// File MIT-Lab-18-06-04-05.txt. Edition 5/15/2012. // Title Explantory_Variable/Error_Term_Correlation // Omitted Variables or Measurement Error ExplErrCorr // 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 // abcd // 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 ` 0010 .00 .00 .30 2 5 50 Objective: Show that when the explanatory variable/error term independence premise is violated, the ordinary least squares (OLS) estimation procedure for the coefficient value is not consistent. _ Note that the explanatory variable/error term correlation coefficient is specified as .30. The explanatory variable and the error term are positively correlated; the explanatory variable/error term premise is violated. ` 0010 .00 .00 .30 2 5 50 1. Initially, the sample size equals 50. Click Start and then after many, many repetitions click Stop. _ What are the mean and variance of the numerical values of the coefficient estimates when the sample size equals 50? ` 0010 .00 .00 .30 2 5 100 2. Next, note that the sample size has been increased from 50 to 100. _ What are the mean and variance of the numerical values of the coefficient estimates when the sample size equals 100? ` 0010 -.00 .00 .30 2 5 150 3. Now, note that the sample size has been increased from 100 to 150. _ What are the mean and variance of the numerical values of the coefficient estimates when the sample size equals 150? _ 4. When the explanatory variable/error term independence premise is violated, is the ordinary least squares (OLS) estimation procedure for the coefficient value consistent? Explain.