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

// Title
Explanatory_Variable_Measurement_Error_and_OLS_-_Bias
//  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 explanatory variable measurement error does  bias the ordinary least
 squares (OLS) estimation procedure for the coefficient value.
_
Note the new check box to the left: XMeas Err. This check box will allow us
 to investigate dependent variable measurement error. The XMeas Var list appears
 below the check box. By default the variance
 of the explanatory variable measurement error random variable is set to 20.

` 0310 .50 .00 .00 2 4 40
1. Be certain that the X Meas checkbox is checked. Note that the actual coefficient
 value is 2. Click the 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. If biased:
__________1) Is the estimation procedure biased upwards of downwards?
__________2) What is the magnitude of the bias?


` 0310 .50 .00 .00 1 4 40
2. Note that the actual coefficient value has been reset to 1. Click the 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. If biased:
__________1) Is the estimation procedure biased upwards of downwards?
__________2) What is the magnitude of the bias?



` 0310 .50 .00 .00 -1 4 40
3. Note that the actual coefficient value has been reset to -1. Click the 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. If biased:
__________1) Is the estimation procedure biased upwards of downwards?
__________2) What is the magnitude of the bias?



` 0310 .50 .00 .00 0 4 40
4. Note that the actual coefficient value has been reset to 0. Click the 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. If biased:
__________1) Is the estimation procedure biased upwards of downwards?
__________2) What is the magnitude of the bias?

`
5. As the magnitude of the actual coefficient decreases, what happens to
 the magnitude of the bias?