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Abstract
This study created an experimental design with which students can empirically assess their risk behavior with respect to exam grades within an expected utility framework. Specifically, the authors analyzed students’ risk preferences associated with taking exams and earning a “risky” unknown grade versus not taking exams and instead obtaining a “sure” grade. Students have grade-choice decisions in nonhypothetical situations that impact their actual exam grades. Estimates indicate that the more risk-averse a student is, the more willing he or she is to accept a lower certain grade and not take an exam than to run the risk of actually taking it. We believe that this experimental setup and its binding results make it an easy but effective way of teaching the obtuse concept of risk aversion.
Acknowledgments
The authors thank Jayson Lusk for his help, Diana Danforth for her time and effort, and Peter Kennedy for his advice and encouragement.
Notes
1. Although this was an agribusiness class, the material covered is equivalent to that of a class on introduction to microeconomics.
2. Internal Review Board (IRB) protocol at the University of Arkansas was followed for this experiment.
3. The results imply that if a student chose Option A for decision 6, he or she would have received four extra credit points, and if the student chose Option B, he or she would have received one extra credit point.
4. This experiment was conducted before the first exam. Quizzes are not given back, and therefore each student is “starting” the experiment with no information about his or her grade. So, theoretically speaking, the marginal utility of a point should be equivalent across students. More research is needed on constant risk aversion versus relative risk aversion as students acquire a more precise picture of what their grade is likely to be. That is, the marginal utility of a point for a student who has a 95 (A) would not be the same as that for a student with an 89 (B), one point away from an A−.
5. When r = 1, the natural logarithm is used; division by (1 − r) is necessary for increasing utility when r > 1.
6. Again, we hypothesize this would change once a grade in the course was more established. This warrants further research.
7. None of the students chose not to participate, thus removing self-selection bias. That being said, some students arrived late to class and were not given the opportunity to participate because they were not present for the instructions. Students were removed from the study if they did not have observations for all three exams.
8. The students knew beforehand that neither the test nor the class was curved, so that uncertainty related to exogenous instructor grade adjustments was removed.
9. The grading scale for the class was the following: A (90–100), B (80–89), C (70–79), D (60–69), and F (< 59). The experiment and were constructed so that all letter grade breaks also fell on an interval break. That is, because a B started at an 80, we let an interval go between 80 and 85; because an A started at a 90, we let an interval go between 90 and 95. In this manner we could attempt to delineate if a student was partial to an A or a B. That is, going from 82 to 83 (both are Bs) will not have much effect on the certainty equivalent, but going from 89 to 90 (going from a B to an A) should have a much bigger impact.
10. The final exam (exam 3) is worth 20 percent of the total grade.
11. When the students took their final exams, they each knew 60 percent of their grade. The remaining 40 percent was split between the final exam (20 percent) and a class project (20 percent) that was due on the last day of class. The unknown 20 percent of the grade (class project) was important in determining the chosen certainty equivalent. For example, if the final grade was the only portion of his or her grade that was unknown, then a student with a B average going into the exam should be indifferent between choosing a certainty equivalent of 80 or that of an 85; they are both Bs. However, because 20 percent of their grade is unknown (his or her class project), that same student should be biased towards choosing the 85.
12. One possible explanation for this is that by the third experiment, with discussion among themselves during the year, the students had learned that it was irrational to “switch back and forth.”
13. The winner drew round 9 randomly out of the jar, for which she had selected Option A (a guaranteed 95). She was awarded a 95 as her final exam grade. The instructor also graded her test, on which she earned a 92, so that the winner gained 3 points on her final exam grade.
14. On the first test, students were asked what their anticipated grade in the course would be. No one anticipated earning below a C in the course, so D and F were not included.
15. These two exams accounted for 40 percent of the total grade in Intro to Agribusiness.
16. The fact that “Grade C” is not significant may be attributed to the fact that these students did not understand the incentives of the first experiment. This also may be a function of students’ not assessing their ability well on the first exam because the test format was unknown prior to the exam.
17. The difference was 6.4 points and 4.3 points for exams 2 and 3, respectively.