Econometrics Final Exam

Transcription

1 Econometrics Final Exam João Valle e Azevedo Erica Marujo June 15, 2010 Time for completion: 2h Give your answers in the space provided. Use draft paper to plan your answers before writing them on the exam paper. Unless otherwise stated, use 5% for significance level. Name: Number: Group I (9 points, 1.5 for each question) Give a very concise answer to the following questions. Conciseness will be valued, avoid unnecessary details. 1. The acronym BLUE stands for what in Econometrics? 2. In one phrase, describe the meaning of Contemporaneous exogeneity in a multiple linear regression (for time series data) context. 3. Explain why, in general, you would want to transform series that are not weakly dependent before using them in a multiple linear regression model for time series data. In which cases is the transformation not needed?

2 4. Write in matrix form the expression for the variance of the OLS Estimator of the parameters of a multiple linear regression model for cross-sectional data, assuming the homoskedasticity assumption is not verified. (Assume the variance of the error term is of known form and that the necessary assumptions hold) 5. Describe succinctly a very parsimonious (i.e., with few variables) test aimed at detecting heteroskedasticity in the error term of a multiple linear regression model. Assume all the necessary assumptions hold. 6. Write a model aimed at testing whether there is any effect on GDP growth of next quarter of an extraordinary (more than 10%) growth in public investment in the current quarter, controlling for other factors. Describe one limitation of your model. 2

3 Group II (10 points) 1. Consider the following output of the model which describes grade point averages ( GPA) for college athletes: Dependent Variable: CUMGPA Method: Least Squares Sample: Included observations: 732 Coefficient Std. Error t-statistic Prob. C SAT HSPERC TOTHRS CRSGPA 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 is cumulative grade point average (GPA prior to the current semester); is SAT score, measured in points; is graduating percentile in high school class; is total credit hours prior to the semester; and is a weighted average of overall GPA in courses taken by each student. a) Interpret the coefficient estimates of the model, and. What can you say about the overall quality of this model? Be complete in your answer. (1 point) 3

4 Now consider the following two outputs: Dependent Variable: CUMGPA Method: Least Squares Sample: IF FEMALE=1 Included observations: 180 Coefficient Std. Error t-statistic Prob. C SAT HSPERC TOTHRS CRSGPA 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) Dependent Variable: CUMGPA Method: Least Squares Sample: IF FEMALE=0 Included observations: 552 Coefficient Std. Error t-statistic Prob. C SAT HSPERC TOTHRS CRSGPA 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)

5 and consider the following model, where is a dummy variable equal to 1 if female and zero otherwise. b) Using the information from the outputs above, compute estimates for the coefficients of this model (,,,,, ). (2 points) c) Test if the expected cumulative GPA for men is statistically different from the expected cumulative GPA for women. Be precise in your answer and indicate all the necessary steps to perform that test. (2 points) 2. 5

6 2. Consider the following output of the model: log invpc t =β 0 +β 1 log price t +β log price t-1 +β 3 log pop t +β t+u t Dependent Variable: LINVPC Method: Least Squares Sample (adjusted): 2 42 Included observations: 41 after adjustments Coefficient Std. Error t-statistic Prob. C LPRICE LPRICE_ LPOP T 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 invpc is real per capita housing investment (in thousands of dollars), price denote a housing price index (equal to 1 in 1982), and pop denote total population in the United States, in thousands. The data are annual observations in the United States for 1947 through a) Interpret each one of the coefficient estimates of the model,,, and. Are they statistically significant? Justify. The included trend is of which type? (1 point) 6

7 b) Given the information in the output above, can you conclude if the errors of this model suffer from any type of serial correlation? In order to take this conclusion, which Gauss-Markov assumption needs to be satisfied? What are the consequences for your answer in a) if this problem is present? (2 points) c) Suppose that you know for sure that: Corr u t,log price t =Corr u t,log price t-1 =Corr u t,log pop t =Corr u t,t =0 and that: Corr u t,log price t 2 0,5. Does this change your conclusions from the previous question? Why? Are the OLS estimators unbiased and consistent in this case? Why? Is it possible to test for serial correlation in this case? How? (2 points) 7

8 Group III (1 point) 1. Give an example of a time series process with 2 observations (you can consider more if you want) that is covariance-stationary and at the same time nonstationary. a) a) the OLS estimator is unbiased but consistent 8