cause the incomes to down, the decline in income using the DIN t measure is less than before. The reason is that this measure of income does not include the cost of calling back P. It can also

Figure 7 plots Dwelfare1 . On the x-axis is each skill level that is called back (49 in total) and on the y-axis is the total difference in IRt that is accrued over 42 periods. The plot shows that there is a welfare loss for calling back workers of low skill levels. The first skill level where the welfare measure becomes 0 is skill level 37. This is the skill level where gain in lifetime incomes of workers of P offsets the cost of calling one worker of this skill back. Beyond this skill level, the gain in lifetime incomes is an increasing function of skill, but so is the cost. The plot shows that the welfare first increases and then decreases. The reason for this non-monotonicity is the way the cost behaves. High skill workers only accept high wage offers and hence earn, on average, higher wages then intermediate and low skill workers. Since the call backs have to paid life time earnings, and wages grow over time, the difference in earnings of what they would earn in P and what they would have earned in R also grows (the difference in the growth rates of earnings in R and P is the key in deriving this result). This welfare measure achieves its maximum value at skill level 54. This skill level is 1.28 standard deviation above the mean skill level in P. Figure 8 plots the welfare function which sums the gains or losses made by all the nationals of P, whether working in P or R, and does not include the cost paid to call backs. This welfare measure is increasing in all skill levels and it achieves its maximum value at skill level 58 which is 1.53 standard deviations above the mean skill level in P.

−5

3

x 10

2 Change in Welfare, Δ welfare1

−2

−7

Change in total income of Nationals, Δ INt

−8

Skill Level 3

Change in total income of Nationals, Δ INt

x 10

Change in total income of Nationals, Δ INt

Change in total income of Nationals, Δ INt

−8

0

317

1 0 −1 −2 −3 −4 −5

0

5

10

15

20

25

30

35

40

45

Skill Level

Figure 7. Effect of calling back workers on Welfare (IR).

50

318

WORLD DEVELOPMENT

(a) Robustness checks

−5

4

(ii) Alternative preferences of workers in R It was assumed in the baseline model that workers in R sent a fraction s of their incomes to P and then treat that income sent home as lost income i.e., they do not get any utility out of the remittances sent to P. In reality, remittances are sent to family or friends and are not treated as lost income by the workers working in rich countries. This subsection assumes that workers working in R do not treat the remittances as lost income and get utility from all the income they earn. Figure 11 shows the result on welfare measure using x 10

5 Change in Welfare, Δ welfare2

κ = 0.0088 κ = 0.0108

Change in Welfare, Δ Welfare1

2 1 0 −1 −2 −3 −4 −5

0

5

10

15

20

25

30

35

40

45

50

Skill Level

Figure 9. Effect of calling back workers on Welfare (IR) for different values of spillovers.

−6

7

x 10

κ = 0.0068 6

κ = 0.0088 κ = 0.0108

5 4 3 2 1 0 −1 −2 −3

0

5

10

15

20

25 30 Skill Level

35

40

45

50

Figure 10. Effect of calling back workers on Welfare (IN) for different values of spillovers.

these alternative preferences for workers in R. The plot shows that under alternative preferences, the gains made are lower than those made with the baseline model. This is because now the cost that has to be paid to bring a worker back is higher as in the baseline case a wage of w was only as good as wð1  sÞ. The cost c now takes the following form.

−6

6

κ = 0.0068 3

Change in Welfare, Δ welfare2

(i) Spillover parameter As a robustness check, two different values of spillover parameter were considered. One value (0.0108) was above the value considered in the baseline case and the other (0.0068) was lower than that. The results are shown in Figures 9 and 10. Figure 9 plots Dwelfare1 for different values of spillovers and the plot shows that higher values of spillovers are associated with both higher gains and higher losses depending on the skill level of the call back. A higher spillover value implies a higher impact of return migrants on the skill growth of workers in P. Thus if the call back has a low skill level then his (negative) impact on the growth rate of skill would be higher than it would be with a lower value of spillovers. On the other hand, calling back a worker of higher skill level would imply higher welfare gains for higher values of spillovers. Hence, the plot shows that the welfare function(s) associated with higher spillover values cut the welfare function(s) associated with lower spillover values from below. The plot shows that the three curves (corresponding to the three different values of j) intersect at skill level 21. This is the first skill level where the initial impact of the call back is positive. Thus higher values of j imply that the change in incomes associated with them lie above the change in incomes associated with lower values for j. Similarly for skill levels below skill level 21, the initial impact is negative and thus the changes in incomes associated with higher values of j lie below the changes in incomes associated with low values of the spillover parameters. The plot also shows that all three welfare functions achieve their respective maximum values at the same skill level namely skill level 54. Hence, the results are qualitatively robust to the choice of spillover parameter but numerically they differ. Figure 10 shows the same result for Dwelfare2 .

x 10

4 3

ci ¼ 2

wt ð1bð1þgÞðT tþ1Þ Þ 1bð1þgÞ

ðT tþ1Þ

RÞ  xðP ;tÞð1bð1þg 1bð1þgR Þ

Þ

Pt

This higher cost leads to lower welfare gains for the workers in R.

1 0 −1 −2 −3

0

5

10

15

20

25

30

35

40

45

Skill Level

Figure 8. Effect of calling back workers on Welfare (IN).

50

(iii) Alternative growth rate of wages in R It was assumed in the baseline model that the wages in R grow at a different rate from the rate at which skill grows. It was also discussed in the calibration section that this assumption was made due to lack of data on the income growth of Pakistani Americans. This subsection assumes that the wages in R grow at the same rate as the skill does (recall that in the baseline model g > gR ). The results are shown in

REVERSING THE BRAIN DRAIN: IS IT BENEFICIAL? −5

6

x 10

Baseline Model Alternate Preferences Model

Change in Welfare, Δ welfare2

5 4 3 2 1 0 −1 −2 −3

15

20

25

30

35

40

45

50

x 10

3 2 1 0 −1 −2

The results from the model used in this paper suggest that the government of a country should finance the return migration of its skilled nationals working abroad by paying them the same wages that they would earn abroad. Results suggest that welfare gains from return migrants would be maximized by calling back workers that have skills that are 1.3 standard deviations above the mean skill level of the locals.

−4 −5

Baseline Model Different Growth Rate of Wages in R 0

5

10

15

20

25

30

35

40

45

50

Skill Level

Figure 13. Effect of calling back workers on Welfare (IR) for alternative growth rate of wages in Rðg ¼ gR Þ.

−5

−5

x 10

6 Baseline Model Alternate Preferences Model

x 10

5 Change in Welfare, Δ welfare2

2 Change in Welfare, Δ welfare1

10

−5

4

−3

1 0 −1 −2 −3

4 3 2 1 0 −1

−4 −5

5

Figure 12. Effect of calling back workers on Welfare (IN) for alternative preferences of workers in R.

6. POLICY IMPLICATIONS

3

0

Skill Level

Change in Welfare, Δ welfare1

Figures 13 and 14. Figure 13 shows that when wages grow at the same rate as skill, the gains made from calling a worker back are higher as compared to the baseline model. This is because the cost that has to be paid to the call back is now lower where as the spillovers are still the same because spillovers are determined by the skill level of the call back where as the cost is determined by the wages he would have earned in R. The wage growth in R is lower than it was in the baseline model. Figures 12 and 14 show that there is no effect on the second welfare measure of these changes in preferences or growth rate of wages in R. Dwelfare2 only depends on the incomes of nationals of P (residing both in P and in R) and there is no cost paid to the returning migrant. Thus, the changes in this measure of welfare remains the same under different preferences and growth rate of wages in R. Note that, the results of previous 3 subsections also predict what will happen in general when one of the key parameters of the model changes. If the spillover parameter increase, the positive benefit from returning migrants increases. If the cost of bringing a worker back increases (decreases) then the benefit from bringing back the worker decreases (increases). Thus the results suggest that to maximize welfare over the lifetime of a generation, the government of P (Pakistan in this case) should consider calling back workers in R (the United States) whose skill levels correspond to the skill level 54 of the model. Since, skill is a combination of education and experience, this skill level can either correspond to highly skilled young professionals or highly experienced professional or a combination of both. If we look at the Pakistani workers in the USA earnings wages corresponding to this skill level, we find that the workers have on average 16 years of education, they are 42 years old, and have spent 18 years in the USA.

319

−2 −3 0

5

10

15

20

25 30 Skill Level

35

40

45

50

Figure 11. Effect of calling back workers on Welfare (IR) for alternative preferences of workers in R.

Baseline Model Different Growth Rate of Wages in R 0

5

10

15

20

25 30 Skill Level

35

40

45

50

Figure 14. Effect of calling back workers on Welfare (IN) for alternative growth rate of wages in Rðg ¼ gR Þ.

320

WORLD DEVELOPMENT

However, before applying to model to the real world economy, a few caveats should be considered. First, this model only considers one variable, namely wage, that affects the decision of an expatriate to return to its home country or not. Microeconomic studies like Gibson and McKenzie (2011) have shown that there are other variables that play important roles in the decision to migrate and return migrate. These variables include preference about being close to family, lifestyle (developing countries often have more conservative cultures than some developed countries), and security. This paper, unlike the microeconomic studies, uses a macroeconomic model in which it is not possible to model all these dimensions of the utility that may affect decisions to move since such preferences cannot be measured. The Appendix to this paper includes an extension to the model which can be used if data on worker preferences over variables other than income is available. In that perspective, the model of this paper can be interpreted as reflecting the overall value that an expatriate places on life in the foreign and home country. Even if wages are not the most factor for expatriates when deciding to come back, they will still require compensation to maintain their lifestyle. Furthermore, as mentioned in the introduction of this paper, it is hard to rationalize how non-monetary preferences would systematically vary with skill level. Second, the government will need to consider the real world problems associated with enforcing such a program. Jonkers (2008) argues that the permanent return migration programs can often be difficult to implement. In particular, he cites the experience of China to show what real world problems governments face when they are incentivizing the return migration of workers from abroad. The two problems that China faced were that high skilled workers would enjoy all the benefits offered by the government while spending little time in the home country. This not only defeats the purpose of bringing expatriates back, but also causes resentment among local workers. Thus, while the model of this paper helps in identifying the workers that would maximize the gain to domestic economy from return migration, it does not take into account the problems governments will face while enforcing such a program. To counter these problems, the governments should first enforce the full time employment of return migrants in the home country. This would increase the cost of the government because it will now have to monitor the progress of the returning worker but this cost will be minute in comparison with the cost that the government will be paying overall. This is important because, as the results presented in the Appendix suggest, spillovers from returning migrants are lower for older people who are either near the age of retirement or have already retired. Such workers will have little spillover on the workers around them since they will either not work or work less than full time. Secondly, the government should consider microeconomic studies to establish the best usage of the compensation it offers to the return migrants. Thus, while the model of this paper does not consider microeconomic based preferences of returning migrants, it can be paired up with the microeconomic studies to establish the efficient use of the compensation that the government pays to returning migrants. Offering benefits and compensations for coming back and working in home country will also cause lesser resentment among the local workers since the wage differential would be small. The model of this paper will allow the government of the home country to assess workers of what skill level will give the highest net benefit to the home country. Furthermore, if microeconomic data reveal that workers have preferences over more than income, then once the government has identified the skill level that it wants to target, it can then

call back those workers of that skill level who are more willing to move back or require lesser compensation. 15 Finally, it is extremely important that the government does not try to diversify the pool of return migrants too much. Rather, the government should try to call back expatriates who are similar in terms of skills and other attributes. As Jonkers (2008) puts it. Highly skilled professionals, be it scientists, other professionals, or entrepreneurs tend not to operate (best) in isolation. It may therefore be expected that on average the willingness to return, partially depends on the perception of other actors operating in the home system. In addition, it is likely that the general interest in return increases when larger numbers of similar returnees are already present in the organization and/or region. Their presence can lead to information flows to potential returnees through personal ties or through the migration networks. . . This shows that not only is it important for the government to ensure that return migrants do not become isolated by bringing back workers in groups, it is also useful to employ the services of existing return migrants to transfer knowledge of and opportunities in the local economy to potential return migrants. Jonkers (2008) calls this phenomenon, where existing return migrants can pave way for the return of further expatriates, chain re-immigration. Other important facilities that the home government can offer include tax exemptions, environment for application of skills of return migrants (e.g., research support for returning academics), and establishment of a separate department to facilitate the return and needs of return migrants. Also, the government should target workers in those countries that have more skilled workers of home country’s origin. This would make it easier for the government to target workers of similar skill level. In the context of Pakistan, this means that the government should try to attract workers back from countries like the United State, United Kingdom, and Canada and not from Middle-eastern countries where most Pakistanis work in professions that require little or not skill. See Jonkers (2008) for a detailed discussion of other factors that may be important in this regard. Thus, the model of this paper would help the government to identify the workers whose return would maximize the welfare gain from return migration and that together with the preferences of the return migrants and knowledge about the local economy would help the government in efficiently using the compensation package offered to the return migrants. 7. CONCLUSION This paper used a life cycle model to analyze the costs and benefits of enforced return migration of workers from a rich country to a poor country. The rich and the poor country are the USA and Pakistan in this paper. The cost of calling back workers is the high compensation that must be paid to them in order to make them indifferent between working in the rich or poor country. The benefits of such return migration are the increase in output of the economy and more importantly the spillovers from the returning migrant that positively affects the skill of everyone else in the economy. Results show that calling back workers of the lowest skill levels result in overall losses in terms of welfare for the country. However, workers of middle to high skill level increase the welfare of the economy. The maximum gain is attained by calling back workers who skill levels are almost 1.28 standard deviations above the mean skill level (in logs of wages) of workers in Pakistan.

REVERSING THE BRAIN DRAIN: IS IT BENEFICIAL?

Practical implementation of a return migration program would require government to actively monitor the work behavior of return migrants to ensure maximum benefit from them. The government should also consider how to pay the compensation to the returning worker. Micro studies suggest that worker take into account many factors when deciding to return to home countries and wage is only one of them. Thus the government can pay the compensation in form of non-monetary benefits which will also ensure that the wage differential between returning migrants and local workers is lower.

321

In the future, it would be interesting to (1) make education choices endogenous to investigate the possibility of brain gain, (2) take into account the preferences of workers working in the rich country while determining the high compensation that will have to paid to them. Some workers value being closer to home and hence will be willing to come back for lesser compensation. Others may value the higher standard of living in the rich country more and may demand higher compensation, and (3) make labor supply and savings decisions endogenous to the model.

NOTES 1. A Pakistani American is a citizen or resident of the USA who is of Pakistani origin. This includes both naturalized citizens and those who are not citizens of the United States.

10. Since data on job offers are neither available nor existent, this restrictive assumption, the distribution of jobs offers is the same as current wage distribution, had to be made.

2. The remittances to GDP ratio in Pakistan was 4.7% in 2006. Source: State Bank of Pakistan

11. Instead of plotting all the ages individually, they were lumped together into groups of 5

3. In the case of Pakistan, most savings are used to buy durable goods like housing services.

12. Note that the Bellman equation for workers in P in the second case will have the additional cost c.

4. The assumption of risk neutrality keeps the model tractable: the timing of consumption will not matter. In reality, however, savings decisions of workers working in R may govern their labor supply decisions in P upon their return. Thus, in future research, it will be useful to allow for a richer utility specification which allows for savings decisions as well.

13. The migration rates were chosen to match the distribution of Pakistanis in the USA. Some of the skill levels in the model did not have any counterpart in the distribution and that is why only 49 skill levels have positive migration rates in the model.

5. A return migrant is a worker who works in R but then comes back to P. 6. Average skill does depend on the composition of returning migrants. The simulation in Section 5 sidesteps this, however, by considering a simple experiment in which only one worker is subsidized to return 7. This may not be true for all the domestic migrations but in a country like Pakistan, most of the movements are towards cities where wages are high suggesting that such movements are motivated primarily by economic reasons. 8. Because of a variety of reasons including low cost of living, the value of being closer to family etc 9. The results from Eqn. (3) in the Appendix show that the value can be above 0.01 as well

14. To understand this, consider a simple example of a worker whose value of skill is 1 at the beginning. Further assume that this value triples every period. Thus, the values of his skill will be 3, 9, 27, . . .in the subsequent periods. Now consider an alternative scenario where the value of his skill doubles in the first period and then triples every period like the previous case. In this case the values of his skill will be 2, 6, 18, . . . 15. In the particular case of Pakistan, an important factor for return migration is the place where they reside because of the differences in quality of life in different neighborhoods of the same cities. Also, people prefer neighborhoods that are secure and power outages are less frequent. Finally, quality education in Pakistan is only provided in private schools which are much more expensive than public schools. Thus, to attract an expatriate back, the government can offer residence in a secure neighborhood and free education to his or her children in private schools.

REFERENCES Ahmed, G. S. & Jha, S. (2010). Remittances and household welfare: A case study of Pakistan. ADB Economics Working Paper Series. Asian Development Bank. Beine, M., Docquier, F., & Rapoport, H. (2001). Brain drain and economic growth: Theory and evidence. Journal of Development Economics, 64(1), 275–289, Retrieved from http://ideas.repec.org/a/ eee/deveco/v64y2001i1p275-289.html. Borjas, G. J. (1995). The economic benefits from immigration. Journal of Economic Perspectives, 9(2), 3–22, Retrieved from http://ideas.repec.org/a/aea/jecper/v9y1995i2p3-22.html. Borjas, G. J., & Bratsberg, B. (1996). Who leaves? The outmigration of the foreign-born. The Review of Economics and Statistics, 78(1), 165–176, Retrieved from http://www.jstor.org/stable/2109856.

Carrington, W., & Detragiache, E. (1998). How big is the brain drain? International Monetary Fund, Research Department, Retrieved from http://books.google.com/books?id=3DtGRpepl_oC. Dustmann, C., Fadlon, I., & Weiss, Y. (2011). Return migration, human capital accumulation and the brain drain. Journal of Development Economics, 95(1), 58–67, Retrieved from http://ideas.repec.org/a/eee/ deveco/v95y2011i1p58-67.html. Dustmann, C., & Weiss, Y. (2007). Return migration: Theory and empirical evidence from the uk. British Journal of Industrial Relations, 45(2), 236–256, Retrieved from http://EconPapers.repec.org/RePEc:bla:brjirl:v:45:y:2007:i:2:p:236-256. Gibson, J., & McKenzie, D. (2011). The microeconomic determinants of emigration and return migration of the best and brightest: Evidence

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APPENDIX A. SUPPLEMENTARY DATA Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/ j.worlddev.2014.10.023.

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