// File New-Lec3-05-04-02-02.txt. Edition 7/14/2010. // Title Irrelevant_Explanatory_Variable // Irrelevant Omit // List for Y on X Constant, Coefficient, and Error Term Variance 10 30 10 10 -2 2 2 2 -5 5 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 .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 ` 0110 .00 .00 .00 2 0 50 Objective: Show that irrelevant explanatory variables provide both good news and bad news. _ Good news: The ordinary least squares (OLS) estimation procedure for the value of the relevant variable's coefficient is unbiased regardless of whether or not the irrelevant variable is included. _ Bad news: The variance of the probability distribution for the relevant variable increases whenever the irrelevant variable is included. Furthermore, as relevant and irrelevant explanatory variable become more correlated, the increase in variance becomes greater. ` By default the actual coefficient of the second explanatory variable equals 0. The second explanatory variable is the irrelevant variable. _ The Coef1 radio button is selected indicating that the estimates for the first variable's coefficient will be reported. ` 0110 .00 .00 .00 2 0 50 The Only X1 checkbox is selected indicating that only the first explanatory variable is included in the regression; that is, the irrelevant variable is omitted. _ 1a. Note that the two explanatory variables are not correlated: .0 is selected from the CorrX1&X2 list. Click Start and then, after many, many repetitions click Stop. Do the results suggest that the estimation procedure for the coefficient value is biased or unbiased? What is the variance of the estimates. ` 0110 .00 .00 .30 2 0 50 The Only X1 checkbox is selected indicating that only the first explanatory variable is included in the regression; that is, the irrelevant variable is omitted. _ 1b. Note that the two explanatory variables are correlated: .30 is selected from the CorrX1&X2 list. Click Start and then, after many, many repetitions click Stop. Do the results suggest that the estimation procedure for the coefficient value is biased or unbiased? What is the variance of the estimates. ` 0110 .00 .00 .30 2 0 50 The Only X1 checkbox is selected indicating that only the first explanatory variable is included in the regression; that is, the irrelevant variable is omitted. _ 1c. Next, select .60, and then .90, and then -.30 from the CorrX1&X2 list. In each case, Click Start and then, after many, many repetitions click Stop. Do the results suggest that the estimation procedure for the coefficient value is biased or unbiased? How does the correlation affect the variance of the estimates. ` 0110 .00 .00 .00 2 0 50 The Only X1 checkbox is selected indicating that only the first explanatory variable is included in the regression; that is, the irrelevant variable is omitted. _ 1d. When we do not include an irrelevant variable explanatory variable is the estimation procedure for the coefficient value biased or unbiased. What do you conclude about the variance of the estimates? ` 0010 .00 .00 .00 2 0 50 The Both X's checkbox is selected indicating that both the first and second explanatory variables are included in the regression; that is, the irrelevant variable is included. _ 2a. Note that the two explanatory variables are not correlated: .00 is selected from the CorrX1&X2 list. Click Start and then, after many, many repetitions click Stop. Do the results suggest that the estimation procedure for the coefficient value is biased or unbiased? What is the variance of the estimates. ` 0010 .00 .00 .30 2 0 50 The Both X's checkbox is selected indicating that both the first and second explanatory variables are included in the regression; that is, the irrelevant variable is included. _ 2b. Note that the two explanatory variables are correlated: .30 is selected from the CorrX1&X2 list. Click Start and then, after many, many repetitions click Stop. Do the results suggest that the estimation procedure for the coefficient value is biased or unbiased? What is the variance of the estimates. ` 0010 .00 .00 .30 2 0 50 The Both X's checkbox is selected indicating that both the first and second explanatory variables are included in the regression; that is, the irrelevant variable is included. _ 2c. Next, select .60, and then .90 from the CorrX1&X2 list. In each case, Click Start and then, after many, many repetitions click Stop. Do the results suggest that the estimation procedure for the coefficient value is biased or unbiased? How does the correlation affect the variance of the estimates. ` 0010 .00 .00 .00 2 0 50 The Both X's checkbox is selected indicating that both the first and second the first and second explanatory variables are included in the regression; that is, the irrelevant variable is included. _ 1d. When we include an irrelevant variable explanatory variable is the estimation procedure for the coefficient value biased or unbiased. What do you conclude about the variance of the estimates?