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]]>Of course, I’ve been saying the problem is definitional for almost three months now. https://uneasymoney.com/2012/01/31/krugman-on-mistaken-identities/#comment-4063

So I don’t expect much, but I do appreciate the confirmation that I’m not out of my mind here.

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]]>My notation in this comment is as follows.

Y, C, I, S are defined as GDP versions (i.e. national income accounting definition)

David Glasner’s versions are indicated as Ydg, Cdg, … etc, when you declare your own definitions.

For “definition” and “identity”, I’ve invented some unusual notations, “=d=” and “=i=”.

A =d= B indicate A is defined as B

A =i= B indicate A = B is an identity.

Note, A =d= B implies A =i= B, but the converse is not always true.

First, let’s look at the definition structure of GDP version variable-system.

Y =d= measured in real world (according to the GDP rule book)

C =d= measured in real world (according to the GDP rule book)

I =d= Y – C

S =d= Y – C

They (GDP officers?) may do some measurements for I and S, but their aim is to re-produce the value of Y -C, so these are essentially the definitions.

It is clear by definition that

Y =i= C + I

I =i= S

No issue so far, I think.

This is some kind of an observation system. We have dedicated variable-system for this purpose such as Y, C and I. Values of some variables come from the real world. We process them according to the definitions of other variables to get their values. In a sense, this variable system is driven by real-world-born figures. With this device we can observe the dynamics of some real world phenomenon. We have concrete definitions for the figures that come from real-world. That concrete definitions are the variable-system’s link to the real-world. Without them the variable system is just an abstract mathematical structure.

Once this statistical or empirical variable system is established, you can think of a model version of it. You can develop models for Y and C. This means that basically what you try to modelize are “come from realty”-parts (with your interpretation of real-world dynamics in mind). Other part is just a mathematical structure. Of course, you can re-define the mathematical part, but you better do this while you stay with empirical version. Because re-define the mathematical part without empirical meaning can be dangerous, it is likely that you will be not so sure about the meaning of the re-defined variables.

When you substitute model-Y and model-C to the variable system, you have models of I or S. Now, the variable-system is driven by the model output.

Note it is important to realize that you have to proceed in the order of “real-world-based-definitions first, model next”. You can’t develop a model if you don’t know what kind of phenomenon to be approximated (or described, mimicked) by the model.

Even if you change the definitions of Y and C (different measurements in the real world or output of some models), as long as you keep the definition structure (i.e. values of Y and C come from somewhere, I and S are calculated according to the definitions),

Y =i= C + I

I =i= S

still hold. So, these identities are “inherent” while you stay in this variable-definition-structure.

Next, let’s look at your model. Based on the available comments so far, it seems

Idg =d= measured in real world (spending by business firms on final output)

Edg =d= C + Idg (As for C, I reckon you are satisfied with the GDP version.)

Sdg =d= “defined in a way that is in accord with the income expenditure model”

Ydg =d= C + Sdg

( You said that “Y” = “C” + “S” is an identity in your version, and

you want to use C and Sdg as “C” and “S”, then “Y” can’t be the GDP

version any more.)

I see a problem here. You broke the rule of “real-world-based-definitions first, model next”. You should define Sdg in “measured in real world”-style first. After that you can talk about models. Otherwise no one can understand the meaning of your model.

You need an explicit real-world type definition (to clarify the differences between your version and the GDP version explicitly is enough). Maybe “accord with the income expenditure model” may suggests something, but again there will be issues like

“What C means in the income expenditure model?”

“What is the definition of the income expenditure model in the first

place?”

Then again you will be at the start point.

By the way, if you want “Y” to be the GDP version, you should live with S instead of Sdg. Because if Y =i= C + S should hold, then the (Y, C, S)-variable system’s dimension is 2, this means that only 2 of them can be defined freely.

Maybe what I called “variable-system” and what I called “model” are both usually referred to as “model”. But I need discrimination between them to explain my view.

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]]>Tokio, Does my response to D R above capture the point that you are trying to make?

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]]>Model-X’s records, (X1, X2), can be displayed graphically in “X-Y (2-D)

plots”, i.e. dots in a sheet. Model-Y’s records; (Y1, Y2, Y3) can be

displayed in “X-Y-Z (3-D) plots”, i.e. dots in a cubic space. So,

Model-Y’s records have “thickness” compared to the Model-X’s. In a

sense, Model-Y is richer in information. Then what about Model-X

equipped with X3? Isn’t it 3-D?

Recall that

Xn = a1*X1 + a2*X2 + …. + a(n-1)*X(n-1) + b

is an equation for (n-1)-dimensional hyper-plane in the n-dimensional space. So, the identity of Model-X : X3 = X1 – X2 can be regarded as an equation for a plane.

This means that with the aid of X3 we can embed Model-X’s records in 3-D

space, but all the dots are on the same 2-D plane. Because Model-X has

essentially 2-dimensional information, even if we equipped it with a

redundant variable to add one dimension, its values (X1, X2, X3) only

fill 2-dimansional area, which has no thickness at all. By defining new

variables, we can fatten Model’s appearance but cannot increase its

intrinsic information.

Model-X with X3 is a, in a sense, quasi-3-D model. The identity reveals

the fact that all the dimensions are not fully used by the model. Note,

it is not like that the identity restricts the output of the model to

the plane, but in fact the output has 2-dimensional shape in the first

place.

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]]>I’m sorry, but you have brought us precisely nowhere. We started out with the identity S=I, and you say that if you use a different definition of S and a different definition of I, then the S=I identity need not hold.

You clearly fail to see the absurdity in employing such an argument and therefore there can be no use whatsoever in arguing beyond this point.

Good luck.

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]]>I is spending by business firms on final output , as opposed to spending on raw materials or on factor payments. The difference between C and I is that only households spend on C and only businesses spend on I.

Business savings is an accounting definition that is not encompassed within the income expenditure model. All savings and consumption is undertaken by households. Business saving does not vanish, but changes in business saving imply a difference between expenditure and income.

The equilibrium for the model can be stated as E = Y or equivalently I = S. So, yes, any difference between E and Y is exactly matched by an equal difference between I and S. And the reason that they are defined that way is to allow us to make the distinction between and equilibrium condition which does not always have to be satisfied and an accounting definition which can never not be satisfied.

I am defining S in a way that is in accord with the income expenditure model, which is not the same way that the accounting definitions of the system of the national income accounts have defined it. Applying national income accounting definitions make it impossible to distinguish between equilibrium and disequilibrium in the model.

Planned inventory accumulation counts as investment in the income expenditure model. The point is that it is not necessary to posit unplanned inventory accumulation to account for disequilibrium in the income expenditure model. There can be disequilibrium even if there is no unplanned inventory accumulation.

I will respond to Tokio Sato’s comment in a separate comment.

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