Savings and Investment Aren’t the Same Thing and There’s No Good Reason to Define them as Such

Scott Sumner responded to my previous post criticizing his use of the investment-savings identity in a post on the advantages NGDI over NGDP, and to my posts from three years ago criticizing him for relying on the savings-investment identity. Scott remains unpersuaded by my criticism. I want to understand why my criticism appears so ineffective, so I’m going to try to understand Scott’s recent response, which begins by referring to economics textbooks. Since it is well documented that economics textbooks consistently misuse the savings-investment identity, it would not be surprising to find out that the textbooks disagree with my position (though Scott doesn’t actually cite chapter and verse).

Economics textbooks define savings as being equal to investment:

S = I

To say that something is equal to investment doesn’t seem to me to be much of a definition of whatever that something is. So Scott elaborates on the definition.

This means savings is defined as the funds used for investment.

OK, savings are the funds used for investment. Does that mean that savings and investment are identical? Savings are funds accruing (unconsumed income measured in dollars per unit time); investments are real physical assets produced per unit time, so they obviously are not identical physical entities. So it is not self-evident – at least not to me — how the funds for investment can be said to be identical to investment itself. The two don’t seem to be self-evidently identical to Scott either, because he invokes another identity.

It’s derived from another identity, which says that in a closed economy with no government, gross domestic product equals gross domestic income:

GDI = C + S = C + I = GDP

But once again, it is not self-evident that GDI and GDP are identical. Income usually refers to earnings per unit time derived by factors of production for services rendered. Or stated another way, GDI represents the payments per unit time – a flow of money — made by business firms to households. In contrast, GDP could represent either a flow of final output from business firms to households and to other business firms, or the expenditures made by households and business firms to business firms. These two flows of output and expenditure are not identical, though, for the most part, representing two sides of the same transactions, there is considerable overlap. But it is clear that payments made by business firms to households in exchange for factor services rendered are not identical to the expenditures made by households and business firms to business firms for final output.

Bill Woolsey in a post commenting on my post and Scott’s earlier post to which I responded attempts to explain why these two flows are identical:

In a closed private economy, saving must equal investment. This is a matter of definition. Saving is defined as income less consumption. All output is defined as either being consumer goods or capital goods. Consumption is spending on consumer goods and investment is spending on capital goods. All expenditure is either on consumer goods or capital goods. Since income equals expenditure, and consumption is itself, then income less consumption must equal expenditure less consumption. By the definition of saving and investment, saving and investment are always equal.

I guess someone might think that is all insightful, but it comes down to saying that purchases equals sales.

Bill is very careful in saying that savings is defined as income less consumption, and all output is defined as either being consumer goods or capital goods, and all consumption is (presumably also by definition) spending (aka expenditure) on consumer goods and investment is spending (aka expenditure) on capital goods. So all expenditures are made either on consumer goods or on capital goods. Then Bill concludes that by the definition of savings and investment, savings and investment are always equal (identical), because consumption is itself and income equals expenditure. But Bill does not say why income equals expenditure. Is it because income and expenditure are identical? But, as I just pointed out, it is not self-evident that income (defined as the earnings accruing to households per unit time) and expenditure (defined as the revenues accruing to business firms in payment for final output produced per unit time) are identical.

Now perhaps Bill (no doubt with Scott’s concurrence) is willing to define expenditure as being equal to income, but why is it necessary to define income and expenditure, which don’t obviously refer to the same thing, as being equal by definition? I mean we know that the Morningstar is Venus, but that identity was not established by definition, but by empirical observation. What observation establishes that income (the earnings of factors of production per unit time) and expenditure (revenues accruing to business firms for output sold per unit time) are identical? As Scott has himself noted on numerous occasions, measured NGDI can differ and has frequently differed substantially from measured NGDP.

It is certainly true that we are talking about a circular flow: expenditure turns into income and income into expenditure. Expenditures by households and by business firms for the final output produced by business firms generate the incomes paid by business firms to households and the income paid to households provides the wherewithal for households to pay for final output. But that doesn’t mean that income is identical to expenditure. Chickens generate eggs and eggs generate chickens. That doesn’t mean that a chicken is identical to an egg.

Then Scott addresses my criticism:

David Glasner doesn’t like these definitions, but for some reason that I haven’t been able to figure out he doesn’t say that he doesn’t like the definitions, but rather he claims they are wrong. But the economics profession is entitled to define terms as they wish; there is no fact of the matter. In contrast, Glasner suggests that my claim is only true as some sort of equilibrium condition:

It’s not a question of liking or not liking, but one ought to be parsimonious in choosing definitions. Is there any compelling reason to insist on defining expenditure to be the same as income? On the contrary, as far as I can tell, there is a decent prima facie case to be made that expenditure and income refer to distinct entities, and are not just different names for the same entity. Perhaps there is some theoretical advantage to defining expenditure and income to be the same thing. If so, I have yet to hear what it is. On the contrary, there is a huge theoretical disadvantage to defining income and expenditure to be identical: doing so makes the Keynesian income-expenditure model unintelligible. Come to think of it, perhaps Scott, a self-described hater of the Keynesian cross, likes that definition. But even if you hate a model, you should try to make it as good and as coherent as possible, before rejecting it. This post is already getting too long, so I will save for a separate post a discussion of why defining income and expenditure to be identical makes the Keynesian income-expenditure model, and the loanable funds doctrine, too, for that matter. For now, let me just say that if you insist that the savings-investment equality (or alternatively the income-expenditure equality) is an identity rather than an equilibrium condition, you have drained all the explanatory content out of your model.

Scott objects to this statement from my previous post:

Scott begins by discussing the simplest version of the income-expenditure model (aka the Keynesian cross or 45-degree model), while treating it, as did Keynes, as if it were interchangeable with the national-accounting identities:

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.

Here is Scott’s response:

David’s characterization of my views is simply incorrect. And it’s easy to explain why. I hate the Keynesian cross, and think it’s a lousy model, and yet I have no problem with the national income identities, and believe they occasionally help to clarify thinking. The quote he provides does not in any way “discuss” the Keynesian cross model, just as mentioning MV=PY would not be “discussing” the Quantity Theory of Money.

OK, I believe Scott when he says that he’s not a fan of the Keynesian cross, but it was Scott who brought up consumption smoothing in response to a decline in aggregate demand caused by central bank policy. Consumption smoothing is a neo-classical revision of the Keynesian consumption function, so I was just trying to put Scott’s ideas into the context of a familiar model that utilizes the equality of savings and investment to determine equilibrium income. My point was that Scott was positing a decrease in saving and asserting, by way of the savings-investment identity, that investment would necessarily drop by the same amount that saving had dropped. My response was that the savings-investment identity does not allow you to infer by how much investment falls in response to an assumed decrease in savings, because savings and investment are mutually determined within a macroeconomic model. It doesn’t have to be the Keynesian cross, but you need more than an accounting identity and an assumption that savings falls by x to determine what happens to investment.

Scott then makes the following point.

[I]t seems to me that David should not be focusing on me, but the broader profession. If economics textbooks define S=I as an identity, then it’s clear that I’m right. Whether they should define it as an identity is an entirely different question. I happen to think it makes sense, but I could certainly imagine David or anyone else having a different view.

If I am focusing on Scott rather than the broader profession, that simply shows how much more closely I pay attention to Scott than to the broader profession. In this particular case, I think Scott is manifesting a problem that sadly is very widely shared within the broader profession. Second, that Scott shares a problem with the rest of the profession does not establish that Scott is right in the sense that there is any good reason for the profession to have latched on to the savings-investment identity.

In response to my reference to posts from three years ago criticizing him for relying on the savings-investment identity, Scott writes:

I have never in my entire life made any sort of causal claim that relied solely on an identity. In other words, I never did what David claims I did. Like all economists, I may use identities as part of my argument. For instance, if I were to argue that rapid growth in the money supply would increase inflation, and that this would increase nominal interest rates, and that this would increase velocity, I might then go on to discuss the impact on NGDP. In that case I’d be using the MV=PY identity as part of my discussion, but I’d also be making causal arguments based on economic theory. I never rely solely on identities to make a causal claim.

We have a bit of a semantic issue here about what it means to rely on an identity. As I understand him, Scott is asserting that because savings is identical to investment he can make a causal statement about what happens to savings and then rely on the savings-investment identity to infer directly, by substituting the word “investment” for the word “saving” into a causal statement about investment. I don’t accept that the savings-investment identity allows a causal statement about savings to be transformed into a causal statement about investment without further explanation. My claim is that savings and investment are necessarily equal only in equilibrium. A causal statement about savings can’t automatically be transformed into a causal statement about investment without an explanation of how savings and investment were brought into equality in a new equilibrium.

Scott had trouble with my expression of puzzlement at his statement that Keynesians don’t deny that (ex post) less savings leads to less investment. I found that statement so confusing that apparently I wasn’t able to articulate clearly why I thought it was confusing. Let me try a different approach. First, if savings and investment are identical, then less savings can’t lead to less investment, less savings is less investment. A pound is defined as 2.2 kilograms. Does it make sense to reducing my weight in pounds leads to a reduction in my weight in kilograms? Second, if less savings is less investment, what exactly is the qualification “ex post” supposed to signify? Does it make sense to say that ex post if I lost weight in pounds I would lose weight in kilograms, as if I might plan to lose weight in pounds, but not lose weight in kilograms?

In the same post that I cited above, Bill Woolsey makes the following observation:

To say that at the natural interest rate saving equals investment is like saying at the equilibrium price quantity supplied equals quantity demanded. To say that savings always equals investment is like saying that purchases always equals sales by definition.

To compare the relationship between savings and investment to the relationship between purchases and sales is clearly not valid. The definition of the activity called “purchasing” is that a commodity or a service is transferred from a seller to a buyer. Similarly the definition of the activity called “selling” is that a commodity is transferred to a buyer from a seller. The reciprocity between purchasing and selling is inherent in the definition of either activity. But the definition of “saving” does not immediately tell us anything about the activity called “investing.” As Bill concedes in the passage I quoted earlier, the identity between saving and investment must be derived from the supposed identity between income and expenditure. But the definition of “income” does not immediately tell us anything about “expenditure.” Income and expenditure are not two reciprocal sides of the same transaction. When I buy a container of milk, there is a reciprocal relationship between me and the store that has no direct and immediate effect on the relationship between the store and the factors of production used by the store to be able to sell me that container of milk. I don’t deny that there is a relationship, just as there is a relationship between chickens and eggs, but the relationship is not at all like the reciprocal relationship between a buyer and a seller.

UPDATE: (2/18/2015): In a comment to this post, Bill Woolsey points that I did not accurately characterize his post when I said “Bill does not say why income equals expenditure,” by which I meant that he did not say why income is identical to expenditure. If I had been a more careful reader I would have realized that Bill did indeed explain why income is identical to output and output is identical to expenditure, which (by the transitive law) implies that income is identical to expenditure. However, Bill himself actually concedes that the identity between output and expenditure is arrived at only by imputing the value of unsold inventory to the profit of the firm. But this profit is generated not by an actual expenditure of money, it is generated by an accounting convention — a perfectly legitimate accounting convention, but a convention nonetheless. So I continue to maintain that income, defined as the flow of payments to factors of production per unit time, is not identical to either expenditure or to output. Bill also notes that, as Nick Rowe has argued, in a pure service economy in which there were no capital goods or inventories, output would identically equal expenditure. I agree, but only if no services were provided on credit. There would then be a lag between output and the expenditure corresponding to the output. It is precisely the existence of lags between output, expenditure and income that allows for the possibility of non-instantaneous adjustments to changes, thereby creating disequilibrium transitions between one equilibrium and another.

28 Responses to “Savings and Investment Aren’t the Same Thing and There’s No Good Reason to Define them as Such”


  1. 1 Richard Lipsey February 17, 2015 at 2:47 pm

    Being on holiday in Mexico I have no access to references so I will comment in general not on particular points in this discussion. .

    ELEMENTARY LOGIC 101: A DEFINITIONAL IDENTITY IS CONSISTENT WITH ALL STATES OF THE UNIVERSE AND SO CANNOT BE USED TO RESITRCT ANY POSSIBLE STATE. END OF STORY.

    EARLY Keynesian WRITINGS AND EARLY UK AND US TEXT BOOKS WERE FULL OF CONFUSIONS ABOUT WHAT COULD AND COULD NOT BE DEDUCED FROM DEFINITIONAL IDENTITIES.

    I always regret that my paper on this matter was buried in the set of essays in honour of Lionel Robbins . It had an impact in the UK where use of the identities pretty well disappeared from text books, but was not noticed in the US. My RA, John Stillwell, wrote an appendix to my article called A BRIEF HISORY Of THE MUDDLE, which is instructive reading in the context of the present discussion.

    Klappholz and Agassi wrote an excellent paper on the misuse of identities in economics in the early 1960s published in Economica.

    In the first few editions of my text book, An Introduction to Positive Economics, I showed a diagrammatic version of the Phillips water machine where savings were not equal to investment except in equilibrium. If you saw the Phillips machine in action, you could never have fallen for the misuse of identities. My graphical version of the water machine is included in my selected essays published by Edward Elgar in the UK.

    RICHARD LIPSEY:

  2. 2 numawan February 17, 2015 at 3:18 pm

    Perhaps I am saying something stupid, but I think that C, S and I are defined in real terms. These equalities do not hold in nominal terms because you need to add cash injected by the central bank as well as movements in cash hoarding by savers in the equations.

  3. 3 Jamie February 17, 2015 at 4:39 pm

    I’m not an economist but I have been reading about economics for several years. I have noticed that accounting identities cause endless debates which are never resolved. I’m never totally clear whether economists are confused about these identities or whether economists understand the identities but can’t explain them to non-economists like me. My assumption is that the confusion arises because economists only ever talk about identities at the aggregate level and never use examples.

    Maybe this is dumb but I assume that these identities are true in any economy and over any time period. Imagine a thought experiment where the economy was trivially small and the time period was also trivially small. Why is it not possible to write down a list of the specific transactions which took place in this trivial economy over this trivial time period and then show how these transactions add up to deliver the identities?

    For example, suppose all that happened in the economy was that my employee paid me $100 dollars for working a shift in his car factory. No parts were purchased by the factory in this period and no cars were completed so none were sold. I then spent $20 on pizza at a restaurant which had already bought the ingredients when the period started. You can’t get much simpler than that. Each of the two transactions has two sides.

    On the income side, I earned $100 and the restaurant earned $20.

    On the expenditure side, my employer spent $100 on my wages and I spent $20 on pizza, a consumption good.

    How would those transactions appear in identities so that the two sides add up? For example, is my employer dis-saving $100 when he pays me and I am saving $100 by earning that money, so total saving is $100 – $100 = 0? Or is he consuming my labour and I am saving? Or what?

    If my trivial example doesn’t make sense, or is too trivial, then why can’t economists provide an alternative, maybe a set of transactions in a spreadsheet with a summary total showing the values of the identities and how they are calculated?

  4. 4 Lord February 17, 2015 at 6:20 pm

    It is interesting we use two terms for the same transaction and the reason for this is money is unlque, so buying means spending money and selling acquiring it, as much along the same lines, savings means not spending it, and investment parting with it, with some ambiguity of whether financial assets are money or investments. Abstracting from money loses all that is important in macro. Identities without a time variable can only ever provide a static picture, unable to indicate what is changing or why, so even if true for all time, explain nothing.

  5. 5 Bill Woolsey February 17, 2015 at 6:46 pm

    I explained why income equals expenditure–by definition. It is because income equals output and expenditure equals output.

    Two things equal to the same thing are equal.

    Income equals output because profit is the difference between output and other incomes and you add it to the other incomes to get aggregate income.

    Output equals expenditures because all of output is defined to be purchased by someone–the odd convention that goods not sold are inventory investment by the producer.

    I don’t think saving and and invested are defined to the be same thing. In my view, they are less alike than the quantity of apples supplied and demanded. At least for those two things, we are talking about apples.

    Saving is a difference between income consumption and investment is a flow of expenditure. They are quite different things.

    But it just takes a little bit of addition and subtraction to see they are always equal,. It is not an equilibrium condition.

    Now, if you want to argue that profit on unplanned inventory investment isn’t really income, then I think you may have a point.

    However, think about an all services economy where everyone is self employed. Everyone’s income is someone else’s expenditure. And output is the same as expenditure.

    Let’s say haircuts is one type of service. Income not spent on haircuts must be equal to spending on things other than haircuts. Call haircuts consumption.

    I am sure Nick Rowe can explain it better than me.

    And, by the way, I don’t remember how Sumner used the saving investment identity three years ago, but I didn’t agree with this argument. And I didn’t agree with his explanation as to why investment varies more over the business cycle than consumption either.

  6. 6 Rob Rawlings February 18, 2015 at 7:47 am

    If I understand this correctly David has a different definition of expenditure to Scott and Bill.

    David says (in his last post):

    “not all output is sold, some of it being retained within the firm as work in progress or as inventory. However, in an equilibrium situation in which variables were unchanging, aggregate income, expenditure and output would all be equal”

    Bill Says (above)
    “Output equals expenditures because all of output is defined to be purchased by someone–the odd convention that goods not sold are inventory investment by the producer.”

    I think this drives most of differences as the implication of Bills view is that all output is “sold” using Bills definition.

    David would seem to have common sense on his side here (as Bill acknowledges), but I suspect Bill has convention,

  7. 7 Rob Rawlings February 18, 2015 at 7:48 am

    And using Bill’s definition “aggregate income, expenditure and output would all be equal” becomes true, as far as I can tell.

  8. 8 Thomas Aubrey February 18, 2015 at 9:00 am

    Great post David. It strikes me that your point “we know that the Morningstar is Venus, but that identity was not established by definition, but by empirical observation” is the crucial one.

    I have not seen empirical data that shows savings and investment are identical. The determinants of investment are not savings per se but future expected returns. If future returns look robust and savings are falling, then investment can still rise through credit expansion. Conversely, if the outlook for future returns is poor and the savings rate increases, there is no necessary reason why investment should increase. Clearly there may well be times when the savings rate rises with investment proportionately.

    It does seem disingenuous, to me at least, to define investment as savings, as it would also appear relevant to then define that portion of savings that is not invested. Then again, this may just be a problem for those of us who have spent too much analysing credit-related data.

  9. 9 David Glasner February 18, 2015 at 6:53 pm

    Richard, Thanks for your comment. Everything I say in this post is derived – I hope accurately – from your wonderful paper, which is one of my all-time favorites. In your paper you cite two papers co-authored by Klappholz, one co-authored with Agassi and published in 1960 is entitled “Methodological Prescriptions in Economics.” The other, co-authored with Mishan and published in 1962 is entitled “Identities in Economic Models.” I am guessing that you meant to cite the latter, but both seem well worth reading.
    Is the Phillips machine still operating at the LSE? Maybe someone could upload a clip of it on YouTube.

    numawan, I don’t see why it would matter whether you were measuring in real or nominal terms. If you are saying that money expansion prevents savings from equaling investment, then the inequality would show up either way.

    Jamie, Obviously, I think that economists are just as confused about identities as everyone else. My understanding, such as it is, is that savings are undertaken by households. If businesses are holding cash, and obviously they do, it seems to me that cash is treated as working capital which would make it an investment good from the point of view of businesses. I don’t think it is all that helpful to focus on a single transaction. What we are interested in is changes over the course of a unit of time.

    Lord, Income, expenditure, savings, etc. are all measured as rates per unit time.

    Bill, Sorry for not reading your post more carefully than I did before quoting from it. In the update which I just added, I explain why your explanation still does not convince me that expenditure and income are identical.

    Rob, I think that we are in agreement on this.

    Thomas, Thanks. See Richard’s comment above, about the Phillips machine.

  10. 10 Jamie February 19, 2015 at 5:57 am

    David said: “I don’t think it is all that helpful to focus on a single transaction. What we are interested in is changes over the course of a unit of time”

    Sorry but I don’t agree with this. I have seen this same problem many times in business. It relates to inconsistent classifications at the transactional level and it causes major confusion.

    For example, in a business, ‘sales’ is just a set of individual transactions. However, it makes no sense for business executives to think about each individual transaction, so businesses classify transactions in different ways and then executives analyse the summary data ‘over the course of a unit of time’ like a day or a week or a month or a year. Classifications may include product classifications, customer classifications and geographical classifications. They may also include employee classifications e.g. which salesman or department made the sale. They may include many other classifications e.g. size of sale, time of day of sale etc.

    Unfortunately what can happen is that different departments in the business use different definitions of classifications so they end up with inconsistent summary analyses. This means that the executives end up arguing about which executive has the correct view rather than about the real problem they are trying to solve.

    Something very similar is happening here. You are an executive who is interested only in discussing the summary analyses. However, you don’t understand how the summary is calculated and you’re not sure if others do either. As with any other summary, the summary is calculated by classifying individual transactions and then adding up the transactions with the same classification.

    In order to solve your problem, you need to understand how different types of transaction are classified and you need to ensure that your colleagues have the same understanding. You also need to agree that the classification is fit for purpose.

    Your post and your comment “obviously, I think that economists are just as confused about identities as everyone else” means that you recognise the problem. If you don’t like my solution then what alternative solution do you propose? How do academic economists teach their students about this when economists themselves are “confused”?

  11. 11 Thomas Aubrey February 19, 2015 at 2:27 pm

    David, the only working Phillips machine that I am aware of is in Cambridge (UK) which was restored a few years ago.

    http://sms.cam.ac.uk/media/1094078

  12. 12 M. February 19, 2015 at 2:28 pm

    My guess is that Scott Sumner takes the national account definition of savings. In the data it is obvious that savings = investment because it is ex-post, just as sales = purchases ex-post.

    But that does not mean at all that savings and investment are the same thing. Savings = investment is not a definition, it is an equilibrium concept (ex-ante) and an identity (ex-post).

    Macro. is interested with ex-ante, not ex-post. S = I ex-post by definition, but there may be rationning at the equilibrium.

  13. 13 dwb February 19, 2015 at 3:13 pm

    I am trying to follow the savings = investment (or not), and all I can discern is that one side is arguing savings = investment, the counterpoint is savings investment, because savings = investment is only true in equilibrium, or in a single period model, unless we introduce something else to mop up the residual ( “imputing the value of unsold inventory to the profit of the firm”).

    It really should not be this hard (especially for someone with formal economics training – me) to concisely figure out what the actual argument is.

    I can probably think of a few models where this might be plausible (for example: A risk averse consumer wants to hold a buffer stock of money assets, and is willing to take negative return to insure against shocks). It is certainly plausible “investment” (expenditure on capital goods) < savings, but I have not dealt with those models in a while so can't say for sure.

    Overall I am wading though all these posts and come up with: So what (either way)? I have never been a fan of the notion of "equilibrium", but it's a useful first approximation.
    What's the impact? What's are the conditions savingsinvestment I have to worry about here? Why isn’t it a useful first approximation in a world of noisy imprecisely measured things?

    Honestly, there are a whole host of other reasons GDI and GDP will not be the same either in a theoretical or practical sense (measurement error & the underground economy come to mind). Both get substantially revised and in any case we only know the “truth” about either with a considerable lag (if ever). A lot of the advantages of one over the other have nothing to do with bona-fida theoretical advantages, and more to do with practical implications (for example: I would rather have a noisy imprecise estimate now than wait 9 months for a more accurate estimate. Even better, I’ll take both and later revise both).

    Forgive me if I’m lost, It just should not be this hard to figure out what the crux of the disagreement is.

  14. 14 dwb February 19, 2015 at 3:21 pm

    The inequality sign I used got left off, I think the blogging software thought it was html brackets

  15. 15 David Glasner February 19, 2015 at 6:05 pm

    Jamie, Fair enough. A good national income accountant should be able to classify every transaction in terms of the national income accounts. I am not a national-income accountant; I don’t have the patience and organizational skills for accounting. So I basically just ignore it. My problem is not an accounting problem; it is a theoretical and philosophical problem. You already have my solution, which is Richard Lipsey’s solution, which is Ralph Hawtrey’s and Dennis Robertson’s and Gottfried Haberler’s and Friedrich Lutz’s who all called Keynes on his misuse of accounting identities. But somehow, Keynes’s confusion was resurrected in the economics textbooks, and has not been effectively countered.

    Tom, Thanks for the link. It’s an interesting video, but I couldn’t make out from the video how investment and savings were represented on the machine.

    M., My point is that the ex post identity is the result of accounting conventions, which don’t establish that savings and investment are the same thing, just that suitably defined we can always calculate them in such a way that they are equal. But there is nothing sacred about that definition. And if income and expenditure were truly identical, the income-expenditure model would be almost nonsensical.

    dwb, All I can say is read Lipsey’s article. You won’t regret it. You’re right that measurement error could account for the persistent failure of NGDI to equal NGDP; the ratio of the two varies from about 97.3% to 101.8%. If they are really measuring the same thing, why should measurement error matter that much? After all, it’s the same thing, right?

  16. 16 sdfc February 20, 2015 at 1:45 am

    To put it simply, savings and investment are essentially the same thing. Whether it’s one or the other is determined by risk appetite.

    GDP(E) = GDP(I) = GDP(P). Any reported difference is measurement error.

  17. 17 dwb February 20, 2015 at 4:52 am

    “If they are really measuring the same thing, why should measurement error matter that much? After all, it’s the same thing, right?”

    Measure twice cut once comes to mind.

    I am not sure sure what your question is but it sounds to me as though you think measurement error should be a lot less than 3% (technically, I prefer to think of the average as closest to the truth, measurement error = difference from average, more like 1% ). You cannot know what the measurement error is unless you try to measure the same thing two ways.

    My prior is that it’s actually pretty remarkable that they are so close, if we are really measuring the same thing two truly independent ways. There are lots of things in both calculations that are modeled, imputed, or only known with certainty with a long lag. I can think of hundreds of reasons to question individual line items, even up to 5%. Finals sales? Retailers lose 1-2% just from inventory shrinkage (employee theft and shoplifting). Illegal drugs? Hundreds of billions. Unreported income, small cash business that are not 100% truthful to avoid taxes. Even at large corporations, there are tax and accounting incentives that cause estimates to be engineered to report results a certain way to time taxes, sales, etc…

    A hundred billion here and there and soon you are talking about real money!

    My preference is always to have two (or more) ways to calculate something, so we know what the measurement error really is. Full disclosure – I am in the second pair of eyes business, so part of my job is to check complex models, find, and estimate model error.

    It seems that a lot of these errors wash out, so the variance is <3%. I am not sure that is an accident though, since I do not really think we are measuring these independently (e.g. benchmarking). Will that always be the case – the error is within 3%? Hard to say, as I said there are incentives (e.g. taxes) to under-report certain items, particularly in cash businesses (been there, done that). Other countries, with more corrupt & inept governments, I highly doubt they really know what's going on.

    Do I think that a 3% variance means these are really two different things? Most certainly not!

  18. 18 David Glasner February 22, 2015 at 8:35 pm

    sfdc, If it can be one or the other, then they cannot be the same thing.

    dwb, Certainly the national income accounts are trying to measure the same thing when they measure savings and investment. But it is possible to define savings and investment so that they are not the same thing, which, it is necessary to do, if the income-expenditure model is to be made coherent. My mention of the persistently substantial measured differences between GDP and GDI was just a way to suggest that it is not entirely self-evident that income and expenditure are the same thing.

  19. 19 Jamie February 24, 2015 at 7:37 am

    David said: “But somehow, Keynes’s confusion was resurrected in the economics textbooks, and has not been effectively countered”

    As a non-economist, I can’t say who is right or wrong. However, it is evident that economists interpret these identities differently from each other and that confuses non-economists.

    I have gone back over your existing posts and have a question which I believe is at the heart of why I have problems with this identity. Maybe you could help resolve my confusion.

    In your Feb 11 post you say,

    “Investment is what business firms spend on plant and equipment”.

    You also say

    “Aggregate expenditure is very close to but not identical with aggregate output. They can differ, because not all output is sold, some of it being retained within the firm as work in progress or as inventory”

    I would say that inventory and WIP are investment. Also, assets built within a business rather than purchased are investment. That means that there appear to be two different types of investment. First, investment can be defined as an exchange between a buyer and a seller as long as the product being exchanged is a durable asset. Call that Ix. Second, investment can be defined as value added within a business. Call that Iva.

    When I look at the identity C + I = C + S, I try to use examples to understand what is happening. For example, if I buy a pizza from a supermarket four things happen.

    The supermarket’s inventory of pizzas is reduced by one. That’s a reduction in I.
    The sale is recorded by the supermarket as the left hand C.
    My purchase is recorded as the right hand C and is, by definition, consistent with the sale e.g. if I buy a pizza for $10 then the supermarket must sell a pizza for $10.
    My saving is reduced by the price of the pizza.

    So that makes sense to me.

    I can also see how the Iva part of investment offsets some saving on the right hand side. Inventory is not sold because the money on the right hand side which could be used to buy the inventory is saved instead.

    So that makes sense too.

    What I don’t understand is how the Ix part of investment is supposed to work. I would expect to be able to tell a story similar to my consumption story but I find that difficult.

    One story would say that Ix is just a type of consumption. However, I don’t like that as it is abusing the normal meaning of consumption.

    Another story would say that it’s not consumption but a separate type of exchange. However, my consumption story works only because the C term exists on both sides of the identity. However, the I term exists only on the left hand side of the identity. If this story were correct I would expect the identity to be something like

    C + Ix + Iva = C + Ix + S.

    However, obviously that is not the identity.

    How should I think about Ix? What story would you tell about an example Ix transaction without identifying Ix in the identity? Or have I misunderstood something?

  20. 20 David Glasner February 24, 2015 at 6:50 pm

    Jamie, I don’t know what you mean by value added within the firm. If the firm is not adding value, what is it in business for? Please forgive me, but I am just not up to working out your accounting for you now.

  21. 21 Jamie February 25, 2015 at 4:10 am

    OK. Thanks for your time. I see you have started a new set of posts on accounting identities so I will read them with interest. I did try to read the Lipsey paper but it is on a website which requires registration using an institutional email. I have only personal emails so I can’t access it.

    I will leave you with one final thought. I think that the question I asked you is both simple and clear. You obviously don’t. This is what perplexes me about economists and accounting identities. When non-economists don’t understand what economists are saying about accounting identities, I have notices that non-economists often use examples including some very basic accounting. Economists then say that they don’t have time to do accounting in order to explain what is going on in terms that the non-economist can understand. What perplexes me is that economists use the word ‘accounting’ in the term ‘accounting identity’ but nevertheless claim that accounting is somehow superfluous to accounting identities. That doesn’t make sense to non-economists.

  22. 22 JKH March 4, 2015 at 4:13 am

    “Or stated another way, GDI represents the payments per unit time – a flow of money — made by business firms to households. In contrast, GDP could represent either a flow of final output from business firms to households and to other business firms, or the expenditures made by households and business firms to business firms. These two flows of output and expenditure are not identical, though, for the most part, representing two sides of the same transactions, there is considerable overlap. But it is clear that payments made by business firms to households in exchange for factor services rendered are not identical to the expenditures made by households and business firms to business firms for final output.”

    This is not relevant. As I said previously working backward through these posts, I think you are confusing flow of funds accounting with income and balance sheet accounting.

    The accounting is watertight from an income perspective as the starting point for continuous coherence and equivalence between GDP and GDI. Flow of funds follows up as events such as cash salaries that replace accruals due, dividend payments, retained earnings kept as cash, etc. etc. etc.

    There is no problem here.

  23. 23 JKH March 4, 2015 at 4:21 am

    “But Bill does not say why income equals expenditure. Is it because income and expenditure are identical?”

    It is because of watertight accounting logic applied first to income statements, then balance sheets, then flow of funds.

    (The economics profession in general does not understand the degree to which it logically depends on accounting foundations for coherence in economic modeling.)

  24. 24 JKH March 4, 2015 at 5:00 am

    “As Bill concedes in the passage I quoted earlier, the identity between saving and investment must be derived from the supposed identity between income and expenditure. But the definition of “income” does not immediately tell us anything about “expenditure.” Income and expenditure are not two reciprocal sides of the same transaction. When I buy a container of milk, there is a reciprocal relationship between me and the store that has no direct and immediate effect on the relationship between the store and the factors of production used by the store to be able to sell me that container of milk. I don’t deny that there is a relationship, just as there is a relationship between chickens and eggs, but the relationship is not at all like the reciprocal relationship between a buyer and a seller.”

    Again, just accounting.

    The store has an investment (inventory) which it is carrying at a certain value.

    You will exchange your cash asset for the milk. The store will use the cash to eliminate payables associated with inventory investment (including wage payables) and write up equity for the difference between its inventory cost and the cash it receives.

    Expenditure equals income. The expenditure is what you paid (GDP) and the income is what the store already accounted for in its inventory investment (factor payments to that point) plus the equity effect (GDI altogether).

    The inventory investment transforms to consumption of course.

    The immediate effect is accounting closure – stuff that has already been accounted for is supplemented by the equity adjustment and then all this is recognized as income statements events which are GDP/GDI compatible.

  25. 25 JKH March 4, 2015 at 5:05 am

    “It is precisely the existence of lags between output, expenditure and income that allows for the possibility of non-instantaneous adjustments to changes, thereby creating disequilibrium transitions between one equilibrium and another.”

    Accounting is instantaneous in effect.

    All lags are accounted for.

    All economic events can be represented as accounting events.

    Equilibrium adjustment is just a path from a to b. The path can be accounted for showing identities hold at every point.

  26. 26 David Glasner March 5, 2015 at 12:09 pm

    Jamie, I don’t know what you mean or whom you are referring to when you say that economists think that accounting is superfluous to accounting identities.

    JKH, I am not saying that it is not possible for accounting conventions to find an income box in which to place every expenditure item. Those accounting identities can be made to balance every possible set of transactions. But they do not establish that the sets of transactions that economists are interested in are identical. You can create an accounting identity that ensures that what accountants call income and what they call expenditure will always balance in every conceivable state of the world. That does not establish that the receipts of firms in a given time period are identical receipts of households from firms in the same time period, or more importantly that the income relevant to households in deciding how much to consume in period t is identical to the total receipts of business firms in the same period.

  27. 27 JKH March 5, 2015 at 2:03 pm

    “That does not establish that the receipts of firms in a given time period are identical receipts of households from firms in the same time period, or more importantly that the income relevant to households in deciding how much to consume in period t is identical to the total receipts of business firms in the same period.”

    David,

    Again, its just double entry bookkeeping.

    Take an extreme example:

    Suppose businesses in a given time period produce consumer and investment goods and all of them are held in inventory and none are sold. (Set aside services.)

    Then the entire goods output is held in inventory as investment. And factor payments made to labor and capital constitute income and are held entirely as saving. We know this because the cost of goods produced is determined by the factor payments – including any payment to equity investment (as retained earnings or dividends) in the case of inter-firm supply chains).

    Paying the factors in cash as required is not an issue. It comes where necessary either from existing bank deposit balances of firms or balances newly created from bank loans.

    So the factors just hold onto the cash, which becomes their form of saving.

    There is no reciprocal exchange of funds between firms and households – (unless you consider the transfer of factor payment income back to bank deposits as such an exchange, which might be argued in some way but which really is not a necessary point here).

    But expenditure equals income.

    It cannot be otherwise. This is just double entry bookkeeping.

    P.S. I think the easiest case is to assume vertical integration of the production of all components of goods produced within the same accounting period. If not, just take out the earlier components that constituted goods produced in prior periods along with their factor payments. Periodicity should not be an issue.


  1. 1 TheMoneyIllusion » What does MV = PY actually mean? Trackback on February 20, 2015 at 9:52 am

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About Me

David Glasner
Washington, DC

I am an economist in the Washington DC area. My research and writing has been mostly on monetary economics and policy and the history of economics. In my book Free Banking and Monetary Reform, I argued for a non-Monetarist non-Keynesian approach to monetary policy, based on a theory of a competitive supply of money. Over the years, I have become increasingly impressed by the similarities between my approach and that of R. G. Hawtrey and hope to bring Hawtrey's unduly neglected contributions to the attention of a wider audience.

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