Fundación de Estudios de Economía Aplicada

Students’ Assessment of Higher Education in Spain by César Alonso-Borrego^* ** Antonio Romero-Medina DOCUMENTO DE TRABAJO 2008-31

Serie Capital Humano y Empleo CÁTEDRA Fedea - Banco Santander

September 2008

Corresponding author. Department of Economics, Universidad Carlos III de Madrid, 28903 Getafe, Spain. Fax: +34-91-6249875. e-mail: cesar.alonso@uc3m.es.

Department of Economics, Universidad Carlos III de Madrid. e-mail: aromero@eco.uc3m.es.

Los Documentos de Trabajo se distribuyen gratuitamente a las Universidades e Instituciones de Investigación que lo solicitan. No obstante están disponibles en texto completo a través de Internet: http://www.fedea.es. These Working Paper are distributed free of charge to University Department and other Research Centres. They are also available through Internet: http://www.fedea.es.

ISSN:1696-750

Jorge Juan, 46 28001 Madrid -España Tel.: +34 914 359 020 Fax: +34 915 779 575 infpub@fedea.es

Studentsíassessment of higher education in Spain

CÈsar Alonso-Borregoy

Antonio Romero-Medinaz

September 25, 2008

Abstract

We explore evidence on the perceived economic value of higher education to college students in terms of their reported expected and shadow wages. Our estimates provide predictions for expected wages that are similar across gender and become closer to actual wages as students approach graduation. This is consistent with an improvement in the quality of student information used to forecast wages. Shadow wages relative to expected wages increase during the academic year for men and are constant for women, which is consistent with the higher reluctance of women to drop out of university. Finally, students with lower socioeconomic background and poor performance exhibit a higher propensity to drop out.

Keywords: university education, subjective valuation, wage expectations, shadow wages, ordered response.

JEL Nos.: I23, J24, J31, C24, C25.

We thank comments from participants at the 2nd International Conference on Economics of Education, Athens, August 2008. We acknowledge research funding from DGI, Spanish Ministry of Education, Grant Nos. SEJ2006-05710/ECON (Örst author) and SEJ2005-06167/ECON (second author). The Örst author thanks hospitality from FEDEA, where part of this research was written.

yCorresponding author. Department of Economics, Universidad Carlos III de Madrid, 28903 Getafe, Spain. Fax: +34-91-6249875. e-mail: cesar.alonso@uc3m.es.

zDepartment of Economics, Universidad Carlos III de Madrid. e-mail: aromero@eco.uc3m.es.

1 Introduction

Spain has experienced a sharp growth in the population share with higher education since the 1980s (San Segundo, 1997). Having started as a country with relatively low educational attainment, the percentage of young people with higher education is currently fairly close to that in the US and is above the OECD average. However, international comparisons suggest that this massive increase in participation in higher education is accompanied by signiÖcant imbalances. In particular, the increase in higher education attainment is primarily observed for university degrees, whereas non-university higher technical education, aimed at skilled blue collar jobs, has been disregarded (see Fina et al., 2000; Petrongolo and San Segundo, 2002, among others). Moreover, there is an excess of long-degree graduates and a lack of short-degree graduates (San Segundo, 2002; Salas Velasco and MartÌn-Cobos Puebla, 2006)¹. These imbalances may decrease the returns on college education in Spain compared to other OECD countries, thus discouraging young people from entering higher education.

This paper contributes to the ongoing debate by using micro data on studentsíselfreported economic value of higher education. In particular, we use a survey of Spanish college students conducted in 2001, 2004 and 2005 to investigate their own monetary valuation of a university degree. We analyze their answers on the wage they expect to earn after completing their degree, as well as the shadow value that they assign to their studies. This unique information allows us to focus on two distinct issues related to the problem of career choice. First, we can explore the reported economic value of a college degree by active college students, conditional on family background and personal and academic characteristics. Second, we can assess to what extent self-reported measures of expected and shadow wages are realistic by comparing them with average actual wages for employees with higher education.

Since the survey wage variables are ordered categorical variables, whereby respondents are o§ered a choice among several monetary intervals, our baseline econometric model consists of a discrete ordered choice model in which the thresholds correspond to known monetary values. Unlike an ordered response model with unknown thresholds, we can identify the scale of estimated parameters and thus obtain predictions of individual wages.

¹We denote licenciaturas and ingeniero superior, which take Öve academic years or more, as long degrees. We denote diplomaturas and ingeniero tÈcnico, which take three or four academic years, as short degrees.

Furthermore, we also check the potential attrition bias in wages and university studies due to non-response, Önding that the reasons for non-response are fairly exogenous with respect to the wage determination models.

We estimate models for both expected and shadow wages, considering two di§erent subsamples according to the time for degree completion. Namely, we consider college students in their Örst and penultimate degree years. Our data set contains information about the degree and academic year for each student, as well as gender, pre-university and college academic performance, and socioeconomic background. We also include individual information on degree choice by each student before entering university, and additional reasons behind their degree choice.

Regarding expected wages, the most recent academic performance of the student appears to be the major determinant. The predictions obtained from the model reveal higher expected wages for students closer to graduation. With respect to shadow wages, our results are in agreement with a simple model of investment in college education. In addition to academic performance, factors related to family characteristics, among others, have a substantial e§ect on shadow wages. Unlike males, we Önd that for females the shadow wage relative to expected wages does not change with degree year, reáecting their higher relative reluctance to drop out of university.

The remainder of the paper is organized as follows. In Section 2 we describe a simple human capital investment model and deÖne the variables of interest to show the economic value of a college education from the point of view of the student. Section 3 outlines the data set, the variables, and alternative model speciÖcations. Sections 4 and 5 present the econometric framework and our estimation results. Section 6 provides some concluding remarks.

2 Theoretical framework

We use a stylized model of human capital accumulation and investment in education that suits the needs of our empirical analysis based on Trostel (2004). For any individual, we assume that her individual wage, W, is proportional to her amount of human capital,

\[H {:} ^ {2}\]

\[W ^ {*} = r H,\tag{1}\]

where is the userís cost of human capital. The amount of accumulated human capital H is assumed to be determined through the following production function:

\[d H _ {t} / d t = \varphi x _ {t} ^ {\alpha} y _ {t} ^ {\gamma} H _ {t} ^ {\delta},\tag{2}\]

where, at time t, x denotes the amount of time invested in human capital, represents those goods used in producing human capital, such as training services, physical capital, etc.; and is a parameter representing individual productivity or capacity. Finally, , and denote the elasticities associated with each of the aforementioned variables. For simplicity, and given that it is irrelevant for our analysis, we disregard the depreciation of human capital. To focus on interior solutions, we impose that

Following Haley (1976), Örst-order conditions for optimal production can be replaced in the production function. Then the previous equation becomes:

\[d H _ {t} / d t = \Phi x _ {t} ^ {\sigma + \gamma} H _ {t} ^ {\delta + \gamma},\tag{3}\]

where

\[\Phi = \varphi (y r / \alpha p) ^ {\gamma},\tag{4}\]

and is the price of Since we are primarily concerned with human capital creation through education, the amount of human capital created is measured in years of education. Assuming that each year of education has the same impact on human capital accumulation over time, and given that x remains constant, the previous equation can be simpliÖed. Without loss of generality, we can then consider so that

\[d H _ {t} / d t = \Phi H _ {t} ^ {\sigma}\tag{5}\]

for , where , i.e., the elasticity of inputs can be accumulated. The equation associated with the production function for human capital is a Bernoulli equation with constant coe¢ cients. Denoting as the total amount of education measured in years, the solution to this equation after years of education is:

²In other contributions, such as Blinder and Weiss (1976) and Rosen (1976), among others, an alternative, but essentially equivalent, deÖnition is proposed, whereby the production technology of human capital is linearly related to wages, although its productivity exhibits a non-linear relationship.

\[H _ {S} = \left\{ \begin{array}{c l} H _ {0} e ^ {\Phi S} & i f \sigma = 1 \\ (H _ {0} ^ {1 - \sigma} + (1 - \sigma) \Phi S) ^ {1 / (1 - \sigma)} & i f \sigma \neq 1, \end{array} \right.\tag{6}\]

where is the stock of human capital before schooling. If individual human capital before and after schooling were observed, the hypothesis that the input elasticity is equal to one could be tested for. In general, a lack of data impedes testing such a hypothesis, which is usually imposed by assumption. Under such conditions, substituting in the relation between wages and human capital, , and taking natural logarithms, we obtain a linearized expression that provides an empirical relation between the logarithm of wages and years of higher education:

\[\ln W ^ {*} = \ln r + \ln H _ {0} + \Phi S.\tag{7}\]

Since human capital before schooling is a function of individual factors, such as abili family and socioeconomic background, some of which are captured by observable factors, , we parameterize as:

\[H _ {0} = \exp (\theta_ {0} + \pmb {\theta} _ {1} ^ {\prime} \mathbf {Z} + v),\tag{8}\]

where v captures individual unobservable factors not captured by Assuming that the userís cost of human capital r is constant, and using i to index individuals, the speciÖcation becomes:

\[\ln W _ {i} ^ {*} = \alpha + \Phi S _ {i} + \pmb {\theta} _ {1} ^ {\prime} \mathbf {Z} _ {i} + v _ {i}.\tag{9}\]

2.1 Expected wages

The equation above, which posits a simple linear relation between observed individual wages and schooling, allows us to obtain the average expected future wages of college students under some additional assumptions. Assuming, without loss of generality, that unobserved individual factors are on average equal to zero, the expected log wage for a level of education S and a given set of observed individual factors equal to is

Moreover, for a university student in the k-th academic year of her college degree, her expected wage after graduation will depend on the information set determining her expectation. In particular,

\[E _ {k} (\ln W ^ {*}) = \alpha_ {k} ^ {e} + \Phi_ {k} ^ {e} S + \pmb {\theta} _ {1 k} ^ {e \prime} \mathbf {Z} + E _ {k} (v),\tag{10}\]

where represents the mathematical expectation, conditional on her information set, and represent the expected returns in the wage equation of the corresponding variables in that information set. Assuming that is equal to zero, then the expected average wage becomes

Therefore, the di§erential between average expected wages and average actual wages arises from the di§erences between the expected and actual returns of each variable,

\[[ E _ {k} (\ln W ^ {*}) - E (\ln W ^ {*}) ] = (\alpha_ {k} ^ {e} - \alpha) + (\Phi_ {k} ^ {e} - \Phi) S + (\pmb {\theta} _ {1 k} ^ {e} - \pmb {\theta} _ {1}) ^ {\prime} \mathbf {Z}.\tag{11}\]

Note that this di§erential ultimately depends on the distribution of information across students. Student information sets are related to the amount and quality of a studentís knowledge about the economic value of her college degree, and to the time until receiving a wage as a graduate, i.e., her prediction horizon. We thus expect that the gap between expected and actual wages would be greatest at the beginning of a university course and would decrease as the student approaches graduation.

2.2 Shadow wages

We deÖne as shadow wage the minimum real wage for which a student would be willing to drop out of university in exchange for a job during her entire labor Decisions to drop out are not only a function of the shadow wage, as dropouts stop bearing the fee and time costs of achieving higher education.

Considering that retirement age occurs during period assuming a discount factor we can formally deÖne the corresponding shadow wage for a student leaving college s years after entering as:

³Given the way in which college students were asked about their shadow wages, it is understood that the discounted real wage will remain constant over time.

\[w ^ {s} = \frac {W _ {s} + \sum_ {t = s + 1} ^ {n} (1 + r) ^ {- (t - s)} W _ {t}}{n - s}.\]

If, instead of the stream of future wages, we consider the di§erence between cumulative wages in a lifetime with and without an investment in human capital we have:

\[v ^ {s} = \frac {G _ {s} + \sum_ {t = s + 1} ^ {n} (1 + r) ^ {- (t - s)} G _ {t}}{n - s},\]

where is the actual value of the investment in human capital G. This value has to be greater than zero and by solving the equation for we can compute the maximum interest rate to be paid for Önancing such human capital investment.

Our model provides two predictions relative to shadow wages. First, if real wages increase with on-the-job experience at a rate that o§sets further education years, the expected wage after graduation must be lower than the shadow wage. Second, as far as the returns to university education are positive, the shadow wage must increase with years of college education.

3 Data

3.1 The survey

The primary source of data is a survey Önanced by the Madrid regional authority and carried out in the academic years 2000/2001, 2003/2004 and 2004/2005. The survey explored attitudes and opinions with regard to the higher education system of young students registered in public universities in the Madrid region. The survey design is based on a nationwide data set produced jointly by the Centro de Investigaciones SociolÛgicas (National Sociological Institute) and the Ministry of Education in 1990, known as ìLos jÛvenes ante la Universidadî(ìYoung people facing college educationî).

The innovation of our data set lies in two unique questions that are central to our research, which refer to wages expected after graduation and shadow wages. Regarding expected wages, each student is asked how much she believes her monthly wage will be after concluding her studies: ìWhat is the monthly wage that you are expecting after graduating?î. The answers provided by students are discretized into Öve ordered categories, in addition to no answer and ìDonít knowî. These categories are: between 450 and 901 euro; between 901 and 1803 euro; between 1803 and 3606 euro; between 3606 and 5409 euro; and more than 5409 euro. With respect to shadow wages, the question is: ìWhat is the minimum monthly wage at which you would leave university in exchange for an indeÖnite contract with that real wage for your whole labor lifetime?î The response categories are the same as for expected wages.

In Table 1, we show the marginal relative frequencies of expected and shadow wages for each wage category in our sample. Expected wages exhibit a remarkable unimodal proÖle, whereby 53 percent of students chose the third category (between 1803 and 3606 euro per month). On the contrary, the sample shadow wages are distributed much more uniformly for all categories above the minimum of 450 euro, although there is a substantial level of right censoring, with 37 percent of students choosing the upper category. Despite these di§erences in the empirical distributions of expected and shadow wages, there is a strong positive rank correlation between the variables, with a Kendall coe¢cient of ordinal correlation of 0:28 and the corresponding p-value below 0:01 percent. Unfortunately, approximately one-third of students provided no answer or declared ìDonít knowî.

Our data set also contains information on gender, academic and personal status, and socioeconomic background for each student. For the latter, there are data on parentsíeducation, their labor market status, and their income. The academic information provides details on secondary studies completed by the respondent, the ranking of alternative university studies considered, university studies actually followed, and college performance. Information on secondary (pre-university) studies includes details such as whether the secondary academic center was public or private (Public secondary), if the science Öeld of specialization was attended (Science secondary), the examination grade needed to access university (Access grade), and whether this examination was passed at the Örst attempt (Access at Örst attempt). In terms of alternatives considered, respondents had to provide a prioritized list of alternative colleges within the Madrid university district and in Spanish universities outside of Madrid considered. We included information on whether the respondent also applied to colleges outside the Madrid university district (External choices) and whether her Örst three choices featured a particular degree that could be chosen in several universities (Same degree) or di§erent degree courses in a particular university (Same university). Data on university studies included details on whether the course was the studentís Örst choice (First choice), a long or a short degree, a Science degree, or a joint degree leading to two university diplomas for two di§erent disciplines.

Information on college performance includes the degree year of the course, whether the student has failed and thus repeated an academic year (Repeater), whether she was granted a scholarship (Grant), and whether she is working (Work) and/or searching for a job.

Descriptive statistics of the main variables are provided in Table 2. Nearly 60 percent of the respondents were women. Concerning family characteristics, approximately 20 percent reported that they belonged to a high-income household. Information on the educational level of parents is collected in eight categories: illiterate, below primary, completed primary, professional high school, lower secondary, complete secondary, short university degree, and long university degree. We Önd that the educational levels of parents are highly correlated: the t-statistic for linear regression of motherís education vs. fatherís education is 28:72, with a Kendall statistic for ordinal correlation of 0:46 and a p-value of less than 0:001 percent. We thus concentrate on the educational level of the fathers, in particular, whether the father has a university degree (University father). The percentage of respondents whose father achieved a university degree (long or short) amounts to 41 percent of the sample.⁴

Nearly 60 percent of the students undertook secondary studies in a public high school, and approximately half followed a science Öeld of specialization in secondary education. In terms of access grade (average examination grade achieved in secondary education, which in our sample was truncated at 50) the minimum score required to enter university was 68 points on average, and 84 percent of the respondent passed the access examination at their Örst attempt. With regard to alternative colleges considered, approximately 22 percent of students also applied elsewhere, 15 percent considered the same degree o§ered in di§erent colleges, and only 7 percent prioritized a particular university.

Approximately 60 percent of the sample students are following courses corresponding to their Örst choice. Long degrees clearly dominate, accounting for 80 percent; of these, approximately 40 percent correspond to science disciplines. The proportion of students following a joint degree is very small. The performance of college students in our sample can be summarized as follows. Less than 20 percent were awarded a grant; nevertheless, it must be noted that grants are awarded for economic reasons if a minimum academic performance is accomplished. Approximately 30 percent of the students have failed and repeated at least one academic year, and one-Öfth of them reported that they are satisÖed with their studies. Finally, nearly 20 percent are also working (including full-time and part-time work).

⁴The remaining parental educational levels correspond to between 10 and 18 percent of respondents, except for the two lower levels, which jointly account for 15 percent of the sample. Compared to the Spanish population as a whole, the educational level of sample fathers is slightly above the average educational level of Spanish parents with children of university age. This same result is observed if we consider maternal education. This bias is coherent with the pervasive intergenerational inertia in educational levels within the same family.

Splitting the sample statistics by gender reveals di§erences in family income; the percentage of students belonging to high-income households is clearly lower for females than for males. However, the major di§erences between men and women are related to academic performance. Concerning pre-university performance, a higher percentage of women passed the access examination at their Örst attempt, and a higher proportion of women are following degrees in colleges that were their Örst choice. Women also seem to perform better at college, with a higher proportion of grants awarded, a lower proportion of repeaters, and a greater proportion reporting satisfaction. This preliminary information thus provides evidence that female students are somewhat di§erent than male students, particularly in terms of academic performance. Nevertheless, the information in Table 2 only allows comparison of sample averages, and the di§erences are not signiÖcant in many cases. Besides, a conditional analysis is needed to provide a proper account of these apparent di§erences.

3.2 Complementary data

We complement the information from our primary data source with the Survey of Wage Structure, carried out by the National Institute of Statistics (INE hereafter, which is the Spanish acronym) to investigate the structure and distribution of wages in Spain for a variety of variables such as age, sex, education level, and region of residence. For comparison with our primary data evidence, we use 2002 wage data.

The average monthly wage for dependent employees aged 20ñ29 years is shown in Table 3. Since this information is widely publicized and easily accessible, it is reasonable to assume that it is part of the information set that university students used when computing their expected wages. Nevertheless, it must be noted that the average wages in this complementary data set are representative of the population that voluntarily decide to work at market wages, and therefore such information is potentially a§ected by two sources of selection bias. The Örst source is related to the decision on labor participation, which di§ers for women and men. In the age range 20ñ29 years, females exhibit a lower participation rate than men. The second source arises from the fact that the Wage Distribution Survey reports wage earnings for dependent employees, and therefore is restricted to those who decide to be wage earners. However, it is not possible to control for these sources of sample selection, since both participation decisions take place after graduation and may thus be conditional on events that take place after the survey. In any case, we use the data in Table 3 as a benchmark to evaluate expected and shadow wages of college students in our sample.

Analysis of the data in Table 3 reveals three remarkable Öndings. First, there is a positive correlation between educational level and earnings. Second, average earnings are greater for men than for women. Third, employees in the Madrid region enjoy earnings above the national average. This is true for all educational levels and both genders, but the di§erential increases with the level of education. Di§erences in the cost of living and in job characteristics (industry, occupation) account for these di§erentials.

Empirical evidence on the positive correlation between education and earnings, irrespective of place of residence and gender, matches one of the major predictions of the theoretical framework in Section 2. This e§ect may partly reáect the fact that individuals who are more able to undertake both academic and professional tasks are more motivated to invest in education, and their return to education may be above average. Our data do not allow us to control for this potential bias; we assume that the distribution of unobserved capabilities of the students interviewed do not di§er from the analogous distribution in the Survey of Wage Structure.

In Table 4 we present the di§erential returns to long university degrees for lower educational levels in the Madrid region. The average wage di§erential between those with a long university degree and those without any university degree is approximately 60 percent. Nevertheless, this di§erential does not capture the average wage di§erential per further year of education in the life cycle for two reasons. First, on average, the greater the years of education for an individual, the higher is his age of entry into the labor market, since many individuals do not enter the labor force until they have completed their studies. Second, university degrees di§er in the number of academic years required for completion, so that some are shorter than four years whereas others may be longer than Öve years. In the upper panel of Table 4, we Önd that the wage di§erential between graduates with a long degree and those with a short degree, is much lower than the di§erential between long-degree graduates and non-graduates. In the lower panel of Table 4, we show the same di§erential returns corrected for the number of years needed to complete each education level. The adjusted returns for long-degree male and female graduates, respectively, are 7:3 and 4:8 percent for those with secondary education, and 10:8 and 9:6 for those with a technical secondary education.

A gender wage di§erential is evident for all educational levels, but it decreases with increasing education level. In more detail, there is a positive di§erential for males that ranges between 15 and 20 percent. Among the potential reasons for the gender gap, we should mention three: pure gender discrimination; the possibility that, with all other things equal, Örm-speciÖc accumulated human capital tends to be lower for women because they are more likely to experience discontinuities in their professional career; and occupational segregation. In the latter case, women are more likely to face restrictions that force them to choose occupations with lower wages in exchange for non-wage compensations such as greater time áexibility.

4 Econometric framework

4.1 Basic model

Our reference speciÖcation is Equation (9) in Section 2, which features the actual wage conditional on the individualís level of education, personal characteristics, and socioeconomic background:

\[\ln W _ {i} ^ {*} = \alpha + \Phi S _ {i} + \pmb {\theta} _ {1} ^ {\prime} Z _ {i} + v _ {i} \qquad (i = 1, \ldots , n).\tag{12}\]

Nevertheless, unlike the objective information provided by actual wages observed for working individuals, we focus on the subjective valuation that the college students reported for their university education. This subjective valuation provides two di§erent values: the expected wage, i.e., the wage that each student expects to earn as an outgoing graduate; and the shadow wage, which is the minimum wage for a labor lifetime job for which the student would be willing to drop out of college without graduating. These data on expected and shadow wages reported by the college students allows us to analyze the value of university education that college students attribute to higher education.

As already mentioned in Section 3, the students surveyed di§ered in their academic and personal information and in their degree year, so that there is individual heterogeneity in their levels of human capital accumulation and other individual characteristics. Such heterogeneity a§ects the individual computation of expected and shadow wages. In particular, with all other things equal, di§erences in the degree year, which reáect the time to completion, a§ect the studentís opportunity cost of education, as well as the amount and quality of her information. These di§erences may thus lead to di§erences in subjective valuation of the same college studies. To account for this, we distinguish among two di§erent groups according to the time for degree completion: college students in their Örst and in their penultimate degree years. Using this breakdown, the years of education for each group can be taken as constant, and therefore will be part of the constant term for each group.

In addition to the variables that characterize socioeconomic background and may be associated with human capital accumulated before higher education, it is also important to account for further individual characteristics. In particular, gender and the academic curriculum during secondary education may have a systematic e§ect on the subjective valuation of wages. Thus, we extend the vector of covariates, denoting it as . In addition to unobservables a§ecting human capital obtained before higher education, there are individual characteristics that are unobserved in the data that a§ect subjective valuations. Therefore, we can write our empirical model as:

\[\ln W _ {i} ^ {*} = \beta^ {\prime} \mathbf {X} _ {i} + u _ {i}.\tag{13}\]

If were observed, appropriate estimates of could be obtained through OLS under certain conditions. However, we have emphasized in Section 3 that we do not fully observe , but a discretized version of it, , that can be deÖned as:

\[W _ {i} = j \text { if } \mu_ {j - 1} < W _ {i} ^ {*} < \mu_ {j} \quad (j = 1, \dots , 5),\tag{14}\]

where the values are known. We can also deÖne indicator variables for

each category as:

\[d _ {i j} = 1 \left(W _ {i} = j\right) = 1 \left(\mu_ {j - 1} < W _ {i} ^ {*} < \mu_ {j}\right) \quad (j = 1, \dots , 5).\tag{15}\]

The censored nature of the observed dependent variable invalidates OLS as an estimation method. We address this problem using the strategy developed for models with multiple ordered responses that has been applied when using contingent-type data as, for example, in Cameron and Quiggin (1994), Cai, Deilami and Train (1998), and Papke (1998). Our empirical model is thus an ordered response model, yet in our case the thresholds determining the di§erent categories are known, so there is no need to estimate them as parameters.

Even though the observed variable is ordinal, knowing the cuto§ points implies that no normalization is required to identify the vector and the likelihood function will generally depend on both and . Maximum likelihood estimation can be carried out after assuming a distribution for . The probability that respondent chooses wage category is:

\[\operatorname * {P r} (W _ {i} = j | X _ {i}) = \operatorname * {P r} (\mu_ {j - 1} < W _ {i} ^ {*} < \mu_ {j})\tag{16}\]

\[= \operatorname * {P r} (\ln \mu_ {j - 1} < \ln W _ {i} ^ {*} < \ln \mu_ {j})\tag{17}\]

\[{ = } { F ( \ln \mu _ { j } - \beta ^ { \prime } \mathbf { X } _ { i } ) - F ( \ln \mu _ { j - 1 } - \beta ^ { \prime } \mathbf { X } _ { i } ) . }\tag{18}\]

Then the log-likelihood takes the form:

\[\ln L (\beta , \sigma) = \sum_ {i = 1} \sum_ {j = 1} d _ {i j} \ln \operatorname * {P r} (W _ {i} = j | \mathbf {X} _ {i}).\]

Given our knowledge of thresholds, we can obtain projections for expected wages and shadow wages as in a standard linear model. Note, in contrast, that if the cuto§ points were not known, the parameter vector would only be identiÖed up to a normalization. In such a case, it is usually assumed that and, therefore the scale of conveys no information.

4.2 Potential selection bias

The fact that a signiÖcant proportion of respondents failed to declare their expected or shadow wages and their university degree leads to a potential sample selection problem (cf. Heckman, 1979). If the unobserved e§ects in the respondentsí wages, , are correlated with random factors a§ecting the probability of answering the wage question in the survey, then using only the subsample of individuals who declare their wages will produce inconsistent estimators. To evaluate the incidence of this potential bias, we analyze a sample selection model in which, in addition to our wage equation, we considere an auxiliary model to account for a respondentís decision to declare her wages and her university course, represented by a binary variable, , that equals 1 if the respondent decides to give an answer and 0 otherwise. We further assume that the respondent decides on whether to declare her wage or not on the basis of a score equation that is a linear function of characteristics of which only some are observed in the data set. In particular,

\[D _ {i} = \mathbf {1} (\boldsymbol {\gamma} ^ {\prime} \mathbf {Z} _ {i} + \varepsilon_ {i} > 0),\tag{19}\]

where 1 ( ) is a binary indicator that equals 1 if the condition in parentheses is true and 0 otherwise; and capture observed and unobserved characteristics determining the decision on whether to declare an answer. The unobserved term is assumed to have a known cumulative distribution that is symmetric around 0, so that the probability that respondent i declares her wage is .

To account for potential selection bias, we reparameterize Equation (13) as:

\[\ln W _ {i} ^ {*} = \beta^ {\prime} \mathbf {X} _ {i} + \rho \varepsilon_ {i} + \zeta_ {i},\tag{20}\]

where represents correlation between the unobserved terms associated with selection Equation and wage Equation , with . Under this new parameterization, we assume an orthogonal decomposition of the unobserved part of the wage equation in two terms, one that is perfectly correlated with the unobserved part of the binary decision on whether to declare a wage value, and an independent random error. The probability that respondent i chooses category can then be written as:

\[\operatorname * {P r} (W _ {i} = j | \mathbf {X} _ {i}, \varepsilon_ {i}) = \operatorname * {P r} (\mu_ {j - 1} < W _ {i} ^ {*} < \mu_ {j})\tag{21}\]

\[= \operatorname * {P r} (\ln \mu_ {j - 1} < \ln W _ {i} ^ {*} < \ln \mu_ {j})\tag{22}\]

\[{ = } { F ( \ln \mu _ { j } - \beta ^ { \prime } \mathbf { X } _ { i } - \sigma _ { \varepsilon } \varepsilon _ { i } ) - F ( \ln \mu _ { j - 1 } - \beta ^ { \prime } \mathbf { X } _ { i } - \sigma _ { \varepsilon } \varepsilon _ { i } ) . }\tag{23}\]

A non-signiÖcant estimate of would imply that, with regard to the wage equation model, the sample selection associated with declaration of a wage value or not is exogenous. In such a case, we could estimate the wage equation by ignoring sample selection at no consistency cost. We have estimated a sample selection ordered probit model by maximum likelihood using the subroutines written for Stata by Miranda and Rabe-Hesketh (2006). Unfortunately, estimation of this type of model is computationally very demanding. Besides, concavity of the likelihood function is not guaranteed, so that convergence cannot be achieved in the presence of a moderately low number of covariates. Thus, we have estimated simpliÖed versions of our wage speciÖcations with sample selection.

In either case, our estimates (not reported here) do not provide evidence against the null hypothesis that sample selection was exogenous. This result suggests that conditioning on the subsample of students with non-missing expected wage values does not bias our estimates. Therefore, we can proceed to estimate the expected wage equation using such a subsample without controlling for sample selection. We thus estimated our speciÖcations for expected and shadow wages disregarding the potential attrition bias due to non-response for wages and university studies.

5 Results

In this section, we analyze the valuation of university studies by college students in the Madrid region as measured by their expected and shadow wages. Our estimates can be subsequently used to compute individual predictions of both expected and shadow wages for comparison with average actual wages for graduates working in Spain and in Madrid.

It must be recalled that values reported for expected and shadow wages represent subjective valuations. In the case of expected wages, this means that interpretation of the e§ects of the conditioning variables is unclear. Such e§ects combine the ináuence of these variables on the potential actual wage, on the one hand, and the information quality used in computing wage expectations, on the other.

Regarding the shadow wage, we are concerned with the extent to which family background, academic performance, and the degree year, among other things, a§ect the income required to prompt a student to drop out of university. Analysis of the shadow wage is of double interest. First, we can learn about the permanent income predicted by college students after entering the labor market as graduates, and how such permanent income a§ects their degree choice. Second, given the studentsíexpectations about their permanent incomeó and their expected wageó after graduation, we can assess whether their estimates of future economic prospects are realistic compared to actual wages.

5.1 Expected wages and university education

To account for the degree year of the respondents, we estimate separately for two di§erent subsamples: Örst degree year and penultimate degree year. We would expect the e§ects of the conditioning variables to di§er very much for these two particular groups, which correspond to extreme cases of the time to graduation. Namely, we would expect students closer to completion to have much lower uncertainty about their academic prospects, as well as a better knowledge of their job market prospects after graduation.

Expected wages are censored into Öve wage categories, with the highest category being unbounded to the right. Given that we observe wage thresholds, the scale of the parameters is identiÖed. Thus, the variance of the error term can be estimated, together with the remaining parameters of interest, by maximum likelihood. Moreover, although both the ordered probit and pointwise censored models are consistently estimated by maximum likelihood, the latter is more e¢cient as it exploits the information available on monetary thresholds in the questionnaire.⁵

The maximum likelihood estimates for expected wages for students in their Örst year and penultimate year are reported in Tables 5 and 6, respectively. In each case, we report unrestricted estimates in the Örst column, and we excluded non-signiÖcant covariates in the last two columns, showing our preferred estimates in the last column. We concentrate our comments on this Önal speciÖcation. The model adjustment is reasonably good for the two student groups. Given that we introduced di§erent interactions related to the type of university course (Long degree, Science degree, and Long degree in Science), the reference group corresponds to short degrees in non-science disciplines.

⁵An important practical advantage of exploiting wage thresholds by means of the pointwise censored model is that we do not need further assumptions about the distribution of the right tail to compute individual expected wages. More precisely, in an ordered probit in which the information on threshold values is not exploited, we must introduce an additional assumption for the right tail of the wage distribution (for declared expected monthly wages above 5409 euro). Using results from the ordered probit estimates, we Önd that predicted individual expected wages are very sensitive to this additional assumption.

Most estimated coe¢ cients in Tables 5 and 6, when signiÖcant, show similar signs, except for some qualiÖcations that are detailed below.

Most of the pre-university variables, particularly those related to access grade as a measure of academic performance shortly before university entrance, seem to be relevant in determining the expected wages of Örst-year college students. Given the parameter values, the net e§ect of access grade is positive, but is more intense for students who passed the access examination at their Örst attempt. These variables are non-signiÖcant for students in later degree years, as observed in Table 6. For this student group, preuniversity performance loses relevance in favor of university performance.

The e§ect of gender is negative, although it is not signiÖcant for Örst-year students. This e§ect is slightly positive for later-year female students in science disciplines.

Among family background variables, the high-income dummy is signiÖcant and negative for Örst-year students pursuing short degrees, and is positive but quantitatively smaller for long-degree students. This result is reversed for later-year students. A university graduate father has a positive e§ect, and is clearly signiÖcant for Örst-year students.

Concerning academic performance (as measured through the variables Repeat, Grant, SatisÖed) in university, signiÖcant e§ects are only observed for long-degree students in their penultimate year, with no e§ect for Örst-year students. Long-degree students in non-science disciplines who have repeated declared lower expected wages. This negative e§ect was not observed for long-degree science students. The same is true for students who reported satisfaction with their college studies. Award of a scholarship was eliminated from the Önal speciÖcation owing to its lack of signiÖcance.

Finally, as expected, variables without direct ináuence on the amount of human capital acquired by the student, such as the reason for choosing a university course, are not relevant in the determination of expected wages.

In Table 7, we use our preferred expected wage estimates from Tables 5 and 6 to predict student expected wages. We Önd that the expected wages for any degree year group are greater than average actual wages for graduate workers aged 20ñ29 years in Spain, and even in the Madrid region, where wages are higher. Hence, wage expectations tend to be greater than actual wages; in other words, college students tend to overestimate their potential wages. In addition to individual quality e§ects, the individual covariates also reáect a studentís ability to compute expected wages.

Predictions of expected wages are higher for Örst-year students than for penultimateyear students. Expected wages for Örst-year women are, on average, lower than those for men in the same group. The fact that expected wages, on average, move closer to actual wages for graduates demonstrates that the formulation of expectations improves as students approach graduation. Finally, the percentage gap is much higher for women than for men, reáecting the wide wage di§erential by gender. In the case of male students, the di§erential is substantial for those in their Örst year and negligible for students closer to completion. On the contrary, the gap between expected and actual wages for female students remains large, even in teir penultimate year, and is smaller for long degrees than for short ones.

The overestimation of expected wages with respect to actual wages for working graduates aged 20ñ29 years is actually greater than the di§erence reáected in Table 7, because the individuals in our sample are not strictly comparable with the sample for which average actual wages were computed, which is restricted to graduates aged 20ñ29 years who have decided to work and have found a job. In contrast, our sample comprises students who have not yet graduated. For those who graduate, a percentage will eventually not work, either because they decide not to enter the labor market or because they will not Önd a job. Moreover, a proportion of them will drop out of college before graduation. Therefore, it is possible that the apparent improvement in the formulation of expectations with increasing degree years merely reáects sample selection of students who are much more likely to work in jobs that require a university education.

5.2 Shadow wages and university education

We now analyze the determinants of lifetime labor income that university students would accept in exchange for leaving university before graduation. It is worth mentioning that the fraction of students not declaring a shadow wage is greater than that not declaring an expected wage.

In Tables 8 and 9, we present estimates of the pointwise censored model for Örst- and later-year students. Our empirical strategy closely follows the previous one for expected wages. Again, the model adjustment is appropriate.

The e§ect of gender is modest for Örst-year students and negligible for later-year students. Therefore, any substantial di§erence in the prediction of shadow wages by gender would arise because of di§erences among individuals. Among the family background variables, the high-income dummy is positive and signiÖcant for the two student groups. However, this e§ect is minor for students in science disciplines.

Fatherís education has a positive and signiÖcant e§ect for students in their Örst and penultimate degree years. This positive e§ect on expected wages is in accordance with the positive e§ect of parental education on potential wages. Besides, we would expect the quality of student information used to formulate wage expectations to improve with fatherís higher education, and therefore students with highly educated parents are less likely to overestimate their expected wage relative to actual wages. These two e§ects tend to complement each other. The e§ect of fatherís education is even higher for students closer to completion.

Concerning pre-university academic performance, grade achieved in the access examination, as a positive indicator of student quality, has a positive e§ect for Örst-year students, and failure to pass this examination at the Örst attempt has a signiÖcant and negative impact for all students. Other academic performance variables, such as science specialization in pre-university education, are non-signiÖcant for later-year students. However, giving priority to the same degree in di§erent universities has a negative and signiÖcant impact in both groups. With regard to university academic performance, having repeated a university year has a negative and signiÖcant impact for all students.

Finally, unlike the results for expected wages, the reasons behind degree choice have an impact on shadow wage determination for Örst-year students. Family tradition and Parental ináuence exert positive and negative e§ects, respectively. For later-year students, only college proximity has a negative e§ect on shadow wages.

In Table 10, we report the average predicted shadow wages. Shadow wages are, on average, greater for Örst-year female students and smaller for later-year female students. When comparing average shadow wages with average actual wages for working graduates aged 20ñ29 years, the relative shadow wage is much greater for women. In Table 11, we report the percentage ratio of shadow wages to expected wages. The pattern is remarkably di§erent by gender, increasing for men and constant for women, in terms of the degree year. The relative shadow wage for females equals, on average, the highest relative shadow wage reported by men. Therefore, women are much more reluctant to drop out of university. Alba-Ramirez and San Segundo (1995) found that whereas the return to primary and secondary education in Spain is lower from women than for men, the relative return to college education is higher for women. Hence, although female graduates are, on average, worse paid than males, women enjoy a higher relative di§erential return to university education compared to lower educational levels. This result suggests that investment in university education is more attractive for women than for men. It is also consistent with the fact that more women than men have registered for university in Spain since 1986.

5.3 Dropout propensity

According to our model, a student who reports a shadow wage lower than her expected wage believes that her wage proÖle throughout her working life as a graduate will not compensate for the cost of Önishing her studies. Under these conditions, the student is prompted to abandon her studies. In Table 12, we report the number of individuals in this situation in our sample, broken down by degree year. A decreasing pattern for dropout propensity is evident for long degrees. However, the pattern is fairly constant for short-degree studies, which are more focused on technical jobs.

To analyze the factors that ináuence this behavior, we used a probit model in which a declared shadow wage lower than the declared expected wage was the dependent variable. The results are presented in Table 13. The Örst column presents results for students excluding those in their last year. In the second and third columns, we report results for students in their Örst and penultimate year, respectively. The proÖle that describes potential dropout can be summarized as a student with poor pre-university and university performance, already a part-time student, with relatively low parental human capital and whose parents ináuenced her college and degree choice.

These Öndings have policy implications. Wage distribution by education level in Spain is relatively narrow, so that the return to higher education is small relative to other OECD countries. In fact, the dropout rate in Spain is remarkably high, which is mostly attributed to failure of the educational system. Our analysis indicates an alternative explanation. There are economic reasons related to observed variables that can explain, at least in part, the dropout propensity in Spanish universities.

6 Concluding remarks

This paper deals with the economic value of university education measured in terms of subjective valuations by college students. We used a microeconomic data set previously exploited by Alonso-Borrego et al. (2007) that includes academic, personal and familial characteristics, as well as expected and shadow wages. Since declared wages were discretized into Öve categories, OLS estimation was inappropriate. However, we used information on wage thresholds to obtain more e¢cient estimates than those provided by a standard ordered probit model.

Di§erences in time to completion may a§ect subjective valuation of studies by students. Such di§erences may a§ect individual processing of relevant information. For this reason, we considered two di§erent subsamples, Örst-year and penultimate-year students.

We found that academic performance was the main determinant of expected wages. There were also di§erences depending on the student degree year, so that expected wages depended on pre-university academic performance for Örst-year students and on college performance for later-year students. Comparison of predicted expected wages with actual wages for young working graduates revealed a positive gap on average. This gap tended to narrow for later degree years. This result reáects the fact that expectations became more realistic as students approached graduation.

In relation to shadow wages, the results are consistent with our theoretical framework. In particular, positive academic performance and family background tend to increase shadow wages. The shadow wage predictions obtained from our estimations are also consistent with the theory. In particular, the precision in predicting shadow wages improves for later-year students. Interestingly, women show a steady pattern in the ratio of shadow to expected wages. Therefore, unlike men, their relative shadow wage is very high from

the start of their university degree course.

We used a rich information set that included degree characteristics in terms of discipline and length, which confers robustness to our results.

References

1. [1] Alba-Ramirez, A. and M.J. San Segundo (1995), The returns to education in Spain. Economics of Education Review 14(2): 155ñ166.
2. [2] Alonso-Borrego, C., R. Mora and A. Romero-Medina (2007), Una valoraciÛn de la enseÒanza superior a partir de los salarios esperados y los salarios sombra de los estudiantes universitarios. Cuadernos EconÛmicos de ICE 74: 11ñ38.
3. [3] Blinder, A.S. and Y. Weiss (1976), Human capital and labor supply: A synthesis. Journal of Political Economy 84: 449ñ72.
4. [4] Cameron, T.A. and J. Quiggin (1994), Estimation using contingent valuation data from a dichotomous choice with follow-up questionnaire. Journal of Environmental Economics and Management 27(3): 218ñ234.
5. [5] Cai, Y., I. Deilami and K. Train (1998), Customer retention in a competitive power market: Analysis of a ídouble-bounded plus follow-upsí questionnaire. The Energy Journal 19(2): 191ñ215.
6. [6] Fina, L., C. GarcÌa Serrano, F. MaÒÈ and L. Toharia (2000), Cambio ocupacional y necesidades educativas de la economÌa espaÒola. In: F. S·ez (ed.): ìFormaciÛn y empleoî. Madrid, FundaciÛn Argentaria, 2000, pp. 47ñ154.
7. [7] Haley, W.J. (1976), Estimation of the earnings proÖle from optimal human capital accumulation. Econometrica 44: 1223ñ1238.
8. [8] Heckman, J. J. (1979), ìSample Selection Bias as a SpeciÖcation Errorî. Econometrica 47(1), 153-161.
9. [9] Miranda, A. and S. Rabe-Hesketh (2006), Maximum likelihood estimation of endogenous switching and sample selection models for binary, count, and ordinal variables. The Stata Journal 6(3): 285ñ308.
10. [10] Papke, L.E. (1998), How are participants directing their participant-directed individual account pension plans? American Economic Review 88: 212ñ216.
11. [11] Petrongolo, B. and M. J. San Segundo (2002), Staying-on at school at sixteen. The impact of labor market conditions in Spain. Economics of Education Review 21(4): 353ñ365.
12. [12] Rosen, S. (1976), A theory of life earnings. Journal of Political Economy 54: S45ñ67.
13. [13] Salas Velasco, M. and M. MartÌn-Cobos Puebla (2006), La demanda de educaciÛn superior: Un an·lisis microeconÛmico con datos de corte transversal. Revista de EducaciÛn 339: 637ñ660.
14. [14] San Segundo, M.J. (1997), EducaciÛn e Ingresos en el Mercado de Trabajo EspaÒol. Cuadernos EconÛmicos de InformaciÛn Comercial EspaÒola, n˙mero 63, pp. 105ñ123.
15. [15] San Segundo, M.J. (2002), El sistema universitario EspaÒol en una perspectiva internacional. In: Hern·ndez, J. (ed.): ìLa Universidad EspaÒola en Cifrasî, CRUE, Madrid.
16. [16] Trostel, P. (2004), Returns to scale in producing human capital from schooling. Oxford Economic Papers 56: 461ñ484.

Table 1 Monthly expected and shadow wages of Madrid college students Relative frequency (%)

Table 2 Main variables and descriptive statistics

Source: Young people towards university, 2001 2004 and 2005. All the variables are binary except for Access grade, which ranges between 50 and 100.

Table 3 Monthly average earnings by educational level completed Employees aged 20ñ29 years

Source: Survey of wage structure, 2002 (INE)

Table 4 Monthly average earnings by educational level completed in Madrid relative (%) to long-degree graduates

Source: Survey of wage structure, 2002 (INE) and our own calculations.

Table 5 Expected wage for Örst-year college students Pointwise censored model without selection

Of the 371 observations, 68 were right-censored. * ** and denote signiÖcance at 20, 10 and 5 percent, respectively. ,

Table 6

Of the 279 observations, 15 were right-censored. See notes to Table 5.

Table 7 Monthly average expected wages for college students in Madrid by degree year

Percentage di§erence between average expected wage and

Percentage di§erence between average expected wage and

Source: Calculated from ìYoung people facing universityî, 2001, 2004 and 2005 and Survey of wage structure.

Of the 360 observations, 156 were right-censored. See notes to Table 5.

Shadow wage for penultimate-year college students

Of the 256 observations, 98 were right-censored

Table 10 Monthly average shadow wages for college students in Madrid by degree years

Percentage di§erence between average shadow wage and Spanish average actual wages for working graduates

Percentage di§erence between average shadow wage and Madrid average actual wages for working graduates

Source: Calculated from ìYoung people facing universityî, 2001, 2004 and 2005 and Survey of wage structure.

based on model predictions (%)

Table 11 Shadow wage relative to expected wage

Table 12 Dropout propensity: Shadow wage lower than expected wage

Percentages are in parentheses.

Dropout propensity: Shadow wage lower than expected wage

See Notes to Table 5.

1. 2008-31: “Students’ assessment of higher education in Spain”, César Alonso-Borrego”, Antonio Romero-Medina.
2. 2008-30: “Body image and food disorders: Evidence from a sample of European women”, Joan Costa-Font y Mireia Jofre-Bonet.
3. 2008-29: “Aggregation and Dissemination of Information in Experimental Asset Markets in the Presence of a Manipulator”, HelenaVeiga y Marc Vorsatz.
4. 2008-28: “The Measurement of Consensus: An Axiomatic Analysis”, Jorge Alcalde-Unzu and Marc Vorsatz.
5. 2008-27: “Macroeconomic Consequences of International Commodity Price Shocks”, Claudia S. Gómez-López y Luis A. Puch.
6. 2008-26: “The Effect of Short–Selling on the Aggregation of Information in an Experimental Asset Market”, Helena Veiga y Marc Vorsatz.
7. 2008-25: “Adult height and childhood disease”, Carlos Bozzoli, Angus Deaton y Climent Quintana-Domeque.
8. 2008-24: “On Gender Gaps and Self-Fulfilling Expectations: Theory, Policies and Some Empirical Evidence” Sara de la Rica, Juan J. Dolado y Cecilia García-Peñalosa.
9. 2008-23: “Fuel Consumption, Economic Determinants and Policy Implications for Road Transport in Spain”, Rosa M. González-Marrero, Rosa M. Lorenzo-Alegría y Gustavo A. Marrero.
10. 2008-22: “Trade-off between formal and informal care in Spain”, Sergi Jiménez-Martín y Cristina Vilaplana Prieto.
11. 2008-21: “The Rise in Obesity Across the Atlantic: An Economic Perspective”, Giorgio Brunello, Pierre-Carl Michaud y Anna Sanz-de-Galdeano.
12. 2008-20: “Multimarket Contact in Pharmaceutical Markets”, Javier Coronado, Sergi Jiménez-Martín y Pedro L. Marín.
13. 2008-19: “Financial Analysts impact on Stock Volatility. A Study on the Pharmaceutical Sector”, Clara I. Gonzalez y Ricardo Gimeno.
14. 2007-18: “The Determinants of Pricing in Pharmaceuticals: are U.S. prices really so high?”, Antonio Cabrales y Sergi Jiménez-Martín.
15. 2008-17: “Does Immigration Raise Natives’ Income? National and Regional Evidence from Spain”, Catalina Amuedo-Dorantes y Sara de la Rica.
16. 2008-16: “Assessing the Argument for Specialized Courts: Evidence from Family Courts in Spain”, Nuno Garoupa, Natalia Jorgensen y Pablo Vázquez.
17. 2008-15: “Do Men and Women-Economists Choose the Same Research Fields?: Evidence from Top-50 Departments”, Juan J. Dolado, Florentino Felgueroso y Miguel Almunia.
18. 2008-14: “Demographic change, pension reform and redistribution in Spain”, Alfonso R. Sánchez Martín y Virginia Sánchez Marcos.
19. 2008-13: “Exploring the Pathways of Inequality in Health, Access and Financing in Decentralised Spain”, Joan Costa-Font y Joan Gil.
20. 2008-12: “Hybrid Consumption Paths in the Attribute Space: A Model and Application with Scanner Data”, Sergi Jiménez Martín y Antonio Ladron-de-Guevara Martinez.
21. 2008-11: “Decomposing Body Mass Index Gaps Between Mediterranean Countries: A Counterfactual Quantile Regression Analysis”, Joan Costa-Font, Daniele Fabbri y Joan Gil.
22. 2008-10: “How Well do Individuals Predicttheir Impact on Regional Employment How Well do Individuals Predict”, Hugo Benítez-Silva, Selcuk Eren, Frank Heiland y Sergi Jiménez-Martín.
23. 2008-09: “From Income to Consumption: Measuring Households Partial Insurance”, José María Casado García.
24. 2008-07: “Differential Grading Standards and University Funding: Evidence from Italy”, Manuel Bagues, Mauro Sylos Labini y Natalia Zinovyeva.
25. 2008-05: “Gatekeeping versus Direct-Access when Patient Information Matters”, Paula González.
26. 2008-04: “'The Child is Father of the Man:' by Implications for the Demographic Transition”, David de la Croix y Omar Licandro.
27. 2008-03: “Trade Liberalization, Competition and Growth”, Omar Licandro y Antonio Navas-Ruiz.
28. 2008-02: “The Costs of Kyoto Adjustments for Spanish Households”, Xavier Labandeira, José M. Labeaga y Miguel Rodríguez.
29. 2008-01: “Institutions, Health Shocks and Labour Outcomes Across Europe”, Pilar García Gómez.
30. 2007-39: “Wide and Narrow Approaches in Climate Change Policies: The Case of Spain”, Xavier Labandeira and Miguel Rodríguez.