|Table 1: Regression Results|
There are two approaches to testing formally for a unit root. For one group of tests, for example, the augmented Dickey Fuller test, the null hypothesis is that the series is non-stationary. For a second group, for example the KPSS test, the null hypothesis is that the series is stationary.
Table 2 presents the results of a Dickey Fuller test where the null hypothesis is that X has a unit root. Here we are looking for a test statistic that is small in absolute value if the series has a unit root, reflecting the fact that there is nothing pulling the series back towards trend. The null hypothesis that X has a unit root cannot be rejected at the 1%, the 5% or the10% level.
|Table 2: Augmented Dickey Fuller Test|
|Table 3: KPSS Test|
What do we learn from this? Much the same as we learn from the fact that unemployment has a unit root. Just as unemployment can remain persistently high, so GDP can remain persistently below trend. There is no evidence that the economy is self-correcting.