E15.2 In the data file USMacro_Quarterly, you will find data on two aggregate price series for the United States: the price index for personal consumption expenditures (PCEP) that you used in Empirical Exercise 14.1 and the Consumer Price Index (CPI). These series are alternative measures of consumer prices in the United States. The CPI prices a basket of goods whose composition is updated every 5–10 years. PCEP uses chainweighting to price a basket of goods whose composition changes from month to month. Economists have argued that the CPI will overstate inflation because it does not take into account the substitution that occurs when relative prices change. If this substitution bias is important, then average CPI inflation should be systematically higher than PCEP inflation. Let pCPI t =

400 × [ln(CPIt) − ln(CPIt−1)], and pPCEP t = 400 × [ln(PCEPt) − ln(PCEPt−1)], and Yt = pCPI t − pPCEP t , so pCPI t is the quarterly rate of price inflation (measured in percentage points at an annual rate) based on the CPI, pPCEP t is the quarterly rate of price inflation from the PCEP, and Yt is their difference.

Using data from 1963:Q1 through 2012:Q4, carry out the following exercises.

a. Compute the sample means of pCPI t and pPCED t . Are these point estimates consistent with the presence of economically significant substitution bias in the CPI?

b. Compute the sample mean of Yt. Explain why it is numerically equal to the difference in the means computed in (a).

c. Show that the population mean of Y is equal to the difference of the population means of the two inflation rates.

d. Consider the “constant-term-only” regression: Yt = b0 + ut. Show that b0 = E(Y). Do you think that ut is serially correlated? Explain.

e. Construct a 95% confidence interval for b0. What value of the HAC standard truncation parameter m did you choose? Why?

f. Is there statistically significant evidence that the mean inflation rate for the CPI is greater than the rate for the PCEP?

g. Is there evidence of instability in b0? Carry out a QLR test. (Hint:

Make sure you use HAC standard errors for the regressions in the QLR procedure.)