93 H. Bonesrønning Economics of Education Review 18 1999 89–105
the students in the Norwegian upper secondary school have to choose which of the specialization subjects —
mathematics, social studies or foreign language — they will study for the last two years in the upper secondary
school. It seems likely that the demand for specialization subjects is determined by the expected pecuniary and
non-pecuniary returns in interaction with abilities, tastes and some other factors. The teachers’ grading practices
may affect the expected returns, for instance by affecting the probabilities of getting admission to the universities.
When the teachers practice hard grading, some students may find that their probability of getting admission to
higher education decreases, while other students may find that their admission probability increases. That is,
the students may sort themselves across subjects depen- dent on their own abilities and preferences. An example
is that the students who choose mathematics given hard grading, may be those students who respond to hard
grading by allocating more time to studying. Thus, even if there exists no relationship between grading and stud-
ent achievement for all students, such relationships may be revealed for mathematics due to sorting.
3. Empirical Specifications
Empirical specification of the modified Correa and Gruver’s model confronts the following problems:
Neither students’ studying time, rent seeking time nor teachers’ teaching time are observable without prohibi-
tive costs and besides, the grading parameters are latent variables. Thus the Eqs. 11–13 cannot be estimated
directly. Inspired by Montmarquette and Mahseredjian 1989 we propose the following solutions.
Students’ academic achievement depends on optimal levels of e
and a . These optimal levels of studying time
and teaching time are interactive and depend on the characteristics of the achievement function, the charac-
teristics of the student’s utility function, the character- istics of the rent seeking function, the characteristics of
the teacher’s utility function and the grading parameters G
T
and g
T
. A reduced form of the achievement pro- duction function will thus link student achievement with
these characteristics and the grading parameters. We have no data for G
T
and g
T
; these parameters are there- fore assumed equal to 3 and 1 respectively. Then we
have a standard education production function v
ij
5 a
1 a
1
X
ij
1 a
2
Y
j
1 a
3
Z
j
1 a
4
X
j
1 e
ij
14 where v
ij
is the exam results for student i in school j, X
ij
is a vector of individual student characteristics for stud- ent i in school j, Y
j
is a vector of teacher characteristics for school j, Z
j
is a vector of school characteristics for school j, X
j
is a vector of student body characteristics for school j and e
ij
is an error term with standard nice properties.
The inclusion of the X
ij
and Y
j
variables should be clear from above. The elements in the Z
j
vector are included as determinants of a, and may also be seen as
control variables capturing potential scale effects. X
j
cap- tures potential peer group effects and are included rather
ad hoc. We would like to separate the teacher characteristics
associated with teaching quality from those associated with teacher strength. We are unable to do this a priori.
The grading equation presented below may provide the information necessary to make the empirical separation
between teaching quality and teacher strength possible.
Teacher grading depends on rent seeking time r ,
teacher strength, the costs of deviating from the grading parameter set by the principal and the grading preferred
by the principal. In Section 2 we have argued that rent seeking time is associated with student characteristics.
Consequently, we estimate the equation
G
3 j
5 b
1 b
1
X
j
1 b
2
Y
j
1 b
3
Z
j
1 m
j
15 where G
3 j
is the grading parameter for school j, m
j
is an error term, and the other variables are defined above.
An indication that rent seeking actually occurs, will be that strong pressure for easy grading is associated
with low achieving students. Unfortunately, we cannot reject the Correa and Gruver’s grading model on the
basis of such findings, since significant relationships between grading and student and teacher characteristics
may as well reflect that teachers are less than fully infor- med and that they conjecture that easy grading is “cor-
rect” for low achievers.
The information provided by the estimation of Eq. 15 can be used to separate between teaching quality
and grading effectsteacher strength effects in the esti- mation of the education production function. First,
departing from the rent seeking interpretation, a two stage procedure where the predicted grading from Eq.
15 is used as an independent variable in Eq. 14, is appropriate. Second, departing from the policy instru-
ment interpretation, the grading parameter should we treated as an exogenous variable and included directly
in Eq. 14.
The remaining problem is how to measure G
3
and g
s
. We propose the following relationship
w
ij
5 G
3 j
1 g
s j
v
ij
2 3 1 n
ij
16 where G
3 j
is the measure of teachers’ grading in school j
, g
s j
describes the degree to which the teachers’ grades vary with achievement as measured by the external exam
between schools, v
ij
is the external exam result for stud- ent i in school j and n
ij
is a random effect with standard nice properties.
Eq. 16 is Eq. 3 with stochastics, that is, the equ- ation should not be thought of as a behavioral relation.
It is important to emphasize this point: If we were searching for the effect of the exam results on teachers’
94 H. Bonesrønning Economics of Education Review 18 1999 89–105
grades, the equation would be misspecified. Eq. 14 should instead be thought of as a definitional relationship
that provides a measure of the divergence between exam results and teachers’ grades for each school.
To deal with the problem that students sort themselves into the specialization subjects, we apply the standard
Heckman 1979 procedure. That is, the probability that a student chooses mathematics is estimated from a probit
equation. The inverse Mill’s ratio is calculated from the probit equation and thereafter included in the education
production function to correct for selectivity bias.
4. Data and Results
