//  File 55-Lec3-05-02-02-02.txt. Edition 7/14/2010.
// Title
Omitted_Variables

//  Omitted Variables or Measurement Error
      Omit

//  List for Y on X Constant, Coefficient, and Error Term Variance
      10 30 10 10
      -2 2 2 2
      -5 5 5 5
      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
//   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 .50 .00 .30 2 5 50
Objective: Show that when both explanatory variables are present the
 ordinary least square (OLS) estimation procedure for coefficient values
 is unbiased. This is true even when
_______both variables affect the dependent variable
and
_______the variable are correlated.
_
The Coef1 radiobutton is selected indicating that the estimates for the
 first variable's coefficient will be reported.


` 0010 .50 .00 .30 2 5 50
5 is selected from the Act Coef2 list and .30 from the CorrX1&X2 list. Therefore,
 both variable affect influence the dependent variable and
 the variables are correlated. Note that the Both x's checkbox is checked; consequently,
 BOTH explanatory variables are included in the regression. There is no
 omitted variable.
_
1. Click Start and then, after many, many repetitions click Stop. What is the mean (average)
 of the estimates for the first variable's coefficient?
_
2. Is the estimation procedure for the value of the first coefficient biased?