“…we had a debate about whether M2 was mean reverting or not. The data says it is.”

That’s a comment by Steven Kopits.

Figure 1: M2 in billions, seasonally adjusted, on log scale (blue). Source: Federal Reserve via FRED.

  • Reject unit root null (intercept) at 10% using ADF: No,
  • Reject unit root null (intercept, trend) at 10% using ADF: No
  • Reject unit root null (intercept) at 10% using DF-Elliott-Rothenberg-Stock: No
  • Reject unit root null (intercept, trend) at 10% using DF-Elliot-Rothenberg-Stock: No
  • Reject mean stationary null at 1% using KPSS: Yes
  • Reject trend stationary null at 1% using KPSS: Yes

If there was a debate of this sort, I missed the conclusion that Mr. Kopits refers to (as well as the general consensus of the economics profession).

Maybe he meant velocity (M2):

Figure 2: Velocity for M2. Source: Federal Reserve, BEA via FRED, and author’s calculations.

  • Reject unit root null (intercept) at 10% using ADF: No,
  • Reject unit root null (intercept, trend) at 10% using ADF: No
  • Reject unit root null (intercept) at 10% using DF-Elliott-Rothenberg-Stock: No
  • Reject unit root null (intercept, trend) at 10% using DF-Elliot-Rothenberg-Stock: No
  • Reject mean stationary null at 1% using KPSS: Yes
  • Reject trend stationary null at 1% using KPSS: Yes