Based on the quarterly data for the U.K. for the period 1990-1Q to 1998-2Q, the following results were obtained by Asteriou and Hall. The dependent variable in these regressions is Log(IM) = logarithm of imports (t ratios in parentheses).

a. Interpret each equation.
b. In Model 1, which drops Log(PPI), the coefficient of Log(CPI) is positive and significant at about the 5% level. Does this make economic sense?
c. In Model 3, which drops Log(CPI), the coefficient of Log(PPI) is positive but statistically insignificant. Does this make economic sense?
d. Model 2 includes the logs of both price variables and their coefficients are individually statistically significant. However, the coefficient of Log(CPI) is positive and that of Log(PPI) is negative. How would you rationalize this result?
e. Do you think multicollinearity is the reason why some of these results are conflicting? Justify your answer.
f. If you were told that the correlation between PPI and CPI is 0.9819, would that suggest that there is a multicollinearity problem?
g. Of the three models given above, which would you choose and why?

Explanatory variable Intercept Log(GDP) Log(CPI) Log(PPI) Adjusted-R2 Model 1 Model 2 Model 3 0.6318 (1.8348) 1.9269 0.2139 (0.5967) 1.9697 0.6857 (1.8500) 2.0938 114117 (12.5619) (12.1322) 1.0254 (3.1706) 0.7706 (-2.5248) 0.9692 0.2742 (1.9961) 0.1195 0.1195 (0.8787) 0.9602 0.9638