//  File New-Lec4-01-04-03-02. Edition 7/14/2010.


//  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 1.0
//    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, the generalized least squares (GLS)
 estimation procedure "cures" the problem encountered by the ordinary least squares (OLS)
 estimation procedure.
_
The generalized least squares (GLS) estimation
 procedure for the value of the coefficient is still unbiased; furthermore, the GLS estimation
 procedure for the variance of the coefficient estimate's probability distributuion is unbiased also.

` 3 0 2 500 10 2 0 30 0 -1
First, note that the "heteroskedasticity factor" is 1: heterskedasticity is present.
_
Second, focus on the drop down box below the Act Coef list. 
 Change the estimation procedure from ordinary least squares (OLS)
 to generalized least squares (GLS). The simulation will now apply the generalized
 least squares estimation procedure rather than the ordinary least squares
 estimation procedure.
 

`
1a. 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 GLS estimation procedure for the coefficient value
 is biased or unbiased when heteroskedasticity is present?
 

`
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 GLS estimation procedure for the variance of
 coefficient estimate's probability distribution is biased or unbiased when
 heteroskedasticity is present?