Cochrane orcutt method procedure 1 we estimated the

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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. Cochrane-Orcutt 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 variance-covariance 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 Durbin-Watson test Analysis of residuals It can be remedied by FGLS method robust variance-covariance 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.

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