1. Economics 310 Lecture 12 Heteroscedasticity

2. Economics 212 Lecture 23 - Heteroscedasticity

3. Heteroscedasticity Violation of classic assumption of constant variance of disturbance. The variance of the disturbance may be different for some or all of the subpopulations. Subpopulations with large variances are not as helpful in estimating our model as subpopulations with small variances.

4. Sources of Heteroscedasticity Error-learning models Discretionary Income Improved Data Collection techniques Outliers

5. Example of Heteroscedasticity-Typing Test WPM Weeks Density

6. Faculty Salaries Across Universities

7. Example Heteroscedasticity - Faculty Salaries _______________________________________________________________11/19/1998_10:25_ FILE: box and whisker for faculty salaries, NO. OF VARIAB(MISS. CASES: 0) E LABEL: none ________________________________________________________________________________ BOX AND WHISKER PLOT VARIABLE: Full PLOT: ----------XXXXXX¦XXXXXX----------------- VARIABLE: Assoc. PLOT: ------XXX¦XXXX--------- o VARIABLE: Asst. PLOT: -----XX¦X------- o ¦--------------¦--------------¦--------------¦--------------¦ 35 51 66 81 97

8. OLS Estimation with Heteroscedasticy

9. Method of Generalized Least- Squares

10. GLS Estimator

11. GLS Estimator Continued

12. Example GLS Estimation

13. Data for GLS Example Statepopautopcincomepc California32.2680.4825.368 Florida14.6540.5024.198 Indiana5.8640.5422.633 Maine1.2420.4621.087 Mississippi2.7310.4617.561 New Hampshire1.1730.6326.772 North Dakota0.6410.5220.476 Rhode Island0.9870.5124.613 Utah2.0590.4019.384 Wisconsin5.1700.4823.390

14. Results of unweighted regression R-SQUARE = 0.4326 R-SQUARE ADJUSTED = 0.3617 VARIANCE OF THE ESTIMATE-SIGMA**2 = 0.23376E-02 STANDARD ERROR OF THE ESTIMATE-SIGMA = 0.48348E-01 SUM OF SQUARED ERRORS-SSE= 0.18700E-01 MEAN OF DEPENDENT VARIABLE = 0.49800 LOG OF THE LIKELIHOOD FUNCTION = 17.2196 VARIABLE ESTIMATED STANDARD T-RATIO PARTIAL STANDARDIZED ELASTICITY NAME COEFFICIENT ERROR 8 DF P-VALUE CORR. COEFFICIENT AT MEANS INCOMEPC 0.13807E-01 0.5590E-02 2.470 0.039 0.658 0.6577 0.6251 CONSTANT 0.18669 0.1270 1.470 0.180 0.461 0.0000 0.3749

15. Results of Weighted Regression R-SQUARE = 0.0749 R-SQUARE ADJUSTED = -0.0407 VARIANCE OF THE ESTIMATE-SIGMA**2 = 0.11092E-02 STANDARD ERROR OF THE ESTIMATE-SIGMA = 0.33305E-01 SUM OF SQUARED ERRORS-SSE= 0.88738E-02 MEAN OF DEPENDENT VARIABLE = 0.48946 LOG OF THE LIKELIHOOD FUNCTION = 17.0600 VARIABLE ESTIMATED STANDARD T-RATIO PARTIAL STANDARDIZED ELASTICITY NAME COEFFICIENT ERROR 8 DF P-VALUE CORR. COEFFICIENT AT MEANS INCOMEPC 0.43115E-02 0.5357E-02 0.8048 0.444 0.274 0.2737 0.2123 CONSTANT 0.38555 0.1295 2.976 0.018 0.725 0.0000 0.7877