Problem Set 4

# Problem Set 4 - Problem Set 4 Economics 103 Winter 2009 Due...

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Problem Set 4 Economics 103 Winter 2009 Due Tuesday, March 3, 2009 Question 1: True/False/Explain 1. If you estimate the following equation with a dummy indicating that you are a noncitizen instead of a dummy=1 if you are a citizen, you will get the same coefficients and standard errors. Y= 142 + 37 * citizen (72) (17.2) 2. In the following regression, if you divide the SAT score by 10, the coefficient will be 10 times larger and the standard error won’t change. Y= 142 + 38 * SAT (72) (17.2) 3. You have to worry about multicollinearity in the multiple regression model because OLS estimators are no longer efficient. 4. If you reject a joint null hypothesis that a group of regressors have no effect on the dependent variable using the F-test, then a series of individual t-tests will reject as well. 5. To decide whether 0 1 i i Y X u or 0 1 ln( ) i i Y X u fits the data better, you can compare the regression 2 R . 6. In the regression model 0 1 2 3 ( ) i i i i i i Y X D X D u , where X is a continuous variable and D is a binary variable, 3 indicates the slope of the regression when D=1. 7. In the regression model 0 1 2 3 ( ) i i i i i i Y X D X D u , where X is a continuous variable and D is a binary variable, 2 is the difference in means in Y between the two categories. 8. To test whether or not the regression function Y i = β 0 + β X i + β X i ²+...+ β p X i p is linear rather than a polynomial of order p, you would use a t-test. 9. In the presence of omitted variables, OLS estimators are unbiased but inefficient. 10. When you include irrelevant variables, OLS estimators are biased.

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Question 2 This problem uses the dataset from the last problem set, ceosal1.dta, which is a sample of CEOs. Note that the return on stock is measured such that a 25% return is recorded as 25. From last problem set: Create a new variable that records the same variables as .25 instead and then estimate a model of CEO salary as a function of sales and return on stock (in the recoded form). Choose a functional form such that you will directly estimate the elasticity of salary with respect to sales, and that allows the effect of the return on stock to possibly be increasing at a decreasing rate.
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