//  File MIT-Lab-18-06-04-05.txt.  Edition 5/15/2012.

// Title
Explantory_Variable/Error_Term_Correlation

//  Omitted Variables or Measurement Error
      ExplErrCorr

//  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
      50 500 25 50
      
// 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
     1.0 3.0 1.0 2.0
     
// 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
//   abcd
//   a: Pause checkbox
//   b: Both 0-Both Xs    1-Only X1
//   c: Parameter to estimate. 0, 1, or 2: 0-Constant  1-X1  2-X2
//   d: Estimation procedure. 0-OLS 1-IV


` 0010 .00 .00 .00 2 5 50
Objective: Illustrate that the OLS estimation procedure is unbaised and consistent
 when the standard ordinary least squares (OLS) premises are satisfied.
_
Note that the explanatory and the error term are independent; their
 correlation coefficient (Corr X&E) equals .00.

` 0010 .00 .00 .00 2 5 50
1. Initially, the sample size is specified as 50. 
 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 50 to 100.
 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 100 to 150.
 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?