Information equilibrium: a common language for multiple schools

Cameron Murray has a great post about the challenge of reforming economics in which he points out two challenges: social and technical. The social challenge is that different "schools" are tribal, and reconciliation isn't rewarded. Just read Murray on this.

The second challenge is something that I have tried to work towards answering:

[H]ow do you teach a pluralist program when there is no recognised structure for presenting content from many schools of thought, which can often be contradictory, and when very few academics are themselves sufficiently trained to to so?

...

What is needed is a way to structure the exploration of economic analysis by arranging around economic problems around some core domains. Approaches from various schools of thought can be brought into the analysis where appropriate, with the common ground and links between them highlighted.

Despite being completely out of the mainstream, the information equilibrium framework does not have to subscribe to a specific school of economic thought. I actually thought this is what you were supposed to mean by framework (other economists disagree and include model-specific results in what they call frameworks). In fact, I defined framework by something that is not model specific:

One way to understand what a framework is is to ask whether the world could behave in a different way in your framework ... Can you build a market monetarist model in your framework? It doesn't have to be empirically accurate (the IT framework version is terrible), but you should be able to at least formulate it. If the answer is no, then you don't have a framework -- you have a set of priors.

This is what pushed me to try and formulate the MMT and Post-Keynesian (PK) models that use "Stock Flow Consistent" (SFC) analysis as information equilibrium model. The fact that I criticized an aspect of SFC analysis upset the MMT and PK tribes (see the post and comments) led me to not end up posting the work I'd done.

But in the interest of completeness and showing that the information equilibrium framework allows you to talk about completely different schools of economics with the same language, let me show the model SIM from Godley and Lavoie as an information equilibrium model.

SFC models as an information equilibrium model

First, divide through by $Y$ (this represents an overall scale invariance), so all the variables below are fractions of total output (I didn't change the variable names, though because it would get confusing).

Define the variable $B$ to be government spending minus taxes.

$$
B \equiv G - T
$$

Define $x$ to be a vector of consumption, the variable $B$, taxes, disposable income and high powered money:

$$
\begin{bmatrix}
C \\
B \\
T \\
Y_{D} \\
H
\end{bmatrix}
$$

Define the matrix $A$ to be

$$
\begin{bmatrix}
1 & 1 & 1 & 0 & 0 \\
1 & 1 & 0 & -1 & 0 \\
0 & 0 & 1 & 0 & 0 \\
1 & 0 & 0 & -\alpha_{1} & -\alpha_{2} \\
0 & 0 & 1 & 1 & 0
\end{bmatrix}
$$

Define the vector $b$ to be

$$
\begin{bmatrix}
-1 \\
0 \\
-\theta \\
0 \\
-1
\end{bmatrix}
$$

The SFC model SIM from Godley and Lavoie is then

$$
A x + b = 0
$$

$$
H \rightleftarrows Y_{D}
$$

with [Ed. note: I originally got my notes confused because I wrote $Y_{D}$ as $D$ through part of them and $B$ instead of the $Y_{D}$ I use here, so left off the following equation]

$$
B \equiv \int_{\Gamma} dY_{D}
$$

where the second equation is an information equilibrium relationship [and the third is a path integral; in the model SIM, they take $\Gamma$ to effectively be a time step]. The issue that I noticed (and upset the SFC community) is that it's assumed that the information transfer index is 1 so that instead of:

$$
H \sim Y_{D}^{k}
$$

You just have

$$
H \sim Y_{D}
$$

and the velocity of high powered money is equal to 1. Also, there is no partial equilibrium -- only general equilibrium so you never have high powered money that isn't in correspondence with debt (or actually in the SFC model, exactly equal to debt).

Even with this assumption, however, the model can still be interpreted as an information equilibrium model. There is supply and demand for government debt that acts as money. This money is divided up to fund various measures e.g. consumption.

Market monetarism as an information equilibrium model

Over time, I have attempted to put the various models Scott Sumner writes down into the information equilibrium framework. The first three are described better here.

1) u : NGDP ⇄ W/H

The variable u is the unemployment rate. H is total hours worked and W is total nominal wages.

2) (W/H)/(PY/L) ⇄ u

PY is nominal output (P is the price level), L is the total number of people employed and u is the unemployment rate.

3) (1/P) : M/P ⇄ M

where M is the money supply. This may look a bit weird, but it could potentially work if Sumner didn't insist on an information transfer index k = 1 (if k is not 1, that opens the door to a liquidity trap, however). As it is, it predicts that the price level is constant in general equilibrium and unexpected growth shocks are deflationary in the short run.

This 4th one is described here.

4) V : NGDP ⇄ MB and i ⇄ V

where V is velocity, MB is the monetary base and i is the nominal interest rate. So that in general equilibrium we have:

V = k NGDP/MB

log i = α log V

Or more compactly:

log i = α log NGDP/MB + β

More models!

More mainstream Keynesian and other models all appear here or in my paper. Here's a model that is based on the Solow model. However, I think showing how the framework can illustrate both Market Monetarism and Post Keynesianism using the same tools gives an idea of how useful it is.

I can even put John Cochrane's asset pricing equation approach in the framework!

The interesting part is that it lays bare some assumptions (e.g. that the IS-LM model is an AD-AS model with low inflation).

And despite my protests, expectations can be included. It just involves looking at the model temporally rather than instantaneously.