A fecund debate is taking place at Mike Norman Economics, 119 comments in less than two days, about a post on Ramanan’s blog criticising the new and extended definition and justification of Steve Keen’s formula for aggregate demand i.e. AD=Income + delta Debt. The number of comments indicates that either something important has been discovered or a major fallacy is out there.Decisions, Decisions, Decisions
Ramanan Lyer on the Keen Change in AD Function – What Lies Between Identities
Andrew Lainton
22 comments:
http://andrewlainton.wordpress.com/2012/10/09/ramanan-iyer-on-the-keen-change-in-ad-function-what-lies-between-identities/#comment-6865
“Expenditure = Income before debt injection plus debt injection.”
That expresses future period expenditure as a function of prior period income, which is fine as a functional expression.
But he should make that time sequence clear in his equation notation. It is Steve who has confused ex post and ex ante in his existing equation.
And that functional expression is certainly nothing like an accounting identity, for a host of reasons that have already been discussed.
"Because we are used to dealing with discrete time and fallaciously treat accounting identities as true at every point in time ..."
Nonsense. They ARE true at every point in time, unless you apply inconsistent and illogical time sequencing to the time period under consideration. You cover at least two different accounting periods with Steve's equation. But you don't specify that. Just specify it and you're OK as far as that aspect is concerned.
And accounting identities don't just apply to the past; they constrain feasible future outcomes.
"the ‘mystery’ of profits also needs explanations"
No mystery. It's all taken care of by proper equity accounting.
Etc. and on and on like that ...
"In [keens] models, loans are taken to purchase financial assets. I don’t know how that “adds to demand”.
To which Kis Rosberg perfectly replies
The sellers of these assets buy goods and services."
I would point out that the Fed has purchased large amounts of financial assets under the QEs, not with "debt" I guess per se but with new reserve balances.... but I dont think MMT thinks that the Fed doing this under the QEs has worked to increase AD...
rsp,
What an equally muddled post this was. In the post Lainton writes as if ΔFA ≡ ΔD is not true or something for an economy as a whole!
Matt,
Yeah some "QE" intuition there. If Lainton's argument is true on what you quote that logic should be true for QE as well.
In the Keen-Krugman debate, Krugman pointed out that Keen's notion is something like creating money is creating demand or something like that. I think he seems to have been right.
JKH,
Yes it is Keen who is confusing ex post and ex ante!
"Ramamam seems to be accusing Keen of confusing consumption (which does not include purchase of financial assets) with investment (which does). "
Investment (I) includes purchases of financial assets??
" In fact Keen extends the standard Y=C+I identity to Y=C+I+A where A = Assets, of all kinds. I take this as splitting the I element into net income from investment (which contra to Keen is the total of all factor returns from investment in retained assets not simply capital goods – easy danger of a capital theory slip up here) and net income from asset sales and purchases."
Whatever :-)
Right, Ram.
And there's absolutely no issue of substance here regarding the difference between discrete time and continuous time.
To suggest otherwise is to confuse continuous time with mathematically continuous accounting events. The former is conceivable. The latter is not.
The analytic infrastructure for accounting logic is premised on the reality that accounting events are recorded discretely, within discrete accounting periods.
JKH: "And there's absolutely no issue of substance here regarding the difference between discrete time and continuous time.
To suggest otherwise is to confuse continuous time with mathematically continuous accounting events. The former is conceivable. The latter is not."
Yes exactly.
In fact discrete time is much more convenient given accounting events happen discretely and haphazardly such as paychecks at the end of the month and shopping.
JKH
"there's absolutely no issue of substance here regarding the difference between discrete time and continuous time" (etc)
You should post this comment over at Lainton's blog.
One thing that strikes me is that Andrew Lainton hasn’t quite got Steve Keen’s expression right. It’s not AD = Y + deltaDebt, but AD = Y + dDebt/dt. In other words, aggregate demand is equal to income plus the change in debt per unit of time. So income and debt have different units: the former, in dollars; the latter, in dollars per accounting period. My question: when you add them together, what units does the resulting sum have—dollars, dollars per year (for e.g.), or something else?
vim,
That is not stock/flow consistent...
rsp,
vimothy,
From a dimensional analysis perspective one can't spot the error.
Even though we say income is some $15T in 2011, it actually means $15T per year. Debt doesn't have a time dimension, so dD/dt has the dimension of per year or per sec (whichever one chooses).
vimothy,
where does he say AD = Y + dDebt/dt ?
http://www.math.mcmaster.ca/~grasselli/KeenGrasselli2012EuropeanDisunionAndEndogenousMoneyFinal.pdf
Ram,
GDP is presumably flow over a year or a quarter, but dD/dt is an instantaneous rate of change. To add it to GDP, I think it ought to be the change in debt over the same period that GDP is measured in. Or is GDP also supposed to be an instantaneous rate of change?
Y,
It's on the video he did. Also in that paper, e.g., equation 1.13.
Vimothy,
I think I know where you are headed, so here is a thought on Keen:
The trouble with using differential equation is that in real world all transactions are happening discontinuously and suddenly however big the economy is.
So a model has to assume a smooth effect in spending, borrowing etc.
But if one wants to describe the model in words, one has to use spikey transactions. Keen uses a spike for debt but forgets that expenditure is also spikey.
So Keen and Grasselli confuse the differential equation treatment as well! (even though they hint that others think in intervals, time period etc and its other who confuse and not them is their hint)
A continuous time formulation is just taking infinitesimal intervals and then treating infinite of them together.
But if we want to treat debt injections as discontinuities, we should also treat income/expenditure flows as discontinuous. Shops close at night.
It makes no sense to say income before debt injection was $100 for real world transactions in a continuous time formulation. It is actually zero just before a debt injection because all income/expenditure flows are spikey.
Just after the debt injection also it is zero because nobody spends the instant a loan is given. The debt inject increases assets and liabilities by the amount of the loan if the borrowing is from a bank.
So after the loan is given at the next infinitesimal, change in debt is zero and income/expenditure is also zero.
Then income/expenditure flow spikes at the moment the transaction happens.
But that is income for someone and for an economy as a whole Income = Expenditure.
Funny, his coauthor is a mathematician from the Fields Institute.
And if you are curious in mathematics, there is a thing called the Dirac Delta Function.
[Paul Dirac didn't get the media attention that Einstein got but he was surely his equivalent. The Delta function is just a small contribution when compared to what he did elsewhere. He was Feynman's hero.]
The delta function δ(x) is zero at all points except 0 where it is infinite. But the integral of δ(x) from over the range of real numbers is 1. That is difficult to digest initially.
A debt injection is a step function jump in debt. The delta function has a curious property that it is the derivative of the step function.
So income flows can be represented as sum of delta functions which different coefficients at different points in time.
So Keen's chart is all wrong.
To get the flow over a period, one has to integrate and this will result in the income over the period to be the sum of the coefficients of these delta functions.
"Lebesgue" is just a showoff :-)
So whether in discrete formulation or continuous time formulation,
Y_E = Y_I
for the whole economy and the reason is not hard to guess because
dD/dt cancels out with dA/dt since assets and liabilities are created equally.
For an individual sector it is true that Y_E = Y_I + dD/dt (but nobody disagrees with that).
Anyway, nothing of his analysis justifies the definition of "aggregate demand" (now renamed by Keen to "effective demand").
Ramanan,
I'll see your appeal to Lebesgue integration
and raise that to Dirac Delta
:)
(BTW, I'm impressed)
:-)
Thanks.
Appeal to Paul Adrien Maurice Dirac!
A now, a brief intermission for some humanity:
Personality
Dirac was known among his colleagues for his precise and taciturn nature. His colleagues in Cambridge jokingly defined a unit of a dirac, which was one word per hour.When Niels Bohr complained that he did not know how to finish a sentence in a scientific article he was writing, Dirac replied, "I was taught at school never to start a sentence without knowing the end of it." He criticized the physicist J. Robert Oppenheimer's interest in poetry: "The aim of science is to make difficult things understandable in a simpler way; the aim of poetry is to state simple things in an incomprehensible way. The two are incompatible."
Dirac himself wrote in his diary during his postgraduate years that he concentrated solely on his research, and stopped only on Sunday, when he took long strolls alone.
An anecdote recounted in a review of the 2009 biography tells of Werner Heisenberg and Dirac sailing on a cruise ship to a conference in Japan in August 1929. "Both still in their twenties, and unmarried, they made an odd couple. Heisenberg was a ladies' man who constantly flirted and danced, while Dirac—'an Edwardian geek', as [biographer] Graham Farmelo puts it—suffered agonies if forced into any kind of socialising or small talk. 'Why do you dance?' Dirac asked his companion. 'When there are nice girls, it is a pleasure,' Heisenberg replied. Dirac pondered this notion, then blurted out: 'But, Heisenberg, how do you know beforehand that the girls are nice?'"
According to a story told in different versions, a friend or student visited Dirac, not knowing of his marriage. Noticing the visitor's surprise at seeing an attractive woman in the house, Dirac said, "This is... this is Wigner's sister". Margit Dirac told both George Gamow and Anton Capri in the 1960s that her husband had actually said, "Allow me to present Wigner's sister, who is now my wife."
Another story told of Dirac is that when he first met the young Richard Feynman at a conference, he said after a long silence "I have an equation. Do you have one too?".
Dirac was also noted for his personal modesty. He called the equation for the time evolution of a quantum-mechanical operator, which he was the first to write down, the "Heisenberg equation of motion". Most physicists speak of Fermi-Dirac statistics for half-integer-spin particles and Bose-Einstein statistics for integer-spin particles. While lecturing later in life, Dirac always insisted on calling the former "Fermi statistics". He referred to the latter as "Einstein statistics" for reasons, he explained, of "symmetry".
Poor Dirac. Mathematicians are often imbalanced.
He he.
Heisenberg being good with girls is surprising given his uncertainty principle: I thought when he found the position he lost momentum and when found momentum, he lost the position.
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