Student Mobility and Highly Skilled Migration: Theory and Evidence

Transcription

1 Università di Torino Università del Piemonte Orientale Student Mobility and Highly Skilled Migration: Theory and Evidence Stella Capuano Dottorato di Ricerca in Scienze Economiche

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3 Università di Torino Università del Piemonte Orientale Student Mobility and Highly Skilled Migration: Theory and Evidence Stella Capuano Dottorato di Ricerca in Scienze Economiche Ciclo XXI Supervisore: prof. Steinar Strøm Coordinatore: prof. Giuseppe Bertola

4 Dipartimento di Economia S. Cognetti de Martiis Dipartimento di Scienze Economiche e Finanziarie G. Prato Dipartimento di Statistica e Matematica Applicata alle Scienze Umane Diego de Castro Dipartimento di Politiche Pubbliche e Scelte Collettive Dipartimento di Scienze Economiche e Metodi Quantitativi Copyright c 2009 Università degli Studi di Torino

5 Acknowledgments This thesis would have never come to a conclusion without my parents and my brother s support, my only source of strength in the last few years. I thank Steinar Strøm for his careful supervision and advice during the development of my research. I am sincerely grateful to Giuseppe Bertola, for the attention he has been always paying to my work, for his availability and precious help. Moreover, I address special thanks to Daniela Del Boca for giving me the chance to benefit from her insightful comments and discussions. I acknowledge also very useful suggestions by Luigi Benfratello and Alessandro Sembenelli. Finally, I thank my fellow PhD students, and in particular Giulia Bizzotto and Serena Trucchi, who have played a relevant part in my daily progress, with all the time we have spent, and I hope we will keep on spending, sharing opinions and ideas on our own research topics. Disclaimer notice Access to the data used in the empirical analysis of chapter 3 has been kindly provided by the Laboratorio Adele, at the National Institute of Statistics in Rome. Only the author is responsible for the views expressed in that chapter, and for any error. v

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7 Contents Introduction xii 1 A theoretical framework for the analysis of student mobility Introduction and motivation Related literature Migration under uncertainty Return migration The Model Description and assumptions Solution Some properties of the model Case 1: C = k Case 2: k C Non-reversible moving choice Discussion and conclusion The determinants of international student flows: Some empirical findings Introduction and motivation Related literature Theoretical insights Empirical analysis Data Empirical model Results Per-capita GDP and its standard deviation Rates of growth and educational expenditure The unemployment rates Summary and conclusion The South-North mobility of Italian college graduates. An empirical analysis Introduction and motivation The determinants of the moving decision vii

8 3.2.1 Family background: parental income, education and network Personal ability Local labor market conditions Data and sample selection Empirical strategy Results College student mobility The choice of where to work Conclusions and directions for future research viii

9 Introduction This thesis focuses on the economic determinants of student mobility and young, highly educated workers residential location decisions. Both topics are important per se: indeed, mobility for the acquisition of skills is a human capital investment, and understanding its driving forces as well as the characteristics of those students who choose to enroll outside their origin may help assess the efficiency of the education system and the growth potential of a given country; whereas, the mobility of talent falls within the migration literature, and in particular the one addressing the so-called brain drain phenomenon, a matter of economic and political debate in recent years, when developed countries are engaged in a global competition for talent. Moreover, and this is what I mostly concentrate upon in this work, the relationship between the two kinds of mobility is interesting. More precisely, studying whether fresh graduates decide to stay in their study place or to move to work may highlight the labor market and economic conditions that attract the highly skilled workforce, which is again relevant from a policy perspective, in particular to foster measures aiming at retaining the most talented and increase the domestic stock of human capital. Each chapter of this research builds on three main ideas. First of all, and as it has long been recognized in previous literature, migration is affected by uncertainty. In this respect, student mobility should not be an exception: indeed, since post-graduation labor market outcomes are not known for sure, it is reasonable that non-predictable changes in economic or personal characteristics imply that returns to out-of-origin education, as well as returns to education in general, could mismatch previous expectations. Second, and closely related to the above consideration, I maintain that the analysis of student mobility cannot overlook post-graduation moving choices. In fact, on the one hand, and as I have just explained, if moving or staying for education entails a given degree of uncertainty, the agent may decide to switch location after graduation, even if his initial intentions were to settle down and work in the study place. On the other hand, coming back or migrating after education can be itself part of an individual plan, since people may acquire skills where they are of better quality, but then they can go and work where educational payoffs are higher. As a consequence, beside migration under uncertainty - and in particular, the Option Value Theory of migration - the Return Migration strand of literature offers an useful framework to interpret student mobility. Hence, I will draw from both when developing my theoretical analysis and interpreting my empirical results. Third, despite the evident relationship between moving for education, coming back and miix

10 grating to find a job, these three decisions have different costs, which are difficult to measure empirically. One of the aims of my work is to single out those factors that are likely to influence the moving costs, recognizing that they can differ across individuals and also across pairs of countries. Chapter 1 brings the above three points together in a very general theoretical model that sets the stage for the empirical analysis of the other two chapters. There are two periods in the model: in the first one the individual decides where to acquire education (i.e. either in the origin or in the destination location), while in the second one he chooses the place of work. In the second period the individual may bear two kinds of moving costs. Indeed, if he has previously moved to study and he wants to return home after education, he must pay a cost of coming back, while if he has studied in his home location and then he wants to migrate to find a job, he will pay a migration cost. The analytical results are such that the relative magnitude of second-period costs drives the impact of uncertainty on the choice of the study place. For example, when the cost of coming back is lower than the migration cost, moving for education becomes more profitable as uncertainty increases. The intuitive interpretation for the above outcome is that if the cost of coming back is lower than that of moving after education, by moving the individual gains the ability to find himself in the location from which reversing the previous choice is less costly. In turn, the influence of uncertainty on the decision to move becomes all the more important the greater it is the above potential gain of ability to exploit new information from the study place in period 2. The opposite happens when the migration cost is lower than the cost of coming back. Although the implications of the model are not easily testable, they suggest interesting directions for empirical investigation, which I follow in the other two chapters of the thesis: the first one deals with uncertainty, and the second one concerns the identification of the components of the moving costs. In chapter 2 I look at student mobility from a macro perspective and at uncertainty over future macroeconomic conditions as a potential push or pull factor of student flows, as suggested by my theoretical framework. To this aim, I estimate a gravity model on data on international student inflows to 15 major destination countries from all over the world. Uncertainty is proxied by the standard deviation of per-capita GDP computed over non-overlapping time windows of 4 years each. In addition, I focus on other factors that are likely to matter for those students wishing to stay or to come back after graduation: namely, the unemployment and growth rates, and expenditure in education in the source and host countries. Due to the many data constraints I describe in chapter 2, my results can only be considered suggestive of the relevant correlations between the endogenous and explanatory variables. However, some of them are interesting and deserve further research. First, the growth rate in the destination is positively associated to student inflows, which may suggest that economic opportunities abroad are relevant for the decision of tertiary students to enroll overseas. Second, uncertainty in the destination has a negative correlation with student inflows, which, with some caveats, is in accordance with the option value theory of migration. Finally, expenditure in education in the origin helps keep students domestically. If expenditure in education is taken as a proxy of the quality of edux

11 cation in a given country, the latter result indicates that tertiary students may cross national borders with the purpose of acquiring high quality skills. The unemployment rates in origins and destinations, instead, do not display any relevant link with student inflows and outflows, which, coupled with the result about expenditure in education supports the view that, at least at the international level, labor market conditions matter less than the prestige of academic institutions for the choice of the study place. Chapter 2 s analysis is carried out on macrodata, and as such it disregards the role of individual heterogeneity on mobility. In Chapter 3, instead, I study the empirical determinants of the South-North mobility of Italian college graduates, using microdata, and hence taking into account the aforementioned individual components of the moving costs, beside the macroeconomic ones. As to the former, in addition to individual ability, already found by previous literature to foster mobility, I consider a less explored one: i.e. the role of family background. A robust finding is that Southern young people with a father entrepreneur or professional man are less prone to move to work and more prone to come back after getting graduated in a Central-Northern region. I interpret this outcome as an indirect evidence of a network effect, which seems to match the results of the social capital and intergenerational mobility literature. Indeed, since the high-income self-employed professions are, in Italy, more likely to be passed on from fathers to children, and they are also more likely to benefit from informal connections in the labor market, it is possible that the offspring of high-income self-employed fathers can exploit their family network to have an easy access to domestic labor markets. Hence, other things being equal, they are observed to choose less often another work location than their origin. Moreover, I find the above effect only for the least able individuals. Overall, the message delivered by the above analysis points out the inefficiency of Southern Italian labor markets, that may be held responsible for the pronounced role of the family network effect that I find. This, in turn, is related to the second important finding of the chapter, which is about the macroeconomic components of the moving costs. Indeed, the unemployment rate in the region of origin turns out to increase the probability to move not only to work but also to study in another region. I interpret the latter as an additional piece of evidence of the link between student and labor mobility. This is a new result, since other studies trying and detect the same effect for other countries have not come to similar conclusions, and no other applied study on Italian student mobility has previously taken the regional unemployment rate into account. With reference to the three main points I have described at the beginning, the overall contribution of this thesis to existing research is twofold: first, as to the relationship between the moving, staying and coming back decisions and their costs, it uncovers an interesting role of individual family background that has not been so far explored. Moreover, I show that at the individual level, and within the same country, local labor market conditions seem to be relevant in shaping student mobility. Second, as to the role of uncertainty, beside adding it in a stylized model of return migration, I try and detect it empirically. Even if, probably due to the short time span and other data problems, I cannot interpret my results in a structural way, my findings open a door to a stimulating line of future research, which it will not be impossible xi

12 to carry out in the future, either at the micro or at the macro level, provided the availability of longer time series. xii

13 Chapter 1 A theoretical framework for the analysis of student mobility 1.1 Introduction and motivation The topic of this chapter is a formal analysis of the determinants of migration. Though the model I am going to present is sufficiently general to be applied to any kind of mobility, it is particularly suitable as a broad conceptual framework to understand student and recent graduates moving choices. 1 From a national perspective, understanding the determinants of internal student mobility may serve as a guidance for the design of measures aiming at enhancing competition among higher education institutions, and improving the quality of the education system in a given country. Moreover, since students are future workers, their mobility can be seen as an indirect channel for the migration of labor, the analysis of which can shed some light on the efficiencies or inefficiencies of local labor markets. From an international point of view, attracting or retaining students from abroad has become a major policy issue in recent years (see Bertoli et al., 2009; OECD, 2008c). Indeed, international students are potential highly-skilled workers who will contribute to the human capital stock of the country where they choose to work. And many developed countries have modified their migration policies in order to make them less strict for foreign students. 2 Mobility for the acquisition of skills is likely to display different features with respect to other kinds of migration. In particular, when modeling student mobility, one cannot rule out the possibility for the agent to modify his previous location choice, which means performing either return migration, i.e. coming back to the origin, or repeat migration, i.e. moving to a new location. In fact, as noticed by Dustmann et al. (2009), moving for education is a human capital investment, which may be motivated by the quality of education in the chosen location, but the benefits of which can be enjoyed in the origin or in another region or country, where 1 The model is intended to be applied to late stages of education, i.e. college or graduate education. 2 Kuptsch (2006) reports the measures applied by UK, Germany and France in order to ease foreign student access to their education system and in application of the Bologna declaration for the integration and harmonization of higher education systems within the EU. 1

14 the rate of return of human capital is higher. This chapter focuses on another reason why the option to return is going to be relevant for student mobility, i.e. uncertainty over after-education labor market outcomes. Indeed, whatever the individual after-graduation intentions (i.e. either staying or coming back) at the time when the study place is chosen, individual and economic conditions may change, possibly leading to modify initial plans. Descriptive evidence on internationally mobile students is not in contrast with the above arguments. For example, Table 1.1 shows the stay rates and intentions to stay of foreign PhD students in the US. 3 The data in the Table confirm that mobile students are also mobile workers, though with remarkable cross-country differences: the Chinese and the Indian display the highest stay rates, and the South-Korean, the Indonesian and some of the Latin American the lowest ones. 4 Moreover, intentions to stay are usually higher than actual stay rates, which seems to suggest that repeat or return mobility may come from changes in economic or individual conditions that were not predictable at the moment the decision of where to study was taken. As to internal mobility, Faggian et al. (2007) document that repeat migration is very frequent among UK students: 53% of them go to college in a different region than their origin and then move again to find a job in another location, while return migrants are very few. Similar patterns are documented by Kodrzycki (2001) for US. The high propensity of mobile students to repeat migration is usually explained with the positive association between human capital and the ability to perform a more efficient spatial job search. This chapter s simple model uses the general framework of the Roy model (Roy, 1951; Borjas, 1987) but it extends it to two-periods, so as to take into account the option to come back. In the first period the individual has to decide the place of study, whereas after education, i.e. in period 2, he chooses where to work. Uncertainty is modeled as a random shock to labor income that realizes in period 2. A crucial assumption of the model, which drives its results, is the asymmetry between after-education moving costs, i.e. the cost of moving from the origin to the destination to find a job (the migration cost ) if one has studied at home, and the cost of coming back to the origin after education in the destination. This asymmetry, coupled with uncertainty, creates an opportunity for the individual to choose the location from which reversing the previous period s choice will be less costly. More precisely, I show that if, in period 2, the cost of coming back is lower than the migration cost, other things being equal, greater uncertainty makes moving for education worthwhile. Indeed, in case the individual regrets his choice after the observation of the realizations of the shocks, he will come back in period 2, paying the lowest of the two costs. On the contrary, if moving in period 2 is less costly than coming back, mobility in period 1 is made less and less 3 The stay rates are measured using tax records, while intentions to stay are generated from the Survey of Earned Doctorates, where people are asked about the time of graduation and their post-graduation plans (see Finn, 2003). 4 The literature has tried to give explanations for those differences, though it has not come to conclusive results. Beside the cross-country differences in the rate of return to human capital, already mentioned, another explanation, proposed by Spilimbergo (2009), is that students from less populous countries tend to come back to their origins, where they can make the difference in political terms, which, in the case of non-democratic countries, could translate in an enhancement of the democratic process. 2

15 profitable when uncertainty increases, while waiting becomes more valuable. In fact, reversing the waiting choice in period 2 entails the lowest cost. While the latter result is in line with the Option Value theory of migration, one of the most recent theoretical approaches to the issue, the former is new, since it hinges upon the assumption of reversibility of the first moving choice. Moreover, the analysis suggests that the intensity with which uncertainty increases or decreases the value of mobility depends on the magnitude of uncertainty itself. Up to a given threshold, greater uncertainty intensifies its own effect on the value of moving. After the threshold, the positive or negative effect of uncertainty on mobility becomes lower when uncertainty increases. As I will explain more extensively later on, the intuition for this result is that the moving or staying decision is increasingly difficult to take when the economic environment features higher uncertainty, and the potential benefits yielded by asymmetry in the moving costs eventually fade away. The reminder of the chapter is organized as follows: in the next Section I review the literature linked to my research. In Section 1.3 I set up and solve the model, and I further analyze its results in Section 1.4. Finally, Section 1.5 discusses how the model can be used to rationalize internal and international student mobility, and envisages possible directions for future research. Table 1.1: Stay rates of foreign Doctorate recipients in United States Percentage of non-us Doctorate recipients Foreign Doctorate intending to stay Recipients in Estimated in United States Origin 1994/1995 stay rates in 1999 (average ) Taiwan, China 2, India 1, South Korea 1, China 1, Brazil Mexico Chile Turkey Indonesia Italy Greece Spain Canada Argentina Colombia Total, all countries 14, Total, all countries excluding China and India 10, Source: Spilimbergo (2009) 3

16 1.2 Related literature In this Section I review the main findings of the studies on migration under uncertainty, in particular the ones applying the Option Value Theory, and those on return mobility. As I will show, both strands of literature are relevant for the theoretical analysis I am going to develop in the next Section Migration under uncertainty In order to understand the importance and novelty of the theories of migration under uncertainty developed in the early nineties, it is worth recalling that the neoclassical theory of migration (Sjaastadt, 1967; Harris and Todaro, 1970) assumes that the moving choice cannot be postponed. Since the individual decides once and for all whether to move or not, the theory predicts migration to occur at the Marshallian trigger, i.e. the point at which the net present value of migration benefits exceeds its costs. The above approach, however, is not able to explain why migration flows can be low even in the presence of large wage differentials between potential host and home countries and low moving costs. 5 Burda (1995) makes a major departure from the neoclassical framework by applying the real option value theory of investment (Dixit and Pindyck, 1994) to the migration decision. The bulk of his model can be summarized as follows: if the individual can delay mobility and if future migration returns are uncertain, postponing mobility might be profitable despite large wage differentials. The reason is that, by waiting, the individual gains the chance of taking the moving choice based upon new information available in the future. In an empirical application to German data, Burda et al. (1998) show that the option value theory can account for the East-West Germany migration intentions in the early nineties. 6 Building on the above seminal contribution, Wang and Wirjanto (1997) analyze the optimal time of migration and extend Burda s model by exploring the effect of individual risk aversion on the optimal waiting time, finding, rather intuitively, that the latter increases with individual risk aversion. Moreover, Chen et al. (2003) and Anam et al. (2008) consider the migration behavior of the family rather than the individual, and combine the option value and portfolio theories. They find that under market uncertainty, and when markets are stochastically correlated, it may be optimal for the family to encourage migration of some of its members for risk-diversification motives, whereas the option value theory would predict a waiting behavior. Daveri and Faini (1999) apply the portfolio theory to Southern Italian people internal (i.e. to the North of Italy) and international migration. They provide evidence that a positive correlation between per-capita Southern and Northern Italian GDP is associated with a raise in 5 Evidence of such migration inertia has been found, for example, by Burda (1995) Burda et al. (1998), Locher (2001) for East-West Germany and East-West Europe migration, and by Basile and Lim (2006) for US interregional migration. 6 Burda et al. (1998) only have survey data on migration intentions, and not on whether the individual has actually moved or not. So, they implicitly assume that intentions perfectly match actual behavior and infer from declared migration propensities the value individuals attribute to the option to postpone the moving choice. 4

17 international migration, while a positive correlation between Southern Italian and foreign (the chosen country is Germany) per-capita GDP is associated with an increase in internal migration. In the authors opinion, the above results prove that migration can have a risk-diversification function. The studies reviewed so far assume that the migration decision is not reversible. As a consequence, other things being equal, uncertainty plays the role of an additional moving cost, making migrants either wait or choose the destinations where the income profile is more predictable (see also Khwaja, 2002). In all the above models, if the irreversibility assumption is relaxed, to account for return migration, the gains from waiting will be lower, and the option value results could be dampened or could no longer hold. However, return migration is not unrealistic and, as argued in the Introduction, it is not unreasonable in the case of student mobility. 7 In light of the these considerations, I now turn to the description of some important studies on return migration. As we will see, in most of them the impact of uncertainty is found to be either opposite, or less straightforward with respect to the findings of the option value models Return migration Return migration is the subject of a vast body of research. While some studies (for example Galor and Stark, 1990, 1991) analyze the consequences of return migration assuming that it is exogenously determined (e.g. for contract migrants), many others treat it as endogenous. A leading example is Dustmann (1997), who develops a stochastic life-cycle model where individuals take their consumption and migration decisions simultaneously. The overall impact of uncertainty on the optimal migration duration cannot be signed unambiguously, and depends on the size of the wage differential and the relative risk in the home and host labor markets. In Dustmann (2003), the author develops a model of the optimal migration duration which predicts that migrants could reduce their stay abroad even if economic conditions in the receiving country are more favorable than at home. That result derives from the assumption that migrants prefer consumption at home to consumption abroad and that there is a finite horizon. As a consequence, the net benefits from staying abroad are increasing in lifetime earnings but decreasing over time, because as time goes by the cost of staying far from the origin, i.e. foregone consumption at home, increases. So, even when wages abroad are higher than at home, a point might be reached in the migrant s life at which he will decide to come back. This happens when the costs and benefits of staying abroad are equal. 8 Empirical evidence in support of this theory, as well as a theoretical treatment of the consequences of return migration for migrants human capital accumulation and assimilation in the host country can be found in Dustmann (1999, 2000). 7 Dustmann (1996) reports that a large part of migration to Central Europe in the years was temporary. Return migration is frequent also in the UK (Dustmann and Weiss, 2007) and in the US (see, for example Ranny and Kssoudji, 1983; Borjas and Bratsberg, 1996). 8 Incidentally, one can notice that the assumption of migrants preference of consumption at home than abroad during their whole life-cycle rules out the possibility that assimilation increases their willingness to stay in the destination. 5

18 To the best of my knowledge, the only study that adds return migration to the option value theory of migration is O Connell (1997). The author finds that, when costly return migration is taken into account, the effect of uncertainty on the decision to move depends on whether wages are locally or globally observable. In the former case, i.e. when the individual cannot observe wages in the host country, greater uncertainty induces a speculative behavior (what the author calls try your luck ). In the latter case, i.e. when wages abroad are observable also at home, the option value result holds: greater uncertainty reduces the probability of moving, because the individual will prefer to wait and see. This study is of particular relevance for the present analysis, since, though using a simpler framework, I also find an ambiguous sign of uncertainty on the value of moving, driven by the asymmetry between the moving costs. As I have already argued, uncertainty over educational payoffs and the option to return are two features that a model aiming at rationalizing student mobility should necessarily display. Thus, in what follows, I will try and combine the insights of the two strands of literature I have just reviewed in a simple formal framework. 1.3 The Model The present and the following Sections are devoted to the set-up and the solution of a two-period model of mobility under uncertainty. Even if the purpose of my work is to examine the case of a reversible, though costly, moving decision, it will be interesting to understand the difference between the results I obtain in case of reversibility and those yielded by a model in which the moving choice is not reversible. I will show the outcome of the latter exercise at the end of the following Section Description and assumptions I assume two locations: the origin, where the individual comes from, and the destination, where the individual possibly decides to move. I indicate them with o and d respectively. As to the timing, there are two periods: in the first one the individual goes to college and does not earn any income, while in the second period he enters the labor market, where education of different quality is differently rewarded. The latter assumption is made in order to match the results of the literature on the labor market outcomes of mobile students, which typically finds that those who have moved to study earn more than otherwise identical individuals both in the host and home country or region. 9 So, in each period a moving decision has to be taken: in period 1 the individual can move to 9 See, for example, Bratsberg and Ragan (2002) for an application to international students in the US and Wiers-Jenssen (2006) about Norwegian youth studying abroad and coming back to Norway to work. As to students from least developed countries, the only study examining the effect of foreign education on wages at home is Thomas (2008). As regards returns to internal student mobility, see e.g. Makovec (2006); Pozzoli (2009) for Italy and Audas and Dolton (1998) for UK. 6

19 go to college in the destination and in period 2 he can come back to the origin or move to work in d after studying in o. 10 Hence, the four possible choices the individual faces are: - Study in the destination and work in the origin, - Study and work in the destination, - Study in the origin, work in the destination, - Study and work in the origin. Future local labor market conditions are the only source of uncertainty and they are modeled as two location-specific random shocks to period 2 labor income. I call them ɛ o and ɛ d for the origin and destination respectively, and I assume they are jointly normally distributed with mean 0, variances σ 2 o and σ 2 d and covariance σ o,d. I denote period 2 realizations of uncertainty with ɛ o and ɛ d. Moreover, there are three types of moving costs in the model. First, there is the moving cost for education in the first period, which I call η, that is interpretable as a mobility cost in strict sense, increased by a given amount that includes tuition fees and the cost of living far from the origin, or as an effort cost. Indeed, if in the destination region colleges are of better quality, it is reasonable to assume that more effort is required in order to attend them. Second, if one decides to move to the destination in period 2 he will have to pay a migration cost C. Finally, I assume that if in period 2, after studying in the destination, the individual decides to come back to the origin and work there, he will have to pay a cost k. Given the above assumptions, the expression for period 2 labor income can be written as follows: r = m = I 2 = γ i + ɛ j rk mc (1.1) i, j {o, d} ɛ o N(0, σ 2 o) ɛ d N(0, σ 2 d) { 0 if i = o and j {d, o} 1 if i = d and j = o { 0 if i = o and j = o 1 if i = o and j = d where i denotes the place of education, so that the parameter γ i, representing the quality of education in different locations is equal to γ o if the individual studies in the origin, and to γ d if 10 Of course, it would be interesting to analyze the option of repeating migration separately from the one to come back. Within the simple framework of this model it would only be a matter of adding a new parameter, e.g. the cost of repeating migration. The issue would be much more relevant in an infinite-horizon dynamic model where each time a moving/staying decision should be taken. Moreover, modeling repeat migration should also take into account the role of human capital accumulation on the cost of repeating migration. This interesting, though more complex issue is beyond the scope of the present work and it is left to future research. 7

20 he studies in the destination. j is the work location, again equal to o or d, according to what the individual decides; r is a dummy variable equal to unity if the individual comes back to o after education in d and m is a dummy variable equal to 1 if the individual moves in period 2 from the origin to the destination to find a job. Finally, I assume risk-neutrality, so individual utility is linear in income, as given in (1.1). Due to the discrete nature of the choice, the assumption of risk aversion rather than risk neutrality (i.e. a concave rather than linear utility function) would not change the results of the model, as long as the utility function is additively separable in educational payoffs and the moving costs. Moreover, additive separability of the utility function in costs and expected earnings is typically assumed by the theoretical literature on return migration and migration under uncertainty reviewed in Section Solution I solve the model by backward induction, i.e. I first find the conditions under which the individual optimally chooses his work location in period 2, and then I solve for period 1 decision. Second period Period 2 decision depends on the realization of the random components of future educational payoffs. From expression (1), i.e. period 2 labor income, I find easily that the condition for the individual to choose to work in the destination is: ɛ d > ɛ o + mc rk (1.2) Similarly, the individual chooses to work in the origin if ɛ d < ɛ o + mc rk.. First period In order to solve for period 1 decision, I proceed as follows: 1. I first find the expressions for the probabilities of working in the origin or destination, conditional on the study place; 2. Then, I compute the expected payoffs that correspond to the four decisions the individual may take; 3. Finally, I use the results of points 1 and 2 to find out the value functions of studying in each location. Since the two random shocks are assumed to be jointly normally distributed, it follows that the random variable ν = (ɛ d ɛ o ) N(0, σν), 2 where σν 2 = σo 2 + σd 2 2σ o,d. For an individual who studies in the destination, the probability of coming back is equal to the probability that period 8

21 2 labor market conditions in o, net of the cost of coming back k, are better than in d. Hence, P (o d) = P (ɛ d ɛ o < k) = (1.3) ( ɛd ɛ o = P < k ) σ ν σ ν ( ) k = 1 Φ σν Where Φ is the standard normal cumulative distribution function. Similarly, the probability of staying permanently in d conditional on going to college there, is: ( ) k P (d d) = Φ σν (1.4) For an agent who chooses to study in the origin, the probability of moving to the destination to find a job is equal to the probability that local labor market conditions in d, net of the migration cost C, are better than local labor market conditions in o. So, ( ɛd ɛ o P (d o) = P > C ) σ ν σ ν ( ) C = 1 Φ σν Finally, the probability of working in the origin conditional on studying there, i.e. the probability mobility not to take place in either period is: ( ) C P (o o) = Φ σν (1.5) (1.6) Now I have to find an expression for expected period 2 payoffs, conditional on each of the four possible decisions the individual may take, which, as I have shown above, depend on the realization of the random variable ν = (ɛ d ɛ o ). Applying well-known results for the moments of a truncated bivariate normal distribution (Heckman, 1979), I find that the expected payoffs of working in the destination conditional on studying there are: E(γ d η + ɛ d ν > k) = γ d η + σ ν,d σ ν φ( k σ ν ) Φ( k σ ν ) Where σ ν,d is the covariance between ν = (ɛ d ɛ o ) and ɛ d and φ(.) is the standard normal probability distribution function. The expected payoffs of working in the origin conditional on studying in the destination are: (1.7) E(γ d η k + ɛ o ν < k) = γ d η k σ ν,o σ ν φ( k σ ν ) 1 Φ( k σ ν ) (1.8) Where σ ν,o is the covariance between ν = (ɛ d ɛ o ) and ɛ o. The expected payoffs of working in the origin conditional on studying there are: E(γ o + ɛ o ν < C) = γ o σ ν,o σ ν φ( C σ ν ) Φ( C σ ν ) (1.9) 9

22 Finally, the expected payoffs of working in the destination conditional on studying in the origin are: E(γ o C + ɛ d ν > C) = γ o C + σ ν,d σ ν φ( C σ ν ) 1 Φ( C σ ν ) It is now possible to write the expression for period 1 value functions. The value function of studying in the destination is: V d = ( ) [ k Φ γ d η + σ ν,d φ( k ] σ ν ) σν σ }{{} ν Φ( k + σ ν ) }{{} P robability of staying in d in period 2 Expected payoffs if staying in d in period 2 (1.10) + [ ( )] k 1 Φ σν }{{} P robability of coming back in period 2 [ γ d η k σ ν,o φ( k σ ν ) 1 Φ( k σ ν σ ν ) }{{} Expected payoffs if coming back in period 2 ] (1.11) While the value of studying in the origin is: [ ( )] [ C V o = 1 Φ γ o C + σ ν,d φ( C ] σ ν ) σν σ }{{} ν 1 Φ( C + σ ν ) }{{} P robability of moving to d in period 2 Expected payoffs if moving to d in period 2 ( ) [ C + Φ γ o σ ν,o φ( C ] σ ν ) σν σ }{{} ν Φ( C σ ν ) }{{} P robability of staying in o in period 2 Expected payoffs if staying in o in period 2 (1.12) Mobility for education occurs if Ṽ = V d V o > 0. Appendix Section 1.A shows how, after some simple algebra, it is possible to rewrite expression (1.11) as: Similarly, expression (1.12) can be rewritten as: ( ) [ ( )] k k V d = γ d η + σ ν φ 1 Φ k (1.13) σν σν ( ) [ ( )] C C V o = γ o + σ ν φ 1 Φ C (1.14) σν σν And the condition for mobility for education to occur becomes: Ṽ = (γ d γ o ) η + (1.15) }{{} 1 ( ) k + σ ν [φ σν ( )] C φ σν } {{ }

23 [ 1 Φ ( k σν )] [ k + ( C σν )] C 1 Φ } {{ } 3 Intuitively, the value of moving in the first period is monotonically decreasing in the cost of coming back k and monotonically increasing in the cost of moving afterward, C. This is illustrated in Figures 1.1 and 1.2 and is shown analytically in Appendix Section 1.B. As to the three components of expression (1.15), part 1 has the intuitive interpretation of the labor market gains from mobility for education, i.e. the difference between location-specific educational qualities, (γ d γ o ), which, according to the assumptions of the model, are exploitable both in the origin and destination in the second period, net of the moving cost for education η. In the remainder of the chapter I will synthetically refer to the term (γ d γ o ) as the wage differential. [ ( ) ( )] The term φ k σ ν φ C σ ν in the second element of expression (1.15) can be interpreted as the gain or loss of ability to exploit profitably the information available in period 2, if moving in the first period. It will be positive if k < C and negative otherwise. Indeed, k and C are the costs of regretting period 1 decision, after observing the realizations of the shocks in period 2. If the individual moves in period 1 and then regrets, he will pay k, while if he decides to stay in period 1 but then regrets, he will pay C. If the former cost is lower than the latter, moving in the first period is the choice to which the cheapest reversibility option is attached, and the individual will be more prone to take it. If instead C < k, by moving in the first period the individual would lose the possibility of paying the lowest cost in case of regret, and so waiting will be more valuable. Finally, in part 3 of expression (1.15) the cost of coming back k is multiplied by its own probability of being paid in period 2, i.e. the probability of moving back to the origin after studying in the destination. The cost C is also multiplied by its own probability of being paid, i.e. the probability of moving to the destination in period 2 after studying in the origin. > Some properties of the model Starting from equation (1.15) it is now possible to analyze some properties of the model. I will focus on the overall impact of uncertainty on the decision to move. To this aim, I start from the case in which the two costs are equal and then compare it with the case in which they differ. Finally, I perform the simple exercise of comparing my model, whose results hinge upon the assumption of a reversible, though costly, moving choice, with a similar one in which the moving choice is assumed to be totally irreversible. As I will show, the results of the latter model are in line with those of the option value theory of migration, in which higher uncertainty unambiguously decreases the value of moving. 11

24 1.4.1 Case 1: C = k When the cost of coming back k and the cost of moving after education C are the same, expression (15) reduces to Ṽ = (γ d γ o ) η (1.16) i.e., period 1 s moving choice is just a matter of comparing the wage differential between the two locations net of period 1 moving cost. The above result is easy to understand if we look again at equation (1.15). In the model, if the two costs are equal, they will also have the same probability of being paid in period 2: so, should the individual stay or move in period 1 the probability of regretting his decision will be the same. As a consequence, the two terms of part 3 of the equation cancel out. Also part 2 fades away, since wherever the individual will find himself in period 2, the costs of reversing the previous choice are the same. As a consequence, neither the moving nor the staying decision are associated to any greater ability to exploit new information in period 2 and paying the lowest cost. The case in which k = C becomes equivalent to a no-uncertainty situation: the individual will acquire education where it is of better quality, without taking care of uncertainty in period 2 labor income, and then he will decide about his work location according to the realizations of the random shocks in period Case 2: k C When period 2 moving costs are different, instead, uncertainty influences the individual decision to move. Taking the derivative of expression (1.15) with respect to σ ν I find: [ ( ) ( )] Ṽ k C = φ φ σ ν σν σν (1.17) (see Appendix Section 1.C). From expression (1.17) it is clear that the sign and magnitude of the impact of uncertainty on the decision to move are equivalent to the ones of what I have called previously the gain/loss Ṽ of ability to exploit new information in period 2. Hence, σ ν if (k C) > 0. > 0 if (k C) < 0 while Ṽ σ ν < 0 So, if period 2 costs are such that the individual will exploit more profitably the new information from the destination (i.e, k < C), greater uncertainty increases the probability to move, while, if the costs are such that waiting is more profitable (i.e, C < k), greater uncertainty increases the probability to stay. Figures 1.1 and 1.2 illustrate the results described so far. In both Figures the wage differential net of the cost of education are set at a value of 0.12, so that nobody would move 12

25 for education in the absence of uncertainty on future labor market conditions. If a positive value of (γ d γ o ) η were chosen, the qualitative results would be unchanged. However, it is interesting to notice that in the model, even in the presence of low or negative observable period 1 returns to mobility, moving can still be profitable, if the expectations about future returns are sufficiently high. Figure 1.1 plots the gains from mobility for education, Ṽ against C, the cost of moving after education for three different values of the parameter σ ν. The cost of coming back k is kept fixed at the value of 0.8. The first thing to notice is that the three curves cross exactly at 0.8, i.e. the point at which the two costs are equal. Indeed, as I have already discussed, the gains from mobility are not affected by the parameter σ ν if the two costs are the same, and the crossing point corresponds to (γ d γ o ) η. Moreover, it is possible to see that the gains from mobility decrease with σ ν when C < k, while, when C > k, greater uncertainty increases the gains from mobility in period 1. In Figure 1.2, instead, the cost of moving after education is kept constant, at the value of 0.8. Again, the three curves cross at the point in which the two costs are the same. Moreover, when k < C, the gains from mobility increase with uncertainty, while the opposite happens when the cost of coming back is greater than the cost of moving after education. 13

26 Figure 1.1: Gains from mobility for education γ d = 0.14, γ o = 0.06, η = 0.2, k = 0.8 σ ν. It is also instructive to analyze how expression (1.17) depends on the uncertainty parameter In particular, I want to detect whether the marginal gain or loss due too uncertainty increases or decreases with uncertainty itself. respect to σ ν I find: Which yields the condition: Taking the derivative of expression (17) with [ ( ) ( )] ( ) ( ) 2 φ k σ ν φ C σ ν 2 = k2 φ k σ ν + C 2 φ C σ ν σ ν σν 3 [ ( ) ( )] 2 φ k σ ν φ C σ ν 2 > 0 = C2 σ ν k 2 (1.18) ( > φ k ( ) (1.19) φ C σν The above expression suggests that as uncertainty increases, the variation in the marginal gain or loss of ability to exploit new information depends on the relative magnitude of the costs, and on uncertainty itself. To illustrate this point more clearly, I plot expression (17) against σ ν in Figures 1.3 and 1.4. In the first Figure the values of the costs are such that the condition k < C holds, so that the individual would gain the ability to exploit new information in period 14 σ ν )

27 Figure 1.2: Gains from mobility for education γ d = 0.14, γ o = 0.06, η = 0.2, C = if moving in period 1. From the Figure we can see that the gain increases with uncertainty if the latter is under a given threshold; above the threshold, the gain decreases with uncertainty. We can interpret this finding in the following way: up to a certain degree of uncertainty, for given values of the two costs, higher volatility of the wage shocks increase the importance to be able to exploit new information in period 2 from the most favorable location. However, when uncertainty exceeds the threshold, the gain, though positive, is lower and lower, since the economic conditions are too noisy for the individual to be able to take a decision that allows him to exploit the asymmetry between the two costs. Figure is just the same as Figure 1.4.2, but the chosen values for the costs are such that the condition C < k holds, hence expression (1.17) is always negative, meaning that the individual would gain from waiting rather than moving in period 1. The loss associated to moving in the first period is in this case magnified for low values of uncertainty, and then, for values of uncertainty greater than the threshold identified by expression (1.19), the loss becomes less severe. The results of the above analysis can be summarized as follows: on the one hand, the impact of uncertainty on the moving choice is driven by the asymmetry between period 2 moving costs, which in turn creates scope for the individual to exploit more profitably new information from 15

28 Figure 1.3: [ ( ) ( )] φ k σ ν φ C σ ν against σ ν C = 3, k = 2. one location than another. The rate of growth of this gain or loss of ability to exploit new information is positive if uncertainty is lower than a given threshold; however, when the threshold is passed, the economic environment is too noisy for the individual to exploit the difference in period 2 moving costs choosing the right location, so that the rate of growth of the gains or loss of ability to exploit new information becomes negative. 16

29 Figure 1.4: [ ( ) ( )] φ k σ ν φ C σ ν against σ ν k = 3, C = Non-reversible moving choice In this Subsection I show the results of a model that shares the same assumptions of the one I have just solved, with the only difference that now I assume that the cost of coming back is so high to prevent return mobility, i.e. k. The situation I am going to describe is thus an extreme case of k > C in the previous model. Similarly to before, I find that the condition for mobility to occur in period 2 is just: ɛ d ɛ o > C (1.20) Using expression (1.18) the probability of moving in period 2 is: ( ɛd ɛ o P (d o) = P > C ) σ ν σ ν ( ) C = 1 Φ σν (1.21) Expected earnings if studying in d in period 1 will be just γ d, since P (d d) = 1 if reversibility is impossible. When deciding whether to move or not in period 1, the individual will compare 17

30 the labor market gains from mobility, that are related to the attendance of better colleges, with expected earnings in period 2, when the individual can move after observing the realizations of the income shocks, or he can stay in the origin, if the earnings differential is not large enough to offset the moving cost. So, the expression for period 2 expected earnings if studying in the origin in period 1 is: [ ( )] C E (γ o C + ɛ d ɛ d ɛ o > C) 1 Φ + (1.22) σν ( ) C +E (γ o + ɛ o ɛ d ɛ o < C) Φ = σν [ ( )] ( ) C C = γ o C 1 Φ + σ ν φ σν σν And mobility will occur in period 1 if: ( ) [ ( )] C C γ d γ o η σ ν φ + C 1 Φ > 0 (1.23) σν σν Expression (1.23) is just the same as expression (1.15), the only difference is that in (1.23) there is not any cost of coming back, and now uncertainty in local labor market conditions decreases unambiguously the gains from mobility, since by moving in the first period the individual looses the possibility of observing the realizations of local labor market variables and to perform a better informed mobility choice. This result is in line with the option value theory of migration reviewed in Subsection Discussion and conclusion In this chapter I have presented a simple model that rationalizes the determinants of student mobility within the theoretical framework of return migration and takes into account uncertainty in future economic conditions. In the model, two main factors affect mobility. The first one is the difference between educational quality in the origin and destination, intended as the labor market rewards to location-specific education. This is rather intuitive, as it is widely recognized that differences in educational quality can drive student inflows and outflows, not only at the international (see Tremblay, 2001; OECD, 2008a) but also at the national level. As far as internal student mobility is concerned, there are a few empirical studies analyzing its relationship with college quality. The latter is usually measured by indicators of research excellence and productivity of academic institutions, that are assumed to be correlated both to their quality of teaching and to the potential labor market outcomes of their graduates. For example, Franklin and Hsing (1994) show how interstate migration of college students in US is significantly associated to the number of highly qualified and productive faculty members, Adkisson and Peach (2008) come to the same conclusions, using, as a quality indicator, a dummy variable equal to 1 if the institution is in the Canergie Classification of Very High Research Activity. Similar results for UK are in Faggian et al. (2007), who use the value of the RAE (i.e. the Research Assessment Exercise - 18

31 which ranks UK universities) index to measure educational quality. As to Italian colleges, on which I will focus in the third chapter of this thesis, there seem to exist differences, both in terms of labor market outcomes of their graduates and of quality of their research products. However, Italy has not a long tradition of university rankings, and synthetic indexes that could be useful in empirical analysis are not yet available (see chapter 3). The second, an perhaps less obvious determinant of student mobility is, in the model, the presence of two different after-education moving costs: i.e. the cost of coming back and the cost of moving for the first time from the origin to find a job in the destination (the migration cost ). On the one hand, I find, intuitively, that the gains from mobility for education increase with the latter, and decrease with the former. On the other hand, when the two costs differ, the sign of the difference between the two costs drives the effect of uncertainty on the gains from mobility. The explanation I have proposed for that result is that, with asymmetric costs, the individual has the opportunity to choose the location from which new information in period 2 can be more profitably exploited. This in turn magnifies the importance of uncertainty in driving the agent s mobility decision. Even if it would be insightful to provide an empirical validation of the above results, a major challenge is to disentangle the effects of the aforementioned after-education moving costs. However, as I will stress several times in this thesis, one can try and characterize the structural and individual factors that are likely to influence both costs, so as to have a hint of their relative magnitude. In the case of international students mobility, the structural components of the costs are likely to be heavily affected by migration policies. For example, consider those students who migrate with the intention to settle down and work in the chosen study place. If the agent knows that, after the completion of his studies, it will be difficult to find a job in the destination, e.g. because converting a student to a worker visa is troublesome and it takes long to obtain a permanent residence permit, this may also prevent mobility for education. In terms of this chapter s model, tight migration policies of the kind described above translate in a greater cost of coming back, for a given migration cost. Indeed, once the agent has invested in overseas education with the aim of accessing the study place labor market, it is harder for him to come back than it is migrating for those who have studied at home. In fact, the latter have not borne the monetary or psychological cost of education abroad. 11 Migration policies may also be such that the cost of coming back is lower than the migration cost. For instance, there are countries that are making labor immigration harder, like US at the aftermath of September 11, with the Enhanced Border Security and Visa Entry Reform Act in 2002, without discouraging student inflows by specific measures. So, for a given cost of coming back, the migration cost can be higher for those wishing to move to given destinations. Another reason why period 2 costs may differ is related to labor market characteristics, and in particular to how much having first-hand knowledge of the labor market is important to perform an efficient job-search. This is going to be relevant both for international and internal student mobility. Indeed, under the assumption that searching is easier in a location already known to 11 See also chapter 2, Section for a brief discussion of migration policies in different OECD countries. 19

32 the individual, moving from the home to the host location to find a job could be more costly than coming back after education, because first-time migrants do not have any experience of the host location. Instead, an individual who has already moved to study has first-hand experience of both source and sending locations, which makes his job search less hard both at home and in the study place. However, it may also be the case that, depending on the source and host countries under analysis, and on the type of occupation the individual wants to find, it can be easy enough for new-comers to find a job (also to find it from the origin) and to get used to the new location, especially if the pair of countries share some cultural similarities. For example, highly skilled occupations may have a higher degree of internationalization than others, so that it is simple to perform a spatial job search for those professions even without direct knowledge of the place of work. Moreover, national governments may implement policies to foster migration of professionals operating in sectors in which domestic labor supply is low (Salt, 1997). From what I have written so far it is clear that the structural components of the costs have different facets. In addition, their effect depend on how people perceive them, and so it becomes relevant to consider how they interact with the individual components of the costs. As to the latter, I tend to identify them with family ties and personal ability. As I will show in chapter 3, if it is possible to find good proxies for them, one can detect how they impact the moving or coming-back decision. For instance, strong family ties at home may increase the opportunity cost of staying in the destination after education, or, which is the same, they may lower the cost of coming back. 12 Sometimes the family exerts an income support function in case the individual is not able to find a job after education in a different location, which may make the individual perceive the cost of coming back as lower than the migration cost. Personal ability is also important in determining the potential magnitude of the two costs, and, as I stated above, it can interact with the structural components of the costs, attenuating their effects. For example, the more able the individual is, the higher it is his probability to find a job both at home and in the host country, and his adaptability to a new economic environment, which makes switching locations less costly. Finally, a remark is in order about the role that the model attributes to uncertainty. Though uncertainty is found to matter only in the presence of asymmetry in after-education moving costs, it is noticeable that the standard results of the option value models of migration as regards the impact of uncertainty are not entirely confirmed even in a simple framework of return migration like the one I have presented in this chapter. In fact, uncertainty does not unambiguously decrease the probability of moving, but it may also increase it, provided that the cost of coming back is lower than the cost of moving afterward. This outcome deserves empirical investigation, which is all the more relevant given the difficulties in measuring period 2 moving costs. In the next chapter I will perform such an exercise using the historical volatility of origin and destination s GDP to proxy uncertainty in a gravity model of international students flows. It could be useful to carry out the same estimation on microdata and/or for internal student 12 In a study on international students at the University of Minnesota Hazen and Alberts (2006) report that most of them, independently of their nationality, indicate family ties as the major advantage of their home country with respect to the US. 20

33 mobility, provided the availability of long enough time series. 21

34 Appendix 1.A Derivations of expressions (1.13) and (1.14) Expression (1.13) is obtained from expression (1.11). Multiplying terms we get: ( ) k V d = Φ (γ d η) + σ ( ) [ ( )] ν,d k k φ + 1 Φ (γ d η) + (1.24) σν σ ν σ ν σν [ ( )] k 1 Φ k σ ( ) ν,o k φ σν σ ν σ ν Simplifying terms we get: Now, notice that: and, So, ( ) ( ) [ ( )] σν,d σ ν,o k k V d = γ d η + φ 1 Φ k (1.25) σν σν σ ν σ ν,d = E[(ɛ d ɛ o )ɛ d ] = E(ɛ 2 d) E(ɛ o ɛ d ) = σ 2 d σ o,d (1.26) σ ν,o = E[(ɛ d ɛ o )ɛ o ] = E(ɛ d ɛ o ) E(ɛ 2 o) = σ o,d σ 2 o (1.27) σ ν,d σ ν,o = σ 2 d + σ 2 o 2σ o,d = σ 2 ν Substituting in 1.19 we get expression 1.13 in the main text. expression Symmetric derivations yield 1.B Derivative of the gains from mobility with respect to k and C The derivative of expression (1.15) with respect to the cost k is: ( ) ( ) ( ) Ṽ k k k k k = φ 1 + Φ + φ σ ν σν σν σν (1.28) Now, notice that, since the expression for the standard normal probability density function is φ(x) = 1 2π e 1 2 x2 (1.29) its first derivative with respect to x is: φ (x) = x e 1 2 x2 = xφ(x) (1.30) 2π 22

35 Using the above result it is possible to rewrite expression (1.28) as: k ( ) k φ + k ( ) ( ) k k φ 1 + Φ σ ν σν σ ν σν σν Simplifying terms, we get: ( ) k 1 + Φ 0 σν Following the same procedure it is possible to find out that: 1.C Derivation of expression (1.17) ( ) Ṽ C C = 1 Φ 0 (1.31) σ ν To take the derivative of equation (1.15) with respect to σ ν, I first rewrite it in the following way: ( ) ( ) ( ) ( ) k k C C Ṽ = [(γ d γ o ) k + C η] + σ ν φ + kφ σ ν φ CΦ σν σν σν σν (1.32) The derivative of the of the above expression with respect to σ ν is: [ ( )] σ ν φ k σ ν σ ν [ ( )] + kφ k σ ν σ ν [σ ν φ ( kσν ) [ ( )] [ ( )] σ ν φ C σν + CΦ C σν σ ν σ ν ( ) ] ( ) ( ) k2 k σν 2 φ [σ ] ν φ C C2 c σν σν σν 2 φ σ ν = (1.33) Now, notice that, for the normal probability distribution, and for a generic x, the following result holds: xφ ( 1 x ) = 1 [ e 2( 1 x) x 1 ( 1 ) 1 2π x σ 2 e 1 2( x) 1 2] = (1.34) 2π ( ( ) ( 1 φ + φ x) x x) Using the above result in equation (1.33) I find: [ ( ) ( ) ( ) Ṽ ] [ ( ) ( ) ( ) ] k = φ + k2 k σ ν σν σν 2 φ k2 k C σν σν 2 φ φ + C2 C σν σν σν 2 φ C2 C σν σν 2 φ (1.35) σν Simplifying terms we get expression (1.17) in the main text. 23

36 24

37 Chapter 2 The determinants of international student flows: Some empirical findings 2.1 Introduction and motivation This chapter focuses on the economic push and pull factors of international student mobility. As I have already noticed, understanding student mobility is relevant both from a macroeconomic and a microeconomic perspective. As to the first one, the internationalization of education can benefit both host and home countries. In fact, not only the former s current accounts improve as a consequence of increasing international enrollment, especially if higher tuition fees are charged to foreign students, but in addition, if international students settle down in their study place and become highly skilled workers, the overall stock of human capital of the receiving country will rise. For instance, Chellaraj et al. (2005) show that international graduate students have a positive and significant impact on the development of innovation, measured as the number of patent applications and the number of patents granted to US academic and non-academic institutions. The above is an example of the well-known brain gain phenomenon, which has been largely debated in recent years, when the shortage of highly educated labor force is making industrialized countries compete to attract talent. 1 As far as the origins are concerned, education abroad of their citizens can represent a way to deal with the unmet domestic demand for higher education, which may be difficult to provide, especially for small countries, and hence increase the overall educational attainment of their population, if at least part of the mobile students come back home after education (Docquier et al., 2008). 2 Moreover, there seem to be evidence (Park, 2004) that international student outflow is a channel of R&D diffusion, even more than international trade can be. So, although 1 It is worth recalling that the benefits from international students for receiving countries, and in particular for US, have been challenged by an authoritative analyst like Borjas (2002, 2004), who has underlined the many inefficiencies of the Visa-system, and its failures in tracking foreign students after the completion of their studies, so that a high number of them become illegal workers. 2 This seems to be the case of Luxembourg, for example (see OECD, 2008c). 25

38 part of mobile students do not come back after education -the so-called brain drain, - their outbound mobility may still be profitable for the source country. 3 From a microeconomic perspective, there are potentially non-negligible payoffs of international education, the amount of which depends on how much the latter is rewarded in the labor market, either at home or abroad. Empirical studies on the topic, mainly for US, show that there are positive returns to foreign education for those immigrants who have studied in the United States, after controlling for selectivity bias (Bratsberg and Ragan, 2002). Recent figures on student mobility (see OECD, 2008a) make a case for trying and study the issue, notwithstanding existing data constraints I will describe later on. Indeed, the inflow of international students in OECD countries from all over the world has experienced a steady increase over the past three decades: overall, the absolute number of students who cross national borders for educational purposes is nowadays nearly four times the one of the mid-seventies (from 0.6 millions in 1975 to 2.9 millions in 2006). This process has been accelerating during the past ten years, mirroring the globalization of economies and societies. Another noticeable fact concerns the characteristics of origins and destinations: while the pool of the sending countries has always been dominated by the Asian ones, the group of the major recipients has grown larger over time. Indeed, beside the traditional destinations (Australia, France, Germany, United Kingdom and United States), other, relatively new ones, like Japan, South Korea, South Africa and New Zealand are now competing for international enrollment. As discussed at length in OECD (2008a), beside the degree of internationalization of the educational systems (e.g. in terms of the language of instruction, the major destinations being those offering courses in English), living costs and tuition fees, migration policies in the receiving countries are likely to be relevant pull-factors of student inflows, which are found to be more intense toward those countries where selective (i.e. highly-skilled oriented) migration measures are into force and where international students have easy access to national labor markets both during and after their studies: Australia, Canada, New Zealand and Sweden are remarkable examples from this point of view. Whether foreign students intend to stay or come back after graduation is instead less clear: indeed, although it is known (see Finn, 2003; Borjas, 2002) that many return to their origins or perform repeat migration after education, the stay rates vary by nationality. For example, in the US, the Chinese and the Indian feature the highest stay rates, and the Latin American the lowest ones. This suggests also that there are other factors, beside economic perspectives, e.g. cultural similarities and/or migration networks, that make the cost of staying and moving differ across pairs of origins and destinations. From the above considerations it is evident that understanding student mobility is not an easy task, since many determinants are likely to play similar roles and interact, and many others are not measurable at all: among the latter, for example, the reputation of academic institutions in the host countries and their attitude toward international students, reflected in their policies to attract them, are to be borne in mind when analyzing student mobility, even if, in most cases, it is not possible to control for them empirically. 3 See Commander et al. (2004) and Docquier and Rapoport (2009) for recent surveys of the literature on the brain drain and its implications for the source countries. 26

39 The attention paid to student mobility by national governments and international organizations has not been so far coupled with a deep economic analysis of its causes. Indeed, apart from few exceptions that I will review in the next Section, the study of highly skilled migration has been confined to workers mobility, disregarding mobility to study as another side of the same phenomenon. Traditionally, student mobility has been focused on with the purpose of assessing the overall status of education systems (the percentage of foreign students being considered a measure of the attractiveness, and, indirectly, of the quality of national academic institutions), but without attributing any explanatory role to economic and labor market perspectives in home and host countries. Furthermore, most of the times only one destination (typically United States) has been taken into account. Using a panel dataset containing information on bilateral student flows among 192 countries in the time period, the analysis of the present chapter studies the inflows of international students to 15 main destinations from all over the world. The purpose of my work is to get some empirical insights that may help further research and to draw a picture of existing patterns of student mobility and its driving forces. To this aim, beside the usual explanatory variables of any gravity model of migration, and following the results of the theoretical framework I have presented in chapter 1, I will explore the relationship between student mobility and those factors that may affect the intentions to stay or to come back after graduation: namely, the unemployment rate at home and in the study place, as a proxy for labor market opportunities, and origin and destination s expenditure in tertiary education, as a proxy for the quality of the educational systems. Moreover, I will use the per-capita GDP standard deviation to try and detect the correlation between uncertainty in future economic conditions and student inflows and outflows. As I will show, some of the traditional gravity variables have the usual sign and are significant. As to the economic factors I am most interested in, I find clearer results when time-variant regressors are allowed to absorb all cross-country and time variation (i.e. without inserting country fixed effects), which could depend on the low variability of my data, especially within the fairly homogeneous group of the destinations. Overall, my findings indicate that higher educational expenditure in the origin is associated with lower outbound mobility to study. Furthermore, uncertainty over the destination s economic conditions, as proxied by its per-capita GDP standard deviation, is associated to lower inflows, which is intuitive if uncertainty is interpreted as an additional cost from the perspective of those individuals who do not want to reverse their moving choice (see Section 2.3). In addition, the destination s GDP growth rate positively affects student inflows. The unemployment rates, instead, do not display any correlation of interest with student inflows or outflows. Though further work is needed before coming to definitive conclusions, the above results seem to suggest that the characteristics of the educational systems, both at home and abroad, matter for student mobility. Whether tertiary students cross national borders seeking also better post-graduation economic opportunities in the study place remains an open issue and a topic for future research, that the present work is just starting-up. The remainder of the chapter is organized as follows: in the next Section I review the main 27

40 empirical literature on student mobility; in Section 2.3 I will recall the theoretical findings of chapter 1 s model and their intuition. Sections 2.4 and 2.5 are devoted to the description of the empirical strategy and its results. Section 2.6 concludes. 2.2 Related literature In this Section I summarize the findings of the few studies on the economic determinants of international students mobility, some of which resemble the outcome of my analysis. Rosenzweig (2006) addresses the determinants of students inflows to the US. The author is interested in testing the implications of two competing models of student mobility: the first one is the Constrained domestic schooling model, according to which international students come from countries where skills are highly rewarded but where there is shortage of supply of higher education. The second one is the Migration model, which assumes that students tend to leave countries where skill-prices are low and move to countries with higher skill premia. The main implication of the Migration model is that tertiary students enroll abroad in order to acquire knowledge that is easily transferable into the destination labor market: their main purpose, hence, should be to stay and work in the host country. Rosenzweig uses a micro-dataset (the NIS, New Immigrant Survey) to estimate global skill prices, and finds strong evidence in support of the Migration model of student mobility. Indeed, according to his results, the lower the skill price in the origin, the higher the outflow of students from that country to the United States. Moreover, the source country per-capita GDP is found to exert a positive influence on student outflows. This is interpretable as evidence that ability to pay for foreign education is an important push factor of student outflows, and, as I will show later on, my own findings lead to similar conclusions. Labor immigration to a given country seems to be strongly influenced by the stock of foreign students living there. For example, Dreher and Poutvaara (2005) show that the migration flow from a given origin to United States is significantly driven by the number of students coming from the same origin and studying in the US. Since the migration flow is measured as the number of worker visas issued yearly, including the conversions from student to worker visas, it is likely that this finding reflects the determinants of the stay rates of foreign students in the United States. This work also supports the view that people who go and study in the US aim at staying, or happen to stay there also to work. The issue of foreign students not returning to their home countries after education has been addressed by Bratsberg (1995), who, using US data on the conversion rate of student visas, focuses on the determinants of the stay rates of foreign students and its impact on immigrants wages. As regards the factors leading people to come back, an interesting result is that students tend to return to countries with higher rewards to education and higher wage inequality - the two proxies for the domestic skill premium used in his empirical model. As to the impact of the stay rates on immigrants wages, he finds that the latter decrease if students who settle down are from countries where the skill premium is low (i.e. students are positively selected): indeed, if it is the most able ones who stay, the total supply of immigrant skills in the US will increase, 28

41 and the immigrants wage will decrease. By analogy, the wage of migrants increases if those students that stay are from countries where skills are highly rewarded, i.e. in case of negative selection of mobile students. Sakellaris and Spilimbergo (2000) look at foreign enrollment from a human capital investment perspective, exploring the impact of business cycles on international enrollment in the United States. Interestingly, they find that foreign enrollment is pro-cyclical for developing countries, where the ability to pay effect of a change in domestic economic conditions is likely to be more relevant, and counter-cyclical for OECD countries, where the opportunity cost effect may prevail, because, in the authors interpretation, OECD countries have better labor market institutions that favor the transition from education to work. This finding is also in accordance with the evidence, mentioned above, that the origin per-capita GDP has a positive impact on foreign enrollment. The research reviewed so far addresses foreign education in just one host country. To the best of my knowledge, the only works focusing on the economic determinants of bilateral student flows are Spilimbergo (2009) and Kim (1998). The first one deals with the issue from an indirect point of view: indeed, what the author is interested in is the impact of foreign education on the level of democracy in a given country. Since the former variable may be endogenous (e.g. foreign students may foster the enhancement of democracy in their origins, but also the lack of democracy may lead students to leave the country), he estimates a gravity model for the determinants of bilateral students flows and uses its predicted value to instrument it. His evidence indicates that foreign enrollment is positively influenced by democracy both in the source and host countries, and also that the level of democracy in the origin is positively affected by the number of students who went abroad for tertiary education. The source of his data is the same as mine, i.e. the UNESCO student migration database, even if he has access to a longer time series. Kim (1998) develops a theoretical model of foreign education from which he derives testable implications for the choice of the destination by foreign students, the determinants of the number of students abroad, and the growth effect of foreign education in the origin. Among his results, the one that is most related to the topic and findings of the present chapter is the negative association between the GDP gap, i.e. the ratio between destination and origin s per-capita GDP, and students outflows, interpreted, as before, as evidence of financial constraints. In the model for the choice of the study place (a multinomial logit model, with 113 choices of destinations for each origin) the effect of the GDP gap is instead positive. He also finds a positive correlation between the destination s GDP growth rate and student inflows, which is also one of my results. In light of the findings of the few works on international education reviewed in this Section, one can conclude that, on the one hand, student mobility can be assumed to follow the same pattern as labor migration, and especially highly skilled migration. On the other hand, it has also its peculiarities. In fact, beside the importance of ability to finance foreign education, which makes the expected sign of the impact of the origin s economic conditions less clear than for workers migration, an interesting feature of student mobility is its tight link with the returning decision. 29

42 Indeed, coming back is much more relevant for those who move to study than those who move to work. So, when addressing student mobility, special attention should be paid to variables that may affect the costs of coming back or staying after education, as well as the migration cost in strict sense, i.e. the cost of moving to find a job. Those costs, indeed, are crucial in the theoretical framework developed in the first chapter, that I am going to recall in the next Section. 2.3 Theoretical insights This Section is devoted to a brief review of the theoretical framework I have presented in the first chapter, which, together with the findings of previous literature I have just described, will provide a guidance for setting up my empirical analysis and interpreting its outcomes. In the model there are only two periods, and in each one a mobility decision has to be taken: at time 1 the individual decides whether to move or not for education, whereas at time 2 he chooses the place of work. The latter choice depends on the realization of uncertainty, modeled as a shock to period 2 labor income, the probability of which is taken into account when solving period 1 s problem. Namely, the individual is assumed to know that if he moves for education in period 1 and then the destination s labor market conditions happen to be worse there than in the origin, he may want to return, in which case he will pay a cost of coming back k. On the contrary, if the agent stays in the origin for education, but in period 2 labor market conditions are more favorable in the destination than in the origin, he may want to migrate, paying a moving cost C. The reader can refer to chapter 1 for a detailed description of the assumptions of the model and its parameters. For the purpose of the present analysis, it is important to recall the following theoretical results: - Intuitively, the gains from mobility increase with the difference between the quality of education in the destination and in the origin. The latter is represented, in the model, by that component of labor market returns to education that only depends on the type of education and not on the characteristics of the place of work. Since it is assumed that quality of education is location-specific, the individual will gain γ d if he gets educated in the destination and γ o if he gets educated in the origin, wherever he chooses to work. The other components of his earnings will depend on the realization of the location-specific shock to labor income. - Asymmetry in period 2 moving costs plays an important role in shaping mobility, in that if the cost of coming back k is different from the one of moving afterward C, there is scope for the individual to use mobility to find himself in the location from which reversing the previous period moving choice is less costly. - The effect of uncertainty over destination/origin relative economic conditions is driven by the above asymmetry in the two costs. Indeed, as I have shown in 30

43 the first chapter (where the reader can also find the analytical derivations) the derivative of the gains from mobility, Ṽ, with respect to the standard deviation of the difference between the destination and origin shocks to labor income, σ ν, that in the model represents uncertainty, is: [ ( ) ( )] Ṽ k C = φ φ σ ν σν σν (2.1) Where φ(.) is the standard normal probability density function. From the above expression the ambiguity of the effect of uncertainty on the gains from mobility is clear. In fact, if the cost of coming back k is lower than the one of moving ( ( ) afterward, then φ k σ ν ) φ C σ ν > 0, i.e. moving in period 1 is more profitable than staying when uncertainty increases. 4 On the contrary, if C is lower than k (a condition similar ( ) ( ) to the assumptions of the Option Value models of migration), then φ k σ ν φ C σ ν < 0, and the greater uncertainty, the more waiting is valued with respect to moving in period 1. Ideally, in order to perform an empirical test of the above theoretical results, one should be able to control for three orders of factors: 1. Returns to domestic and foreign education in both locations; 2. Relative economic conditions in the source and host countries, and their volatility; 3. The costs of coming back and migrating after education. As I will further discuss when motivating the choice of the explanatory variables, the above ideal data are difficult to find. In some cases, it is possible to follow previous literature and resort to imperfect proxies for them, but in the case of period 2 moving costs k and C, distinguishing them one from each other is empirically very difficult. Indeed, the standard proxies for the monetary and psychological costs of migration, e.g. geographical distance, cultural and/or political variables, presumably affect the cost of coming back and of migrating after education to the same extent. Moreover, the two costs are likely to be influenced by individual rather than macroeconomic factors, so that a microdata analysis on the determinants of international student mobility (for which data do not exist) should be more appropriate. Despite that measurement problem, it is not unreasonable to think that coming back after education or migrating to work have a different cost. One reason may lie on migration policies: e.g. if a country wishes to foster temporary rather than permanent immigration, it may favor students rather than workers inflows, since the first are usually thought to come for a limited time period: this case would be translated as C > k in the model s notation, since coming back is encouraged by the measure, and migrating to work may be very hard. 5 In addition, what 4 k and C are positive parameters by assumption, being two costs, so they will fall in the decreasing portion of the normal probability density function φ(.). 5 For example, in order to get a student VISA in the US the person is asked to declare that he has no intention to stay in the United States after the completion of his studies (GAO, 2007). 31

44 matters for the first period decision, according to the model, is how the individual conceives the relative magnitude of the two costs: since agents are heterogeneous, they may have different conceptions of how much difficult it will be to come back after studying or to move after education. For example, if, as some authors point out (see Dustmann, 2003), migrants are assumed to strictly prefer living in their origin, then the longer the time spent abroad, the lower the cost of coming back for a given cost of moving in period 2. Following this line of reasoning, students willing to come back should have a lower k, in particular if the time they have spent on education has been long. This strict preference for living in the home country can be also due to cultural factors: it should be stronger the wider the cultural difference between two countries. Finally, coming back may be less costly for the individual than moving for the first time to find a job, because the former decision does not entail the effort cost to get accustomed to a new environment. On the contrary, if students move with the purpose of settling down to work in the destination, which seems to be the case, for example, of foreign students of given nationalities in the US (Borjas, 2002), coming back is hard, since it is induced by unemployment after graduation, or because migration policies make the access to national labor market more difficult for foreign fresh graduates. Finally, the cost of coming back may be high if the skills acquired in the destination are not easily exploitable in the origin or in other countries: not only the formal recognition of certain education titles may be difficult outside the country, but people may have attended specific training programs that make them more easily employable in their study place. Given all the above identification issues, the purpose of the following analysis will not be to test the implications of the theoretical model, but to get the sign of the correlations between student flows and economic characteristics of origins and destinations, so as to have some hint on whether the theoretical relationships just described can be detected in the data. 2.4 Empirical analysis In this Section I first describe the dataset I use, stressing some important issues to bear in mind when interpreting the empirical results. Then, I will discuss more in detail the empirical specification and the assumptions underlying the choice of the explanatory variables Data Data on bilateral student flows come from the UNESCO on-line student migration database. As explained in UNESCO (2006), international (or internationally mobile ) students are defined as Students who have crossed a national or territorial border for the purpose of education and are now enrolled outside their country of origin. Hence, the criterion for identifying international students is the permanent residence one, namely, a student is considered mobile if he is not a permanent resident of his country of study. Data refer to tertiary education, i.e. ISCED (International standard classification of education) levels 5 and 6 (University or graduate education). The available time period is

45 Some important caveats concerning the data are worth discussing at this point. First of all, notwithstanding UNESCO efforts to homogenize it, the classification of international students still differs across recipient countries, which are the primary sources of UNESCO data. As it is shown in Appendix Table A -2.1, the destinations I take into account use different criteria to identify international students, some of which do not entirely correspond to the definition given above. For example, Table A -2.1 points out the distinction between the aforementioned permanent residence and the citizenship criteria. According to the latter, international students are identified on the basis of their country of citizenship, which may lead to an overestimation of their true number, since non-citizens of the host country could have migrated for other purposes than tertiary education (e.g. they may have migrated with their parents when they were younger). Furthermore, some countries use the prior education criterion, i.e. international students are defined as those ones who acquired their latest level of education abroad. If that definition is adopted, citizens who had previously moved for education and have then come back to complete their studies at home will be counted as international students even from the perspective of the home country. The direct consequence of the above definitional discrepancies is that one has to put special caution when using these data for cross-country comparisons. A second problematic aspect of the data on bilateral student flows is the high number of zero values in the series. The documentation explains that a value of zero does not necessarily correspond to zero flow in a given year, but it may indicate a flow of negligible magnitude. In my estimation sample, however, all the chosen destinations report also values of 1 for the flows, so it is very likely that those zeros are informative. 6 This is not uncommon in migration datasets, since it may well be the case that for given pairs of countries and years there is no bilateral flow, and it is advisable to retain them, since zero flows may occur because of high distance, lack of financial resources in the origin or other interesting reasons. A challenging econometric issue is that, because of those zeros, around 20% in my estimation sample, the distribution of the dependent variabile is highly skewed and OLS estimates can be biased (Beine et al., 2009). This is precisely what happens in my data, as Figure A shows. An usual way to overcome this problem is to take a logarithmic tranformation of the dependent variable, but taking the natural logarithm of a zero will yield a missing observation in the series, and hence a loss of information that I would like to avoid. Above all, as it is shown in the bottom panel of Figure A - 2.1, even when its natural logarithm is taken (and the zero values are thus dropped), the dependent variable still displays a distribution that is far from normal (though the parameters of skeweness and kurtosis are much more similar to the ones of the normal distribution than before the transformation). Following previous literature dealing with the same problem, I will adopt three strategies to treat the zeros. First, I will replace them with a very small value ( ), so as not to lose observations when the natural logarithm is taken. The log of bilateral student flows will be used as a dependent variable for both an OLS and a Tobit estimation. The latter approach has been used to deal with zero values in a migration database by Mayda (2007), and it is usually adopted when the dependent variable displays a mass at some 6 Only for United States the lowest reported value is 2, but there are just 8 zeros in US data. 33

46 value (in my case, the mass is at ). Finally, following Beine et al. (2009), and as a robustness check, I run Poisson regressions on the data without taking the natural logarithm of the dependent variable. Poisson estimates are presented in the Appendix Tables, and they are fairly similar to the OLS and Tobit ones. 7 I select 15 destinations, and 192 origins of international student flows. Among the chosen host countries there are the traditional top-five destinations of international students, i.e. United States, United Kingdom, Australia, France and Germany, and other non-traditional destinations which have witnessed an increase of their pool of international students during the considered time span, like Japan, South Korea and New Zealand. Other European minor destinations, i.e. Austria, Belgium, Italy, Netherlands, Spain, Sweden and Switzerland are also included: the above countries have been, over the period and with some changes in their relative rank position, among the top-10 European destinations. 8 Figure 2.1 gives an overall picture of the pattern of international student mobility by destination countries (only the ones analyzed here). The Figure confirms the rankings reported by UNESCO and OECD in their yearly reports (for the most recent ones, see UNESCO, 2006 and OECD, 2008b), the major destinations being United States, United Kingdom, Germany, France and Australia. The 15 host countries differ in several respects that regressors I will use in the empirical analysis can proxy only to a limited extent, but that are likely to be relevant for student inflows. An important difference among them lies in national policies to foster student inflows and their staying after the completion of education (Jan et al., 2007; OECD, 2008a; Gnisci, 2008; Chaloff and Lemaitre, 2009). For example, the procedures to convert a student visa into a long-term residence permit vary considerably across countries: in some cases (e.g. Australia, Belgium, Netherlands, New Zealand, Italy, Sweden, United States) the time as student can be counted in order to be eligible for a permanent residence visa, while in some others (like Austria, Germany, Spain, Switzerland) it cannot. In United Kingdom conditions for eligibility for a permanent residence leave are very unfavorable for international students, who have to wait until 10 years to apply (even if their time as students counts for the fulfillment of the eligibility criteria). In most countries labor market access of international students is encouraged: this is particularly true where selective (i.e. favoring the highly skilled) migration policies are in force, like in Sweden, Australia and New Zealand. Moreover, the costs of foreign education are not the same among the sample of recipients. For example, some countries charge higher fees to international than national students (Australia, United States, New Zealand; Austria, Belgium, United Kingdom and Switzerland only to students from Non-European Union non-european Economic Area countries), while in others (France, Japan, Italy, Korea, Spain) international students pay the same as national ones for tertiary education. In Sweden, instead, tertiary education is free both for national and international students. Finally, a potential source of cross-country unobserved heterogeneity is the 7 The estimated specifications for the Poisson regressions are fewer than the Tobit and OLS ones. Indeed, some specifications could not be estimated due to convergence problems. 8 It would have been interesting to include also Canada, which is known as one of the most preferred destinations by international students. Unfortunately, Canadian data in the UNESCO on-line database are only for the years 2006 and

47 average quality of education and prestige of national academic institutions. I have merged the data on international student flows with the following additional informa- Figure 2.1: average percentage of student flows, by destination countries. Source: Own computations on UNESCO on-line student migration database. The Figure plots the average percentage of internationally mobile students in a given destination, over the total number of international students. tion: proxies for economic and labor market conditions, i.e. per-capita GDP (PPP-adjusted at constant 2005 international dollars), per-capita GDP growth rate and unemployment rate in origin and destinations; proxies for the average quality of the education system, i.e. per-student expenditure in education as a percentage of per-capita GDP, and demographic variables, i.e. total population and total enrollment in tertiary education. The above data come from the World Bank, World Development Indicators (WDI) dataset. Finally, like any gravity model of migration, I include some proxies for the moving costs, namely the geographical distance between pairs of countries and dummy variables indicating whether the countries share a common border, a common official language and whether they ever had former colonial relationships. For most pairs of countries, this information was collected from Glick and Rose (2002). When information on the distance was not available, I have computed it using the great-circle formula, following the same procedure described in Glick and Rose (2002) and using their same data source for latitudes and longitudes of each country s capital city (see the data Appendix for details). At first glance, cultural links seem to matter in shaping the pattern of international student flows. This is shown in Figure 2.2, where I plot the average percentage of international students from a given continent to each destination. It is interesting to notice how the ranking of Figure 1 is modified when the flows are disaggregated by continent of origin. For example, France is by far the most frequently chosen destination by 35

48 Figure 2.2: average percentage of student flows by continent of origin and destination countries Source: Own computation on UNESCO on-line student migration database. The Figure plots the average percentage of internationally mobile students from a given continent to each of the 15 destinations, over the total number of international students from that continent. African students, which can be explained by former colonial relationships and common official language. The same holds for international students from South America, who, after United States, seem to prefer Spain. Students from Europe tend to choose European countries among the top-five destinations, which is explainable with geographical proximity as well as with the easier movement of European students within the EU rather than to other countries Empirical model In order to test whether there is an association between bilateral student mobility and the economic variables previously discussed, I estimate the following reduced form: IS ij,t = β 0 + β 1 ȳ i,4 + β 2 ȳ j,4 + β 3 σ yi,4 + β 4 σ yj,4 + β 5 X ij,t + β 6 X ij + ɛ ij,t (2.2) where: IS ij,t is the annual flow of international students, as provided by UNESCO, from country 9 It is important to recall that international students enrolled in student exchange programs (e.g. Erasmus- Socrates) are not included in the above statistics, since they are formally enrolled in their country of origin. 36

49 i to country j; ȳ i,4 and ȳ j,4 are per-capita GDP averages computed over the 4 years preceding the one of the student flow, in the origin and destination respectively. I will consider three nonoverlapping time windows: , and As a consequence, the 1999 student flow from country i to country j will be explained by the GDP per-capita average, the 2003 flow by the average and the 2007 flow will be explained by the average. The choice of computing the mean is motivated by my theoretical model, according to which the mean wage (difference) and its standard deviation are the main components of returns to mobility for education. Moreover, choosing to explain student flows with past values of the GDP I make the implicit assumption that past values of economic conditions help predict both their contemporaneous and future values. In order to achieve a perfect correspondence between the theoretical and the empirical model, a proxy for the foreign education premium, possibly estimated on micro data, should be available. Moreover, macrodata on wages are not available too, and this is the main reason why I resort to GDP per-capita to proxy average economic opportunities in a given country. In a separate specification I will control for the GDP gap, namely the 4-years average difference in the destination and origin s per-capita GDP (i.e. ȳ j,4 ȳ i,4 ). The literature on labor mobility usually finds a negative and a positive sign for per-capita GDP in the origin and destination, respectively. If per-capita GDP is interpreted as a proxy for average wages in a given country, this finding is going to reflect the fact that workers choose locations where wages are higher and are more likely to leave those countries where the level of wages is lower. In the case of student mobility the sign of the above variables is likely to be less clear. Indeed, as found by some of the studies reviewed in Section 2.2, per-capita GDP in the origin may also capture its overall economic resources, and hence its population s ability to pay for foreign education, which should have a positive effect on student outflows. As to per-capita GDP in the destination, it may have a positive sign, as in a standard model of migration, which would confirm that international students look at future economic opportunities after graduation. As I will show, I find conflicting results as to the relationship between per-capita GDP in the origins and the destinations, and I will try to give some explanations for this outcome. σ yi,4 and σ yj,4 are the standard deviations of country i and country j per-capita GDP, i.e. the empirical counterparts of the volatility of the income process in the origin and destination. In the specification where I control for the difference between the destination and origin s per capita GDP I will instead use the standard deviation of the difference, namely σȳi,4 ȳ i,4. X ij,t contains time-variant controls. Specifically, I will include the total population in the origin and destination as scale variables and, in separate specifications, I will include per-capita GDP growth rates (computed over the same time windows as the average per- 37

50 capita GDP and its standard deviation), per-student destination and origin expenditure in tertiary education as a percentage of GDP, total enrollment in tertiary education, and the origin and destination s unemployment rates. X ij includes the time-invariant controls, i.e. the geographical and cultural variables I was mentioning before, whose expected sign is the same as in the gravity models of labor migration (i.e. negative for distance, and positive for common language, common border and colonial relationships). Year effects, destination and origin fixed effects will also be included in separate specifications. Finally, ɛ ij,t is the error term, assumed to be i.i.d. normally distributed in the Tobit and OLS models and poissonly distributed in the Poisson model. Summary statistics for all the explanatory variables are presented in Table 2.1. It is important to point out how the variables related to the destinations are much less dispersed than the origins ones. This may depend on existing similarities among host countries as to their economic conditions, whereas the sending countries are a larger and more heterogeneous group. So, even if time-variation is low in all the sample (since there are only 9 years), cross-country variation is higher for the sources than the recipients. This will prove relevant in the interpretation of my empirical findings, since it is plausible that most results (in particular when the difference between the economic variables of the origins and destinations are used as regressors) are driven by the origins variability. 2.5 Results In this Section I present my empirical findings. As I will discuss in what follows, some of them are intuitive and in accordance both with previous literature and with the theoretical framework summarized in Sections 2.2 and 2.3. Some others instead are somewhat puzzling, and I will try and explain them both in light of data characteristics and of relevant correlations among the explanatory variables Per-capita GDP and its standard deviation Table 2.2 presents the results of a base specification, where I control for the origin and destination s per-capita GDP and their volatility over the considered time windows. In each column I present the OLS and Tobit coefficients, and specifications differ according to whether destination/origin fixed effects and year effects are inserted or not. 10 As it is shown in the Table, the sign of the coefficients of origin and destination s per-capita GDP changes according to whether country and year fixed effects are controlled for or not. Indeed, when the GDPs absorb all the cross-country and time variation (columns (1) and (3) of Table 2.2), I find that both have a positive impact on international student flows, from which one should conclude that 10 Excluding country effects while keeping year effects leads to similar results as the ones without any fixed effects. 38

51 richer countries send and attract a larger number of students. In fact, if GDP captures financial resources at home, it is reasonable that students from high-income countries find it easier to go and study overseas. The positive sign of the destination s GDP can instead be interpreted as in traditional migration models: namely, if GDP proxies economic opportunities abroad, and if on average foreign students have the intention to stay in the study place to work, then high-income destinations should be preferred. However, when all cross-country time invariant differences and common trends are captured by country and year fixed effects (columns (2) and (4) of Table 2.2), the relationship between origin an destination per-capita GDP and student flows is negative. This result seems more robust for the destination s GDP than for the origin s one: indeed the coefficient of the latter most of the times loses significance when dummies are inserted, though the sign is still reversed (see also the next Tables). Given the short time span considered, it is possible that the above negative relationship is spurious, since, when fixed effects absorb all the variation, what the destination s GDP is probably left to capture is the impact of other (unobserved) time-variant and country specific factors that are likely to restrain mobility and that happen to be correlated with per-capita GDP. To further explore this issue, in Figure 2.3 I plot the relationship found in the regressions: the Figure is the partial correlation between the destination s 4-years average of per-capita GDP and international student inflows from all origins with and without controlling for country and year effects. From this Figure it is not possible to single out those countries and years that are driving the negative relationship of the bottom panel. So, in Figure 2.4 I plot the partial correlation between the total student inflow (i.e. the sum of all foreign students in a given destination and year) and the 4 years average of per-capita GDP. Qualitatively, the outcome of this exercise is the same as in the regressions and in the previous Figure, but now it is easier to see that the negative correlation found could be attributed to countries that, for different reasons, may have witnessed a decrease in their foreign student inflows during the considered time span: e.g. US are known to have received less international students from 2001 to 2003, following the implementation of stricter migration policies after September 11. In the next Section I will explore whether this result is robust to the insertion of other potentially relevant explanatory variables. As to the proxies for uncertainty, I find that the destination s standard deviation of per-capita GDP is negatively correlated to student inflows, while uncertainty in the origin seems to be positively (but the result is not robust to every specification) correlated to student outflows. The negative association between uncertainty in the destination and student inflows may be interpreted in terms of the theoretical model of Section 2.3: namely, uncertainty is a cost for individuals who do not want to reverse their moving choice in the future, and so higher uncertainty induces a waiting behavior. However, one has to bear in mind an important concern when interpreting the results for the standard deviation. Namely, the latter is likely to be correlated with the GDP growth rate in the same time window. So, it will be useful to insert the latter variable in the previous specifications, and check how results change. I will address this issue in Table

52 10 Log bilateral stud. flows Figure 2.3: Student flows and per-capita GDP in the destinations. Partial correlations GDP per capita destination (4 years average) Log bilateral stud. flows GDP per capita destination (4 years average) The Figure plots the partial correlation between the 4-years average of per-capita GDP in the destinations and the bilateral student flows from all the origins, without (top panel) and with (bottom panel) time and country fixed effects. The other controls are the same as the ones in regression Table 2.2. Finally, the gravity variables have the expected signs and are highly significant, apart from the common border dummy. The result for the common border is however not surprising, since the major destinations in my sample either do not share borders at all (like Australia, New Zealand, Japan, United Kingdom) or do not share a common border with the major origins of their international students (e.g. the flow of international students from Africa to France is much more intense than the one from Belgium to France). As it is possible to notice from the following Tables, these results do not change in any specification and whatever estimation method is used. In Table 2.3 I try and estimate a more coherent specification with the theoretical predictions summarized in Section 2.3. Indeed, in Table 2.3 all the economic explanatory variables are expressed as differences between their values in the destination and in the origin. However, the results, as it was already possible to imagine from the descriptive statistics, are likely to be driven by the origin s variability. Hence, for example, in col. (1) of the Table, the magnitude of the coefficient of the average difference in destination/origin per-capita GDP is the same as the one of the origin average per-capita GDP in the previous Table, but with an opposite sign, 40

53 Figure 2.4: Student flows and per-capita GDP in the destinations. Partial correlations International students DEU03 07 DEU99 DEU JAP07 07 JAP03 03 JAP GDP per capita destination (4 years average) 07 International students JAP JAP DEU DEU DEU GDP per capita destination (4 years average) JAP99 The Figure plots the partial correlation between the 4-years average of per-capita GDP in the destinations and the total inflows of of foreign students from all origins, without (top panel) and with (bottom panel) time and country fixed effects. The other controls are the same as in regression Table 2.2. since the variable is computed as the destination/origin difference. Given this feature of the data, in the following specifications the economic variables for sending and source countries will be always kept separate Rates of growth and educational expenditure As I have already noticed, the standard deviation of per-capita GDP in the previous regressions may capture the effect of per-capita GDP growth rates. Moreover, also the level of per-capita GDP may be correlated to its rate of growth if, for example, high-income countries grow less fast than developing countries and vice-versa. To take into account this issue, in Table 2.4 I insert the origin and destination s per-capita GDP growth rates, while the other controls are the same as in Table 2. An interesting outcome is that the standard deviation of the origin s per-capita GDP loses significance when the growth rate is controlled for, while the sign and significance of the destination s standard deviation is unchanged. Moreover, the result for both growth rates is robust to the inclusion of year and country fixed effects and to the estimation method used. According to this specification, they are both positively associated to student 41

54 mobility. Before coming to any conclusive interpretation of the above result one has to consider that the GDP growth rate may be correlated to other variables that are not inserted in these regressions: for example, if the countries that are growing faster are the developing ones, there may be a negative correlation between the GDP growth rate and expenditure in education, since expenditure in education is lower in developing than industrialized countries. If, in turn, expenditure in education is positively associated to domestic enrollment of tertiary students, then the sign of the growth rate of the origin s GDP may just be driven by this correlation. Hence, to find out whether the above result is masking the effect of other omitted variables, it is interesting to run the same regressions with the addition of per-student expenditure in education as a percentage of GDP (which is also a proxy for the average quality of education in a given country), in both origins and destinations. This is done in Table 2.5, where also total enrollment in tertiary education is included. Educational expenditure in the origin has a negative sign, which suggests, intuitively, that the greater the amount of resources devoted to tertiary education, the less necessary it is for national students to enroll abroad. Moreover, when expenditure in education in the origin is inserted, the sign of the origin s growth rate becomes negative. In order to check whether and how this may depend on the correlation between the two variables, I look at their partial correlation, plotted in Figure 2.5. In the top panel all countries are plotted, and the negative fitted correlation seems to be driven by some countries more than others. In the bottom panel of the Figure I only plot those countries that in the top panel fall within the 95% confidence interval of the fitted regression line: with the exceptions of Japan and Australia, they are all developing countries. The negative association between expenditure in education and GDP per-capita growth in those countries is now clearer. Educational expenditure in the destination should matter for student mobility in that quality of education should be appealing for international students. The outcome of my estimation yields again a puzzling result as regards the effect of expenditure in education in the destinations, which mirrors the one found for per-capita GDP: namely, the correlation is positive when country and year dummies are not controlled for, while it is negative otherwise. Moreover, when fixed effects are controlled for, the coefficient of the destination s GDP per capita, though negative, is not significant. Again, a further look at the data may help understand this result. First of all, I look at the correlation between destinations expenditure in education and per-capita GDP. The simple correlation is positive, as it is shown in the top panel of Figure 2.6. However, the bottom panel of the Figure shows that controlling for the variables inserted in regression Table 2.5, with country and year fixed effects included, the relationship becomes negative, though not well-fitted. It is not easy to understand this result: in fact, on the one hand, the correlation between the two variables may be responsible for the lack of significance of the GDP per-capita coefficient, which however only occurs when controlling for country and year fixed effects; on the other hand, educational expenditure has itself a negative coefficient when fixed effects are inserted. Once again, this may be simply a spurious result, driven by some unobservable, country-specific and time varying factors that are positively correlated to educational expenditure, and negatively to student inflows. In order to explore this hypothe- 42

55 Figure 2.5: Expenditure in education and per-capita GDP growth rate in the origins. Partial correlation. Per student expenditure in tertiary education, % of GDP per capita MAC CMR TJK ARG UKR KWT POL VUT BGR IRL ROM KGZ MYS NOR MEX TUN BDI CZE HUN CRI BOLHRV CYP DNK ISR LSO PAN SVK PRT MDG LVA IRN CHN ISL BRA LAO SWZ LBN EST ZAF GRC MAR BGD BGD BLZ CAN TCD CIVFIN FIN HKG IND JAM LTU EST GRC CHL LBN MAR NAM NPL PHL PER RUS WSM CYP COL BOL MRT ZAF PRYDNK SLV HRV SWZ TUR ISR LVA MLI HUN CZE BDI PRT SVK KGZ SVN ARE TUN MEX NOR MUS TTO IRL COG POL ERI ARG MAC CPV Growth rate GDP per capita origin Per student expenditure in tertiary education, % GDP per capita CMR BDI LBN CYP PER CHL TUR Growth rate GDP per capita origin LBN CYP BDI CPV In the top panel of the Figure all the origins are plotted, while the bottom panel only shows the observations that fall within the 95% confidence interval of the estimated regression line. sis, I perform the same exercise as before: namely, in Figure 2.7 I plot the partial correlation between per-student expenditure in education as a percentage of GDP and the total inflow of foreign students in the 15 considered destinations. When country and year dummies are controlled for, the relationship turns negative, as we saw for the GDP, and as it was expected, given the outcome of the regressions. Notice, however, that now the negative relationship does not seem to be driven by any particular destination: it seems that all the considered recipients experienced an increase in their international student inflows at times when public expenditure in education was lower. In principle, this outcome lends itself to an interpretation suggested by a migration model of student mobility, i.e. in countries where expenditure in education is higher the education wage premium is probably lower. This, in turn, should restrain the inflows of international students who come to the chosen destinations with the intention to stay and work there. 43

56 Figure 2.6: Correlation between destination per-capita GDP and expenditure in education GDP per capita destination (4 years average) Log(per student expenditure in tertiary education, % GDP per capita) GDP per capita destination (4 years average) Log(per student expenditure in tertiary education, % GDP per capita) The Figure plots the simple (top panel) and partial (bottom panel) correlation between GDP per-capita and expenditure in education in the destination. The other controls are the same as the ones of Table 2.5, with country and year fixed effects included. 44

57 Figure 2.7: Correlation between expenditure in education in the destination and student inflows International students JAP JAP Per student expenditure in tertiary education,% of GDP per capita destination International students JAP JAP Per student expenditure in tertiary education, % of GDP per capita destination The Figure plots the partial correlation between the total student inflows and expenditure in education in the destination without (top panel) and with (bottom panel) year and country fixed effects. The other controls are the same as in Table

58 2.5.3 The unemployment rates International students may come to a given destination with the intention to stay there to work after the completion of their studies. This is what it is usually assumed by most existing research on international education (see Section 2.2). If it is so, labor market conditions in the origin and destination should be found to have the same correlation with student mobility as in standard bilateral models of migration, i.e. positive for sending countries and negative for the host ones. Regression Table 2.6 addresses this issue: here, I use the four-years average in the unemployment rate in both origins and destinations (computed over the same time windows as the average GDP per-capita) as a proxy for labor market conditions. Results do not indicate any significant correlation between unemployment rate at home and student outflows, while the destination s unemployment seems to be always positively (and significantly, when fixed effects are not controlled for) correlated to student inflows. Both findings seem to reject the hypothesis that international students come to the chosen destinations with the aim of staying to work, but, if anything, reveal a positive (most probably spurious) correlation between high-unemployment countries and student inflows in the considered years. Moreover, when country and year fixed effects are inserted, the coefficient of expenditure in education in the origin loses significance, and also the effects of per-capita GDPs are less efficiently estimated. This probably happens because the unemployment rate is correlated with the other economic variables, and it is also persistent over the considered time span, so it is also very collinear with year and country dummies. Indeed, the sign of the relationships is preserved, though the estimates are more imprecise, which typically happens in case of collinearity. 2.6 Summary and conclusion In this chapter I have carried out an exploratory analysis of data on international student flows using a gravity model approach. The main purpose of the present work has been to detect the potential explanatory power of some economic variables, which previous literature, as well as my own theoretical framework, suggest to be relevant for understanding student mobility. The data issues I have described in detail, which essentially amount to a potential comparability problem and to the short time span available, may undermine my results and call for caution in their interpretation. However, some preliminary conclusions are worth drawing, because they may represent a valid starting point for future research: 1. Among the 15 considered destinations, those ones that grow faster seem to attract more students. This is confirmed by previous literature, and it is robust to any of the estimated specifications. If the growth rate of the recipient country proxies economic opportunities abroad, this result suggests that countries that are offering better economic perspectives also attract a higher number of foreign students. Whether this can be taken as evidence of the intentions of mobile students to settle down in their study place after graduation cannot be assessed at this stage of the analysis. Indeed, the growth rate can be correlated 46

59 to many other variables relevant for student inflows, but for which I cannot control for. My findings also indicate that the origin s growth rate is negatively associated to expenditure in education, which in turn may spur tertiary students outbound enrollment, if public expenditure in education proxies the average quality of the public education system. 2. Another interesting finding, related to the previous one, and robust to several specifications, is that the origin s expenditure in education prevents outbound mobility. Thus, international enrollment is associated either to lack of educational supply, or to low educational quality at home, provided that expenditure in education is correlated to the overall status of public education. In terms of the theoretical model of Section 2.2, this may suggest that tertiary students are interested in the acquisition of high quality skills, which are probably going to matter for their future labor market payoffs, either at home or abroad. 3. The effects of per-capita GDP in the source and home countries, as well as expenditure in education in the destination are not clear. They seem to depend on whether year and country fixed effects are controlled for. In order to check whether this result is simply due to the low variability in my data, I should be able to perform the same estimation on a longer time series. It is also possible, as I have explained when commenting the results, that the above economic variables are correlated to unobservable factors that are relevant for student mobility, but for which I cannot control for: for instance, my data span a period of important changes in migration policies at the aftermath of September 11, which have involved some countries (US above all) more than others. 4. The volatility of per-capita GDP in the destination is negatively associated to student inflows, which lends itself to an option value interpretation. Indeed, if international students care of after-education economic or labor market chances in the study place, they will be led to choose those locations where the economic environment is stable enough to make them think they will be able to settle down after the completion of tertiary education. 5. The origin and destination s unemployment rates do not seem to matter for student mobility. If anything, a positive association between unemployment in the destinations and student inflows is found, which does not have any interpretation other than that some of the 15 considered destinations may have been experiencing high unemployment rates alongside a more intense inflow of international students. Again, a longer time series may help assess the spuriousness of this result. Indeed, over a longer time span, the above relationship could lose significance. Further research can be carried out along several directions. First, there are many other effects on international student mobility that it could be interesting to study by simply extending the set of regressors used in the present analysis. For example, the lagged value of student flows may exert a positive influence on international enrollment. Including this variable in my empirical 47

60 model will of course entail a careful treatment of its endogeneity. Moreover, among the cultural driving forces of student mobility, one could include the number of co-nationals working in the host country as an additional explanatory variable. If a positive and significant relationship were found between the latter variable and student flows, one could take it as evidence of cluster mobility, which so far has been explored only for labor migration. If instead the correlation were not significant, one could conclude that student mobility differs from standard migration also from this point of view, and argue that those ones who move for education are less attracted by ethnic or national ties. Finally, two more involved points are worth mentioning: first, since it is very important to take migration policies into account, one could study the way of constructing a synthetic migration policy index, with a particular weight given to measures to attract foreign students, and use it as a regressor; second, it would be useful to estimate skill premia at home and in destination countries, following the same procedure as in Rosenzweig (2006). Beside being interesting per se, this will allow me to test the implications of my theoretical model, giving a more structural interpretation to my results. 48

61 Data Appendix The 15 destination countries considered in the empirical analysis are the following: Australia, Austria, Belgium, France, Germany, Japan, Italy, Netherlands, New Zealand, South Korea, Spain, Sweden, Switzerland, United Kingdom and United States. The origin countries are all the other countries from the rest of the world (the destinations are included), for a total of 192 origin countries. The sample is only slightly unbalanced panel, in that only 3.26% observations in the series of international student flow is missing, for different origins and destinations. In the base specification I will use only 7690 of the total number of non-missing observations (25076) because I will consider only three years of student flows, i.e. the 1999, 2003 and The number of observations then reduce further to 5077 when I control for the unemployment rate, due to the high number of missing data (75.98%) in the latter variable. Variable definitions and sources: Bilateral student flows (dependent variable): Number of international students that crosses national borders and are now enrolled in a different country than the origin. Source: UNESCO on-line student migration database. Years: UNESCO is provided with this information by the destination countries. As mentioned in the main text, the definition of international student sometimes differs across countries, so that special attention is to be paid in comparative studies. Figure A shows the density of the dependent variable, Table A presents a synthetic overview of the different definitions in the considered destinations. Pop. origin/destination: Total population in the origin/destination country. Source: World Bank, World Development Indicators (WDI). GDP per-capita origin/destination (4 years average): 4 years average of GDP per-capita PPP-adjusted (thousands constant 2005 international dollars). The considered time windows are: , and Source: Own computations on World Bank, World Development Indicators (WDI). Standard dev. GDP per-capita origin/destination: Standard deviation of the above variable, computed over the same time windows. Destination/origin GDP per capita difference (4 years average): 4 years average of the difference between destination and origin GDP per capita as defined above. Standard dev. destination/origin GDP per-capita difference: Standard deviation of the above variable, computed over the same time windows. Growth rate GDP per-capita origin/destination: Growth rate of GDP per capita in the origin/destination country, computed over the 4 years time-windows described above. Source: Own computations on World Bank, World Development Indicators (WDI). 49

62 Per-student expenditure in tertiary education, % GDP per-capita origin/destination. Source: World Bank, World Development Indicators (WDI). Total enrollment tertiary education, origin/destination. World Development Indicators (WDI). Source: World Bank, Unemployment rate origin/destination (4 years average): 4 years average of the origin/destination unemployment rate, as a percentage of total labor force. The considered time windows are: , , Source: Own computations on World Bank, World Development Indicators (WDI). Log(distance): Log of great-circle distance. Source: Glick and Rose (2002). For the pairs of countries for which the great circle distance was not available the data was computed using the same procedure as Glick and Rose as well as the same data source for latitudes and longitudes (i.e. the CIA World Factbook, Common Language, Colony, Common border: Dummy variables equal to 1 if the pairs of countries share a common official language, if they were ever in colonial relationships and if they share a common border, respectively. Source: Glick and Rose (2002) and own computations. Figure A - 2.1: Flows of internationally mobile students Distribution of internationally mobile students flows, in levels (top panel) and in logarithm (bottom panel). Top panel. Skewness: 15.35, kurtosis: Bottom panel. Skewness: 0.39, kurtosis: Source: UNESCO on-line student migration database. 50