How Do Stock-Flow Relations Work in Economics and Are They Inappropriate for Price Dynamics?

Bathtub stock flow diagram

The other day I did a post on the work of Katharina Pistor and included some very broad details of something related that I’m working on. Despite me saying clearly and multiple times in the piece that I was massively oversimplifying I nevertheless got some response pointing to supposed “errors” and “banalities” in what I was saying.

The most substantive was that prices cannot be understood in terms of stock-flow equilibria. What followed was a rather muddled argument but one that I think can be summarised by quoting here two comments that were left on that blog. The first ran like this:

At any moment, price in financial exchanges is determined by current orders placed by participants. There is no reason why those should be linked to past purchases in a mechanistic way implied by stock-flow relationship. Also, stock variables evolve, by definition, continuously, and thus cannot jump, while prices jump all the time.

So, the criticism here is that whereas with, say, income the stock rises in lockstep with the accumulation of flows and there are no “jumps” in the case of prices we sometimes see such “jumps”. The latter part of this statement is obvious nonsense and rests on taking too literally the term “flow”. What the commenter was presumably imagining was a bathtub with a tap turned on, and the steady “flow” of the water out of the tap adding to the “stock” of water in the tub.

But this metaphor, taken too literally, can blind us what we’re really dealing with here. In economics they can indeed “jump”. Imagine we have a flow of income that adds $5 to the stock every second. After ten seconds had passed the stock would have risen by $50 in a smooth, flow-like manner. But now let’s say that we alter this and say that $50 are added at every ten second interval. Then we will no longer see the same steady flow dynamic that we saw before and rather we will see what appears to be a “jump” in the stock every ten seconds.

Of course, this is actually an illusion because the second scenario is no more a “jump” than the first scenario, it just appears that way due to our having first conceived of the flow relation as being the accumulation of $5 every second and then later changing the nature of the flow relation.

The second criticism was tied to this and made slightly more sense, but was nevertheless based on another misconception. Here it is:

If asset price was stock variable driven by investment flows, that would mean that whenever I invest 1$ in the asset, the price always goes up by 1$ (or some multiple of it, but always by the same amount). That’s how a stock-flow relationship is defined, and it’s also how financial markets DO NOT work, period.

The ambiguity here is in the brackets. In a Keynesian multiplier stock-flow relationship, for example, the stock will rise by the amount of income times, say, the marginal propensity to consume (MPC). So, say we have a rise in income of $1 and the MPC is 0.2 we will have a total rise in income of $1.20. As the commenter says this is indeed “always the same amount”, but only over a set period.

So, what is the corollary when thinking of price dynamics? Simple. It’s a Marshallian construction called the price elasticity of demand. If a financial asset has a very low price elasticity of demand any buying/selling of this asset will have substantial price effects, while if there is a high price elasticity of demand any buying/selling of this asset will have far less significant price effects.

In marginalist economics, of course, it is thought that there is a negative relationship between, for example, price and quantity demanded. In my framework this is not necessarily true, yet the basic insight in the price elasticity of demand holds nevertheless — if in slightly modified form.

For an excellent real world example of this with reference to the gold market see this post by hedge fund manager Mark Dow.

Thus, if we imagine that we know the price elasticity of demand at any point in time — just as we imagine that we know the MPC in the multiplier relation — we can ensure that there are fixed relations between investment flows and price, as mediated by the price elasticity of demand. Just as the MPC provides the “bridge” between income received and total income in the multiplier relationship, the price elasticity of demand provides the “bridge” between investment flows into a financial asset and the price.

This is, of course, not a very heterodox idea at all, but it seems that some mainstream economists, so used to their downward-sloping demand curves and their efficient markets, have never really thought through in detail how prices work in the real world. But then, that is what my work is trying to remedy. That everyone will tell me that what I am saying is “sooooo obvious” is a given. But I’ve seen too many mistakes and misconceptions to be convinced that what I’m doing is not important; and, ironically, it seems to be those who tell me how banal and unimportant what I’m doing is that could do with being exposed to it the most. But is that not always the case in economics?

Addendum: We can lay this argument out mathematically with reference to the equations we laid out in the last post. The first equation laid out there was as follows:

eq1We can modify this by adding a price elasticity of demand term, d, as follows:1We can then take the second equation we laid out in our previous post, which was:

eq2And we can substitute this in to get:

2Now we can see that if the price elasticity of demand is a larger number, say above 1, then the effects of increased/decreased investment on price will be greater. While if it is a smaller number, say below 1, then the effects of increased/decreased investment on price will be lesser.


About pilkingtonphil

Philip Pilkington is a macroeconomist and investment professional. Writing about all things macro and investment. Views my own.You can follow him on Twitter at @philippilk.
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5 Responses to How Do Stock-Flow Relations Work in Economics and Are They Inappropriate for Price Dynamics?

  1. ivansml says:

    First of all, you still haven’t answered the basic question – why we should be modelling price in stock-flow framework at all. With bathtub, the underlying relationship is given by laws of physics. With debt, it’s given by accounting identities. I don’t see any such underlying theory for prices. In fact, thinking about it a little more, it’s not even clear what these investment flows are – if a supply of security is fixed (reasonable assumption in financial markets in the short run), any flow of investment from buyers will be exactly offset by opposite flow of disinvestment by sellers.

    As for jumps – your bathtub example doesn’t prove anything. *If* I sampled the water level at increasing frequency, the differences would get smaller and smaller – mathematically, the level is a continuous function of time. This is the sense in which there are no jumps. And in fact there is a large literature that analyzes jumps in high-frequency financial data and indeed finds evidence for their presence.

    Still I’m glad you have discovered and found useful the concept of price elasticity, the cutting edge of economic research circa 1890’s. Alfred Marshall would be proud!

    • (1) An investment flow is the same in my theory of prices as in the Keynesian theory of income. It is a money flow. If I buy a security from you then you receive money and I receive the security just like if I buy a machine from you then I receive the capital good and you receive the money. This really is basic stuff.

      (2) I have absolutely no idea what you’re talking about here.

      (3) I didn’t “discover” anything. You didn’t think this through properly and made a very stupid criticism that I had to correct you on by pointing to a very basic component of price theory that is taught at the undergrad level. Yes, this is an old theory; that is why it should have been clear to you when you were trying to criticise.

      • ivansml says:

        (1) So it’s a traded volume? Then I don’t see how you can determine “sign” of the flow. When the demand goes up, there’s a flow of money from buyers to sellers and price goes up. When the demand goes down, there’s again a flow from buyers to sellers (perhaps with their identities reversed compared to previous situation), but now the price goes down. Peculiar theory…

        (3) Obviously I see it in the opposite way. But I don’t think that I have anything else to add, so signing off for now.

      • pilkingtonphil says:

        (1) Assume, for the sake of argument, a fixed quantity in the market. When demand/investment rises the price is bid up. This is a pretty standard economic theory and I don’t think anyone would debate it. If quantity supplied is fixed and demand rises, prices respond. When demand falls sellers find it harder to find buyers and reduce the price. This is, again, pretty basic stuff.

        (3) You see it the “opposite way”? So, that must mean that I made a stupid criticism of your theory that highlighted my poor understanding of basic micro? Hmmm… not sure what universe you’re living in buddy.

    • Sorry, I should clarify.

      (2) I know what you are referring to now regarding price jumps, but I have no idea why it is relevant to what we are discussing.

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