Summary
ResEc 702 – Econometrics I
III.
General Linear Model
A.
Introduction
:
Theory suggests the variables we should include in our GLM.
In class,
we reviewed results from a few microeconomic models.
The consumer’s utility
maximization problem was used because it also provides restrictions that might be
incorporated into our modeling.
What specific lessons can be learned from going through
the process of specifying a theoretical model?
B.
Classical Regression Model
:
We revisited the same set of assumptions using matrix
notation and added one additional assumption – no perfect multicollinearity.
What, in
general, do each of the assumptions mean for our statistical model?
Why do we require
these assumptions?
C.
OLS
:
Derived the OLS estimators using matrix notation.
The process is the same.
Discussed the final CRM assumption (no perfect multicollinearity) and its implications
for estimation.
D.
Properties of b:
Reviewed the properties of the OLS estimators.
Derived the covariance
matrix and considered variances for general linear model with two independent variables.
The latter exercises, the Y = f(X1, X2) derivations using summation notation, allows us
to see the effects of too much collinearity or zero collinearity.
E.
OLS estimator for
2
σ
and
Goodness of fit:
2
R
F.
Inference:
We spent quite a bit of time on these topics including:
•
Individual Parameter Inference
–not much different from our approach in the
Simple Linear Model.
•
Tests of Significance for All Regressors
– joint tests using, Ftests.
•
Tests for Linear Combinations of Parameters
– Ftests for
Restrictions
. This is
perfectly general and allows us a test of the model (all parameters equal zero) and
tests of subsets of parameters. As long as we can express our tests as
R
β
= r
, we
can complete the test.
•
Prediction Intervals
– revisited the creation of confidence intervals for the
expected value and an individual value.
G.
Specification Errors and Model Selection Tools:
Discussed the two specification
errors we might make and the consequences of the errors.
First we considered the
omission of relevant independent variables.
We saw that the OLS estimators were
biased, but they did have “less sampling variability.”
But, as we discussed, the
conclusion that sampling variability is less was made using the true value
2
.
In the real
world, we’ll be using a biased estimator for
2
, which will affect our estimates of
sampling variability. (Plus, we will logically not explain as much variation in the
dependent variable when we leave out important variables.) We then turned to the case of
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View Full Documentincluding irrelevant regressors.
We found that
b
was unbiased, but inefficient.
There are
many model selection tools at our disposal.
We talked about the use of theory and logic
to properly specify the model.
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 Spring '08
 STAFF
 Econometrics, Regression Analysis, Utility, OLS, Covariance matrix, OLS estimators, general linear model

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