Unformatted text preview: −1 X −1 Example of GSL estimator for AR(1) error term (on the
lecture)
24 / 30 F EASIBLE G ENERALIZED L EAST S QUARES
Usually, we do not know the matrix Ω
We can estimate it from our data and use the estimate Ω:
β FGLS = −1 XΩ X −1 −1 XΩ y. CochraneOrcutt method
Procedure:
1. We estimated the equation by OLS (consistent)
2. We save the residuals and use them to estimate Ω
3. We use Ω to ﬁnd FGLS estimate 25 / 30 B ACK TO EXAMPLE 26 / 30 B ACK TO EXAMPLE 27 / 30 A DDITIONAL REMARKS
Note that autocorrelation does not lead to inconsistent
estimates, only to incorrect inference  similar to
heteroskedasticity problem
If we use robust variancecovariance matrix
Var β = X X −1 X ΩX X X −1 , we get rid not only of heteroskedasticity, but also of serial
correlation
Note also that all derived results hold if the assumption
Cov(x, ε) = 0 is not violated
First make sure the speciﬁcation of the model is correct,
only then try to correct for the form of an error term
28 / 30 S UMMARY
Autocorrelation does not lead to inconsistent estimates,
but it makes the inference wrong
It can be diagnosed using
DurbinWatson test
Analysis of residuals It can be remedied by
FGLS method
robust variancecovariance matrix Readings:
Studenmund, Chapter 9
Wooldridge, Chapter 12
29 / 30 W HAT ’ S NEXT
Next exercise session:
Gretl  estimation, inference, and testing Next lecture:
we will address the issue of endogenous variables
we will explain the principle of IV estimation
we will derive the 2SLS formula Home assignment: deadline December 5 30 / 30...
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This document was uploaded on 02/26/2014.
 Spring '14
 Econometrics

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