UvA-DARE

There has been ample debate about heterogeneous returns to a college degree, and so far, findings have been mixed on the question of whether individuals who attend college are also those who benefit most from it (positive selection), whether returns would be larger for those who never went (negative selection), or whether there is heterogeneity in returns at all. We argue that these diverging findings have two sources: First, they may arise from different conceptualizations of selection into college. We argue that different selection mechanisms have to be distinguished. We separate the college selection process into two meaningful dimensions, one capturing school-irrelevant factors related to social origin and the other capturing school-relevant factors related to individual capabilities. We, then, study heterogeneous returns to a college degree for the two dimensions separately. Second, the structure of the educational system and the labor market might contribute to different patterns of returns to college. We study heterogeneous returns to a college degree in the United States and the Netherlands, two countries with strong differences in how education and labor market are structured. Overall, we find returns to college to be rather homogeneous instead of heterogeneous. For the school-relevant dimension of selection, we do see a tendency towards positive selection for US-men and a tendency towards negative selection for US-women. For the Netherlands, we find that returns are truly homogeneous.


Introduction
During recent decades, the wage premium for college degree holders has been constantly rising (Katz and Murphy, 1992;Oreopoulos and Petronijevic, 2013), and, in general, educational certificates have become increasingly important for labor market attainment (Bernardi and Ballarino, 2016;Blau and Duncan, 1967).Although there is ample evidence that higher education is beneficial for earnings, not all graduates benefit equally from their degrees in terms of wages and other labor market outcomes.Heterogeneous returns to a college degree have been reported for graduates from different fields of study and in different occupations, as well as for different types of higher education institutions (Oreopoulos and Petronijevic, 2013).Another important source of heterogeneity that has been discussed in both economics and sociology is the likelihood of obtaining a college degree (Card, 1999;Brand and Xie, 2010;Carneiro et al., 2001Carneiro et al., , 2011)).The central question regarding this form of heterogeneity is whether the individuals who are likely to complete college are also those who benefit most from it or whether returns to college would be higher for those who typically do not go.
Previous research on the question of who benefits more from college has reported mixed findings (Card, 1999).Some studies show that returns to education are higher for traditional college students and that it would therefore not be beneficial for other students to obtain a college education; this pattern has been described as positive selection (Carneiro et al., 2001(Carneiro et al., , 2003;;Heckman et al., 2006).In contrast, other studies report an equalizing effect of college, also called negative selection, which is a scenario in which unlikely college graduates catch up to those who traditionally earned a degree (Bernardi and Ballarino, 2016;Breen and Jonsson, 2007;Breen and Luijkx, 2007;Dale and Krueger, 2011;Tolsma and Wolbers, 2014;Torche, 2011;Vallet, 2004).Examining these studies, it can be observed that the direction in which heterogeneous returns to higher education run remains contested.Even considering the extensive research that has been done on this topic, certain questions remain to be answered.
We propose two contributions to the existing literature.First, the mixed results regarding the direction of heterogeneous returns might arise from the different conceptualizations of selection into college.Some students are likely to complete college because they come from privileged family backgrounds that are focused on education and have the necessary wealth to finance it (Bernardi and Ballarino, 2016;Brand and Xie, 2010;Hout, 1988;Torche, 2011).Other students are more likely to complete a degree because of their extraordinary academic abilities.The previous studies on this topic differ in terms of which of these factors they take into account and the specific ways in which they measure these factors.Additionally, the studies in which different factors have been accounted for, often have assumed that selection is one-dimensional; thus, these studies assume that whether a student is likely to complete college for one reason or another does not matter in the context of returns.However, the meaning of this likelihood is very different depending on whether we examine for example family circumstances or individual capabilities.The conceptualization of selection into college may also be important in terms of the direction of heterogeneous returns.In particular, we hypothesize that selection into college should be divided into two meaningful dimensions.One of these dimensions concerns a broad measurement of the personal environment that we call school-irrelevant factors; the other focuses on individual capabilities and college preparedness, which we term school-relevant characteristics.
We choose to label these categories in this way to relate them to the debates on fair and unfair inequalities and yet use different terms to distinguish our position from that of luck-egalitarianism.Luck egalitarians argue that all inequalities that are beyond one's control are unfair (i.e., not only inequalities based on social background but also those based on personal attributes such as intelligence (Dworkin, 2002)).Another view states that among the luck-based factors, genetic endowments and certain types of partiality, which are constitutive of loving family relationships, should be considered legitimate as long as they do not directly aim to transmit economic advantages (Swift, 2005).While a detailed discussion of these concepts is beyond the scope of our study, our conceptualization of selection into college leans towards the second perspective and we, therefore, choose the terms "school-relevant" and "school-irrelevant".The circumstances determined by an individual's upbringing, in this context, would be unfair bases of school achievement (thus falling under the category of school-irrelevant factors), even if those factors do sometimes promote educational attainment in practice (such as parenting styles).However, criticizing the role of personal attributes such as intelligence in students' academic careers would bring into question the educational process as such, which is not what this article is about.Therefore, these factors can be viewed as fair advantages and can be characterized as school-relevant characteristics. 1o study selection, we disentangle the two dimensions that comprise the likelihood of college completion.School-irrelevant factors include socio-economic origins, family structures and parenting styles as well as geographic factors.School-relevant factors are characteristics related to individual capabilities such as ability and motivation.We study heterogeneous returns to a college degree for these two dimensions separately.
These different dimensions will provide us with a better understanding of whether an expansion of higher education has the potential to improve social mobility.Expanding college education to include individuals who were previously unlikely to obtain a degree based on their school-irrelevant characteristics could increase social mobility if these new college students benefit from a college degree at least as much as traditional college students do.If, however, higher education primarily benefits students from advantaged personal circumstances, social mobility will not increase with increases in educational expansion and equalization.Furthermore, examining the different dimensions of selection will also provide us with new insights into the efficiency of the sorting process in the educational system by showing whether educational degrees effectively capture school-relevant factors such as demonstrated ability or whether these factors have additional pay-offs on the labor market.
Second, we contribute to the literature by viewing heterogeneous effects through a comparative lens.A large share of the existing evidence concerns a very specific context, namely, the United States of America.The educational system and the labor market in the US have unique structures that affect who goes to college and what the returns to a college degree are.We examine heterogeneous returns to college in the US and in the Netherlands, a country with very different labor market structures and educational systems.Overall, the Netherlands is characterized by a much higher level of intergenerational income mobility than the United States (Jerrim and Macmillan, 2015).The educational system of the Netherlands, although it implements a relatively strict between-school tracking regime, is organized strongly according to performance criteria that are enforced by a high degree of nation-wide test standardization.In terms of higher education, Dutch universities exhibit fewer differences in prestige than US universities, and college costs are lower than they are in the US.Finally, the Dutch labor market is strongly structured according to educational degrees; this is less true of the US labor market (Di Stasio and van de Werfhorst, 2016;DiPrete et al., 2017).All of these characteristics potentially influence the completion of higher education and whether we observe a pattern of positive or negative selection.This is why it is essential to examine different contexts when answering the question of who benefits the most from college.
We use detailed longitudinal survey data from two student cohorts, one from the United States and one from the Netherlands, to study heterogeneous returns to college.First, we revisit the previous research from the US that views selection as one-dimensional, and we apply these models to the context of the Netherlands.Second, we extend this research by taking into account the two different dimensions of selection.

Heterogeneous returns to higher education
Heterogeneous returns to a college degree are closely related to the origin-education-destination (OED) triangle of social mobility (Blau and Duncan, 1967;Hout, 1988), in which social origin is viewed as the source of differential educational participation rates and labor market positions.The focus of the study of the heterogeneous effects of higher education is on the interaction between social origin and education when it comes to determining social destination.The main question is whether some socioeconomic status groups benefit more from education than others.
The presence and direction of this interaction effect between social origin and education are contested.One stream of research argues that students from low-SES families benefit less from a college degree than those from high-SES families.This means that the direct effect of social origin on social destination increases for higher levels of education.This scenario is compatible with the sociological theories claiming that an affinity with dominant cultural codes promotes individuals' opportunities in the labor market even among people with equal qualifications (Bourdieu and Passeron, 1977); and that this phenomenon is especially true for the higher end of the educational distribution (Rivera, 2012).It is also in accordance with the neo-classical economic theory of rational used in the literature such as fair versus unfair, meritocratic versus nonmeritocratic or ascribed versus achieved as they are more neutral and as they do acknowledge that the two dimensions are correlatedas we explain belowand cannot be clearly separated along the lines of fair and unfair (Goldthorpe, 1996).A.G. Forster et al. decision-making, to the extent that SES correlates with resources.In this framework, individuals decide whether an investment in higher education would benefit them economically while taking costs, benefits and success probabilities into account (Becker, 1964;Mincer, 1974).For high school graduates who do not pursue a higher education degree, the costs are assumed to outweigh the benefits.According to this model, sorting into education is efficient because it ensures that those who will benefit most from college are also those who obtain a college degree.In this case, policies leading to an expansion of education would only push students who will not benefit from higher education into college (Cameron and Heckman, 1998).
A contrasting view on this subject is the notion of college as the great equalizer; this view assumes that the direct effect of social origin on social destination is weaker among college graduates than it is among individuals who are less educated (Hout, 1988;Pfeffer and Hertel, 2015;Torche, 2011).This pattern has also been termed negative selection, as the students who are unlikely to select into college are those who would benefit the most from a college degree (Brand and Xie, 2010).The mechanism that is assumed to underlie this phenomenon is that a college degree provides individuals with access to meritocratic labor market segments in which educational degrees matter more than social origin (Breen and Jonsson, 2007;Hout, 1988;Torche, 2011).Another explanation for this phenomenon is that a college education helps disadvantaged students to close gaps in social and human capital, which is beneficial to their labor market returns (Karlson, 2018;Torche, 2011).Finally, negative selection is also compatible with relative risk aversion theory (Breen and Goldthorpe, 1997), which argues that the importance of cost-benefit analyses differs among students from different social origins.High-SES students do not rely on maximizing the monetary benefits that they receive from college.For them, a college degree is necessary to maintain their status; however, they are less pressured to obtain monetary returns on their educational investment, which leads to lower returns to college.Furthermore, in addition to economic resources, factors such as cultural and social capital, family composition and ethnicity are assumed to influence the likelihood of completing higher education (Boudon, 1974;Bourdieu and Passeron, 1977;Brand and Xie, 2010;Coleman, 1988;Karlson, 2018;Lucas, 2001;Mare, 1980Mare, , 1981)).Studies on educational attainment have shown that the cultural resources available in students' home environments were more strongly related to educational attainment among lower-SES children than among higher-SES children (Aschaffenburg and Maas, 1997;De Graaf et al., 2000;DiMaggio, 1982).Similarly, lower-SES students may receive more gains from higher education; thus, economic mobility could be accelerated by promoting access to education.
It needs to be noted that the focus of these studies differs also in their goal.Especially economists of education but also some sociologists have focused on estimating the causal effect of education on earnings and potential heterogeneity in this causal effect (e.g.Dale and Krueger, 2011;Card, 2001;Carneiro et al., 2001Carneiro et al., , 2011;;Brand and Xie, 2010).A large part of the sociological literature on the OED-relationship is more descriptive in nature, showing patterns of social mobility across levels of education (e.g.Hout, 2012;Torche, 2011).However, recently, also this literature has tried to address the issue of selection into college (Karlson, 2018).The evidence for positive or negative selection is not divided along these lines, both types of studies have found evidence for either pattern of returns.
Finally, a homogeneous rather than heterogeneous effect of college education is a possibility.A homogeneous effect would mean that all students would receive equal relative benefits from a college degree, namely, their wage premiums would be the same.However, students who are more likely to obtain a college degree still receive higher absolute wages than those who are less likely to obtain a degree.Homogeneous effects can occur even if the effects of social origin on educational attainment and the direct effects of origin on earnings persist when educational attainment is controlled.While the (mostly American) literature has debated whether positive or negative selection underly heterogeneous returns of college, a scenario of homogeneity of returns could be typical for societies where school-to-work linkages are standardized and regulated, and specific occupational labor markets exist for large shares of the graduates of the educational system (DiPrete et al., 2017).In this scenario, the college graduate labor market is not more or less meritocratic than the labor market for non-graduates; employment in all the labor market segments is determined to a similar extent by educational degrees.

Heterogeneous returns to school-relevant and school-irrelevant characteristics
We add to this debate the idea that the diverging results of the previous research might arise from the ways in which those studies conceptualize the college selection process and how they, thereby, define the likelihood of completing college.Adjusting for selection into college additionally determines who is likely to complete college and who is unlikely to complete college.These varying degrees of likelihood are then used to examine the heterogeneous returns among different individuals.We argue that additional insight concerning theories of college access and returns can be obtained if the likelihood of obtaining a college degree is meaningfully measured.
As mentioned above, we consider two potential reasons behind the different patterns of heterogeneous returns to college: the ways in which social groups are defined and the ways in which individual capabilities are treated.We argue that selection into college should be distinguished into two dimensions.One dimension concerns a broad measurement of social origin and other personal circumstances; the other dimension focuses on individual capabilities and college preparedness.
Previous research has taken different approaches when defining social origin as a basis for the probability that an individual will obtain a college degree.Some studies have focused on single aspects of socioeconomic origin, such as financial resources (Carneiro et al., 2001(Carneiro et al., , 2003)), occupational status, or social class (Hout, 1988;Torche, 2011).Others have combined different characteristics of social origin, such as ethnicity, family structure, and socioeconomic status, into one measure of social origin that reflects multiple sources of educational inequality (Brand and Xie, 2010).We follow the latter approach and argue that a multi-faceted measurement of personal circumstances that comprises as many sources of inequality as possible is crucial to address the overall social inequality in individuals' access to higher education.We call this dimension that comprises different aspects of social origin and personal circumstances school-irrelevant characteristics, as in a meritocratic school system, these factors would not matter for students' success net of their influence on students' performance.
As the second dimension of selection, we examine factors related to capabilities that lay within the individual, or what we call school-relevant characteristics.The treatment of individual capabilities in the previous research is another reason why the existing results are difficult to interpret.Rational choice theory, which is employed in many studies on the topic in the field of economics, considers ability to be central to costbenefit calculations.Most of the sociological studies on college as the great equalizer, however, have not controlled for capabilities; rather, they have compared correlations of socio-conomic measures across generations (Hout, 1984;Torche, 2011).An exception is the work of Karlson (2018), who includes social origin and individual capabilities in a study that controls for selection into college.Furthermore, certain studies on heterogeneous treatment effects and negative selection have controlled for individual capabilities in addition to measures of social origin and other personal circumstances (Brand and Xie, 2010).Therefore, groups with different levels of likelihood to complete college were defined jointly in terms of environmental factors and capabilities placing them into the same dimension of likelihood.It is important to control for individual capabilities; however, by treating these capabilities as an indistinguishable part of social origin, these studies have confounded various distinct processes.Capabilities and personal circumstances might be correlated; however, putting them into a one-dimensional vector of likelihood ignores interesting cases relating to low-SES students with high levels of capability.This makes it difficult to discuss the social consequences of heterogeneous returns across likelihood groups.
We argue, therefore, that the study of heterogeneous returns to higher education must measure personal circumstances and capabilities with two distinct dimensions oras we will dowith two separate measures of the probability of college completion.To address these considerations, we distinguish between two selection dimensionsschool-relevant and school-irrelevant factors for selection into collegeand we examine heterogeneous returns to a college degree based on the likelihood of obtaining a college degree according to these two dimensions.School-relevant factors include individual capabilities such as ability, school performance, and college preparation.The schoolirrelevant dimension captures personal circumstances in a broad sense.This dimension includes environmental, sociodemographic, and cultural characteristics such as socioeconomic background, ethnicity, family structure, geographic location, and the socio-psychological influences of family and peers.Empirically, these two dimensions are intertwined, as school-relevant and school-irrelevant characteristics are correlated.It is well established by the literature on the primary and secondary effects of social origin that school-irrelevant characteristics have an influence on demonstrated ability (Boudon, 1974;Jackson et al., 2007).If this is true, it is difficult to argue in favor of implementing pure meritocratic selection in the educational system as a type of selection intended to equally address students from different social origins (Solga, 2005;Goldthorpe, 1996).Therefore, it is important to clarify that we do not assume that school-relevant characteristics operate in a "pure" fashion.Nevertheless, it would be equally wrong to assume that personal circumstances and capabilities are indistinguishable from one another.As outlined above, there are individuals with high levels of capability but adverse personal environment; additionally, there are individuals with low levels of capability and advantageous personal circumstances.These groups can only be studied if the influences of the social environment and capabilities are separated empirically.Additionally, from the perspective of social policies, it is important to be able to assess the separate influences of circumstances and capabilities.While capability-based differences in returns to college might be justifiable under a meritocratic model, direct influences of social origin and other personal circumstances are more worrisome for social policies that are concerned with equal opportunities in society.
Therefore, it is worthwhile to examine the separate contributions of school-relevant and school-irrelevant factors to educational inequality and returns to education.
With this in mind, we distinguish between school-relevant and school-irrelevant characteristics, and we examine heterogeneous returns to college based on each dimension separately while accounting for the other dimension.To assess the influence of school-relevant characteristics, we examine the component of these capability-related factors that is not explained by school-irrelevant characteristics; thus, we examine individuals with different capabilities but similar levels of schoolirrelevant factors.Methodologically, this will be achieved by residualization, as will be explained in more detail below.Finally, distinguishing two dimensions of selection also means that the question of positive or negative selection is not one that can be answered globally or on the level of individuals.Instead, different selection patterns may occur based on which background characteristics of a student we look at.

Heterogeneous returns in different contexts: the United States and the Netherlands
We hypothesize that different forms of heterogeneous returns can be connected to the structure of the educational system and the labor market of a particular society.While most of the research so far has only considered the United States of America with its unique educational system and labor market structure, we compare the context of the US to that of the Netherlands, which is a society quite different in terms of those structures.Heterogeneous returns might differ across societies due to two factors.First, different selection processes within the educational system play a role, as they influence which and how many students obtain a college degree.Second, labor market structures determine heterogeneous wage returns.
Concerning the educational system, we hypothesize that the extent to which selection is based on school-relevant factors rather than schoolirrelevant factors is particularly important.If selection is mostly "meritocratic", students with college degrees will be more homogeneous in terms of school-relevant factors.Less heterogeneity in terms of returns is to be expected within a more homogeneous group, as students who enter the labor market with the same degree are fairly similar to each other.
Two factors play a role in the effect of the labor market.The first question in this context is related to the extent to which employment opportunities and earnings are determined by degree certificates.Do employers rely mostly on degrees as signals of productivity or do other factors play a considerable role?If earnings are mostly determined by degrees while individual characteristics (both school-relevant and school-irrelevant) only play a minor role, the likelihood of obtaining a college degree does not determine an individuals' earnings beyond its influence on their selection into college.The second question is related to whether this reliance on certificates differs between the labor market segments in which college graduates work and those in which nongraduates work.If this reliance does not differ between these different segments of the labor market, we will observe homogeneous returns; otherwise, we will observe a type of heterogeneous returns.Whether heterogeneous returns show a pattern of negative or positive selection depends on whether the labor markets for higher education graduates rely more or less on certificates than the labor market for non-graduates; additionally, it depends on whether school-relevant or school-irrelevant characteristics receive greater rewards.If college graduates ultimately work in labor market segments that are more meritocratic than those that high school graduates work in, school-relevant characteristics are more important; thus, we can expect positive selection within the dimension of school-relevant characteristics.In contrast, the pattern of school-irrelevant factors will resemble negative selection, as college graduates receive fewer rewards for high levels of social origin than nongraduates.
In the cases of the two countries that we examine, there are some indications that selection into college is more strongly based on schoolrelevant factors in the Netherlands than it is in the United States.The highly differentiated school system in the Netherlands fosters performance-based selection into secondary school tracks; this selection is promoted by a national system of standardized tests and examinations that establishes students' paths towards selection into higher education.Students are subjected to nationwide standardized tests at the age of 12 that determine which secondary-school track they will attend; thus, these tests also determine what kind of college preparation they will receive.However, between-school tracking has a bad reputation in regard to promoting social equality; even if standardization mitigates against this issue, a certain level of SES-related between-school variance remains in the Netherlands (Holtmann, 2017).In the United States, schooling is more decentralized, and college preparation depends largely on factors such as the quality and financial resources of individual schools; these factors are in turn strongly connected to social origin (Lafortune et al., 2018;Ushomirsky and Williams, 2015).
Furthermore, the Dutch labor market is organized more strongly according to certificates and diplomas than the US labor market, and school-to-work linkages are stronger in the Netherlands for all levels of education (DiPrete et al., 2017).Having a certain degree, therefore, influences an individual's labor market outcomes more strongly than additional school-relevant or school-irrelevant characteristics.In the US labor market, degrees themselves matter less, and there is more room for school-relevant and school-irrelevant characteristics to play a role.The amount of meritocracy might vary across the different labor market segments, and this phenomenon could lead to more heterogeneous returns to college in the US than in the Netherlands.

Hypotheses
Taking these considerations together, we expect that returns to higher education are rather homogeneous in the Netherlands, as the selection of students is more strongly based on school-relevant characteristics and the labor market relies more strongly on degrees alone without rewarding other individual characteristics.As this extends to both school-relevant and school-irrelevant personal characteristics as well as all levels of education, the Netherlands is expected to show homogeneous returns to both of the dimensions of selection.
Similar to previous research, we expect that heterogeneous returns to a college degree exist in the US.When examining the direction of heterogeneous returns in the United States, we rely on the two dimensions that we outlined above.As the labor market for college graduates is hypothesized to be more meritocratic, college graduates receive higher returns to their school-relevant personal characteristics than high school graduates.This means that along the dimension of school-relevant characteristics, a pattern of positive selection emerges where returns to a college degree are higher for those with high levels of individual capabilities and other school-relevant characteristics.For schoolirrelevant characteristics, we expect the opposite.These characteristics are less rewarded by the college-graduate labor market, and this leads to a pattern of negative selection along this dimension.In summary, we make the following predictions: H 1. Returns to a college degree increase with the likelihood of obtaining a college degree based on school-relevant characteristics in the United States.
H 2. Returns to a college degree decrease with the likelihood of obtaining a college degree based on school-irrelevant characteristics in the United States.
H 3. Returns to a college degree are homogeneous based on both school-relevant and school-irrelevant characteristics in the Netherlands.

Data and sample
An overview of the data sets that we use can be found in Table 1.We use longitudinal educational cohort data from the National Longitudinal Study of Youth (NLSY) from 1979 for the United States (Bureau of Labor Statistics and U.S. Department of Labor, 2012).This survey has already been used several times to study the interaction effect between social origin and education in their effect on heterogeneous returns.Therefore, we first revisit previous findings that have used the same data but have employed different models, and we subsequently extend this research.The NLSY 1979 contains data for 12,686 respondents who were between 14 and 22 years old in 1979.These youth were then followed for more than 35 years until the present day.Until 1994, they were surveyed every year; after 1994, they were surveyed every two years.We restrict our analytical sample largely based on the considerations of Brand and Xie (2010) as follows: We restrict our sample to students who do not have any missing data related to the covariates that are used (= 8192 students left), students who were years or younger in 1979 (= 4201 students left) and students who completed at least 12 years of education (= high school degree) by 1990.2This leaves us with a sample of 3483 students.
For the Netherlands, we combine survey data with register data.The survey data come from the longitudinal educational cohort study VOCL (Voortgezet Onderwijs Cohort Leerlingen) collected by Statistics Netherlands (CBS, 1965).This survey began following a nationally representative sample of secondary school students in 1989.All the students in this sample were enrolled in their first year of secondary school in 1989; subsequently, the survey followed up with these students throughout their secondary school careers and for several years thereafter.This survey offers a rich set of these students' origin characteristics.To obtain additional information on these students and their families, we match these data with register data from the System of Social-statistical Datasets (SSD) of Statistics Netherlands (CBS).From this database, we obtain information on completed higher education degrees as well as these students' later earnings.The household income of the students' parents, which is not part of the VOCL study, is also obtained from the registers.
The initial VOCL sample comprised 19, 524 students.From this starting sample, 413 students are unable to be linked to the register data.For some of the other students, the entire VOCL questionnaire or test scores are missing (1324), the parents did not fill in their VOCL questionnaires (737), or the parental income information in the registers could not be matched (2410).Furthermore, all the students with missing data on any of the covariates are excluded (1909).Finally, we restrict our sample to students who were 17 years or younger in 1989 (− students) and those who were eligible for higher education by (− 4230 students). 3This leaves us with a sample of 8441 students.It needs to be noted here that the students in the VOCL were born about 10 years after the students in the NLSY.Of course, we would have preferred to study the same birth cohort for both countries, however data limitations make the present comparison the closest two birth cohorts that can be studied across these two countries.This different needs to be kept in mind when drawing conclusions from our results.

Variables
The summary statistics for all the variables in both countries can be found in Table 2.
The main variables that we use to measure selection into college closely follow previous research (Brand and Xie, 2010;Karlson, 2018).For school-irrelevant characteristics, we use an array of measures corresponding to social origin and living circumstances.First, we use two indicators for socioeconomic position: parental education and parental income.The education of students' fathers and mothers is measured in years by the NLSY and in five categories (primary, lower secondary, upper secondary, college, advanced degree) by the VOCL.We convert the Dutch categories into years of education and use the highest level of education achieved by either parent.Parental income in the US is measured by the yearly total net family income standardized for the full NLSY sample.For the Netherlands, we do not have household income information for when the students were still young.As a proxy for household income, we use income data from the 2003 registers.The income data in these registers represent standardized disposable household income after taxes and contributions to social security are subtracted. 4We standardize the income variable for the full VOCL sample based on the birth year of the parents to adjust for life course effects that might arise due to using a measure of income that is derived from a period relatively late in these parents' labor market careers.
In addition to the indicators of socioeconomic measures, we include indicators for race and ethnicity for both countries.In the Netherlands, we include an indicator for whether a student is a member of one of the following minority groups: Moroccan, Turkish, Surinamese/Antillean or another minority.For the US, indicators for being Black, Hispanic or Jewish are included.Concerning family structure, we include a variable indicating whether both parents lived together with the respondent.In the case of the NLSY, this indicator refers to whether both parents lived together when the student was 14; for the VOCL, this measure refers to the first wave of the survey (when the students were aged 12/13).A second indicator captures the total number of children who were living in the household of the student.Furthermore, we add geographic indicators for the living environments of the respondents.For the US, we include a dichotomous variable indicating whether a respondent lived in a rural environment in 1979, and we include another indicator denoting whether a respondent lived in a Standard Metropolitan Statistical Area (SMSA) in 1979; we do this because living near such an urban hub increases a student's accessibility to college from his or her home.For the Netherlands, we include an indicator denoting the urbanization of the living environment in 1989 that includes five categories: very rural, rural, small town, medium sized town, large city.The geographical availability of college does not pose a major problem in the Netherlands due to the fact that the country is densely populated but has a very small surface area.Finally, we are interested in the influence of the significant others in students' lives: peers and parents.For the US, the influence of peers on a respondent is measured by the educational expectations of his or her closest friend.This measure indicates whether the closest friend of a respondent plans to obtain more than 12 years of education (= if he or she plans to go to college).For the Netherlands, we measure the influence of significant others via a scale of parental encouragement; this scale consists of four items related to talking about school and performance, providing motivation to work hard and giving praise.
The school-relevant characteristics of students are measured with several test scores that indicate the demonstrated abilities of each student.All the NLSY79 respondents participated in the Armed Services Vocational Aptitude Battery (ASVAB) test in 1980.The ASVAB consists of ten different subtests regarding different subject areas.5Similar to the work of Brand and Xie (2010), we residualize the ten test scores on age and race and create a standardized test score with a mean of 0 and a standard deviation of 1.Then, we combine all ten of these test scores into one scale denoting ability (Cronbach's alpha = 0.91).For the Netherlands, we use a shortened version of the Cito test.The Cito test is the entrance test for secondary education in the Netherlands and is taken by students during their final year of primary school (at the age of 11).The Cito test results determine, together with teacher recommendations, the secondary school track that a student will be allocated to.For the VOCL study, a shortened version of the Cito test was taken by all the students during their first year of secondary school in 1989.The Cito test is designed to measure school readiness.In addition to the Cito scores, we use an intelligence test administered during the first year of the VOCL survey as a more general measure of ability that also captures innate and school-independent components.Both of these test scores are standardized for the full VOCL sample.Finally, we use a measure corresponding to the college preparatory curriculum that each respondent received.For both countries, we include an indicator of whether a student is enrolled in a track that includes college preparation.For the US, this indicator is based on self-reported data.In the Netherlands, we rely on information from the VOCL study to determine whether a student is enrolled in havo or vwo.All these variables were measured during the first year of the survey (1979 for the NLSY, 1989 for the VOCL).Exceptions to this rule are the measure of ability in the NLSY, which comes from 1980, and the measure of parental income in the Dutch data, which is taken from 2003 (these are the oldest data that are available on household income in the registers).
College education is measured by a single dichotomous indicator that denotes whether a respondent had obtained a higher education degree by the age of 25-28 (by the year 1990) in the NLSY and by the age of 26/27 (by the year 2003) in the VOCL.We use this variable as our "treatment variable" for determining returns to college education.For the NLSY, we determine whether a respondent had more than 16 years of education (the equivalent of at least a bachelor's degree) in 1990.For the Netherlands, information about higher education degrees is obtained from the SSD for 2003.This information is collected by the CBS from different sources (e.g., tax offices and social security information).Regarding information on higher education, the registers are very reliable; thus, we can assume that all the tertiary degrees are registered.Tertiary degrees are bachelor's degrees or higher that are awarded by research universities or universities of applied sciences (hbo).
Our outcome of interest is the log hourly wage of the respondents at different points in their (early) labor market careers.We use this wage to determine returns to college.We begin measuring social destination four years after the last respondents in our sample have received their high school or college degrees.For the NLSY, we use the respondents' hourly wages in 1994, 1996, 1998, 2000, 2002, 2004, and 2006 when the respondents were roughly between 31 and 44 years old.As the respondents could report up to five current jobs, we take the average hourly wages of all the jobs listed.We convert the original values from cents to dollars.Additionally, we cap the wage variable, only including observations in the range between 1 and 100 dollar and correct the wage observations for inflation across the years we observe (base year 2015).Finally, we transform the variable using the natural logarithm to adjust for skewness.For the Netherlands, we use the respondents' hourly wages during the years from 2007 to 2018, when the respondents were between 30 and 43 years old.The SSD provides the monthly salaries and working hours of all the jobs in which the respondents were insured as employees in the social security system.Therefore, our variables exclude self-mployed individuals and those without regular employment.We calculate the hourly wages of the respondents for each year using monthly earnings and contracted hours.Also for the VOCL, we cap this variable, only including values between 1 and 100 euro per hour and correct wages for inflation (base year 2015).A more detailed description regarding the coding of all the variables is available in Appendix A.

Empirical approach
Our empirical approach consists of two steps.First, we assess the processes of selection into a higher education degree.Second, we examine the (potentially heterogeneous) returns to such a degree.We assess the heterogeneity of returns based on the likelihood of having obtained a higher education degree.Therefore, we first examine selection as being a one-dimensional construct; second, we examine two different dimensions of selection that address school-relevant and school-irrelevant characteristics separately.We estimate selection into and returns to higher education separately for women and men, as labor market patterns still differ considerably between men and women while education patterns have converged (in some cases, women have overtaken men in terms of educational attainment).This is also the standard approach in social mobility research.
We use a set of observable variables to account for selection into a  higher education degree.These observables, which were described in the variable section above, concern both the school-relevant and schoolirrelevant characteristics of the respondents.Using these variables, we estimate the propensity scores of obtaining a college degree for each individual.The estimation of these propensity scores is based on binary logistic regression models that take the possession of a higher education degree (0/1) as their dependent variable.In Equation (1), p is the probability of obtaining a tertiary degree based on all the k selection variables (X).
Predicted probabilities are estimated for each individual based on these regressions.We use all the background variables in the propensity models and include the squared terms of all the continuous variables to account for nonlinear effects.For the final models, we only use the squared terms that were significant (see Karlson (2018) for a similar strategy).
We use these propensity scores to construct the inverse probability of treatment (IPT) weights that adjust our sample for selection in order to estimate the average treatment effect (ATE) in all our subsequent analyses. 6The IPT weights adjust the sample of treated and untreated students based on the array of observable background characteristics that influence the likelihood of obtaining a college degree.We are left with a balanced sample in which both the treated and the untreated group have similar average levels of all these characteristics; they differ only in terms of whether they have a college degree or not.This method will provide use with the ATE of having a college degree if the assumption of ignorability holds.This means that we must assume that the background characteristics that we observe are the only meaningful predictors of a college degree and that any other factors can be ignored.This is obviously a strong assumption in the context of any observational data.Nevertheless, compared to an unadjusted estimation of the college effect, adjusting for selection in this way improves the estimation of the ATE substantially.
Next to determining the average effect of a college degree using propensity-based weights, we are also substantively interested in the propensity of obtaining a college degree, as we want to study heterogeneous returns based on how likely a person is to obtain a college degree in the first place.Therefore, we carry out two sets of analyses.First, we follow the previous research on the topic of heterogeneous returns to higher education (e.g., Brand and Xie, 2010) and treat selection into college as a unidimensional construct. 7For these analyses, we rely on the same propensity score model as we do for the construction of the IPT weights, and we use this propensity as a predictor in our models.Second, we previously argued that selection into college can be separated into at least two meaningful dimensions.Therefore, we examine returns to college based on school-relevant characteristics and returns to college based on school-irrelevant characteristics separately.For these analyses, we construct two separate propensity scores; one of these scores is based only on school-relevant characteristics and the other is based on school-irrelevant factors.The first score is composed of ability and college preparation.The second focuses on personal circumstances such as socio-economic background, geography, family structure and the influence of significant individuals.
As outlined above, these two dimensions are not independent from each other.In particular, school-irrelevant characteristics influence  6 The weights are constructed as follows: The average probability of being treated of the whole sample is divided by the individual propensity of obtaining a college degree for those who actually received treatment.The average probability of not being treated in the whole sample is divided by the individual propensity of not obtaining a college degree for those who did not receive a college degree.
school-relevant factors.Therefore, we examine a specific component of school-relevant characteristics that is independent of school-irrelevant characteristics.In other words, we are interested in the schoolrelevant characteristics of students with similar levels of schoolirrelevant factors.To obtain a measure of school-relevant characteristics, we residualize each school-relevant measure by regressing it on all the school-irrelevant factors.We use the residuals of these regressions as the new measures of the school-relevant characteristics.Then, we estimate the propensity score of the school-relevant characteristics using these residualized measures.The propensity models are displayed in Table 3 for the United States and in Table 4 for the Netherlands.Finally, we are interested in the wage returns to a college degree across the different levels of the propensity score.Wages in the NLSY and in the Dutch registers are observed during different years for each respondent.As we do not expect systematic differences in returns over the life of a respondent, we maximize our available sample by using each year that a wage is available for each respondent as the dependent variable. 8We pool our data to obtain a sample of wage observations nested in individuals.With this sample, we run multilevel random effects models using maximum likelihood estimation.The respondents in this sample are between 30 and 45 years old.We use the respondents' ages when their wages were observed as a control variable in all the models.Age is thereby centered on the youngest age in the data, which is 30 for the Netherlands and 31 for the US.
Table 5 in the results section displays the results for the onedimensional propensity of completing college.Table 6 shows the results for the returns to the school-relevant characteristics and Table 7 shows the results for the returns to the school-irrelevant factors.As shown in Equation ( 2), the first model in each set of analyses only contains the main effects of a college degree and those of the propensity score.This model estimates the average effect of a college degree across all the levels of propensity.
The second model, as shown in Equation (3), includes an interaction term between the respective propensity score and having a college degree, and it shows the heterogeneity of the effect of college across the different levels of the propensity score:9  8 We carry out a robustness check in which we examine age trends in returns to higher education.Overall, this check reveals no systematic patterns across the different ages of the respondents.The results of this check are reported in Appendix B. tional analyses we have explored the patterns of heterogeneous returns using higher order polynomials and bins of the propensity score.The results confirm the conclusion that returns are homogeneous along the propensity score and are available upon request.
Fig. 1 (one dimension) and Fig. 2 (two dimensions) show the marginal effects of a college degree for people with different propensities to obtain such a college degree.
All the models are weighted on the student level based on the inverse probability of treatment as outlined above in order to estimate the effect of a college degree for a sample that is balanced in terms of all the background characteristics.We use the one-dimensional propensitywhich contains all background characteristicsas IPT-weight in all models, also when we investigate two dimensions of propensity.Furthermore, we restrict the data for our models to the area of common support.This means that we only examine the segment of the propensity score for which we have observations in the treatment and the control group; otherwise, we would not be able to identify the effect of a college degree.These areas of common support are shown in Appendix C.

Selection into college: propensity score models
First, we examine selection into college completion.Table 3 shows the related results for the US.Table 4 displays the propensity models for the Netherlands.These tables show the three different logistic regression models that predict the different propensities of completing college (i.e., one dimension, school-relevant characteristics, and school-irrelevant characteristics) for men and women.
In the US, we observe that in the one-dimensional propensity model, students' performance on the ASVAB test and taking college preparatory courses positively influence college completion for both men and women.For men, socioeconomic resources (parental income and education) are positively related to college completion.For women, the effect of parental education assumes a curvilinear shape, while parental income does not have an additional effect once parental education is accounted for.Being Black has a negative effect on college completion for men but not for women.For women, being Hispanic is detrimental to college completion.Family structure and geography do not independently impact college completion.The college plans of friends have a positive influence for both men and women.Overall, the onedimensional propensity model explains 33 percent of the variance in college completion for men and 31 percent of this variance for women.Examining the school-relevant dimension, we see that ASVAB scores and college preparation courses matter for college completion.The schoolrelevant dimension explains 7 percent of the variance for men and 8 percent of the variance for women.10In the school-irrelevant dimension, we see that socioeconomic resources have an impact for both men and women.In this model, family structure is also important.The likelihood of college completion is lower for families with many children, and it is higher for women who are growing up in a two-parent family.Additionally, the college plans of friends have a positive and significant influence on college completion.The school-irrelevant dimension explains 21 percent of the variance in college completion for men and 18 percent of this variance for women.
The same results for the Netherlands are shown in Table 4.The Cito test scores have a positive influence on college completion.This association assumes a curvilinear pattern for both men and women.Intelligence scores do not exert an additional influence once the Cito scores are taken into account.Being placed in a college preparatory track has a strong positive association with college completion.Additionally, socioeconomic resources positively influence college completion in the Netherlands.For men, parental education is the most important factor; for women, also parental income has an independent influence on obtaining a tertiary degree.Race and ethnicity do not impact college completion once SES is controlled.Concerning family structure, twoparent families positively influence the college completion of men; however, two-parent families negatively influence the college completion of women.The number of children in a household, geography and parental encouragement do not impact the likelihood of college completion.The one-dimensional propensity score explains 13 percent of the variance in college completion for men and 18 percent for women; this is a much smaller percentage than was observed in the case of the US.In terms of school-relevant characteristics, we again observe that the Cito score and being in a college preparatory track are important.The variance explained by the school-relevant dimension is 6 percent for men and 9 percent for women (for the residualized measure).Regarding school-irrelevant characteristics, parental encouragement has a negative effect on college completion.The explained variance is rather low for the school-irrelevant dimension, at 5 percent for men and 8 percent for women.

Returns to college: one dimension of selection
In this section, we examine the returns to college for the different levels of likelihood of selection into college.First, we reassess our findings regarding heterogeneous returns across one dimension of the propensity of college completion.The results for both countries and genders are shown in Table 5.All the models include inverse probability of treatment weights.
Model 1 shows the main effect of a college degree while controlling for the propensity of completing college and for the respondents' ages at each observation of their wages.This main effect represents the average effect of a college degree for all the respondents.On average, in the US, men with a college degree earn 36 percent11 more per hour than men without a college degree.For women, the college premium is slightly smaller at 34 percent.On average, in the Netherlands, men with a college degree earn 28 percent more than men without a college degree.The college premium for women is almost the same with 27 percent.
Model 2 includes an interaction term between having a college degree and the propensity score.We are mainly interested in the direction of this interaction effect, as it indicates whether there is a pattern of positive or negative selection.None of the interaction terms are significant, meaning that we do not find evidence for heterogeneous returns to a college degree across the different levels of the propensity score.The respondents who are unlikely to complete college have similar returns to their degrees as those who are likely to complete college.
However, it is interesting to examine the size and direction of these effects even if they are not significant.For men in the US, we find an effect size of 0.10; this means that returns to college do increase some-what with a higher likelihood of college completion.
This tendency can also be observed in Fig. 1, which displays the marginal effects of college completion.For men in the US, we find that returns trend slightly upward with an increasing propensity of completing college.For the other three groups, we see a highly flat line.Overall, despite this slight upward trend for US men, we conclude that returns to a college degree are very homogeneous for both genders and countries.

Returns to college: school-relevant and school-irrelevant characteristics
In this section, we address our main hypotheses about schoolrelevant and school-irrelevant characteristics.The results corresponding to school-relevant characteristics (residualized score) can be seen in Table 6.
Again, Model 1 shows the average college wage premium across the levels of school-relevant characteristics, which is 40 percent for US men and 38 percent for US women.In the Netherlands, this premium is 28 percent for both men and women.
Again, the interaction effects shown in Model 2 are not significant.Nevertheless, we see interesting tendencies when we examine the sizes and directions of the effects.For the US, we observe that the interaction effect for men runs in a positive direction with an effect size of 0.3.For women, however, the direction of the effect is negative (0.18).For the Netherlands, the effects are negative; however, they are rather close to zero.This means that for US men, there is a tendency towards positive selection for school-relevant characteristics, for US women there is a tendency towards negative selection, and, for the Netherlands, returns are highly homogeneous.
Next, we examine the selection dimension of school-irrelevant characteristics shown in Table 7.
Again, the average effect of college is very similar to that of the previous models.For American men, this effect is 39 percent; for American women, it is 38 percent.For Dutch men and women, it is again 28 percent.All the interaction effects in Model 2 are again not significant.All of these interaction terms run in a negative direction and are relatively close to zero.The negative tendency is somewhat stronger for US women and NL men than for the other two models.
To investigate these tendencies more closely, we examine Fig. 2. We see that for the US men, there is a tendency towards positive selection for the school-relevant dimension (green line in upper left panel).For US men with low levels of school-relevant propensity (0.1), the effect of college is 1.36 dollars; for those with high levels of this propensity (0.8), the effect of college is 1.68 dollars.12For US-women there is a tendency towards negative selection for school-relevant characteristics (green line in lower left panel).All other groups show extremely homogeneous returns with lines that are almost completely flat or have a slight tendency to negative selection.
Therefore, we cannot confirm H 1 and H 2 on heterogeneous returns in the US, as the interaction effects are not significant and the effect sizes are close to zero.Only for US men, we find a tendency towards positive selection for school-relevant characteristics which we would have expected.Overall, for the Netherlands, we find that returns to college are strongly homogeneous, as can be observed from the flat lines in the related figure.This confirms H 3.

Discussion and conclusion
In this article, we examined whether individuals who are likely to complete college are also those who benefit most from a degree or whether returns to college would be greater for those who typically do not attend.We discussed several approaches to the study of heterogeneous returns, and we argued that the variation in the results and interpretations on this topic might be related to the ways in which personal circumstances and individual capabilities are accounted for and thereby to how the likelihood to complete college is defined.Based on this, we proposed a new approach that distinguishes between two dimensions of selection into college.One of these dimensions captures social origin as a multifaceted concept that includes not only individuals' socioeconomic positions but also other characteristics of the personal environment such as ethnicity, family composition or geographic location.We called this dimension the school-irrelevant dimension, and we distinguished it from the school-relevant factors (i.e., individual capabilities and college preparedness).We examined returns to the two dimensions of selection separately while controlling for the entire selection process by applying inverse probability of treatment weights.Furthermore, we studied (heterogeneous) returns to these two dimensions for two countries that have different educational systems and labor market structures, namely, the United States and the Netherlands.
In general, we did not find evidence for the existence of heterogeneous returns along our two dimensions, as none of the tested interactions between propensity and college degree were significant.When we employed models with one dimension of selection, as previous research has done, we found a tendency towards positive selection for US men and very homogeneous returns for the other three groups.This is interesting, as it does not confirm the results of the previous studies that found negative selection for the US with the same data but with other modeling strategies.Specifically, this is the case for the work of Brand and Xie (2010).Their study uses stratification on the propensity score to estimate returns to higher education (Austin, 2011;Xie et al., 2012) which requires strong assumptions about the distribution of the observed and unobserved baseline characteristics within the propensity strata and has been criticized by Breen et al. (2015).These authors show that the results of Brand and Xie might not be robust; this conclusion can also be drawn from this paper.Our results do also not show college to be "the great equalizer" as we do not observe the negative interaction effect typically found in studies on the OED-model (Hout, 1984(Hout, , 1988;;Torche, 2011).However, these studies typically restrict themselves to measure personal circumstances in socio-economic terms.Therefore, our results might not be directly comparable to these studies.
In the analyses in which we separated selection into two dimensions, we did not find evidence for heterogeneous returns either.For US-men, there is a tendency towards positive selection for the school-relevant dimension of selection, for US-women this tendency is negative.All other return patterns are strongly homogeneous.In general, the differences across the countries are rather small, and all the returns are rather homogeneous.
In the context of school-irrelevant factors, homogeneous returns mean that the college premium in terms of wages for students who have a low likelihood of completing college is similar to that of students who have a high likelihood of completing college; however, their absolute earnings are still different.Higher education is, therefore, not capable of closing the gaps between students with differing school-irrelevant characteristics.However, college does not increase the wage gap either; rather, school-irrelevant characteristics have approximately the same influence on the wages of college graduates as they do on the wages of those who have not received a college degree.This might be due to the fact that the labor markets for college graduates and the labor markets for those without a college education are meritocratic to a similar extent.Therefore, obtaining a college degree is still beneficial for students who typically do not go to college because of their adverse social environment, as a college degree provides these individuals with the ability to obtain higher absolute wages.This pattern seems to hold for all four groups in our analysis.
For school-relevant characteristics, we observed a tendency towards positive selection for US-men; this means that the school-relevant characteristics of college graduates are more strongly rewarded on the labor market than those of non-college graduates.For US-women there is a tendency towards negative selection, meaning that the return to school-relevant characteristics is lower for college-educated women.For the Netherlands, we did not observe such heterogeneous returns.In the Netherlands, the college graduate labor market seems to be structured similarly to the labor market for high school graduates.In the US, we hypothesized that individuals with college degrees enter a labor market that is more meritocratic and in which school-relevant characteristics are emphasized, while school-irrelevant characteristics are less important (Hout, 2012;Torche, 2011).However, we find that this is only the case for men but not for women.We did not focus on gender differences in this study but future research might want to look into the causes of these differences between men and women in return patterns.One possible explanation could be that we study the age-range in which women typically also face the largest penalties due to childcare responsibilities and these penalties might vary between women with and without a college education.
Examining the likelihood of completing college in terms of the two different dimensions explored (school-relevant and school-irrelevant) provided insight regarding educational sorting and returns.From the school-irrelevant dimension, we learned that social mobility is not attained through college.The school-relevant dimension shows us that there are still some payoffs related to abilities after the possession of a college degree is accounted for; however, these payoffs are equal in graduate and nongraduate labor markets.Employers rely on certificates, but they also reward skills directly.The diverging results of the previous studies on this topic might be connected to the different return patterns of these two dimensions.The studies that defined likelihood in terms of abilities and success probabilities are more likely to find positive selection, while studies that emphasize social origin without controlling for ability might find negative selection instead.
Of course, our study also faces limitations.Our models are based on the assumption that the observable factors that we measure are the only factors that impact selection into having a college degree.Although our data include a rich set of observables in both of the domains, other factors such as social capital or motivation may still have an effect.Moreover, the measures that we had at our disposal may not fully capture the relevant substantive factors.For example, it is difficult to capture ability even with observables such as standardized test scores and IQ measures (Hout, 2012).Although our method accounts for selection in a more elaborate way than many of the existing studies do (e.g., Torche, 2011), caution is warranted when causally interpreting the results.Also concerning outcome measures, our study is limited in that it only studies earnings and not other labor market outcomes such as occupational status, social class or unemployment risks.With earnings we capture an important dimension that has been studied extensively also by previous research.However, for future research, it would be valuable to explore additional dimensions of labor market outcomes.
Furthermore, the use of two country cases is insightful; however, we can only hypothesize about the ways in which the examined differences are connected to institutions, as we can not directly test institutional influences.Therefore, further research should be devoted to investigating the mechanisms behind our results.We have described patterns and suggested interpretations for these results; however, a direct measure of the influences of educational and labor market institutions obtained through studying a larger set of countries would provide a valuable addition to this topic.In addition, one needs to stay very careful in general when making direct comparisons across such a small set of countries using different data sources, samples and cohorts as we do.Nevertheless, it is interesting to explore patterns of heterogeneous returns beyond the US context by showing results side-by-side as we have done in this paper.We believe that our results are insightful for the research on heterogeneous returns to college based on selection, as they study the contributions of two different selection dimensions to educational inequality and to heterogeneous returns to college.

Table 1
Description of data sets.

Table 2
Descriptive statistics by college completion status, gender, and country.
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Table 3
Propensity models predicting a college degree (United States).

Table 4
Propensity models predicting a college degree (Netherlands).

Table 5
Returns to collegeone dimension of propensity.