Saturday, March 12, 2016

The entropy term and the unreasonable effectiveness of NGDP

I realize I've now said this at least twice in comments, but I think it deserves a post on its own. Awhile ago, I used an elaborate analogy to write nominal output the sum of the output in several markets, plus a money market, plus an entropy term. Each term in that sum represents an economic (entropic) force -- microeconomic forces for the individual markets and a macroeconomic force for the entropy term.

NGDP* = TS + k P M + k P₁ X₁ + k P₂ X₂ + ...

I labeled this NGDP* for reasons that will be clear later. In the individual markets, the microeconomic forces represent supply and demand for the individual products. But what about the purely macroeconomic entropic force arising from the entropy term? Functioning much like the arrow of time, this represents the macroeconomic resistance agents collectively have to undoing their economic gains. Without coordination, it is unlikely that agents will undo a large portion of their aggregate gains. Unfortunately, the coordination usually comes in the form of panics and recessions.

That entropy term represents an economic force acting against agents undoing their gains. And that's great! Because in my version of the model, agents are random (or so complex/dependent on unknown initial conditions -- i.e. financial histories -- that they appear random). Real individual humans don't make random transactions (at least most of the time), so the random agent model needs way for agents to not on average sell their house at a loss if they don't have to. Voilà: the entropy term.

Many people on first coming to my blog ask if I've heard of Duncan Foley (because he's also applied thermodynamics to economics). I have checked out his work, but his approach is much different than mine. However, I am indebted to him (and his co-author Eric Smith) for this idea about entropy (coming from this paper). They couched it in terms of reversible versus irreversible processes, but irreversible processes are exactly entropy producing processes. In economics using the potential above, that entropy producing process would be economic growth. Economic growth is exploration of the state space along with an aggregate tendency not to undo the gains in output (i.e. entropy).

One more thing: if you were to just sum up the output in the individual markets, you'd technically miss out on the entropy term. You ask: But isn't that how NGDP is calculated ... just adding up all the (final) purchases of goods and services? So isn't NGDP missing that entropy term?

Technically, yes. But since the entropy term is (for a large economy) proportional to the sum of all final purchases of goods and services in the individual markets, NGDP plus the entropy term will be proportional to NGDP. So

k P₁ X₁ + k P₂ X₂ + TS = NGDP + TS ~ (1 + α) NGDP ≡ NGDP*

This clears up a minor mystery (at least for me). Everyone is so down on NGDP (except Scott Sumner); they (e.g. Diane Coyle) say it misses a lot of things that happen in a real economy. And according to what I just said, it does! How in the 1930s did we come up with a measure that happens to capture the aggregate economy in a theory developed 80 years later?

Apparently Simon Kuznets stumbled upon a measure that just happens to be proportional to the true measure in the information transfer model. And since economics has a scale invariance (e.g. add zeros to everything denominated in money an there's no change), and NGDP is measured in money, we lucked out. NGDP turns out to be a measurement of the entropy term.

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