Table 7-7 (found on the textbook's Web site) gives data on indexes of aggregate 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 period 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.
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 impact 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?