//  File MIT-Lab-18-03-01-04.txt. Edition 5/15/2012.


//  Lab Specs
//    Window Title
         Unbiased_and_Consistent_Estimation_Procedure:_OLS
//    Option (0 Normal, 1 Auto, 2 Heter, 3 X-e correlation, 4 Measurement, 5 Consistency (Is this used?)
         0
//    Constant List
         40 60 10 50
//    Coefficient List
         -2.0 6.0 2.0 2.0
//    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 50 2 0 30 0 0
Objective: Illustrate that the OLS estimation procedure is unbaised and consistent when
 the explanatory variable/error term premise is satisfied..
_
Focus your attention on the drop down box just above the Start button. This is the Procedure drop down box.
 Check to be certain that the OLS estimation procedure. 
_
Note that the Act Coef radio button is selected. Also, the explanatory variable/error term
 independence premise is satisfied.

` 3 0 2 500 50 2 0 30 0 0
1. By default, the sample size is specified as 3. Click the Start button and after
 many, many repetitions click the Stop button.
1a. What does the mean of the coefficient estimates equal?
1b. What does the variance of the coefficient estimates equal?
_
2. Increase the sample size from 3 to 6. Click the Start button and after many,
 many repetitions click the Stop button. 
2a. What does the mean of the coefficient estimates equal?
2b. What does the variance of the coefficient estimates equal?


`
3. Increase the sample size from 6 to 10. Click the Start button and after many,
 many repetitions click the Stop button. 
3a. What does the mean of the coefficient estimates equal?
3b. What does the variance of the coefficient estimates equal?
_
4. Based on these results, when the explanatory variable/error term premise is satisfied
 is the ordinary least squares (OLS) estimation procedure
________3a. unbiased?
________3b. consistent?