Econometrics. Midterm (A) March 22 nd, 2010

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1 Econometrics Midterm (A) March 22 nd, 2010 João Valle e Azevedo Erica Marujo For each question, please identify the correct answer. For each question, there is one and only one correct answer. A correct answer is worth 1 point; an incorrect answer shall be attributed 0 points. Mark your choice on the answer sheet provided at the end of this examination paper. EITHER USE A PENCIL OR DO NOT MAKE CORRECTIONS. Identify your answer sheet with your name and student number. To answer questions 1 through 6, please consider the following Eviews output of a model which aims to study the effect of school size on student performance, in Michigan, in 1993: Dependent Variable: MATH10 Method: Least Squares Sample: Included observations: Coefficient Std. Error t-statistic Prob. C LTOTCOMP LSTAFF LENROLL R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid Schwarz criterion Log likelihood Hannan-Quinn criter F-statistic Durbin-Watson stat Prob(F-statistic) where represents the percentage of students receiving a passing score on the Michigan Educational Assessment Program (MEAP) standardized tenth grade math test; represents average annual teacher compensation, in dollars (a measure of teacher quality); represents number of staff per one thousand students (a measure of how much attention students receive); and stands for student enrollment (which represents school size). 1

2 1. What is the sample size? a) Approximately 500 b) Approximately 450 c) Approximately 410 d) Approximately 408 e) We don t have enough information to answer this question f) None of the above 2. What is the meaning of the coefficient on? a) If the average annual teacher compensation increases by 1 dollar, then it is expected that the percentage of students receiving a passing score on the MEAP standardized tenth grade math test will be 21,155% higher, on average, ceteris paribus b) If the average annual teacher compensation increases by 1%, then it is expected that the percentage of students receiving a passing score on the MEAP standardized tenth grade math test will be 21,155% higher, on average, ceteris paribus c) If the average annual teacher compensation increases by 1%, then it is expected that the percentage of students receiving a passing score on the MEAP standardized tenth grade math test will increase by 0,21155 percentage points, on average, ceteris paribus d) It is the elasticity of with respect to and it bears the expected sign e) It is the semi-elasticity of with respect to and it bears the expected sign f) Both b) and e) above are correct g) Both b) and d) above are correct h) Both c) and e) above are correct 3. Considering a significance level of 5%, which coefficients are statistically significant (consider a two-sided alternative to perform the test): a) and b) All c) and Just d) Just e) None f) and g) and 2

3 4. Now assume that another variable, (which represents average teacher salary, in dollars), was omitted from this model. Knowing that:, which Gauss-Markov assumptions are being violated in this model? a) All b) None c) Linearity in Parameters, Zero Conditional Mean and Homoskedasticity d) Zero Conditional Mean e) No Perfect Collinearity f) Random Sampling, Zero Conditional Mean and No Perfect Collinearity g) Zero Conditional Mean and Homoskedasticity h) Both d) and e) i) Both e) and g) 5. About this regression, it is also known the following Coefficient Variance- Covariance matrix: What is the estimate for the t-statistic of the following null hypothesis:? a) b) c) d) e) 1,25 f) We don t have enough information to answer this question g) None of the above 3

4 6. Now consider the following output: Dependent Variable: MATH10 Method: Least Squares Sample: Included observations: 408 Coefficient Std. Error t-statistic Prob. C LTOTCOMP LSTAFF+LENROLL R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid Schwarz criterion Log likelihood Hannan-Quinn criter F-statistic Durbin-Watson stat Prob(F-statistic) Is it possible to test the same null hypothesis as in the previous question,, but using a different test statistic, given the information presented in this output? a) No, the information reported in this output is useless to perform this test b) Yes, and the new test statistic is equal to -1,730679, the t-statistic of the coefficient on c) Yes, and the new test statistic is an F-statistic equal to 1, , approximately d) No, because we still would need the coefficient variance-covariance matrix to compute any type of test statistic e) Both c) and d) f) None of the above 7. Assume that you have estimated the following model:, where is a dummy variable equal to one if a person is unemployed and zero otherwise. The following 90% confidence interval was estimated for :. If we want to test the null: against a one-sided alternative with a 5% significance level then: a) We will reject for sure, because the 95% confidence interval associated with the 5% significance level becomes wider than the one above and so 1,7 will be inside the confidence interval 4

5 b) We will reject for sure, because the 95% confidence interval associated with the 5% significance level becomes thinner than the one above and so 1,7 will be outside the confidence interval c) We will reject for sure, because the upper extreme of the 90% confidence interval coincides with the critical value associated with the one-sided alternative at a 5% significance level, and so 1,7 will be outside the confidence interval d) We will reject for sure, because the upper extreme of the 90% confidence interval coincides with the critical value associated with the one-sided alternative at a 5% significance level, and so 1,7 will be inside the confidence interval e) None of the above 8. Consider a multiple linear regression model for cross-sectional data that analyses the impact of the demand for football matches tickets on TV audiences of football matches. Among other regressors, you include dummy variables for Sporting, Porto and Benfica (that equal one if a person is, respectively, a supporter of Sporting, Porto and Benfica, and zero otherwise). The No Perfect Collinearity Assumption is not violated in this model as long as: a) The sum of the three dummy variables is not equal to 1 across all observations b) The sum of the three dummy variables is equal to 1 across all observations c) In this case, the No Perfect Collinearity assumption is always violated, no matter what, because the three dummies are perfectly linearly correlated d) In the sample there are people that are not supporters of none of these three football clubs e) Both a) and d) are correct f) Both b) and d) are correct g) None of the above 9. Consider the model: Suppose that when you decided to regress the model, the variable was not included. Then, assuming that the correlation between and is negative, what would be the expected sign in the bias in (estimated by OLS) in that regression, assuming the original (full) model is correctly specified? a) Negative, because and Correlation(, )<0 b) Positive, because and Correlation(, )<0 5

6 c) Positive, because and Correlation(, )<0, as long as we assume that the correlation between and and the correlation between and is zero d) Positive, because and Correlation(, )<0, as long as we assume that the correlation between and is zero e) Negative, because and Correlation(, )<0, as long as we assume that the correlation between and is zero f) None of the above 10. Now consider the following model: where is a gender dummy equal to 1 if female and zero otherwise, and equals 1 if Portuguese and zero otherwise. If you want to perform the Chow test in this model in relation to gender, then the null hypothesis will be: a) b) c) d) e) None of the above 11. In testing multiple exclusion restrictions in the multiple regression model under the Classical assumptions, we are more likely to fail to reject the null that some coefficients are zero if: a) The Residual sum of squares of the restricted model is large relative to that of the unrestricted model b) The Residual sum of squares of the restricted model is small relative to that of the unrestricted model c) The R-squared of the unrestricted model is large d) The intercept parameter is negative e) Both a) and d) above are correct f) Both c) and d) above are correct g) Both a) and c) above are correct h) Both b) and c) above are correct 6

7 12. Consider a multiple linear regression for cross-sectional data satisfying the Gauss-Markov assumptions. Suppose you want to test multiple exclusion restrictions in you model. Which of the following is true? a) You cannot perform such test because only the t-test is valid in large samples b) You cannot use the usual F test for multiple exclusion restrictions c) You can use the usual F test for multiple exclusion restrictions d) You can only use the LM test for multiple exclusion restrictions e) You can use the LM test for multiple exclusion restrictions f) Both b) and d) above are correct g) both c) and e) above are correct h) b) and e) above are correct 13. Consider a multiple linear regression model for cross-sectional data. If the Gauss-Markov assumptions hold, then: a) Ds The OLS estimator will be consistent and unbiased b) We can only guarantee the OLS estimator is unbiased c) The OLS estimator is consistent only if the sample size is very large d) The OLS estimator will be biased e) Both b) and c) above are correct f) Both c) and d) above are correct g) Both a) and d) above are correct 14. If under certain assumptions the OLS estimator is BLUE, Best Linear Unbiased Estimator, then we can conclude that it is: a) the minimum variance unbiased estimator b) an unbiased estimator c) a linear estimator d) an estimator e) both b), c) and d) above are NOT correct f) both b), c) and d) above are correct 15. The adjusted R-squared is a good measure to compare the goodness-of-fit of multiple linear regression models because: a) it can be used to compare models with different dependent variables b) it always increases if we include additional regressors c) all else equal, it is lower than the usual (unadjusted) R-squared 7

8 d) it increases once we add more regressors only if the residual sum of squares does not decrease enough e) it increases once we add more regressors only if the residual sum of squares does not increase enough f) both a) and b) above are correct g) both c) and d) above are correct h) both c) and e) above are correct 16. Consider a multiple linear regression model where the Zero Conditional Mean assumption fails, but the remaining Gauss-Markov assumptions hold. Specifically, suppose E[u X]=δ, where u is the vector of error terms, X is the matrix of regressors and δ has at least one element different than zero. What can you say about the bias (E[ X]-β) of the OLS estimator in this situation? a) the OLS estimator is still BLUE b) the bias equals (X X) -1 X δ c) the bias is still zero, always d) the bias equals X X δ e) the bias equals X δ f) None of the answers above is correct 17. Why would you want to use heteroskedasticity-robust standard errors to perform hypothesis testing on a multiple linear regression model for cross-sectional data? a) because the zero conditional mean assumption might fail b) because there is the risk that the error term of the model is homoskedastic c) because the error term of the model is for sure heteroskedastic, but the form of heteroskedasticity is unknown d) because you are not sure the homoskedasticity assumption holds e) both a) and b) above are correct f) both b) and c) above are correct g) both c) and d) above are correct h) both a) and d) above are correct 8

9 18. Consider a simple regression model, satisfying the Gauss-Markov assumptions, with the height of the individual as dependent variable and with the only regressor being a dummy variable for gender (equal to 1 if the individual is a male and zero otherwise). What is the proportion of males in the sample that minimizes the variance of the OLS estimator for the coefficient on the dummy variable? a) Any proportion between 25% and 75% b) 33% c) 50% d) 0% e) 100% f) either 50% or 100% g) none of the answers above is correct 19. WLS stands for what in Econometrics? a) Without Large Sample b) With Large Squares c) None of the answers above and below is correct d) None of the answers below is correct e) Weighted Least Squares f) Windows Live Search 20. In a multiple linear regression model, the random sampling assumption implies: a) the variance covariance matrix of the errors u=(u₁,u₂,...,u n ) is diagonal, i.e., all the elements out of the diagonal are equal to zero b) the variance covariance matrix of the errors u=(u₁,u₂,...,u n ) is not diagonal, i.e., at least one off-diagonal element is different than zero c) the variance covariance matrix of the OLS estimator is not diagonal, i.e., at least one off-diagonal element is different than zero d) the variance covariance matrix of the OLS estimator is diagonal e) none of the answers above is correct 9

10 Answer Sheet Version A Mark your answer with an X in the table below Any answers outside the table will not be considered Either use a pencil or do NOT make corrections Name: Student Number: _ Question Nr. a) b) c) d) e) f) g) h) i) 1. X 2. X 3. X 4. X 5. X 6. X 7. * X 8. * X 9. X 10. X 11. X 12. X 13. X 14. X 15. X 16. X 17. X 18. X 19. X 20. X * Also considered as a correct answer 10