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Unformatted text preview: ution. Introduction Heteroscedasticity Past Exam Practice Question Moving Forward: Model B Today’s Lecture GaussMarkov Theorem Theorem
Provided that Model A assumptions are satisﬁed, the OLS estimators are
BLUE:
Best; most efﬁcient
Linear; in terms of how Yi ’s enter the estimator expressions
Unbiased; expectation of the estimator equals the true value of the
parameter
Estimator. Introduction Heteroscedasticity Past Exam Practice Question Today’s Lecture Today’s Pathology Of Least Squares OLS and some estimation issues in the context of Model A:
Omitted Variable Bias (Chapter 6)
Including Irrelevant Variables (Chapter 6)
Heteroscedasticity (Chapter 7) Moving Forward: Model B Introduction Heteroscedasticity Past Exam Practice Question Moving Forward: Model B Today’s Lecture Today’s Pathology Of Least Squares OLS and some estimation issues in the context of Model A: Heteroscedasticity (Chapter 7)
What assumption of Model A is violated?
A.4 as the variance of disturbance term is not homoscedastic. Introduction Heteroscedasticity Past Exam Practice Question Moving Forward: Model B Deﬁnition Disease 3: Heteroscedasticity Standard results for OLS assume u homoscedastic. (“equal dispersion”)
Not all results go through if u heteroscedastic. (“differing dispersion”)
In English: the variance of the disturbance term is different for different
observations.
Sometimes can be interpreted as symptom of underlying misspeciﬁcation.
Example:
True model is nonlinear. (pg. 236) Introduction Heteroscedasticity Past Exam Practice Question Moving Forward: Model B Deﬁnition Important Note Heteroscedasticity deals with the variance of disturbance terms.
Hence it relates to the distribution of the disturbances.
This is not to be confused with the realizations (actual values) of
disturbance terms. Introduction Heteroscedasticity Past Exam Practice Question Moving Forward: Model B Deﬁnition Important Note Heteroscedasticity deals with the variance of disturbance terms.
Hence it relates to the distribution of the disturbances.
This is not to be confused with the realizations (actual values) of
disturbance terms.
For example, assume heteroscedasticity present through variance of
disturbance terms increasing in X .
Then it does not mean that u will be larger the larger is X .
Rather that u ’s value will be potentially farther away from 0 (its
expectation by A.3) because its distribution will get “wider”. Introduction Heteroscedasticity Past Exam Practice Question Moving Forward: Model B Consequences Heteroscedasticity Consequences There are two main consequences:
1
OLS estimators will be inefﬁcient.
OLS estimators are no longer BLUE (Best Linear Unbiased Estimator).
Even though they are unbiased, they will no longer be most efﬁcient.
2 s.e.’s will be wrong.
s.e.’s will likely be underestimated.
Therefore tstatistics and Fstatistics will also be invalid. Introduction Heteroscedasticity Past Exam Practice Question Moving Forward: Mode...
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This document was uploaded on 03/12/2014 for the course ECON 202 at University of London University of London International Programmes (Distance Learning).
 Spring '13
 ChristopherDougherty
 Econometrics

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