Presentation on theme: "Welcome to Econ 420 Applied Regression Analysis"— Presentation transcript:
1 Welcome to Econ 420 Applied Regression Analysis Study GuideWeek Eleven
2 Perfect Multicollinearity (Chapter 6) When two or more independent variables have a perfect (error free) linear relationship with each otherWhich assumption does this violate?Violates Assumption 2ExampleEquation 6-1, Page 116Consequences: OLS is not able to estimate the modelRemedyDrop one variable
3 Imperfect Multicollinearity When two or more independent variables have an imperfect linear relationship with each otherExampleEquation 6-3, Page 117
4 Consequences of Imperfect Multicollinearity B hats are unbiasedB hats have higher than normal standard errorsWhat does this imply with regards to t- test?We may conclude that Bs are not significantly different from zero while they are significantly different from zero.Adding and subtracting variables and observations will affect B hats significantlyThe adjusted R squared remains largely unaffectedThe B hats of uncorrelated variables remain unaffected
5 Detection of Multicollinearity If you have high adjusted R squared but low t-scores suspect a multicollinearity problem
6 Test for Multicollinearity Calculate the correlation coefficients between each pair of independent variables and each independent variable and the dependent variable.EViews direction: quick group statistics correlationTwo rules1) If |rX1, X2| > |rX1, Y | problem, or2) If |rX1, X2 |> 0.8 problemProblem: this approach only detects the multicollinearity between two variables
7 Test for Multicollinearity Regress each independent variable on the other independent variableDo an F-test of significance at 1% levelIf reject the null hypothesis multicollinearity is a problem
8 Sometimes 3 or more independent variables are correlated ExampleIncome = f (wage rate, tax rate, hours of work, ….)Wage rate, tax rate and hours of work may be all highly correlated with each otherSimple correlation coefficient may not capture this.
9 Test of Multicollinearity among 3 or more independent variables Regress each independent variable (say X1) on the other independent variables (X2, X3, X4)Then calculate VIFVIF = 1 / (1- R2)If VIF >4 then X1 is highly correlated with the other independent variablesDo the same for other independent variables
10 Remedies for Multicollinearity 1) If your main goal is to use the equation for forecasting and you don’t want to do specific t- test on each estimated coefficient then do nothing. This is because multicollinearity does not affect the predictive power of your equation.2) If it seems that you have a redundant variable, drop it.Example: You don’t need both real and nominal interest rates in your model
11 Remedies for Multicollinearity 3) If all variables need to stay in the equation, transform the multicollinear variablesExample:Number of domestic cars sold = B0 + B1 average price of domestic cars + B2 average price of foreign cars +…..+ eProblems: Prices of domestic and foreign cars are highly correlatedSolution:Number of domestic cars sold = B0 + B1 the ratio of average price of domestic cars to the average price of foreign cars +…..+ e4) Increase the sample size or choose a different random sample
12 Assignment 9 (30 points) Due: Before 10:00 PM, Friday, November 9 11, Page 13113, page 132
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