Eastern Mediterranean University Department of Economics ECON 503: ECONOMETRICS I. M. Balcilar. Midterm Exam Fall 2007, 11 December 2007.

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1 Eastern Mediterranean University Department of Economics ECON 503: ECONOMETRICS I M. Balcilar Midterm Exam Fall 2007, 11 December 2007 Duration: 120 minutes Questions Q1. In order to estimate the demand for roses consider the following models: (1) Y t = α 1 + α 2 X2 t + α 3 X3 t + α 4 X4 t + α 5 X5 t + u 1t (2) log(y t ) = β 1 + β 2 log(x2 t ) + β 3 log(x3 t ) + β 4 log(x4 t ) + β 5 log(x5 t ) + u 2t where Y = quantity of roses sold, dozens X2 = average wholesale price of roses, $/dozen X3 = average wholesale price of carnations, $/dozen X4 = average weekly family disposable income, $/week X5 = the trend variable taking values of 1, 2, and so on, for the period 1971 III to 1975 II in the Detroit metropolitan area The OLS regression results are given in the following tables for both models: Dependent Variable: Y -- Model 1 Included observations: 16 Variable Coefficient Std. Error t-statistic Prob. C X X X X 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 F-statistic Durbin-Watson stat Prob(F-statistic)

2 Dependent Variable: LOG(Y) -- Model 2 Included observations: 16 Variable Coefficient Std. Error t-statistic Prob. C LOG(X2) LOG(X3) LOG(X4) LOG(X5) 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 F-statistic Durbin-Watson stat Prob(F-statistic) Source of Variation DF Sum of Squares Mean Square Explained Unexplained Total R-squared = Dependent Variable: LOG(Y) Model 3 Included observations: 16 Variable Coefficient Std. Error t-statistic Prob. C LOG(X2) LOG(X5) 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 F-statistic Durbin-Watson stat Prob(F-statistic)

3 (a) β 2, β 3 and β 4 give, respectively, the own-price, cross-price, and income elasticities of demand. What are their a priori signs? Do the results concur with the a priori expectations? (5%) (b) Based on your analysis, which Model, 1, 2 or 3, would you choose to be the best and why? (10%) (c) How would you compute the own-price, cross-price elasticity for the linear Model 1 and 2? (5%) (d) Two variables were dropped in Model 3, do you think the X3 and X4 have the joint effect on Y or not? Use the 95 percent level to test it. Remember to state your hypothesis. (5%) (e) My printer, again, did not print two numbers in the above ANOVA table. Fill in the missing numbers. (5%) (f) Which model do you think fits the data better? Why? Based on what criteria? (5%) (g) Construct a 95% confidence interval for β 3 using the estimates for Model 2. (10%) (h) Test the overall significance of Model 1 using the overall F test. Note my printer did not print the F-statistics properly. Can you calculate it? Q2. Regressing GNP on the various definitions of money, we obtain the results shown in the following table: Dependent Independent Variable Constant Variable R 2 SEE RSS F GNP t M1 t (77.96)* (.21) GNP t M2 t (61.01) (.04) GNP t M3 t (42.98) (.02) GNP t L t (44.76) (.02) *Note: The values in parentheses are standard error (a) Are these regressions statistically satisfy the monetary theory M = kpq? (3%) (b) Which definition of money seems to be closely related to nominal GNP? Give your judgment. (3%) (c) Since the R 2 terms are uniformly high, does this fact mean that our choice for definition of money does matter? (3%) (d) If the Federal Bank wants to control the money supply, which one of these money measures is a better target for that purpose? Can you tell from the regression results? (5%) Q3. The City Planning Department of Happyland estimated the following relationship: where log H t = log Y t log P t + û t (.8) (10.7) (1.5) _ R 2 = 0.98 n = 27 3

4 H t = is the total number, at time t, of housing Y t = is aggregate income in constant dollars (that is, corrected for inflation) P t = the Happyland s population. The values in parentheses are t-statistics. (a) Test each of the regression coefficients for significance at 5 percent level. Which variable is statistically significantly different from zero? 5% (b) City councilman A says, This model is missspecified because per capita income (Y t /P t ) should be used instead of Y t. Councilman B says, Because the model is in double-log form, it doesn t matter whether you use Y t or (Y t /P t ) in its place. The models are essentially identical. Which of the councilmen is correct and why? (3%) If A is correct, what can you say about the bias, hypothesis test, and so on? (3%) If B is correct, show how the regression coefficients of Councilman A s alternative model can be obtained from those above, without rerunning the regression. (3%) (c) Councilman C says, The model is misspecified because other variables which belong to the model are omitted. List at least two important variables that ought to be there. Carefully explain the implication of the variables you suggest. (4%) (d) Write down or derive the expressions for the elasticity of number of housing with respect to (i) aggregate income, and (ii) population. (4%) Q4. Dr. Kmenta, Maddala, Gujarati and Johntson are arguing about what determines final exam grade (G) in the class of econometrics. They agree that hours (H) studied somehow is important, but some think that the mathematics (M) background of students might matter too. In Figure 1, the regression results are reported which are based on the data of a class examination and run by four researchers using the following functional forms: Kmenta s model: G = α 1 + α 2 ln H + u 1 Maddala s model: ln G = β 1 + β 2 ln H + u 2 Gujarati s model: G = γ 1 + γ 2 (1/H) + u 3 Johntson s model: G = θ 1 + θ 2 H + θ 3 H 2 + u 4 Figure 1: Estimation Results Kmenta s model: G = ln H + û 1 R 2 =0.69 Maddala s model: ln G = ln H + û 2 R 2 =0.55 Gujarati s model: G = (1/H) + û 3 R 2 =0.40 Johntson s model: G = H 0.10 H 2 + û 4 R 2 =0.60 (a) What is the marginal effect of an additional hour of study in each model? (4%) (b) Johntson argues that Kmenta s and Maddala s models are suspect because they imply that the longer you study, the higher the grade (i.e., there is no maximum of the functions), and that Gujarati s model is suspect because it does not permit a perfect exam score of 100. Check if Johntson s points are true by finding the maximum grade in each model. (6%) 4

5 (c) Kmenta argues that his model is better than others because he has a higher adjusted coefficient of multiple determination. Is his model better? Which model do you think is the most reasonable representation of the population function generating exam grade? Why? (4%) 5

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