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Economics 310

Economics 310 . Lecture 12 Heteroscedasticity. 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.

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Economics 310

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  1. Economics 310 Lecture 12 Heteroscedasticity

  2. 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.

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

  4. Example of Heteroscedasticity-Typing Test Density Weeks WPM

  5. Faculty Salaries Across Universities

  6. 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

  7. OLS Estimation with Heteroscedasticy

  8. Method of Generalized Least-Squares

  9. GLS Estimator

  10. GLS Estimator Continued

  11. Example GLS Estimation

  12. Data for GLS Example State pop autopc incomepc California 32.268 0.48 25.368 Florida 14.654 0.50 24.198 Indiana 5.864 0.54 22.633 Maine 1.242 0.46 21.087 Mississippi 2.731 0.46 17.561 New Hampshire 1.173 0.63 26.772 North Dakota 0.641 0.52 20.476 Rhode Island 0.987 0.51 24.613 Utah 2.059 0.40 19.384 Wisconsin 5.170 0.48 23.390

  13. 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

  14. 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

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