// File New-Lec3-05-01-04-05.txt. Edition 2/24/2012.

// Title
Omitted_Variables

//  Omitted Variables or Measurement Error
      Omit

//  List for Y on X Constant, Coefficient, and Error Term Variance
      10 30 10 10
      -2.0 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
//   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



` 0110 .00 .00 .00 2 5 50
Objective: Illustrate the omitted variable proxy effect. The ordinary least
 squares (OLS) estimation procedure for the estimating the coefficient value
 of the included explanatory varaible will be biased whenever the omitted
 explanatory variable
______affects the dependent variable
and
______is correlated with an included explanatory variable.
_
If either of these two conditions is not met, no bias results.


` 0110 .00 .00 .00 2 5 50
This simulation includes two explanatory variables. By default, the actual value of the first
 variable's coefficient is 2 and the actual value of the second variable's coefficient is 5.
 The CorrX1&X2 list indicates how the two explanatory variables are correlated. Initially,
 the variables are not correlated because 0 is selected from this list.  
_
Also, the Coef1 radiobutton
 is selected indicating that the estimates for the first variable's coefficient 
 will be reported.
`
To investigate the omitted variable pheanomeon, the Only X1 check box is selected
 indicating that only the first explanatory variable is included in the regression;
 the second explanatory variable is omitted from the regression.


` 0110 .00 .00 .00 2 5 50
1a. Again, note that the explanatory variables ARE NOT correlated because .0 is selected from the
 CorrX1&X2 list. Also, in the Act Coef2 list, 5 is selected indicating that the second variable
 DOES affect the dependent variable. Be certain that the Pause check box is cleared. Click Start
 and then after many, many repetitions click Stop. What is the mean (average)
 of the estimates for the first variable's coefficient?
` 0110 .00 .00 .00 2 5 50
1b. Does this suggest that the estimation procedure for a coefficient value is biased or unbiased
 whenever we omit an explanatory variable that
______DOES affect the dependent variable
and
______IS NOT correlated with an included explanatory variable?
Explain.


` 0110 .00 .00 .30 2 0 50
2a. Next, suppose that the omitted variable DOES NOT influence the dependent variable, but
 the omitted explanatory variable IS correlated with an included variable.
 To explore this case, select 0 from the Act Coef2 list and .30 from the CorrX1&X2 list.
 Click Start and then after many, many repetitions click Stop.
 What is the mean (average) of the estimates for the first variable's coefficient?
` 0110 .00 .00 .30 2 0 50
2b. Does this suggest that the estimation procedure for a coefficient value is biased or unbiased
 whenever we omit an explanatory variable that
______DOES NOT affect the dependent variable
and
______IS correlated with an included explanatory variable?
Explain.


` 0110 .00 .00 .30 2 5 50
3a. Next, suppose that the omitted variable DOES influence the dependent variable and
 the omitted explanatory variable IS correlated with the included variable.
 To explore this case, select 5 from the Act Coef2 list and .30 from the CorrX1&X2 list.
 Click Start and then after many, many repetitions click Stop.
 What is the mean (average) of the estimates for the first variable's coefficient?
` 0110 .00 .00 .30 2 5 50
3b. Does this suggest that the estimation procedure for a coefficient value is biased or unbiased
 whenever we omit an explanatory variable that
______DOES affect the dependent variable
and
______IS correlated with an included explanatory variable?
Explain.