Enrolment into Higher Education and Changes in Repayment Obligations of Student Aid Microeconometric Evidence for Germany

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1 Enrolent into Higher Education and Changes in Repayent Obligations of Student Aid Microeconoetric Evidence for Gerany Hans J. Baugartner *) Viktor Steiner **) *) DIW Berlin **) Free University of Berlin, DIW Berlin, IZA Bonn Abstract: We evaluate the effect of the federal students financial assistance schee (BAfoeG) on enrolent rates into higher education by exploiting the exogenous variation introduced through a discrete shift in the repayent regulations. Supported students had to repay the full loan until Thereafter, 50 percent of the student aid has been offered as a non-repayable grant. Our results fro siple difference-in-difference estiates suggest that student aid is ineffective in raising enrolent rates. Our findings ay have iportant iplications for the current debate on the refor of financing higher education in Gerany and elsewhere. JEL classification: Keywords: I28, I22, J24 educational decision, educational finance, higher education, difference-in-difference, discrete-choice Correspondence to: Viktor Steiner DIW Berlin Königin-Luise-Str. 5 D Berlin

2 1 Introduction In Gerany students fro low-incoe failies are eligible to financial aid under the federal students financial assistance schee (Berufsausbildungsfoerderungsgesetz, BAfoeG). This subsidy covers a substantial share of the onthly living costs of students enrolled at universities or technical colleges (Fachhochschulen). There are both efficiency and incoe distribution arguents justifying subsidies to higher education (see, e.g., Poterba 1996; Barr 2004). First, there ay be positive external effects in the sense that social returns ay exceed private returns to higher education. These ay arise fro progressive taxation and reduced welfare dependency of highly educated people, or spill-over effects fro a highly educated and trained workforce to innovation and econoic growth. Second, there ay be too little investent into education of youth fro low-incoe failies. Governents ay therefore want to provide subsidised loans or grants to students to foster equal opportunities for otherwise disadvantaged youth. These arguents also doinate the current discussion on the financing of higher education in Gerany. In this paper, we evaluate the effect of BAfoeG on enrolent rates by exploiting an exogenous variation induced by a change in the BAfoeG repayent regulations in Before this refor, the full aount of financial aid obtained during university education had to be repaid (without interest) after graduation; since the refor only the half of this aount has to be repaid, the other half being offered as a non-repayable grant to eligible students. This iplies that the debt burden of a fully supported student was on average reduced by soe 23,500 DEM (12,000 EUR) fro 47,000 DEM (24,000 EUR). Given this substantial subsidy, the refor was expected to induce ore students fro low-incoe failies to enrol into higher education. Using data fro the Geran Socio Econoic Panel (GSOEP) our estiation results fro siple difference-in-difference estiations show that the 1990 BAfoeG refor sees to have been ineffective in raising enrolent rates into higher education. This soewhat surprising result ay have iportant iplications for the current policy debate on how to finance and secure access to higher education in Gerany, and elsewhere. The reainder of this paper proceeds as follows. In the next section we discuss the rationale for public subsidies to students and suarize epirical studies on the effects of student aid on enrolent decisions. In section 3, we present our epirical ethodology to identify the effect of the entioned policy change on enrolent rates into higher education in Gerany. Estiation results are suarized and discussed in section 4, and section 5 concludes. 1

3 2 Theoretical Background and Previous Epirical Evidence Following Becker (1962), econoists usually analyze the decision to enrol into higher education in the fraework of huan capital theory. 1 According to standard huan capital theory, an individual s education decision depends on the coparison between the discounted costs and future returns of an additional year of education. The higher the private costs of an additional year in educational is, the higher its private return in ters of future wages has to be to induce the individual to invest in education. In this siple odel, higher direct costs of educational investent, such as tuition fees, would be associated with a lower optial level of education and a higher private return to education. Likewise, lower financial educational net costs, by subsidised loans or grants to finance tuition fees and living expenses, would increase the optial level of education and reduce its private return. Under the assuption of perfect capital arkets, the private return to education just equates its private arginal costs in a present value sense. Given tie preferences, the optiu level of education is then defined by individual abilities or learning productivities. For a given ability level, individuals with a higher rate of tie preference (individual discount rate) will choose a lower level of education, other things equal, and realise a higher return to education. Likewise, individuals who have to pay a higher rate of interest to finance their educational investent will choose a lower investent level. Given iperfect capital arkets and/or a higher tie preference prevailing aong low-incoe households, the optiu level of investent in education would negatively depend on household incoe even if ability between students was controlled for. Of course, if iperfections in capital arkets would not only result in different arket interest rates but in binding credit constraints, this effect would be even stronger (Kodde and Ritzen 1985). There are various distribution and allocation arguents for state intervention in the arket for higher education (for suaries c.f. Hanushek (2002) and Poterba (1996)). One of the ost iportant concerns the supposed existence of binding credit constraints for students fro low incoe failies. Not surprisingly, in this case state intervention can be rationalised not only by a distribution arguent but also for reasons of econoic efficiency. The efficiency arguent is even stronger in case of external effects of higher education, i.e. if the social returns of higher education exceed its private return. In this case, higher enrolent rates into tertiary education ay in fact lead to higher econoic growth and social welfare. 2 Another iportant issue in education policy concerns the relative efficiency of loans and 1 2 This literature is surveyed by Willis (1986) and Card (1999), aong others. For a suary of the theoretical and epirical literature on the relationship between private and social returns of education, as easured by its effect on econoic growth see, e.g., Topel (1999). 2

4 grants subsidised or/and guaranteed by the state, and their financing in increasing enrolent rates in higher education (Barr and Crawford 1998; Barr 2003). The positive correlation between enrolent rates and the level of parents incoe found in several epirical studies for various countries has typically been interpreted as evidence for the existence of credit constraints in the arket for student loans. This epirical correlation has been used to rationalise the provision of loans or grants along the lines entioned above. This causal interpretation, however, is criticised on the basis of recent epirical research. Caeron and Heckan (1998) and Carneiro and Heckan (2002) show that the observed correlation between students educational achieveent and parental incoe can also be explained by a positive correlation between the latter and parental ability which itself is correlated with their children s ability. In another line of recent epirical research it has been shown that the potential effects of credit constraints ay be very uch itigated if there is the option of soe arket work for students while enrolled at a college, and that the entioned positive correlation can be explained by parental financial transfers which acts the sae way as a reduction of tuition fees (Keane and Wolpin 2001; Keane 2002). In contrast to this ore structural estiation approach, recent epirical research on the effects of loans and grants on enrolent decisions into higher education siply relate this decision to variables suggested by basic huan capital theory. These variables typically include financial indicators, such as parents incoe, tuition fees, and student loans or grants. Most of these studies have been undertaken for the United States, while it sees that this topic has reained rather unexplored for Gerany so far. 3 As suarized by McPherson and Schapiro (1991), ost US studies up to the beginning of the 1990s tend to find statistically and econoically significant positive effects of financial factors on enrolent decisions. These studies also tend to find that the responsiveness of enrolent decisions is higher for students fro low-incoe failies. In McPherson and Schapiro s (1991) epirical investigation based on tie series data on enrolent rates of three incoe groups between 1974 and 1984 finds that reducing the netcosts by 1,000 US-$, which is defined as the difference between tuition fees and the subsidy value of the student aid, would increase enrolent of low incoe students on average by about 6.8 percentage points, but would have an insignificant effect on enrolent rates of students fro higher incoe groups. This is usually interpreted as evidence supporting the hypothesis of credit constraints in education choices. 3 There see to be only very few epirical studies on this topic for other European countries, see Winter- Eber and Wirz (2002). 3

5 In a couple of recent related papers Dynarski analyzes the effect of various policy changes related to financial aid on students college enrolent decisions in the US. Dynarski (2002a) uses a difference-in-difference ethodology on data frz the Current Population Survey. The exogenous variation used to analyze college entry is the introduction of the Georgia HOPE scholarship which allows free attendance at the state s public colleges for residents with a certain iniu scholarly attainent in high school. The control group is coposed of college freshen in other south-eastern states. She finds that the introduction of the scholarship rose college attendance by 7.9 percentage points. Using the sae ethodology, Dynarski (2003) analyses the ipact of the eliination of the US Social Security Student Benefit Progra in The reoval of this progra affected youth entitled to student aid in case of the death of a parent during an individual s childhood. Dynarski (2003) finds that this policy change has increased enrolent rates by about 18 percentage points one average. This relatively large effect is, however, not coparable to the effect for the HOPE scholarship progra because these progras affected different groups of people. In another paper also based on a difference-in-difference ethodology, Dynarksi (2002b) uses as an natural experient the reoval of hoe equity fro the set of assets that are taken into account for the assessent in federal financial aid forula by the US Higher Education Aendent in Since hoe equity is a large proportion of US household net worth, this change was expected to have a strong ipact on students eligibility for financial aid and, hence, on enrolent decisions. Although, the effect of this policy shift on enrolent rates is insignificant in the full saple, she detects a significant positive effect in a sub-saple of hoeowners, arguably the group of people ost affected by the policy change. In another frequently cited paper, Kane (1995) also applies a difference-in-difference ethodology to evaluate the introduction of the Pell Grant progra in the US, which is siilar to the Geran BAfoeG by providing eans tested financial support for student fro low-incoe failies. He copares the years around the introduction in 1973 and eligible students as the treatent group. According to his estiates, the introduction of the Pell Grant progra had no effect on enrolent rates into higher education. For Gerany, the question how financial aid ay effect enrolent decisions is rather unexplored. There sees to be only one econoetric study that relates student aid to enrolent into higher education. Lauer (2000) includes soe indicators for the provision of BAfoeG, derived fro the Geran Socio Econoic Panel (GSOEP), as explanatory variables in a discrete choice odel. Her epirical results see to show that increasing the study subsidy by 1,000 DEM (about 500 EUR) increases the enrolent rate by 0.8 percentage 4

6 points on average. This relatively low estiate ight be related to the other two BAfoeG indicator variables included as explanatory variables, naely BAfoeG entitleent and the loan share of the subsidy. Furtherore, her estiation results ay be biased because of potential endogeneity of the BAfoeG indicator variables included in her enrolent equations. 3 Epirical Methodology We use a large panel data set which allows us to identify for all youth who graduated fro upper secondary education transitions into higher education and the eligibility to student aid according to the Geran federal financial assistance schee. Since our panel data set spans the period 1984 to 2001 we can identify the effect of the change in the loan repayent obligation in 1990 which substituted 50 percent of the previously fully re-payable loan into a 50 percent grant on enrolent rates into higher education. We view this as a natural experient which allows us, using both the siple difference-in-difference ethod and discrete choice odels estiated on panel data, to identify the causal effect of this policy change on enrolent rates into higher education in Gerany. In the next subsection we provide soe institutional background and, in particular, describe the natural experient in federal financial aid for students. After a brief description of our data and saple design we then discuss the identification and estiation of the effect of this policy change on enrolent rates into higher education in Gerany. 3.1 The Refor of the BAfoeG Repayent Obligation as a Natural Experient To provide soe background for the discussion of our epirical ethodology applied to identify potential enrolent effects of changes in student aid, we start with a brief description of the Geran federal financial assistance schee to proote education (Bundesausbildungsfoerdungsgesetz, BAfoeG). When introduced in 1971, this law was eant to allow all qualified young people to enter a university regardless of parent s financial capacity. BAfoeG has been changed any ties since then and today subsidizes also pupils in secondary education, further education, and also youth enrolled in vocational training courses. The ain political goal of BAfoeG reains, however, to encourage students fro low-incoe failies to study at universities or technical colleges. The axiu aount of the subsidy is defined by the schee and depends on whether the student attends a technical college or an university, whether the student lives with her parents, and how she is insured for health care. This so pre-defined aintenance need (Bedarfssatz) is copared to the financial capacities of the parents or in instances where the student is arried by her spouse. The financial capacity takes various sources of incoe into 5

7 account and is reduced by actual paid taxes, a lup su for social security and considers also if an obligation exists to pay aliony for other persons. And finally, there is a basic allowance. Students are eligible for BAfoeG if the calculated aintenance need exceed the calculated financial capacities of the parents. Initially, BAfoeG was usually provided in the for of a non-repayable grant to ost eligible students, but in a few instances was granted as a loan. This was the case if the study subject was changed, or if the student had already copleted an university degree and continued her study with another subject (Zweitstudiu). The aounts for the aintenance needs and the basic allowances is to be adjusted every second year to keep pace with the cost of living. In winter 1983/84, the first ajor BAfoeG refor changed the repayent regulations fro a non-repayable grant to an interest-free loan that had to be paid back fro future earnings. This change was associated with a arked reduction in enrolent rates of graduates fro low incoe failies, which dropped by soe 18 percentage points fro 81 percent to 63 percent between 1976 and 1986 (Beirat für Ausbildungsförderung 1988; table 26). On the basis of this observation the Advisory Board on BAfoeG (Beirat für Ausbildungsförderung) suggested to refor the repayent obligations and to split the financial aid into a 50 percent grant and a 50 percent loan. It was expected by the Board that such a substantial reduction of the BAfoeG debt burden would otivate students fro low incoe failies to increase their enrolent into tertiary education (Beirat für Ausbildungsförderung 1988; 111). Following the suggestions of the Advisory Board, the 12 th revision of BAfoeG refored the repayent regulation in July Fro then onwards all supported students have had to pay back only 50 percent of the support fro their future earnings. The eligibility criteria for BAfoeG reained by and large unchanged. Hence, this discrete change in the BAfoeG repayent regulations affected the net present value of the financial aid for those students who were eligible to BAfoeG. For a fully supported student, this changed repayent regulation eant on average a reduction of her debt burden fro 47,000 DEM (24,000 EUR) to 23,500 DEM (12,000 EUR) (HIS 1987; 10). 3.2 Data and Saple Design Our epirical analysis is based on the Geran Socio-Econoic Panel Study (GSOEP). This is a longitudinal survey of individuals living in private households in Gerany covering each year since Since the BAfoeG repayent regulation was changed in 1990 (the year of 4 We use all waves up to the year Since we obtain the incoe inforation fro the calendar data, which refers to the previous calendar year, our observation period ends in Haisken-DeNew and Frick (2001) 6

8 unification of east and west Gerany), we have to restrict our saple to west Gerany. We also restrict the saple to people who have copleted upper secondary schooling, since only these people are entitled to enrol into higher education at universities or technical colleges. We thus analyze, respectively, enrolent probabilities at these institutions and transition rates fro upper secondary schooling into higher education observed within the period In 2001, there was another change of the BAfoeG rules which ade the subsidy ore generous, but this will not affect our analysis since the observation period of our data ends before this change becae effective. We distinguish between universities and technical colleges because students at these two institutions differ in ters of their upper secondary education, their future careers and the likely effect of their response to the change in BAfoeG rules. Whether an individual is eligible to the study subsidy depends, as entioned above, ainly on the financial capacity of the parents relative to the aintenance need of the individual student. However, whether an individual receives BAfoeG is only observed for students and not for those who decided not to enrol into tertiary education, even though these individuals ight be eligible for BAfoeG. Potential eligibility has thus to be inferred fro parents incoe and other relevant inforation contained in GSOEP. We built thus a odel to siulate BAfoeG eligibility for all individuals and for each year within the observation period. The siulation approach is briefly described in the appendix. Our saple includes 735 school leavers with an entrance qualification for higher education. 133 are right-censored due to saple attrition or at the end of the observation period, and for 53 observation we could not calculate BAfoeG eligibility because of issing inforation on parents. If an individual has not enrolled into higher education within four years after the copletion of upper secondary schooling she is defined as a non-student. Saple attrition is handled in the estiation by treating these observations as right-censored at the tie they are last observed in the saple, as described below. The construction of the saple and the exact coding of the basic variables are described in detail in the appendix. Descriptive statistics for the reaining 561 observations are shown in table A1 in the appendix: 59 percent enrolled within four years after copleting upper secondary schooling; 15 percent are observed to have enrolled at a technical college, 44 percent at an university. About 78 percent of our saple qualified for higher education by copleting a gynasiu, i.e. 22 percent obtained this qualification fro a specialised gynasiu. The enrolent provide detailed inforation on the GSOEP data. 7

9 descision is taken by 66 percent after the BAföG repayent regulations were changed in 1990 and our siulation shows that 22 percent are eligible for the financial study support. 5 Table A1 presents also descriptive statistics for the treatent and the control group, respectively. The incoe of parents of eligible students is on average only one third the incoe of parents of students not entitled to BAfoeG. The two groups also differ arkedly in their parents educational background. As regards enrolent rates into higher education, average rates differ between the two groups, while enrolent into a technical college does not differ between the treatent and the control group. 3.3 Identification and Estiation We use the data and saple design as described to identify the effect of the change in the loan repayent obligation introduced by the BAfoeG refor in 1990 on students enrolent decisions. We interpret this change as a natural experient. The discrete policy shift affected only the group of students entitled to the subsidy because of relatively low parental incoe. Ineligible students are not affected by the refor. This introduces an exogenous variation which we exploit to identify the effect of the refor. To do so, we eploy a siple difference-in-difference estiator and several discrete choice odels including appropriately defined duy variables to account for the discrete policy shift. We also try to account for the potential presence of dynaic selection bias related to our saple design on the basis of a discrete-tie hazard rate odel. Siple Difference-in-Difference Estiator We use a difference-in-difference to exaine the effects of BAfoeG eligibility on enrolent. A difference-in-difference estiation copares the enrolent decision of two groups (first difference): a treatent group eligible students and a coparison group that is not affected by the policy shift ineligible students. This difference is then copared between the two tie periods: before and after the discrete policy shift (second difference). Thus, the siple difference-in-difference estiator is: 5 At the first glance, this ight look like a sall ratio. But we would like to stress that 79 percent of students did not receive BAfoeG between 1985 and 2001 (AG Hochschulforschung 2001; table 105a). 8

10 (1) α = S( EB= D= ) S( EB= D= ) S( EB= D= ) S( EB= D= ) 1, 1 0, 1 1, 0 0, 0, where S(EB, D) := share of people enrolled at university with (EB=1) / without (EB=0) BAfoeG eligibility, after (D=1) / before (D=0) the refor. The coefficient α easures the average effect of the refor on the enrolent share in the group of people affected by the refor, which is also known as the average treatent effect on the treated in the epirical policy evaluation literature (c.f. Meyer 1995; Blundell and Costa Dias 2000). The key identifying assuption is that the causal effect would be zero in the absence of the policy shift, i.e. any shift in the probability of enrolent of eligible students is attributable to the policy change. The siple difference-in-difference estiator fro equation (1) is equivalent to the α coefficient on the interaction ter in the following siple pooled regression: S = α EB D + βeb + γd + ϕ +υ, (2) ( ) it it it it it where S it is the schooling variable for person i in period t, EB and D are duy variables as defined above, υ is an error ter and α, β, γ and ϕ are paraeters to be estiated. In order to yield unbiased estiates of the paraeters in regression (2), the key identifying assuption entioned above has to hold. This also iplies that the expectation of the difference of the error ters after and before the policy change is the sae for the two groups, i.e.: ( ) ( E υ υ EB= 1 = E υ υ EB= 0). i1 i0 i1 i0 Since S it is a dichotoous dependent variable, a siple OLS regression (2) would obviously not be an appropriate estiation ethod. To take into account the inherent nonlinearity of (2), we could estiate soe non-linear function, such as siple binary logit odel. This will be a special case of the discrete-choice odels we now turn to. Discrete-Choice Models Econoetric analyses of the decision to enrol into higher education using icro data are typically based on discrete-choice odels ranging fro siple static reduced-for binary logit odels to dynaic structural odels based on explicit inter-teporal optiisation (see in increasing order of sophistication Manski and Wise (1983), Caeron and Heckan (1998), Keane and Wolpin (2001)). The basic idea underlying these odels is that educational decisions are based on the coparison of utility levels associated with alternative choices, with the chosen education level deterined by the highest obtainable utility level. In ost epirical applications estiation is 9

11 based on relatively siple reduced for odels which relate the probability of enrolent into higher education to various financial variables, such as parental incoe, tuition fees, loans, grants, and a set of control variables. McFadden (1974) shows that a discrete choice odel derived fro stochastic utility axiization can be represented by a ultinoial logit (MNL) odel. Fro a practical point of view, an iportant advantage of the MNL odel is that it can easily be applied to decisions involving ore than two alternatives. This is iportant for our analysis because, for the reasons given in section 3.2 above, we want to differentiate between enrolent into technical colleges and universities. One potential disadvantage of the MNL specification is that it iplies the so-called independence fro irrelevant alternatives (IIA) assuption. That is, the relative log-odds-ratio between university and technical college does not depend on other alternatives siilar to one of the included alternatives. In the estiation of the odel we will test whether this assuption can be aintained. Identification of the causal effect of the BAfoeG refor on individual enrolent decisions in the MNL odel is the sae as discussed above, and the estiated α coefficient still represents the average effect for those affected by the policy refor. We also control for covariates that potentially affect students enrolent decisions into higher education, such as parental incoe and education, student s gender and age at graduation fro secondary school. These control variables are captured by the vector X. The probability of attaining a particular education level j for individual i in period t can be expressed by: 1 Pr Eit = j =, j = exp (3) ( ) (4) ( ) j= 1 j= 1 ( α j ( EB D) β jebit γ jdit δ jxit ε j ) it ( α j ( EB D) + β jebit + γ it jdit + δ jxit + ε j ) ( α j ( EB D) β jebit γ jdit δ jxit ε j ) exp Pr Eit = j =, j = 1,2,... J exp it The coefficients in the base category not enrolled (S = 0) have been noralized to zero. Hence, equation (3) gives the probability of this alternative. If there are only two possible alternatives (j = 0,1), the MNL reduces to the binary logit odel. For reasons of coparison, we will also estiate this odel and test it against the ore general specification with three alternative states. 10

12 The tie-invariant individual effect ε j accounts for unobserved heterogeneity and is assued to coe fro an arbitrary discrete probability distribution with a sall nuber of ass points, (5) M = 1 ε j, with the following properties: M ( ) ( ) E ε = Pr ε ε = 0 E j j j = 1 ( ε j ) Pr = 1 ( ε j Xit) = 0, where the vector X contains not only the controls as above but also the group indicator variables and their interaction for the difference-in-difference; ε j is assued to be uncorrelated with all explanatory variables. Instead of explaining educational attainent at a particular point in tie one could also odel transition rates between education levels. As stressed by Caeron and Heckan (1998), one iportant advantage of this alternative odel specification is the possibility to account for dynaic selection bias in education decisions over tie. Given that we only look at enrolents into higher education within a relatively short tie period of 4 years, this potential odelling advantage ay see soewhat liited at first sight. However, taking into account the relatively large nuber of right-censoring in our data due to saple design and attrition, it turns out that accounting for this potential selection bias by odelling transitions between states to be iportant. A further advantage of the MNL described above is that it can easily be re-stated in ters of a discrete-tie hazard rate odel (Steiner 2001). This allows us to account for saple attrition in a straightforward way, and also provides a ore appealing interpretation of enrolent decisions in ters of transition rates into higher education. The observed variable statistically related to these transition rates is the duration between graduation fro upper secondary school and enrolent into one of two possible states, j =1: technical college, 2: university. This duration is described by a non negative rando variable, T, which takes on integer values only. If an observation ends in the interval [I t 1, I t ], which will be one year in the epirical analysis, this variable takes on a value of T = t. The hazard rate for individual i, λ ij () t, is the conditional probability, of a transition into state j in year t. Given that no transition has occurred until the beginning of t the hazard rate is: 11

13 (6) λ ( ) t X = P T = t, Ω= j T t, X, ε ij it i i it j with i = 1,2,...n; j = 1,2; X it = vector of covariates of individual i in interval t Ω: = 1, if transition into technical college = 2, if transition into university. ε j = tie-invariant individual effect, with the above stated properties. Assuing independence of transitions into the two states, conditional on the vector of covariates, the hazard rate into higher education is given by 2 (7) λ ( t it, ε j ) λj ( t it, j ) X = X ε. j= 1 In ters of the hazard rate, the probability of not having enrolled into higher education in period t, conditional on not having been enrolled up to period t-1 is given by (8),, P Tk > t Tk t it ε j = 1 λ( t it, ε j ) X X. The survivor function which gives the (unconditional) probability of not having enrolled into higher education up to period t, can be written as t 1 (9) PT ( > t ) = St ( ) = ( X, ε X, ε 1 λ τ, ε ) X. k it j it j it j τ = 1 In ters of the respective hazard rate and the survivor function, the probability of a transition into state j in period t is given by t 1 (10) PT ( = tω= j ) = ( t ) ( X X X. k, it, ε j λj it, ε j 1 λ τ it, ε ) j τ = 1 Assuing that, conditional on X it, all observations are independent, the saple likelihood function is given by n M 2 δ i ij (11) L= Pr ( ε j ) λij ( ti it, ε j ) 1 λi ( τ it, ε j ) t 1 X X i= 1 = 1 j= 1 τ = 1 1, if individual i akes educational transition j with δij = 0, otherwise. Hence, for a person with an observed transition into higher education the contribution to the likelihood function is given by the respective transition probability in equation (10), for a censored spell it is given by the survivor function in equation (9), both written in ters of hazard rates. Note that the survivor function not only provides inforation for individuals right-censored at the end of the observation period, but also for those who left the panel due to saple attrition. 12

14 It reains to specify a functional for for the hazard rate, which is forally equivalent to the MNL specification, i.e.: (12) λ ( t X ) ij j= 1 ( α j ( EB D) + β jebit + γ it jdit + δ jxit + ε j ) ( α j ( EB D) β jebit γ jdit δ jxit ε j ) exp it =, j = 1, exp it where the vector X it also includes three duy variables (with the first year duy as the base category) to account for duration effects on the hazard rate. The rando effect is assued to share the sae properties as above. Note that the explanatory variables in (12) are allowed to vary of tie, which provides an additional source of inforation for the estiation of the odel. Plugging the hazard rate (12) into the likelihood function (11), ML estiates of the paraeters, the ass points and their probabilities, taking into account the above entioned restrictions on the individual effects, can be obtained by standard nuerical optiization procedures. 6 4 Estiation Results We first present siple difference-in-difference estiates by calculating the eans of enrolent rates of the treatent and the control group, before and after the repayent regulations were changed. Using siple linear regression analysis we show that the results fro siple difference-in-difference estiates ay depend on the saple design. Then we present estiation results fro a binary logit odel, which is a ore appropriate specification for the binary outcoe variable, where we also control for other potential deterinants of individual enrolent rates. The binary logit odel is a special case of the discrete choice odels described in section 3.3 above. Since enrolent decisions ay differ between technical colleges and universities due to eligibility criteria, expected careers as well as future earnings, we also estiate ultinoial logit odels as described in section 3.3 and test for these potential differences. Finally, instead of enrolent probabilities we odel transition rates into higher education on the basis of the discrete-tie hazard rate odel also described in the previous subsection, which allows us to account for dynaic selection bias related to saple attrition. 6 The glla prograe as ipleented in Stata 8 is used for the estiation. For a description and technical details see Rabe-Hesketh, Skrondal and Pickles (2001). 13

15 4.1 Siple Difference-in-Difference Estiates Given the validity of the identifying assuptions entioned in the previous section, it is straightforward to calculate the siple difference-in-difference estiator of the effect of the BAfoeG refor on the average enrolent rate of eligible students fro Table 2. The table shows average enrolent rates for four groups: the treatent group of low incoe youth eligible to BAfoeG and the control group of non-eligible youth, both after and before the policy refor. The third colun shows the first differences. Enrolent rates of eligible students rose by 28.8 percentage points, while enrolent of the control group increased by only 21.3 percentage points. As shown in the table, the difference-in-difference in ean enrolent rates aounts to 7.6 percentage points, which is the average treatent effect for those affected by the BAfoeG refor. Table 2: Difference in difference of eans after before difference eligible for BAfoeG ineligible for BAfoeG difference-in-difference Note: Means of the school leaver cohorts and This treatent effect can also be obtained fro a linear probability odel estiated on individual data as given by equation (2) in the previous section. Since estiated standard errors fro OLS regressions are known to be biased due to heteroscedasticity, we calculate adjusted standard errors based on the estiated variances of the errors. The first two coluns of Table 3 report WLS estiation results for the selected saple of school leavers in two periods of equal length before and after the policy change, which corresponds to the saple used for the siple difference-in-difference estiate derived above. Hence, the coefficient on the interaction between the group duy and the tie duy in colun (1) of Table 3 is nuerically identical to the difference-in-difference estiate in table 2. However, as the estiated standard error of the coefficient estiate in Table 3 shows, the estiated treatent effect is not statistically significantly different fro zero. Estiation results in colun (2) of Table 3 refer to the full saple of freshen. Thus, we do not restrict the observation period to be of equal length before and after the policy change. This increases the saple size substantially and ay also avoid soe potential selectivity effects associated with the saple selection in the previous estiation. Estiation results in colun (2) show that the estiated coefficient on the relevant interaction ter is arkedly reduced in size and also reains statistically insignificant. 14

16 Table 3: Enrolent probability in higher education constant (0.048)** after (0.071)** eligible for BAfoeG (0.103) after eligible for BAfoeG (0.143) Linear Probability Models Logit Model (1) (2) (3) (4) (0.041)** (0.050) (0.080) (0.100) (0.170)* (0.206) (0.372) (0.461) (1.815)** (0.225) (0.413) (0.504) father self-eployed (0.352) father white collar (0.250) father civil servant (0.318)* father out of labour force (0.506) ale (0.192) abitur (0.233)** school leaving age (0.091)** father copleted upper secondary schooling other copleted upper secondary schooling (0.259) (0.335) R² log-likelihood χ² observations Notes: a) Estiation results in colun (1) refer to a selected saple of school leavers in two periods of equal length before and after the BafoeG refor, i.e. school leaver cohorts and b) Estiation of the linear probability odel in coluns (1) and (2) is based on Weighted Least Squares to account for heteroscedasticity. c) Standard errors are in parentheses. + significant at 10%; * significant at 5%; ** significant at 1%. d) The base category for father's occupational status is blue-collar worker. 4.2 Binary Logit Estiates To account for the inherent non-linearity of the dichotoous dependent variable, in coluns (3) and (4) of Table 3 we present logit estiates for the siple odel and for the odel with addition control variables. Estiation of this odel is based on all observations within the observation period and should therefore be copared to estiation results in colun (2). As expected, the WLS and logit coefficient estiates in coluns (2) and (3) are virtually identical after noralization. Other things equal, enrolent rates are higher if the father has 15

17 copleted upper secondary schooling, if students obtained their entrance qualification for a higher education institution by a degree fro a general gynasiu rather than a specialised gynasiu, and the higher the school leaving age. However, controlling for these covariates does not change the insignificance of the estiated treatent effect. 7 We have also tested for hoogeneity of coefficients of explanatory variables for the treatent and the control group. Although the null hypothesis of equality of coefficients was rejected for alost all explanatory variables, allowing the coefficient of these variables to differ between the two groups has essentially no effect on the estiated treatent effect. 4.3 Multinoial Logit Estiates In table 4 we suarize estiation results for the MNL odel with enrolent at a technical college or at an university as alternative choices of higher education. Coefficients are to be interpreted relative to the base category, which is not being enrolled at either of the two entioned alternatives. Note, however, that the arginal effect of a MNL odel depends not only on the estiated coefficient but also on all other estiated coefficients which ay affect both the size and the sign of the effect (Greene 2003; 722). Estiation results for odel (1) show that the effect of a change in the BAfoeG repayent regulation is insignificant for both choices. This holds true regardless whether or not we include other control variables, as in odel (2). Only a few of these variables are significant: Males have a higher probability to register with a technical college and having a father, who copleted upper secondary schooling, raises the probability to enter an university, whereas having obtained a degree fro a general gynasiu only affects enrolent into university but not into a technical college. Finally we have tested the validity of the independence of irrelevant alternative (IIA) assuption underlying odels (1) and (2). The IIA assuption can be tested by introducing an additional alternative which is siilar to one of the already included choices. A potential relevant alternative could be to pursue vocational training after copleting upper secondary schooling. Büchel and Bausch (1998) argue that risk averse students ight pursue vocational training before or instead of enrolent into higher education. On the basis of a Hausan specification test (Hausan and McFadden 1984) we cannot reject the null hypothesis that the IIA assuption is not violated. 7 A test on the joint significance of parents incoe and its square shows that parent s incoe has no significant effect on enrolent rates (χ²=0.97 with 2 degrees of freedo). We thus disregard these variables in our analysis. 16

18 Table 4: Enrolent probability in technical college or university ultinoial logit estiates technical college after (0.305) eligible for BAfoeG (0.624) after eligible for BAfoeG (0.730) (1) (2) (3) university (0.221) (0.383) (0.480) technical college (0.319) (0.657) (0.769) father self-eployed (0.476) father white collar (0.357) father civil servant (0.470) father out of labour force (0.668) ale (0.297)** abitur (0.282) school leaving age (0.113)** father copleted upper secondary schooling other copleted upper secondary schooling constant (0.250)** ass points: (0.381) (0.570) (0.181) (2.243)** university (0.248) (0.451)* (0.551) (0.391) (0.280) (0.348)* (0.611) (0.211) (0.383)** (0.110)** (0.278) (0.358) (2.236)** technical college (0.568) (1.284) (1.354) (0.835) (0.575) (0.888) (0.995) (0.547)** (0.540) (0.225)** (0.749) (0.923) (4.850)** ε (1.371)** university (0.594) (1.320)* (1.442) (0.854) (0.580) (0.923)* (1.051) (0.555) (0.719)** (0.275)** (0.746) (0.881) ( ) ( ) ε prob(ε 1 ) (0.043)** prob(ε 2 ) Observations log-likelihood χ² Notes: a) Standard errors in parentheses. + significant at 10%; * significant at 5%; ** significant at 1%. b) Base category: staying out of tertiary education. c) The χ² statistic of colun (3) copares the log-likelihood of odel (3) versus odel (2). d) ε 1 and its probability is estiated. ε 2 is calculated according to the properties entioned in the text. The last two coluns show the estiation results of odel (3) where individual rando effects account for unobserved heterogeneity. Including two ass points for each category iproves the log-likelihood significantly suggesting that unobserved heterogeneity effects are 17

19 present in our data. Taking these unobserved effects into account, however, does not alter the insignificance of the average treatent effects, neither for the choice to enrol into a technical college nor for the choice to enrol into an university. 4.4 Estiation Results for Transition Rates Multinoial logit estiates for transition rates into higher education are presented in table 5. As in the previous subsection, we present results for the base odel (1), for odel (2) with additional control variables, and for the rando effects specification (3). These odels differ fro the MNL in the previous section in that, instead of explaining the enrolent at a technical college or an university at a particular point in tie, they explain the respective transitions into higher education within a period of four years (in the uncensored case). In addition to the control variables also included in the MNL odels of the previous subsection, the transition odels also include baseline hazard duies to account for the effect of process tie ( duration dependence ) on enrolent rates. The estiated treatent effect is insignificant for both the transition rate into a technical college and into university in all specifications. However, the sign of the treatent effect turns negative for enrolent into a technical college but reains highly insignificant. Another interesting result in table 5 concerns duration effects on transition rates into higher education. The estiation results show that transition rates are decreasing over tie, that is students are less likely to pursue higher education if they have not enrolled right after having copleted higher secondary schooling. However, this duration effect is only significant for the transition rate into university, whereas the baseline duies are neither individually nor jointly significant in the transition rate into a technical college. Including control variables does not change these patterns. Enrolent rates into university still depend negatively on duration, whereas we could not find any duration effects for enrolent into a technical college. The last tow coluns show the estiation results of odel (3) where individual rando effects account for unobserved heterogeneity in transition rates. Including two ass points for each category iproves the log-likelihood significantly suggesting that unobserved heterogeneity effects are present. Taking these unobserved effects into account, however, does not alter the insignificance of the average treatent effects, neither for the transition into a technical college nor for the transition into an university. 18

20 Table 5: Enrolent rates into technical college or university technical college year (0.271) year (0.316) year (0.371) after (0.269)+ eligible for BAfoeG (0.364) after eligible for BAfoeG (0.523) (1) (2) (3) university (0.157) (0.220)** (0.296)** (0.162)* (0.230) (0.310) technical college (0.266) (0.321) (0.383) (0.274)* (0.364) (0.521) father self-eployed (0.400) father white collar (0.291) father civil servant (0.403) father out of labour force (0.665) ale (0.265)** abitur (0.237)** school leaving age (0.093)** father copleted upper secondary schooling other copleted upper secondary schooling constant (0.258)** ass points: (0.317) (0.490) (0.140)** (1.862)** university (0.163) (0.230)* (0.304)** (0.172)* (0.243) (0.336) (0.283) (0.210) (0.245) (0.530) (0.149) (0.339)** (0.084)** (0.185)* (0.247) (1.607)** technical college (0.294) (0.346) (0.408) (0.317)* (0.420) (0.589) (0.445) (0.339) (0.450) (0.851) (0.309)** (0.482)* (0.106)** (0.363) (0.554) (2.136)** ε (1.055) university (0.241)** (0.363) (0.506) (0.254)** (0.339) (0.462) (0.492) (0.330) (0.398) (0.713)** (0.278)** (0.477)** (0.132)** (0.309) (0.414) (2.889)** (0.738)** ε prob(ε 1 ) (0.265)+ prob(ε 2 ) Observations Log-likelihood χ² Notes: see table 3. 19

21 5 Suary and Conclusion We have analysed the effect of a discrete policy shift in federal student aid in Gerany introduced by the BAfoeG refor in 1990 on enrolent rates into higher education. In 1990, the repayent regulations were changed with the expectation that enrolent rates would raise, and that ore young people originating fro low-incoe failies would pursue tertiary education. Before the refor, the full loan becae due after graduation. The refor reduced the debt burden of student aid by 50 percent, the other half was transfored into a nonrepayable grant. We interpret this as a natural experient and exploit this supposedly exogenous variation to identify the causal effect of ore generous student aid on enrolent rates into higher education. Estiation results fro both siple difference-in-difference estiates and discretechoice on the basis of data fro the Geran Socio Econoic Panel (GSOEP) spanning the years show that this substantial reduction of the debt burden was ineffective in raising enrolent rates. This soewhat surprising result is robust to various odel specifications. One possible explanation for the insignificant effects of the BAfoeG refor on enrolent rates is that our basic identifying assuption of a coon tie trend for the treatent and control groups is violated. We cannot test this hypothesis, of course, nor can we rule out this possibility on a priori grounds. For exaple, it could be possible that the decline in the private returns to education docuented for Gerany in Boockann and Steiner (2000) and Lauer and Steiner (2001) has had different effects on enrolent decisions of youth fro low-incoe households and those not entitled to BAfoeG. Although this ay see theoretically plausible because youth fro low-incoe households ay, due to credit constraints and/or a higher rate of tie preference, request a higher private return to education to induce the to enrol into higher education, there sees to be no evidence supporting this view. Hence, for the tie being, we interpret our epirical results as indicative for the ineffectiveness of ore generous student aid in raising enrolent rates into higher education in Gerany. 20

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