Sunday, November 15, 2015

Miracles

Scott Sumner says:
The 2% inflation rate since 1990 would be an amazing coincidence, almost a miracle.
Is it?

This is another place where reasoning using scales and dimensional analysis would really help. A 2% inflation rate sets a time scale (it is per year) so t = 1/π. For it to be a miracle (i.e. a fine tuning problem) that the Fed's (implicit) target and the inflation rate to match up there would have to be no other scales T ≈ t. So we should ask: Are there any other time scales T in a nation such that T ≈ t  from 1990 on besides the central bank target? 

How about say ... labor force growth?


Actually employment growth (T = 1/λ) matches up pretty well too, including the times before 1990. Nearly all of the major differences are recessions:



The information equilibrium model gives a mechanism for t = 1/π ≈ 1/λ = T for this latter example through nominal shocks.

Something that would be a major coincidence (i.e. finely tuned) if it wasn't the result of some underlying theory is the Grand Unified Theory (GUT) scale:


Another place where the value of a parameter considered something of a miracle is the strong CP problem. It's somewhat of a miracle that the CP-violating term of the QCD Lagrangian is about a trillion times too small. It's such a fine-tuning problem that the axion was proposed to fix it.

But there exists at least one scale T that is approximately equal to t (i.e. π ≈ λ), so it's not necessarily a miracle that inflation is on the order of 2%.

Actually, it's more of a miracle that central banks chose to (implicitly) target 2% inflation. A larger target might have shown persistent undershooting earlier. However, the Fed never announced an explicit inflation targeting policy, and only has said 2% is consistent with its mandate more recently. Overall, the onset (1990s) and explicit target (about 2%) have a lot of wiggle room. And saying the Fed has targeted 2% PCE inflation does not explain the unbroken trend towards lower inflation since the 1980s (something that comes out of the IT model: see here or here).

...

PS I don't really want to link to the Insane Clown Posse, but their music video Miracles, which Brad DeLong frequently posts a screenshot from is immediately what I thought of when Scott called 2% inflation in the absence of effective central bank targeting a 'miracle'. In it, the ICP asks "#$%@ magnets; how do they work? And I don't want to talk to a scientist ..." Anyway, that's the rationale for the title.

7 comments:

  1. "And I don't want to take to a scientist"

    "talk to" or "take to?"

    ReplyDelete
    Replies
    1. I found it...:

      "And I don't wanna talk to a scientist
      Y'all motherfuckers lying, and getting me pissed"

      Yes, that's a classic! LOL

      BTW, what's "LEP" stand for in the 3rd figure? I didn't see it defined on your linked page.

      Delete
    2. I'm pretty sure it refers to the energy available from the "Large Electron-Positron" collider, the predecessor of the LHC at CERN.

      LEP wikipedia

      Delete
  2. No comprende señor. I don't see how "2% inflation" sets any time frame. Yes, it means 2% per year, but that is cultural, ultimately based upon astronomy. It is not clear that it has any macroeconomic significance, that it is not just conventional. What difference would it make if the time scale were one month, or one week, or 60 years?

    ReplyDelete
    Replies
    1. Bill, I don't see what it would matter if it was a month or week or 60 years... but the point is another "force of nature" (labor force growth) has approximately the same time constant when measured in those units. At least that's what I think the point is. As long a we're consistent and measure everything in term of the basic unit of 60 years (for example), then we can still speak of variables changing on the same time scale (even if we have to introduce scientific notation to do it). As an example, in Jason's 3rd figure, we could change GeV to MeV and m to mm, and add three to all the exponents on the horizontal scales.... and the point that plot is making (whatever it is) would still be made.

      Now we can both see what the real point is when Jason comes along to answer your question correctly. (c:

      Delete
    2. 2% inflation means

      P ~ exp r t

      Where r = 0.02 and t is years. You'd have to divide 0.02 by 12 if t is in months.

      This means that

      P ~ exp t/t0

      Since the argument of the exponential must be dimensionless (a pure number) and t0 = 1/r.

      Delete

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