I'm taking a break from all economics/finance/accounting-related activities (blogging included) tonight to attend the opening ceremony for the inaugural Fields Medal Symposium, which celebrates the work of a recent Fields medalist each year, right here at the Fields Institute.

This year's symposium is dedicated to Ngo Bao Chau and you can watch his public lecture from 7:00pm onwards by following the link provided in the website above (his lecture will actually start a bit later, after the ceremonial speeches by a string of dignitaries, but if you tune in at 7:00 you can catch a glimpse of yours truly, sitting beside Ngo on the second row of the theatre and looking totally starstruck).

## Monday, October 15, 2012

## Saturday, October 13, 2012

### Of course it's a model, duh! A final post on income, expenditure, and endogenous money

Many comments on the different threads related to Ramanan's critique of my paper with Steve Keen amount to saying that if we were trying to write down some kind of model for a perceived phenomenon (in this case the role of private debt in macroeconomics), then it would be ok, but because we violated an accounting identity (or more) in the process, oh boy, we have been very very naughty indeed.

The thing is, we never claimed to be doing any accounting, let alone violating it. Accounting is about recording stuff during a given period (a year, a month, a day, but NOT an instant, since you need to wait for stuff to happen to record it) and in the only part in the paper where we mention any recording (Appendix, page 24, last paragraph of the paper) we say that "recorded expenditure and income over a finite period (t2 − t1 ), such as those found in NIPA tables, necessarily agree".

So I'll say this again in a separate line and in capital for emphasis (with some superlatives in bracket, as commenters like):

RECORDED EXPENDITURE AND INCOME OVER A FINITE PERIOD NECESSARILY AGREE (*always, toujour, siempre*) !!!

Now suppose you read income statements for an economy months after months, year after year, and wonder why recorded spending (= recorded income !!) for the different periods happen to be different. You might think it has something to do with the Mayan calendar, or with the incidence of flu during that period, or maybe that it's completely random. If you are an economist you might want to explain it with a DSGE model that ignore private debt. Heck you might even write down a regression model that includes the change in private debt in one period as an explanatory variable for the spending (= income !!) to be recorded over the next period, as one commenter suggests. Or if you are Steve Keen you write down a model using differential equations, because they happen to be tractable and cool and predict many properties that sort of look like what goes on in real life. But none of that is accounting - all of it is modelling.

Everything else we wrote in the paper was with the view of explaining why the heck recorded spending (= recorded income !!) changes from year to year. If along the way we wrote stuff down that looked like a violation of an accounting identity, then I profusely apologize for it (in fact I already bought a whip to punish myself) and pinky-promise never to do it again. So will the accounting police chill out and move on? Unless you actually care about the model, in which case please read on.

As far as the model goes, what we are trying to capture is Minsky's assertion that "for real aggregate demand to be increasing, . . . it is necessary that current spending plans, summed over all sectors, be greater than current received income and that some market technique exist by which aggregate spending in excess of aggregate anticipated income can be financed."

So our Y_E represent "current spending plans" (per unit of time) and our Y_I represent "current received income" (per unit of time). Equation 1.5 in the paper is the key behavioural assumption that links investment to change of debt, and is a schematic representation of the mechanism that both Steve and I have in the back of our minds, what I call the "Keen model" described in this paper, where investment (the rate of change in capital) is a function of current net profits, but can exceed profits in times of boom and therefore be financed by debt.

All of this is pure modelling: in reality nobody looks at a differential equation before spending. The true test of the model is to see if it predicts the right behaviour for the key variables (employment rate, wage share, output, level of private debt, etc) over time, once the parameters of the several structural equations are calibrated using historical data (which includes income and flow of funds statements over many periods).

As a final word, notice that neither Y_E nor Y_I are meant to represent recorded expenditure or income over a period anywhere in the paper (which again, are necessarily equal !!). Both are modelling abstractions of what goes on in the economy and could include stuff like the Mayan calendar and incidence of flu, but happen to depend on the level of private debt.

The thing is, we never claimed to be doing any accounting, let alone violating it. Accounting is about recording stuff during a given period (a year, a month, a day, but NOT an instant, since you need to wait for stuff to happen to record it) and in the only part in the paper where we mention any recording (Appendix, page 24, last paragraph of the paper) we say that "recorded expenditure and income over a finite period (t2 − t1 ), such as those found in NIPA tables, necessarily agree".

So I'll say this again in a separate line and in capital for emphasis (with some superlatives in bracket, as commenters like):

RECORDED EXPENDITURE AND INCOME OVER A FINITE PERIOD NECESSARILY AGREE (*always, toujour, siempre*) !!!

Now suppose you read income statements for an economy months after months, year after year, and wonder why recorded spending (= recorded income !!) for the different periods happen to be different. You might think it has something to do with the Mayan calendar, or with the incidence of flu during that period, or maybe that it's completely random. If you are an economist you might want to explain it with a DSGE model that ignore private debt. Heck you might even write down a regression model that includes the change in private debt in one period as an explanatory variable for the spending (= income !!) to be recorded over the next period, as one commenter suggests. Or if you are Steve Keen you write down a model using differential equations, because they happen to be tractable and cool and predict many properties that sort of look like what goes on in real life. But none of that is accounting - all of it is modelling.

Everything else we wrote in the paper was with the view of explaining why the heck recorded spending (= recorded income !!) changes from year to year. If along the way we wrote stuff down that looked like a violation of an accounting identity, then I profusely apologize for it (in fact I already bought a whip to punish myself) and pinky-promise never to do it again. So will the accounting police chill out and move on? Unless you actually care about the model, in which case please read on.

As far as the model goes, what we are trying to capture is Minsky's assertion that "for real aggregate demand to be increasing, . . . it is necessary that current spending plans, summed over all sectors, be greater than current received income and that some market technique exist by which aggregate spending in excess of aggregate anticipated income can be financed."

So our Y_E represent "current spending plans" (per unit of time) and our Y_I represent "current received income" (per unit of time). Equation 1.5 in the paper is the key behavioural assumption that links investment to change of debt, and is a schematic representation of the mechanism that both Steve and I have in the back of our minds, what I call the "Keen model" described in this paper, where investment (the rate of change in capital) is a function of current net profits, but can exceed profits in times of boom and therefore be financed by debt.

All of this is pure modelling: in reality nobody looks at a differential equation before spending. The true test of the model is to see if it predicts the right behaviour for the key variables (employment rate, wage share, output, level of private debt, etc) over time, once the parameters of the several structural equations are calibrated using historical data (which includes income and flow of funds statements over many periods).

As a final word, notice that neither Y_E nor Y_I are meant to represent recorded expenditure or income over a period anywhere in the paper (which again, are necessarily equal !!). Both are modelling abstractions of what goes on in the economy and could include stuff like the Mayan calendar and incidence of flu, but happen to depend on the level of private debt.

## Friday, October 12, 2012

### More on income, expenditure, and endogenous money - a non-vacuous response

A reader of Mike Norman's very useful blog calls my last post a vacuous response to Ramanan. Of course it was not a response at all, merely a commentary. Notice how I said that "all the criticisms can be defended in two words: endogenous money!", not that they were defended... Plus I thought it implicit that whenever one says something like "I got n words for you: word_1 ... word_n", one's tongue is firmly in one's cheek. But I'm quickly learning that there is no such thing in the econo-blogosphere.

In any event, after the avalanche of comments on Mike's re-posts (last count: 21 on the post above, 66 on Ramanan's second take down, and 124 on its predecessor), perhaps it's time for a point-by-point reply (I originally called it a "point-by-pint" reply, which is perhaps a measure of what was on my mind while I was writing it).

Let me start by saying that I'll refer mostly to this paper, since I had something to do with the notation and ideas presented in it, rather than to Steve's presentation at the UMKC conference, thought I might occasionally refer to it too. Let me also say that said paper (which is being refereed and therefore can sill improve quite a lot), could use a great deal of clarifications. Many of the ideas that were in the back of our minds as we were writing it clearly didn't make it to the printed page, so I welcome the opportunity to elaborate.

With these in mind, here are the essential points:

(1) Our "closed" economy does consist of firms, households, and banks, but we find it useful to

**separate the banking sector from the rest of the private sector**. We do this explicitly on pages 18 to 23, but leave it implicit on page 15, which contains the passages that Ramanan has a beef with. So our "change in debt" is really change in debt of the non-bank private sector to the banking sector, which obviously does not need to cancel out in the aggregate (i.e excluding banks). This is in contrast with the view that "one person's asset is another person's liability", which underlines the view that firm's debt is mirrored by household's savings.

(2)

**Debt only matter after it has been spent**. This is the point of equation (1.5): we assume that investment is financed by retained earnings plus change in debt. If new debt is not spent, it doesn't finance anything, so we don't count it in the model.

(3)

**Accounting rules!**The whole point of the Appendix in the paper is to show that recorded income equals recorded expenditure at the end of a given period (say one year). We don't use continuous mathematics to upset accounting identities, but rather as "a simple way to represent the conceptual difference between spending plans and current received income".

Observe that all 3 points are intimately connected with the idea of endogenous money, which is what I meant by my "two words" zinger. The effects of endogenous money only become apparent when banks are disaggregated from the rest of the private sector (1), capitalists finance new investment above and beyond savings by creating deposits through endogenous money (2), and spending plans exceed current received income for the same reason, even if this is not apparent when one measures recorded income and recorded expenditure (3).

In the end, what we are tying to capture is the idea expressed on page 10, namely that "the essence of endogenous money hypothesis is that banks create spending power for borrowers without reducing the spending power of savers."

Judging by the criticism, we haven't quite succeeded yet, but we'll keep on trying.

## Thursday, October 11, 2012

### Income, expenditure, and endogenous money

My supervisor Ray Streater used to quote an example of a physicist's version of proof by

I was reminded of that as I read this take down of my paper with Steve Keen, where we claim that expenditure is income plus change in debt. In an attempt to show that we are wrong, Ramanan shows that our model violates the "savings equals investment" identity. What an absurd!

Hmm, actually, not only this is not an "inconsistency" of the model (we never claim that this was true, or rely on it to show anything else in the paper), but it is rather essential: in our model, investment is equal to savings plus change in debt. This is the essence of equation (1.5) in the paper, and we were always acutely aware of it.

So much for the rather bombastic conclusion that we must be wrong because we violate the sacrosantity of "savings = investment" -- this is a feature of the model, not a bug!

Having said that, it is nevertheless a feature that ought to be defended, together with the other criticisms raised in both the take down mentioned above and its predecessor.

As it turns out, without engaging in a point-by-pint reply (which would be a very boring read for anyone not called Grasselli, Keen, or Ramanan), it suffices to say that all the criticisms can be defended in two words: endogenous money!

*reductio ad absurdum*that goes more or less like this: "Assume that asymptotic completeness doesn't hold in quantum field theory. What an absurd!"I was reminded of that as I read this take down of my paper with Steve Keen, where we claim that expenditure is income plus change in debt. In an attempt to show that we are wrong, Ramanan shows that our model violates the "savings equals investment" identity. What an absurd!

Hmm, actually, not only this is not an "inconsistency" of the model (we never claim that this was true, or rely on it to show anything else in the paper), but it is rather essential: in our model, investment is equal to savings plus change in debt. This is the essence of equation (1.5) in the paper, and we were always acutely aware of it.

So much for the rather bombastic conclusion that we must be wrong because we violate the sacrosantity of "savings = investment" -- this is a feature of the model, not a bug!

Having said that, it is nevertheless a feature that ought to be defended, together with the other criticisms raised in both the take down mentioned above and its predecessor.

As it turns out, without engaging in a point-by-pint reply (which would be a very boring read for anyone not called Grasselli, Keen, or Ramanan), it suffices to say that all the criticisms can be defended in two words: endogenous money!

## Tuesday, October 2, 2012

### Further thoughts on mathematics and economics

After almost 3 years of blogging to a reduced audience, I observed a sudden spike in my stats after my post about the UMKC conference got re-blogged (or re--tweeted, who knows) in the legendarily active econo blogosphere. So I thought I should ride the wave and elaborate on my remarks.

First of all, as pointed out by a commenter, I only attended the last day of the conference, which according to the unwritten laws of scheduling was

bound to be the least exciting (especially on a Saturday!). I guess I should expect that - after all that was the spot on the schedule reserved for me... But still,

after being blown away by the vibrance and intellectual rigour of the likes of Stephanie Kelton and Scott Fulwiller when I met them at Fields a few months ago, I had great

expectations about the event, and was disappointed to find out that most of the people I wanted to meet had already left (his lordship notwithstanding).

But on a more substantive note, I see from the comments (here and elsewhere), that the role of mathematics in economics is a bit of a raw nerve, hence the urge to elaborate.

Despite being a mathematician, I do not think that mathematical modelling is the most important part of economics, but I do think that it is somewhat essential. Here I'm reminded of the famous

saying that "logic is to mathematics what hygiene is to life: it's clearly essential, but not what it's all about". The same goes for mathematics and economics: historical awareness, acute observations, and empirical plausibility come first in economic reasoning, but I don't see how much progress can be made without mathematics. Notice that this is not about pedagogy, but about being able to even formulate crucial statements.

To borrow from other fields, it would be nearly impossible to even conceptualize something like the basic reproductive number in epidemiology without a mathematical model, and this means the difference between being able to handle a pandemic or not. For another example, no amount of analogy or logical thinking can pinpoint the phenomenon of bifurcations. The fact that smooth changes in some underlying parameter can cause a system to completely change its qualitative behaviour is not something that is predicated by logic and hard thinking alone - it needs mathematics. Needless to say, the list could go on and on.

Finally, just in case you associate mathematics too heavily with neoclassical economics, remember that the final blow to general equilibrium was dealt by a mathematical result: the SMD theorems essentially tell us that the whole framework (and much of neoclassical economics with it) is only guaranteed to work for the trivial case of one agent and one good.

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