Matheus clarifies.
Quantitative Finance: Foundations and Applications
Of course it's a model, duh! A final post on income, expenditure, and endogenous money
Matheus Grasselli | Associate Professor and Sharcnet Chair in Financial Mathematics working with the PhiMac group in the Department of Mathematics and Statistics at McMaster University, currently Deputy Director at the Fields Institute
Here is his previous post, which had not yet been link to here at MNE through an oversight on my part.
More on income, expenditure, and endogenous money - a non-vacuous response
Matheus Grasselli
I am not in a position to speak authoritatively on this matter, but it seems to me that everyone involved is on same side, and trying to get the Keen-Minsky model sharpened for debate with the real opponents. The people who are experienced in finance and accounting as simply trying to clear up areas that don't seem to them to be stock-flow consistent, which is a major objection to mainstream models. So let's all work together to test the strengthen and keenness (no pun intended) of this blade before it is used in combat.
6 comments:
Unfortunately, the claim that their model respects the equality of recorded income and recorded expenditure is incorrect - as in if one is extra careful, anyone can see that their model does not produce an equality.
The appeal to Lebesgue doesn't work.
how's that Ramanan? (I'm 'anyone' so I should be able to get it :)
They only get an identity Ye=Yi if debt incurred over the period is... zero. In other words their model is accounting consistent only if they turn it off. Either the integral of dD is zero or not. If it is, there is no model (but they get accounting consistency), if it isn't - the model is accounting inconsistent. As simple as that.
There is a fuller exchange between PeterP, Ramanan and myself on the comments for this post on my blog for anyone who is interested, but the gist of it is that \Delta D(t) is the change in debt at time t, which is finite and occurs at just one point. No need to invoke Dirac deltas or anything of the sort, since we are not talking about the rate of change in debt.
So the change in debt over the period IS non zero and also does NOT affect the integral. We even put a picture there to explain it for heavens sake.
Recall that this whole thing
started with Ramanan saying that we violated accounting identities (we didn't!), then moved to us making a mathematical error because of Dirac deltas and what not (we didn't), and now rests on us modelling debt injections as jumps and income as continuous flows (we did!).
Now you might say that the model stinks because you disagree with which variables should be continuous or not, but that is a heck of a lot weaker than saying it is inconsistent with accounting or mathematically wrong.
Matheus,
The claim that many of your equations do not satisfy accounting relations is still there.
From the ones where saving over the whole economy doesn't equal investment to the same old income-expenditure discussion.
Income minus Expenditure cannot be both zero and change in debt at the same time unless the change in debt is zero.
And as PeterP says, you do not need intergals to check the accounting: can you invent a transaction in which income is not equal to expenditure?
It is true for a sector that income can be different from expenditure but not true for the economy, but you have equations which are not consistent with the latter.
The point is that you hold contradictory beliefs which makes the approach paradoxical. You have both A and not A.
You can dodge by claiming that these are ex ante and ex post, but have different variables for them - you cannot have the same variable describing two different things.
But there are more paradoxes.
In the later model, your definition of expenditure is different! You include purchases of financial assets in your expenditure (actually you include purchases of assets - which is double counting since "I" is already included).
Now with this new definition, if I were to repeat your proof using the integrals, the conclusions shouldn't change and income = expenditure ex-post. But this shouldn't be so since the new definition of expenditure includes purchases of financial assets.
fight! fight! fight!
(clueless non-math rube looks on in bemused amazement)
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