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

// Title
Dependent_Variable_Measurement_Error_and_OLS

//  Omitted Variables or Measurement Error
      Meas

//  List for Y on X Constant, Coefficient, and Error Term Variance
      10 30 10 10
      -2.0 2.0 2.0 2.0
      -5.0 5.0 5.0 5.0
      100  500  200  300

// List Sample Size
      10 100 10 10
      
// 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
     20.0 80.0 30.0 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



` 0010 .50 .00 .00 2 4 10
Objective: Show that dependent variable measurement error does not bias the ordinary least
 squares (OLS) estimation procedure for the coefficient value.
_
Note the new check box to the left: YMeas Err. This check box will allow us
 to investigate dependent variable measurement error. 
 
` 0010 .50 .00 .00 2 4 10
1. The YMeas Err check box are cleared; consequently, there is no dependent
 variable measurement error. 
 Click Start and then after many, many repetitions click Stop. 
_
1a. Do the results suggest that the estimation procedure for the coefficient
 value is biased or unbiased? Explain.
_
1b. What is the variance of the numerical values of the coefficient estimates?


` 0110 .50 .00 .00 2 4 10
2. We have now introduced dependent variable measurement error by checking the 
 YMeas Err check box. The YMeas Var list now appears. By default the variance
 of the dependent variable measurement error random variable is set to 20.
 Click Start and then after many, many repetitions click Stop. 
_
2a. Do the results suggest that the estimation procedure for the coefficient
 value is biased or unbiased? Explain.
_
2b. What is the variance of the numerical values of the coefficient estimates? 


` 0110 .50 .00 .00 2 4 10
3. Increase the variance of the dependent variable measurement error random
 variable from 20 to 50.
 Click Start and then after many, many repetitions click Stop. 
_
3a. Do the results suggest that the estimation procedure for the coefficient
 value is biased or unbiased? Explain.
_
3b. What is the variance of the numerical values of the coefficient estimates? 


`
4. Increase the variance of the dependent variable measurement error random
 variable from 50 to 80.
 Click Start and then after many, many repetitions click Stop. 
_
4a. Do the results suggest that the estimation procedure for the coefficient
 value is biased or unbiased? Explain.
_
4b. What is the variance of the numerical values of the coefficient estimates? 
_
5. What is the impact of dependent variable measurement error?