//  File MIT-Lab-18-02-04-05.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
      50 150 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 60
Objective: Show that when the explanatory variable/error term independence
 premise is violated, the ordinary least squares (OLS) estimation procedure
 for the coefficient value is biased.
_
That is, when the explanatory variable is correlated with the error term, the
 ordinary least squares (OLS) estimation procedure for the coefficient value
 is biased.

`
The Const, Coef and Err Var lists on the extreme left describe the relationship
 between explanatory variable (X) and the dependent variable (Y):
_  Y = 10 + 2X + Err
The list Corr X&E list specifies the coefficient of the
 of the explanatory variable and the error term. Also, the sample
 size equals 50.


` 0010 .00 .00 .00 2 5 50
1. Initially, .00 is selected from the Corr X&E list. The explanatory variable and
 the error term are independent. Click Start and then after many repetitions click Stop.
 Does the  simulation suggest that the ordinary least squares (OLS) estimation
 procedure for the coefficient value is unbiased or biased when the explanatory
 variable and error term are independent? Explain.


` 0010 .00 .00 .30 2 5 50
2. Next, note that .30 is selected from the Corr X&E list. The explanatory variable and
 the error term are positively correlated. Click Start and then after many repetitions click Stop.
 Does the  simulation suggest that the ordinary least squares (OLS) estimation
 procedure for the coefficient value is unbiased or biased when the explanatory
 variable and error term are positively correlated? Explain.



` 0010 -.00 .00 -.30 2 5 50
3. Next, note that .30 is selected from the Corr X&E list. The explanatory variable and
 the error term are positively correlated. Click Start and then after many repetitions click Stop.
 Does the  simulation suggest that the ordinary least squares (OLS) estimation
 procedure for the coefficient value is unbiased or biased when the explanatory
 variable and error term are positively correlated? Explain.