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# a425_het - Heteroskedasticity APS 425 Advanced Managerial...

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Heteroskedasticity APS 425 - Advanced Managerial Data Analysis (c) Prof. G. William Schwert, 2001-2010 1 APS 425 Winter 2010 Heteroskedasticity Instructor: G. William Schwert 585-275-2470 [email protected] Heteroskedasticity (Nonconstant Variance of the Errors) Recall assumption 5: – Homoskedasticity: var( e i ) = constant – That means, the variance of e i is the same for all observations in the sample, and thus, the variance of Y i is the same for all observations in the sample – The uncertainty in Y i is the same amount when X i is small as when X i is a large • When you have heteroskedasticity, the spread of the dependent variable Y could depend on the value of X , for example • Some observations are inherently less influenced by unmeasured factors

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Heteroskedasticity APS 425 - Advanced Managerial Data Analysis (c) Prof. G. William Schwert, 2001-2010 2 Heteroskedasticity • Graphical example: • Appears that there is more dispersion among the Y - 10 15 20 25 values when X is larger 0 5 0 5 10 15 Heteroskedasticity • Example: database with 249 small to medium sized companies, containing both employee and sales information for the year 2000 SALES = total company sales in \$1000 EMPLOYEES = number of FTEs = number of FTEs employed by the company • Model: SALES i = 0 + 1 EMPLOYEES i + e i
Heteroskedasticity APS 425 - Advanced Managerial Data Analysis (c) Prof. G. William Schwert, 2001-2010 3 Heteroskedasticity & Eviews Heteroskedasticity & Eviews

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Heteroskedasticity APS 425 - Advanced Managerial Data Analysis (c) Prof. G. William Schwert, 2001-2010 4 Heteroskedasticity & Eviews • Look only at this part: • Consider the p -value for the F-statistic • The null hypothesis for the White test is Homoskedasticity • If fail to reject the null hypothesis, then we have homoskedasticity • If reject the null hypothesis, then we have heteroskedasticity • Significance level of 5% is commonly used for this test • Conclusion: REJECT, so assume heteroskedasticity Heteroskedasticity & Eviews • How to tell Eviews to assume Heteroskedasticity: – Click on the Estimate button at the top of the Equation window – Click on the Options button in the Equation Specification window – Check the Heteroskedasticity checkbox
Heteroskedasticity APS 425 - Advanced Managerial Data Analysis (c) Prof. G. William Schwert, 2001-2010 5 Heteroskedasticity & Eviews Indicates h t k d ti it heteroskedasticity was assumed by Eviews in these results Heteroskedasticity & Eviews Since there is heteroskedasticity, – Estimators ( b 0 and b ) for both sets of results are unbiased and consistent – Standard errors in standard results are WRONG (i.e., incorrect) – Standard errors in White results are correct – Estimators ( b 0 and b ) are not efficient (i.e., they don’t have minimum

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## This note was uploaded on 03/03/2010 for the course APS 425 taught by Professor Schwert during the Spring '10 term at Rochester.

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a425_het - Heteroskedasticity APS 425 Advanced Managerial...

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