information on GPA in the analysis, we do not have an indicator for the student’s motivation. When SOFES students are more motivated than the average student, we might find a positive treatment effect on student performance while this is actually a selection effect. To take such selection effects into account, the question whether SOFES students put in more effort can yield some insight into the importance of “credit-induced” motivation, although it only captures part of the story.

These potential sources of selection bias should be kept in mind. However, as we shall describe in more detail below, our econometric strategy employing the administrative data does not suffer from selection bias, as treatment is “randomly” assigned. A comparison of the results from both data sources should enable us to get an idea of the quantitative importance of selection bias in the survey data.

An alternative to a controlled experiment is a natural experiment, in which the researcher uses creative solutions to construct a randomly selected treatment group. In our case, we can design a natural experiment by using discretionary changes in the assignment rules. As we have seen in Section 3, the amount of credit a student can receive depends on the student’s so-called economic need factor (ENF) in a discretionary way. For instance, a student can receive a credit of 30% of the tuition fee when her ENF is 0.079, but she can receive a credit of 40% when her ENF is 0.08. However, students just below and just above the threshold will be closely comparable. Assignment to treatment thus involves a random element around the threshold. This identification strategy is known as the Regression-Discontinuity (RD) approach (cf. Van der Klaauw, 2002; Kane, 2003). Formally, the financial aid allocation process can be characterized as: where 1{} is the indicator function, taking the value 1 if the logical condition in brackets holds and the value 0 if not. In words, this equation says that the credit level assigned to students depends on the ENF with known discontinuities at cut-off points ENF<sup>*</sup> . As ENF is the only systematic determinant of the credit category for which the student is eligible, this structure is known in the literature as a sharp RD design.<sup>14</sup> The assumption behind the RD design is that in the absence of the student loan program, the relationship between the dependent * and the independent variables would be continuous. The cut-off points are (cf. Table 1): ENF1 =0.08; ENF2*=0.15; ENF3*=0.30; ENF4*=0.50. We compare the outcome variable around the cut-offs.

> 14 It should be noted that ENF is not a perfect predictor of student loans, and some randomness is present in the data. We therefore also performed the econometric analysis using a “fuzzy” RD design (cf. Van der Klaauw, 2002). In the fuzzy RD design we adopt a two-stage least squares method. In the first stage we estimate the credit level from the dummy indicating whether the student’s ENF is above or below the threshold. In the second stage we use the credit level as the treatment variable, and perform the sensitivity analysis as presented in Tables 5, 7 and 9. Results hardly changed, and therefore we do not present them.

18