Immigration and the School System

Transcription

1 Immigration and the Shool System Faundo Albornoz Antonio Cabrales Esther Hauk Marh 2015 Abstrat Immigration is an important feature of many soieties, and it has wideranging effets on the eduation systems of host and soure ountries. There is now a large empirial literature, but very little theoretial work on this topi. We study a model of family immigration in a framework where shool quality and student outomes are determined endogenously. We explain the seletion of immigrants in terms of parental motivation and disuss the seletion effet of different immigration poliies. We provide novel evidene that is onsistent with one of our main theoretial results: for a given soioeonomi bakground and skill level of parents, shool performane of immigrant hildren in Spain improves with parental immigration osts. We also provide a detailed analysis of the effet of immigration on the different dimensions of the shool system, suh as student effort, parental involvement, shool inentives and resoures and how the endogenous response of the shool system to immigration is interrelated with both immigrants and natives eduational hoies. JEL-Classifiation: I20, I21, I28, J24. J61. Key-words: eduation, immigration, shool resoures, parental involvement, immigrant sorting. We thank Paula Calvo for exellent researh assistane. We thank Roberto Burguet, Jesus Fernández-Huertas Moraga, Hétor Calvo-Pardo, Omar Liandro, Paolo Giordani and seminar partiipants at the IAE, LUISS, Universidad de San Andrés, UB, University of Valenia, MOVE Workshop on Cultural Eonomis, INSIDE-MOVE, NORFACE, CReAM: VI Workshop on Migration and Labor Eonomis and CSEF Naples for valuable omments. Hauk thanks the LSE for its hospitality and aknowledges finanial support from the Spanish Ministry of Eonomy and Competitiveness through the Severa Ohoa Programme for Centres of Exellene in R&D (SEV and through CICYT projet number ECO and from the government of Catalonia. Universidad de San Andrés; falbornoz@udesa.edu.ar Department of Eonomis, University College London; a.abrales@ul.a.uk Instituto de Análisis Eonómio (IAE-CSIC and Barelona Graduate Shool of Eonomis, Campus UAB, Bellaterra (Barelona; esther.hauk@iae.si.es 1

2 1 Introdution Immigration is a prevalent feature of many soieties. Given that immigration involves families, the future of the host soieties depends on how immigrant hildren perform at shool and how their presene affets the shool system. 1 Clearly, the shool suess of immigrant hildren has a diret impat on human apital aumulation in the host ountry. But also, as immigrant hildren are to be shooled, they hange lassroom omposition and shool resoures. Therefore, they might have a sizable (not neessarily negative impat on shool quality and the performane of their native peers. 2 The goal of this paper is to larify the effet of immigration on shooling through hanges in lass omposition, shool resoures and parental and teahers involvement in the learning proess. Logially, the eduational effet of immigration is a ore onern of poliy makers and has attrated a massive researh effort to understand this phenomenon. 3 Most of this effort is empirial and there is relatively little theoretial work to ontextualize the many reent findings in the literature, to larify the main mehanism at work and to inform future empirial investigations. In this paper, we develop a framework to study the theoretial links between 1 To grasp the importane of immigrant hildren, aording to the US Census Bureau, 34% of all youth aged in 2000 were from minority groups and one in five shoolage hildren live in immigrant families (Kao and Thompson, The Innoenti Researh Center reports that almost a quarter of hildren were immigrants in 2009 in the Netherlands, Germany, Sweden and the United States. This proportion is about one-sixth in Frane and Great Britain (Alba, Sloan, and Sperling, Similarly, immigration may affet lass omposition and shool resoures in the soure ountry when migrants take their hildren with them. 3 Studies like those onduted by PISA, and other international organizations (like TIMSS or PIRLS, have allowed for the empirial analysis of immigrant eduational suess and the externalities imposed on natives. In many ountries, a large fration of immigrant hildren fae substantial disadvantages in reahing eduational parity with native hildren (Heath, Rothon, and Kilpi, 2008; Anghel and Cabrales, Australia and Canada are the big exeptions where immigrants often outperform natives before ontrolling for individual harateristis (Shnepf, It is also not at all rare for some immigrant students to be top of the lass (see Card (2005, Dustmann and Theodoropoulos (2010 and Dustmann, Frattini, and Theodoropoulos (2010. Dustmann and Glitz (2010 has an overview on migration and eduation. Researhers by now agree that immigrant students perform differently by origin group (Levels, Dronkers, and Kraaykamp, 2008 and (Levels and Dronkers, 2008 and ross-nationally (Marks, Even immigrants from the same origin perform differently aording to their destination ountry (Bertoli, Fernandez-Huertas Moraga, and Ortega, 2013, Moreover, the immigration mix differs onsiderably aross ountries, whih is only partially due to olonial links (Alba, Sloan, and Sperling (2011, based on Kirszbaum, Brinbaum, and Simon (

3 immigration and shooling and, within the onfines of this unified framework, we explain different fats unovered by the empirial literature and our own work. In any theory onneting immigration with shooling, student outomes must be determined endogenously as a result of the interplay between different families (immigrants and natives and the shool system. In our model, parents (immigrants and native not only differ in their wages (refleting different talent or skills, but also in (parental motivation ; a term we use to refer to parents onerns about their hildren s eduation ahievement. Thus, the shooling effets of immigration must be mediated by parents harateristis, refleted in their wages and parental motivation. We show how introduing this dimension into a theory of eduation and migration hoies help us understand the empirial relationship established between immigration osts and student performane, as well as many other important fats already unovered by the literature. Within our framework, we address two different but related researh questions. We explain the seletion of immigrants in terms of parental motivation and disuss how different types of immigrants are seleted aording to different immigration poliies. We also study the effet of immigration on the different dimensions of the shool system, suh as student effort, parental involvement, shool inentives and resoures and how the endogenous response of the shool system to immigration is interrelated with both immigrants and natives eduational hoies. In our framework, hildren are short-sighted and need to be motivated to study. Parents divide their time between working and motivating their hildren, and they deide whether or not to emigrate. Shools provide additional motivational shemes to enhane hildren s learning effort. The effet of these shemes depends on shool resoures, whih are determined by the eduation poliy. The ontribution of this framework is to emphasize that learning is a proess involving the interation among hildren, parents, shools and the deision of shool resoures. Thus, attainment and shool quality are endogenously determined by lassroom omposition, whih is itself affeted diretly by immigration. We show that the eduational effet of immigration ruially depends on immigrant parental motivation. We first establish why immigration reeiving ountries would like to attrat immigrants with a high parental motivation. First, we obtain the obvious but reassuring result aording to whih hildren s learning effort inreases in parental motivation; hene highly motivated immigrant parents are more likely to have skilled hildren thereby positively ontributing to the future human apital of their host ountry. But we also 3

4 obtain a subtler result between shool quality and immigration: when shool quality is suffiiently high, as it is usually the ase of host ountries, shool involvement inreases in parental motivation. In other words, the endogenous shool quality improves with higher parental motivation. By embedding our theory of eduation into a model of immigration deisions, we identify onditions under whih migration is seleted by parents with higher parental motivation. These onditions involve a suffiiently high expeted absolute skill premium for the immigrant hildren relative to the parental wage gain from immigration and suffiiently strong eduation inentives at the host ountry. Meeting these onditions implies a positive seletion in terms of parental motivation within different skill levels. 4 The empirial observable impliation of this result is that, under the onditions for positive seletion, student performane of immigrant hildren should be better the higher the osts assoiated with migrating from the soure ountry. In the empirial appendix of this paper, we disuss original empirial evidene onsistent with this result. More speifially, we exploit the standardized evaluation of the universe of students at the region of Madrid (Spain and show that immigrant hildren in the Madrid region perform better if their parents faed higher emigration osts. Importantly, this result is robust to ontrols for different family and ountry of origin harateristis. That is, the positive assoiation between immigration osts and shool performane annot be easily explained by pure seletion of immigrations in skills or eduation levels. Another impliation of our result on motivation-based seletion is that the performane of immigrants at shool from the same origin ountry varies aross destinations. Dustmann, Frattini, and Lanzara (2012 find that Turkish immigrants outperform those of the same ohort who stayed in Turkey. This differene in eduational ahievement between migrants and non-migrants from the same ountry persists even after ontrolling for family eduation bakground and soioeonomi harateristis. Although onsistent with our model, this result may reflet a higher quality of the shool system at the host ountries. In fat, Dustmann, Frattini, and Lanzara (2012 onsider Austria, Germany, Switzerland and Denmark; destination ountries whih perform similarly in 4 Notie that our notion of positive immigrant seletion is very different from the typial notion of positive immigrant seletion in terms of skills in the immigration literature as analyzed for example by Borjas (1987, In this literature the skill premium is also important: Grogger and Hanson (2011 aount for positive seletion in terms of skills assoiated with the absolute differene in earnings of skilled workers at the host and soure ountry. But the only skill premium that matters in this literature would be our parental skill premium. In our model seletion is in terms of parental motivation and the expeted skill premium of the hildren is ruial. 4

5 reading and maths at the PISA assessment but with sores onsiderably higher than those obtained by Turkey. However, Turkish emigrants in Switzerland and Denmark outperform those who migrated to Germany and Austria despite the relatively similar levels of the shool quality in these ountries. Again, this result is not explained by differenes in eduation levels of parents and soioeonomi harateristis. 5 Our model an explain this fat as osts of migrating to Switzerland and Denmark are arguably higher than those assoiated with Germany and Austria; where the Turkish ommunity is large and strong. 6 Next, we turn to a more nuaned analysis of the effet of immigration on the shool system. Of ourse, more (less motivated immigrant parents would involve more positive (negative effets on the host ountry shool system, but these effets are mediated by the harateristis of both the native parents and the pre-immigration shool system. We show, for example, that, although a negative seletion of immigrant parents redues the shool effort of native students, this partiularly hits native students with relatively low parental motivation; a result that has been unovered as a regularity in many empirial studies (Gould, Lavy, and Paserman, We also show that positive seletion in parental motivation might not have a positive effet on the shool quality if immigration mainly involves low skilled workers. In this ase, high parental involvement of immigrant parents will rowd out shool involvement and negatively hit native students. We also look at the effet of immigration on shool resoures in a world where publi shools are finaned by parents through taxes. We assume that the poliy maker maximizes the utility of the median voter parent, and show that shool resoures inrease in immigrant parental motivation. Hene, a negative seletion in parental motivation hits the native students diretly through the reation of teahers and indiretly through a redution in shool resoures by the poliy maker. Evidene of immigration reduing publi eduation expenditures in Europe is provided by Speiale (2012. Therefore, immigration also affets shooling through the responses of the eduation poliy, not only by the presene of immigrants themselves. This paper is related to a reent literature that fouses on how the effet of different eduation poliies depends on the behavioral responses of the different ators involved in the eduation proess. For example, Pop-Elehes and Urquiola (2013 find a positive effet of shool quality on student sores for the ase of Rumanian high shools. Furthermore, they show as well that 5 The evidene provided by Dustmann, Frattini, and Lanzara (2012 suggests that there has to be a within skill attribute. 6 Our analysis also shows how the exogenous quality of the shool system influenes immigrant seletion in terms of parental motivation. 5

6 parental effort and quality-improving shool ativities substitute with eah other, as in our model. 7 Stinebrikner and Stinebrikner (2008 and De Fraja, Oliveira, and Zanhi (2010 provide empirial evidene on the positive impat of parental and student effort on eduational ahievement. De Fraja, Oliveira, and Zanhi (2010 also find that shool motivational ativities are positively assoiated with student sores. 8 Albornoz, Berlinski, and Cabrales (2011 rationalize all these empirial findings in a model that onnets the effet of eduation poliy on student outomes with the behavioral responses of students, teahers, parents and eduation authorities to poliy-driven hanges in lassroom omposition. Our model retains this element but fouses on the endogenous determination of immigration seletion and its effets on native students and shool quality. Our work ontributes to an inipient theoretial literature fousing on how immigration affets the eduation system at the host ountry. In a reent paper, Dottori, Estevan, and Shen (2013 show that if the immigrant population has low skills, there is a push for high-skilled natives to segregate into private shools. This, in turn, makes them less keen to finane of publi eduation, whih entails a negative shok on the welfare of less-skilled natives. Farre, Ortega, and Tanaka (2011 establish similar results in a alibrated model for the Spanish eduation system. In partiular, they find that the inrease of the immigrant population led to a large redution of about 11 perent in publi spending per student. The remainder of the paper is organized as follows. Setion 2 introdues the model of parental motivation and the shool system. In setion 3, we study immigrant seletion and disuss under whih irumstanes higher emigration osts an improve parental seletion. Appendix A provides evidene of a positive relationship between immigration osts and immigrant hildren shool performane. Setion 4 studies the impliations of the model for the shool performane of natives and immigrants. Setion 5 examines how these impliations differ aording to the skill omposition of immigrant parents. Setion 6 looks at the impliations of immigration for shool resoures. Setion 7 disusses some immigration poliy impliations and onludes. 7 Additional evidene of the substitution between parental effort and shool resoures is provided by Houtenville and Smith Conway ( Sahin (2004 provides another example of how parent and student responses affet the impat of eduation poliies for the ase of higher eduation tuition subsidies. Evidene of the interation between parents and the shool system mediated by monitoring of shools is offered by Liang and Ferreyra (

7 2 Parental motivation and the shool system In this setion, we develop the basi model of the shool system. To fix ideas, we fous on the host ountry, although our analysis extends straightforwardly to the ase of the soure ountry. As in Albornoz, Berlinski, and Cabrales (2011, our shool system results from the interation of students (hildren, who need inentives to put effort on learning, parents (who work and set up ostly inentives shemes for students, and teahers/headmasters (who deide on the inentive sheme provided at shools. We also assume that every parent has one hild. We now desribe our different ators in detail. The students utility funtion: The students are hildren who pereive learning as ostly, beause they would rather play, and do not internalize the future benefits of studying today. As a onsequene, they need to be motivated to exert learning effort. The inentive sheme is put into plae by parents and the shool. Let pi be the strength of parental involvement for every unit of hild s effort e i. 9 Similarly, T refers to the strength of the shool /teaher s involvement. 10 As suggested by empirial evidene (Houtenville and Smith Conway, 2008; Pop-Elehes and Urquiola, 2013, we assume that parents and shool involvements are substitutes. 11 We assume that both parental and shool involvement enter positively into the hildren s short-term utility whih is given by: where 1 2 e2 i is the ost of learning. 12 The parents utility funtion: U i = ( pi + T e i 1 2 e2 i, (1 9 Parental involvement inludes ativities at home like supervising hildren, expliit help with the homework, disussing shool issues and providing reward shemes as well as shool based ativities like volunteering at shool, attending shool funtions et (Hoover-Dempsey and Sandler ( Shools organize motivational shemes and speial outings (e.g. shool trips, theatre and museum visits and set learning goals hoosing reward shemes. 11 No qualitative hange ensues if we assume the inentives to be omplementary. This is beause the substitutability at the hildren s utility level is mitigated by omplementarities elsewhere. Albornoz, Berlinski, and Cabrales (2011 disuss this issue in depth. 12 Instead of using positive reinforement for learning efforts parents and shools ould also work with punishment when hildren do not study. It is not diffiult to see that negative reinforement indues the same behavior in hildren than the positive reinforement we model here. 7

8 Unlike hildren, parents understand the long-term onsequenes of their hildren s hoies today, namely how the hild s learning effort when young influenes the hild labor market prospets in the future. In partiular, the probability that the hild will work in a high-skilled job equals the hild s learning effort e i, while the hild will beome an unskilled worker with probability (1 e i. Wages at skilled jobs and unskilled jobs are denoted by w s and w u respetively. 13 Hene a hild s future labor market prospet is given by w i = w se i + (1 e i w u. (2 Parents differ in their parental motivation 14 whih is modeled as the weight θ i a parent gives to her hild s labor market prospet in her utility funtion. 15 Parents also value their own welfare W P i. Hene parental utility is given by U P i = θ i w i + W P i. A parent has to split her total time T between working and setting up and exeuting an inentive plan for her hild. The time to generate the reward is given by pi e i /2, while the ost of generating inentives for their hild is the foregone parental wage w p. 16 Hene, the parental utility funtion is given by the expression Ui P = θ i (wse i + (1 e i wu + (T 12 pi e i w p. (3 The shool s utility funtion: Shools/teahers also fully understand and are about the future job perspetives of their students, assigning weight θ T to the average student s suess. The teahers have to deide how muh of the time T T that remains 13 These wages an differ aross ountries as well as between natives and immigrants. 14 Heterogeneity in parental motivation is one of the major differenes of the present model to Albornoz, Berlinski, and Cabrales ( Empirially, parental motivation is likely to be positively orrelated with parental work ethi. Although this link is not aptured in the present model, it is easy to extend the model to inorporate work ethi by letting parents alloate their time between leisure, eduation and work and assuming that the same parameter affets the weight given to eduation and inversely the enjoyment of leisure. This speifiation was used in a former version of the model leading to qualitatively similar results. 16 Our model ould be modified to inorporate parental talent vi P. On the one hand, parental talent vi P inreases wages wi P = v P φ P i where φ P i refers to the parental baseline wage rate. On the other hand parental talent dereases the time parents need to spend for generating their hild s inentive reward. This time is now given by pi e i /2vi P. Introduing talent into our model would only ompliate the exposition but would not affet the main results. 8

9 after teahing their ompulsory hours they will use to motivate their students (suh as training or preparing learning ativities, and how muh they will use for outside job opportunities (suh as private tutoring whih are paid at wage rate w T. The teaher s time spent generating the reward T is equal to 1 N 1 N i=1 2 T e i where N is the total number of hildren in the lassroom. The shool/teaher s utility funtion is therefore U T = θt N ( N (wse i + (1 e i wu + T T 1 2N i=1 N T e i w T. (4 Let N = N I + N N where N I is the number of immigrant hildren and N N the number of native hildren. We an rewrite the shool s utility funtion as ( ( NN U T = θt N I (ws w N u e k + e l + wun k=1 i=l ( ( + T T NN N I T e k + e l w T. (5 2N k=1 The struture of the game: The shool system is modeled as a twostage game. In the first stage, parents and shools simultaneously deide and announe the optimal strength of their eduational involvement in eah unit of hild s effort: pi and T respetively. 17 After observing these announements, hildren deide their optimal effort e i. Equilibrium: We solve the game by bakward indution. In the seond stage hildren hoose their optimal effort e i by maximizing their utility funtion (1 taking parental inentives pi and shool inentives T as given. This leads to the following optimal effort deision by the hildren l=1 i=1 e i = pi + T. (6 In words, hildren s effort is simply the sum of parental and shool eduational involvement. We an now turn to the first-stage of the game where we need to substitute this expression (6 into the parent s utility (3 and the shool s utility (5. Taking the optimal effort deision of hildren (6 into aount, the teaher s problem is to hoose the level of T that maximizes 17 In order to ensure a interior solution, we impose motivation rewards to be positive as to avoid orner solutions where pi and T may be zero. 9

10 ( ( NN U T = θt N I (ws w N u ( pk + T + ( pl + T + wun k=1 l=1 ( ( + T T NN N I T ( pk + T + ( pl + T w T. 2N k=1 leading to the optimal shool involvement/inentives l=1 where T = θt w T (w s wu N N N p + N I I p, (7 2N N p = 1 N N N N k=1 N p k, I p = 1 N I N I l=1 I p l. The strength of the shool involvement depends on the average parental involvement of both natives and immigrants, to whih we turn now. Parents hoose their inentive sheme pi to maximize U P i = θ i (w s ( pi + T + (1 ( pi + T w u + leading to the optimal parental hoie (T 12 ( pi + T pi w p. pi = (w s w u θ i w p 1 2 T. (8 We define relative parental onern ψ i as the ratio of parental motivation to their wage ψ i = θ i w p. (9 Also, we define the average relative parental onern among the native and foreign population as Ω k = 1 N k N k i=1 θ i w p i = 1 N k ψ i for k = N, I. (10 N k i=1 Using this notation, we an now derive the interior solution of the game. 10

11 Lemma 1 For a given shool the optimal strength of parental and shool involvement are [ ( j p l = max 0, (ws wu ψ j l 2 θ T 3 w + N ] IΩ I + N N Ω N (11 T 3(N N + N I [ T = max 0, 2 ( 2θ 3 (w s wu T w N ] IΩ I + N N Ω N. (12 T (N N + N I where j = N refers to natives and j = I to immigrants. If both the shools and the hild s parent l hoose a positive strength of involvement the orresponding hild i s effort is ( e j i = (w s wu ψ j l + 2 θ T 3 w N IΩ I + N N Ω N for j = N, I (13 T 3(N N + N I Proof. See Appendix B.1. The above expressions indiate that shool and parental involvement are substitutes. Both involvements are driven by the potential gains from eduation aptured by (ws wu. Shool involvement inrease in shool motivation θ T and derease in teaher s outside job opportunities w T and in average relative parental onern sine N IΩ I +N N Ω N (N N +N I = 1 N N i=1 ψ i. The higher this average, whih implies the more parents are on average for eduation, the higher parental involvement in their hild s eduation. An interior solution (i.e. a solution with 0 < e j i < 1 exists where both the parents and the shool hoose positive strengths of learning involvement for some onditions on the distribution of ψ j l. Speifially, positive strengths require ψ j l + N IΩ I +N N Ω N 3(N N +N I > 2 θ T > N IΩ I +N N Ω N 3 w T 3(N N +N I whih is a relationship omparing parental motivation and their wages with shool motivation and wages for outside job opportunities for teahers. Observe that θt an be interpreted as w T a measure of shool quality and we will refer to it as net/relative shool onern. Hene the ondition for positive inentives an be interpreted as a relationship between shool quality measured by the relative shool onern and individual and average parental quality measured by the relative individual parental onern and relative average parental onern respetively. Until now, we have allowed parental onerns to be unrelated to shool onerns. However, it is realisti to assume that parental motivation positively reinfores shool motivation. This orresponds to situations where teahers inentives are enouraged by interating with highly motivated parents. It is demoralizing for teahers to deal with disinterested parents or, more generally, with student apathy. To apture this link formally, we postulate: 11

12 Assumption 1 θ T depends on the average parental motivation. That is, θ T = kθ = k N N θ i, (14 i=1 where N is the number of parents affeting the eduation of a partiular shool lass of hildren and k indiates the exogenous weight that the shool assigns to the future wages of their students. We are now in a position to analyze how parental motivation in general and immigrants parental motivation in partiular affet the quality of the shool system. Using assumption 1 in equation (12, we an express the optimal strength of shool involvement as: T = max [ 0, 2 (w s w u 3N N i=1 (( 2k w 1 ] θ T w p i, (15 i Hene, shools will only hoose a positive strength of involvement if N i=1 ( 2k w 1 θ T w p i > 0. (16 i In words, parental involvement will not rowd out shool involvement if the relative shool onern is at least half the size of the average relative parental onern. Shools must are suffiiently about their students performane. Moreover, Proposition 1 Shool involvement T inreases in parental onern θ i if and only if w p > wt 2k. Proof. To see how positive shool involvement hanges with parental motivation we need to look at sign ( T 2k = sign θ i w 1 T w p, i whih tells us that shool involvement (15 inreases in parental motivation for parents whose wages are suh that 2k/w T > 1/w p i The ratio k is the exogenous term determining the net shool onern w T θ T = k θ and an therefore be interpreted as the exogenously given shool w T w T 12

13 quality. It is also (proportional to the marginal effet of parental motivation of parent i on the net shool onern while the marginal effet on average 1 relative parent onern is (proportional to. The ondition of Proposition w p i 1 relates parental wage, namely the opportunity ost of parental involvement, to the inverse of exogenous shool quality whih is the ratio of the shool s opportunity ost of teaher s involvement to the weight shools give to the future performane of their students. A higher parental onern will inrease parental involvement but this inrease might affet shool involvement negatively sine parental and shool involvement are substitutes. A suffiiently high exogenous shool quality make shool involvement more valuable and allows for both parental and shool involvement to inrease in parental onern. Therefore the lower bound on parental wage for shool involvement to inrease in parental onern is proportional to the inverse of exogenous shool quality. Assumption 1 allows us to haraterize how a hild s learning effort depends on parental motivation, namely ( e i = (ws wu θ i w p + 1 N ( 2k i 3N w 1 T w p θ i, (17 i i=1 From this equation it is straightforward to establish: Proposition 2 Children s learning effort is always inreasing in parental motivation θ i. Proof. This follows from e i θ i > 0 Propositions 1 and 2 reveal the ruial role of parental onern/motivation. On the one hand, more motivated parents produe hildren with higher learning efforts. On the other hand, if shools have a suffiiently high exogenous quality, more motivated parents have a positive spillover on the entire system by leading to a higher shool involvement T. Therefore, immigration reeiving ountries would like to attrat immigrants with a high parental onern. 3 Immigrant self-seletion In this setion, we study the immigration deision. There are two ountries: Home (H, the soure or origin ountry, and Abroad (A, the destination or host ountry. Eah parent i in ountry H faes a fixed ost of immigration F i. The variable F i follows the distribution F (. in a large ompat interval. Immigration poliies may affet this distribution in various ways and we larify 13

14 their impat in terms of whether they indue immigration to have a positive impat on the shool system. Both ountries have a skilled and unskilled labor market and their shools system an be desribed by the model of the previous setion. 18 However, they may differ in the eonomi opportunities and the quality of the shool system. Based on these parameters, parents estimate the expeted utilities of both staying and leaving their ountry of origin. Immigration requires the utility differene to be higher than the immigration ost. Let U j P i denote parental utility when living within ountry j, namely U j P i = θ i (e j i (w sj w uj + w uj 1 2 j p i e j i wp i j + T w p i j for j = H, A (18 Using the optimal involvement and effort deisions derived in Lemma 1, the parental utility after some simplifiation beomes U j P i = T w p i j + θ i wu j + wpi j 2 ( e j i 2 for j = H, A (19 where e j i is the optimal learning effort of i s hild when shooled in ountry j whih by (13 is ( ( e j i = ws j wu j ψ j l θ T j w T j Ω j 3 for j = H, A where Ω j = 1 Nj N j k=1 ψj k is the average relative parental onern in a shool in ountry j. We an therefore write parental utility as U j P i = T w p i j + θ i wu j (20 2 ( ( (w sj w uj + θ2 i 2 θj T 2 w p + 2θ i i Ω j + w p 2 θ i j T j Ω 2 j j Observe that the first term of parental utility T w p i j orresponds to the maximum earnings from working (what a parent an get by working all the time, while the seond term θ i wu j reflets the parental utility if the hild does not make any eduational effort. Parental involvement in the hild s eduation 18 We are impliitly assuming that how learning inentives translate into the probability of getting a skilled job in the ountry in whih eduation was reeived is the same aross ountries. The ruial element in our analysis is that learning effort is endogenously determined aording to different ountry harateristis. 14 w T j w T j

15 inreases the parental utility whenever future skilled jobs are better paid than future unskilled jobs; that is if w s j > w u j as is refleted in the third term of (20. A parent i will emigrate from ountry H to ountry A if U A P i F i > U H P i. From (20 it follows that Lemma 2 UP A i F i > UP H i if and only if T (w p i A wp i H + θ ( i w ua wu H (( w sa wu 2 ( A w sh wu 2 H + θ2 i 2 > F i. w p i A ( ( (w +θ i sa wu 2 2 A 3 ( + 1 ( w p i 2 θa T A 2 3 w T A θa T wa T w p i H Ω A 3 ( ( ws H wu 2 2 H 3 ( 2 Ω 2 A ( w s 3 A wu 2 A w p i H 3 θh T wh T θh T wh T Ω H 3 (21 Ω H 3 2 ( w s H wu 2 H Sine the primary motive for emigration is the possibility of better eonomi opportunities, we assume that wages abroad are at least as high as wages at home and one of the three wage parameters (expeted parental wage w P i, expeted hild s wage if skilled ws and if unskilled wu must be stritly higher. Then we an interpret the ondition for immigration in Lemma 2 as follows: T (w p i A wp i H + θ ( i w ua wu H desribes the wage gain due to immigration if the immigrant parent dediates all the time to work. The parent might get a higher expeted pay w P i A wp i H and the unskilled hild might also earn more money w u A w u H whih is weighted by the parental onern parameter θ i. The remaining 3 lines of the sum desribe the hange in parental utility from emigrating that is ahieved by inentivizing the hild at shool and an be rewritten as wp i A 2 e2 A wpi H 2 e2 H (see equation (19. Parents and shools want to inentivize hildren to inrease their hane to get a high-skilled job, whih is why the absolute differene between skilled and unskilled wages enters in the three parts of the sum that orresponds to the parental utility derived from the hild s effort. Sine the parental wage is the opportunity ost of parental involvement in inentivizing the hild, a higher wage has a negative effet on effort as aptured by w p i dividing in the seond line of the sum. However, sine shool involvement and parental involvement are substitutes a higher w p i has an indiret effet by inreasing effort that is aptured by the final line of the sum. The third term of the sum aptures the hange in parental utility due to a hange in shool quality ombined with the inentives for eduation. 15

16 Suppose the heterogeneity is suh that the vetor of variables ξ i (θ i, w p i A, wp i H Ξ, haraterizes eah individual belongs to a finite set of types Ξ. At the same time the variable F i follows the distribution F (. in the ompat interval [0, A], where we assume A > max ξi Ξ U Pi. Note that aording to equation (21 if an individual with type ξ i and value for the ost of moving F i wants to move, another individual with type ξ j = ξ i and F j < F i also wants to move. Hene, the equilibrium an be haraterized by a set of thresholds. For eah type ξ Ξ there is some F ξ suh that for all i with ξ i = ξ Ξ the individual moves to A if and only if F i < F ξ. Thus, Proposition 3 An equilibrium in immigration deisions always exists. Proof. See Appendix B.2. Understanding the effets of differenes in parental motivation on the host and soure ountries requires further larifiation about how individuals from H self-selet into the migrant population. We turn to this question in the following subsetions. 3.1 When immigration does selet the most motivated parents We aim at identifying the onditions under whih the most motivated parents from a soure ountry are those who self-selet into immigration. As migrating is an individual deision, potential immigrants take Ω A and Ω H as given. This is the same as assuming: Ω A θ ξ = Ω H θ ξ = 0 Using the link of shool motivation to parental motivation stipulated in assumption 1 and the ondition for immigration stated in Lemma 2, we obtain the following ruial result: Proposition 4 Assume that wages in the host ountry are at least as high as wages in the soure ountry. Then, for any skill level, immigrant seletion is positive in parental motivation if the following onditions are satisfied: 16

17 1. Absolute Skill Premium: ( w sa w u A ( w sh w u H > w p i A w p i H 2. External Eduation Inentives: wu A + 1 ( ( w 3 sa wu 2 2kA A θ wa T A Ω A wu H + 1 ( ( w 3 sh wu 2 2kH H θ wh T H Ω H (22 (23 Proof. It follows from inspetion of equation 21. See Appendix B.3 for the details. The ratio of absolute skill premia for hildren between the reeiving and sending ountries has to be higher than the (square root of ratio of parental wages in sending and reeiving ountries (the gain from immigration. 19 This ondition plaes an upper bound on parental wages abroad, whih niely aptures the trade-off parents fae when inentivizing their hildren: forgo parental wage versus higher expeted wages for their hildren. A suffiiently high absolute skill premium for hildren guarantees that parents inentivize their hildren more abroad than at home. But this is not suffiient for positive parental seletion. The external environment at the host ountry has to be suffiiently favorable. To see this, notie that ondition (23 an be reformulated as: wu A + 1 ( w 2 sa wu A A T wu H + 1 ( w 2 sh wu H H T (24 Thus, we an interpret eduation inentives as a measure of the expeted wage inrease for a skilled hild weighted by the eduation inentives provided by the shool. This measure has to be higher at the host ountry. It is instrutive to onsider a situation in whih both ountries are idential exept for their wage struture. More tehnially, Corollary 1 If the host and the soure ountries have the same exogenous quality of the shool system (2k A /wa T = 2k H/wH T ; the same initial distribution 19 Notie that this ondition an be satisfied even if the relative skill premium is lower in the host ountry. We are interested in the future human apital of hildren and therefore in parental seletion, for whih the absolute skill premium for hildren matters more. Grogger and Hanson (2011 doument the importane of the absolute skill premium for parents to explain immigrant seletion in parental eduation. 17

18 of parental motivation; the same distribution of parental motivation among skill groups; and the same proportion of people in skilled employment, then a higher absolute skill premium at the host ountry is suffiient for inequality (23 to hold. Proof. Notie that due to the equality in exogenous shool quality ( ( 2kA 2kH θn Ω A > θ H Ω H Ω A Ω H, w T A w T H or equivalently 1 θi /w p i H N 1 θj /w p i A H N. A This is true sine wages in ountry A are at least as high as wages in ountry H, and the distribution of parental motivation among skill groups is idential. Obviously, if the exogenous shool quality is better abroad than at home so that 2k A /wa T > 2k H/wH T, ondition (23 is relaxed. This result suggests that immigration is more likely to positively selet motivated parents when the host ountry pays a higher future absolute skill premium and shool quality is better, provided that intrinsi parental motivation is not muh higher in the soure ountry. Arguably, this desribes a situation where immigrants arrive to highly developed ountries from developing ountries. Proposition 4 sheds light on how immigration poliies that affet immigration osts for all immigrants influene the seletion of immigrants and onsequently the eduational performane of immigrant hildren, whih is inreasing in parental motivation. Notie that onditions (22 and (23 being satisfied haraterize a situation where highly motivated parents enjoy relatively higher benefits from emigrating. As a onsequene, seletion improves with higher emigration osts. Proposition 5 For a given host ountry, immigrant hildren who perform better are those whose parents faed the higher emigration osts In Appendix A, we provide empirial support to this result. More preisely, we present novel empirial evidene aording to whih immigrant performane in the standardized exams for all primary shools in the Madrid region do indeed improve with emigration osts. Proposition 4 also implies the flip-side of the argument: Proposition 6 For a given origin ountry, immigrant hildren perform better in host ountries for whih the emigration osts are higher. 18

19 An interesting ase onsistent with this result is provided by Dustmann, Frattini, and Lanzara (2012, who show that Turkish immigrant hildren not only outperform kids staying in Turkey but also their student ahievement varies aross four ountries with relatively similar eduation quality: Germany, Austria, Switzerland and Denmark. Aording to Dustmann, Frattini, and Lanzara (2012 Turkish immigrant hildren do onsiderably better in Switzerland and Denmark ompared to similar Turkish immigrant hildren in Germany and Austria - onditional and unonditional on parental bakground harateristis and the quality of shools they attend. Given than migration osts from Turkey are arguably higher for Switzerland and Denmark than for Germany and Austria, this orollary provides an explanation to this fat. 20 Our theory an also guide us when the onditions of proposition 4 fail and immigration no longer selets the most motivated parents. 3.2 When immigration does not selet the most motivated parents In this setion, we briefly disuss the ases where the onditions for a positive seletion of immigration in terms of parental motivation no longer hold. In these ases, migrants are not among those who are more motivated and thus the effet of immigration on the shool system will be negative. When both ondition (22 and ondition (23 are violated, both the parental trade-off, and the external eduation inentives are worse abroad than at home. This typially happens beause the benefits from eduation abroad (the absolute skill premium are lower than at home. Hene the inentives to eduate hildren are weaker. Moreover, unskilled wages abroad annot be muh higher than at home. For this reason, parents with higher parental onerns would not migrate and immigrant seletion would likely fall on the least motivated parents. When ondition (22 is violated but (23 is satisfied, parental seletion is likely to fall on intermediate levels of parental motivation. On the one hand the tension between parental wages abroad and the hild s future wages is resolved in suh a way that parents work more hours and inentivize their hildren less, whih is a loss for motivated parents. On the other hand, the external environment hildren fae abroad is more favorable, whih is a gain 20 The size of the Turkish ommunity in Germany and Austria provides a reason why the migration osts from Turkey might be lower in these ountries. Language distane between Danish and Turkish and relatively more strit immigration laws in Switzerland provide additional reasons. 19

20 for motivated parents. These two ountervailing fores are likely to prevent the most motivated and the least motivated parents from emigrating. When ondition (22 is satisfied but (23 is violated, then parents set higher eduation inentives abroad than at home, but the external environment for hildren is worse abroad. The benefits of immigration (whih are a quadrati funtion of θ first fall in parental motivation till they reah a minimum and then raise again. Hene, parents willing to emigrate, are likely to fall into the extreme ends of the distribution of parental motivation. Observe, that this ase only ( happens rarely. ( To see this, reall that wu A > wu H by assumption, hene w sa wu A > w sh wu H is a neessary (but not suffiient ondition for ondition (22 to hold. This implies that the returns to eduation are higher abroad, whih positively affet both parental inentives and shool inentives. Therefore ondition (23 an only be violated if external shool quality and average parental motivation at home is muh higher than abroad, and unskilled wages are very similar. But in this ase also the last line of the ondition to emigrate given by (21 will beome negative and even very low F i might not be suffiient to indue emigration. 21 The empirial impliations of the model an hange onsiderably if we look at host and origin ountries where ondition (22 is violated. This happens for example if it is mainly the unskilled jobs that are better paid in the destination ountry than in the origin ountry. If ondition (23 is also violated, it makes sense for the destination ountry to adopt poliies that redue immigration osts in order to be able to attrat also immigrants with a high parental motivation, irrespetively of their level of skills. An example of this situation is given by the immigrants hosted in Argentina from ountries like Bolivia, Peru or Paraguay (Gasparini, Crues, and Tornarolli, These origin ountries are haraterized by a very high differenes between skilled and unskilled wages, ertainly as high as in Argentina. Also, the wages in Argentina are not that muh higher. This gives some theoretial support to the immigration strategy of Argentina, whih has one of the most lenient immigration regulations in the world (Albarraín, If (23 holds, seletion falls on the intermediate range of parental motivation. In this ase whether it is good for a ountry to adopt poliies that redue or inrease immigration osts depends on the exat distribution of θ. Under intermediate seletion a deline in immigration osts will expand the interval of values of θ for whih emigration ours at both extremes whih an influene in either diretion the immigrants average level of θ. More speifially, 21 Observe that at least for low-skill immigrants, the main eonomi motive for immigration refleted by the value of T (w pi will also be very low. A wpi H 20

21 if θ follows a non-inreasing density funtion, then a redution in immigration osts indues a deline in the average level of θ (MKenzie and Rapoport, 2010 The above results indiate that immigration poliies should be speifi to the ountry of origin. For origin ountries where both the ondition on the absolute skill premium (22 and the ondition on the external eduation inentives (23 are satisfied, imposing additional osts will improve immigrant seletion in parental motivation. Otherwise, lowering immigration osts but setting strit and low quotas might be the better poliy. 3.3 Shool quality In the previous setion, inentives to immigrate where both shaped by the eonomi inentives and possibly the differene in shool systems. It will be useful to understand the effet of differenes in shool quality in isolation. In order to do so, we assume that shool quality is the only differene between H ( (Home and( A (Abroad, and that shool quality is better abroad, i.e. 2 θa T Ω 3 wa T A 2 θh 3 > T Ω 3 wh T H 3. Under these assumptions immigration ours if (21 holds whih redues to > F i. (( 2 θ i (ws wu 2 θa T Ω ( A 2 θh T Ω H 3 wa T 3 3 wh T 3 ( ( (w s wu 2 w p θ i A T Ω 2 ( A 2 θh T Ω 2 H w T A w T H (25 whih after some examination implies: Proposition 7 The ost that a parent is willing to pay to immigrate inreases in shool quality, but it inreases proportionally more for parents with higher motivation. Proof. It is easy to see that the ross derivative of left hand side of (25 with θ T A θ T H respet to θ and 2 Ω 3 wa T A 3 > 2 Ω 3 wh T H 3 is positive. In other words, if immigration osts inrease, but at the same time shool quality inreases, the seletion of immigrants should improve sine those that get disouraged with the higher osts are more likely to be those for whom the inrease in shool quality matters less. Although we do not believe that shool 21

22 quality per se is the main reason of emigration for the majority of people who leave their ountry, the result nevertheless has an interesting testable impliation: the shool performane of immigrant hildren should be better in ountries with higher immigrations osts and high quality (publi shools. Gibson and MKenzie (2011 provide some evidene for this predition: they show that the quality of Australian shools is a key pull fator for the most qualified immigrants arriving from New Zealand, Tonga and New Guinea Papua. 4 The shool performane of immigrant and native hildren Our model reveals that the effet of the immigration on the shool system depends on the type of parents that immigrate. It an therefore guide us to understand empirial observations on immigrant shool performane and their effets on native performane. In empirial studies, student outomes onstitute a typial empirial measure of shool quality. Sine these outomes depend on hildren s learning effort we now examine this effort in more detail. It is lear from equation (13 that among hildren in the same shool it is their parents harateristis ψ i, namely the relative parental onern - the net payoff from parental investment -, that determines who has the higher learning effort. If we apply this to the differene in learning effort between an immigrant hild and a native hild, then e I i e N j = ( ψ I i ψ N j (w s w u whih implies that the effort of immigrant hildren is greater than of natives on average if and only if Ω I > Ω K. Having established this, the next proposition follows immediately: Proposition 8 The hildren of immigrants exert more effort at a given shool than natives if and only if the average relative parental onern is higher among immigrant parents than natives. 22 Therefore, immigrant hildren performing below average is a sign that immigration poliies do not selet on average the most motivated parents. Similarly, we an onlude that a highly performing immigrant hild will have 22 While Proposition 8 is stated for the shool level, it generally holds when the environment of immigrants and natives are the same. In a ountry as a whole it would hold if all shools are the same and immigrants and natives are equally distributed among shools. 22

23 highly motivated parents. Indeed, Proposition 2 reveals that a higher parental motivation always translates into a better performing hild via a higher eduation effort. From Proposition 1 we know that shool involvement only inreases in parental motivation of parents whose wage is not too low, in partiular for parents where w p > wt. Shools will still set inentive shemes for 2k their students when this ondition is violated for some parents but is satisfied for a suffiient amount of parents (tehnially, ondition (16 holds. Highly motivated parents with too low wages in these types of shools have a negative effet on shool involvement, but the diret effet of rising parental involvement on student effort offsets this negative impat on the shool. Hene, the greater learning effort of hildren from highly motivated parents must ome beause of the parents higher demands. The empirial evidene of pushy immigrant parents is vast in the ase of immigration to the US. As shown by Glik and White (2004 and Hao and Bonstead-Bruns (1998, immigrant parents are assoiated with greater demands on their hildren in terms of shool engagement and aademi ahievement. Keller and Tillman (2008 find that both parental and self-reported expetations have signifiant diret effets on ollege attendane. Goyette and Xie (1999 provide evidene that in the US the behaviors and expetations of Asian immigrant parents tend to raise their hildren s shool attendane above the average. The net parental onern ψ i = θ i, also plays an important role in explaining the variation in shool performane of native hildren due to immigration. w p i Observe that we an rewrite the hild s effort (17 as e i = (w s w u ψ i T. (26 This expression allows us to analyze how immigration affets the performane of native pupils. For a given shool, the relative effet of immigration on native hildren varies with the net parental onern. A hange in T simply shifts the initial effort up (if immigrant parents are better on average or down (otherwise,and therefore the relative hange in effort is lower the higher the pre immigration effort level or equivalently, for hildren assoiated with a higher ψ i. In other words, the performane of disadvantaged hildren (low ψ i parents is more affeted by immigration than that of their more advantaged lassmates (high ψ i parents. The evidene for this effet is onsiderable. Fousing on the mass migration wave from the former Soviet Union to Israel in the early 1990s, Gould, Lavy, and Paserman (2009 find a negative effet of immigrants on native outomes whih is larger for natives from a more disadvantaged soial bakground. Similarly, Betts (1998 shows that immigration 23