Functional Form Specification
regressors, the functional form, and the stochastic error. Today we focus on
is
Y
t
related to the regressors? Do we expect a graph of the two to be linear or
curved? Does the impact of a regressor peak at one value and then decline? As in
selecting regressors, we look to economic theory to guide our choice of functional
form.
The baseline regression model is linear in both the coe¢ cients and the regres
sors
Y
t
=
1
+
2
X
t;
2
+
+
K
X
t;K
+
U
t
:
Each coe¢ cient is given by
k
=
@Y
t
@X
t;k
;
that is, the change in
Y
t
brought about by a small change in
X
t;k
holding all
other regressors constant. If
k
= 4
, then an increase of 1 unit in
X
t;k
leads
to a 4 unit increase in
Y
t
. For such a model, the partial derivative (or slope) is
constant. A scale invariant measure is obtained directly from the slope coe¢ cient
by standardizing all variables, that is
Y
t
±
Y
S
Y
=
1
+
2
X
t;
2
±
X
2
S
X
2
+
+
K
X
t;K
±
X
K
S
X
K
+
U
t
:
Logarithmic Forms
Often economic theory tells us that the elasticity of
Y
t
with respect to
X
t;k
is
constant. Because this elasticity is
@Y
t
Y
t
@X
t;k
X
t;k
=
k
X
t;k
Y
t
;
the elasticity depends on the values of the variables in the baseline model. To
obtain a constant elasticity, we work with the logarithms of the variables
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Fall '08
 Staff
 Economics, Derivative, Xt, Yt

Click to edit the document details