Everaert and Pozzi \({ }^{20}\) develop a model to examine the predictability of consumption growth in 15 OECD countries. Their data is stored in the file oecd. The variables used are growth in real per capita private consumption (CSUMPTN), growth in real per capita government consumption (GOV), growth in per capita hours worked (HOURS), growth in per capita real disposable labor income (INC), and the real interest rate \((R)\). Using only the data for Japan, answer the following questions:

a. Estimate the following model and report the results

Are there any coefficient estimates that are not significantly different from zero at a \(5 \%\) level?

b. The coefficient \(\beta_{2}\) could be positive or negative depending on whether hours worked and private consumption are complements or substitutes. Similarly, \(\beta_{3}\) could be positive or negative depending on whether government consumption and private consumption are complements or substitutes. What have you discovered? What does a test of the hypothesis \(H_{0}: \beta_{2}=0, \beta_{3}=0\) reveal?

c. Re-estimate the equation with \(G O V\) omitted and, for the coefficients of the remaining variables, comment on any changes in the estimates and their significance.

d. Estimate the equation

and use these estimates to reconcile the estimates in part (a) with those in part (c).

e. Re-estimate the models in parts (a) and (c) with the year 2007 omitted and use each of the estimated models to find point and \(95 \%\) interval forecasts for consumption growth in 2007.

f. Which of the two models, (a) or (c), produced the more accurate forecast for 2007 ?

CSUMPTN B+ BHOURS + 3GOV + B4R+B5INC + e