Econometrics-I-15

# Can be extremely bad gls vs ols the efficiency ratios

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Unformatted text preview: Can be extremely bad. GLS vs. OLS, the efficiency ratios can be 3 or more. A very important exception - the lagged dependent variable yt = xt + yt-1 + t. t = t-1 + ut,. Obviously, Cov[yt-1 ,t ] 0, because of the form of t. How to estimate? IV Should the model be fit in this form? Is something missing? Robust estimation of the covariance matrix - the Newey-West estimator. &#152;&#152;™™™ ™ 18/45 Part 15: Generalized Regression Applications GLS and FGLS Theoretical result for known - i.e., known . Prais- Winsten vs. Cochrane-Orcutt. FGLS estimation: How to estimate ? OLS residuals as usual - first autocorrelation. Many variations, all based on correlation of et and et-1 &#152;&#152;&#152;™™™ ™ 19/45 Part 15: Generalized Regression Applications Testing for Autocorrelation A general proposition: There are several tests. All are functions of the simple autocorrelation of the least squares residuals. Two used generally, Durbin-Watson and Lagrange Multiplier The Durbin - Watson test. d 2(1 - r). Small values of d lead to rejection of NO AUTOCORRELATION: Why are the bounds necessary? Godfrey’s LM test. Regression of et on et-1 and xt . Uses a “partial correlation.” &#152;&#152;&#152;™™™ ™ 20/45 Part 15: Generalized Regression Applications Consumption “Function” Log real consumption vs. Log real disposable income ( Aggregate U.S. Data, 1950I – 2000IV. Table F5.2 from text)---------------------------------------------------------------------- Ordinary least squares regression ............ LHS=LOGC Mean = 7.88005 Standard deviation = .51572 Number of observs. = 204 Model size Parameters = 2 Degrees of freedom = 202 Residuals Sum of squares = .09521 Standard error of e = .02171 Fit R-squared = .99824 <<<*** Adjusted R-squared = .99823 Model test F[ 1, 202] (prob) =114351.2(.0000)--------+------------------------------------------------------------- Variable| Coefficient Standard Error t-ratio P[|T|>t] Mean of X--------+------------------------------------------------------------- Constant| -.13526*** .02375 -5.695 .0000 LOGY| 1.00306*** .00297 338.159 .0000 7.99083--------+------------------------------------------------------------- &#152;&#152;&#152;™™™ ™ 21/45 Part 15: Generalized Regression Applications Least Squares Residuals: r = .91 &#152;&#152;&#152;™™ ™ 22/45 Part 15: Generalized Regression Applications Conventional vs. Newey-West +---------+--------------+----------------+--------+---------+----------+ |Variable | Coefficient | Standard Error |t-ratio |P[|T|>t] | Mean of X| +---------+--------------+----------------+--------+---------+----------+ Constant -.13525584 .02375149 -5.695 .0000 LOGY 1.00306313 .00296625 338.159 .0000 7.99083133 +---------+--------------+----------------+--------+---------+----------+ |Newey-West Robust Covariance Matrix |Variable | Coefficient | Standard Error |t-ratio |P[|T|>t] | Mean of X|...
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Can be extremely bad GLS vs OLS the efficiency ratios can...

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