//  File MIT-Lab-19-03-04-05.txt. Edition 5/15/2012.

// Title
Explanatory_Variable_Measurement_Error_and_OLS_-_Consistency

//  Omitted Variables or Measurement Error
      Meas

//  List for Y on X Constant, Coefficient, and Error Term Variance
      10 30 10 10
      -1.0 2.0 1.0 2.0
      -4.0 4.0 4.0 4.0
      100  500  200  300

// List Sample Size
      40 100 10 40
      
// Correlation Coefficients: X1Z, X2Z, and X1X2
      .50  .75  .25  .50
      .00  .10  .10  .00
     -.30  .60  .30  .30
// Correlation Coefficient Betas
//   The order is X1Z X2Z X1X2
    .493 .000 -.296    .721 .000 -.289    .549 .091 -.363    .827 .091 -.398
    .366 .000  .000    .532 .000  .000    .383 .091 -.038    .568 .091 -.057
    .311 .000  .186    .457 .000  .183    .305 .091  .162    .461 .091  .145
    .290 .000  .348    .459 .000  .367    .267 .091  .333    .429 .091  .326


// Measurement Error X1Z Correlation Betas
    .500 .662
// Measurement Error Variance
     10.0 25.0 5.0 20.0
     
// Data Check: Needed to account for violatile IV behavior
// Simulation ignores repetition in which the estimate differs
// from the actual value by more than the Data Check value.
    25
     

//  Problem Specs: abcd Corr[X1,Z] Corr[X2,Z] Corr[X1,X2] Coef1Value Coef2Value SampleSize
//                                  I'm not sure what C[X1,X2] does here - I must check it.
//   a: Pause checkbox
//   b: YMeasErr/XMeasErr
//        0 Y - box cleared   2 X - box cleared
//        1 Y - box checked   3 X - box checked
//   c: Parameter to estimate. 0, 1, or 2: 0-Constant  1-X1  2-X2
//   d: Estimation procedure. 0-OLS 1-IV




` 0310 .50 .00 .00 2 4 40
Objective: Show that when explanatory variable measurement error is present
 and the actual coefficient is nonzero, the the ordinary least squares
 (OLS) estimation procedure for the coefficient value is not only biased,
 but also not consistent.
_
By default the variance of the explanatory variable measurement error random
 variable is set to 20.

` 0310 .50 .00 .00 2 4 40
1. Initially the sample size is 40.
 Click Start and then, after many, many repetitions click Stop.
 When the sample size is 40:
________1a. What does the mean of the coefficient estimates equal?
________1b. What does the variance of the coefficient estiamtes equal?




` 0310 .50 .00 .00 2 4 50
2. The sample size has been increased from 40 to 50.
 Click Start and then, after many, many repetitions click Stop.
 When the sample size is 50:
________2a. What does the mean of the coefficient estimates equal?
________2b. What does the variance of the coefficient estiamtes equal?



` 0310 .50 .00 .00 2 4 60
3. The sample size has been increased from 50 to 60.
 Click Start and then, after many, many repetitions click Stop.
 When the sample size is 60:
________3a. What does the mean of the coefficient estimates equal?
________3b. What does the variance of the coefficient estiamtes equal?
_
4. When explanatory variable measurement error is present and the actual
 coefficient is nonzero, is the ordinary least squares (OLS) estimation
 procedure for the coefficient value consistent? Explain.