//  File MIT-Lab-20-03-04-05.txt

// Title
Instrumental_Variables_-_Omitted_Variables:_Bad_Instrument

//  Omitted Variables or Measurement Error
      OmitIV

//  List for Y on X Constant, Coefficient, and Error Term Variance
      10 30 10 10
      -2.0 2.0 2.0 2.0
      -4.0 4.0 4.0 4.0
      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






// IV: Bad Instrument - Biased and Not Consistent
` 0111 .50 .10 .60 2 5 50
Objective: When an omitted variable problem is present the instrument variable
 squares (IV) estimation procedure for "problem" explanatory variable's coefficient
 is not consistent when the second "good" instrument condition is violated.
_
The Const, Coef and Err Var lists on the extreme left describe the relationship
 between explanatory variables (X1 and X2) and dependent variable (Y):
_  Y = 10 + 2X1 + 4X2 + Err


`
The Corr X1&Z specifies the correlation coefficient for the included explanatory
 variable, X1, and the instrument, Z. By default, the X1/Z correlation coefficient
 equals .50.
_
The Corr X2&Z specifies the correlation coefficient for the omitted explanatory
 variable, X2, and the instrument, Z. By default the X2/Z correlation coefficient
 equals .10. 
_
The Corr X1&X2 specifies the correlation coefficient for the two explanatory
 variables, X1 and X2. By default the X1/X2 correlation coefficient
 equals .60.



`
The Only X1 check box is selected; consequently, only the first explanatory variable,
 X1, will be included in the regression.
_
The actual coefficient of the omitted variable, X2, equals 4.0;
 the omitted explanatory variable affects the dependent variable. Also,
 the correlation coefficient of the omitted and included explanatory
 variable equals .60; they are correlated.
_
Consequently, the included explanatory variable, X1, becomes a
 "problem" explanatory variable because it will be correlated
 with the error term.


` 0111 .50 .10 .60 2 5 50
The instrument variable estimation procedure has been selected.
_
Focus on the Corr X1&Z list. The correlation coefficient for the "problem" variable, X1,
 and the instrument, Z, equals .50. The instrument, Z, is correlated 
 with the "problem" explantory variable, X1.
_
1. Consider the first "good" instrument condition:
______Instrument/"problem" explanatory variable correlation.
Is the first "good" instrument condition satisfied?


` 0111 .50 .10 .60 2 5 50
Now, focus on the Corr X2&Z list. The correlation coefficient of the 
 omitted variable, X2, and the instrument, Z, 
 equals .10. The instrument and the omittted variable are correlated.
_
2. Consider the second "good" instrument condition:
______Instrument/error term independence.
Is the second "good" instrument condition satisfied?


` 0111 .50 .10 .60 2 5 50`
3. The sample size equals 50. Click Start and then after many, many 
 repetitions click Stop. 
_
3a. What does the mean of the coefficient estimates equal?
_
3b. What does the variance of the coefficient estimates equal?
_
3c. Is the instrumental variable (IV) extimation procedure for the coefficient
 value biased or unbiased?



` 0111 .50 .10 .60 2 5 100
4. The sample size has been increased from 50 to 100. 
 Click Start and then after many, many repetitions click Stop. 
_
4a. What does the mean of the coefficient estimates equal?
_
4b. What does the variance of the coefficient estimates equal?
_
4c. Is the instrumental variable (IV) extimation procedure for the coefficient
 value biased or unbiased?


` 0111 .50 .10 .60 2 5 150
5. The sample size has been increased from 100 to 150. 
 Click Start and then after many, many repetitions click Stop. 
_
5a. What does the mean of the coefficient estimates equal?
_
5b. What does the variance of the coefficient estimates equal?
_
5c. Is the instrumental variable (IV) extimation procedure for the coefficient
 value biased or unbiased?


`
6. Is the instumental variable (IV) estimation procedure for the "problem" 
 coefficient's estimate unbiased?
_
7. When the second "good" instrument condition is violated, is the 
 instumental variable (IV) estimation procedure for the "problem"
 coefficient's estimate consistent?