Regression of Inflation on Percent M3 Change

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1 ECON 497 Final Exam Page of ECON 497: Economic Research and Forecasting Name: Spring 2006 Bellas Final Exam Return this exam to me by midnight on Thursday, April 27. It may be ed to me. It may be delivered to my office in Minneapolis or faxed to me before 4:00 on the 27 th at After 4:00 on that date you should fax it to my home. If you are going to fax it to my home, please let me know via the day before. You can also send it to my office through the regular post or to my home via regular post, but it should be postmarked before the midnight deadline. You may consult any written source you like regarding the answers to these questions but you may not ask any person other than me any questions about this test. Questions to me must be sent via and responses will be sent to the entire class. Answer all questions, and explain your answers. Fifty points total, points per part indicated in parentheses.. There is a real dataset (taken from the 2004 Economic Report of the President) for this exam that includes, for the years 960 through 2003 the inflation rate (percent change in CPI for all goods excluding energy) and the percentage change in real money supply (M3). This question asks you to investigate the relationship between the rate of growth of the money supply and the inflation rate. A. Regress the inflation rate on real M3 growth rate and discuss the results. (2) Regression of Inflation on Percent M3 Change Summary.478 a a. Predictors:, REALM3 REALM3 a. Dependent Variable: INFLATIO a The model has decent explanatory power, except that the relationship is negative and significant, which is really unexpected.

2 ECON 497 Final Exam Page 2 of 2 B. Is there evidence of serial correlation from the model in part A? Explain. (2) Regression of Inflation on Percent M3 Change Summary b Durbin-W atson.478 a a. Predictors:, REALM3 b. Dependent Variable: INFLATIO REALM3 a. Dependent Variable: INFLATIO a Graph of Regression Residuals Against Year Residual YEAR Yes, there is evidence of serial correlation. The Durbin-Watson statistic is much smaller than two and the scatterplot of the residuals on year suggests serial correlation. C. Regress the inflation rate on lagged M3 growth and discuss the results. How does the explanatory power compare to the explanatory power from part A? (2) Regression of Inflation on Lagged M3 Growth Rate Summary.254 a a. Predictors:, LAGM3

3 ECON 497 Final Exam Page 3 of 3 LAGM3 a. Dependent Variable: INFLATIO a The estimated coefficient on lagged M growth is still negative, which is weird, but at least now it s not significant. Explanatory power is lower. D. Regress the inflation rate on M3 growth and on M3 growth that is lagged one, two, three and four times (so there will be five explanatory variables). Does this model have better explanatory power than the model in part C? (2) Regression of Inflation on M3 Growth and Lags Summary.494 a a. Predictors:, LAG4M3, LAGM3, REALM3, LAG3M3, LAG2M3 Regression Residual Total ANOVA b Sum of Squares df Mean Square F Sig a a. Predictors:, LAG4M3, LAGM3, REALM3, LAG3M3, LAG2M3 b. Dependent Variable: INFLATIO REALM3 LAGM3 LAG2M3 LAG3M3 LAG4M3 a. Dependent Variable: INFLATIO a

4 ECON 497 Final Exam Page 4 of 4 Explanatory power is better than in Part C, but this may be only because of the inclusion of current change in real M3. E. Estimate a Koyck distributed lag model for this data with the inflation rate as the dependent variable. Use the examples from class as a guide. (2) Regression - Koyck Summary.832 a a. Predictors:, LAGINFL, REALM3 REALM3 LAGINFL a. Dependent Variable: INFLATIO a F. Calculate the first four lag coefficients based on your results from the Koyck model and compare them to your results from part D. (2)

5 ECON 497 Final Exam Page 5 of 5 Π t = α0 + αm t + λπ t + εt Π t = β0 + βm t + β2m t + β3m t 2 + β4m t 3 + β5m t 4 + ηt α β0 = = = = λ β = α = β2 = α λ = = β3 = α λ = = β4 = α λ = = β5 = α λ = = Estimated Lagged Koyck Constant t t t t t Here in Minnesota, the latter part of football season tends to coincide with the onset of winter. Imagine that a Granger causality test were conducted looking at the relationship between football games and winter. Is it more likely that this test would conclude that football games Granger-cause winter or that winter Granger-causes football games? Explain your answer. (2) Because football comes before winter, we would likely find that football Granger causes winter, but winter does not Granger cause football. 3. At the end of this exam you will find some output from a binomial logistic regression. A. Discuss the impact of each explanatory variable on the probability that Y=. (3) An increase in X makes it more likely that Y will take a value of. An increase in X2 makes it less likely that Y will take a value of.

6 ECON 497 Final Exam Page 6 of 6 B. What is the predicted probability that Y= for an observation where X =200 and X 2 =0? (3) Pˆ i Pˆ i Pˆ i = ( X ) i X 2i + e = ( ( 200 ) ( 0 ) + e ) = = = ( e ) Explain briefly what multicollinearity is and give three methods for detecting it. (3) Multicollinearity is a situation where explanatory variables are correlated with each other. It may be detected through -high R 2 values with few or no significant estimated coefficients -high correlation coefficients between explanatory variables -high VIF numbers 5. Explain briefly what heteroskedasticity is and what its implications are for regression results. (3) Heteroskedasticity is when the variance of the error term is not constant. Heteroskedasticity does not bias the estimated coefficient. Heteroskedasticity results in the reported standard errors being too small and the resulting t-stats being too big, so that estimated coefficients will appear to be significant when, in fact, they are not. 6. It is generally believed that there is a link between the amount of studying a person does and their grade in, for example, a principles of microeconomics course. Imagine that a researcher collects data on a number of students taking principle of microeconomics, including their age, gender, the number of math courses they've had, the number of hours they spent studying each week and their final grade in the class. The regression that the researcher does has the final grade as the dependent variable. Surprisingly, this researcher finds a negative relationship between hours of studying and final grade. That is, the estimated coefficient on hours spent studying was found to be negative and significant. A. Explain the endogeneity problem in this situation. (3)

7 ECON 497 Final Exam Page 7 of 7 While the hours of studying may determine the grade, a person s grade may also determine how much they study. Someone who is doing very well in the class may skip studying for other activities while someone who is in danger of failing may study a lot simply to try and pass the class. Also, the number of hours spent studying may depend on the amount of math they ve had before. If they ve had lots of math, then they won t need to study as much to understand the math used in micro. (Thanks JS). B. Explain the excluded variable problem in this situation. (3) Smartness is excluded. It may be that smart people study less because they can get a good grade without studying very much. C. Describe, briefly, how you might use two stage least squares (2SLS) to deal with the endogeneity problem here. (3) You could model the expected number of hours spent studying and then use this predicted number of hours of studying in a regression of grades on the various explanatory variables. 7. There is fake data on the course web site describing some adult individuals who are employed full time and their salaries. The variables include their age, their years of work experience, a dummy variable indicating whether they have a high school diploma, a dummy indicating whether they have a college degree, a dummy variable indicating whether they are male, a dummy variable indicating whether their current job involves managerial responsibilities and a variable indicating which of four industries they work in. A. Do a linear regression of Salary on Age, HS, College and Male. Explain what each of the estimated coefficients mean and discuss whether or not they are significant. Is there evidence of a gender-based wage gap? (3) B. Add Experience and Managerial to the regression. Discuss the estimated coefficient on Experience and how the other estimated coefficients change. For the estimated coefficients that changed significantly from Part A, explain why the change occurred. (3) C. How do the results change when the industry in which a person works is also included in the model? Explain your answer. (3) Part A Age, HS, College and Male are all positive and significant. Aging a year gets you an extra $222, completing high school gets you an extra $758 and getting a college degree gets you an extra $8458. Being male gets you an extra $452.

8 ECON 497 Final Exam Page 8 of 8 Part B Age and Male stop being significant because Experience was correlated with Age and with Male. An extra year of experience gets you $336. This suggests that the gender-based wage gap was more about experience and the effect of being a manager than it was about gender. Of course, you might think about a two stage model in which you model the expected probability that a person gets to be a manager. Part C To do this properly, you need to generate industry dummy variables. Male again becomes significant when the Industry dummies are added to the model. Regression Part A Summary.853 a a. Predictors:, Male, Age, HS, College Age HS College Male a. Dependent Variable: Salary Regression Part B a Summary.929 a a. Predictors:, MANAGERI, EXPERIEN, HS, MALE, COLLEGE, AGE

9 ECON 497 Final Exam Page 9 of 9 AGE HS COLLEGE MALE EXPERIEN MANAGERI a. Dependent Variable: SALARY a Regression Part C Summary.993 a a. Predictors:, Industry4, Managerial, Male, Age, HS, Industry2, College, Industry3, Experience Age HS College Male Experience Managerial Industry2 Industry3 Industry4 a. Dependent Variable: Salary a Use the auto acceleration data from the course web site to discuss whether, according to Studenmund s four criteria, a car s weight should be included in a model of acceleration times. (3)

10 ECON 497 Final Exam Page 0 of 0 Regression of Acceleration Time without P Summary.839 a a. Predictors:, H, T, E T E H a. Dependent Variable: S a Regression of Acceleration Time with P Summary.842 a a. Predictors:, P, E, T, H T E H P a. Dependent Variable: S a Theoretically, weight should be included because it should affect acceleration. 2. Adjusted R 2 falls when P is added, suggesting that it shouldn t be included. 3. The estimated coefficient on P is not significant, suggesting that it shouldn t be included. 4. None of the other estimated coefficients changes much when P is added, suggesting that it is not an important excluded variable and so should not be included.

11 ECON 497 Final Exam Page of 9. What three bits of advice would you offer to students who take this course in the future? They should be three distinct things, please. A. () B. () C. ()

12 ECON 497 Final Exam Page 2 of 2 Binomial Logistic Regression Output Logistic Regression Block 0: Beginning Block Classification Table a,b Predicted Observed Step 0 Y 0 Overall Percentage a. Constant is included in the model. b. The cut value is.500 Y Percentage 0 Correct Block : Method = Enter Summary Step -2 Log Cox & Snell Nagelkerke likelihood R Square R Square Classification Table a Predicted Observed Step Y Overall Percentage a. The cut value is Y Percentage 0 Correct Variables in the Equation Step a X X2 Constant a. Variable(s) entered on step : X, X2. B S.E. Wald df Sig. Exp(B) E+2

ECON 497 Midterm Spring

ECON 497 Midterm Spring 2009 1 ECON 497: Economic Research and Forecasting Name: Spring 2009 Bellas Midterm You have three hours and twenty minutes to complete this exam. Answer all questions and explain