Use the data in INVEN.RAW for this exercise; see also Computer Exercise.(i) Obtain the OLS...

Use the data in INVEN.RAW for this exercise; see also Computer Exercise.

(i) Obtain the OLS residuals from the accelerator model Δinvent = β0 + (β1 ΔGDPt + ut and use the regression ût on ût-1 to test for serial correlation. What is the estimate of ρ? How big a problem does serial correlation seem to be?

(ii) Estimate the accelerator model by PW, and compare the estimate of β1 to the OLS estimate. Why do you expect them to be similar?

Exercise Let invent be the real value inventories in the United States during year t, let GDPt denote real gross domestic product, and let r3t denote the (ex post) real interest rate on three-month T-bills. The ex post real interest rate is (approximately) r3t =i3t – inft, where i3t is the rate on three-month T-bills and inft is the annual inflation rate [see Mankiw (1994, Section)]. The change in inventories, Δinvent, is the inventory investment for the year. The accelerator model of inventory investment is

Δinvent = β0 + β1ΔGDPt + ut, where β1 ≻ 0. [See, for example, Mankiw (1994), Chapter 17.]

(i) Use the data in INVEN.RAW to estimate the accelerator model. Report the results in the usual form and interpret the equation. Is statistically greater than zero?

(ii) If the real interest rate rises, then the opportunity cost of holding inventories rises, and so an increase in the real interest rate should decrease inventories. Add

the real interest rate to the accelerator model and discuss the results.

(iii) Does the level of the real interest rate work better than the first difference, Δr3t?