Econometrics-I-9

# Econometrics-I-9 - Applied Econometrics William Greene...

This preview shows pages 1–9. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Applied Econometrics William Greene Department of Economics Stern School of Business Applied Econometrics 9. Hypothesis Tests: Analytics and an Application General Linear Hypothesis Hypothesis Testing Analytical framework: y = X β + ε Hypothesis: R β - q = , J linear restrictions Procedures Classical procedures based on two algebraically equivalent frameworks Distance measure: Is Rb - q = m 'far' from zero? (It cannot be identically zero.) Fit measure: Imposing R β - q on the regression must degrade the fit ( e'e or R 2 ). Some degradation is simple algebraic. Is the loss of fit 'large?' In both cases, if the hypothesis is true, the answer will be no. Test Statistics Forming test statistics: For distance measures use Wald type of distance measure, W = (1/J) m ′ [Est.Var( m )] m For the fit measures, use a normalized measure of the loss of fit: [(R 2 - R* 2 )/J] F = ----------------------------- [(1 - R 2 )/(n - K)] Testing Procedures How to determine if the statistic is 'large.' Need a 'null distribution.' Logic of the Neyman-Pearson methodology. If the hypothesis is true, then the statistic will have a certain distribution. This tells you how likely certain values are, and in particular, if the hypothesis is true, then 'large values' will be unlikely. If the observed value is too large, conclude that the assumed distribution must be incorrect and the hypothesis should be rejected. For the linear regression model, the distribution of the statistic is F with J and n-K degrees of freedom. Distribution Under the Null Density of F[3,100] X .250 .500 .750 .000 1 2 3 4 FDENSITY Particular Cases Some particular cases: One coefficient equals a particular value: F = [(b - value) / Standard error of b ] 2 = square of familiar t ratio....
View Full Document

{[ snackBarMessage ]}

### Page1 / 19

Econometrics-I-9 - Applied Econometrics William Greene...

This preview shows document pages 1 - 9. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online