Before continuing my summary of the key points of Richard Lipsey’s important paper, “The Foundations of the Theory of National Income,” I want to clear up a point that the deliberately provocative title may have obscured. The accounting identities that I am singling out for criticism are the identities between income and expenditure (and output) and between savings and investment. It is true that, as Scott Sumner points out in a comment on my previous post, every theory has to define its terms in some way or another, so there is no point in asserting that a definition is wrong. Scott believes that I am a saying that it is wrong to define investment and savings as the same thing, but I am not saying that. I am saying that, in the context of the basic income-expenditure theory of national income, it makes the theory incoherent, so that there is a mismatch between the definition and the theory.
It is also true that sometimes identities follow directly from basic definitions. Such identities are like conservation laws in physics. For example, purchases must equal sales, because purchasing and selling are reciprocal activities; to assert that purchases are, or could be, unequal to sales would be self-contradictory. Keynes, when ridiculed by Hawtrey for asserting that a) savings and investment are equal by definition, and b) that the equality of savings and investment is achieved by variations in income, responded by comparing the equality of savings and investment to the equality of purchases and sales. Purchases are necessarily equal to sales, but prices adjust to achieve equality between desired purchases and desired sales.
The problem with Keynes’s response to Hawtrey is that to assert that purchases are unequal to sales is to misconstrue in a really fundamental way the meaning of the terms “purchase” and “sales.” But when it comes to national-income accounting, the identity of “investment” and “savings” does not follow immediately from the meaning of those terms. It must be derived from the meaning of two other terms: income and expenditure. So the question becomes whether the act of spending (i.e., expenditure) necessarily entails an immediate and corresponding accrual of income, in the same way that the act of purchasing necessarily entails the act of selling. To assert that expenditure and income are identical is then to assert that any expenditure necessarily and simultaneously entails a corresponding accrual of income.
Before pursuing this line of thought further, let’s just pause for a moment to recall the context for this discussion. We are talking about a fairly primitive model of an economy in which there are households that are units of consumption and providers of factor services. Households purchase consumption goods and provide factor services to business firms. Business firms are units of production that combine factor services provided by households with raw materials purchased from other business firms, and new or existing capital goods produced now or previously by other business firms, to produce raw materials, consumption goods, and capital goods. Raw materials and capital goods are sold to other business firms and consumption goods are sold to households. Business firms are owned by households, so profits earned by business firms are remitted, along with payments for factor services, to households. But although the flow of payments from households to business firms corresponds to a flow of payments from business firms to households, the two flows, which can be measured separately, are, at not identical, or at least not obviously so. When I bought a tall Starbucks coffee just now at a Barnes & Noble cafe, my purchase of $1.98 was exactly and necessarily matched by a sale by Barnes & Noble to the guy who writes for the Uneasy Money blog. But expenditure of $1.98 by the Uneasy Money blogger to Barnes & Noble did not trigger an immediate and corresponding flow of $1.98 to households from Barnes & Noble.
Now I grant that it is possible for income so to be defined that every act of expenditure involves a corresponding accrual of income to providers of factor services to the firm, and of profit to owners of the firm. But expenditure entails simultaneous accrual of income only by virtue of an imputation of income to providers of factor services and of profit to owners of firms. Mere imputation does not and cannot constitute an actual flow of payments by firms to households. The identity between purchases and sales is entailed by the definition of “purchase” and “sales,’ but the supposed identity between expenditure and income is entailed by nothing but an act of imagination. I am not criticizing imagination, which may often provide us with an excellent grasp of reality. But imagination, no matter how well attuned to reality, does not and cannot establish identity.
Uneasy Money 
David, I don’t understand this at all. Aren’t GDI and GDP identical by definition? It seems obvious to me that if you spend $1.98 on coffee it generates precisely $1.98 in gross income. How could it be otherwise?
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David, thank you for this very helpful post.
Where I did not follow is I did not see exactly where the processes of “saving” and “investing” take place. I also did not understand exactly how “income” is defined.
When you buy a $1.98 coffee, that is an expenditure for you. Is it income to the firm? I will assume that it is. Then, as Scott suggests, total income and total expenditure must be exactly equal as a matter of identity, for the same reason that total sales equals total purchases; two sides of the same coin.
To get from there to “S=I”, one has to figure out where “saving” takes place, and where “investing” takes place, and that’s where I’m totally lost. If a household earns $80,000 in income, and makes $70,000 in expenditures, and stuffs $10,000 currency in a mattress, then clearly $10,000 was saved. Was that $10,000 “invested” in US currency? If so, then it does seem that S=I as a matter of definition, though the term “invest” has been stripped of the meaning that I usually think of.
Anyway, any clarifications greatly appreciated.
Thanks,
-Ken
Kenneth Duda
Menlo Park, CA
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Scott, GDP and GDI are only identical by definition if you choose to define them in a certain way that ensures that will always add up to the same thing. There is no way that you can choose to define purchases and sales not be the same thing, because purchases and sales are inherently referring to two aspects of the same activity. Savings and investment are not referring to the same activity.
Scott and Ken, Here is what, I think, you are missing. I am defining income as a flow of money from firms to households. My payment of $1.98 for a cup of coffee is a flow of money from a household to a firm. The $1.98 sits in the Barnes & Noble cash box when I make a payment, it does not reach households until wages and other factor payments are made and dividends are paid. You may say that without my payment for the cup of coffee, Barnes & Noble would not be able to pay its workers and pay stockholders dividends. That is true, but without eggs there would be no chickens. My payment to Barnes & Noble is not identical to a payment of wages by Barnes & Noble to its workers or dividends to its stockholders, just as eggs are not identical to chickens. I don’t accept that putting currency into a mattress or depositing it into a bank or buying a T-bill is identical to an investment in a factory, although certain types of saving may be more conducive to investments in factories than others. But that is a separate issue.
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In the main, I agree with David Glasner and only seek to add some additional comments in the spirit of his.
1. The main issue in this whole discussion is, I think, can we use a definitional identity to rule out any imaginable state of the universe. The answer is “No”, which is why Keynes was wrong. The definitional identity of S ≡ I tells us nothing about what will happen if agents wish to save a different amount from what agents wish to invest.
2. We make an empirical non-empty theory when we define Y and E not as equal by definition, but let Y be actual GDP and E be desired expenditure, as most text books do today but did not do a few decades ago. This makes the equilibrium condition become that agents desire to purchase the present GDP, no more and no less.
3. Definitions are needed to define the terms we wish to use in our theory and all we can ask of them is that they be consistent with each other and that they define useful magnitudes.
4. Definitions are also needed if we wish to measure economic magnitudes. The definitional identity Y ≡ E is useful to national income accountants because they wish to measure the GDP over a period of time by adding up expenditures made and income generated and then reconcile the two measures. (Perhaps I should state my qualification here as a member for 25 years of the Statistics Canada, National Accounts Advisory Committee.)
5. To see the problem if we try to infer something about reality from our definitions, look at the case discussed in the above comments that what is bought, B, is identical to what is sold S. Fine as a definition, but what if we try to infer what happens in actual transactions from this identity. We then say that the value passed over the counter by the buyer is equal to the value passed over the same counter by the seller. But, case 1: what if the seller is myopic and trusting while the buyer is dishonest. The buyer passes a $5 bill saying it is a $10 bill and takes a commodity worth $10 in return. Talking about the real world we have to say that the values going in both directions are not equal. To maintain the identity we must define B ≡ S so that it is, in this case, either $5 or $10. The decision may be arbitrary or it may depend on what we are interested in. If it is the market value of sales that interests us, then it is $10; but if we are interested in the actual income received by sellers, it is $5. Case 2: the buyer is myopic and trusting while the seller is dishonest. The buyer looks at three different qualities of some commodity worth $9, $10 and $11. He decides on the middle-quality version and hands over $10. But the dishonest seller wraps up a low value good worth only $9. Again there is no single answer that is right and another that is wrong, is B ≡ S = $9 or is it $10. Again the is no right and wrong answer
6. Of course this is an imaginary example but it makes the point in a simple way. In reality, national income accountants deal with similar, although more complex, examples all the time. They remove the discrepancies that arise from such situations by having an error correction term that ensures that recorded income is exactly equal to recorded expenditure, even though they never come out as such in actual measurements.
7. For an example closer to home, consider the valuation of a change in an inventory, which is an investment in the national accounts. It might be valued at cost, in which case it would reflect the actual expenditure to produce it. But in the system of national accounts the change is valued at its market price (or average market price when many goods are involved). Thus the difference between the production cost of the inventory and its market value is an imputed profit that will not actually accrue until the good is sold. But it must appear as an income in the accrual period in order for income to equal expenditure.
Richard Lipsey
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Richard Lipsey.
Is your theory in (2) any different if you define E as actual expenditure (allowing it to be identically equal to Y) and then make the equilibrium condition that desired (E) equals Y? I completely agree that the definitional identity of S ≡ I tells us nothing about what will happen if agents wish to save a different amount from what agents wish to invest. But I can’t see how playing around with the definitions tells us anything more.
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I agree with Richard and not just because he has 25 years experience. From my own non-economist experience, I could quote a number of examples where a product or service is provided at one point in time but where the payment for that product or service is not made until much later.
For example, in the UK, a supermarket may buy apples from its suppliers and take delivery of those apples. Within a few days the supermarket will sell the apples and receive payment from its customers even if the customers pay by credit card. However, the terms of the contracts between the supermarket and its suppliers, and disputes over those contracts, may mean that the supermarket does not pay for its supply of those same apples until several weeks, or even months, after it has received the revenue from selling the apples. This is a very significant issue and causes cash flow problems for the supermarket’s suppliers.
http://www.theguardian.com/business/2015/feb/05/tesco-faces-investigation-over-how-it-pays-suppliers
I can fully understand why this would cause major problems in compiling a set of national accounts which balance and are accurate.
However, it seems to me that this leaves economists with four options:
Option 1: Develop an identity model and pretend that anomalies in the actual data don’t happen.
Option 2: Abandon the idea of an identity.
Option 3: Develop an identity model which ignores timing problems etc, but document the ways in which the real world does not comply with the model so it’s clear to everyone that economists are aware that the real world is not the same as the model.
Option 4: Develop an identity model which tries to take account of real world anomalies.
When I read many economics blogs (not this one) I am often left with the feeling that the economists have mistaken their identity model for a real world truth rather than just a useful tool. They choose option 1 which makes them appear as though they don’t understand the real world. Economists should choose option 3. This would allow the models to be used to discuss the dynamics of the economy while openly acknowledging (and understanding in the case of many economists!!) that the real world is messy. Option 4 would require a model so complex that only an expert like Richard would understand it. This would have no value as a teaching tool as the data anomalies would overwhelm the basic logical structure of the model.
I have some other comments and will return later.
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David
Sorry to take so long to get back about your reply to my comment about investment and saving being basically determined by risk appetite. This post seems related so I suppose it won’t hurt to reply here.
You said,
sfdc, If it can be one or the other, then they cannot be the same thing.
You’ll notice I said essentially the same thing. The spectrum is continuous. Investors, meaning anyone who has income in excess of their consumption, can make a decision to invest in a very low risk liquid asset, a very high risk illiquid asset, or anything in between.
Those with a relatively high risk appetite can of course borrow to invest, but that’s another story.
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David,
From your reply to Scott and Ken, it appears that you want to define income as being something along the lines of what, in SNA terms, amounts to the disposable income of the household sector. Which in the primitive model you set out would I guess be identically equal to expenditure less the disposable income of the corporate sector. Is that right?
Are you then saying that, in equilibrium, expenditure will equal this definition of income, i.e. that corporate disposable income is zero? Because, in general, I would not expect that to be the case, certainly not if the corporate sector was incurring gross investment expenditure.
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OK. I’ve attempted to show how this all works using some simple examples on a spreadsheet. I have published the spreadsheet at the link below so you should be able to see it. There are five examples on five sheets.
Example 1: This reflects Kenneth Duda’s comment where a household has an income of £80,000 and expenditure of £70,000. This example shows that saving is a CALCULATED CONSEQUENCE of the sum of the income and expenditure transactions.
Example 2: This example reflects a car manufacturing business where the business buys the materials and labour required to manufacture five cars, manufactures the five cars, and then sells three of those cars. This example shows that investment is a CALCULATED CONSEQUENCE of the sum of the income and expenditure transactions (and allocations of costs).
Example 3: This example reflects the rest of the economy’s view of example 2. Every time the manufacturing business in example 2 buys something, someone in example 3 sells the exact same thing. Every time the manufacturing business in example 2 sells something, someone in example 3 buys the exact same thing. This example shows that C + S in this example exactly matches C + I in example 2.
Example 4: This example is the same as example 2 except that all five cars are manufactured AND sold. This example shows that, when all five cars are sold, investment reduces to zero.
Example 5: This example is the same as example 3 except that it reflects the rest of the economy’s view of example 4. This example shows that, when all five cars are purchased, saving reduces to zero.
I think that it’s clear from these examples why I = S. I and S represent the gap between all of the transactions in the economy (where income = expenditure by identity) and the subset of transactions associated with consumption (where income = expenditure also by identity). Subtract one from the other and the residual that you are left with must also be an identity.
The only thing that is difficult about these examples is the concept of investment in a manufacturing business. In these examples, investment increases when the business purchases materials that will eventually find their way into cars or the labour that will manufacture cars. It also increases due to an allocation of a fraction of the business’s overhead costs for each car. It then decreases by the unit cost of a car when each car is sold.
Link to spreadsheet is here.
https://docs.google.com/spreadsheets/d/1yfxAX9apvuNwJuTcmHpTj-1cy07Vs0YenfFUj5IMuD4/pubhtml
This work has raised some questions in my head about the identity model itself. I’ll try and write these down later.
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David said: “We are talking about a fairly primitive model of an economy in which there are households that are units of consumption and providers of factor services”
I agree that the model is fairly primitive. Here are some thoughts on the components of the model itself. Some of these came from just looking at the model and some came from thinking about the spreadsheet examples I produced.
First, my very first thought when I saw this model for the first time was to ask how a household buys a house. Households are on the right hand side (RHS) of the identity. However, the RHS allows only the choice of consuming a house or saving a house. This is not intuitive to put it mildly. I suspect that you would lose most non-economists here? Why does the model not allow a householder to invest in a house (including building it himself, buying it from someone else, or making improvements to it after the initial investment)?
Second,
David said: “Business firms are owned by households, so profits earned by business firms are remitted … to households”
I’m happy with that. However, if households own businesses and receive dividends then how does a new business obtain investment if households can only consume and save? That’s really another example of the house investment issue, but with a different type of investment.
Third, businesses can buy and sell things from / to each other, including assets, consumables and labour. However, in order to get a proper flow of both materials and money the left hand side (LHS) of the identity must represent selling and not buying while the RHS must represent buying and not selling. That means that businesses must be thought of as being somehow on both sides of the identity depending on whether they are selling or buying. You can see that in my example 2 on the spreadsheet where the car manufacturing business is on the LHS but where its suppliers have to appear on the RHS in order to create a balance and make the identity work when the other businesses are selling to the car manufacturing business.
Fourth, households buy consumption but they sell labour so, again, they must somehow be on both sides of the identity.
Fifth,
David: “But expenditure of $1.98 by the Uneasy Money blogger to Barnes & Noble did not trigger an immediate and corresponding flow of $1.98 to households from Barnes & Noble”
You are correct that it is essential to create a circular flow. That’s what some of my earlier points about LHS and RHS are really about. I don’t think that the immediacy of the flow back to households is what matters. Rather, it is how your money flows back. I’d say that it was a combination of the wages of the person who served you; the costs of the coffee, cups and tables etc (although those flow via other businesses; the rent paid for the real estate (although that flows via another business too); and the dividend on the profits which comes directly back to households.
Sixth, this may be my misunderstanding but does the government play any role here as a consumer? What happens to any products or services produced by businesses for government? For example, suppose that the private sector is building a fighter plane for the military. Does the private sector model include the purchasing and labour associated with the plane, but not the final sale to government? Are taxes and benefits etc included in this model? What about households that are employed by the government? What about businesses that import their raw materials, or export their products and services? I am having problems identifying the precise boundaries for this model. I have seen other identity models that include government and overseas specifically as additional sectors. I am not clear whether these sectors are somehow embedded inside the C + I = C + S identity or whether the other two sectors are external to this model. This point makes my head hurt.
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I always thought (and in fact this was part of my history of economic theory course in grad school in the early 1970s) that the S = I identity began with “classical” economists. The argument (please realize this is based on things I read 40 years ago) was that is we begin by thinking of an economy with two “classes” of households: H1 and H2). One class of household (H1) spends all its income on consumption goods and services. So:
Y(H1) = C(H1); S(H1) = 0
The second group of households (H2) consists of people who own the means of production and whose saving is directed immediately to the business owned by the household:
Y(H2) = C(H2) + S(H2)
S(H2) = I
Given that conceptualization of households, the S = I “identity” flows rather nicely.
But once we begin thinking of households differently, and begin to think of businesses as distinct entities from households, the basis for the S = I identity collapses. (I think not even Keynes got this one right.)
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Let us define national investment as an addition to capital stock of the country over given period. National investment could be calculated as gross or net.
Let us define household saving as excess of income above consumption of a household over given period.
I think that definitions given above track fairly closely meaning given to those terms in business media and in national political conversations. I am not sure about current cutting edge macro, though, but we are talking about Keynes and Lipsey.
Now, meaning of national saving in non-academic conversation is much more ambiguous than of national investment or household savings.
We might, for example, define national savings as an aggregation of household savings in a country. That sounds natural and reasonable. Then it is clear that national saving thus defined is NOT equal to nominal value of net investment. Reasons for such discrepancy are several. One of them flows from the fact that investment undertaken by firms does not constitute income of its owners, by any reasonable definition. Movements of stock prices could be described as changes in income of stock owners (though it is very peculiar kind of income), but not investment undertaken by such firms, and those two things are definitely not equal. Another, simpler reason is that households hold part of their wealth in the form of money. There are yet other reasons.
Keynes (GT, chapter 6), however, defined national saving as expenditure of „investor- purchasers“ (minus „user costs“ which I shall ignore) and then noted that this is identical to national investment, which he defined more or less identically with me above. I assume that he choose those definitions because he thought that exposition of his theory with them will be easier and more comprehensible than if he would define national saving and investment as different things. He was probably very wrong about that, but that does not mean his theory itself is incoherent.
Defining national saving and national investment as identical has natural appeal because it exposes important truth. Household saving is instrument of wealth building for a household. Wealth of a country, unlike that of a household, is not increased when citizens hoard more money or make more loans (assuming closed economy) or when stock prices magically double. National wealth building means investment. Thus national income is quite properly defined as investment plus consumption, while household income is divided between saving and consumption. That however, does not mean that defining national saving and investment as identical is good idea for the purposes of the theory of employment.
Now, according to „textbook Keynesianism“ , disequilibrium arises when desired savings, regarded as a fraction of household incomes, are greater than desired investment. Since realised savings are by definition equal to realised investment, equilibrium will be restored by shrinking of the national income. Is this a prediction that could be right or wrong? I do not think so. Really this is convoluted way of saying that when the volume of consumption is given, income depends on investment, which is true by definition.
Leap from the definitions to predictions in the theory comes right after that, when it is implicitly predicted that fall in investment not compensated by an increase of consumption might be caused by behaviour of savers (or banks managing households savings), who shift their wealth portfolios from funding investment to other things, like for example piling up money and government bonds. I also think that economists understand Keynesian theory in this way, but imposed convention identifying investment with saving causes them to use some convoluted and barely comprehensible language.
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David, I agree that GDI and GDP are only equal if the profession chooses to define them as equal. My point was that the profession has in fact chosen to define them as equal, and hence they are equal.
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“When I bought a tall Starbucks coffee just now at a Barnes & Noble cafe, my purchase of $1.98 was exactly and necessarily matched by a sale by Barnes & Noble to the guy who writes for the Uneasy Money blog. But expenditure of $1.98 by the Uneasy Money blogger to Barnes & Noble did not trigger an immediate and corresponding flow of $1.98 to households from Barnes & Noble.”
If you believe that is a problem, I think you are confusing elements of income accounting and flow of funds accounting.
Your purchase means Starbucks sold some inventory off their balance sheet while writing up the realization of revenue on their income statement along with salaries payable and other administrative costs as expenses. The net of all that will be a writing up of equity on their balance sheet corresponding to the earnings realized.
The accounting connection occurs through a daily income statement and balance sheet. It is immediate and bullet-proof.
The related flow of funds detail will be a follow up as such things as cash salaries are paid (and corresponding payables reduced) and as dividends are paid from equity or revenues are kept in the form of retained earnings and cash on the other side of the balance sheet (for example).
“The supposed identity between expenditure and income is entailed by nothing but an act of imagination”
This is wrong. It is done by robust, coherent accounting.
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David said (in your next post): ”I apologize for having been unable to respond to a number of comments to previous posts. I will try to respond in the next day or two”
Just to be clear, I am not expecting you to reply to my individual comments. What my comments are intended to show is that examples make these discussions easier for everyone to understand, including pointing out deficiencies in the models being used and understanding deviations between the models and the real world. I know that is true for non-economists like me. However, I am 99% sure that examples would also help resolve disputes between economists.
Having said that, here are a few more comments on my thinking, based on the spreadsheet examples from earlier.
One of the reasons that identities are hard to understand is that they represent the perspectives of different sets of actors on the same base set of transactions (by actor I mean a car manufacturing company or a household or a government).
It is much easier to follow if you start by itemising all of the transactions in the example economy and then think of the identities as being derived from the transactions. As a result, I have added some more sheets to my spreadsheet to itemise the relevant transactions. For example, sheet Example 2/3t contains a table which itemises all of the transactions in Examples 2 and 3.
You can see that I have classified the different transactions so that it is obvious which transactions are consumption transactions and which are not. I have also added a summary table showing transactions by type alongside the list of transactions.
This also made a couple of other things clear to me.
First, businesses have savings as much as households. A business’s net savings are its profits. However, one of the assumptions of the identity model is that businesses distribute their profits to households so, in the model, businesses always end up with zero net savings. However, in a more general model, it would be necessary to show businesses as having savings. For example, Apple does not distribute all of its profits to its shareholders.
Second, earlier I was confusing myself about whether government and overseas were included or not. I have realised that it makes more sense to make the model more general by assuming that these actors are included. As a result, I have assumed in my examples that cars can be purchased by government and by overseas businesses. Hence, government and overseas runs deficits in my examples. I have summarised this by including actors and sector balance summaries alongside the new list of transactions.
Note that I have also colour coded the actors involved in each transaction so that you can see easily that most actors are involved in buying things AND selling things. For example, households sell labour and buy cars. This is not obvious from the identity itself. However, this must be the case if we are to create a monetary circuit. In your coffee example, a household buys coffee from a business. In order to complete the circuit and get that money to return to a household, we need to have other transactions where households are on the opposite side of the transaction e.g. selling their labour or receiving dividends.
I’d also like to make a point about expectations. In my example 2, the car manufacturing company manufactured five cars but sold only three. It must have expected demand for five cars as there is no other reason to manufacture five cars. However, its expectations were not met. It sold only three cars, leaving it with two cars. It is the investment in the two unsold cars that we see in the identity. In example four, where the same business sells all five cars, investment reduces to zero.
Imagine you were the business in example 3. How many cars do you think will be demanded next period? If you use the current period demand to make your estimate then you will expect that there will be demand for three cars in the next period. However, you already have two cars from this period’s manufacturing activity, so you will plan to manufacture only one more car next period. Of course, this means that you will buy materials and labour for only one more car so the rest of the economy will have lower income than in the current period so, other things being equal, you may cause a recession.
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Richard, Thanks, as always, for taking time to comment in this forum. Point 1 is the critical issue in this discussion, because people somehow do feel entitled to make inferences about the real world from definitional identities. I find it interesting that defining E as planned expenditure seems to dovetail with Keynes’s definition of aggregate demand at the beginning of the GT. If so, he got it right in one place but messed up in another.
Point 5 is useful in explaining why even the purchase-equals-sales identity is not a true conservation law like the first law of thermodynamics. On the other hand, a violation of the purchase equals-sales identity doesn’t seem to relate to whether the system is in equilibrium or not. The system could be in equilibrium with planned expenditure equal to planned sales but not satisfy the definitional identity.
Nick, I think the message is that what is important is to specify the equilibrium condition appropriately without confusing it with an accounting identity and not to draw empirical inferences about the disequilibrium behavior of the system from an accounting identity.
Jamie, As always the real world is messier than the models we use to try to understand it. And I agree that option 3 is best way to handle the messiness.
A new business is started when households take some of their accumulated assets and use those assets to create a business firm which uses the assets provided by the household to purchase plant and equipment. The purchase of plant and equipment is financed by accumulated the savings provided by the households.
The primitive model with which we are working does not have a government sector. Introducing a government sector adds a whole new level of complication.
Don, I don’t think that you will find any reference to a savings-investment identity until Keynes, but I am just guessing. In earlier treatments, the interest rate was supposed to adjust to equilibrate savings with investment, the equality of savings and investment being a condition of equilibrium, not an identity.
Ales, Just to be clear, Keynes expressed his theory in an incoherent way by insisting on the savings-investment identity at the same time he used it as an equilibrium condition. It is quite possible, as Richard Lipsey has shown, to express the theory in a coherent way, but avoiding the savings-investment identity. I would just add, as a clarification, that just because a theory can be expressed coherently it doesn’t follow that the theory gives you a good grasp on reality.
Scott, GDI and GDP may be defined to be equal. Who defines them to be equal doesn’t matter. The definition is merely a convention and doesn’t entitle anyone to treat the terms as interchangeable.
JKH, The distinction between my consumption expenditure and the generation of income from that expenditure is not a problem. You are talking about the firm’s income accounting, and I am talking about the income received by households from firms. My reference to an act of imagination was not intended to denigrate accounting. It was meant to underscore a distinction between a bookkeeping entry and a physical or electronic funds transfer.
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