ECON 497 Final Exam Page 1 of 12

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1 ECON 497 Final Exam Page of 2 ECON 497: Economic Research and Forecasting Name: Spring 2008 Bellas Final Exam Return this exam to me by 4:00 on Wednesday, April 23. It may be ed to me. It may be delivered to my office in Minneapolis or faxed to me before 4:00 on the 25 th at You could even drop it by my house if you like, and I d be pleased to introduce you to my wife and my kids. You can also send it to my office through the regular post or to my home via regular post, but it should be post-marked by the 23rd. 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.. It will probably come as no surprise to you that economists love a good fight. Graduate school was a long series of scuffles, brawls and flat out donnybrooks. Happily, we always noted who was involved and, more importantly, who won. We estimated a binomial logit model of the fight outcomes and came up with the following: ln P i P i = F i + 0.2MI i + 0.0A i Where F i is a female dummy variable, MI i is a microeconomist dummy and A i is the age of the participant in question. A. Without knowing any of the characteristics of his opponent (an admitted weakness of the model) calculate the probability that a 40 year old male microeconomist will win a fight. (3) + e ( ) = + e.3 = = B. This is a bit trickier. Based on this model and assuming that no econ fight ever ended in a tie, discuss how you might arrive at the probability a 25 year old male macroeconomist would win a fight against a 50 year old female microeconomist. Remember, and this is the trick, that there are no ties and that the probability of all possible outcomes must sum to one. (2) = + e ( ) = + e ( ) + e.65 = + e 0.8 = = =

2 ECON 497 Final Exam Page 2 of 2 You might say that the probability that either one of these economists wins the fight is equal to their probability divided by the sum of the predicted probabilities. So, for the 25 year old male macroeconomist, the predicted probability would be: 0.6 = 0.6 = Use the coffee data from assignment #2 to estimate the attendance elasticity of coffee demand (basically dc t C t da t A t explanatory variables in your model. or, if you prefer, % C ). You should also include the other % A To do this you need to regress the natural log of coffee sales on the natural log of attendance. You should also include the other explanatory factors as well. A. Present your results. (2) SUMMARY OUTPUT Multiple R R Square Square Error Observations 8 Regression Residual Total Intercept E-33 lna E-09 lnt N The elasticity is the estimated coefficient on ln(a), which is You might also have done this with T instead of lnt as an explanatory variable and gotten the following:

3 ECON 497 Final Exam Page 3 of 2 Multiple R R Square Square Error Observations 8 Regression Residual Total Intercept E-34 lna E-09 T N In this case the elasticity is B. Explain the implications of this elasticity being either greater than one or less than one. (3) Because this is less than one, a % increase in attendance will lead to a less than % increase in coffee sales. In fact, a % increase in attendance should lead to an increase of about 0.25% in coffee sales. You may speculate as to why this is. 3. Use the coffee data from assignment #2 to estimate a linear model of coffee sales (C) on temperature (T), attendance (A) and the night game dummy (N). A. Present your results. (2) Multiple R R Square Square

4 ECON 497 Final Exam Page 4 of 2 Error Observations 8 Regression E+08.45E Residual E Total 80.03E+09 Intercept E-20 N T A E-09 B. Do a Park test for heteroskedasticity and discuss the results of this test. (3) To do a Park test you need to save the residuals from the original regression and then square them and take the natural log of the squared residuals and then regress the log of the squared residuals on the explanatory factor that you think is responsible for the heteroskedasticity, which, in this case, is likely to be attendance. So, we estimate the model: ln(e i 2 ) = B 0 + B *ln(a) + ε Here are the results. Multiple R R Square Square 0.77 Error Observations 8 Regression Residual Total

5 ECON 497 Final Exam Page 5 of 2 Intercept lna The estimated coefficient on lna is significantly different from zero which suggests that there is heteroskedasticity. 4. The best way to determine if there is multicollinearity in your model is to calculate (or ask a software package to calculate) VIFs for the explanatory variables. Explain carefully where these VIF numbers come from. (3) A VIF is derived from the R-squared value that results from regressing one explanatory variable on all other explanatory variables. The VIF is equal to VIF = R 2 5. There is data on real personal consumption spending (in billions of year 2000 dollars) and population for the U.S. available on the course web site. The data are from Microeconomics: Principle and Policy, 0 th edition, by William J. Baumol and Alan S. Blinder. Use this data to do the following. A. Estimate a linear model of real consumption spending as a function of population and year. Briefly discuss your results. (2) Multiple R R Square Square Error Observations 35 Regression Residual Total t Stat P-value

6 ECON 497 Final Exam Page 6 of 2 Error Intercept Year Population E-0 Population is in hundred millions, so this suggests that an additional hundred million people will increase spending by about 00 billion dollars, or that an extra person will increase spending by about $000 and that, adjusting for population, spending decreases by about 6 billion dollars per year. B. Is there evidence of serial correlation in your model in part A? Offer three different pieces of supporting evidence. (3) Here is a scatterplot of the residuals: This suggests that there is serial correlation because there are long periods of either positive or negative residuals. Here are the results of a regression of residuals on lagged residuals: Multiple R R Square Square Error

7 ECON 497 Final Exam Page 7 of 2 Observations 33 Regression Residual Total Intercept Lag Resid E-09 The significant estimated coefficient suggests that there is serial correlation. You could also calculate a Durbin-Watson statistic. Here is the output from doing this in the statistical analysis package Stata:. reg consumption year population Source SS df MS Number of obs = F( 2, 32) = Model Prob > F = Residual R-squared = Adj R-squared = Total Root MSE = consumption Coef. Std. Err. t P> t [95% Conf. Interval] year population _cons estat dwatson Durbin-Watson d-statistic( 3, 35) = The D-W value of is close to zero, suggesting that there is positive serial correlation. C. Estimate a semi-log model in which the dependent variable is the natural log of per capita consumption spending and the explanatory variable is year. Present your results. (2) Here are the results from Stata:. reg lnpercap year Source SS df MS Number of obs = 35

8 ECON 497 Final Exam Page 8 of F(, 33) = Model Prob > F = Residual R-squared = Adj R-squared = Total Root MSE = lnpercap Coef. Std. Err. t P> t [95% Conf. Interval] year _cons D. What is the interpretation of the estimated coefficient on year in the model in part C? (2) The interpretation is that per capita consumption increases by about 2.9% annually. E. Estimate a generalized least squares (GLS) model to correct for the serial correlation in your model from part C. Show clearly how you estimate the GLS model and present your results. (2) Starting with the D-W stat of we can calculate an estimate of rho. ρ = DW = = So we recalculate the dependent variable as lnpercap t lnpercap t and we recalculate the explanatory variable, year, as year t year t and then re-do the regression with these new dependent and explanatory variables. Here are the results as reported in Stata:. reg glsdepvar glsexplvar Source SS df MS Number of obs = F(, 32) = Model Prob > F = Residual R-squared = Adj R-squared = Total Root MSE =.0586 glsdepvar Coef. Std. Err. t P> t [95% Conf. Interval] glsexplvar _cons

9 ECON 497 Final Exam Page 9 of 2. estat dwatson Durbin-Watson d-statistic( 2, 34) = The new Durbin-Watson statistic of.248 suggests that serial correlation is less of a problem than it was before. The estimated coefficient on year (the GLS explanatory variable, glsexplvar) is still but the t-stat has fallen to Use the Age-Wisdom data that is available on the web site to do some stuff. A. Estimate a pooled model in which wisdom is the dependent variable and age is the explanatory variable. Present your results. (3) Multiple R R Square Square Error Observations 32 Regression Residual Total Intercept Age E-3 B. Briefly discuss your results from part A. (3) The pooled results suggest that wisdom increases with age. C. Estimate a fixed-effects model in which wisdom is the dependent variable. Present your results. (3) To do this in SPSS or Excel, you need to create a dummy variable for each person.

10 ECON 497 Final Exam Page 0 of 2 Multiple R R Square Square Error Observations 32 Regression Residual Total Intercept 0 #N/A #N/A #N/A Age P E-04 P E-63 P E-8 P E-6 P E-42 P E-32 P E-93 P E-06 P E-44 Here are the fixed-effects results from Stata:. xtreg wisdom age, fe Fixed-effects (within) regression Number of obs = 32 Group variable: person Number of groups = 9 R-sq: within = Obs per group: min = 5 between = avg = 4.7 overall = max = 33 F(,22) = 5.94 corr(u_i, Xb) = Prob > F = wisdom Coef. Std. Err. t P> t [95% Conf. Interval] age _cons

11 ECON 497 Final Exam Page of sigma_u sigma_e rho (fraction of variance due to u_i) F test that all u_i=0: F(8, 22) = Prob > F = D. Explain the important difference between the results of the pooled and the fixed effects models. Discuss what these results mean in a couple of plain old, English language sentences that don t have any numbers in them. (3) The fixed effects results suggest that, when you adjust for individual differences, wisdom doesn t really increase with age. In fact, it seems to decrease with age. The secret is that people with more wisdom live longer, so it seems that wisdom increases with age. In fact, there s no fool like an old fool. 7. Use the Metropolitan State University library resources to access the article Do Students Go to Class? Should They? by David Romer which appeared in The Journal of Economic Perspectives, Vol. 7, No. 3, (Summer, 993), pp Answer the following questions. A. In which types of economics courses is the rate of student attendance higher? (3) From Table, absenteeism is lower in classes that are smaller, mathematical and,usually, are upper division courses requiring only principles courses as prerequisites. B. According to the paper, does attending class more often help students do better, or is it simply the case that better students generally attend class more often and attending doesn t really seem to matter to a student s grade given her pre-existing level of talent? Support your answer with material from the paper. (3) Table 2, models 4 and 5 suggest that even when you correct for previous GPA (which is a measure of how good a student a person is) attending class does improve performance. 8. 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. ()

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