// File New-Lec3-05-03-02-02.txt. Edition 7/14/2010. // Title Multicollinearity // Multicollinearity Omit // List for Y on X Constant, Coefficient, and Error Term Variance 10 30 10 10 -2 2 2 2 -5 5 5 5 100 500 200 300 // List Sample Size 50 150 25 50 // Correlation Coefficients: X1Z, X2Z, and X1X2 .50 .75 .25 .50 .00 .10 .10 .00 -.30 .90 .30 .30 // Correlation Coefficient Betas // The order is X1Z X2Z X1X2 .000 .000 -.458 .721 .000 -.289 .549 .091 -.363 .827 .091 -.398 .000 .000 .000 .532 .000 .000 .383 .091 -.038 .568 .091 -.057 .000 .000 .239 .532 .000 .000 .383 .091 -.038 .568 .091 -.057 .000 .000 .428 .457 .000 .183 .305 .091 .162 .461 .091 .145 .000 .000 .674 .673 .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 ` 0010 .00 .00 .00 2 5 30 Objective: Show that the multicollinearity phenomenon provides both good and bad news. _ Good news: When two (or more) explanatory variables are included in the regression, the ordinary least squares (OLS) estimation procedure for the coefficient values of the explanatory variables is unbiased. _ Bad news: As the explanatory variables become more correlated, however, the variance of the coefficient estimate's probability distribution increases. ` 0010 .00 .00 .00 2 5 30 This simulation includes two explanatory variables. To study multicollinearity the Both X's checkbox is selected indicating that both explanatory variables are included in the regression. _ The Act Coef1 radio button is selected indicating that the estimates for the first variable's coefficient will be reported. ` 0010 .00 .00 .00 2 5 30 1a. Suppose that the two explanatory variables are not correlated. To illustrate this, .00 is selected from the CorrX1&X2 list. Click Start and then after many, many repetitions click Stop. What is the mean (average) of the estimates for the first variable's coefficient? What is the variance of the estimates? _ 1b. Does this suggest that the estimation procedure for coefficient value is biased or unbiased when both explanatory variables are included in the regression and the explanatory variables are not correlated? Explain. ` 0010 .00 .00 .30 2 5 30 2a. Next, note that .30 has been selected from the CorrX1&X2 list. The explanatory variables are now correlated. Click Start and then after many, many repetitions click Stop. What is the mean (average) of the estimates for the first variable's coefficient? What is the variance of the estimates? _ 2b. Does this suggest that the estimation procedure for coefficient value is biased or unbiased when both explanatory variables are included in the regression and the explanatory variables are correlated? Explain. ` 0010 .00 .00 .60 2 5 30 3a. Now, note that the correlation coefficient of the two explanatory variables has been increased from .30 to .60. Click Start and then after many, many repetitions click Stop. What is the mean (average) of the estimates for the first variable's coefficient? What is the variance of the estimates? _ 3b. Does this suggest that the estimation procedure for coefficient value is biased or unbiased when both explanatory variables are included in the regression and the explanatory variables are correlated? Explain. ` 0010 .00 .00 .90 2 5 30 4a. Now, note that the correlation coefficient of the two explanatory variables has been increased from .60 to .90. Click Start and then after many, many repetitions click Stop. What is the mean (average) of the estimates for the first variable's coefficient? What is the variance of the estimates? _ 4b. Does this suggest that the estimation procedure for coefficient value is biased or unbiased when both explanatory variables are included in the regression and the explanatory variables are correlated? Explain. ` 5. As the explanatory variables become more and more correlated, what does not happen and what does happen? _ 6. As the explanatory variables become more and more correlated, how is the relatibility of an estimate from one repetition of the experiment affected? Explain.