Sample size 30 mean average variance of the actual of

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Sample Size: 30 Mean (Average) Variance of the Actual of the Estimated Estimated Coefficient Estim Value Values, b x , from Values, b x , from Rho Proc of β x All Repetitions All Repetitions .6 OLS 2.0 2.0 1.11 .6 GLS 2.0 2.0 1.01 Table 17.7: Autocorrelation Simulation Results
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31 Robust Standard Errors Like heteroskedasticity, two issues emerge when autocorrelation is present: The standard error calculations made by the ordinary least squares (OLS) estimation procedure are flawed. While the ordinary least squares (OLS) for the coefficient value is unbiased, it is not the best linear unbiased estimation procedure (BLUE). As before, robust standard errors address the first issue arising when autocorrelation is present. Newey-West standard errors provide one such approach that is suitable for both autocorrelation and heteroskedasticity. This approach applies the same type of logic that we used to motivate the White approach for heteroskedasticity, but it is more complicated. Consequently, we shall not attempt to motivate the approach here. Statistical software makes it easy to compute Newey-West robust standard errors: 4 [Link to MIT-ConsDurDisInc-2004-2009.wf1 goes here.] Getting Started in EViews___________________________________________ Run the ordinary least squares (OLS) regression. In the equation window, click Estimate and Options In the Coefficient covariance matrix box select HAC (Newey-West) from the drop down list. Click OK. __________________________________________________________________ Ordinary Least Squares (OLS) Dependent Variable: ConsDur Explanatory Variable(s): Estimate SE t -Statistic Prob Inc 0.086525 0.028371 3.049804 0.0032 Const 290.7887 268.3294 1.083701 0.2822 Number of Observations 72 Estimated Equation: EstConsDur = 290.8 + .087 Inc Interpretation of Estimates: b Inc = .087: A $1 increase in real disposable income increases the real consumption of durable goods by $.087. Table 17.8: OLS Regression Results – Robust Standard Errors
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32 1 Recall that to keep the algebra straightforward we assume that the explanatory variables are constants. By doing so, we can apply the arithmetic of means easily. Our results are unaffected by this assumption. 2 Recall that to keep the algebra straightforward we assume that the explanatory variables are constants. By doing so, we can apply the arithmetic of variances easily. Our results are unaffected by this assumption. 3 The Durbin-Watson statistic is the traditional method of testing for autocorrelation. Unfortunately, the distribution of the Durbin-Watson statistic depends on the distribution of the explanatory variable. This makes hypotheses testing with the Durbin-Watson statistic more complicated than with the Lagrange multiplier test. Consequently, we shall focus on the Lagrange multiplier test. 4 While it is beyond the scope of this textbook, it can be shown that while this estimation procedure is biased, the magnitude of the bias diminishes and approaches zero as the sample size approaches infinity.
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