CHAPTER
11
MODEL SELECTION: CRITERIA AND TESTS
QUESTIONS
11.1.
Specification errors occur when the form of the relationship between the
dependent variable and the explanatory variables is wrongly specified
because of:
1.
Exclusion of relevant variables from the model, or
2.
Inclusion of redundant variables in the model, or
3.
Incorrect functional form (e.g., a linear model is fitted whereas the
true model is log-linear), or
4.
Wrong specification of the error term.
Notice that one or more of these problems might coexist.
11.2.
Specification errors arise because:
1.
The researcher is not sure of the theory underlying his research;
2.
The researcher is not aware of the previous work in the area;
3.
The researcher does not have data on the variables relevant for the
model.
4.
Of errors of measurement in the data.
11.3.
A good econometric model:
1. Should be parsimonious;
2.
Should obtain unique estimates of the parameters of the model;
3.
Should fit the data at hand reasonably well;
4. Should have the signs of the estimated coefficients in accordance
with theoretical expectations, and
5.
Should have good (out of sample) predictive power.
11.4.
Exclusion
of
relevant
variables;
inclusion of irrelevant variables;
wrong functional form;
wrong specification of the error term.
Yes, one or more specification errors can occur simultaneously.
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11.5.
If a variable(s) is wrongly excluded from a model, the coefficients of the
variables included in the model can be biased as well as inconsistent, the
error variance is incorrectly estimated, the standard errors of the variables
included in the model can be biased, and the conventional hypothesis testing
based on the
t
and
F
tests can be unreliable.
11.6.
The “relevancy” of a variable depends on the theory underlying the model.
Thus, in a demand function for money, income of the consumer, the interest
rate, etc. are relevant variables but not, say, the amount of bananas produced
in Mexico.
11.7.
In the presence of the irrelevant variables, the OLS estimators are LUE
(linear unbiased estimators) but not BLUE, that is, they are not efficient.
11.8
Since the inclusion of the irrelevant variables increases the standard errors
of the coefficients, one may tend to accept the null hypothesis that a
particular coefficient is zero, although in fact it may not be. Therefore, one
should not include unnecessary variables in the model.
11.9.
See answers to questions (11.7) and (11.8) above.
11.10.
This is a common problem that one faces in any econometric analysis.
Here
theory should be the guide to model building.
If the empirical results are not
in accord with theory, one should be very wary of accepting those results,
for in econometric model building our primary objective is to test a theory.
PROBLEMS
11.11.
(
a
)
t
Y
ˆ
n
l
=
-7.8439
+
0.7148
t
X
2
ln
+
1.1135
t
X
3
ln
t
=
(-2.9270)
(4.6636)
(3.7221)
2
R
= 0.9837
The output-labor and output-capital elasticities are, 0.7148 and
1.1135,
respectively,
and both are individually statistically significant at
the 0.005
level (one-tail test).

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