Commenting on the Kansas Palmer Drought Severity Index, Rick Stryker writes: “From a theoretical point of view it must be stationary.” He reasons that this is so, because it is bounded between -10 and +10. Question: Is this a relevant piece of information when examining finite samples? Let’s look at consumption as a share of GDP, which must be bounded between 0 and 1.
I retrieve the latest vintage of national income and product accounts, and apply the unit root tests readily available to me (ADF, DF(GLS), Phillips-Perron, Elliott-Rothenberg-Stock point optimal, and Ng-Perron), constant and trend. Using default settings, all fail to reject the unit root null. Applying the Kwiatkowski-Phillips-Schmidt-Shin test, the trend stationary null is rejected. The results are here. The conclusions are unchanged if the specifications involve only constants.
Truncating the sample so as to start in 1952 (thereby omitting the high consumption ratio at the beginning) does not change the conclusions.
Now, it is true that consumption-to-GDP cannot stray outside the 0-1 bounds. But in a finite sample, the series might look a lot like a random walk. (Perhaps Rick Stryker, like the HeeChee, has access to the infinite sample, in which case he can find out for sure what the time series characteristics of the consumption-GDP series is.)