migration effect of education

Economics of Education Review 32 (2013) 234–246

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Economics of Education Review

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The effect of immigration on the school performance of natives: Cross country evidence using PISA test scores

Giorgio Brunello a,b,c, Lorenzo Rocco a,* a Department of Economics, University of Padova, Italy b Cesifo, Germany c IZA, Germany

A R T I C L E I N F O

Article history:

Received 19 November 2011

Received in revised form 20 October 2012

Accepted 22 October 2012

JEL classification:

I24

J15

Keywords:

Efficiency

Human capital

Demand for schooling

Educational economics

A B S T R A C T

We use aggregate PISA data for 19 countries over the period 2000–2009 to study whether a

higher share of immigrant pupils affects the school performance of natives. We find

evidence of a negative and statistically significant relationship. The size of the estimated

effect is small: doubling the share of immigrant pupils in secondary schools from its

current sample average of 4.2–8.4 percent would reduce the test score of natives by 1–3.4

percent, depending on the selected group of natives. There is also evidence that –

conditional on the average share of immigrant pupils – reducing the dispersion of this

share between schools has small positive effects on the test scores of natives. Whether

these findings can be generalized to a larger sample of countries is an open question that

we leave to future research.

� 2012 Elsevier Ltd. All rights reserved.

1. Introduction

Immigration flows have changed the composition of students in schools and classes. The integration of immigrants is often problematic, and these flows have triggered in some countries the flight of natives from public to private schools. A key question is whether the increased share of immigrants in schools and classes has affected the school performance of natives. In spite of the importance of this question for education policy, and of the abundance of research investigating the labour market effects of immigrants, relatively little is known about the impact of immigration on the education system (see Gould, Lavy, & Paserman, 2009).

To our knowledge, this paper is the first to address this important question using cross-country data covering 19

* Corresponding author at: Department of Economics, via del Santo,

33-35123 Padova, Italy. Tel.: +39 049 8274260.

E-mail address: [email protected] (L. Rocco).

0272-7757/$ – see front matter � 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.econedurev.2012.10.006

countries from Europe, the Americas, Oceania, Asia and the Middle East. Measuring the effect of immigrants on the school performance of natives is complicated by the fact that immigrants sort across countries and both immigrant and native students self-select into schools and classes. For example, the share of immigrants in the total population is typically higher in more developed countries, where economic opportunities are more abundant. At the same time, students in these countries tend to have a better performance, because their schooling systems are more effective. Therefore, in cross section data the average test scores of native students and the share of immigrants tend to be positively correlated across countries, but this correlation is spurious and driven by cross-country differences in economic development.

Due to economic conditions, immigrants usually concentrate in less affluent neighbourhoods, where housing prices are lower. Typically, the schools of these neighbourhoods are attended both by immigrant students with limited language proficiency and by native students with a relatively poor parental background (Jargowsky,

3 Hoxby (2000) identifies peer effects by exploiting the variation in the

composition by gender and race of students attending a particular grade

G. Brunello, L. Rocco / Economics of Education Review 32 (2013) 234–246 235

2009). By virtue of this sorting, a negative correlation between the test scores of natives and the share of immigrants in the school is likely to emerge within each country, quite independently of whether immigrants have or have not any impact on the school performance of native students. Non random allocation of students to schools implies that it is difficult to tell whether the correlation between the performance of natives and the share of immigrants in a school can be treated as a causal relationship. For this, we would need a source of exogenous variation in the share of immigrants, which is very hard to find.

In this paper, we address sorting within countries by aggregating at the country level the key information on the test scores of natives and the shares of immigrant students, in line with Borjas et al. (1997), who suggest the country level as the appropriate unit of analysis. By virtue of aggregation, we remove the sorting of individuals across schools.1 However, immigrants can also sort among different countries. Using data that vary by country and time, we control for between-country migration flows by conditioning on country fixed effects, country specific trends, per capita GDP, education expenditure and the stock of immigrants in a given country at a given time. Conditional on these covariates, changes in the share of immigrant pupils in each country depend mainly on demographic factors and are as good as random, as pointed out by Gould et al. (2009), in their study of the effects of immigration in Israel schools.

We find that a higher share of immigrant pupils reduces the school performance of 15-years-old natives. The marginal effect, however, is small and varies with the gender and the parental background of natives. Our evidence suggests that doubling the share of immigrant students from the current average 4.2–8.4 percent2 would reduce the average school performance of natives by 1–3.4 percent, depending on the group of natives. The highest negative effect is found for native females.

We also find that the estimated negative effect of immigrant pupils on the school performance of natives is higher in countries where the segregation of immigrants in schools is higher. However, the quantitative impact of desegregation policies is small: we estimate that reducing the segregation index by 10 percent while keeping the foreign student share constant at its average sample value increases the test score of natives by only 0.11 percent.

We view these results as an interesting initial step in an important but understudied topic for the following two reasons. First, we have a small non-representative sample of 19 countries. Whether our results can be extended to a broader sample is an open issue for further research. Second, our empirical approach, which controls for a range of country and time varying effects, does not fully

1 Borjas (2003), Mishra (2007), and Aydemir and Borjas (2007) among

others use a similar strategy to estimate the impact of the share of

immigrants on wages. 2 To illustrate, if immigrant students were evenly distributed across the

schools in our sample, doubling their share would be equivalent to

increasing the number of immigrants from 1 to 2 in classes with about 20

students.

guarantee that the identified effects are causal. For this, one would need exogenous variation in the share of immigrant pupils, which is very difficult to find.

The paper is organized as follows: Section 2 is a brief review of the relevant literature and Section 3 presents our empirical approach. The data and the main results are presented in Sections 4 and 5. Section 6 presents some robustness checks and Section 7 investigates how the distribution of immigrant students across schools influ- ences their impact on native students. Conclusions follow.

2. Review of the literature

The influence of immigrant students on their native peers is a particular sort of peer effect: immigrants are peers with a different culture, a different way to interact with others and, most often, limited language proficiency. In a recent contribution to the vast literature on peer effects, Lavy, Silva, and Weinhardt (2009) have shown that the effect of peers is not constant but strongest when peers are students either at the very bottom or at the very top of the academic ability distribution. Since immigrant pupils typically perform less well than natives at school for several reasons, including difficulties with the language of instruction, less educated parents and problems of integration, they are often concentrated at the bottom of the distribution of academic ability. According to Lavy’s work, their effect on native pupils should be stronger than the effect generated by native peers.3

While the economic literature on peer effects in education is extensive, there is surprisingly little being done on the influence of immigrant students on native students. The existing research includes both contribu- tions which emphasize the negative impact of immigration on the school performance of natives and contributions that find small effects or no effects at all. Early papers in the first group include Betts (1998) and Hoxby (1998). Betts shows that immigration reduces the probability of completing high-school for American-native minorities (Blacks and Hispanics). The reason is that an influx of students with limited proficiency in English absorbs teaching resources especially at the expense of those native students who are at the margin of dropping out and typically belong to American minorities. No negative effect of immigrants is found for non minority groups.

More recently, Betts and Fairlie (2003) find that American native students fly towards private secondary schools in response to the influx of immigrants into public institutions.4 At least two reasons might explain this flight

in adjacent years over a sample of schools. She finds that peer effects are

stronger within races than across races, meaning that students of a given

race are mainly influenced by students of the same race. This result is

consistent with the findings by Card and Rothstein’s (2007), indicating

that segregation in racially homogenous schools widens the white-black

gap in test scores. In their paper, the key issue of student sorting is

resolved by aggregating micro-data by race and city and by taking first

differences between races in each city. This strategy removes sorting both

across schools and across cities. 4 No flight has been observed out of primary schools.

G. Brunello, L. Rocco / Economics of Education Review 32 (2013) 234–246236

towards private fee-based schools. First, native households may dislike sending their children to schools that attract immigrants; second, a high share of immigrants may signal to households that the school is low quality.5

A higher share of immigrants can affect not only school choice and school completion but also the test scores of native pupils. In their study of the mass migration of Jews from the former Soviet Union to Israel in the early 1990s, Gould et al. (2009) show that a higher share of immigrants in the fifth grade has had a negative influence on the probability that native students pass the final matricula- tion exam. Their identification strategy is based on the assumption that, conditional on the total number of immigrant students admitted to a given school, the variation in the proportion of immigrants across grades of the same school can be considered as due solely to exogenous demographic factors.

Negative effects of the share of immigrants on the performance of native pupils are found also by Jensen and Rasmussen (2011), who look at the reading and math test scores of 15-years-old Danish students. They use school data and an identification strategy which consists of instrumenting the share of immigrants in the school with the concentration of immigrants in a wider area about the school. Instrument validity relies on the assumption that families mobility is imperfect because of personal ties and the need to reside near the workplace.

Less pessimistic views on the influence of immigrants are expressed by Neymotin (2009), who finds no clear evidence that immigration reduces the test scores of native students and their propensity to apply to top schools in Texas and California, and by Hunt (2012), who uses a panel of US states spanning the period 1940–2010 to estimate the effect of the share of immigrants in the population when natives are aged 11–17 on native high school attainment. She exploits the exogenous variation in the distribution of immigrants by continent of origin to instrument decennial variations in immigration and finds that immigration has increased education attainment in the general population and among Blacks in particular, as a reaction to the growing pressure of immigrants on the market of low skilled jobs.

In a recent contribution, Ohinata and van Ours (2011) use the within-school variation generated by the presence of multiple classes in some of the Dutch schools included in the PIRLS and TIMMS surveys and find little evidence that immigrants negatively affect native students.6 Although not dealing explicitly with migrants, Angrist and Lang (2004) estimate the impact of a de-segregation program

5 Crowding our effects are emphasized also by Hoxby, who suggests

that immigrant students crowd minority natives out of universities and

colleges by competing for scarce remedial resources, and Borjas (2007),

who finds that the increasing number of immigrant students in the US

crowds white American-native males out of universities, especially in

elite institutions. 6 In this paper, identification rests upon the hypothesis of random

allocation of immigrant students within schools. To test this assumption,

the authors regress teacher characteristics on the proportion of

immigrant students in the class. In support of their identification

strategy, they do not find any statistically significant correlation.

(METCO) carried out in the Boston area, which transferred black students to the ‘‘whites only’’ schools in the more affluent Boston belt. They find no effect of de-segregation on the test scores of white students in the receiving schools and a modest effect on minority students. Non random allocation of black students is addressed by looking at the within-school variation across multiple classes in the same school.

3. The empirical setup

The large literature on the effects of immigration on economic outcomes has used alternative strategies to identify causal effects. Some papers have relied upon instrumental variables, exploiting either shocks which occurred in the countries of origin (Angrist & Kugler, 2003; Friedberg, 2001 among others) or the historically and geographically determined variation in the distribution of immigrants by country of origin (Card, 2001; Hunt & Gauthier-Loiselle, 2010 among others). Our approach combines aggregation, selection on observables and fixed effects, and is close to the identification strategies adopted by Hoxby (2000), Angrist and Lang (2004), Card and Rothstein (2007), Gould et al. (2009), and Ohinata and van Ours (2011).7

We address the endogenous sorting of students across schools and classes by aggregating data at the country level, as suggested by Borjas et al. (1997), among others.8

In general, the choice of the appropriate unit of analysis depends on the specific problem under scrutiny. For instance, more disaggregated units have been adopted by Betts and Fairlie (2003), and by Card and Rothstein (2007), who have looked at the metropolitan areas in the US.

The selected unit of analysis should be large enough to account for the mobility of natives in response to immigration and narrow enough to limit aggregation bias. The concentration of immigrants in some local areas may induce native families not only to send their children to schools with few immigrant students but also to move to areas with less immigrants (Betts & Fairlie, 2003). To minimize the risk that native households move out of the boundaries of the unit of analysis, this unit should be broad. On the other hand, aggregation bias (Theil, 1954) can emerge when the unit of analysis is too broad, mainly because aggregation averages out the heterogeneous effects that may be present at a more disaggregated level.

In this paper, we aggregate information at the country level. This choice satisfies the need to choose a broad unit of analysis and to include the mobility of natives, which in Europe tends to occur within rather than between countries, but requires that we address aggregation bias. We do so by investigating in some depth in Section 7 how

7 Recently, researchers have used structural models to assess the effect

of immigrants on the wages of natives when there is imperfect

substitution between native and immigrant workers. The relevant

elasticity of substitution is estimated at the national level by exploiting

the variation over time in wages and immigrant status across groups of

workers with different education and experience (Manacorda, Manning,

& Wadsworth, 2012; Ottaviano & Peri, 2012 among others). 8 Borjas (2003), Borjas and Katz (2007), and Aydemir and Borjas (2007).

9 See OECD, Comparison over Time on the PISA Scales, Paris, 2007.

G. Brunello, L. Rocco / Economics of Education Review 32 (2013) 234–246 237

the average test score of natives vary with the distribution of immigrants within each country and among schools.

We use repeated country observations over time, pool different subjects and identify the relationship between the share of immigrants and the test scores of natives by removing country-specific un-observables and by exploit- ing the country by time variations in the data. Define ȳcrt as the average test score of 15-years-old native pupils in subject r, country c and time t, m̄ct as the average share of their 15-years-old immigrant peers, and Xct as a vector of country by year covariates. Since year-to-year variations in these two variables may be too small to identify the relevant effect, we use variations over periods of three years.

A simple regression of ȳcrt on m̄ct is unlikely to produce unbiased estimates of the causal effect. For instance, long- run trends in test scores and the foreign student share could generate a negative correlation between these variables even in the absence of a causal effect. We capture these long-run effects by adding Xct to the regression and by including in Xct country specific linear trends. In addition, positive school expenditure shocks affecting a country could increase test scores and at the same time attract more immigrants in the country if this expenditure is induced by higher income per capita, thereby imparting a positive bias on the estimated effect of the immigrant share on log test scores. To avoid this, we add to the vector Xct both the growth rate and the level of real GDP per capita, and secondary school expenditure per pupil as percentage of GDP per capita.

We also add to Xct the average number of books at home and the proportion of students with at least one parent who attained tertiary education as measures of average parental background, and a dummy equal to one if the share of immigrants who originate from low income countries is larger than the overall median share, and to zero otherwise. The last variable controls for the average human capital of immigrants in a country. Therefore, our empirical model is

ȳcrt ¼ ūr m̄ct þ bXct þ fc þ ft þ fr þecrt (1)

where fc , ft and fr are country, time and subject effects, which we capture with country, time and subject dummies, and the marginal effect of the foreign student share on the test score of natives, ūr , can vary with the subject r.

We include in the vector Xct also the total stock of immigrants in the country and the population of students aged 15. Our identification assumption is that, conditional on these stocks and the other covariates in vector Xct , the variation in the share of immigrant pupils who are in school at age 15 in a given country is mainly determined by demographic factors and is therefore as good as random. We thus implement at the country level the same approach used by Gould et al. (2009), at the school level, with an important difference: while they need to worry about the residual correlation between the share of immigrants and unobserved school characteristics, we control for unob- served country characteristics in a flexible way by using country dummies.

Notice that the marginal effect of the foreign student share on the average test score of natives in subject r, ūr , in Eq. (1) is the weighted average of school-level marginal effects urs. To illustrate, consider a country with N native and M immigrant students enrolled in S schools. Let ysr be the average performance of native students attending school s in subject r and let the share of immigrant students in school s be ms = Ms/(Ns + Ms), where Ms and Ns are immigrant and native students in school s. Furthermore, let the performance of natives in school s depend linearly both on school characteristics msr and on the share of immigrants, as in the expression below

ysr ¼ msr þ usr ms (2)

where the marginal effect usr is allowed to vary among schools as well as among subjects. Aggregation of (2) at the country level yields

ȳr ¼ 1

N

X s

Ns ysr ¼ 1

N

X s

Nsðmsr þ usr msÞ

¼ m̄r þ X

s

ns n̄

ms m̄

zsusr

! m̄ ¼ m̄r þ ūr m̄ (3)

where ns is the share of native students in school s, zs is the relative size of school s, defined as zs ¼ðMs þ NsÞ=ðM þ NÞ, and n̄ and m̄ are the share of natives and immigrant students in the country, respectively.

For any subject r, the country-level marginal effect ūr is the weighted average of the school-level marginal effects urs, with only the schools having a strictly positive number of immigrant and native students contributing to this average.

4. The data

We use data from the four available waves – 2000, 2003, 2006 and 2009 – of the OECD Programme for International Student Assessment (PISA). PISA is a large scale project that measures the cognitive abilities of 15-years-old students, using standardized tests that focus on reading, mathemat- ics and science skills. The project compares average scores across countries, but also monitors trends over time in student performance. Each wave focuses on a major domain (reading, maths or science) and treats the rest as minor domains. As suggested by PISA technical reports, we enhance the comparability over time for each domain by retaining only the wave where it is treated as major and the following waves.9 Therefore, we use all four waves for reading and exclude wave 2000 for maths and waves 2000 and 2003 for science.

PISA evaluates students aged between 15 years and 3 (complete) months and 16 years and 2 (complete) months at the beginning of the assessment period, who are enrolled in an educational institution at grade 7 or higher. The sample is two-stage stratified: in the first stage, schools are randomly selected in each country. In the second stage, 35 students are randomly selected from each school.

Table 1

Test scores and the share of immigrant pupils; by country.

Country Test score % Immigrant

students

% Immigrant

students – corrected

% Immigrant students –

broader definition

Segregation

index

Australia 522.2 0.102 0.105 0.221 0.494

Austria 507.5 0.067 0.073 0.138 0.551

Belgium 526.0 0.057 0.060 0.129 0.598

Switzerland 529.4 0.098 0.104 0.221 0.442

Canada 533.3 0.097 0.104 0.211 0.689

Czech Rep. 500.8 0.008 0.009 0.018 0.815

Germany 519.9 0.065 0.068 0.145 0.521

Denmark 506.9 0.030 0.039 0.081 0.595

Spain 486.8 0.054 0.066 0.074 0.607

Finland 549.0 0.014 0.017 0.022 0.769

France 506.9 0.030 0.032 0.127 0.662

Greece 471.3 0.060 0.062 0.077 0.631

Hungary 491.1 0.014 0.015 0.019 0.702

Ireland 508.7 0.042 0.046 0.057 0.481

Iceland 501.3 0.012 0.021 0.023 0.712

Italy 480.0 0.028 0.033 0.040 0.629

Israel 455.2 0.085 0.089 0.196 0.581

Latvia 486.9 0.006 0.006 0.060 0.856

Mexico 415.2 0.015 0.016 0.022 0.802

Netherlands 531.8 0.034 0.034 0.111 0.548

Norway 500.9 0.031 0.038 0.066 0.577

New Zealand 528.6 0.144 0.160 0.227 0.473

Portugal 480.9 0.027 0.030 0.052 0.650

Russia 466.0 0.048 0.048 0.096 0.471

Sweden 513.0 0.046 0.052 0.115 0.596

UK 508.1 0.035 0.038 0.089 0.692

USA 498.4 0.058 0.065 0.162 0.634

Source: PISA.

Note: col. 1: average score in reading, mathematics and science over the selected waves; col. 2: average share of immigrant pupils aged 15; col. 3: corrected

average share of immigrant pupils; col. 4: corrected average share of immigrants, including those born in the country from foreign parents.

G. Brunello, L. Rocco / Economics of Education Review 32 (2013) 234–246238

The original sample consists of 66 countries. We treat as immigrant students the pupils born abroad from two foreign parents,10 and exclude from the sample the countries with an average share of immigrant pupils below 1 percent in all the four waves (19 countries, including Japan and Korea) and with less than two observations on the share of immigrants (9 countries, including Singapore). Additional 11 countries, including Argentina and Brazil, are excluded either because of missing data for the selected controls in vector X or because of their very small size (Luxembourg, Liechten- stein, Macao and Hong Kong). We end up with a sample of 27 countries (20 from Europe, 3 from the Americas, 2 from Oceania, 1 from the Middle East and 1 from Asia) and 238 observations.

Selected summary statistics by country are reported in Table 1. Columns 2 and 4 in the table report the percentage of immigrant students in the stricter and broader definition (second generation immigrants added in). The share of first generation 15-years-old immigrant students (born abroad from foreign parents) is close to or above 10 percent in Switzerland, Australia and New Zealand and below 2 percent in Latvia, Hungary, Finland and Mexico. The other countries lie in between these two extremes. The average share of immigrant pupils in our sample is 4.8 percent, with a standard deviation equal to 0.035. While

10 A broader definition adds those born in the country from foreign

parents (second generation immigrants).

two thirds of the total variation in this share occurs between countries, one third takes place within countries and over time. Table A1 in the Appendix (available on the website of the journal) reports average reading test scores and the proportion of immigrant students by country and year. Between survey changes in test scores and in the share of immigrant pupils range between �4.71 and 7.43 percent and �3.59 and 4.16 percentage points, respectively.

Following Wossmann and West (2006), we obtain from the PISA dataset country-specific information on parental background, which we measure with the number of books in the household and with the share of students with at least one parent who has attained tertiary education.11

Data on GDP per capita in 2005 US dollars and on the expenditure per pupil in secondary education as percent- age of GDP per capita are from the World Bank World Development Indicators. The stock of immigrants by country and year is drawn instead from the UN Depart- ment of Economic and Social Affairs – Population Divi- sion,12 and the stock of students aged 15 from OECD and Eurostat databanks. Finally, the proportion of immigrants originating from low income countries (according to the World Bank definition) is computed using the Global Migrant Origin Database.

11 PISA includes a qualitative indicator of the number of books, which

ranges from 1 (0–10 books) to 6 (more than 500 books). 12 Trends in the International Migrant Stock: The 2008 Revision.

[(Fig._1)TD$FIG]

− .0

4 −

.0 2

0 .0

2 .0

4 −.02 −.01 0 .0 1 .0 2 .0 3

raw data Fitted values

ch a

n g

e in

lo g

t e

st s

co re

s

change in migration share

all subjects

− .0

4 −

.0 2

0 .0

2 .0

4

−.02 −.01 0 .0 1 .0 2 .0 3

raw data Fitted values

ch a

n g

e in

lo g

t e

st s

co re

s

change in migration share

reading

− .0

4 −

.0 2

0 .0

2 .0

4

−.02 −.01 0 .0 1 .0 2 .0 3

raw data Fitted values

ch a

n g

e in

lo g

t e

st s

co re

s

change in migration share

maths

Fig. 1. Within-country changes in test scores and in the share of immigrants – net of controls. 19 countries, 2000–2009.

G. Brunello, L. Rocco / Economics of Education Review 32 (2013) 234–246 239

5. Main results

The empirical model described by Eq. (1) assumes that the marginal effect of the share of immigrant pupils on the performance of natives does not vary across countries. We test whether this assumption is tenable in our data by estimating Eq. (1) on the full sample of 27 countries and by interacting the share of immigrants with country dum- mies. If these interactions are jointly not statistically significant, we conclude that the assumption holds. If they are statistically significant, we use the following iteration procedure: we drop the countries with statistically significant interactions, re-estimate the model and repeat the test on the sub-sample of countries. If the test still rejects the null (interactions are jointly not statistically significant) we drop additional countries with statistically significant interactions and repeat both estimates and test until the latter fails to reject the null at the conventional level of confidence. When this happens, the residual set of countries can be ‘‘pooled’’ with respect to the relevant marginal effect.

It turns out that we need to exclude eight countries (Austria, Belgium, Canada, Greece, Latvia, Norway, Sweden, and Switzerland) from the original sample before attaining our final sample with homogeneous marginal effects of the share of immigrants on the test score of natives. By so doing, we end up with a sample consisting of 19 countries and 167 observations.13 While this is an informative sample for the purpose at hand, we do not

13 The average share of immigrants in this sub-sample is 4.2 percent,

slightly less than in the full sample. We report the estimates of Eq. (1) for

the full sample of 27 countries sample in column 1 of Table A2 in the

Appendix available in the journal website.

claim it to be representative. Therefore, we warn the reader against easy generalizations of our results.

In the absence of sources of exogenous variation in the share of immigrant pupils, we identify the effect of changes in the share of immigrant pupils on changes in test scores by using the within-country variation of these variables over time. Fig. 1 documents this variation by plotting the residuals from regressions of y and m on the set of covariates in the right side of (1), both for the full sample and separately for reading and maths test scores. Visual inspection clearly suggests that these changes are nega- tively correlated, both in the full sample and in the two main subjects.14

In the empirical estimates, we use the log of the test score rather than the test score as the dependent variable.15 Since the share of immigrants in Eq. (1) – defined as the share of students born abroad from foreign parents – is at a higher level of aggregation than test scores, which vary also by subject, we cluster standard errors by country and time.

We start by regressing log test scores on the share of immigrant students, gender, year and subject dummies. As expected, this specification yields a spurious positive correlation between the test scores of natives and the share of immigrant students, as more developed countries attract more immigrants and have better schools. To remove this spurious effect, one needs to control for

14 We do not add to the figure the data for science because of the limited

number of observations available for this subject. 15 The log-linear specification improves the goodness of fit with respect

to the linear specification, without affecting the results in a qualitative

sense. To derive this specification from model (1), one needs only to

divide both sides of (1) by my, the mean of y, and to use the approximation log(y/my) � (y/my) � 1.

Table 2

OLS estimates of the effects of the share of migrants on the test score of natives. Dependent variable: log test scores.

(1) (2) (3) (4) (5) (6)

Share of immigrant pupils (marginal effect) 0.369*** �0.315** �0.407** �0.502*** �0.573*** �0.670*** (0.136) (0.129) (0.175) (0.143) (0.139) (0.120)

Percentage boys 1.016*** 0.266* 0.350*** 0.350*** 0.396*** 0.449***

(0.316) (0.136) (0.104) (0.104) (0.108) (0.102)

Average number of books in household 0.123*** 0.139*** 0.134*** 0.130***

(0.029) (0.029) (0.029) (0.032)

Total stock of immigrants �0.037 �0.032 �0.031 (0.025) (0.021) (0.021)

Total number of students aged 15 0.120*** 0.082 0.078

(0.040) (0.054) (0.048)

Real GDP per capita �0.001 0.001 (0.002) (0.002)

Growth rate of real GDP per capita 0.172 0.173*

(0.108) (0.101)

Education expenditure in secondary education

per capita (as % of GDP per capita)

0.003**

(0.101)

Proportion of students with at least one

parent who attained tertiary education

0.003**

(0.002)

Higher-than-median proportion of immigrants from

low income countries

�0.021*** (0.006)

Subject and Time dummies Yes Yes Yes Yes Yes Yes

Country dummies No Yes Yes Yes Yes Yes

Country specific trends No No Yes Yes Yes Yes

Observations 167 167 167 167 167 167

R-squared 0.119 0.928 0.948 0.951 0.952 0.953

Notes: Robust standard errors clustered by country and time within parentheses.

* Estimated coefficients are statistically significant at the 10 percent level of confidence.

** Estimated coefficients are statistically significant at the 5 percent level of confidence.

*** Estimated coefficients are statistically significant at the 1 percent level of confidence.

16 An alternative definition of ‘‘good’’ parental background uses the

terciles of the distribution of books. As reported in Table A3 in the

Appendix available in the website of the journal, our estimates are

qualitatively similar to those presented in Table 3. 17 The estimated effects are quite precise in spite of the small number of

observations. 18 The test for gender differences in the marginal effect of the share of

immigrants on the test scores of natives has p-value equal to 0.318. On the

other hand, the p-value of the test for parental background differences is

equal to 0.000.

G. Brunello, L. Rocco / Economics of Education Review 32 (2013) 234–246240

country-specific effects. This can be done with our data, which include both between and within country variation in test scores and shares of immigrants.

When country fixed effects are included in the second column of Table 2, the positive correlation disappears and we find that an increase in the share of immigrant pupils has a negative and statistically significant effect on the (log) test scores of natives. We then add progressively the following controls: country specific trends and the number of books at home in column 3, the total stock of immigrants in the country and the population of students aged 15 in column 4, real GDP per capita and its growth (column 5), school expenditure as a percentage of GDP, the proportion of students with at least one parent who attained tertiary education and the proportion of immigrants from low income countries in column 6. We find that the absolute value of the effect of the share of immigrant pupils on the test score of natives increases as we move from column 2 to final column 6, indicating that the additional controls remove sources of positive bias in our estimates.

Table 3 reports in its first column the specification shown in column 6 of Table 2, and in the second column the same specification augmented with the interaction of the share of immigrant pupils with two subject dummies, one for maths and the other for science. While in columns 1 and (2) we consider all 15-years-old native pupils, in columns 3 and 4 we distinguish between male and female natives, and in columns 5 and 6 we consider separately native pupils with a ‘‘good’’ and ‘‘poor’’ parental back- ground, where ‘‘good’’ is for students who have a number of books in the household higher than or equal to the

country mean, and ‘‘poor’’ is for those with fewer books.16

We find that the share of immigrant pupils attracts a negative and statistically significant coefficient in all the specifications in the table.17 The estimated effect is larger for females than for males and for natives with poor parental background than for better endowed pupils. While the former difference is not statistically significant at the 5 percent level of confidence, the latter is.18

Compared to column 1, in column 2 we allow the marginal effect to vary by subject, but find no evidence of heterogeneous responses. A similar specification is run for males and females, with similar qualitative results.

The size of the estimated effect is small: a ten percent increase in the share of immigrant students reduces the average test scores of natives by 0.28 percent in the full sample. This implies that doubling the share of immigrant pupils from the average 4.2 percent in the estimation sample to close to 8.4 percent reduces the average test score of natives by 1–3.4 percent, with the smaller effect

Table 3

OLS estimates of the effects of the share of migrants on the test score of natives. Dependent variable: log test scores.

(1) (2) (3) (4) (5) (6)

All All Males Females Good parental

background

Poor parental

background

Share of immigrant pupils (marginal effect) �0.670*** �0.657*** �0.325* �0.815*** �0.231** �0.558*** (0.120) (0.124) (0.163) (0.183) (0.102) (0.111)

Share of immigrant pupils � mathematics �0.113 (0.073)

Share of immigrant pupils � science 0.061 (0.084)

Percentage boys 0.449*** 0.447*** 0.508*** 0.436*** 0.442*** 0.515***

(0.102) (0.104) (0.175) (0.100) (0.115) (0.119)

Real GDP per capita 0.001 0.001 0.003 �0.000 0.001 0.002 (0.002) (0.002) (0.002) (0.002) (0.002) (0.002)

Growth rate of real GDP per capita 0.173* 0.182* 0.196 0.203* 0.146 0.156

(0.101) (0.102) (0.143) (0.108) (0.106) (0.106)

Education expenditure in secondary education 0.003** 0.003* 0.004* 0.004* 0.003* 0.007***

per capita (as % of GDP per capita) (0.002) (0.002) (0.002) (0.002) (0.002) (0.002)

Total stock of immigrants �0.031 �0.030 �0.052*** �0.004 �0.037*** �0.024 (0.021) (0.021) (0.017) (0.019) (0.013) (0.019)

Total number of students aged 15 0.078 0.078 0.056 0.071 0.031 0.058

(0.048) (0.049) (0.052) (0.053) (0.038) (0.049)

Average number of books in household 0.130*** 0.131*** 0.023* 0.122*** 0.057*** 0.093***

(0.032) (0.032) (0.013) (0.035) (0.012) (0.008)

Proportion of students with at least one

parent who attained tertiary education

0.036* 0.036 0.045 0.021 0.031 0.022

(0.021) (0.022) (0.031) (0.024) (0.033) (0.021)

Higher-than-median proportion

of immigrants from low income countries

�0.021*** �0.021*** �0.018** �0.015 �0.016** �0.022*** (0.006) (0.006) (0.008) (0.012) (0.007) (0.006)

Observations 167 167 167 167 167 167

R-squared 0.953 0.954 0.954 0.952 0.949 0.945

Notes: each regression includes country, subject, time dummies and country specific linear trends. Robust standard errors clustered by country and time

within parentheses.

* Estimated coefficients are statistically significant at the 10 percent level of confidence.

** Estimated coefficients are statistically significant at the 5 percent level of confidence.

*** Estimated coefficients are statistically significant at the 1 percent level of confidence.

G. Brunello, L. Rocco / Economics of Education Review 32 (2013) 234–246 241

accruing to students with good parental background and the largest effect to female students.19

Our estimates also show that average test scores are higher when the expenditure in secondary education as a share of GDP per capita and the average number of books are higher and the proportion of immigrants from low income countries is lower. On the one hand, no statistically significant effect (at the 5 percent level of confidence) is found for real GDP per capita and its growth, for the stock of students aged 15 and for the share of students with at least one parent with college education. On the other hand, the stock of immigrants attracts a negative coefficient, which is statistically significant in the case of females and pupils with good parental background. There is also evidence that the average share of boys in schools has a positive effect on the average math test scores of natives. This result is at odds with the findings by Hoxby (2000) and Lavy and Schlosser (2007). The latter study, for instance, finds that educational outcomes in Israel primary, middle and high schools are higher when the proportion of boys is smaller.20

19 The size of the effect is even smaller if we consider the sample of 27

countries – see Table A2 in the Appendix. 20 Whitmore (2005) finds mixed results when studying performance in

US kindergarten and primary schools. She uses the gender variation

generated by the random assignment of students into classrooms in the

Tennessee’s Project STAR.

6. Attenuation bias

In this section we investigate whether the small size of the effect of immigrant students on the test score of natives is due, at least in part, to attenuation bias induced by measurement error. We consider two possible sources of measurement error. First, the sampling standards used in PISA permit countries to exclude up to 5 percent of the relevant population, either by excluding schools (up to 2.5 percent) or by excluding students (up to 2.5 percent of the relevant population). One exclusion criterion refers to students with limited proficiency in the assessment language.21 Since immigrants are more likely to have insufficient language experience, this sampling design implies that the measured share of immigrants in the school is likely to be under-estimated. Second, as discussed at length by Aydemir and Borjas (2010), the share of immigrants calculated from the PISA sample can be affected by a sizable sampling error. This bias can be particularly relevant in setups that use longitudinal information and control for fixed effects, as in the current study.

We use the information provided by PISA at the country level both on the weighted number of students excluded because of language problems and on the weighted number

21 An additional criterion for exclusion is disability. See PISA Technical

Report 2006, OECD, Paris.

Table 4

Corrected measures of the share of immigrant pupils.

Variables (1) (4)

Corrected IV method

Share of immigrant pupils (marginal effect) �0.527*** �0.645 (0.161) (0.232)

[0.239]

Percentage boys 0.437*** 0.333

(0.108) (0.107)

[0.116]

Real GDP per capita 0.001 0.000

(0.002) (0.001)

[0.002]

Growth rate of real GDP per capita 0.185* 0.194

(0.104) (0.066)

[0.110]

Education expenditure in secondary education per capita

(as % of GDP per capita)

0.003* 0.002

(0.002) (0.001)

[0.002]

Total stock of immigrants �0.026 �0.031 (0.020) (0.011)

[0.022]

Total number of students aged 15 0.081 0.073

(0.049) (0.030)

[0.051]

Average number of books in household 0.124*** 0.124

(0.032) (0.019)

[0.033]

Proportion of students with at least one

parent who attained tertiary education

0.045** 0.040

(0.022) (0.016)

[0.028]

Higher-than-median proportion of immigrants

from low income countries

�0.022*** �0.013 (0.007) (0.008)

[0.009]

Observations 167 167

R-squared 0.952

Notes: see Table 2. In column 2 we report within parentheses the standard deviations of the empirical distribution of parameters generated by 500

replications and between brackets average standard errors computed in each replication.

* Estimated coefficients are statistically significant at the 10 percent level of confidence.

** Estimated coefficients are statistically significant at the 5 percent level of confidence.

*** Estimated coefficients are statistically significant at the 1 percent level of confidence.

G. Brunello, L. Rocco / Economics of Education Review 32 (2013) 234–246242

of participating students to correct the measure of the share of immigrants, under the plausible assumption that students excluded because of language problems are typically immigrants. Column 3 in Table 1 presents the corrected shares of foreign pupils for each country and column 1 in Table 4 shows our estimates for the full sample when the corrected measure is used. We find that the estimated effect of the share of immigrant pupils is slightly smaller in absolute value than in Table 3.

We address sampling error by implementing the IV strategy suggested by Aydemir and Borjas (2010).22 The IV approach requires that two measurements of the variable subject to sampling error are available. By construction, while these measures are highly correlated, their mea- surement errors are not, whatever the error distribution. Therefore, the second measure can be used as instrument for the first. We randomly split the original sample of pupils into two half samples, compute the share of immigrants in both sub-samples and use the immigrant share in the second-half sample as instrument for the

22 This strategy can only be applied to the raw share, because the

information required to compute the corrected share is only available at

the country level.

immigrant share of the first-half sample. The procedure is repeated 500 times to derive the empirical distribution of the parameter of interest. As shown in column 2 of Table 4, we find that the absolute value of the estimated coefficients is marginally smaller than the estimates in the baseline column 1 of Table 2. We conclude that attenuation bias is a minor problem in the current context.23

7. The distribution of foreign pupils

The linear specification used in Eq. (1) overlooks the fact that – conditional on the mean share of immigrant pupils – the average test score of natives could vary with the distribution of immigrants within each country and among schools. In particular, the effect of immigrants could be higher in absolute value – for a given average share – when they concentrate in a few schools than when they are

23 The use of the analytical formula provided by Aydemir and Borjas

(2010, p. 12) to compute an approximate assessment of the sampling

error bias is recommended only in settings with at least 50–100 cells. In

our case the number of cells is 74. For this reason we prefer to use the IV

method discussed in the text.

[(Fig._2)TD$FIG]

AUS

CZE

DEU

DNK

ESP

FIN

FRA GBR

HUN

IRL

ISL

ISR

ITA

MEX

NLD

NZL

PRT

RUS

USA

.5 .6

.7 .8

.9

0 .05 .1 .15

raw data fitted data

se g

re g

a tio

n in

d e

x

share of immigrant pupils

Fig. 2. The cross country correlation between the share of immigrant

pupils and the segregation index D. Note: the R squared of the linear

regression of the segregation index on the reciprocal of the share of

immigrant pupils is equal to 0.66.

G. Brunello, L. Rocco / Economics of Education Review 32 (2013) 234–246 243

evenly distributed across all schools. By looking at the distributional effects of immigration we also address the aggregation bias implicit in our choice of countries as the relevant unit of analysis.

We investigate these effects by using the country and wave-specific segregation index (see Duncan & Duncan, 1955)

D ¼ 1

2

X s

Ms M �

Ns N

���� ���� ¼ 12

X s

zs ms m̄ �

ns n̄

��� ��� ¼

1

2

X s

zs ms � m

m̄n̄

��� ��� (4) which ranges between 0 (equal distribution) and 1 (full segregation).24 Table 1 reports the index for the 27 countries in our initial dataset and Fig. 2 plots it against the share of immigrant pupils for the sub-sample of 19 countries used in the estimates.

In order to establish a relationship between the Duncan Index and the marginal effect of the foreign student share on the test score of natives, we consider two alternative cases. In the first and simplest case, we assume that this effect in Eq. (2) is linear and common across schools, that is, usr ¼ ūr . Using a first order Taylor expansion of ms � m2s around m̄ � m̄2 , Eq. (3) can be rewritten as

ȳr ¼ m̄r þ X

s

ns n̄

ms m̄

zsusr

! m̄

¼ m̄r þ ur X

s

ms � m2s n̄m̄

zs

! m̄

� m̄r þ ur X

s

ðm̄ � m̄2Þþð1 � 2m̄Þðms � m̄Þ m̄ � m̄2

zs

! m̄

¼ m̄r þ ur m̄ (5)

24 Compared to more recent indices of polarization/fractionalization,

which are closely related to the Herfindhal Index, the Duncan Index is

more natural to use in cases such as ours where there are only two

complementary groups.

In this case, when ms is not far from m̄, the distribution of immigrants across schools does not alter the average (country level) marginal effect of the foreign student share on the test scores of natives.

In the second and more complex case, we assume that the marginal effect at the school level is increasing in ms, that is, usr ¼ ur ms in Eq. (2). Using this assumption into (3) we obtain

ȳr ¼ m̄r þ X

s

ns n̄

ms m̄

zsur ms

! m̄

¼ m̄r þ ur X

s

m2s � m3s n̄m̄

���� ����zs

! m̄

� m̄r

þ ur X

s

ðm̄2 � m̄3Þþð2m̄ � 3m̄2Þðms � m̄Þ n̄m̄

����� �����zs

! m̄

(6)

where we have used again a Taylor expansion of m2s � m3s around m̄2 � m̄3. Since ðm̄2 � m̄3Þ is negligible for small values of m̄, Eq. (6) can be rewritten as

ȳr � m̄r þ urð2m̄ � 3m̄ 2Þ X

s

ms � m̄ n̄m̄

���� ����zs

! m̄

¼ m̄r þ 2urð2m̄ � 3m̄ 2ÞDm̄ ¼ m̄r þ urðm̄; DÞm̄ (7)

where ūr ¼ 2urð2m̄ � 3m̄2ÞD. In the presence of nonlinear effects at the school level, the country-level average marginal effect of the foreign student share on the average test score of natives depends both on m̄ and on the index D.

By construction, D is negatively correlated with the share m̄. This correlation is apparent in Fig. 2, where we plot the country-specific share of immigrant pupils and the segregation index. For instance, countries such as New Zealand, where the share of immigrant pupils is relatively high, have a relatively more homogeneous distribution of immigrants across schools than Finland, where immigrant pupils are few.

Carrington and Troske (1997) have shown that the Duncan Index tends to be larger the smaller the share of immigrant students, even in the presence of random allocation. In order to purge the index D from the effect of the share m̄, we decompose it into two components, one parallel and one orthogonal to 1=m̄, the function of m̄ suggested by Fig. 2. Denote the former component as l=m̄ and the latter as D. Then Eq. (7) can be written as

ȳr � m̄r þ 2urð2m̄ 2 � 3m̄3Þ

l m̄ þ D

� � (8)

and the marginal effect of m̄ on the average test score is equal to

@ȳr @m̄ ¼ 2ur½lð2 � 6m̄Þþð4m̄ � 9m̄2ÞD� (9)

The decomposition of D into its orthogonal components yields in our data l = 0.002 and a value of D that ranges from 0.350 to 0.678, depending on the country. Using the values of m̄ in our sample of countries – see Table 1 – we obtain that the term within brackets in Eq. (9) is positive

Table 5

The effects of the segregation index D.

Variables (1) (2) (3) (4) (5)

All Males Females Good parental

background

Poor parental

background

Polynomial of share of immigrant pupils � D index �3.172*** �2.960*** �3.727*** �1.276* �2.531*** (0.706) (0.723) (1.107) (0.653) (0.674)

Percentage boys 0.402*** 0.415*** 0.381*** 0.426*** 0.485***

(0.105) (0.128) (0.105) (0.116) (0.120)

Real GDP per capita 0.001 0.001 0.000 0.001 0.003

(0.002) (0.002) (0.002) (0.002) (0.002)

Growth rate of real GDP per capita 0.180 0.160 0.207* 0.153 0.154

(0.110) (0.128) (0.117) (0.111) (0.115)

Education expenditure in secondary

education per capita (as % of GDP per capita)

0.004** 0.004** 0.004** 0.003** 0.007***

(0.002) (0.002) (0.002) (0.002) (0.002)

Total stock of immigrants �0.028 �0.044** �0.000 �0.036*** �0.022 (0.020) (0.020) (0.017) (0.013) (0.019)

Total number of students aged 15 0.072 0.072 0.065 0.028 0.057

(0.049) (0.046) (0.055) (0.039) (0.049)

Average number of books in household 0.127*** 0.120*** 0.116*** 0.057*** 0.095***

(0.032) (0.031) (0.036) (0.012) (0.008)

Proportion of students with at least

one parent who attained tertiary education

0.039* 0.043* 0.026 0.031 0.025

(0.021) (0.025) (0.024) (0.033) (0.021)

Higher-than-median proportion of

immigrants from low income countries

�0.020*** �0.027*** �0.013 �0.016** �0.021*** (0.006) (0.009) (0.011) (0.007) (0.006)

Observations 167 167 167 167 167

R-squared 0.952 0.958 0.951 0.949 0.945

Notes: see Table 2.

* Estimated coefficients are statistically significant at the 10 percent level of confidence.

** Estimated coefficients are statistically significant at the 5 percent level of confidence.

*** Estimated coefficients are statistically significant at the 1 percent level of confidence.

G. Brunello, L. Rocco / Economics of Education Review 32 (2013) 234–246244

and increasing in D. Therefore, the sign of the marginal effect in (9) depends on the parameter ur , which we estimate by running the following regression

ȳcrt ¼ ur Pðm̄ctÞDct þ bXct þ fc þ ft þ fr þecrt (10)

where Pðm̄ctÞ¼ 2ð2m̄2ct � 3m̄ 3 ctÞ. Our estimates are reported

in Table 5, both for the full sample and for the sub-samples of males, females and individuals with different parental background.

We find that the interaction term Pðm̄ctÞDct attracts a negative and statistically significant coefficient, and that the effect of a higher foreign student share on the test scores of natives is higher when foreign students are more segregated. Using the estimates for the full sample and evaluating (9) at the sample mean value of the share of foreign students, we find that a ten percent increase in the share reduces the test score of natives by 0.21 percent at the first quartile, by 0.23 percent at the median and by 0.26 percent at the third quartile of the distribution of D.25 Due to the presence of nonlinearities, the marginal effect of the foreign student share is much higher if we evaluate (9) at the 90th percentile of the distribution of m̄ (10.3 percent) and at median D. In this case, a ten percent increase in the share reduces the test score of natives by 1.12 percent, more the four times the effect observed at the mean of m̄.

25 Since Eqs. (1) and (10) are non-nested, we use both the Davidson and

McKinnon J test and the Cox and Pesaran test to verify which specification

is better supported by our data but cannot reject either model.

At the school level, a ten percent increase in the share of immigrants causes a 0.1 percent reduction of native test scores in schools at the mean of the distribution of ms and a 0.9 percent reduction in schools at the 90th percentile. This finding suggests that a desegregation policy which holds the average foreign student share constant but redis- tributes immigrant pupils from schools with a high to schools with a low immigrant share improves average native tests scores. Because of this redistribution, natives in the former group of schools benefit – in terms of a higher test score – and natives in the latter group lose. Although overall gains are higher than losses, the positive net effect is small: conditional on the foreign student share, a 10 percent reduction in the orthogonal component of the segregation index increases the average test score of natives by 0.11 percent.

8. Conclusions

The proportion of immigrant students has increased over time in most developed countries, especially during the last two decades. Many parents and politicians fear that too many immigrant students could have a negative influence on the school performance of natives, either because of negative peer effects or because immigrants – with their limited proficiency in the language of the host country – can reduce teacher attention for natives. In Italy, for instance, the Education Minister has taken public sentiment very seriously and established a threshold of 30 percent to the number of immigrant pupils in Italian primary school classes.

G. Brunello, L. Rocco / Economics of Education Review 32 (2013) 234–246 245

Is this fear supported by empirical evidence? Using a sample of 19 countries participating to the PISA project, we have reached the following conclusions. First, there is evidence that a higher share of immigrant pupils in secondary schools reduces the test scores of natives.26 The size of the effect, however, is small. Our cross country estimates suggest that doubling the share of immigrant pupils in a country reduces the average test scores of 15- years-old male and female natives in secondary schools by 1.4 and 3.4 percent, respectively. This effect is equal to 1 percent for native students with good parental background and to 2.3 percent for students with poor parental background. Second, there is evidence that the marginal effect of the share of immigrant pupils on the test score of natives is higher in absolute value, but still small in size, in those countries where immigrants are concentrated in few schools and the segregation index is higher.

We have also shown that the negative effect of immigrant students is not borne within each country by all native students to the same extent. To further illustrate this point, we notice that, in our sample of countries,27

about 59 percent of all native 15-years-old students have no immigrant peers in their schools, and the average foreign student share in the schools attended by at least some immigrants is 9.7 percent. As a thought experiment, consider two hypothetical schools in a country, equal in all respects except for the share of immigrant students, equal to zero in the first and to 9.7 percent in the second school. Our baseline estimates in Table 2 suggest that the test scores of natives are 2.2–7.9 percent lower in the second school because of the presence of immigrant students.

This gap is much larger when we compare a school belonging to the top decile of the distribution of the share of immigrants with a school without immigrants. In countries where the share of immigrant students in the schools of the top decile is high – Australia, Israel, Spain New Zealand and the US – the estimated gap in the test scores of natives can exceed 20 percent. Students belonging to these schools would clearly benefit from policies that pursue a more even distribution of immigrant students across schools.

We view our results as an interesting initial step in an important but understudied topic. Since they are based on a small non-representative sample of 19 countries, we cannot tell whether they could be extended to a broader sample of countries. While our empirical approach controls for a range of country and time varying effects, our identification assumption that, conditional on these controls, the variation in the share of immigrant pupils who are in school at age 15 in a given country is mainly determined by demographic factors and is therefore as good as random, is plausible but cannot be tested. These limitations suggest that further research is required to throw additional light on the relationship between the

26 One mechanism by which native students perform worse in classes

with a higher share of immigrant pupils is the expenditures schools make

on special instruction for immigrant students, which crowd out other

school expenditures more focused on native students. 27 We refer to the sample used in the estimates of Table 2.

share of immigrant pupils in a class and the performance of natives.

Acknowledgements

We are grateful to the Editor, two anonymous referees, Erich Battistin, Alessandra Venturini, Christoph Weiss and to the audience at the first CSEA workshop in Padova for comments and suggestions. A previous version of this paper appeared as CSEA working paper (www.decon.u- nipd.it/index.php?p=project01). Financial support from Centro Studi Economici Antonveneta is gratefully ac- knowledged. The usual disclaimer applies.

Appendix A. Supplementary data

Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/ j.econedurev.2012.10.006.

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