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Empirical Exercises 627

14.10 A researcher carries out a QLR test using 30% trimming, and there are
q = 5 restrictions. Answer the following questions, using the values in
Table 14.5 (“Critical Values of the QLR Statistic with 15% Trimming”)
and Appendix Table 4 (“Critical Values of the Fm, ∞ Distribution”).

a. The QLR F-statistic is 3.9. Should the researcher reject the null
hypothesis at the 5% level?

b. The QLR F-statistic is 1.1. Should the researcher reject the null
hypothesis at the 5% level?

c. The QLR F-statistic is 3.6. Should the researcher reject the null
hypothesis at the 5% level?

14.11 Suppose that ∆Yt follows the AR(1) model ∆Yt = b0 + b1∆Yt - 1 + ut.
a. Show that Yt follows an AR(2) model.
b. Derive the AR(2) coefficients for Yt as a function of b0 and b1.

Empirical Exercises

E14.1 On the text website, www.pearsonglobaleditions.com/Stock_Watson,
you will find the data file USMacro_Quarterly, which contains quarterly
data on several macroeconomic series for the United States; the data are
described in the file USMacro_Description. The variable PCEP is the
price index for personal consumption expenditures from the U.S. National
Income and Product Accounts. In this exercise you will construct forecast-
ing models for the rate of inflation, based on PCEP. For this analysis, use
the sample period 1963:Q1–2012:Q4 (where data before 1963 may be used,
as necessary, as initial values for lags in regressions).

a. i. Compute the inflation rate, Infl = 400 * 3 ln (PCEPt) - ln (PCEPt - 1)4.
What are the units of Infl? (Is Infl measured in dollars, percentage
points, percentage per quarter, percentage per year, or something
else? Explain.)

ii. Plot the value of Infl from 1963:Q1 through 2012:Q4. Based on the
plot, do you think that Infl has a stochastic trend? Explain.

b. i. Compute the first four autocorrelations of ∆Infl.
ii. Plot the value of ∆Infl from 1963:Q1 through 2012:Q4. The plot

should look “choppy” or “jagged.” Explain why this behavior is
consistent with the first autocorrelation that you computed in part (i).