Friday, December 4, 2015

Supply, demand, stock, flow

Steve Roth of Asymtosis, Angry Bear, and other places stopped by the blog the other day and over the course of some discussion -- and perusing his links -- I wanted to note a couple things.

I.

Steve says:
Am I foolish to suggest that the central concepts of economics, supply and demand, are embarassingly un(der)theorized?
I agree! Actually, I think economists might not even understand supply and demand (except Gary Becker). For one, the supposed experiment designed by Vernon Smith (Nobel prize winner for this very kind of experimental economics) actually assumes its result. If you assign numerical utility to people, along with a budget constraint, you get supply and demand. This is how monkeys can end up illustrating supply and demand. Additionally, various classroom experiments don't show what they purport to show. Supply and demand is a property of the state space. Gary Becker showed this way back in 1962.

II.

There was also some discussion of stocks and flows. This is one area where many economists and non-economists get a little too fastidious. It is true that in one case you can have an associated time (well, 'velocity') scale (flows) and one where you don't (stocks) and it is important to understand where this scale comes from.

However, in the information equilibrium model, I frequently put a flow in information equilibrium with a stock -- notably in the relationship NGDP ⇄ M0. Nominal output is dollars per year (or annualized), whereas the money supply is a stock of currency. And there is nothing particularly wrong with this. Why? Because the information in a distribution doesn't really care too much about the domain it's over ... just what the distribution is over the domain. This post has a bit of background (it goes over the rationale behind the blog's favicon and the meaning of the diagram up in the upper right corner on a desktop browser).

Let's say we have a spatial-temporal distribution of an information source distribution (demand, translucent white) and one for the destination (supply, blue):


As you move along the time axis, you have different "stocks" at different instants in time; the change as you move along the time dimension is a "flow". When these are in information equilibrium, they match up:


When they don't match up (demand doesn't meet supply at the right place and right time), you have information loss that can be measured with the KL divergence between the two 2-dimensional distributions:


However, I can also integrate over the time dimension (add up the areas under the blue and white surfaces in one direction) and still see the information loss as a "stock" (an integrated flow):


For a simplified version of this with widgets, you can go to that aforementioned post. Once I've done this integration, I am free to compare it to the information content of a probability distribution of something else:


Since information doesn't really have units per se (bits can be changed to nibbles by multiplying by a constant pure number), it is perfectly fine for the information content in the distribution of a stock to be in equilibrium with the information content in the distribution of a flow.

Now maybe you don't buy this. That's fine. But here's a well known equation in physics that says a stock is equal to a flow (plus a change in flow):

ẍ + (1/τ) ẋ + ω² x = 0


This equation for a damped harmonic oscillator is essentially

change in flow + flow + stock = 0

There are just parameters (scales τ and ω) that make the units work out. If I say

stock Y = flow X

There is just an implicit time scale T (parameter, or constant of proportionality) so that:

Y = T X

If you never couple stocks to flows (putting a stock and a flow in the same equation 'couples' them -- makes them depend on each other), then all flows will be independent of all stocks! There will be a stock description of the economy and a flow description of the economy, and the two will have nothing to do with each other.

Caring a bit too much about stocks and flows is a bit like saying you can't set time equal to a position. And while it's true x = t gets the units wrong, time and position can be in equilibrium -- just add a constant of proportionality (velocity) so that x = v t.

In fact, the great achievement of Einstein was creating the idea of space-time -- space and time are in a sense equivalent. The reason they're equivalent is the existence of a universal constant of proportionality: the speed of light c. Or you could say the equivalence means there must be a universal constant with units of velocity.

...

Update 06 December 2016

Since I wrote this I found that SFC analysis does couple stocks to flows -- it also forgets those time scales T -- by looking at stock-to-flow ratios.

4 comments:

  1. Not that I disagree with your general point, but if we are not fastidious about flows, we cannot demonstrate conservation laws. Things do not add up. IMX, economists are not so fastidious about flows, because they do not see a causal story in them. It's just bookkeeping to them.

    ReplyDelete
    Replies
    1. Not really -- a conservation follows from a symmetry principle; respect the symmetry, and you get the conservation for free.

      Be fastidious about scales and symmetries!

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    2. We're talking on different levels, I think. The lack of fastidiousness about flows that I perceive with economists strikes me as a symptom of their lack of empiricism.

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    3. Also, on a more theoretical level, the lack of fastidiousness about flows is implicated in fallacies of composition that Cameron Murray refers to in his post, "Macroeconomics = Fallacy of Composition" ( http://www.fresheconomicthinking.com/2015/04/macroeconomics-fallacy-of-composition.html ). Not being fastidious gives you an additional degree of freedom.

      Delete

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