10 Questions on Applied Econometrics - Final Exam | ECON 446, Exams of Introduction to Econometrics

Download 10 Questions on Applied Econometrics - Final Exam | ECON 446 and more Exams Introduction to Econometrics in PDF only on Docsity! Final Exam Economics 446 Applied Econometrics and Economic Modeling May 2, 2007 R. Sickles i i You have three hours for this final exam. You may use a two-sided 81/2 x 11 piece of paper with notes, etc. Problems (10 points each) 1. Consider the multiple regression model 1 2 2, 3 3,i iy x xβ β β ε= + + + for i=1,…,n. Explain the five key assumptions needed in order to establish the desirable properties of best linear unbiasedness of the ordinary least squares estimates of 1β , 2β , and 3β . 2. Answer the following questions about multicollinearity: a. Define what it is. b. Why does it occur? c. What are its consequences? d. How can it be detected? e. Is it true that multicollinearity is always a bad thing and nothing can be done about it? Give reasons for your answer together with illustrative examples. 3. Consider the following model of market equilibrium, i 0 1 i i i 0 1 i i Q = + p +u i (demand equation) Q = + p +v (supply equation) α α β β a. Show that ip is an endogenous regressor in both equations, i.e., it is correlated with the error term. b. Show that OLS estimates of 1α and 1β are biased (this is usually called "endogeneity bias"). c. Outline an alternative method for consistently estimating the coefficients. 1 4. One of the more important implications of combining assets into portfolios is that pooling assets results in a diversification of risk. A prominent model that explains why different assets have different expected risk premia is the capital asset pricing model (CAPM). In terms of data on rates of return observed over time t, the CAPM may be expressed as: ( )jt ft j mt ft tR r R rβ ε− = − + where jtR is the random return on asset (at time t), is the risk-free rate of return (not a random variable because it is guaranteed), j jtr mtR is the random return on the market as a whole, and tε is assumed to be an independently and identically distributed error term. a. What data would you need to estimate the “beta” for different stocks in your portfolio? How would you interpret the stocks (aggressive- passive) with betas greater than or less than one? b. Since the test of whether or not beta is greater or less than one is crucial in the CAPM, the correct standard error is crucial. How would you modify your testing procedure if you were told that the conditional variance of tε was serially correlated, following an AR(1) process in variances, instead of in levels. That is, large shocks are followed by large shocks and small shocks are followed by small shocks (this is call an ARCH (autoregressive conditionally heteroskedastic) process. 5. Results from estimating the relationship between peanut yield Y (in pounds per acre) and the application of nitrogen fertilizer N (in hundreds of pounds per acre) and phosphorus fertilizer P (in hundreds of pounds per acre) are found in the following table. The specified relationship is: 2 2 1 2 3 4 5 6t t t t t tY N P N P N Pβ β β β β β= + + + + + +t te a. Find and comment on the estimated functions describing the marginal response on yield to nitrogen when P=1, P=2, and P=3. b. Find and comment on the estimated functions describing the marginal response of yield to phosphorus when N=1, N=2, and N=3. Variable Coefficient Std. Error t-statistic Prob C 1.385 1.264 1.10 0.2855 N 8.011 0.941 8.52 0.0000 P 4.800 0.941 5.10 0.0000 N2 -1.944 0.220 -8.85 0.0000 P2 -0.777 0.220 -3.54 0.0019 2