//  File MIT-Lab-16-04-03-02. Edition 1/21/2013.


//  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 ordinary least squares.
_
The generalized least squares (GLS) estimation procedure for the variance of the
 coefficient estimate's probability distributuion is unbiased.
_
Also, the generalized least squares (GLS) estimation procedure is better because the variance
 of the coefficient estimate's probability distribution is less.



` 3 0 2 500 10 2 0 30 0 -1
The "heteroskedasticity factor" is 1; heterskedasticity is present.
_
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 OLS 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 OLS estimation procedure for the variance of
 coefficient estimate's probability distribution is biased or unbiased when
 heteroskedasticity is present?


`
1c. For future reference, record the variance of the coefficient estimate's
 probability distribution (in the "Mean" line under "Coef Dist Var Est").
_
Next, focus on the drop down box immediately above the Start button. 
 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.
 

`
2a. 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?
 

`
2b. Compare the mean (average) of the GLS 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?

`
2c. When the GLS estimation procedure is used, what is the variance of the coefficient
 estimate's numercial values (in the "Var" line under "Coef Est")?

_
3. In which estimation procedure, OLS or GLS, is the variance smaller? Why is
 this important?