1 / 16

MF-852 Financial Econometrics

MF-852 Financial Econometrics. Lecture 8 Introduction to Multiple Regression Roy J. Epstein Fall 2003. Topics. Formulation and Estimation of a Multiple Regression Interpretation of the Regression Coefficients Omitted Variables Collinearity Advanced Hypothesis Testing.

frey
Download Presentation

MF-852 Financial Econometrics

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. MF-852 Financial Econometrics Lecture 8 Introduction to Multiple Regression Roy J. Epstein Fall 2003

  2. Topics • Formulation and Estimation of a Multiple Regression • Interpretation of the Regression Coefficients • Omitted Variables • Collinearity • Advanced Hypothesis Testing

  3. Multiple Regression • Used when 2 or more independent variables explain the dependent variable: Yi = 0 + 1X1i + 2X2i + … + kXki + ei or Yi = Xi + ei

  4. The Error Term • Same assumptions as before: E(ei) = 0 var(ei) = 2 cov(X,e) = 0 cov(ei, ej) = 0

  5. The Error Term • Same assumptions as before: E(ei) = 0 var(ei) = 2 cov(X,e) = 0 cov(ei, ej) = 0

  6. The Estimated Coefficients • Measure the marginal effect of an independent variable, controlling for the other effects. • I.e., effect of Xi “all else equal” • Can be sensitive to what other variables are included in the regression.

  7. Omitted Variables • Suppose true model is: Yi = 0 + 1X1i + 2X2i + ei • But you leave out X2. (by ignorance or lack of data) Does it matter?

  8. Analysis of Omitted Variables Error term now includes e and X2: Yi = 0 + 1X1i + ui = 0 + 1X1i + [2X2i + ei] Two cases: • X2correlated with X1. biased — picks up effect of X2 and attributes it to X1. • X2uncorrelated with X1. No bias.

  9. Case Study — MIT Lawsuit

  10. Collinearity • Let Yi = 0 + 1X1i + 2X2i + ei • Suppose X1 and X2 highly correlated. • What difference does it make? • Hard to estimate 1 and 2. • No bias, but large standard errors.

  11. Collinearity—Diagnosis • Neither X1 or X2 has a significant t statistic BUT • X1 is significant when X2 is left out of the regression and vice versa. • Test joint significance with F test.

  12. Exact Collinearity • Let Yi = 0 + 1X1i + 2X2i + ei • Suppose X2 is exact linear function of X1 • E.g., X2 = a + bX1 • Then cannot estimate model at all! • Can also occur with 3 or more X’s.

  13. Exact Collinearity—Example • Regression to explain calories as function of fat content of foods • X1 is fat in ounces per portion • X2 is fat in same food in grams • Then X2i = 28.35 X1i • Can’t estimate Yi = 0 + 1X1i + 2X2i + ei • Intuition: no independent information in X2.

  14. Tests of Restrictions • Suppose H0: 2 = 21 in Yi = 0 + 1X1i + 2X2i + ei • Test H0 with reformulated model that embeds restriction: Yi = 0 + 1(X1i + 2X2i) + 2X2i + ei • Under H0, 2 = 0 • Can test with usual t statistic

  15. Test your Understanding! • What is difference between exact collinearity, e.g., • X2i = 2X1i • And a coefficient restriction, e.g., • H0: 2 = 21 ? • Relate the concepts to the model.

More Related