Problem Set 4 Solutions

# Problem Set 4 Solutions - Problem Set 4 Answer Key...

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Problem Set 4 Answer Key Economics 103 Winter 2009 Prepared by: Luis Gonzalo Llosa 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) Solution: False . Both the slope and the constant will change. Also, the standard error of the slope coefficient remains the same but the standard error of the constant changes. 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) Solution: False . Both, the coefficient and the standard error will be 10 times larger. 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 01 ii YX u β =+ + or ln( ) u = ++ fits the data better, you can compare the regression 2 R .

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6. In the regression model 01 2 3 () ii i i i i YX D X D u β βββ =+ + + × + , where X is a continuous variable and D is a binary variable, 3 indicates the slope of the regression when D=1. Solution: False . The slope when D=1 equals ߚ ൅ߚ 7. In the regression model 2 3 i i i i 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. Solution: False. 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. Solution: False . 10. When you include irrelevant variables, OLS estimators are biased. Solution: False . Including irrelevant variables results in unbiased estimates. 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.
Solution: 1. Start with the model from above. In the wake of the Enron scandal, you are concerned that the entire CEO salary generating function is different for utility companies versus non-utility companies. Write down the implied unrestricted model and the null hypothesis regarding it that this concern would imply testing.

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Solution: 2. Now, test this null hypothesis. Calculate the F statistic and the degrees of freedom. Would you accept or reject the null hypothesis?
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## This note was uploaded on 03/20/2009 for the course ECON 103 taught by Professor Sandrablack during the Winter '07 term at UCLA.

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Problem Set 4 Solutions - Problem Set 4 Answer Key...

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