Use CONSUMP.RAW for this exercise. One version of the permanent income hypothesis (PIH)...

Use CONSUMP.RAW for this exercise. One version of the permanent income hypothesis (PIH) of consumption is that the growth in consumption is unpredictable. [Another version is that the change in consumption itself is unpredictable; see Mankiw (1994, Chapter 15) for discussion of the PIH.] Let be the growth in real per capita consumption (of nondurables and services). Then the PIH implies that where I_t-1 denotes information known at time (t − 1); in this case, t denotes a year.

(i) Test the PIH by estimating Clearly state the null and alternative hypotheses. What do you conclude?

(ii) To the regression in part (i) add the variables gy_t−1, i3_t−1, and inf_t−1. Are these new variables individually or jointly significant at the 5% level? (Be sure to report the appropriate p-values.)

(iii) In the regression from part (ii), what happens to the p-value for the t statistic on gc_t−1? Does this mean the PIH hypothesis is now supported by the data?

(iv) In the regression from part(ii), what is the F statistic and its associated p-value for joint significance of the four explanatory variables? Does your conclusion about the PIH now agree with what you found in part (i)?