//  File MIT-Lab-20-02-04-05.txt. Edition 1/22/2013.

// Title
Instrumental_Variables_-_Omitted_Variables

//  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: Good Instrument - Biased but Consistent
` 0111 .50 .00 .60 2 5 50
Objective: When an omitted variable problem is present while the instrument variable
 squares (IV) estimation procedure for "problem" explanatory variable's coefficient
 is biased, it can be consistent.
_
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 .00. 
_
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.


`
1a. What is the first "good" instrument condition?
_
1b. Do the default values satisfy the first "good" instrument condition? Explain.
_
2a. What is the second "good" instrument condition?
_
2b. Do the default values satisfy the second "good" instrument condition? Explain.


` 0111 .50 .00 .60 2 5 50
3. Initially, 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 .00 .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 .00 .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. When an omitted variable problem is present and the "good" instrument
 conditions are satisfied, is the instumental variable (IV) estimation
 procedure for the "problem" coefficient's value unbiased? Explain.
_
7. When an omitted variable problem is present and the "good" instrument
 conditions are satisfied, is the instumental variable (IV) estimation
 procedure for the "problem" coefficient's value consistent? Explain.


` 0111 .75 .00 .60 2 5 150
8. Focus your attention on the first "good" instrument condition:
_______Instrument/"problem" explanatory variable correlation.
_
The correlation coefficient for the "problem" explanatory variable, X1,
 and the instrument has be increased from .50 to .75. The instrument is
 now more highly correlated with the "problem" explanatory variable.
 Click Start and then after many, many repetitions click Stop. Does
 the instrument provide better estimates for the "problem" coefficient's
 value? Explain.