Essentials of Econometrics
7.14. Table 7-6 (found on the textbook's Web site) gives data on the real rate of re¬turn (Y) on common stocks, the output growth (X2), and inflation (X3), all in percent for the United States for 1954 to 1981.
a. Regress Y on X3.
b. Regress Y on X2 and X3.
c. Comment on the two regression results in view of Professor Eugene Fama's observation that "the negative simple correlation between real stock returns and inflation is spurious (or false) because it is the result of two structural relationships: a positive relation between current real stock returns and expected output growth and a negative relationship between expected output growth and current inflation."
d. Do the regression in part (b) for the period 1956 to 1976, omitting the data for 1954 and 1955 due to unusual stock return behavior in those years, and compare this regression with the one obtained in part (b). Comment on the difference, if any, between the two.
e. Suppose you want to run the regression for the period 1956 to 1981 but want to distinguish between the periods 1956 to 1976 and 1977 to 1981. How would you run this regression? (Hint: Think of the dummy variables.)
7.15. Table 7-7 (found on the textbook's Web site) gives data on indexes of aggre¬gate final energy demand (Y), the real gross domestic product, the GDP (X2), and the real energy price (X3) for the OECD countries-the United States, Canada, Germany, France, the United Kingdom, Italy, and Japan-for the pe¬riod 1960 to 1982. (All indexes with base 1973 = 100.)
a. Estimate the following models:
Model A: In Yt= B1+ B2 In X2t + B3 In X3t + u1t
Model B: In Yt = A1+ A2 In X2t + A3 In X2(t-1), + A4 In X3t + u2t
Model C: In Yt = C1 + C2 In X2t + C3 In X3t, + C4 In X3(t-1) + u3t
Model D: In Yt = D1 + D2 In X2t + D3 In X3t + D4 In Y(t-1) + u4t
where the u's are the error terms. Note: Models B and C are called dynamic models-models that explicitly take into account the changes of a variable over time. Models B and C are called distributed lag models because the im¬pact of an explanatory variable on the dependent variable is spread over time, here over two time periods. Model D is called an autoregressive model because one of the explanatory variables is a lagged value of the dependent variable.
b. If you estimate Model A only, whereas the true model is either B, C, or D, what kind of specification bias is involved?
c. Since all the preceding models are log-linear, the slope coefficients represent elasticity coefficients. What are the income (i.e., with respect to GDP) and price elasticities for Model A? How would you go about estimating these elasticities for the other three models?
d. What problems do you foresee with the OLS estimation of Model D since the lagged Y variable appears as one of the explanatory variables? (Hint: Recall the assumptions of the CLAM.)
7.17. Table 7-8 on the textbook's Web site gives data on variables that might affect the demand for chickens in the United States. The dependent variable here is the per capita consumption of chickens, and the explanatory variables are per capita real disposable income and the prices of chicken and chicken substi¬tutes (pork and beef).
a. Estimate a log-linear model using these data.
b. Estimate a linear model using these data.
c. How would you choose between the two models? What test will you use? Show the necessary computations.
7.21. Table 7-10 on the textbook's Web site contains data about the manufacturing sector of all 50 states and the District of Columbia. The dependent variable is output, measured as "value added" in thousands of U.S. dollars, and the independent variables are worker hours and capital expenditures.
a. Predict output using a standard linear model. What is the function?
b. Create a log-linear model using the data as well. What is this function?
c. Use the MWD test to decide which model is more appropriate.
Attachment:- Tables.rar