Maybe this adds to the discussion: The identity approach would imply that the measures of GDP and GDI would have not only the same value, but the same errors — the measured data from which GDI was constructed would be exactly the measured data from which GDP is constructed if it is an identity. The equilibrium condition approach allows them to have independent errors, since they aren’t constructed from the exact same measurements.

In the former case (constructed from same measurements) there is no content (empirical or theoretical), in the latter there is:

]]>“Suppose we accept the theory version of MV = PY. Then you need to model M, V and the discrepancy. In the identity version you just have to model M and V, to explain NGDP.”

Forgive me, but I don’t understand this at all. If I have a monetary theory of NGDP — and, despite your disclaimer, I believe that you do, as well — I am saying that NGDP in some loose sense are causally related to M and V, so that if I can know or can predict what happens to M and V, I can predict (approximately) what will happen to NGDP. My theory of NGDP may be right or wrong (or somewhere in between), but it has empirical content. It could be refuted by the observed movements of M, V and NGDP. So it has some explanatory power.

But if all you are working with is the identity that MV is equal, by definition, to NGDP, you have no basis for making any causal inference about NGDP from changes in M or V. No possible observation could ever refute the identity, because V is defined as NGDP divided by M.

In a monetary theory of NGDP, V is modeled. In the MV = PY identity, V is not modeled; it is a residual.

Milton Friedman would be spinning in his grave if he could hear you saying that. The idea that making a MV=PY an irrefutable identity rather than a refutable theory with empirical content would have flabbergasted him. (Actually, I am kind of flabbergasted, myself, at the thought that I am invoking Friedman to make a point in a disagreement with you. What is this world coming to?)

You said:

“GDI = GDP is also viewed as an identity–at least that’s how I’ve always seen it presented. And the reason is simple, if S=I is an identity, then ipso facto C + S = C + I is also an identity.”

Actually, I think the derivation usually goes in the other direction. GDI and GDP (alternatively E and Y) are defined to be always equal, and the identity of savings and investment follows from the ncome-expenditure identity. But that’s just a quibble. The substantive point is that in the identity approach, I and S are not treated as independently measurable quantities, so the theory has no empirical content. There is no way any prediction about I or S or E or Y could ever be refuted, just as the quantity identity cannot be refuted if V is treated as a residual rather than as an independently observable and measurable magnitude.

]]>As far as I know GDI = GDP is also viewed as an identity–at least that’s how I’ve always seen it presented. And the reason is simple, if S=I is an identity, then ipso facto C + S = C + I is also an identity.

]]>You say that you agree that savings and investment are not the same thing, but assert that they must have the same numerical value. I am not sure how to interpret that. One dollar and one hundred cents are not the same thing, but they do necessarily have the same value. In your view is the identity between savings and investment of the same character as the identity between one dollar and one hundred cents? If not, how would you characterize the difference?

Obviously A = B allows A and B to be different, but we are talking about A ≡ B, not A = B. The question is whether the investment and saving are potentially different, but equal in equilibrium, or whether they are identically equal so that there is no possible state of affairs in which they are not equal.

In a system of simultaneous equations, the only possible solution occurs at the point of intersection of all the lines. No other point is viable as a solution. That doesn’t mean that the lines have no meaning anywhere except at the point of intersection.

Scott, I don’t believe that I have ever seen savings defined as “funds spent on investment.” Saving is usually defined as “unspent income.” The question is how is it that unspent income winds up being identically equal to “funds spent on investment.” As far as I can tell “funds spent on investment” is the definition of investment. Now in the world of microeconomics, we do say that purchases are identical with sales. That is because there is an identity between purchases and sales that is implied by the definitions of purchase and sale, which are reciprocal activities. So it would make sense to say that if you explain the changes in purchases you have ipso facto explained the changes in sales. But certainly that would not be the same as saying that if you explain the change in quantity demanded you have explained the change in quantity supplied. I would hope you would agree that explaining the change in quantity demanded does not explain the change in quantity supplied. But I don’t believe that most people (or most economists) believe that the equality between investment and savings is directly entailed by the definition of either saving or investing in the same way that equality between purchases and sales is entailed by the definition of purchasing and selling.

]]>I never, ever, make that sort of idiotic argument. Instead I argue that IF, and I emphasize IF, you define S and I to be equal, by defining S to be the funds spent on investment, then any explanation of changes in S is, ipso facto, an explanation of changes in I. I can’t imagine anyone disagreeing with that proposition. It’s logic 101.

I can understand someone claiming that S=I is not a useful definition, that they’d prefer not to define them in such a way that they are equal, and that seems to be your position. That’s fine. If we define saving as you prefer, then any explanation of a change in savings is NOT an explanation of a change in investment. Again, that’s logic 101.

]]>Given my particular interest in your approach to your subject in this series (I imagine not many do approach it), I appreciate your patience with so many comments. And I look forward to your next post in the series.

It seems very reasonable that physical conversation laws cannot be violated.

I agree investment and saving are not the same thing and have also said so a number of times in my comments.

But in a coherent (macroeconomic) accounting framework, the quantity of investment must the same as the quantity of saving. This holds for realized outcomes ex post and FEASIBLE planned outcomes ex ante. In other words, viable ex ante forecasts are constrained by the same accounting identities that measure realized ex post outcomes.

This also goes to the very meaning of algebra.

A = B does not mean that A and B are the same thing in algebra. It means they are different things that feature the same numerical measure in context. I’m surprised this is coming up as a point.

I agree there is no reason to believe that planned saving and planned investment are equal, but I think this is best qualified in the sense of aggregating up individual plans.

I disagree that you can’t just invoke an accounting identity to explain how it is that realized investment and realized saving are always equal. This is the consequence of a coherent accounting framework.

I agree that the algebraic equation that relates planned expenditure to income is a line, but there is only one point on that line that is realizable, which is the point on the 45 degree line. That planned expenditure line has to shift (i.e. change) for other points on the 45 degree line to be realizable. And that is a contradiction in terms of the alleged range of applicability of the given line. So the line is a non-line in terms of viable outcomes for actual expenditure and income. The line must itself change (i.e. shift) to achieve any other outcome.

I personally believe that macroeconomics requires coherent accounting foundations, and that business and household accounting need to be consistent from a macroeconomic application perspective. There is no reason why this can’t be achieved. Whether households view their own accounting framework in quite the same way as a coherent macroeconomic framework is a second order concern. That sort of disparity can be wrapped up into a behavioral model. But it shouldn’t be confused with the required integrity of accounting foundations for measuring outcomes for the entire economy.

A parameter change changes the expenditure “line”. The planned expenditure line will drop with a reduction in “aggregate demand”. This is a new line. That has the likely effect of pulling down actual expenditure as you point out in your inventory accumulation example I believe. But the effect occurs on the 45 degree line. It can’t be anywhere else. The visible “gap” between the two lines that is intended to portray inventory accumulation does not correspond to any realized point away from the 45 degree line – because there are no such points. Moreover, that static gap portrayal does not capture the dynamic which overtakes it – which is that of rolling down the 45 degree line instead of remaining in such a depicted state of inventory accumulation.

My own interpretation of that quote from Scott S as you state it: I see no problem. That’s just explaining the outcome of a model whose feasible outcomes are properly vetted by required accounting identities. That doesn’t mean reasoning from an accounting identity. It means explaining a model outcome in total that happens to be coherent and therefore feasible with respect to accounting foundations. Big difference.

Perhaps one may view accounting identities as laws of mathematical conservation.

]]>You are free to interpret the algebraic equation that relates expenditure to income as a point if you like, but you have provided no mathematical or economic basis for doing so. The equation clearly defines a line not a point.

I don’t say that accountants can’t consistently define income, I’m just saying that for purposes of a theory of income and how it changes, the categories of national income accounting may not be the most useful way of formulating a theory. The way that a business firm defines income is not necessarily the way that a household determines what its income is. The household may only consider income to be received when the payment is actually made.

Scott, I’m sorry if I have misrepresented your position:

Explain to me please what you meant by this statement on your econolog blog which got me started on this series of posts:

In the standard national income accounting, gross domestic income equals gross domestic output. In the simplest model of all (with no government or trade) you have the following identity:

NGDI = C + S = C + I = NGDP (it also applies to RGDI and RGDP)

Because these two variables are identical, any model that explains one will, ipso facto, explain the other.

Rob, I prefer not to assume that savings and investment are both different words for “that part of output that is not consumer in the current period.” That is a fine definition of investment, but the people who decide how much to save are deciding how much of their disposable income not to consume in the current period. In deciding how much of their income they plan not to consume, they have no idea what total output is going to be.

JKH, The expenditure function is a notional construct. Just because only one point on the function corresponds to the actual solution of the model does not mean that the function is meaningless except at the point of intersection with the 45-degree line. If that were the case, how could you talk about the effect of a parameter change on equilibrium?

Rob, See my next post, which I am about to post.

Min, Conservation laws are identities because they embody an assumption about how the world works, namely you can’t create something out of nothing. The identity follows from the assumption about how the world works. Accounting identities may also embody some deeper assumption about how the world works, for example purchases equal sales, but it is not clear to me that the savings equals investment identity is an identity of that character.

]]>When Lipsey says, “The main issue in this whole discussion is, I think, can we use a definitional identity to rule out an imaginable state of the universe. The answer is “No”, which is why Keynes was wrong,” he is mistaken. In fact, identities eliminate almost all imaginable states of the universe.

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