1 / 29

Applied Quantitative Methods

Applied Quantitative Methods. Lecture 9 . Multiple Regression Analysis: Further Issues (Cont.). November 25 th , 2010. Model Specification Errors. Coefficients are biased Standard errors are invalid. Correct specification, no problems. Correct specification, no problems.

stefano
Download Presentation

Applied Quantitative Methods

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Applied Quantitative Methods Lecture 9. Multiple Regression Analysis: Further Issues (Cont.) November 25th, 2010

  2. Model Specification Errors Coefficients are biased Standard errors are invalid Correct specification, no problems Correct specification, no problems

  3. Model Misspecification: Omitted Variable • True population model • Estimated model • Omitted variable bias

  4. Model Misspecification: Omitted Variables (Cont.) • TE Schooling production function

  5. Model Misspecification: Omitted Variables (Cont.) • TE Schooling production function • Estimated model Omitted Variable Bias • Will the bias be positive or negative?

  6. Model Misspecification: Omitted Variables (Cont.) • The bias is positive • Criteria for including additional variables: • - Economic theory: is there any sound theory? • - Student t statistic: is it significant in the correct direction? • - Has improved? • Do other coefficients change sign when the variable is included? • Wrong approaches: data mining and stepwise inclusion of variables

  7. Detecting Misspecification • Residual plot • Residuals exhibit noticeable patterns • Higher order terms

  8. Residuals Plot • Something is wrong • the mean of the residuals is not 0 • residuals have a trend

  9. Residuals Plot • Nonlinear association

  10. Unobservable Omitted Variable • Proxy (substitute) • True population model • Z is a proxy for X2 • Revised model • Gain: unbiasedness and valid standard errors • Cost: Unable to identify β2and β1 • N!B! (Approximately) Same R2 and t-statistic for Z as in original model • TE IQ test score as a proxy for ability

  11. Model Misspecification: Irrelevant Variables Coefficients are biased (in general). Standard errors are invalid. Correct specification, no problems Coefficients are unbiased , but inefficient. Standard errors are valid Correct specification, no problems

  12. Model Misspecification: Irrelevant Variables (Cont.) • The cost of overspecification: larger variance of => Loss of efficiency • The coefficient for irrelevant regressor will be insignificant and close to 0 • TE Determinants of earnings

  13. Model Misspecification: Irrelevant Variables (Cont.) • General tests for specification errors: • - Regression specification error test (RESET) by Ramsey • - Durbin-Watson d test • Lagrange multiplier test

  14. Multicollinearity • Population model • Exact linear relationship between X2 and X3 • Slope coefficient for X2 is not defined

  15. Multicollinearity (Cont.) • TE Wage equation

  16. Multicollinearity (Cont.) • Consequences of multicollinearity • - Point estimates are not biased but erratic! • Standard errors are valid but large • variance of the disturbance term • number of observations • variability of Xj • correlation between regressors

  17. Multicollinearity (Cont.) TE Educational attainment Both SM and SF are equally important: β2 = β3

  18. Heteroskedasticity

  19. Heteroskedasticity (Cont.) • Scatter plot for the initial data

  20. Heteroskedasticity (Cont.) • Residuals plot

  21. Heteroskedasticity (Cont.) • Implications for OLS estimates • Does not bias estimates of regression coefficients • OLS estimates are inefficient • - OLS gives equal weight to all observations • 3. Standard errors are invalid • - Homoskedasticity assumption

  22. Heteroskedasticity (Cont.) TE Manufacturing output vs GDP for 30 countries

  23. Detecting Heteroskedasticity • Goldfeld-Quandt test • Key assumption: s.d. of disturbance term is increasing with X • Proportions: 3/8 – 1/4 – 3/8

  24. Detecting Heteroskedasticity (Cont.) • Test statistic • Conclusion: H0 of homoskedasticity is rejected at 1 % level of significance • White test:

  25. Correction for Heteroskedasticity • Weighted OLS • But σi is not known

  26. Correction for Heteroskedasticity • Weighted OLS

  27. Conclusion: H0 can not be rejected at 5 % significance level -> Homoskedasticity

  28. Correction for Heteroskedasticity (Cont.) • Heteroskedasticity robust standard errors (White, 1980) Regression with robust standard errors

  29. Next Lecture Topic: Dummy Variables !Wooldridge, Chapter 7& 17.1 &17.5 Paper: Heckman, J. (1979). Sample selection bias as a specification error. Econometrica, Vol. 47, No. 1, pp 153-161.

More Related