Therefore, when regression (2) is estimated by OLS, do not forget to
multiply the value of the estimated slope coefficient by 0.01, or, what
amounts to the same thing, divide it by 100. If you do not keep this in
mind, your interpretation in an application will be
highly misleading
.
For example, if in an application one finds that
1
= 300, the absolute
change in Y is (0.01)(300) = 3 (See
Appendix 1
for interpretation
issue).
C. Reciprocal Models
Models of the following type are known as
reciprocal models
.
0
1
1
t
t
t
Y
u
X
(3)
which may also be expressed as follows:
0
1
t
t
t
Y
Z
u
where
1
t
t
Z
X
.
Here, note that
1
1
2
2
1
.(
)
t
t
t
t
t
t
t
t
dY
dY dZ
dX
dZ dX
X
X
, hence it is not
constant.

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ECON 301 - Introduction to Econometrics I
April, 2013
METU - Department of Economics
Instructor: Dr. Ozan ERUYGUR
e-mail:
[email protected]
Lecture Notes
19
Example
TC=FC+VC(Q)=
0
1
t
X
. Then
0
1
1
t
t
ATC
u
X
.
Below you can find a summary for the functional forms in terms of
slope and elasticity relationships.
Table
Functional Forms: Slope and Elasticities
Appendix 1
Interpretation of Semi-log Models
Note hat the relative
in
t
Y
is given by:
t
t-1
t
t-1
Y
Y
relative
in Y
Y
.
Hence, if
t
Y
has increased from 100 to 130,
t
relative
in Y
is 0.30.
On the other hand, the percentage
in
t
Y
is given by:
t
t-1
t
t-1
.
Y
Y
percentage
in Y
100
Y

ECON 301 - Introduction to Econometrics I
April, 2013
METU - Department of Economics
Instructor: Dr. Ozan ERUYGUR
e-mail:
[email protected]
Lecture Notes
20
Hence, if
t
Y
has increased from 100 to 130,
t
percentage
in Y
is
30%.
(1) Suppose that you are given the following estimated log-lin model:
ln
2
0.2
t
t
Y
X
Here,
t
1
t
relative
in Y
0.2
absolute
in X
implies that:
1
t
unit
in X
(causes)
0.2 relative
t
in Y
or
1
t
unit
Δ in X
(causes)
20 percent
t
Δ in Y
Hence, the estimated model says that:
1 unit change in
t
X
will lead
to 20% change in
t
Y
.
(2) Suppose that you are given the following estimated lin-log model:
ˆ
12
0.6ln
t
t
Y
X
Here,
t
1
t
absolute
in Y
0.6
relative
in X
implies that:
1
t
relative
in X
(causes)
0.6 unit
t
in Y
or
100
t
percent
in X
(causes)
0.6 unit
t
in Y
or,
simply
;
1
t
percent
Δ in X
(causes)
0.006 unit
t
Δ in Y
Hence, the estimated model says that:
1 % change in
t
X
will lead to
0.006 unit change in
t
Y
.

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