Wednesday, September 9, 2015

Predictions doing well after 18 months

69 days into 2014, and less than a year since I started this blog I (and my hubris) decided to try to predict the next two years of macroeconomic indicators: core CPI, short (3-month) and long (10-year) interest rates, RGDP and the unemployment rate. OK, the last two weren't really model predictions -- RGDP falls out of the NGDP projection and the core CPI (so it's not really independent of the CPI prediction) and the unemployment rate model was actually just some speculation and a "metastability" model I invented in the original prediction post. There have been two previous updates (one, two).

The model took as input some ('theory-free') simple quadratic extrapolations of the data from 2013 Q1-Q4 out to the end of 2016. I only later came up with the NGDP-M0 path which would turn NGDP into a predicted value.

Since there are some new readers out there, I thought I'd write up the details of the procedure so you don't have to go hunting around the blog. The basic models appear in the draft paper. All of the data is from FRED.


  • NGDP 1960 Q1 to 2013 Q4 (GDP)
  • M0 1960 Q1 to 2013 Q4 (MBCURRCIR)
  • MB 1960 Q1 to 2013 Q4 (BASE)

Model fit to price level: α, m0 with γ fixed
Model fit to (long and short) interest rates: a and b
Model fit to total unemployed: kL/kU = u*
[Hence the "not bad for 5 parameters" title of the prediction updates since α is actually arbitrary depending on which year you normalize the price level.]

Interest rate model used the bound formulation (data ≤ model) based on non-ideal information transfer, however it only used a single function for the long and short interest rates.

Data used in fit:

  • NSA core CPI 1960 Q1 to 2013 Q4 (CPILFENS, as available March 2014)
  • 3-month secondary market rate 1960 Q1 to 2013 Q4 (WTB3MS, as available March 2014)
  • 10-year constant maturity rate 1960 Q1 to 2013 Q4 (DGS10, as available March 2014)
  • Unemployment level (UNEMPLOY), total employed (PAYEMS) and civilian labor force (CLF16OV) 1960 Q1 to 2013 Q4 (all as available March 2014)

Extrapolations (log-quadratic):

  • NGDP 2014 Q1 to 2015 Q4
  • M0 2014 Q1 to 2015 Q4
  • MB 2104 Q1 to 2015 Q4

Here's how the extrapolations have performed:

The monetary base came in a bit under the extrapolation.


  • Year over year core CPI (NSA)
  • RGDP
  • 3-month interest rate (bound and band)
  • 10-year interest rate (bound and band)
  • "Natural rate" of unemployment (just a single number u* = 5.7%)

There was a spike in short term rates this past summer -- likely stemming from talk of the Fed raising rates after the upcoming meeting.

There wasn't any noticeable pause in the blue region, so the metastability theory may not be correct. Or maybe we're heading directly to the utopian 4% green band that hasn't been realized since the 1990s.

Aside from the extrapolated paths, I had one other "caveat" that there wouldn't be any 'nominal (NGDP) shocks' in during the prediction period. Since these appeared to be unpredictable at the time (and only later did I come up with a tentative metric for determining whether shocks were likely), I had a plot of predicted value of NGDP shocks (based on NGDP and the model prediction from CPI):


  1. Hi Jason,

    I never seem to be able to understand which variables are exogenous and endogenous in your model. You list NGDP, M0, and MB as 'inputs', but what variables are exogenous in the more conventional macro-model sense (i.e. what is the government/CB supposed to be controlling)?


    1. Hi John,

      In this specific instance (it's an early version of the model) the central bank essentially controls M0 (currency) and MB (currency + reserves) -- exogenous inputs from the central bank -- and NGDP comes from outside the model (is exogenous with unknown source).

      As I mention above, later work seemed to show a relationship between M0 and NGDP, so in the most up-to-date version of the model M0 and MB are set by the central bank and NGDP is determined from M0. It is even possible [1] that the bank sets MB and reserve requirements and M0 is determined from that, but I haven't worked out the details there other than a few observations:

      However, since there is a fixed relationship between interest rates and M0 and MB it is possible to formulate [2] the model as the central bank setting interest rates (long and short) with M0 and MB being endogenously determined. This doesn't seem to make as much sense as I discuss a bit here:

      And you could go further and combine [1] and [2] so that the central bank sets short term interest rates and reserve requirements and you get NGDP and M0 from that ... but that is a long way off as yet. And it doesn't seem like it'd be particularly accurate given the second link above.


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