Appendix A: Unit root tests
Table A1
Unit root tests, USA (1978:1-2006:4)
|
Series |
Augmented Dickey- Fuller |
KPSS | ||
|
Levels |
First differences |
Levels |
First differences | |
|
GDP |
-3.07 |
-4.07*** |
0.05 |
0.04 |
|
U |
-3.74** |
-4.68*** |
0.06 |
0.07 |
|
π |
-2.51 |
-12.41*** |
0.19** |
0.07 |
|
π2 |
-3.95** |
-2.63* |
0.20** |
0.05 |
|
∏ |
-4.04** |
-4.09*** |
0.20** |
0.08 |
|
π4 |
-3.45* |
-3.30** |
0.20** |
0.13 |
|
π5 |
-3.78** |
-4.18*** |
0.20** |
0.14 |
|
π6 |
-4.36*** |
-2.48 |
0.20** |
0.20 |
|
π7 |
-3.57** |
-3.23** |
0.20** |
0.25 |
|
πs |
-2.88 |
-3.70*** |
0.20** |
0.31 |
|
sMeed |
-4.79*** |
-5.64*** |
0.11 |
0.17 |
|
sDff |
-7.56*** |
-5.59*** |
0.11 |
0.13 |
|
S^Mom |
-4.06*** |
-10.49*** |
0.06 |
0.13 |
|
sWMeed |
-2.83 |
-5.37*** |
0.09 |
0.08 |
|
Sr 20 |
-4.30*** |
-5.33*** |
0.14* |
0.03 |
Notes: For the ADF tests, the lag length is automatically selected based on AIC. The only exogenous
variable in the first-differenced model is a constant, while the test in levels also includes a time trend.
The null hypothesis states that the time series has a unit root. The test statistics are compared with
MacKinnon (1996) one-sided p-values. *** (**) (*) denotes rejection of the null hypothesis at the 0.99
(0.95) (0.90) level.
For the KPSS tests, the bandwidth is automatically selected based on a Newey-West using a Bartlett
kernel. The only exogenous variable in the first-differenced model is a constant, while the test in levels
also includes a time trend. The null hypothesis states that the time series is (trend-) stationary. The test
statistics are compared with the critical values from Kwiatkowski-Phillips-Schmidt-Shin (1992, Table
1). *** (**) (*) denotes rejection of the null hypothesis at the 0.99 (0.95) (0.90) level.