Optimal admission to higher education

ABSTRACT

This paper analyses admission decisions when students from different high school tracks apply for admission to university programmes. I derive a criterion that is optimal in the sense that it maximizes the graduation rates of the university programmes. The paper contains an empirical analysis that documents the relevance of theory and illustrates how to apply optimal admission procedures. Indirect gains from optimal admission procedures include the potential for increasing entire cohorts of students' probability of graduating with a higher education degree, thereby increasing the skill level of the work force.

KEYWORDS:

• Educational economics
• college admission
• human capital

JEL CLASSIFICATION:

• I21

Acknowledgments

Thanks for comments from the editor, two referees, Atila Abdulkadiroglu, John Kennes, Dean Lillard, Rune Vejlin and seminar participants at the Copenhagen Business School, the conference of the Danish Economic Society, the Barcelona workshop of the European Network for Research on Matching Practices in Education and Early Labour Markets, the Congress of the European Economic Association in Gothenburg, and the International Workshop on Applied Economics of Education in Catanzaro.

Disclosure statement

No potential conflict of interest was reported by the author.

Notes

1 See the ‘admission index’ at University of California, http://admission.universityofcalifornia.edu/.

2 The interpretation of the expression is straightforward if students apply to only one university programme. However, students often apply to more than one programme. In this case the function is the density of students after the process has taken place that allocates students to different programmes. See the next section for a description of this allocation process in Denmark.

3 It is straightforward to adjust the exposition in the following by replacing the assumption of a local uniform distribution with alternative distributions. However, such an amendment would make the exposition substantially more involved, with limited gain in insight.

4 Similar to that in Germany, see Albæk (2009) for an overview of the Danish apprenticeship system.

5 The data stem from the admission office at the University of Copenhagen.

6 The secondary school grades of the students in the data are standardized by subtracting the mean of the grades and dividing by the standard deviation for the population of Danish secondary school students. The grading scale in the sampling period was the ‘13-scale’, which ranges from 0 to 13. The average GPA for all students in the common high school was approximately 8, and the standard deviation was about 1.

7 For a programme with sample size n the bandwith becomes , where is the bandwith for the law programme and is the sample size for the law programme. This expression is obtained from the formulas in Wand and Jones (1995, p. 139).

8 If no students below the common admission thresholds were admitted, the conditional graduation functions would be truncated at the common threshold. In such a case extrapolation of the conditional graduation functions below the threshold is necessary for constructing optimal admission thresholds. Graduation probabilities below the common thresholds in Figure 3 are not estimates of population parameters but are contingent upon the policy determining admission of students with GPAs below the common threshold. To the extent that institutions are able to identify students with a high probability of graduating, contingent on their GPA, the graduation probabilities below the common threshold in Figure 3 are higher than the average amongst the applicants.

9 The top panel of Figure 2 shows that the density functions are approximately identical for the three groups of students. I assume that the (unobserved) distributions of the applicants are also identical and that the shares of students in Table 1 apply in the calculations.

10 The gain from implementing a differentiated threshold is obtained from Equations (9(9) ) and (12(12) ). On the basis of simulations, I assess the correction factor in Equation (9(9) ) to be 0.5 for the programmes analysed in this paper.

11 At a GPA level of 1.0 (the admission threshold for language students in the law programme), language students have a 9% lower graduation probability than mathematics students in the law programme but an 18% lower graduation probability in the economics programme.

12 The statistics for graduation rates and shares in Table 1 enter the calculation as .

13 For example, the University of California frequently adjusts the ‘admission index’ for California residents.

14 Estimation of a structural model including identification of the distribution of unobserved preferences and abilities is beyond the scope of this paper. Identification requires instruments for selection into the different high school paths (see e.g. the discussion in Altonji, Blom, and Meghir 2012). The present data do not contain variables that are suitable as instruments in such an analysis.

15 Joensen and Nielsen (2009) provide evidence for derived gains of optimal admission as they find substantial effects of advanced high school mathematics on subsequent earnings. The authors exploit an educational reform in Denmark where a change in the content of the high school tracks implied that more students chose advanced mathematics. The main part of the effect on earnings is indirect and goes through choice of higher education.