// File New-Lec4-01-02-03-02.txt. Edition 11/6/2012. // Lab Specs // Window Title Heteroscedasticity // Option (0 Normal, 1 Auto, 2 Heter, 3 X-e correlation, 4 Measurement, 5 Consistency (Is this used?) 2 // Constant List 40 60 10 50 // Coefficient List -2 6 2 2 // iListVarErrors 50 500 150 500 // iListSamples 3 250 1 5 // iListSamplesAutocorrelation 3 50 1 40 // iListSamplesMeasurement 3 50 1 5 // iListXMinima 0 10 10 0 // iListXMaxima 20 30 10 30 // strListFromCoef -1.0 4.0 .5 1.0 // strListToCoef 1.0 6.0 .5 3.0 // strListRho -.9 .9 .3 .0 // strListHeter -2.0 2.0 1.0 .0 // strListCoefXAndError -.9 .9 .3 .0 // iListXMeasErrVar 0 100 50 0 // Problem Specs // SampleSize // PauseCheckbox (-1 checked, 0 cleared) // EstType (0 Error, 1 Constant, 2 Coefficient) // ErrorVar // ConstValue // CoefValue // xMinValue // xMaxValue // ErrTermCheckbox (0 not visible and unchecked, -1 visible and checked, 1 visible and unchecked)) // VarEstAndFromTo (-1 VarEst visible, 0 nothing visible, 1 From-To visible) ` 3 0 2 500 10 2 0 30 0 -1 Objective: Show that when heteroskedasticity is present, there is good news and bad news for the ordinary lease squares (OLS) estimation procedure. _ Good news: The OLS estimation procedure for the value of the coefficient is still unbiased. _ Bad news: The OLS estimation procedure for the variance of the coefficient estimate's probability distributuion is biased. ` We shall exploit the relative frequency interpretation of probability to assess the "unbiasness" of two OLS estimation procedures: the estimation procedure for the _ value of the coefficient. _ variance of the coefficient estimate's probability distributuion. ` OLS estimation procedure for the value of the coefficient: _ Compare the mean (average) of the coefficient estimate's numercial values _ (in the "Mean" line under "Coef Est") and the actual value of the coefficient _ (in the "Act Coef" list) after many, many repetitions. ` OLS estimation procedure for the variance of the coefficient estimate's probability distribution: _ Compare the mean (average) of the OLS estimates of the variance for the coefficient estimate's probability distribution _ (in the "Mean" line under "Coef Dist Var Est") and the variance of the coefficient estimate's numercial values _ (in the "Var" line under "Coef Est") after many, many repetitions . ` 3 0 2 500 10 2 0 30 0 -1 1a. Initially, the heteroskedasticity factor is 0: no heterskedasticity is present. The Pause checkbox is cleared. Click Start and then after many, many repetitions, click Stop. _ Compare the mean of the coefficient estimate's numercial values _ (in the "Mean" line under "Coef Est") and the actual value of the coefficient _ (in the "Act Coef" list) _ Does this suggest that the OLS estimation procedure for the coefficient value is biased or unbiased? ` 1b. Compare the mean (average) of the OLS estimates of the variance for the coefficient estimate's probability distribution _ (in the "Mean" line under "Coef Dist Var Est") and the variance of the coefficient estimate's numercial values _ (in the "Var" line under "Coef Est") _ Does this suggest that the OLS estimation procedure for the variance of coefficient estimate's probability distribution is biased or unbiased? ` 3 0 2 500 10 2 0 30 0 -1 2a. Change the heteroskedasticity factor to 1: heterskedasticity is now present. Click Start and then after many, many repetitions click Stop. _ Compare the mean of the coefficient estimate's numercial values _ (in the "Mean" line under "Coef Est") and the actual value of the coefficient _ (in the "Act Coef" list) _ Does this suggest that the OLS estimation procedure for the coefficient value is biased or unbiased when heteroskedasticity is present? ` 2b. Compare the mean (average) of the OLS estimates of the variance for the coefficient estimate's probability distribution _ (in the "Mean" line under "Coef Dist Var Est") and the variance of the coefficient estimate's numercial values _ (in the "Var" line under "Coef Est") _ Does this suggest that the OLS estimation procedure for the variance of coefficient estimate's probability distribution is biased or unbiased when heteroskedasticity is present?