Problem Set 3 Solutions - Problem Set 3 Economics 103...

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Problem Set 3 Economics 103 Introduction to Econometrics Due Thursday, February 20, 2009 True/False/Explain 1. In the regression model: Y= β 0 + β 1 female + β 2 education + ε , β 2 represents the intercept for females. False, β 0 + β 1 is the intercept for females 2. In the model Y = β 0 + β 1 log(X) + ε , the effect of X on Y does not depend on the level of x. False, dy/dx = β 1 /X so the effect of X on Y depends on the level of X. 3. In the model Y = β 0 + β 1 X + β 2 X 2 + ε the effect of X on Y does not depend on the level of x. False, dy/dx = β 1 + 2 β 2 X is the effect of X on Y which depends on the level of X. 4. An insignificant coefficient (not statistically different from zero) means you should not include that variable in the model. False, we should consider other factors such as whether the adjusted R-squared increases. We also might introduce omitted variable bias into the model if we drop that variable 5. In the regression model: Y= β 0 + β 1 female + β 2 education + β 3 education*female+ ε , β 3 represents the return to education for females. False, β 2 + β 3 represents the return to education for females 6. If you estimate the regression model: Y= β 0 + β 1 female + β 2 education + β 3 education*female+ ε , where Y is earnings, the constant term will represent the average earnings for men and Beta1 will represent the average earnings for women. False, β 0 represents the average earnings for men with no education, and β 0 + β 1 represents the average earnings for women with no education. 7. In the multiple regression model, the Adjusted- R 2 cannot be negative.
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False, the adjusted R-squared can be negative if 1 1 1 1 1 1 ) 1 ( 1 1 ) 1 ( 1 0 1 ) 1 ( 1 2 2 2 2 2 2 n k R n k n n R n k n R R n k n k n n R k n n R 8. In the multiple regression model, the Adjusted R 2 is the same as the R-Squared when the explanatory variables are all statistically significant. False, the R-squared and adjusted R-squared are only the same if k=1 (we only estimate the model with a constant). 9. Under perfect multicollinearity, the OLS estimator cannot be computed. True, perfect multicollinearity means that one of the explanatory variables can always be expressed linearly in terms of the others. Therefore, under perfect multicollinearity it is impossible to compute the OLS estimator since it is impossible to change one variable while holding all other variables constant 10. Wages tend to be lower in the south than other regions (total of 4 regions), as seen by the following estimated model: ln(wage)=1.56+.05north+.15west+.12northeast If instead we include south and drop north, then the coefficient on south will be -.05 and all the other coefficients (including the intercept) will stay the same.
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