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

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?