// 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?