RESPONSE OF ECONOMICS PRINCIPLES STUDENTS TO A

CHANGE IN HIGH-SCORER DISINCENTIVES

Johnnie B. Linn III

Concord University

The Linear Transformation (Curve)

• Y = mx + b

• Mean score was curved to 77• In first half of study, highest score was limited to

100.• In second half of study, highest score was

limited to 110.• If highest score constraint was binding, the value

of m was reduced.

Curve Coefficients Solved For

• Where h is highest score and k is binding limit on highest curved grade

.77

,77

xh

xkhb

xh

km

The Expected Outcome (Envelope Theorem)

dbx

dm

,)),()(( nnNcnxyUU

The Results--Microeconomics

423

322

2 3233 4 32

44

4

4

22

22

22

3

33

333

4

4 44

44

0

10

20

30

40

50

60

1.23 1.73 2.23 2.73 3.23 3.73 4.23 4.73m

b

The Results--Macroeconomics

2

4 3

2

3

2

4

324

324

3 2

4

2

43

3

4

3

2

4

222

222 22

3

33 3

3 3

3

3

4

4 444444

0

10

20

30

40

50

60

1.23 1.73 2.23 2.73 3.23 3.73 4.23 4.73m

b

Why the Difference?

• Macroeconomics is more difficult, or less difficult, than microeconomics, or

• Microeconomics students are seeing some material for the second time, or

• The incentives to cheat are different, or,• The composition of business and non-business

majors are different,• Or what?

The Discovery of Cheating

• In the midst of the study, it was discovered that students were peeking at each others’ test papers.

• Countermeasures were taken against peeking.• The model was re-worked to incorporate

cheating.• Countermeasures were incorporated into the

regression as a dummy variable.

Individual Student Behavior, No Peeking

Effort

Score A

D C

C’

O N

E

F

U

A’

Individual Student Behavior, Peeking

CC’

AA’

EE

UU

Effort

Score A

C’

O N

E

F

U

A’

Expected Results, Peeking

• Peeking is equivalent to an increase in productivity (in effect, a theft of productivity), with an increased substitution effect.

• Peeker will select neighbors who have not initiated guessing (if all neighbors are guessing, no gain from peeking).

• If income effect is zero or negative, peeker will increase effort.

• If income effect is strongly positive, peeker will decrease effort.

The Regression

ln( ) ln( )y b m C

1 2 3 4

5 6 7 8 2

YBLN a MLN a NOPEEK a K a BUSP

a SPR a OWNQ a HBUS a NOSTEP C

The Variables

• YBLN is the natural logarithm of 77 less b. • MLN is the natural logarithm of m. • NOPEEK is a dummy variable whose value is 1.

if countermeasures against peeking were taken for the exam and zero otherwise.

• K is a dummy variable whose value is 1 if k was 110 and zero otherwise.

The Variables, continued

• BUSP is the fraction of the class who were business majors at the time grades were issued

• SPR is a dummy variable whose value is 1 for classes in the spring semester and zero otherwise

• OWNQ is a dummy variable whose value is 1 when the instructor composed his own exam questions and zero otherwise

The Variables, Continued (2)

• HBUS is a dummy variable whose value is 1 if at least one of the highest scorers was a business major and zero otherwise

• NOSTEP2 is a dummy variable whose value is 1 if Step 2 was not used in the curve and zero otherwise

• Sign of a variable’s coefficient is positive if it lowers b or raises m, negative if it raises b or lowers m.

One Tail, or Two?

• MLN, negative, inversely related to b.

• NOPEEK, indeterminate.• K, indeterminate.• BUSP, positive, because the more “curve

busters”, the lower the b.• SPR, positive, students are more experienced,

hence a lower b.

One Tail or Two, continued

• OWNQ, positive, easier questions, lower b.• HBUS, negative, business highest scorer is

likely to reduce m for a given mean.• NOSTEP2, negative, as students select a higher

b when there is a ceiling on m.

The Results, Microeconomics

Variable Parameter S.E. t 2 tailed p 1 tailed p MLN 1.205 0.1402 8.60 0.000 NOPEEK -0.157 0.0626 -2.50 0.019 K 0.025 0.0574 0.43 0.671 BUSP -0.039 0.2383 -0.16 0.435 SPR 0.006 0.0416 0.15 0.440 OWNQ 0.117 0.0560 2.09 0.023 HBUS 0.046 0.0467 1.00 0.164 NOSTEP2 0.016 0.0540 0.29 0.387 C 2.361 0.1934 12.21 0.000

The Results, Macroeconomics

Variable Parameter S.E. t 2 tailed p 1 tailed p MLN 1.337 0.1541 8.67 0.000 NOPEEK -0.090 0.0537 -1.67 0.102 K -0.170 0.0682 -2.49 0.017 BUSP -0.004 0.2914 -0.01 0.494 SPR 0.046 0.0467 0.97 0.168 OWNQ 0.043 0.0675 0.64 0.263 HBUS -0.011 0.0358 -0.31 0.378 NOSTEP2 -0.167 0.0542 -2.98 0.003 C 2.291 0.2001 11.55 0.000

Interpretation of the Results--Peeking

• The negative result for the two-tailed test in microeconomics indicates that there is a strong income effect (aversion to effort) and that there is a payoff to peeking.

• The null result for macroeconomics indicates that there is lack of a payoff for peeking.

• Outcome is consistent with hypothesis that macroeconomics is more difficult than microeconomics.

Interpretation of the Results—Highest Curved Score

• The significant negative result for K for macroeconomics indicates that students know that high scorers will reduce effort.

• The lack of significance for microeconomics indicates that students do not expect the high scorers to reduce effort.

• Outcome is consistent with hypothesis that macroeconomics is more difficult than microeconomics.

Interpretation of the Results—Exam Question Database

• Significant result for microeconomics indicates that exam questions composed by the instructor were easier than those in the database.

• Lack of significance for macroeconomics indicates that instructor’s questions were not easier than those in the database.

• It is likely harder to compose plausible wrong answers in microeconomics than in macroeconomics.

Interpretation of the Results—No Step 2 on the Curve

• Significant result in macroeconomics indicates that students took note of the likelihood of Step 2 not being employed.

• Lack of significance in microeconomics indicates that students did not expect that Step 2 would not be employed.

• Outcome is consistent with hypothesis that macroeconomics is more difficult than microeconomics.

• If Step 2 is not employed, the only effect seen is the income effect.

Interpretation of the Results--Other

• The percentage of business majors in the class and the likelihood that the high scorer was a business major had no significant impact on the results.

• Whether the class took place in the spring or fall had no significant impact on the results.

Application—the Income Effect

• The peeking results for microeconomics and the No Step 2 results for macroeconomics confirm the existence of a strong income effect for students in both courses.

• The No Step 2 results for macroeconomics indicate that the students would like a stronger substitution effect.

Application—High Scorer Moral Hazard

• A value for k of 110 is excessive for macroeconomics because it reduces high scorer effort.

Remedies

• A lower value of k, especially for macroeconomics.

• A reduced number of items on the exam for macroeconomics, resulting in a higher value of m.

• For macreconomics, reduction of k to 105, 20 items on exams.

• For microeconomics, reduction of k to 107, retain 25 items on exams.