(Requires Internet Access for the test question) The following question requires you to download data from the internet and to load it into a statistical package such as STATA or EViews

Question

a. Your textbook estimates an AR(1) model (equation 14.7) for the change in the inflation rate using a sample period 1962:I — 2004:IV. Go to the Stock and Watson companion website for the textbook and download the data "Macroeconomic Data Used in Chapters 14 and 16." Enter the data for consumer price index, calculate the inflation rate, the acceleration of the inflation rate, and replicate the result on page 526 of your textbook. Make sure to use heteroskedasticity-robust standard error option for the estimation.

b. Next find a website with more recent data, such as the Federal Reserve Economic Data (FRED) site at the Federal Reserve Bank of St. Louis. Locate the data for the CPI, which will be monthly, and convert the data in quarterly averages. Then, using a sample from 1962:I — 2009:IV, re-estimate the above specification and comment on the changes that have occurred.

c. Based on the BIC, how many lags should be included in the forecasting equation for the change in the inflation rate? Use the new data set and sample period to answer the question.

What will be an ideal response?

Answer 1

Answer:
a. The EViews output would look as follows:

Dependent Variable: D2LP
Method: Least Squares
Date: 12/30/10 Time: 20:29
Sample: 1962Q1 2004Q4
Included observations: 172

White Heteroskedasticity-Consistent Standard Errors & Covariance

Coefficient Std. Error t-Statistic Prob.

C 0.017 0.127 0.135 0.893
D2LP(-1) -0.238 0.097 -2.467 0.015

R-squared 0.056 Mean dependent var 0.017
Adjusted R-squared 0.051 S.D. dependent var 1.708
S.E. of regression 1.664 Akaike info criterion 3.868
Sum squared resid 470.691 Schwarz criterion 3.904
Log likelihood -330.634 Hannan-Quinn criter. 3.883
F-statistic 10.157 Durbin-Watson stat 2.166
Prob(F-statistic) 0.002

b. Not much has changed. The intercept became smaller, but was statistically insignificant anyway. The slope coefficient increase somewhat (as did the Regression R2 with it) and its t-statistic also became stronger. Some of this is the result of data revisions (even for the old sample period the slope coefficient increased somewhat) while part of it has changed because of the longer sample period.

Dependent Variable: D2LP
Method: Least Squares
Date: 12/30/10 Time: 21:19
Sample: 1962Q1 2009Q4
Included observations: 192
White Heteroskedasticity-Consistent Standard Errors & Covariance

Coefficient Std. Error t-Statistic Prob.

C 0.014 0.153 0.089 0.929
D2LP(-1) -0.290 0.094 -3.070 0.002

R-squared 0.084 Mean dependent var 0.010
Adjusted R-squared 0.079 S.D. dependent var 2.203
S.E. of regression 2.114 Akaike info criterion 4.345
Sum squared resid 849.127 Schwarz criterion 4.379
Log likelihood -415.161 Hannan-Quinn criter. 4.359
F-statistic 17.428 Durbin-Watson stat 2.203
Prob(F-statistic) 0.000

c. Using the BIC for p = 0, 1, 2, …, 6, the minimum continues to be at p = 2. Hence the BIC still favors an AR(2).