The influence of extracurricular activitieson salary : should a student participate in leisure-related activities or study-related activities

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The influence of extracurricular activities

on salary

Should a student participate in leisure-related activities or

study-related activities?

J.C.D. Chin

Student number: 5870186

Date of final version: December 30, 2015 Master’s programme: Econometrics

Specialisation: Free track

Supervisor: dr. J.C.M. Van Ophem Second reader: dr. M.J.G. Bun

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Introduction

In recent years the higher education system in the Netherlands has faced many reforms. Most of these measures are taken to reduce costs of higher education by stimulating students to graduate more quickly, for example: replacing student funding by a borrowing system (sociaal leenstelsel ) and abolishing subsidies for tuition of second bachelor or master. Students are asked to pay a greater part of their study costs themselves and are punished financially when they take too long to graduate. The effect of these measures is that students become more devoted to their study-program, but the downside is that they have less room to get involved in other activities. However, past research in the United States has shown that participation in these activities is profitable for students and their development (Massoni, 2011). Students themselves are also aware that the possibilities for development besides studying get more and more limited. More recently, this awareness was one of the main drivers behind a proposal to let students pay per course instead of an annual tuition (Wirken et al.,2015). This would provide students with more room to compose their own study-program with room for extracurricular activities. However, as with other attempts to alleviate the pressure of students, this proposal is not likely to be executed. Moreover, students face increased pressure due to increased competition in the job market after graduation. More and more people have access to higher education, which decreases the value of formal credentials (Collins, 2002). So students need extracurricular activities to distinguish themselves from the crowd, and simultaneously they need to study faster. Students simply have to deal with this situation and consider their time and financial resources more carefully.

In this thesis, we analyze the influence of extracurricular activities. We quantify the value of participating in extracurricular activities and thus giving students a broader perspective on the consequence of the current reforms. Therefore, the main question of this thesis is: ”What is the effect of extracurricular activities during the higher educational career on future salary?”. We will approach this question from a student’s standpoint. We will investigate what it yields to students when they choose to participate in extracurricular activities. Since extracurricular activities are still a broad concept, we will use the categorization of Tchibozo (2007) to dis-tinguish two types of extracurricular activity: leisure-related and study-related. We emphasize

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CHAPTER 1. INTRODUCTION 2

that we focus on the effects on an individual level and thus not approach this question from a regulatory standpoint, at which we would measure the value for society when giving students more room to participate in extracurricular activities. For this thesis we have used data from

SEO (2015), a Dutch institute for economic research, which distributes a survey under gradu-ates in the Netherlands every year. In order to examine the effects we have applied two types of selection models on this data set. We have applied a parametric model inspired by the model ofHeckman(1979) and a semiparametric model inspired by the model ofCosslett (1991). Both models are estimated in two stages. Furthermore, we have altered both models to be suitable for this particular situation. Moreover, in contrast to what is conventional in literature, we added a second selection variable in the outcome equation of both models.

From our results, we find evidence that the use of selection models are appropriate here, that is, the participation decision is indeed endogenous. By comparing the conditional selection corrections we conclude that the parametric model of Heckman may be too restrictive and therefore prefer the Cosslett model. In both selection models we find that the participation in extracurricular activities positively affects salary. The upward effects are somewhat larger for leisure-related activities than for study-related activities in Heckman’s model, but this cannot be said for the Cosslett’s model. In Cosslett’s model with one selection variable we find that study-related activities have a larger effect. For the two selection variables model we find that the estimated effects are not significantly different. We conclude that we find statistical evi-dence for positive effects of both types of activity. We also conclude that the results are not unequivocal on which type has the largest effect.

This contribution of this thesis is two-fold. To our knowledge this thesis is the first to ex-amine extracurricular activities with a selection model. All other researches are based on linear regression, logistic models or instrumental variables models. Secondly, as far as we know, this thesis is the first to apply a selection model with two selection dummy variables. Selection mod-els are extensively discussed in literature, but all of these modmod-els incorporate only one selection variable. This thesis enriches literature by including a second selection dummy. We intend this thesis to be the starting point for selection models with two selection variables.

The remainder of this thesis is organized as follows. In chapter 2 we provide with some back-ground information on the concept of extracurricular activities. We discuss the definition of this concept, we discuss the examined effects and the methods which were used in examination of these effects. In chapter 3 we give insights in selection models and we discuss the models used for this thesis. Inchapter 4we discuss the data set used in this thesis. Inchapter 5 we discuss the results of our model. And we conclude this thesis with chapter 6 in which we give the conclusion, discuss limitations of our model and give some opportunities for future research.

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Literature overview

In this chapter we will discuss previous studies on extracurricular activities. We will define the concept of extracurricular activity. Additionally, we will discuss the effects on an academic level, a personal level and on a job market level. Furthermore, to put all these effects in perspective, we will give some insights in the differences between the Netherlands and the United States on which most researches on this topic are executed. This chapter concludes with an overview of the common used methods in researches on extracurricular activities.

2.1 Definition of extracurricular activities

Extracurricular activities were introduced in the United States by the introduction of literacy clubs at Harvard University and Yale University in the 19th century. These clubs are the first known extracurricular activities (Massoni,2011). After that, more and more types of activities were added. Several American schools added academic clubs, school clubs or athletic clubs. Today, schools and universities are surrounded by different types of activities for students with different interests.

All these activities can be seen as extracurricular activities, which Valentine et al. (2002) defined as activities which take place in the context of an educational institution and its envi-ronment. These distinguish themselves from regular curricular activities in three ways. First, these extracurricular activities are optional. Students are not obliged to participate in them. Second, extracurricular activities are not graded and are thus not listed on any certificate re-ceived after graduation. Third, the activities take place outside regular study hours (Mahoney and Cairns,1997).

Because of the great variety of activities, researchers have made an attempt to categorize extracurricular activities. Valentine et al. (2002) distinguished five categories: study-related activities, sports, cultural clubs, social or political activities and unstructured activities. An-other categorization is applied by Tchibozo (2007), who distinguished two types of activities: employment activities, and leisure or social activities. In this thesis, we apply a modified form of this categorization. We also distinguish two types of activity. We adopt the definition of

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CHAPTER 2. LITERATURE OVERVIEW 4

leisure or social activities and abbreviate this to leisure-related activities. However, we do not include employment activities due to the lack of data. Instead we define study-related activities, which are extracurricular activities which have to do with study affairs. This will be further explained inchapter 4.

2.2 Effects of extracurricular activities

Effects on learning

Although extracurricular activities consume time, which could also be allocated to studying, participation in these activities is associated with multiple positive effects on education ( Mas-soni, 2011). All types of extracurricular activities can induce an increase in the engagement of students. Engagement is considered to be one of the most important aspects for students. Students develop a positive attitude towards learning and enlarge their interest in studying (Marks,2000). Furthermore, they invest more time and energy in education which causes lower drop-out rates (Mahoney and Cairns,1997) and results in higher grades (Marsh,1992). These enhancing effects on academic performance is estimated to be larger than the effects resulting from paid student jobs (Cooper et al.,1999).

Effects on personal development

Besides positive effects on learning, the participation in extracurricular activities also con-tributes to a better personal development. Participants in extracurricular activities are asso-ciated with a lower probability of showing risky behavior. The probability of excessive drug or alcohol use is lower than for non-participants (Eccles and Barber, 1999). Furthermore, ex-tracurricular activities provide room to develop better self-esteem (Holland and Andre,1987). Students become more aware of their capacities and participation is also related with a devel-opment of individual and group responsibilities (Finn and Voelkl,1993). This is also reflected in the positive effects on education, which we discussed earlier. Furthermore, extracurricular activities offer the possibility to develop social norms (Willems,1967), which will also be useful in a job setting.

Extracurricular activities are also studied in the context of for example college decision making (DesJardins et al.,1999) and generosity of alumni (Tucker,2004). Since this does not bear any relevance for the present research, these potential effects will not be discussed.

Effects on the job market

Compared to other potential effects of extracurricular activities, effects on the job market have generally been ignored. Due to the increased number of graduates who have participated in extracurricular activities, the number of researches on this topic has been increasing in recent years and this thesis also contributes to this topic. The effects have been studied in various

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countries. Tchibozo (2007) has analyzed transition to the job market in the United Kingdom. He found that extracurricular experience gives a better occupational status. He also noticed that these activities lengthened the period of unemployment between graduation and the first job. In the United States, Eide and Ronan (2001) found that participation in sports activities contributes to a better wage. The higher wages may be a result of leadership experience. Kuhn and Weinberger (2005) found that leadership experience gives access to higher wages and that it also increases the chances of becoming a manager. Extracurricular activities may also re-sult in improved ability to perform in job interviews. Ming Chia (2005) examined the process towards a first job. He investigated the effects of academic performance, extracurricular activ-ities and emotional intelligence. He concentrated on job offers of the Big 5 public accounting firms. Results indicated that emotional intelligence enhances the graduate’s performance at job interviews and extracurricular activities are stated to be an appropriate experience to develop emotional intelligence. In conclusion, extracurricular activities have positive effects on the fu-ture access on the labor market (Light,2001).

Students mostly participate in extracurricular activities to gain skills or expand their social network (LKvV, 2012). This personal development is also acknowledged by employers. Com-panies are not looking for students who only have a high educational level. Students need also to be developed on a social level. Indeed, big consultancy firms appear to attach more value to extracurricular activities than graduating cum laude (Ackerman,2008).

The recognition of the value of extracurricular activities by employers causes more and more students to participate (ASVA,2010). Moreover, students feel extra pressure due to a highly competitive job market after finishing their higher educational program. One of the main rea-sons for this is the rise of mass higher education (Brown et al.,2003). More and more people have access to higher education and this results in a high number of graduates with a similar degree and experience entering the job market and competing for a limited number of jobs. Because of the increase in number of graduates, the value of formal credentials like university degrees has decreased (Collins, 2002). Students themselves also have realized this and they know that degrees are not a guarantee of future employability anymore (Tomlinson,2007). To improve their chances, students need to distinguish themselves from other students both during and besides studying. Participation in extracurricular activities is a way to accomplish this. The increased competition is also visible in the Netherlands, where the number of students has steadily grown in the last decades (CBS,2015) and the prognosis for the next decade is an even further increase (VSNU,2012).

2.2.1 Important differences between the United States and the Netherlands

Most of the aforementioned discussed literature is executed in the United States. However, there are a number of important differences between the Netherlands and the United States

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CHAPTER 2. LITERATURE OVERVIEW 6

concerning extracurricular activities. First, choice of university is much more important in the United States than it is in the Netherlands. Extracurricular activities can increase chances to get access to a good university. Therefore, the majority of the studies on extracurricular activ-ities is executed at high schools. In the Netherlands, grades usually do not determine whether one has access to a university. Only an appropriate high school certificate is sufficient (more on this insubsection 2.2.1). Moreover, the universities do not differ in quality. As a consequence, extracurricular activities are less important at a high school level. Another difference between the countries is the focus on sports. In the United States, outstanding athletic abilities can be rewarded with an admission to a good university. Athletics is therefore more intensively exercised than in the Netherlands, where sports count as an important form of leisure. The last difference is the structure of the higher educational system. For one thing, tuition in the Netherlands is much lower since it is heavily subsidized. This puts less financial pressure on the participation in extracurricular activities. On top of that students get in some cases a reimbursement of their university, for example in the case of a board membership of a student association. The different interests and different forms of pressure on students can result in different motivations for students to participate.

Furthermore, we briefly explain the concept of student associations in the Netherlands since this will be included in our model as an explanatory variable. There are typically two types of associations: study associations and student associations (ASVA,2010). Study associations are typically affiliated with one specific study or sometimes a group of similar studies. These associations unite students with a similar study background by organizing events. In addition, these associations can effectively organize study-related events or setup study-related structures like discount on book sale, study trips or tutoring classes. A great number of students is member of study associations without being actively involved. As a consequence, the relation between participation in student associations and salary may be heavily influenced by non-active mem-bers. In contrast, student associations are not study specific. Therefore, they encompass a much broader range of types of students. These associations lay the emphasis on a specific activity. Mostly the emphasis lays on the social aspect. Other examples are an emphasis on international relations, religion or philosophy. Student association can be compared to fraterni-ties and sororifraterni-ties in the United States. These associations are more interesting for our study, since members are more likely to be active at these associations and as a consequence they are more likely to develop skills that will affect their future salary.

Finally, in the Netherlands there are two types of higher educational institutions, which are hbo and wo. One difference between the two lies in the admission requirements. In contrast to many other countries, there are multiple difficulty levels distinguished at secondary school. The level of secondary school is adapted to the intelligence of the children and their performance at primary school. The highest level of secondary school is vwo and gives access to both hbo and

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wo. The second highest level is havo and gives access to only hbo. Another difference is that wo has a more academic nature and hbo have a more practical nature. Students at wo institutions are educated to become an academic researcher, but most of them do not choose an academic career in the end. Another important difference is that the bachelor program of hbo takes four years and the bachelor program of wo takes three years. A last important difference is that students can only attain master certificates at wo. The most important takeaway for this thesis is that wo has stricter admission requirements and therefore generally selects students with a higher intelligence.

2.2.2 Research methods for extracurricular activities

The aforementioned researches on extracurricular activities are executed from the perspective of different fields of study. Sociological studies treat the participation decision as exogenous, which is likely to lead to biased estimates due to unobserved ability measures (Lipscomb,2007). Economists generally adopt a different approach. The majority of their researches uses an in-strumental variable (IV) approach (Stevenson, 2010). Other seen approaches are fixed effects with time-constant factors (Lipscomb, 2007) and a logistic model without endogeneity taken into account (Tchibozo,2007).

As far as we know there exists no literature on extracurricular activities that uses a selec-tion model. This thesis is the first to apply this model for this topic. EvenSEO(2015) does not use a selection model. They applied a linear regression model with participation in extracur-ricular activities as an explanatory variable. Hereby, they ignore potential selection bias, which we will explain in the next chapter.

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Chapter 3

Model

In this chapter we will shed light on the models applied in this thesis. The chapter starts with an introduction to selection models. Thereafter, we explain the parametric and the semiparametric estimation techniques used in the first estimation stage. Then we explain the techniques used in the second stage. We discuss the selection correction terms by Heckman and Cosslett and how we extend these to the case of two selection variables.

3.1 Model setup

Introduction to selection models

For regular econometric analyses it is often required to use a sample that is randomly drawn from the population. Samples that are not completely random are samples in which the prob-ability of inclusion of an observation in the sample is contingent on the phenomenon that we are explaining. These samples are called selected samples, which can lead to selection bias. This means that the sample is not representative of the population and that the mean-zero restriction on the errors does not hold. This causes that standard estimation methods may have misleading results and that estimated parameters are inconsistent (Verbeek,2008). There are various reasons for selection bias to occur, for example: sample selection, nonresponse and self-selection. Sample selection is when participants of a particular policy are significantly over-or underrepresented in the sample; nonresponse is when individuals with specific characteristics refuse to report in surveys; and self-selection is when the dependent variable is determined by the individual’s choice whether or not to be a participant.

The latter is the source for selection bias in our case. The dependent variable is determined in part by the participation decision (Cameron and Trivedi,2005). In other words the students select themselves whether to participate in extracurricular activities in a non-random way. Due to this the explanatory variable is correlated with the error term (endogeneity) which causes inconsistent OLS estimates. A common way to approach the endogeneity problem is with the instrumental variables method. In case of selection bias, selection models are also an option. We apply the latter in this thesis.

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To cope with selection bias we apply a parametric model inspired byHeckman(1979) and a semiparametric model inspired byCosslett(1991) in which we relax the distributional assump-tions. Both are further explained in the remainder of this chapter. Even though the models used here are not pure Heckman or pure Cosslett, we will keep referring to these models as Heck-man’s model and Cossletts model. One difference is that we add a second selection variable to the outcome equation in both models. Another difference with the standard Heckman model is that we always observe the dependent variable. In Heckman’s model this is only observed for participants. The dummy variable which indicates participation is in this thesis referred to as selection variable.

Model with one selection variable

For models with one selection variable we have two equations for both the Heckman model and the Cosslett model: an outcome equation and a selection equation. The outcome equation describes the relation between the outcome of interest yi and the explanatory variables Xi (see

(3.1)). The selection equation describes the relation between the selection variable DA_i and another vector of explanatory variables Zi (see (3.2)). For Heckman’s model we will assume

normality on the errors. This distributional assumption is relaxed in Cosslett’s model. We get:

yi= Xi0β + DiAδiA+ εi, (3.1)

DA_i = I{Z_i0γA+ uA_i > 0}, (3.2)

for i = 1, . . . , N and with A ∈ {L, S} and I{Z_i0γA_{+ u}A

i > 0} is an indicator function of

the event {Z_i0γA+ uA_i > 0}. We will use superscript L to associate a variable with Leisure-related activities and we use superscript S to indicate to associate variables with Study-Leisure-related activities. We use superscript A to denote the collection of both Activities.

Model with two selection variables

The model with two selection variables consists of three equations: one outcome equation and two selection equations. The extra selection equation is defined in similar fashion as the first selection equation. For simplicity, we will use the same set of explanatory variables Z in both selection equations. The outcome equation has been increased with one extra selection variable. For the Heckman model we assume that the errors follow a multivariate normal distribution and we relax this assumption for Cosslett’s model.

yi = Xi0β + DLi δiL+ DiSδiS+ εi, (3.3)

D_iL= I{Z_i0γL+ uL_i > 0}, (3.4) D_iS = I{Z_i0γS+ uS_i > 0}, (3.5)

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CHAPTER 3. MODEL 10

3.2 First stage estimation

In the first stage we estimate the selection equation. For the parametric model of Heckman, we estimate this with a probit model, which specifies:

pi = Pr[yi = 1|xi] = Φ(x0iβ), (3.6)

where Φ(·) is the cumulative distribution function for the standard normal. For the semipara-metric model of Cosslett, we also relax the parasemipara-metric estimation in the first stage and estimate the selection equation semiparametrically. For this we choose a semiparametric estimator by

Gallant and Nychka (1987). They put the density equal to a Hermite series and write it as a squared polynomial times a normal distribution with a polynomial expansion with Gaussian leading term (Stewart,2005). We get:

fK(ε) = 1 θ K X k=1 γkεk !2 φ(ε), (3.7) θ = Z inf − inf K X k=1 γkεk !2 φ(ε)dε, (3.8)

where φ(·) a normal density function.

3.3 Second stage estimation

3.3.1 Heckman’s approach

In the second stage we estimate the outcome equation. Due to self-selection we cannot assume the conditional errors to have mean zero, thereby leading to inconsistent OLS estimates. Heck-man’s model restores the mean-zero condition by the inclusion of an estimate of the selection bias.

One selection dummy

We find the correction term for the Heckman model by writing out the conditional expectation:

E[yi | DAi = 1] = E[X 0 iβ + DiAδA+ εi | DAi = 1], (3.9) = X_i0β + D_iAδA+ E[εi | DAi = 1], = X_i0β + D_iAδA+ E[εi | uAi > −Zi0γA], = X_i0β + D_iAδA+ φ(Z_i0γA)/Φ(Z_i0γA),

for i = 1, . . . , N and A ∈ {L, S}. The last step follows after some rewriting and from our normality assumption. The last term in the last line on the right-hand side is used as the selection correction term. The expectation conditional on DA_i = 0 can be written out in similar

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fashion from which we obtain the selection correction term for nonparticipants. Taken together we get: yi = Xi0β + DAi δiA+ Hλ + εi, (3.10) H =    φ(Z0_iγ) Φ(Z_i0γA₎ if DA_i = 1, φ(Z_i0γ) 1−ΦZ0 iγA) if D A i = 0, for i = 1, . . . , N and A ∈ {L, S}.

Two selection dummies

For two selection dummies, the conditional expectation of the errors becomes more complex. For instance, when both dummies are equal to one, we get the following conditional expectation:

E[yi | DiL= 1, DSi = 1] = E[X 0 iβ + DiLδLi + DiSδiS+ εi | DiL= 1, DiS= 1] = X_i0β + DL_i δ_iL+ D_iSδ_iS+ E[εi | DiL= 1, DiS= 1], = X_i0β + DL_i δ_iL+ D_iSδ_iS+ E[εi | uLi > −Z 0 iγL, uSi > −Z 0 iγS], (3.11)

for i = 1, . . . , N . Therefore, we need an estimate for the last term on the right-hand side of (3.11). For this, we use an expression constructed by Pudney (1991). He constructed this for cases involving more than one truncation rule. More specifically, he considered a p-dimensional joint distribution with a truncation of the last p − 1 variables. The conditional expectation in (3.11) can be seen as a truncation rule with two truncation rules. Corresponding to Pudney’s notation for two truncation rules, we can describe this compound event as:

Ξ = {2≥ c2, 3≥ c3}. (3.12)

Under the assumption of normality he obtained useful expressions. The parameters of the multivariate normal distribution are defined as follows:

=     1 2 3     , µ =     µ1 µ2 µ3     , Σ =     σ11 σ12 σ13 σ21 σ22 σ23 σ31 σ32 σ33     , (3.13)

with in our case: 0 = (ε, uL, uS), µ = 0 and Σ a symmetric matrix. With the normality assumption he shows how to write out the expectation conditional on the truncation rules. For the special case of two truncation rules he gets (after some manipulation) the following expressions: E[|Ξ] = µ1+ σ12 σ221/2 φ(c∗₂) Pr(Ξ) 1 − Φ c∗₃− ρc∗₂ (1 − ρ2₎1_/2) + σ13 σ331/2 φ(c∗₃) Pr(Ξ) 1 − Φ c∗₂− ρc∗₃ (1 − ρ2₎1_/2) , (3.14) with c∗_i = (ci = µi)/σ 1/2 ii and ρ = σ23/(σ22σ33)

1_/2_{. For different values of D}L

i and DiS, the

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CHAPTER 3. MODEL 12

to zero the direction of the inequality changes. Under the assumption of a normal distribution which is symmetric around zero, the change of inequality ultimately results in a change of expression for c2 and c3. We get:

c2i= ( −Z_i0γL if DL_i = 1, Z_i0γL if DL_i = 0, c3i= ( −Z_i0γS if D_iS= 1, Z_i0γS if D_iS= 0,

for i = 1, . . . , N . Ultimately, we get the following outcome equation:

yi = Xiβ + DiLδLi + DiSδiS+ π1P1i+ π2P2i+ εi, (3.15) P1i= φ(c∗₂) Pr(Ξ) 1 − Φ c∗₃− ρc∗₂ (1 − ρ2₎1_/2) (3.16) P2i= φ(c∗₃) Pr(Ξ) 1 − Φ c∗₂− ρc∗ 3 (1 − ρ2₎1_/2) (3.17)

for i = 1, . . . , N and where we used µ1 = 0. These last expressions are used to estimate the

model. We name P1 and P2 the Pudney terms and they are the analogue of the inverse Mills

ratio in the one selection variable model.

3.3.2 Cosslett’s model

The second approach which we applied is the selection model of Cosslett (1991). This model can be seen as the semiparametric analogue of Heckman’s selection modelHussinger(2008). In this model the selection bias is estimated using selection correction dummies.

One selection variable

The selection dummies are defined by cutting the value-ordered propensity scores into M in-tervals. The number of intervals can be determined in different ways. We apply three different algorithms and compare their results. The algorithms are explained in more detail in subsec-tion 5.2.1. We get: yi= Xi0β + DiAδiA+ M X m=1 λmCimA(Z 0 iγA) + ξi, (3.18)

for i = 1, . . . , N , A ∈ {L, S} and where C_imA(·) is an indicator function which indicates whether observation i is in interval m. This indicator function differs for different dummy algorithms, which we will discuss in subsection 5.2.1.

Two selection variable

For two selection variables, we estimate the selection bias using an interaction between the selection correction dummies. Because of the binary nature of the correction dummy, the interaction term itself is also a dummy. This product is one if and only if the two individual

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correction dummies are equal to one. Furthermore, this interaction term naturally incorporates the correlation between the two selection dummies. We get:

yi = Xi0β + DAi δi+ M1 X m1=1 M1 X m2=1 λm1,m2C L m1,i(Z 0 iγL) · CmS2,i(Z 0 iγS) + ξi, (3.19)

for i = 1, . . . N and where M1 and M2 are the number of intervals for ECAL and ECAS

respectively. Again, C_imA₁ is an indicator function. This function is constituted in similar fashion of the one selection variable model.

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Chapter 4

Data

In this chapter we will discuss the data set we used in this thesis. We provide more information on the source of our data. Furthermore, we discuss the selected dependent and explanatory variables and explain why we selected these. Also the creation of the dummies for the selection variable is explained. Finally, we provide more insights in the data set using descriptive statistics and information on deleted observations.

4.1 Data sets

Studie & Werk

We use data from the database Studie & Werk. The data is collected by SEO Economisch onderzoek, which is an institute for economic research. Commissioned by Elsevier, which is a weekly Dutch news magazine, the labor market position of graduates in the Netherlands is examined with this data set. The data is collected from a written survey in which graduates from Dutch higher education institutions are questioned about their career in higher education and their career after higher education. The main objective of their research is to determine which studies give the best job market opportunities. The most important results are published yearly in a special edition of the Elsevier magazine. This research started in 1997 and since then about 120,000 graduates are questioned. We used the most recent version of Studie & Werk which was published in 2015. It contains graduates questioned until the first two months of 2015. This means that the most recent respondents in this data set graduated in the academic year 2012/2013.

CROHO

In order to obtain more detailed information about the studies the data set has been merged with the CROHO-register obtained from the website of Dienst Uitvoering Onderwijs (DUO). This way, the large number of different studies is categorized in nine different study categories. The categories are listed inTable 4.1.

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Field of study Frequency Percentage Economics 9,970 18.71 Social sciences 9,806 18.41 Health sciences 6,983 13.11 Agriculture 1,839 3.45 Nature 3,667 6.89 Education 3,586 6.73 Law 2,008 3.77 Linguistics 4,957 9.31 Engineering 10,448 19.62 Total 53,264 100.00

Table 4.1: Frequency table for fields of study

Note: In Dutch, from top to bottom: Economie; Gedrag en maatschappij; Gezondheidszorg; Landbouw en natuurlijke omgeving; Natuur; Onderwijs; Recht; Taal en cultuur; Techniek;. There was also a tenth field of study, but we omitted this due to the low frequency in our data set.

4.2 Variable selection

Dependent variable

As a dependent variable we use the log of the gross salary per month of the current job. Here, current means at the time when the survey was conducted. Respondents were not obligated to share their salary which leads to 16% missing values for this variable. Furthermore, it should be noted that the salary variable has been extensively checked for correctness by SEO. The reason for this is that this variable is the most important variable in their annual research on studies and jobs. Therefore, we prefer to use monthly salary over hourly salary in order to use the cleaned data to our advantage and to minimize measurement errors.

Selection variables

The selection variables are the variables which incorporate the treatment decision. Here, these variables capture the participation decision on the extracurricular activities. We distinguish two types of extracurricular activities: leisure-related activities (ECAL) and study related activities (ECAS). Both types of activities are incorporated in our model as a dummy variable. For leisure-related activities, we use the engagement in a student association as a proxy. Student associations connect students from different fields of study and let them interact in social activ-ities. These associations help students to expand their network and to develop themselves on a social level, rather than on an academic level. By the lack of other suitable variables in the data set, this is only variable to measure engagement in leisure-related activities. For study-related activities, we capture whether the individual excels on an academic level. For this, we use data

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CHAPTER 4. DATA 16

Variable Frequency Percentage ECAL 12,687 23.82 – Student assoc. 12,687 23.82 ECAS 13,606 25.54 – Cum laude 4,513 8.47 – Honours 320 0.60 – Two studies 10,072 18.91 Both ECAL and ECAS 3,597 6.75

Table 4.2: Frequency table for selection vari-ables 2004 2006 2008 2010 2012 6 8 10 12 Year of graduation P articipation rate Leisure Study

Figure 4.1: Participation rate over time

Note: We do not observe any participation in extracurricular activities in the period 1996-2001. In 2002 we observe an participation rate of around 1% for both types of activities. This suggests that the questionnaire of SEO was enriched with questions on extracurricular activities since 2002. Therefore, we omit all observations from 1996-2002. Since graduates are questioned two years after graduation, we observe only those who are graduated not later than 2013.

on whether an individual has achieved cum laude, whether an individual has participated in a honours program or whether an individual has finished two study programs. If either one of these is true, than we set the dummy variable for study-related activities to one and zero otherwise.

Explanatory variables in the first stage

To explain the decision on participating in either one of the two types of extracurricular activi-ties, we use explanatory variables which are carefully selected to be consistent with literature on extracurricular activities. First, we include two variables about high school achievements. We include the grade point average (GPA) at high school and a categorical variable on which profile one has chosen. Four profiles can be discerned: CM encompasses courses on culture and society; EM encompasses mostly economic courses; NG encompasses courses on science and health; and NT encompasses courses on science and technology. Not all individuals have chosen a profile. We use having no profile as a benchmark. Next, we include a dummy which is one for males and zero for females. We hypothesize that females are significantly more inclined to participate in extracurricular activities than males (LKvV,2012). A dummy for whether the respondent lives at his/her parent’s house is included under the hypothesis that these students are less inclined to participate in extracurricular activities. Accordingly, these students are less independent and live further away from university which causes their lower probability of participation. Also, a dummy which is one for wo and zero for hbo is included. A field study in Amsterdam has pointed out that wo-students have a much higher participation rate for extracurricular activities

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than hbo-students (ASVA,2010).

Since individuals with a lower socioeconomic background have a lower probability of partic-ipating in extracurricular activities (Eide and Ronan,2001), we include variables to control for this. We capture the individual’s background characteristics by including a dummy on whether the respondent has Dutch origins and a variable on the level of education of the mother. The nonnative-variable is one if the respondent is does not have Dutch origins, that is, whether ei-ther the moei-ther or the faei-ther is not born in the Neei-therlands. The possible levels of education of the mother are (from high to low): wo (wetenschappelijk onderwijs), hbo (hoger beroepsonder-wijs), mo (middelbaar onderberoepsonder-wijs), lbo (lager beroepsonderwijs) and lo (lager onderwijs). The last category is used as a benchmark. Lastly, we add a year variable and this variable squared to correct for all time related variations. Also we include a variable on the region where the respondent has studied with region west as a benchmark.

Explanatory variables in the second stage

In the outcome equation we use eighteen explanatory variables. In order to determine which variables to include we followed the most recent research of SEO (2015). All variables that have an effect larger than 1% in their research are also included here except for all variables on job specifics. The reason for this is that we only want to examine the effects of individual characteristics during the higher educational career on salary irrespectively of the type of job one chooses. Therefore, in contrast to SEO, we do not include the required level of thinking for the job acquired by the respondent, the type of profession of the respondent and whether the respondent has a permanent contract or a temporary contract as explanatory variables. Nevertheless, we do include the number of working hours per week to be able to compare the wages more consistently. Furthermore, all explanatory variables on extracurricular activities are not included in the explanatory variables matrix X since these are utilized to constitute the selection variables.

We include the age at graduation, which according to SEO has a positive effect on salary. We also include a dummy variable which is one for males and zero for females. According to SEO being a male has a positive effect of 2% on salary. A dummy which is one if the respondent lives at his/her parent’s house is also included, which has according to SEO a negative effect of 7% on future salary. A dummy which is one for wo and zero for hbo is included with the hypothesis that wo-graduates earn more because the required thinking level for wo is higher (seesubsection 2.2.1

for explanation of the difference between wo and hbo). Using the CROHO-register we classified the studies of the respondents into nine categories. This categorical variable is also included and we use the category economics as a benchmark. Analogous to the explanatory variables in the first stage, we include variables on graduation year and region.

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CHAPTER 4. DATA 18 ECAL ECAS Variable 1 0 1 0 Total age at start 19.39 19.51 20.54 19.11 19.46 age at graduation 24.76 24.01 25.27 23.94 24.28 lives at parents 0.07 0.21 0.11 0.41 0.16 wo 0.69 0.37 0.75 0.18 0.49 nonnative 0.14 0.16 0.15 0.14 0.14 region north 0.09 0.09 8.73 0.09 0.10 east 0.18 0.20 18.40 0.19 0.19 west 0.56 0.48 54.87 0.51 0.52 south 0.17 0.21 18.00 0.20 0.19 profile CM 0.08 0.13 0.13 0.10 0.10 EM 0.11 0.13 0.14 0.11 0.12 NG 0.14 0.12 0.14 0.12 0.13 NT 0.09 0.07 0.09 0.08 0.08 mother’s education lo 0.03 0.05 0.04 0.04 0.4 lbo 0.27 0.36 0.29 0.33 0.32 mo 0.29 0.30 0.28 0.30 0.30 hbo 0.29 0.24 0.28 0.25 0.26 wo 0.11 0.05 0.10 0.07 0.08

Table 4.3: Mean of explanatory variables

Notes: This table shows the mean of the explanatory variables used in our models with the exception of the study-categories. These are shown inTable 4.1. The calculated means are for the selected sample and thus not for the full sample. This means that these are averages over graduates from 2003 until 2013.

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Observations deleted Total

Full sample 119,112

Drop 1996-2002 44,968 74,144

Missing values in dependent variable 11,843 62,301 Missing values in explanatory variables Z 5,718 56,583 Missing values in explanatory variables X 3,319 53,264

Selected sample 53,264

Table 4.4: Deleted observations

Data manipulation

We drop data from 1996 until 2002 since we do not observe any extracurricular activity in this period. This is probably because this has not been measured in that period. This reduces the samples size from 119,112 to 74,144. We also face a great amount of missing values in the dependent variable wage, which reduced our sample size to 62,301. Furthermore, we corrected missing values for the cum laude variable. We assigned a zero to this dummy variable for all individuals with a GPA at university lower than 8. Remaining observations with missing values were dropped from the sample. Also, we also reduced the number of missing values for the student association variable. For this, we used information from a dummy variable which was one for participants of either student associations or study associations. Despite these operations, we had to reduce our sample even more to 53,264 due to missing values in the explanatory variables. These results are summarized inTable 4.4.

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Chapter 5

Results

In this chapter, we present the results of our estimations. We start with discussing the results of one selection variable and then we discuss the results for two selection variables. For both models we present the first and second stage results in separate sections. The algorithms used for dummy creation in both Cosslett’s models are explained in subsection 5.2.1. Comparison of these algorithms showed that the ratio-algorithm is most suitable here and this is also used in the model with two selection variables. Also, we note that all standard errors in every second stage are bootstrapped with 200 replications.

5.1 One selection variable: first stage estimation

In the first stage we estimate the selection equation as given in (3.2). We present the results in Table 5.1. We use different model specifications, since the semiparametric model has a variance which is not restricted to 1. Therefore, the estimated coefficients are not comparable in magnitude. However, we can interpret the sign of the coefficients. We observe that for each variable in each model, the signs are the same, which indicates the robustness of our results. Before we compare the different model specifications, we briefly discuss the estimated coefficients.

The probability of participating in study-related activities is positively influence by the age at which an individual starts the educational program. The estimated coefficients for starting age in the leisure-model are not significant. As expected high school GPA has a positive effect on the participation rate of study-related activities. There is also an indication that this has a positive effect on leisure-related activities, but these results are not significant. Males tend to participate less in study-related activities. In contrast to the research ofLKvV(2012), we find that males have a higher probability of participating in leisure-related activities. Studying at a hbo has a negative effect on the probability of participating in either type of activity. Also, living at your parents’ and having parents with a non-Dutch background have significantly negative effects on the probability of participating in either type of activity. For consideration of the effects of high school profiles we use having no profile as a benchmark. We observe that NG and

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NT have positive effects on both types of activity. Profiles CM and EM have negative effects on the participation leisure-related activities and positive effects on study-related activities. The last four variables in Table 5.1 show the educational level of the mother ordered from low to high. These results show that the higher the education of the mother the more an individual is inclined to participate in either type of activities.

For the semiparametric case, we employed the model by Gallant and Nychka (1987). For the parametric case, we used a probit specification. We also tested with a logit specification, which we do not present in our table. This specification gave very similar results with the probit specification, which is a common phenomenon in empirical studies (Verbeek,2008). Therefore, we stay with the probit specification. When we compared the percentage of correctly classified observations, we observed that the probit model tend to give slightly better results than the semiparametric model. However, these differences were very small. For the determination of the percentage correctly classified observations, we used:

b yi =

(

1 if F (Z_i0γ) > 1/2,b 0 if F (Z_i0γ) ≤ 1/2,_b

with F (·) either the probit distribution function or the semiparametric distribution function.

5.2 One selection variable: second stage estimation

We present the estimation results of the second stage in Table 5.2. In the second and the fifth column we present the estimation results of a one stage OLS estimation, which is used as a benchmark. The significant coefficients of the correction terms suggest that selection bias is present and therefore the use of selection models is justified. The models only differ in the selection variable and in how they handle selection bias. Since this does not change the relation between the remaining explanatory variables and the dependent variable, the estimated coefficients of the explanatory variables are very similar for the different models. All models use an OLS estimation in the second stage. Therefore, all estimated coefficients are comparable in sign and in magnitude. Before we compare the different model specifications, we briefly discuss the estimated coefficients.

Age of graduation positively affects salary in all model specifications. Furthermore, in accordance with the literature, males earn more than females. The estimated difference is around 5.7%. Individuals who live at their parents’ house earn less, than those who live on their own. One of the largest effects emerges from whether an individual studies at a wo-university rather than a hbo-wo-university. This increases salary by 15%. Because wo imposes stricter admission requirements better students are selected and this is reflected in salary. Quite naturally the number of working hours per week positively influences salary. The number of working hours per week is also found to be endogenous (Lundberg,1984). Next, in accordance with literature (SEO,2015), we also observe differences in salary for different fields of study. We used economics as benchmark and notice that almost all other fields of study tend to yield a lower

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CHAPTER 5. RESULTS 22

ECAL ECAS

Probit G&N Probit G&N start age -0.001 -0.001 0.209*** 0.179*** (0.003) (0.004) (0.003) (0.003) GPA hs 0.013 0.016 0.209*** 0.179*** (0.011) (0.013) (0.011) (0.009) male 0.126*** 0.163*** -0.132*** -0.113*** (0.013) (0.019) (0.013) (0.012) parents’ -0.424*** -0.551*** -0.049** -0.042** (0.021) (0.030) (0.020) (0.017) hbo -0.447*** -0.581*** -0.493*** -0.421*** (0.014) (0.016) (0.014) (0.012) nonnative -0.101*** -0.132*** -0.096*** -0.082*** (0.020) (0.023) (0.020) (0.017) north -0.188*** -0.245*** -0.041* -0.035 (0.023) (0.026) (0.023) (0.022) east -0.245*** -0.318*** 0.045*** 0.039*** (0.017) (0.024) (0.017) (0.015) south -0.229*** -0.297*** 0.046*** 0.040*** (0.017) (0.023) (0.017) (0.015) profile CM -0.166*** -0.216*** 0.281*** 0.240*** (0.026) (0.035) (0.024) (0.019) profile EM -0.051** -0.066** 0.315*** 0.269*** (0.023) (0.032) (0.022) (0.018) profile NG 0.080*** 0.103*** 0.151*** 0.129*** (0.022) (0.029) (0.022) (0.018) profile NT 0.024 0.032 0.201*** 0.171*** (0.025) (0.036) (0.025) (0.023) mama lbo 0.097*** 0.126*** 0.100*** 0.085*** (0.036) (0.046) (0.035) (0.031) mama mo 0.219*** 0.284*** 0.100*** 0.086*** (0.036) (0.045) (0.035) (0.031) mama hbo 0.366*** 0.475*** 0.137*** 0.117*** (0.036) (0.045) (0.036) (0.032) mama wo 0.670*** 0.870*** 0.155*** 0.133*** (0.040) (0.050) (0.040) (0.034) Correctly classified: 76.85% 76.55% 76.95% 74.85%

Table 5.1: First stage estimation results

Notes: For readability reasons, we omitted the two time variables (graduation year and

graduation year2) and the constant from this table. Both were significant at a 1% level for all model specifications. Asterisks denote significance at *** 1%, ** 5% and * 10% level.

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salary. Dummies for fields of study being education or engineering have positive coefficients. However, these effects are only significant in the leisure-model and study-model respectively. The only fields of study with significantly higher salaries are law and health studies.

The coefficients of interest here are those of the selection variables, the inverse Mills ratio in Heckman’s model and the selection correction dummies in Cosslett’s model. For both selection variables, we observe positive significant coefficients in all models. The estimated effect of involvement in leisure-related extracurricular activities is larger than involvement in study-related extracurricular activities except for the Cosslett model. Another observation is that the estimated effects for both activities are larger in the selection models than in the OLS model which serves as a benchmark. Furthermore, we observe a negative coefficient for the inverse Mills ratio, which suggests a negative correlation between the error terms. This was not expected in advance, but it appeared to be consistent with the two selection variables model. The coefficient of the inverse Mills ratio is significant, which justifies the use of a selection model. For the selection correction dummies, we employed a LR-test on joint significance of the selection correction dummies (Table 5.3). Results show that these dummies are jointly significant for almost all dummy specifications. Again, this justifies the use of selection models.

5.2.1 Cosslett’s selection correction dummies

For the determination of the selection correction dummies we applied three algorithms. First, an algorithm is used byAyer et al.(1955) to determine the selection correction dummies endoge-nously. We used a slightly modified version of this followingHussinger(2008). Second, we used an algorithm with fixed interval widths. This method will be referred to as fixed-algorithm. Fi-nally, we used an algorithm that creates intervals of an equal number of observations in it. This method will be referred to as ratio-algorithm. Now a brief discussion of the three algorithms follows. All algorithms produce intervals, which are then used for dummy variable creation. A dummy takes the value of one when the propensity score of this particular observation lies within the interval. We create separate dummies for treated and non-treated observations.

Algorithm of Ayer (1955)

Hussinger (2008) used a modified version of the algorithm of Ayer et al. (1955) to determine the selection correction dummies for Cosslett’s model. We applied the same technique for the selection correction dummies. First, we ordered the estimated propensity scores from low to high. The first interval starts at the lowest propensity score and ends when the first treated observation is located. The next interval ends with the next switch from non-treated observation to treated observation. This procedure is repeated until the end of the sample. Obviously, this approach could yield a huge number of intervals with a low number of observations per interval. Therefore, just like Hussinger we limit intervals to contain at least 20% treated observations. The threshold of 20% is chosen because the percentage of treated observations in Hussinger’s data set was approximately 20%. Because we have approximately the same percentage of treated

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Leisure model Study model

OLS Heckman Cosslett OLS Heckman Cosslett const. 6.378*** 6.391*** 6.364*** 6.392*** 6.392*** 6.486*** (0.016) (0.024) (0.030) (0.016) (0.024) (0.045) grad. age 0.013*** 0.013*** 0.013*** 0.013*** 0.013*** 0.010*** (0.001) (0.001) (0.001) (0.001) (0.001) (0.001) male 0.056*** 0.057*** 0.058*** 0.056*** 0.056*** 0.059*** (0.003) (0.003) (0.003) (0.003) (0.003) (0.003) parents’ -0.058*** -0.062*** -0.069*** -0.060*** -0.061*** -0.059*** (0.004) (0.004) (0.007) (0.004) (0.004) (0.004) wo 0.156*** 0.158*** 0.162*** 0.155*** 0.157*** 0.150*** (0.003) (0.004) (0.006) (0.003) (0.004) (0.004) hours 0.021*** 0.021*** 0.021*** 0.021*** 0.021*** 0.021*** (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) cat. social -0.054*** -0.054*** -0.054*** -0.056*** -0.056*** -0.058*** (0.005) (0.005) (0.005) (0.005) (0.005) (0.005) cat. health 0.097*** 0.097*** 0.099*** 0.098*** 0.098*** 0.098*** (0.005) (0.005) (0.005) (0.005) (0.005) (0.005) cat. agric. -0.053*** -0.051*** -0.050*** -0.050*** -0.049*** -0.049*** (0.008) (0.007) (0.007) (0.008) (0.007) (0.007) cat. nature -0.062*** -0.061*** -0.060*** -0.062*** -0.062*** -0.061*** (0.006) (0.005) (0.005) (0.006) (0.005) (0.005) cat. educ. 0.010* 0.010* 0.010* 0.007 0.007 0.007 (0.006) (0.006) (0.006) (0.006) (0.006) (0.006) cat law 0.027*** 0.027*** 0.027*** 0.027*** 0.027*** 0.027*** (0.008) (0.007) (0.007) (0.008) (0.007) (0.007) cat. lingu. -0.192*** -0.191*** -0.191*** -0.194*** -0.194*** -0.195*** (0.006) (0.007) (0.007) (0.006) (0.007) (0.007) cat. engin. 0.005 0.005 0.006 0.007* 0.007* 0.008** (0.004) (0.004) (0.004) (0.004) (0.004) (0.004) ECAL 0.017*** 0.041*** 0.048** (0.003) (0.006) (0.019) ECAS 0.016*** 0.027*** 0.073*** (0.003) (0.005) (0.027) inv. Mills -0.031*** -0.016*** (0.007) (0.006)

Table 5.2: Second stage estimation results: one selection variable

Notes: For readability reasons, we omitted the two time variables (graduation year and

graduation year2) and three region dummies from this table. All were significant at a 1% level for all model specifications. The standard errors are bootstrapped using 200 replications. Asterisks denote significance at *** 1%, ** 5% and * 10% level.

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Non-treated Treated Both Algorithm (k) LR-χ2(k) p > χ2 LR-χ2(k) p > χ2 LR-χ2(2k) p > χ2 ECAL – Ayer (1153) 1266.6 0.004 924.67 1.000 2213.5 0.875 – Fixed (20) 39.71 0.006 42.67 0.002 72.53 0.001 – Ratio (49) 81.56 0.002 80.56 0.003 151.93 0.000 ECAS – Ayer (1149) 1851 0.018 1374.5 0.000 3271 0.000 – Fixed (31) 63.03 0.001 75.51 0.000 149.04 0.000 – Ratio (49) 80.72 0.003 77.12 0.006 167.41 0.000

Table 5.3: LR-test for different dummy series algorithms

Note: Here we test whether the dummy variables are jointly significant different from zero.

observations we use the same threshold. In practice this means that the interval is only closed when at a switch from non-treated to treated occurs and the percentage of treated observations is higher than 20%. When the percentage is lower than 20% at the switch from non-treated to treated, this switch is ignored. Dummy variables are created for each interval and these variables are equal to one when an observation has a propensity score within this interval.

We ran the algorithm twice: once for the leisure-model and once for the study-related model. For the study-related model, we obtained 1,150 intervals. A LR-test shows that the corresponding dummies are jointly significant (Table 5.3). For the leisure-related model, we obtained 1,154 intervals which were not jointly significant, except for the dummies for non-treated observations. This would suggest to include only non-non-treated dummies in the leisure-model. Nevertheless, we will not use the dummies created by this algorithm due to the high number of dummies, since this would lead to an intractable amount of dummies in the model with two selection variables. In that case, we would need approximately 1.3 million (1149*1153) dummies, which is not possible when having around 53,000 observations. Furthermore, we note that the number of intervals is also very large when compared with the number of intervals in Hussinger’s research (1,153/53,264 = 0.022 and 20/3,744 = 0,005). From this we conclude that the algorithm of Ayer is not suitable for our data set and we will therefore shift our attention to the fixed-algorithm and the ratio-algorithm.

Algorithm with fixed interval width

A natural approach to determine the intervals for the propensity scores is by fixing the interval widths. We set the lowest threshold equal to the 1st _{percentile of the value ordered propensity}

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scores. In between, we keep a fixed interval width of 0.1. Since we use different values for the minimum and maximum thresholds, the number of intervals of the leisure-model differs from those of the study-related model. The spread in propensity score in the study-related model is larger, which yields a higher number of intervals. The dummies associated with the 21 intervals in the leisure-model are jointly significant. The same holds for the dummies in the study-model.

Algorithm with equal number of observations in each interval

Finally, we applied an algorithm which we referred to as ratio-algorithm. Here, all intervals have the same number of observations. A similar approach has been employed in a discussion paper of Hussinger, which is a predecessor of Hussinger (2008). In this discussion paper, ten intervals are used with a fixed number of observations. Since we have a larger sample, we have chosen to increase the number of intervals. We have used 50 intervals with an equal number of observations. The outcomes from the LR-test in Table 5.3show that the dummy variables are jointly significant in both models.

Figure 5.1, Figure 5.2and Figure 5.3show the distribution of the observations over the inter-vals. We also show the fragment of treated observations per interval. First, for the histograms of algorithm of Ayer we omitted interval zero from the figures. The reason for this is that these consisted of around 45,000 observations, which would produce an unreadable figure. The fragment of treated observations increases with the intervals. However, due to the high number of intervals, the fragment of treated observations is not distinguishable in the figure. Second, for the fixed-algorithm, we clearly see that the fragment of treated observations is higher for the upper intervals. Furthermore, we see that the upper intervals contain fewer observations. Due to the relatively low number of treated observations in the data set, the propensity score for most observations is relatively low (since one means treated and zero means untreated). This causes a relatively heavy tail on the lower side of the distribution. Third, for the ratio-algorithm, due to construction we see that the observations are equally distributed over the intervals. We also see that the fragment of treated observations steadily increases for higher intervals, which is a product of our semiparametric estimation in the first stage.

Both the fixed-algorithm and the ratio-algorithm provides with jointly significant dummies. Thus, both are suitable options in this application and one is not necessarily better than the other. Here, we choose to employ the ratio-algorithm but we emphasize that this algorithm is not necessarily better than the fixed-algorithm. ‘

5.2.2 Unbounded propensity score

We use the expression unbounded to denote an unrestricted propensity score. That means that the propensity score is not bounded between zero and 1 and is equal to Z0γ. In Figure 5.4

and Figure 5.5 we present a graphical representation of the estimated conditional selection correction terms. We make a distinction between the treated and untreated observations and

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0 100 200 300 400 500 600 700 800 900 1,000 1,100 0 10 20 30 40 50 60 Interval Frequency All Treated (a) ECAL 0 100 200 300 400 500 600 700 800 900 1,000 1,100 0 5 10 15 20 25 Interval Frequency All Treated (b) ECAS

Figure 5.1: Frequency of observations per interval (Ayer-algorithm)

Notes: Interval 0 is omitted from this figure. This interval consists for both types of extracurricular activities of about 45,000 observations. Including this high number of observations would cause an unreadable figure. 0 2 4 6 8 10 12 14 16 18 0 500 1,000 1,500 2,000 2,500 3,000 3,500 4,000 4,500 Interval Frequency All Treated (a) ECAL 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 0 500 1,000 1,500 2,000 2,500 3,000 3,500 4,000 4,500 Interval Frequency All Treated (b) ECAS

Figure 5.2: Frequency of observations per interval (fixed-algorithm)

0 5 10 15 20 25 30 35 40 45 0 200 400 600 800 1,000 Interval Frequency All Treated (a) ECAL 0 5 10 15 20 25 30 35 40 45 0 200 400 600 800 1,000 Interval Frequency All Treated (b) ECAS

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CHAPTER 5. RESULTS 28 −3 −2 −1 0 1 2 −4 −2 0 2 4 6 ·10−2

Unbounded propensity score Heckman Cosslett (a) Untreated −3 −2 −1 0 1 2 −6 −4 −2 0 2 4 ·10−2

Unbounded propensity score Heckman

Cosslett

(b) Treated

Figure 5.4: Conditional selection corrections for leisure-model

Note: The unbounded propensity score is computed as Z0γ

we show both the results for the leisure-model and the study-model. The figures show the contribution of selection correction specification for different values of the unbounded propensity score. We observe a moderate slope for Heckman’s correction term, which is natural for the inverse Mills ratio. The aggregate correction terms of Cosslett produce a non-smooth graphical representation. This is due to the use of dummy variables. For both models the size and shape of the graphs differ, which suggests that the parametric restriction in Heckman’s model may be too strict.

5.3 Two selection variables: first stage estimation

For the parametric model, we use a bivariate probit specification in the first stage. The estimated results are shown in Table 5.4. We observe that ρ is 0.021, which is very small. This means that there is almost no correlation present. An LR-test on ρ = 0 shows that this estimate is significantly different from zero (LR_-χ2(1) = 6.50, prob > χ2 = 0.011) for a 5% significance

level, but not for a 1% significance level. Since ρ is close to zero and not significant on a 1% significance level, we find sufficient grounds to assume that the selection equations for leisure-related activities and study-leisure-related activities are independent. The independence assumption eases the computations in the second stage dramatically. Therefore, we assume ρ = 0 and for both the parametric and the semi-parametric model we estimate the two selection equations independently. We emphasize that the assumption of ρ = 0 is not relevant for Cosslett’s model in which this relation is incorporated in the interaction between the dummy variables.

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ECAL (s.e.) ECAS (s.e.) start age -0.002 (0.003) 0.205*** (0.003) GPA hs 0.010 (0.010) 0.212*** (0.010) male 0.124*** (0.013) -0.126*** (0.013) parents’ -0.427*** (0.021) -0.049*** (0.019) hbo -0.456*** (0.013) -0.492*** (0.014) nonnative -0.092*** (0.019) -0.097*** (0.019) north -0.169*** (0.022) -0.042* (0.022) east -0.235*** (0.017) 0.047*** (0.017) south -0.223*** (0.017) 0.039** (0.017) profile CM -0.167*** (0.025) 0.281*** (0.023) profile EM -0.05** (0.023) 0.312*** (0.022) profile NG 0.078*** (0.021) 0.147*** (0.021) profile NT 0.012 (0.024) 0.197*** (0.024) mama lbo 0.087** (0.035) 0.110*** (0.034) mama mo 0.210*** (0.035) 0.110*** (0.034) mama hbo 0.355*** (0.035) 0.149*** (0.034) mama wo 0.654*** (0.038) 0.169*** (0.038) grad. year -0.014*** (0.003) 0.059*** (0.003) const. -0.513*** (0.101) -6.800*** (0.106) ρ .021** (0.008)

Table 5.4: First stage estimation results: two selection variables (bivariate probit)

Notes: We observe that ρ = 0.021, which is sufficiently small enough for us to assume ρ = 0 for Heckman’s model in the case of two selection variables. The standard errors are bootstrapped using 200 replications. Asterisks denote significance at *** 1%, ** 5% and * 10% level.

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CHAPTER 5. RESULTS 30 −3 −2 −1 0 1 2 −4 −2 0 2 ·10−2

Unbounded propensity score Heckman Cosslett (a) Untreated −3 −2 −1 0 1 2 −0.1 −5 · 10−2 0

Unbounded propensity score Heckman

Cosslett

(b) Treated

Figure 5.5: Conditional selection corrections for study-model

Note: The unbounded propensity score is computed as Z0γ

5.4 Two selection variables: second stage estimation

In this section we discuss the models with two selection variables. We use a one stage OLS estimation with the two selection variables as explanatory variables as benchmark. We also notice that the coefficients of all explanatory variables are very similar. Before we treat the different selection models, we briefly discuss the estimated coefficients.

The estimated coefficients are presented inTable 5.5. Similar to the model with one selection variable, the age of graduation has positive effects on salary. This effect is significant under all model specifications. Again, males earn significantly more than females. Like in the one selection variable models, studying at a wo-university yields an increase in salary of about 15% with respect to studying at a hbo-university. The number of hours worked have a positive effect on salary. For the fields of study, we observe again that the category law has positive effects. Now, also category engineering has significantly positive effects. Category education has non-significant effects and all other categories have negative effects compared to economics. Furthermore, we observe that for the fields of study education and engineering the sign switches with respect to the OLS model. At least for education this is due to the non-significance of the estimated coefficient. In conclusion, the coefficients of the explanatory variables are very similar in both sign and magnitude to the ones estimated in the model with one selection variable.

We now consider the coefficients of the selection variables. The results show that both selection variables have significantly positive effects on salary. The estimated effects are much larger in Cosslett’s model than in all other specifications and lie around a 10% increase in salary. However, we also observe that these effects are only significant at a 10% significance

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level, where the other two models produce significant effects at a 1% level. However, the results are not unambiguously about which type of activity has the largest effects. Heckman’s model suggests that leisure-related activities tend to lead to higher salary levels than study-related activities. For Cosslett’s model the estimated coefficients are approximately the same. Using a Wald test we find that we cannot reject the null hypothesis that the coefficients of ECAL and ECAS are equal (Wald_-χ2(1) = 0.021, prob > χ2 = 0.88). Thus, the results suggest that the

estimated effects are approximately the same.

Heckman’s selection correction terms

For Heckman’s model the selection correction term is estimated with the two Pudney terms (P1

and P2). Both of these terms are estimated with significant coefficients which justify the use of

a selection model also in the case of two selection variables. The negative coefficients indicate a negative correlation between the error terms. This may not be as expected, but it is consistent with the results for the inverse Mills ratio in the one selection variable model.

Cosslett’s selection correction dummies

The selection correction term in Cosslett’s model consists of interaction terms between the selection correction dummies for leisure-related activities and the selection correction dummies for study-related activities. In (3.19) the intervals appear in the function C_imA₁. This function is constituted consistently with the same approach as for one selection variable. Again, we use the ratio-algorithm to determine the selection correction dummies. However, the 50 intervals defined for the one selection variable model appeared to be computational intractable. For 50 intervals we obtained around 5,000 selection dummies, which consisted of 492 _{interaction terms}

for the untreated individuals and 492 interaction terms for the treated individuals. Hence, a great number of the interaction terms where supported by none or a low number of observations. Therefore, we halved the number of intervals to 25, which produced 1,155 interaction terms in total. Consequently, a LR-test showed that these selection correction interaction terms were jointly significant (LR-χ2(1, 155) = 1, 406; prob > χ2 = 0.000). Again, the use of a selection

model is justified.

5.4.1 Average treatment effects

We compare the results by calculating the estimated treatment effect for each model. The estimation of treatment effects is not that straightforward (Angrist et al., 1996). We only observe one of two potential outcomes and treatment effects can be different across individuals. However, in our case we do not consider treatment effects to differ across individuals, and take

The influence of extracurricular activitieson salary : should a student participate in leisure-related activities or study-related activities