Introduction to Econometrics 3rd Edition by James Stock, Mark Watson

Exercise 4

In the data file USMacro_Monthly, you will find data on two aggregate price series for the United States: the Consumer Price Index (CPI) and the Personal Consumption Expenditures Deflator (PCED). 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. The PCED uses chain-weighting 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 PCED inflation. Let
, is the monthly rate of price inflation (measured in percentage points at an annual rate) based on the CPI, is the monthly rate of price inflation from the PCED, and Y i is the difference. Using data from 1970:1 through 2009:12, carry out the following exercises.
a. Compute the sample means of Are these point estimates consistent with the presence of economically significant substitution bias in the CPI
b. Compute the sample mean of Y t. 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:
. Show that
. Do you think that u, is serially correlated Explain.
e. Construct a 95% confidence interval for 0. 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 PCED
g. Is there evidence of instability in 0 Carry out a QLR test.