You Have Collected Quarterly Data for Real GDP (Y)for the United

question 19

Essay

You have collected quarterly data for real GDP (Y)for the United States for the period 1962:I (first quarter)to 2009:IV.
a. Testing the log of GDP for stationarity, you run the following regression (where the lag length was determined using the AIC): $\widehat{\Delta \ln Y_{t}}=0.03-0.0024 \ln Y_{t-1}+0.253 \Delta \ln Y_{t-1}+0.167 \Delta \ln Y_{t-2}$
$(0.03)\quad(0.0014)\quad\quad(0.072)\quad\quad(0.072)$
$t=1962: \mathrm{I}-2009: \mathrm{IV}, R^{2}=0.16, \text { SER }=0.008$ Use the ADF statistic with an intercept only to test for stationarity. What is your decision?
b.You have decided to test the growth rate of real GDP for stationarity for the same sample period. The regression is as follows:S ${\widehat{\Delta^{2} \ln Y_{t}}}=0.0041-0.543 \Delta \ln Y_{\mathrm{t}-1}-0.186 \Delta 2 \ln Y_{\mathrm{t}-1}$
$(0.0009)(0.082)\quad\quad(0.071)$
$t=1962: \mathrm{I}-2009: \mathrm{IV}, R^{2}=0.16, S E R=0.008$ Use the ADF statistic with an intercept only to test for stationarity. What is your decision?c. integration terminology, what order of integration is the log level of real GDP? The growth rate?
d. Given that the SER hardly changed in the second equation, why is the regression R²larger?

---

Definitions:

Right Atrium

The right upper chamber of the heart that receives deoxygenated blood from the body through the vena cava and pumps it into the right ventricle.

Blood

A vital fluid in humans and other animals that delivers necessary substances such as nutrients and oxygen to the cells and transports metabolic waste products away.

Pulmonary Veins

Blood vessels that carry oxygenated blood from the lungs to the left atrium of the heart.

Left Atrium

The upper left chamber of the heart that receives oxygenated blood from the pulmonary veins and pumps it into the left ventricle.