Monday, October 30, 2017

Forecast head-to-head performance (and looking back)


Here's the latest data on core PCE inflation compared to my information equilibrium model (single factor production monetary model) along with the FRB NY DSGE model forecast (as well as the FOMC forecast) of the same vintage:



The IE model is biased a bit low by almost as much as the DSGE model is biased high (but the former is a far simpler model than the latter). I've been tracking this forecast since 2014 (over three years now). There's now only one more quarter of data left. What's probably most interesting is how I've changed in looking at this model. If I were writing it down today, I'd define the model as I do in the parenthetical: a single factor production model with "money" as the factor of production. In particular, I'd take the ensemble approach, considering a set of markets that turn "money" $M$ into various outputs ($N_{i}$):

$$
N_{i} \rightleftarrows M
$$

(notation definition here) such that (assuming $\langle k \rangle$ is slowly varying)

$$
\langle N \rangle \approx N_{0} \left( \frac{M}{M_{0}} \right)^{\langle k \rangle}
$$

with the ansatz (consistent with slowly varying $\langle k \rangle$)

$$
\langle k \rangle \equiv \frac{\log \langle N \rangle/C_{0}}{\log M/C_{0}}
$$

and therefore the price level is given by

$$
\langle P \rangle \approx \frac{N_{0}}{M_{0}} \langle k \rangle \left( \frac{M}{M_{0}} \right)^{\langle k \rangle - 1}
$$

The parameters here are given by

$$
\begin{align}
\frac{N_{0}}{M_{0}} = & 0.661\\
C_{0} = & 0.172  \;\text{G\$}\\
M_{0} = & 595.1 \;\text{G\$}
\end{align}
$$

for the case of the core PCE price level and using the monetary base minus reserves as "money".

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