Degree choice evidence from stated preferences

Abstract

This paper studies the factors driving the choice of university degree or college major. Previous research shows that students choose the degree/major that reports them the maximum utility level. This evidence relies on data from revealed preferences, implicitly assuming that the degree/major a student pursues is the student’s preferred degree. However, numerus clausus and other restrictions can condition the choice of major. Under these restrictions, the revealed choice is not necessarily the alternative that maximizes utility. We analyze data from pre-enrollment student-stated preferences regarding degrees within a natural field choice experiment setting. Our findings are in line with the rational choice results obtained in the literature, thus contributing external validity in a previously unexplored setting. In addition, we also contribute a discrete choice modeling strategy and estimation method. The discrete choice model accounts for individual characteristics, degree attributes and their interaction in an specification that is as general as discrete choice models used in the literature. The estimation method can handle cases where the number of alternatives and individual observations is large while other methods are unfeasible.

Appendices

Appendix 1

To see that model 2 nests the mixed logit model, note that 2 also admits an alternative parametrization of the form

$$\begin{aligned} U_{ij}(Z_{i},X_{ij},W_{j},\eta _{ij})= & {} X_{ij}\beta +W_{j}\alpha _{i} +\varepsilon _{ij}\end{aligned}$$

(8)

$$\begin{aligned} \alpha _{i}= & {} \left( I_{L}\otimes Z_{i}\right) \gamma ^{*}+v_{i}, \end{aligned}$$

(9)

where $\alpha _{i}$ is a $K\times 1$ vectors of coefficients, $I_{L}$ is the $L\times L$ identity matrix, $\gamma ^{*}=(\gamma _{1}^{*\prime },..,\gamma _{k}^{*\prime },..,\gamma _{K}^{*\prime })^{\prime }$ is a $KL\times 1$ vector of coefficients where $\gamma _{l}^{*}=\left( \gamma _{1l}^{*},\,\gamma _{2l}^{*}, \ldots ,\gamma _{Kl}^{*}\right) ^{\prime }$ and $v_{i}$ is a $L\times 1$ vector of iid zero mean random disturbances. Also note that, under this parametrization, $\eta _{ij}=W_{j}v_{i}+\varepsilon _{ij}$ and $\gamma ^{*}$ contains the same elements as $\gamma$ in a different order. It follows that when $\gamma _{k1}=0$ for all k, so that the utility specification does not incorporate individual-specific characteristics’ mean effect on utility, Eq. 9 can be written as

$$\begin{aligned} \alpha _{i}=\gamma _{1}+\Gamma Z_{i}^{*}+\Phi \xi _{i}, \end{aligned}$$

(10)

where $\gamma _{1}$ is a $(L\times 1)$ vector of fixed mean effects of attributes, $Z_{i}^{*}$ is a $\left( K-1\right) \times 1$ vector whose elements are those of $Z_{i}$ except unity, $\Gamma =\left[ \gamma _{2},\,\gamma _{3},\ldots ,\gamma _{K}\right]$ is a $\left( L\times (K-1)\right)$ matrix of parameters, $\xi _{i}$ is a $L\times 1$ vector of zero mean iid random disturbance and $\Phi$ is a $L\times L$ matrix of parameters. Equations 8 and 10 form the mixed logit model as specified in Hensher and Greene (2003). Moreover, when $\gamma _{kl}=0$ for all k and l greater than one and $\Phi \ne 0$, the model simplifies to the random parameter mixed-logit model proposed in McFadden and Train (2000). Finally, when $\gamma _{kl}=0$ for all k and l greater than one and $\Phi =0$, then $\alpha _{i}=\gamma _{1}$, so Eq. 8 boils down to Conditional Logit Model.

Appendix 2: the variables

1.1 Personal characteristics

• Gender takes the value 0 if the individual is a woman and 1 if the individual is a man.

• Age measured in years.

• Vehicular Language takes the value 1 if the students took the entrance exam in Basque and 0 otherwise.

• Basque, Philosophy, History, Spanish, English, and Mathematics are equal to the grade obtained in the corresponding part of the entrance exam, or take the value 0 if the student did not take that part of the exam.

• Selectividad is the overall mark obtained in the entrance exam.

• Overall Grade is the weighted average between the grade obtained in the entrance exam (40 %) and the grade obtained in High School (60 %).

1.2 Degree attributes

• Bizkaia and Gipuzkoa are dummies that take the value 1 if the degree is taught in the province of Bizkaia/Gipuzkoa and 0 otherwise.

• Threshold Grade is the minimum grade needed to access to a degree.

• Basque Ratio is the percentage of credits that are offered in Basque over the total number of compulsory credits.

• Student/Teacher Ratio is the ratio of the number of students with respect to the number of instructors in each School.

• Wage is the average wage of employed graduates 3 years after graduation.

• Credits records the number of credits necessary to complete a degree.

• Find Job is the average number of months graduates need in order to find a job from the moment they start looking for a job.

1.3 Variables that vary with students and degrees

• Province is a dummy that takes the value 1 if the student’s residence is in the province where degree is taught.

• Distance between the town of residence of a student and the town where a degree is taught, measured in kilometers.