Saturday, May 3, 2014

A neo-Fisherite rebellion? Yes, please.

I miss all the good stuff when I'm on vacation. I missed most of the Steve Williamson debate, and now I missed the neo-Fisherite rebellion. The rebellion is linked to secular stagnation and deflationary monetary expansion, to both of which I think the information transfer model lends support. But let me tackle Noah Smith's characterization rather directly. First, here's the characterization:
... the Neo-Fisherite idea is NOT that a fall in interest rates causes the price level to jump up and then drift back down to its original level. If the Neo-Fisherites are right, holding interest rates at low levels for a long time will cause a long-term deflationary trend that will eventually push the price level lower than if interest rates had been kept at the old, higher level
And here's the tackling (in graph form**):

The red lines represent constant interest rates, the black line represents the "information trap"/"liquidity trap" criterion ∂P/∂M0 = 0 (it is the top of a ridge in the price level function P = P(M0, NGDP) that is graphed in 3D here, the gray lines in the graph above are the level curves of that surface). On the left side of the ∂P/∂M0 = 0 line in the graph, the price level has a positive relationship to changes in the monetary base (printing currency causes inflation) but on the right side printing currency causes deflation.

You can see that lower interest rates (red lines in the graph) run into the ∂P/∂M0 = 0 line at a lower monetary base relative to higher interest rates. This is exactly the neo-Fisherite claim! Holding interest rates low runs runs you into low inflation faster than holding rates higher.

Noah Smith also asked for some microfoundations for this effect -- I have them here. It is the competition between the unit of account and medium of exchange functions of money that leads to a diminishing marginal utility of monetary expansion. Eventually there is enough currency to base transactions on and more currency just means each unit is smaller relative to NGDP and doesn't carry as much information.

** This graph is just the 2D projection of the 3D graph that is at the upper right of every blog page. The red lines are the level curves of the red "interest rate surface" r = r(M0, NGDP) and the gray lines are the level curves of the white "price level surface" P = P(M0, NGDP).


  1. Jason, what do you do your simulations/calculations with? Matlab?

    1. Mathematica. Actually I was trying to find a good repository for all the codes/data I use in the blog ...

  2. Jason, how do you read this?:
    Williamson backing away from the Neo-Fisherite stance? I found it here:

    What about the stability analysis argument that Krugman, DeLong, Rowe and Beckworth put forward? I'll find the links if you're not familiar with those arguments. Basically they're saying that Williamson's equilibrium analysis was flawed because he wasn't considering the stability of the equilibrium.

    Edward Lambert, however, seems to be arguing that Williamson's equilibrium is stable here:

    1. I discussed the stability of equilibrium stuff at the time in this two-parter:

      Overall, I have an issue with what is meant by equilibrium in that discussion. I buy the Krugman argument and his take on Williamson on the basic economics (inside that model). In the information transfer model, any state with a given NGDP and monetary base is "stable" in the sense that small perturbations around it leave you nearby. But a given growth rate r and inflation rate i cannot be sustained over any period of time (the second post above).

      Here is some more information:

      I'm sympathetic to Williamson opening the possibility to deflationary monetary expansion, but it's one of the more controversial aspects of the information transfer model.

  3. "** This graph is just the 2D projection of the 3D graph that is at the upper right of every blog page. The red lines are the level curves of the red "interest rate surface" r = r(M0, NGDP) and the gray lines are the level curves of the white "price level surface" P = P(M0, NGDP)."

    Thanks for explaining that.... I always wondered what that was. Now in the 3D version the red surfaced intersects the white price level surface along.... what curve? The current (nominal?) interest rate?

    "Holding interest rates low runs runs you into low inflation faster than holding rates higher."

    Faster? wrt to what? movement from left to right along the log(M0) axis?k

    Also, I found out recently that Wikipedia is wrong (see their article on the "Money Supply"): there is not such thing as M0 in the United States and apparently there never has been: there's MB (monetary base) and M1 and M2 etc. I can give you a reference if you're interested.

    1. Movement along either axis tends to follow the time variable fairly well (NGDP and the monetary base are log-linear functions) so yes, but as indicated by the years on the blue line in the graph above, this is not perfect. I actually had to do some old school differential geometry to take the time derivatives with respect to the blue path (I discussed it here).

      Regarding the red/white surface in the upper right corner, you can click on it an it takes you to the reference post. The relative vertical position of the two surfaces is not relevant (they measure different things, interest rate and price level); the curve of intersection is not meaningful. However, the domain (MB, NGDP) is common to both so they can both be projected onto the same graph shown in the post above.

      I realized there is no explicit "M0" in the US, which is why I have tended to call MB without reserves (the currency component of the base) "M0" in quotation marks -- it's called notes and coins in the UK. It represents actual printed currency, but there is no official monetary aggregate name for it in the US.

  4. When Williamson first brought to the fore what became "neo-Fisheritism" last Winter, Nick Rowe, Brad DeLong and Paul Krugman all wrote exasperated posts wondering what was wrong with how macro was being taught (that's when Krugman and DeLong brought up the stability issue). Rowe made an interesting statement in his post saying "he didn't know" why we haven't fallen off a deflationary cliff (essentially), and so when this whole business came up again this spring, I asked him again if he still didn't know. He confirmed that's the case:
    Does Information Transfer Economics (do you mind if I call this ITE?) have an explanation?

    1. Because in ITE** there isn't so much of a cliff. The response of the price level to monetary policy just kind of fades away (becoming ever so slightly negative) when the base is large compared to NGDP. I like to imagine it as saturating an economy with money so changes in the amount of money (up or down) don't do very much. Flooding the engine may be another good analogy.

      The only things that are deflationary in that case are NGDP shocks (I don't have a specific model, but large changes in government spending and financial crises could play a role).

      **I've used that acronym before referring to the "framework" so that's fine -- I also use ITM (for Model) for the specific model of the price level, interest rates, etc.


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