T ρ x t 1 e t since e t u t ρ u t 1 this quasi

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t ρ x t-1 ) + e t , since e t = u t ρ u t-1 This quasi-differencing results in a model without serial correlation
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Fall 2008 under Econometrics Prof. Keunkwan Ryu 9 Feasible GLS Estimation Problem with this method is that we don’t know ρ , so we need to get an estimate first Can just use the estimate obtained from regressing residuals on lagged residuals Depending on how we deal with the first observation, this is either called Cochrane- Orcutt or Prais-Winsten estimation
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Fall 2008 under Econometrics Prof. Keunkwan Ryu 10 Feasible GLS (continued) Often both Cochrane-Orcutt and Prais- Winsten are implemented iteratively This basic method can be extended to allow for higher order serial correlation, AR( q ) Most statistical packages will automatically allow for estimation of AR models without having to do the quasi-differencing by hand
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Fall 2008 under Econometrics Prof. Keunkwan Ryu 11 Serial Correlation-Robust Standard Errors What happens if we don’t think the regressors are all strictly exogenous? It’s possible to calculate serial correlation- robust standard errors, along the same lines as heteroskedasticity robust standard errors Idea is that want to scale the OLS standard errors to take into account serial correlation
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Fall 2008 under Econometrics Prof. Keunkwan Ryu 12 Serial Correlation-Robust Standard Errors (continued) Estimate normal OLS to get residuals, root MSE
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