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.