// File MIT-Lab-04-04-04-05.txt. Edition 5/15/2012. // Title Explanatory_Variable_Measurement_Error_and_Instrumental_Variables // Omitted Variables or Measurement Error MeasIV // 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 40 100 10 40 // 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 .366 .531 // .500 .662 // Measurement Error Variance 10.0 25.0 5.0 20.0 // 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. 50 // Problem Specs: abcd Corr[X1,Z] Corr[X2,Z] Corr[X1,X2] Coef1Value Coef2Value SampleSize // Not sure what Corr[X1,X2] does - I must check it. // a: Pause checkbox // b: YMeasErr/XMeasErr // 0 Y - box cleared 2 X - box cleared // 1 Y - box checked 3 X - box checked // c: Parameter to estimate. 0, 1, or 2: 0-Constant 1-X1 2-X2 // d: Estimation procedure. 0-OLS 1-IV ` 0311 .50 .00 .00 2 4 10 Objective: Show that when explanatory variable measurement error is present and the actual coefficient is nonzero, the the instrumental variable (IV) estimation procedure for the coefficient value is biased, but consistent. _ Focus your attention on the drop down box above the Start button. IV has been selected to study the instrumental variable estimation procedure, ` By default, the variance of the explanatory variable measurement error random variable is set to 20. _ The Corr X1&Z list indicates that the correlation coefficient for the explanatory variable and the instrument equals .50. ` 0311 .50 .00 .00 2 4 40 1. Initially the sample size is 40. Click Start and then, after many, many repetitions click Stop. When the sample size is 40: ________1a. What does the mean of the coefficient estimates equal? ________1b. What does the variance of the coefficient estiamtes equal? ` 0311 .50 .00 .00 2 4 60 2. The sample size has been increased from 40 to 60. Click Start and then, after many, many repetitions click Stop. When the sample size is 60: ________2a. What does the mean of the coefficient estimates equal? ________2b. What does the variance of the coefficient estiamtes equal? ` 0311 .50 .00 .00 2 4 80 3. The sample size has been increased from 60 to 80. Click Start and then, after many, many repetitions click Stop. When the sample size is 80: ________3a. What does the mean of the coefficient estimates equal? ________3b. What does the variance of the coefficient estiamtes equal? ` 0311 .50 .00 .00 2 4 80 4. When explanatory variable measurement error is present and the actual coefficient is nonzero, is the isstrumental variable (IV) estimation ________4a. unbiased? ________4b. consistent?