Consider the U.S. gasoline data from 1950-1987 given in Table 4.2, and obtained from the file USGAS.ASC on the Springer web site.

(a) For the period 1950-1972 estimate models (1) and (2):
logQMG = β1 + β2logCAR + β3logPOP + β4logRGNP (1)
+β5logPGNP + β6logPMG+ u logQMG CAR = γ1 + γ2logRGNP POP + γ3logCAR POP + γ4log PMG PGNP + ν (2)

(b) What restrictions should the β’s satisfy in model (1) in order to yield the γ’s in model (2)?

(c) Compare the estimates and the corresponding standard errors from models (1) and (2).

(d) Compute the simple correlations among the X’s in model (1). What do you observe?

(e) Use the Chow-F test to test the parametric restrictions obtained in part (b).

(f) Estimate equations (1) and (2) now using the full data set 1950-1987. Discuss briefly the effects on individual parameter estimates and their standard errors of the larger data set.
(g) Using a dummy variable, test the hypothesis that gasoline demand per CAR permanently shifted downward for model (2) following the Arab Oil Embargo in 1973?
(h) Construct a dummy variable regression that will test whether the price elasticity has changed after 1973.