Why Theories of National Income Based on Accounting Identities Are Nonsensical and Error-Ridden, Part IV

In my previous post, I tried to relate the discussion of accounting identities to the familiar circular-flow diagram with injections into and leakages out of the flows of income, expenditure and output. My hopes that framing the discussion in terms of injections and leakages, with investment viewed as an injection into, and savings as a withdrawal out of, the flows of income and expenditure would help clarify my position about accounting identities were disappointed, as defenders of those accounting identities were highly critical of the injections-leakages analogy, launching a barrage of criticism at my argument that the basic macroeconomic model of income determination should not be understood in terms of the income-expenditure or the investment-savings identities.

I think that criticism of the injections-leakages analogy was, for the most part, misplaced and a based on a misunderstanding of what I have been aiming to do, but much of the criticism was prompted by my incomplete or inadequate explanation of my reasoning. So, before continuing with my summary of Lipsey’s essay on the subject, on which this series is based, I need to address at least some of the points that have been made by my (and Lipsey’s) various critics. In the course of doing so, I believe it will be helpful if I offer a revised version of Lipsey’s Table 1, which I reproduced in part III of this series.

First, I am not saying that the standard accounting identities are wrong. Definitions are neither right nor wrong, but they may be useful or not useful depending on the context. In everyday conversation, we routinely ascribe one of many possible meanings to particular words used by selecting one of the many possible definitions as that which is most likely to make an entire sequence of words – a phrase, a clause, or a sentence – meaningful. Our choice of which definition to use is generally determined by the context in which the word appears. Choosing one definition over another doesn’t mean that others are not valid, just that the others would not work as well or at all in the context in which the word in question appears. Working with an inappropriate definition in a given context can lead, as we all know from personal experience, to confusion, misunderstanding and error. Defining savings and investment to be equal in every state of the world is certainly possible, and doing so is not invalid, but doing so is not necessarily useful in the context of formulating a macroeconomic theory of income determination.

There are two reasons why defining savings and investment to be identically equal in all states of the world is not useful in a macroeconomic theory of income. First, if we define savings and investment (or income and expenditure) to be identically equal, we can’t solve, either algebraically or graphically, the system of equations describing the model for a unique equilibrium. According to the model, aggregate expenditure is assumed to be a function of income, but if income and expenditure are identical, expenditure is simply identical to itself, so the system of equations described by the model collapses onto the 45-degree line representing the expenditure-income identity.

Second, even if we interpret the equality of income and expenditure as an ex ante equilibrium condition, while asserting that identity between income and expenditure must always hold ex post, the ex post definitional equality tells us nothing about the adjustment process that restores equilibrium when, owing to some parameter change that disturbs a pre-existing equilibrium, the ex ante equilibrium condition does not hold. For a dynamic adjustment path to take the model from one equilibrium to another via a sequence of discrete adjustments, the model must incorporate some lags. Without lags, the adjustment would be instantaneous, and the model would move from its old equilibrium to a new equilibrium in one fell swoop. But in the course of a sequence of partial adjustments, savings and investment will typically have to be defined by the model so that they are not equal, and this will be reflected in the implied course of savings and investment if the model is worked out period-by-period. Or if you were to observe the Phillips machine (a hydraulic macroeconomic model built by A. W. Phillips of Phillips Curve fame) in action, you could actually see that the savings and investment flows were of unequal magnitudes as machine responded to a change in the settings and moved from one hydraulic equilibrium to another.

It is a common mistake, and the primary object of Richard Lipsey’s scorn in his essay, to attribute causal significance to the savings-investment identity, as if it were the force of the identity itself that guided the dynamic adjustment, when, in reality, the identity, which can always be recovered if one does all the necessary accounting and classifies all the transactions according to the accounting conventions, is irrelevant to the adjustment path. Doing the accounting does not explain how the model moves from the old to a new equilibrium; it just assures us that nothing has been omitted from a final description of what has happened. Rather, the causal mechanism driving the adjustment process can be described using the intuitive idea that income changes because there are injections (in the form of investment) into the income and expenditure flows and leakages (in the form of savings) out of those flows, and when the injections and leakages are unequal in magnitude, the discrepancy between the injections and the leakages causes a corresponding change in the income and expenditure flows.

One commenter pointed out that, even in the numerical example (taken from Lipsey’s essay) that I gave in my earlier post, the sequence of adjustments preserved the definitional equality between savings and investment and income and expenditure, even though the verbal explanation of the adjustment process showed that the equality of savings and investment required a rather forced interpretation of the meaning of savings: the difference between the cash balance expected at the end of a period and the actual cash balance at the end of the period. This peculiar interpretation of savings and its equality with investment reflected the way that Lipsey chose to introduce a lag between expenditure and income into the model: by assuming that income was disbursed by businesses to households at the end of the period in which households provide services to businesses. The income received at the end of one period is then used to finance consumption expenditures and savings in the following period.

I should have pointed out that if one made the trivial adjustment in the expenditure-income lag, so that incomes earned in one period are not at the end of the current period, but at the beginning of the following period, then income and expenditure and savings and investment would not remain equal over the course of the adjustment from the old to the new equilibrium. The sequence of adjustments under the alternative assumption is shown in Table 1 below.

Of course, if we assume that there is a one-period lag between expenditure and income, one could define something called total savings, which would be household savings plus business savings, where business savings is defined as the difference between cash held by businesses at the end of the current period and cash held by businesses at the end of the previous period. And total savings is identically equal to investment. However, it is important to bear in mind that from the point of view of the simple income-expenditure model, the relevant causal variable in determining equilibrium is not total savings, but household savings.

Why do I say that household savings, not business savings, is the relevant causal factor in determining equilibrium income in the simple income-expenditure model? The reason should be obvious: the solution for equilibrium in the simple income-expenditure model is Y = A/(1 – MPC), where A represents the autonomous component of consumption plus planned investment by business firms and MPC is the marginal propensity to consume by households, so that (1 – MPC) is the marginal propensity to save (MPS) . . . by households!

In this setup, business savings is a pure residual adjusting to make up the difference between household savings and investment. When household savings exceeds investment, businesses accumulate their holdings of cash, and when investment is greater than household saving, businesses reduce their accumulate cash. The operation of the banking system might be relevant at this point, but that analysis would take this discussion to a whole new level, which I am not going to get started on at this point.

I will close at this point by just saying that I think that I have provided an answer to the following comment on my previous post asking what is gained by introducing an alternative set of definitions of saving and investment under which savings and investment are equal only in equilibrium, but not otherwise:

But let’s just say you have a system of accounts where definitions are different and saving is different from investment. I can do a mathematical transformation to a new set of variables in which standard identities hold. What is the point of writing so much? Absolutely nothing.

The point of course is that by defining savings and investment so that they are equal only in equilibrium, we now have a system of two linear equations in two unknowns that can be solved for a unique solution, something that cannot be done if savings and investment are identically equal. Second, when we have defined savings and investment so that they can be unequal, but define their equality to be a condition of equilibrium, we can write the following dynamic relationships characterizing the system:

dY/dt = 0 <=> I = S

dY/dt > 0 <=> I > S

dY/dt < 0 <=> I < S

where I and S are defined under the behavioral assumptions in this example as actual investment by businesses and saving by households. The precise definition of I and S would depend, in each particular case, on the specific behavioral assumptions about the underlying lag structure of the model for that particular case. The definitional equality of total savings and investment has no causal significance, but simply reflects the fact that total savings is defined in such a way that it must equal investment.

The definitional equality of savings and investment, as Scott Sumner has observed, is exactly analogous to the quantity identity MV ≡ PY, when V is treated not as the reciprocal of the amount of money demanded as a fraction of income — which is to say as a measurable magnitude understood to be a function of specifiable independent variables — but simply as a residual whose value, by definition, must always be identically equal to PY/M. The quantity identity, lacking being consistent with all possible states of the world, because V is defined not as an independent variable, but as a mere residual. The quantity identity is therefore of no use in describing the dynamic process of adjustment to a change in the quantity of money or what in telling us what are the causes of such a process.

UPDATE (3/29/15): In writing a response to Jamie’s comment, I realized that in the third paragraph after the table above, I misstated the relationship between business savings and the difference between investment and household savings. I have made the correction, and apologize for not being more careful.

63 Responses to “Why Theories of National Income Based on Accounting Identities Are Nonsensical and Error-Ridden, Part IV”


  1. 1 roger erickson March 25, 2015 at 8:23 pm

    This was stated much more simply & effectively by Marriner Eccles, in 1938

    https://fraser.stlouisfed.org/scribd/?item_id=465651&filepath=/docs/historical/eccles/077_03_0002.pdf#scribd-open

  2. 2 Ramanan March 26, 2015 at 1:51 am

    There are two reasons why defining savings and investment to be identically equal in all states of the world is not useful in a macroeconomic theory of income.

    Your definition of saving please?

    First, if we define savings and investment (or income and expenditure) to be identically equal, we can’t solve, either algebraically or graphically, the system of equations describing the model for a unique equilibrium

    This is simply wrong. It’s hilarious.

  3. 3 Ramanan March 26, 2015 at 2:07 am

    To be even clearer, your posts simply read:

    “Accounting is wrong”.

    But that’s not the end. You attempt to hedge your posts by also claiming “accounting is right”, so that nobody can accuse you of claiming “accounting is wrong”.

    But all your posts simply read: “accounting is wrong”.

  4. 4 elwailly March 26, 2015 at 8:32 am

    Ramanan:
    “This is simply wrong. It’s hilarious.”

    I don’t think so. The post is a clear explanation of two ways in which variables can be equal, only one of which is useful.

    Your comment, on the other hand, is so empty that it can only inform us that you failed to understand the post.

  5. 5 doncoffin64 March 26, 2015 at 9:57 am

    I continue to think that part of the confusion stems from what was at least a plausible (early) 19th century argument, which, in fact, I believe “classical” economists made.

    Divide the economy into two groups, “workers” and “capitalists.” *Assume* that workers spend their entire income on consumption. And that “capitalists” spend part of their income on consumption and “save” the rest–but that their saving is in the form of reinvestment in their businesses. In this case, saving *is* investment.

    As soon as we have “workers” who save, and “capitalists” who do things other than run businesses, the act of saving becomes separated from the act of acquiring new capital goods. And for some reason in thinking about national income accounting, some people never got past the first stage.

  6. 6 Rob Rawlings March 26, 2015 at 11:19 am

    +1 to what elwailly said.

  7. 7 Miguel Navascués March 26, 2015 at 1:30 pm

    David: for your fault😉 I’m reading a lot about this topic. I think that the nuclear problem is the break of Keynes from de classical theory of “natural” interest rate that equate saving & investment.
    More frequently than not, economist & politics more or less classics (including MM) confound the account identity with the equilibrium condition of S=I thanks to the interes rate adjusted to the “natural rate”. So, an increase in saving would be followed by an increase in investment.
    Thank you for your clever post!

  8. 8 Nick Edmonds March 26, 2015 at 2:42 pm

    I think part of the problem here is that you are thinking of savings as a causal factor. That is indeed problematic if savings and investment are identically equal. It is better to think of the propensity to save as the causal factor and savings as an outcome.

  9. 9 David Glasner March 26, 2015 at 2:53 pm

    Roger Erickson, Thanks for the link. I took a quick look, but the document is a 25-page speech., which seems to be mainly a defense of the government’s attempt to stimulate the economy in the 1930s under FDR. So I would appreciate it if you could point me to a particular passage that addresses the point that I was trying to make, however inadequately.

    elwailly, Thanks very much for your response to an unpleasant comment that I had decided not to respond to myself.

    Don, An interesting idea, but I am not so sure that classical writers believed that all funds invested in businesses were generated by the profits accruing to the owners of existing businesses. But I haven’t read much of the classical writers on interest and what I have read was read decades ago, so I am not going to say that you are wrong.

    Rob, Thanks.

    Miguel, I’m glad that these posts have been of interest to you. You are certainly right that Keynes introduced the savings investment identity as an alternative to neo-classical theory of interest, and wanted to use it to reject the idea that rate of interest adjusts to equate savings and investment. That got him into a huge muddle, which Hawtrey, Robertson, Haberler, and Lutz immediately criticized him for. For some reason the savings investment identity was reintroduced into the macroeconomics textooks in the 1950s by Samuelson, among others, and led to the confusion that Lipsey tried to dispel in his wonderful essay.

  10. 10 Ramanan March 27, 2015 at 5:44 am

    “I don’t think so. The post is a clear explanation of two ways in which variables can be equal, only one of which is useful.

    Your comment, on the other hand, is so empty that it can only inform us that you failed to understand the post.”

    elwailly,

    Going by your argument everything in the internet is right: either the author or some supporter says “this post is clear, you fail to understand”. What an argument!!

  11. 11 Ramanan March 27, 2015 at 7:36 am

    I have a post here

    http://www.concertedaction.com/2015/03/27/respect-for-identities/

    Nothing new. Just a record of the quote “we can’t solve” (!!!) and a quote by Tobin.

  12. 12 doncoffin64 March 27, 2015 at 10:20 am

    David–I’m not sure that classical economists believed all funding for investment came from retained earnings; I do think they used that as a plausible simplification. (And that’s the problem with plausible simplifications, I think.)

  13. 13 Jamie March 27, 2015 at 12:19 pm

    As I’ve said before, this debate is predominantly about definitions of terms.

    In Table 1, as you point out, the column I (t) and the column Total Savings are identical in every period. Hence, the identity holds if you use those columns. On the other hand, the column I (t) does not equal the column S (t). It is only possible to have a sensible conversation on identities if definitions and assumptions are properly documented.

    In your latest example,

    I (Business) = S (Households) + S (Business) = S (Whole economy)

    In earlier discussions, you appeared to be assuming that S (Business) was zero i.e. there was no retained profit and no operational business loss. In that case,

    S (Business) = 0

    As a result,

    I (Business) = S (Households) = S (Whole economy)

    This is entirely consistent. When S (Business) equals 0, it doesn’t matter whether you define S to be S (Households) or S (Whole economy). If S (Business) does not equal zero, it does matter. You must use S (Whole economy) for the identity to hold.

    This problem has got nothing to do with time lags and it’s got nothing to do with whether you can solve a particular set of equations. You appear to have solved your equations even though I = S (Whole economy) in every period in your example. The problem is about definitions and assumptions.

    The root cause of the ambiguity in this debate can be traced back to that fact that the context diagram you included near the start of your Bathtubs post is not fit for the purpose of helping to define the vocabulary you are using in your posts. For example, there is no injection corresponding to household spending in the diagram. Also, there is only one saving, so the diagram does not support the separate discussion of business saving and household saving.

    I agree that it makes sense to focus on S (Households) in your period by period calculations. The Business Cash column is, effectively, dead money. Businesses will not spend money unless they believe that it will contribute to sales but, by not distributing it to households in dividends, businesses prevent anyone else from spending it either.

  14. 14 Ramanan March 27, 2015 at 2:59 pm

    “You appear to have solved your equations even though I = S (Whole economy) in every period in your example.”

    Nice point Jamie. Nice comment overall.

  15. 15 Nick Edmonds March 28, 2015 at 10:19 am

    David,

    I don’t think either of us is going to succeed in convincing the other on this, so I’m just going to say that I think we agree on what I believe is the most important point here, being that accounting identities tell us nothing about behaviour. In particular, it is wrong to conclude that investment levels can be deduced by considering saving behaviour alone, regardless of how these terms are defined. Also that we cannot deduce equilibrium conditions simply from accounting definitions, nor can we say what happens out of equilibrium. Finally, and perhaps least obviously, that if terms are defined so that they are identically equal, it makes no sense to ask what mechanism it is that ensures they are equal.

  16. 16 Ramanan March 28, 2015 at 12:14 pm

    Nick,

    Finally, and perhaps least obviously, that if terms are defined so that they are identically equal, it makes no sense to ask what mechanism it is that ensures they are equal.

    I think it does make sense. Perhaps the question should be asked differently. From a purely mathematical and modeling point of view, it seems it makes no sense to ask what mechanism it is that the variables in an identity are equal. We just use them as input to our model and hence that itself is an explanation of their truth.

    However, from an economic viewpoint, it is not so satisfying as one is still left with a question as to how it is that they are equal. One one hand we have economic units making decisions on capital formation and on the other we have units making decisions on saving. How is it that saving = investment always?

    Neoclassical authors typically use the price mechanism for everything. So interest rate in this example (with the rate of interest as “price”). They always use the price mechanism for everything. Keynes argued all this is wrong and went on to show how the story is wrong in everything.

    Here’s Joan Robinson on this:

    “For purposes of theoretical argument we are interested in causal relationships, which depend on behavior based on expectations, ex ante, whereas the statistics necessarily record what happened ex-post… An ex-post accounting identity, which records what has happened over, say, the past year, cannot explain causality; rather it shows what has to be explained. Keynes’ theory did not demonstrate that the rate of saving is equal to the rate of investment, but explained through what mechanism the equality is brought about.”

    https://fixingtheeconomists.wordpress.com/2014/08/19/mistaking-behavioral-equations-for-accounting-identities/

    My view about all this is exactly opposite of Glasner: accounting identities are revelations.

  17. 17 Rob Rawlings March 28, 2015 at 1:44 pm

    I agree with Nick on “Finally, and perhaps least obviously, that if terms are defined so that they are identically equal, it makes no sense to ask what mechanism it is that ensures they are equal.’

    In David’s example it is the behavioral assumption about consumers spending a % of income, and businesses always investing $100, while correctly anticipating consumption that drives the model (and allows one to track the series of adjustment that occurs when the behavioral assumption about consumption changes from 90% to 80% of Y).

    “Total Savings” is just a derived value entirely dependent upon the other values driven by the behavioral assumption and will always equal I , and doesn’t add much to the narrative.

    My only quibble is this. David could have named “Total Savings” as “Savings” (S) to keep the accounting geeks happy, and used a different term (“saved Income?”) for his S , and driven the same results with less scope for terminology nit-picking that has hindered and confused the discussion IMO.

  18. 18 JKH March 28, 2015 at 6:07 pm

    To summarize a different view:

    If one is opposed to national income accounting as the measurement foundation for a model of national income determination, there’s little hope for a coherent result in simulating a real world process that gets routinely measured using real world accounting entries. Cost accounting for expenditures sums up to what factors of production earn as income. If one denies that, then you deny the role of cost accounting and income accounting.

    Actual expenditure equals actual income.

    In the simplified 2 sector model, the measured quantity of actual investment equals actual saving.

    In that context, I think the national income determination model you portray is incorrect from the outset– even before getting to the bathtub model.

    The model that I understand is based on the idea of planned expenditure versus actual expenditure and income, the latter two being equivalent in measure, as portrayed on the 45 degree line. The model is based on planned injections and implied withdrawals (leakages) of potentially differing value – not actual injections and actual withdrawals of differing value, because the latter are always equivalent.

    The actual economy is always on the 45 degree line.

    Consider the simplified two sector model (4 sectors is an easy extension once the basic logic of the identity issue is understood).

    On that line, C + I = C + S, and actual injections I equal actual withdrawals S.

    The reason for the 45 degree line is that it depicts the relationship between two different things that have the same quantitative measurement in a monetary economy – expenditures on real goods and services on the y axis and income earned in the monetary unit on the x axis.

    The planned expenditure line represents planned expenditure as a function of income. Its lesser slope than the 45 degree line reflects the fact that MPC < 1. The line starts at the level of autonomous injections on the Y axis and with a lower slope than 45 degrees intersects the 45 degree line at the equilibrium point where actual E equals actual Y.

    Points on such a planning line other than the single point at its intersection with the 45 degree line represent plans for expenditure that are a function of actual income on the x axis, but that do not coincide with corresponding actual expenditure, which must be equal to actual income. Therefore, these non-intersection points are all unrealizable as plans corresponding to their coordinates.

    The intersection of the planned expenditure line with the 45 degree line is a potential equilibrium, where planned expenditure equals actual expenditure and income. Plans can be realized at that point. And it is the only point where plans can be realized according to the assumed expenditure function.

    Depending on context, the 45 degree line can also depict the economy at points of disequilibrium – for example, when the planned expenditure line suddenly rises or falls from its previous equilibrium level.

    For example, suppose the economy starts at an equilibrium point where planned expenditure intersects with the 45 degree line. Suppose planned expenditure then suddenly drops down from there. In the two sector model, this could reflect a planned reduction in investment relative to the counterfactual of no planned reduction in current investment levels. The actual economy is still on the 45 degree line but is now in disequilibrium. The intersection point of the new planned expenditure with the 45 degree line represents a potential future equilibrium point, down to the left and toward the origin of the 45 degree line. Using that new lower potential intersection and equilibrium as a reference point, planned expenditure would fall short of current actual income at income higher levels higher than at that reference point. In the simplified model, planned investment is less than current saving, and so planned injections are less than actual current withdrawal levels.

    Actual S and I will always be equal in the two sector model (more generally, actual injections and withdrawals will always be equal), as the economy proceeds toward a new equilibrium point based on the impetus of planned expenditure. With the subsequent “implementation” of the plan to reduce investment, the behavior of actual injections and withdrawals begins to get traction and this is reflected in the continuous satisfaction of the identity. When actual I is reduced relative to the counterfactual of an unchanged I, it follows that actual S and therefore actual Y must decline by the same amount – because of the inviolable accounting identity that portrays how a reduction in I reduces factor income by the same quantity. And as investment is reduced, the multiplier starts to work in reverse, as actual declining incomes result in reduced consumption as well. Depending on the pattern of the actual implementation of the plan, the economy will gradually work its way down to the new equilibrium point (unless otherwise disturbed) through iterative shrinking of I and S and C and Y, until planned E equals actual E and actual Y once again.

    Non-equilibrium planning points can never be realized because they are off the 45 degree line. All planning points away from the 45 degree line can only be in effect the wishful plans of planners who do not incorporate the inevitable knock-on income effects of realizing their plans to change expenditures.

    This sort of model does not depict a circulating flow of actual injections and actual withdrawals where the two are not equal. There is no such model. Actual injections are always equal to actual leakages. The model instead depicts such differences only in the context of plans for injections and leakages that can never be realized as they are depicted away from that 45 degree line.

    Yet a circulating flow of different actual injections and actual withdrawals is exactly what you have described in this series. That is impossible.

    It is incorrect, and that is why your bathtub model doesn’t work from the get go.

    Second, it certainly appears that your objection to income accounting as the basis for a model of national income determination stems from a lack of familiarity with flow of funds accounting – and implicitly an apparent lack of familiarity with each of income accounting, flow of funds accounting, and balance sheet accounting and the role that each of those financial statement types play in understanding the measurement of economic and financial outcomes. Because what has been proposed is an attempt in effect to convert in some way income accounting to a kind of flow of funds accounting in order to establish some sort of measurement foundation that captures “lags”. But this entirely ignores a standard flow of funds accounting framework that already exists and that is normally used in capturing such cash flow timing differences as a normal complement to income accounting. And ironically, in attempting to create a home grown version of flow of funds accounting, the argument becomes reliant on this customized version of accounting in an attempt to explain behavior. But the behavioral piece comes not from any first order accounting choice. Rather in the model it comes from the marginal propensity to consume assumption and the autonomous injection factors that are built into the planned expenditure equation. It does not come from an attempted bespoke conversion of income accounting to flow of funds accounting, and nor for that matter does it come from the accepted normal accounting system framework.

    Flow of funds accounting is already an established standard accounting framework that complements income accounting and helps explain the cash flow nuances that complement income accounting. The primary accounting tool that underpins a national income determination model obviously has to be the accounting tool that measures income – not flow of funds. Flow of funds information is complementary to this, and is easily incorporated into any logical explanation about how behavior unfolds into actual economic transactions.

    Third, the criticism that accounting does not explain behavior (or as Sumner puts it that one does not reason from an accounting identity) is certainly valid in cases where that mistake is actually made. For example, within the economics profession, this seemed to have been the case when Krugman wrote his “Dark Age of Macro” post in respect of the reasoning of some members of the Chicago school. But this criticism is also the straw man that the economics profession habitually trots out as a more general indictment of the role and importance of accounting. That sort of generalized attitude is an ignorant reflex from the profession and nothing more. Those who understand the connection between accounting and economics obviously know that accounting does not explain behavior. One has to be ignorant of the role of measurement not to understand that. But as the foundation measurement system for realized economic and financial events, it also constrains the nature of the path of feasible economic outcome in the future. It doesn’t determine them, but it does constrain the characteristic of their path in its own way and shapes the feasibility of what those outcomes can end up looking like in the future – if they materialize in fact. So this fact is tremendously important in forecasting – and in planning – and in risk management.

    Fourth, I have no idea how you come to the conclusion that the intersection of the expenditure planning function with the 45 degree line does not determine a unique solution. That conclusion seems to have something to do with a characterization of the expenditure planning function as a function that depicts events that actually happen rather than those which are planned. It is beyond me how one can think that this is not a system of simultaneous equations that determines a unique economy point on the 45 degree line.

    Fifth, the issue of the differentiation of saving as between households and businesses is really of minor concern in context. Model the saving nexus of the two sectors as the alternative of assuming a full distribution of earnings as dividends to households – or model it as separate business sector saving and make some reasonable adjustment to the interpretation of MPC as necessary. This is just not a substantive issue for this topic. The required flexibility in interpretation is easy compared to some of the other issues in debate.

    The Lipsey/Glasner transformation draws from one part of an established accounting framework (income accounting) in an attempt to construct by implication a hybrid version of a second piece that already exists (flow of funds accounting) and which already works very effectively as part of an interconnected accounting system with several different required parts. This tendency to reinvent something that already exists and works very well seems to be a creative impulse that is quite widespread in the economics blogosphere.

  19. 19 JKH March 28, 2015 at 11:10 pm

    Ramanan,

    “I think it does make sense.”

    Totally agree

    As in Robinson’s “rather it shows what has to be explained”

    It’s an accounting mechanism

    A form of mathematics after all

  20. 20 Nick Edmonds March 29, 2015 at 3:23 am

    Ramanan,

    I picked my words carefully. I did not want to exclude the possibility that some form of explanation might be useful in showing how the equality arises from the data.

    However, it makes no sense to me to ask, for example, whether it is changes in interest rates or changes in income levels that makes savings equal investment. They are equal for no other reason than we have defined them that way. No mechanism is necessary.

    But of course that is not to say that we cannot ask what happens if people’s desire to save or invest changes. And we can talk about what mechanism might reconcile these desires.

    It’s like with supply and demand. We can ask what makes the amount people want to buy equal to the amount others want to sell. But we don’t bother asking what makes the quantity actually purchased equal to the quantity actually sold.

  21. 21 Ramanan March 29, 2015 at 8:47 am

    Nick,

    Agree, my point was that these questions are perhaps not the best worded. But their intuition in the question posed has a point, whether or not their actual proposed solution is right or wrong.

    “It’s like with supply and demand. We can ask what makes the amount people want to buy equal to the amount others want to sell”

    Yes that’s a nice way to say it. It’s just that other people word it as if the two sides of the identity are somehow not equal at some times, diverge from each other and made equal and things such as that. Some understand that identities are always true but have some other variables such as planned and so on. What the assumed mechanism before Keynes arrived (and still with most economists) is that if people want to save more, interest rates change (perhaps instantaneously) so that investment also rises with saving. But Keynes showed how the causality is from investment to saving and that output is changing while things such as propensity to consume changes and his mechanism is different.

    So my point was that there’s still some right intuition (at least at the level of posing a question, although the answer may be wrong) even though it is not the best worded usually.

  22. 22 Rob Rawlings March 29, 2015 at 10:30 am

    JKH,

    I suspect I may be missing something basic here but I don’t understand “This sort of model does not depict a circulating flow of actual injections and actual withdrawals where the two are not equal. There is no such model. Actual injections are always equal to actual leakages”.

    I’m imagining a very simple and unrealistic model were each period investment is funded by newly created money (injections) and people save each period by putting some of their income under the bed (withdrawals). If $100 new dollar bills were printed each period and injected via investment spending and $200 leaked out by being put under the bed, why isn’t this a net leakage ? ( you could define savings as defined by the difference between income and consumption, and guaranteed to be $200 in this simple model no matter what assumptions are made about consumption, but that doesn’t seem to provide an explanation for the decline in income caused by the apparent leakage).

    Similarly for the bath tub model. if you take the volume of water in the bath to be income in a given period, and have an input pipe that delivers 100 gallons each period, and an outlet that initially drains 10% of the water each period, then you will start with an equilibrium of 1000 gallons. If you change the outflow from 10% of total content to 20% then the water will drain until you get to a new equilibrium of 500 gallons. In this case outflow exceed inflows until the new equilibrium is reached. Defining S to be the difference between total content minus water that didn’t flow out gives you an equality between S and I (inflow) but not an intuitively very helpful one.

    I suppose you could say that the bathtub must be part of larger model where the leakages must go somewhere so are not really lost but that just seems to be dodging the issue which is about explaining the volume of water in the bathtub.

  23. 23 sumnerbentleys March 29, 2015 at 12:10 pm

    Miguel, I can’t speak for other MMs, but I certainly don’t believe an increase in saving would be “followed by” an increase in investment. Nor do I believe an increase in saving causes an increase in investment. Rather some third factor causes both S and I to change, simultaneously.

    And I certainly don’t believe the so-called Wicksellian “natural rate” has any bearing on any of this.

  24. 24 JKH March 29, 2015 at 2:28 pm

    Rob R.

    Suppose the central bank does “currency QE” by swapping currency for bonds with private sector counterparty firm F.

    Firm F buys newly manufactured capital good from firm G using currency to pay.

    Firm G is a fully vertically integrated firm that pays labor and capital the full cost of goods sold using currency. It pays out dividends to its owners.

    Labor and the owners hide the currency under the mattress.

    The price of the investment good equals what is paid out as income to the factors of production. Other things equal the economy must save all of that income – because no new consumption goods have been produced that can be purchased – only investment goods.

    Investment equals saving.

    Injections equal withdrawals.

    The QE production of currency has nothing to do with the issue at hand. That’s because it is a flow of funds event but not an income event.

  25. 25 David Glasner March 29, 2015 at 3:49 pm

    Don, Just out of curiosity, which classical economists are you referring to when you say they used the assumption that all funding for investment came from retained earnings?

    Jamie, You said:

    “This problem has got nothing to do with time lags and it’s got nothing to do with whether you can solve a particular set of equations. You appear to have solved your equations even though I = S (Whole economy) in every period in your example. The problem is about definitions and assumptions.”
    Actually, it has everything to do with time lags, because the period by period adjustment described by the table depends on the assumption that households receive the income earned only at the beginning of the period after it was earned. That is why, if you check the expenditure (E) column and the income (Y) column, you will see that beginning with period 0, expenditure is less than income in each period..

    “The root cause of the ambiguity in this debate can be traced back to that fact that the context diagram you included near the start of your Bathtubs post is not fit for the purpose of helping to define the vocabulary you are using in your posts. For example, there is no injection corresponding to household spending in the diagram. Also, there is only one saving, so the diagram does not support the separate discussion of business saving and household saving.”

    There is no injection corresponding to household spending because household spending is derived from the incomes earned by households, so it is a constituent part of the circular flow. It is household saving that leaks out of the flow. It is possible that household consumption could suddenly increase, but unless the increase was so large that households were dissaving rather than saving, it would still not be a net injection into the circular flow from the household sector. You are correct that there is only one savings leakage shown in circular flow diagram in my earlier post. The reason is that households, having changed their marginal propensity to save out of income from .1 to .2, are the only source of the increased leakage out of the circular flow. Perhaps as a result of my own misstatement (now corrected) in the third paragraph after the table, you seem to be confused about the role of business firms in this process. All they are doing is letting their total cash balance at the end of each period go down compared to what it was in the previous period. So their saving is going from 0 in the initial equilibrium to a negative number exactly equal in size (but of opposite sign) to the increase in household savings. So there is only one leakage out of the circular flow (the leakage through household savings). There is an ex post adjustment in savings reflecting the willingness of businesses to allow their cash balance at the end of the period to decline in response to the reduction in consumption spending by households. But that reduction in cash holdings represents not a real leakage, but a (strictly bookkeeping) injection(!) (i.e., a negative leakage).

    “I agree that it makes sense to focus on S (Households) in your period by period calculations. The Business Cash column is, effectively, dead money. Businesses will not spend money unless they believe that it will contribute to sales but, by not distributing it to households in dividends, businesses prevent anyone else from spending it either.”

    Thank you for your acknowledgment that it is household saving that explains what is going on this example. But again you seem to be treating the negative savings by businesses as if it were a separate and independent leakage in its own right, when all that is happening is that end of each period in the adjustment process they wind up holding less money than they held at the end of the previous period. So where is the dead money that they are not distributing to households in dividends that they are preventing anyone else from spending when their cash holdings are diminishing all through the adjustment process?

    I would also point out to you that in each period the following relationship holds: the change in expenditure from the previous period equals the negative of the difference between savings in the current period and savings in the previous equilibrium. Thus E(-1) – E(0) = 900 – 1000 = -100, and S(0) – S(-1) = 100. So it is only household savings that has any effect on changes in expenditure and income. Business savings in each period is merely a reflection of the change in expenditure in that period, i.e., business savings is a residual effect that has no influence on the change in expenditure, rather it is the result of the change in expenditure which is the direct result of the change in household savings.

    Nick, I agree with all your conclusions but one. I believe that my tables show that it is possible to say what happens out of equilibrium (i.e., what happens in the model out of equilibrium) if we specify with sufficient precision what behavior assumptions we are making about the agents and about the lag structure.

    Rob, I think that whatever it is that is causing the very negative reactions to my posts by some commenters, it would not have been assuaged by renaming the variables as you suggest. But I don’t have any problem with your terminology.

    More responses to come

  26. 26 David Glasner March 29, 2015 at 10:16 pm

    In reviewing this comment, I found that before my next to last response to various passages from JKH’s comment above, I somehow quoted the wrong passage. I have crossed out the incorrect passage and inserted the passage to which I meant to respond. I apologize to JKH for this inadvertent error.

    JKH, Thanks for your comment/reply to my post.

    You said:

    “Cost accounting for expenditures sums up to what factors of production earn as income.”

    In my example, with a one-period lag between expenditure and income, income exceeds expenditure in every period starting with period 0 when the MPC falls from .9 to .8. It is possible to equalize income and expenditure, in my example, but only by adding the entirely notional decrease in business savings (caused by the increase in household savings) to income in each period starting with period 0. If you wish to make such an adjustment, that is fine with me, but you cannot say that the reduction in business saving plays a causal role in process. It is a pure residual effect in an adjustment process that is independent of any action taken by business firms.

    You said:

    “The model that I understand is based on the idea of planned expenditure versus actual expenditure and income, the latter two being equivalent in measure, as portrayed on the 45 degree line.”

    This is one possible way of understanding the income-expenditure model, which is commonly presented in the textbooks. The expenditure curve represents desired or planned expenditures as a function of income, and equilibrium occurs when actual expenditures equal planned expenditures. The problem with this version of the model arises when one attempts to explain what happens when planned expenditures don’t equal actual expenditures and what mechanisms operate to bring planned and actual expenditures into alignment. The idea that there is a real world mechanism operating to ensure that a definitional equality is realized is problematic, and I see nothing in your comment that dispels that difficulty.

    You said:

    “The planned expenditure line represents planned expenditure as a function of income. . . . The line starts at the level of autonomous injections on the Y axis and with a lower slope than 45 degrees intersects the 45 degree line at the equilibrium point where actual E equals actual Y.

    “The intersection of the planned expenditure line with the 45 degree line is a potential equilibrium, where planned expenditure equals actual expenditure and income. Plans can be realized at that point. And it is the only point where plans can be realized according to the assumed expenditure function.”

    Why do you say that the intersection of the planned expenditure line with the 45-degree line is a potential equilibrium rather than an actual equilibrium? What prevents that point of intersection from being an actual equilibrium? Is it possible for plans not to be realized? If so, how would you represent a non-equilibrium situation in the Keynesian cross framework? Is it a point on the 45-degree line? Is it a point of intersection between an expenditure line and the 45-degree line? If it is not, how does one go about finding which point on the 45-degree line the economy is at?

    You said:

    “[S]uppose the economy starts at an equilibrium point where planned expenditure intersects with the 45 degree line. Suppose planned expenditure then suddenly drops down from there. In the two sector model, this could reflect a planned reduction in investment relative to the counterfactual of no planned reduction in current investment levels. The actual economy is still on the 45 degree line but is now in disequilibrium.”

    You say that the economy is still on the 45-degree line at the moment at which the expenditure line shifts downward? I would like to know which expenditure line it is on. Are you saying that it is still on the old expenditure line, or on some new expenditure line? By what method do you determine which expenditure line the economy is on when it is not in equilibrium?

    You said:

    “The intersection point of the new planned expenditure with the 45 degree line represents a potential future equilibrium point, down to the left and toward the origin of the 45 degree line. Using that new lower potential intersection and equilibrium as a reference point, planned expenditure would fall short of current actual income at income higher [sic] levels higher than at that reference point. In the simplified model, planned investment is less than current saving, and so planned injections are less than actual current withdrawal levels.”

    This is not at all clear. You are implying, but not actually saying that the economy is somehow moving down the 45-degree line from the old equilibrium to “the new lower potential intersection and equilibrium as a reference point.” What “reference point” might mean in this context is completely unclear, a reference point to whom? To households, to businesses, or to the modeler? Does that reference point affect anyone’s behavior in the model in the transition from the old to the new equilibrium? If so, how? You say that planned expenditure would fall short of current actual income at income levels higher than at the reference point. So? What is the implication of planned expenditure being less than actual income for the transition from the old to the new equilibrium? What is happening to actual expenditure when the economy is in transition? Or are you saying that the transition is instantaneous? I don’t understand.

    You said:

    “Actual S and I will always be equal in the two sector model (more generally, actual injections and withdrawals will always be equal), as the economy proceeds toward a new equilibrium point based on the impetus of planned expenditure.”

    You are asserting that actual injections and withdrawals are always equal in the transition from the old to the new equilibrium even though you just explained that planned expenditure falls short of current actual income during that transition. By what mechanism is actual investment made equal to actual savings even though planned investment is less than planned savings?

    You said:

    “With the subsequent “implementation” of the plan to reduce investment, the behavior of actual injections and withdrawals begins to get traction and this is reflected in the continuous satisfaction of the identity.”

    What does “subsequent implantation” mean? The expenditure curve has just shifted. How long after the expenditure curve shifts does the plan get implemented?

    What does it mean for “the behavior of actual injections and withdrawals to begin to get traction?” How long does it take for the process of getting traction – what “getting traction” can possibly mean in this context I have no clue – to be completed? If the process of “getting traction” is not instantaneous, but is nevertheless essential to continuous satisfaction of the identity – otherwise why even mention it in this context? – why is it that the identity is satisfied when the process of “getting traction” is only beginning?

    You said:

    “When actual I is reduced relative to the counterfactual of an unchanged I, it follows that actual S and therefore actual Y must decline by the same amount – because of the inviolable accounting identity that portrays how a reduction in I reduces factor income by the same quantity.”

    Here you simply assert that a reduction in investment causes an actual reduction in savings because of an “inviolable accounting identity” without explaining (insofar as I can tell) how the “inviolable accounting identity” induces any change in the behavior of actual savers. Do you believe that the decline in savings occurs with or without a change in the behavior of savers. If you believe that the behavior of savers does change, please explain to me how their behavior has changed and how that change is related to an “inviolable accounting identity?”

    You said:

    “And as investment is reduced, the multiplier starts to work in reverse, as actual declining incomes result in reduced consumption as well.”

    You seem to be positing a one-time reduction in planned investment. You then assert that there is an instantaneous reduction in savings as a result “because of [an] inviolable accounting identity.” You then posit that the multiplier starts to work in reverse, with declining incomes causing reduced consumption.” Well, with the MPC < 1, declining incomes cause reduced savings as well as reduced consumption. So, according to you, savings keep falling during the transition from the old to the new equilibrium, even though savings fell immediately along with investment when the old equilibrium was disturbed, and the fall in savings exactly matched the fall in investment. And now, according to your own description, savings, having already fallen as much as investment fell, continue to fall because income is now falling toward the new equilibrium, even though the fall in investment, by assumption, has stopped.

    You said:

    “Depending on the pattern of the actual implementation of the plan, the economy will gradually work its way down to the new equilibrium point (unless otherwise disturbed) through iterative shrinking of I and S and C and Y, until planned E equals actual E and actual Y once again.”

    You have provided no explanation at all of the adjustment process, merely a vague and, as far as I can tell, self-contradictory description of what happens based on a supposed “inviolable accounting identity.”

    You said:

    “Non-equilibrium planning points can never be realized because they are off the 45 degree line. All planning points away from the 45 degree line can only be in effect the wishful plans of planners who do not incorporate the inevitable knock-on income effects of realizing their plans to change expenditures.”

    Why is a point on the 45-degree line, but off the planned expenditure any more realizable than a point on the planned expenditure line, but off the 45-degree line?

    You said:

    “This sort of model does not depict a circulating flow of actual injections and actual withdrawals where the two are not equal. There is no such model.”

    Actually there is; it is right in front of you in the table above, and you have not said a word to disprove it even though you keep asserting that an inviolable accounting identity requires that savings and investment, and leakages and injections, are necessarily equal.

    You said:

    This sort of model does not depict a circulating flow of actual injections and actual withdrawals where the two are not equal. There is no such model. Actual injections are always equal to actual leakages. The model instead depicts such differences only in the context of plans for injections and leakages that can never be realized as they are depicted away from that 45 degree line.

    “I have no idea how you come to the conclusion that the intersection of the expenditure planning function with the 45 degree line does not determine a unique solution. That conclusion seems to have something to do with a characterization of the expenditure planning function as a function that depicts events that actually happen rather than those which are planned. It is beyond me how one can think that this is not a system of simultaneous equations that determines a unique economy point on the 45 degree line.”

    If one distinguishes between planned expenditure and actual expenditure, I agree that the simple income expenditure model can be solved for a unique equilibrium. The problem arises when one interprets the expenditure function in the Keynesian cross naively as an expenditure function without distinguishing between planned and actual expenditure. Lipsey makes this point very clearly in his essay, and if I have not been clear enough in making that point, I apologize. However, the distinction between planned and actual expenditure solves only the first of the seven problems listed by Lipsey with using the savings investment identity as if it were the mechanism by which the equality between planned and actual expenditure is actually achieved.

    You said:

    “Fifth, the issue of the differentiation of saving as between households and businesses is really of minor concern in context. Model the saving nexus of the two sectors as the alternative of assuming a full distribution of earnings as dividends to households – or model it as separate business sector saving and make some reasonable adjustment to the interpretation of MPC as necessary. This is just not a substantive issue for this topic. The required flexibility in interpretation is easy compared to some of the other issues in debate.”

    What does “saving nexus of the two sectors” mean? The MPC is perfectly well defined. Where in the basic Keynesian model with which we are dealing is there a corresponding magnitude for business saving. As I have already explained above and in my earlier response to Jamie, business saving in this case is simply a notional bookkeeping entry of opposite sign to the additional saving undertaken by households. It is not the result of any behavioral decision taken by businesses. It is only a reflection of the reduction in consumption spending imposed on business by the desire of households to increase their savings.

  27. 27 Ramanan March 30, 2015 at 1:00 am

    “business saving in this case is simply a notional bookkeeping entry of opposite sign to the additional saving undertaken by households. It is not the result of any behavioral decision taken by businesses.”

    There’s a strange notion people have that some accounting entries “are just book-keeping entries”, as if there is some degree of book-keeping-ness or something which you can assign to various entries.

    Anyway, opposite sign? What’s that? And no, it is not correct to say that business saving is not the result of any behavioural decision taken by businesses. Businesses decide to distribute the amount of dividends and retained earning is the result of that.

  28. 28 JKH March 30, 2015 at 2:37 am

    David,

    Thanks for your very thorough response to my comment.

    I will return later with an example that puts some meat on those bones.

  29. 29 JKH March 31, 2015 at 2:35 am

    JKH 2.0

    David,

    I’d like to make several comments further to your last response. I’ll do this in stages.

    First , I’d like to describe my interpretation of the K multiplier.

    After that, the application of the K multiplier to the K cross.

    At both of these steps I will be mapping the economic ideas to income accounting.

    I’ll try to get more specific on the Lipsey/Glasner approach sometime after that. The generics of how I interpret all this seem to be getting in the way of doing that though. The 40,000 foot level is a prerequisite when approaches are so different.

  30. 30 JKH March 31, 2015 at 7:49 am

    2.1

    (I will not be responding directly to your questions in this comment or the one that follows. These two comments are a basis for how I approach the subject. I hope this will be useful. After that, I’ll try to address some of the questions you put to me in that context.)

    The following is my interpretation of the Keynesian multiplier. The basics should be straightforward. But the result of mapping the mathematical process to national income accounting is rather surprising. I first thought of this some time ago and at that point hadn’t seen it in any textbook. That doesn’t necessarily mean it’s wrong – especially considering the somewhat loose connection between economics and financial accounting. I’m also guessing that Godley and Lavoie may have touched on this sort of reconciliation and a whole lot more in their book, although I don’t recall seeing this exact piece when I read it.

    So consider an investment injection of  quantity 100 with an MPC of 2/3.

    The usual math produces a total delta effect of:

    Y = I + C = 100 + 200 = 300

    I think of this as the leveraging of an investment injection with consumption flowing from the income that is created for the factors of investment good production. The real world process may be more complicated, but I’ve always thought of the multiplier as intuitively reasonable, even if oversimplified. I can’t see why it should be fundamentally wrong as an idea about economics.

    But here are some income accounting implications of the economic effect:

    First, the investment injection creates income that accrues to the factors of production – labor and capital. This works through cost accounting. The price at which the investment good is sold covers all costs – including the cost of capital. That said, the price may not cover the theoretical “hurdle rate” for the cost of capital. But that is a technical detail. The equity holders earn some sort of actual residual return, positive or negative. So in the more general sense, the actual cost of capital is accounted for.

    So the investment injection creates an equivalent amount of income.

    Consider the effect at the moment the income is fully accrued to the factors of production – before anything else happens. That amount of income must be saved by the macroeconomy – other things equal. We know this because no new consumer goods or services are produced in this initial standalone scenario of a new investment injection. Therefore, given that saving in the generic sense is income not used to purchase consumer goods and services, this new income created by an assumed investment injection must be saved in the first instance.

    So at this incipient stage before the multiplier process starts, S equals I. That’s before the marginal propensity to consume or save is in motion.

    One’s eyes may roll at this point, since the operation of the MPC includes the complementary MPS, and the MPS is a saving function that also operates as the multiplier iterates with successive waves of income creation and consumption.

    So one may ask – how can these apparently opposing ideas be reconciled – the contention that S equals I at a point when the multiplier saving dynamic hasn’t even started?

    The investment injection results in an equivalent quantity of income and saving as described earlier. I think you question this off the top while I have claimed it must be the case. But please suspend disbelief for purposes of what I want to describe next, because given that assumed starting point, this should at least reinforce the idea that S = I at all times following that same assumption for the investment injection.

    So now assume that the first round of the multiplier math works and there is an initial consumption burst of quantity 66, representing the MPC effect on the income of 100 that was just newly created.

    And correspondingly there is new saving of 33.

    A pertinent question then is how this gets reflected in income accounting.

    As a simplification, assume that the factors of the investment good production who received the new income of 100 are the ones who spend the 66.

    So the economy has earned 100 in its factors of investment good production capacity and has now spent 66 in its MPC capacity.

    Recall that at the investment injection stage considered on its own, before the multiplier starts to work, the economy saved 100.

    Then, in the first stage of the multiplier, the economy spent 66 on consumption. For simplicity of exposition, I’ve assumed those who initially saved were the ones who then spent (I.e. the factors of investment production) But no more income has been assumed to be earned by them. So they have dissaved 66 in the second stage. At the same time, those who produced the 66 of consumer goods have earned 66 as factors of production for those consumer goods. But the consumer goods they produced have been purchased. So there are no remaining consumer goods for them to purchase with their income of 66. And that means they have saved 66.

    Therefore, the net saving result of the first round of the multiplier effect is 0.

    Thus an MPS of 1/3 has resulted in 0 incremental saving for the macroeconomy. That is because the opening saving of 100 by the factors of production for the investment good has only been redistributed as cumulative saving as between 33 for the investment good producion factors and 66 for the consumer good production factors. So the amount of cumulative S still equals the amount of original S, which equals I. And the important observation is that the entire quantity of saving was created originally and at the outset as equivalent to the income earned by the factors of the investment good production.

    Each successive round of the multiplier features a similar combination of equal dissaving and saving.

    The result is that cumulative saving remains constant at 100 from the outset and  I = S remains in tact always.

    The important point is that an original investment injection associated with a Keynesian multiplier process accounts for all the macroeconomic saving to come out of that process, and the MPS fallout of the MPC sequence accounts for none of it.

    Tomorrow I’ll write out my interpretation of how the multiplier algebra translates to the Keynesian cross geometry.

    P.S.

    My motivation in part for writing this out was this section of your previous response:

    ” You seem to be positing a one-time reduction in planned investment. You then assert that there is an instantaneous reduction in savings as a result “because of [an] inviolable accounting identity.” You then posit that the multiplier starts to work in reverse, with declining incomes causing reduced consumption.” Well, with the MPC < 1, declining incomes cause reduced savings as well as reduced consumption. So, according to you, savings keep falling during the transition from the old to the new equilibrium, even though savings fell immediately along with investment when the old equilibrium was disturbed, and the fall in savings exactly matched the fall in investment. "

    My explanation above is framed in the generic expansionary mode but applies readily to the previous contractionary example on which you commented. The injection and consumption multiplier just work in reverse. I'll return to that contractionary example with my next comment on the application of this to the Keynesian cross.

  31. 31 JKH April 1, 2015 at 1:49 pm

    2.2

    This is my follow up comment regarding the multiplier and the Keynesian cross.  But before getting to that, it occurred to me that I would be able to transform your table 1 and the story that it tells into conventional financial accounting. Instead of modifying standard income accounting as you have done, I will be able to present an integrated treatment of your story using balance sheet, income, and flow of funds accounting. I think I can do this, but it’s going to take several days to think through how to do that in a reasonably concise and understandable way.

    It may make more sense following that to return to some of the more specific questions in your last comment.

    I’m not sure how interested you are at this point, but with your permission I’d like to use this space to develop my response to your series further. I will assume that is OK unless you interject at some point. This is something I’m interested in for purposes of my own satisfaction at least.

    Anyway, here is what I suggested yesterday. It is a brief explanation adapting the multiplier to the Keynesian cross with standard income accounting. I want to emphasize this description has nothing to do with explaining behavioral motivation. It is the adaptation of algebra to geometry using accounting. Pending my planned reformulation of your table 1 using standard accounting, suspending judgement on my stubborn quantitative equating of expenditure and income and of investment and saving is always an option.

    Here is my interpretation of the Keynesian cross, using the previous multiplier discussion as the basis. I’ll  return  to the first example of an investment contraction to keep continuity with the scenario you have already responded to.

    Assume the economy is at an alleged equilibrium point – at the intersection of a planned expenditure line with the 45 degree line.

    Suppose planned investment falls by 100. Again, assume MPC = 2/3.

    The scenario is one in which investment will be 100 lower than its previous level (bearing in mind we are referring to the level of investment flows here).

    Using comparable logic as in my previous comment, that means that both I and S drop by 100 at the outset. There is that much less investment injected and saving created as a result of the economy not operating at a counterfactual level of activity equal to its previous pace.

    So expenditure drops by 100 – and that considered just on its own can be represented by a direct vertical drop from the previous equilibrium point down to the planning line.

    But as I have said before, such a point is unrealizable in fact, because it lies off the 45 degree line. And that corresponds to the fact that I of 100 generates S of 100 (or in this case a decline in I from previous levels means a decline in S from previous levels). So what happens is that instead of landing on that 100 vertical drop down point, the economy combines (in measured effect) that move with a second move horizontally to the left, where it lands on the 45 degree line at a point where both E and Y have declined by 100. This simply reflects the fact that I = S at all times as described in my previous comment (which again I realize is a contentious supposition for purposes of the broader discussion).

    And so what has really happened from the standpoint of the KC geometry is that the economy has slid directly down the 45 degree line as a result of this discrete drop in both investment and saving.

    This happens in steps representable by discrete accounting. Common sense suggests that a “plan” can consist of a series of such discrete steps – in which case there is a ratcheting of reduced investment injections down the 45 degree line – or a plan can consist of a single discrete step depending on the scale or on the preference for stepwise analysis. The single discrete step is the clearest way to analyse the accounting record for the economics.

    As in my previous example depicting economic expansion, such a discrete investment step occurs logically prior to knock-on consumption multiplication, which in this case will be a multiplied contraction from the unchanged level of the counterfactual.

    Similar steps can be visualized for the operation of the multiplier in reverse. The first wave in which income has dropped by 100 results in 66 less consumption expenditure with that much less income created and so on. The economy falls down the 45 degree line in stages. At each stage a simple vertical drop in expenditure is precluded by the fact that income has also declined, which directs the net result back to the 45 degree line. One can visualize successive falls down the 45 degree line in this way. And note that the economy remains above the planned expenditure curve all the way down until it finally converges to the intersection of the planning line with the 45 degree line. That is the point where the multiplier effect finally exhausts itself mathematically because new iterations of forgone income have become vanishingly small. And comparable to the expansion version I described before, there is no additional reduction in macroeconomic saving beyond the initial drop associated with the investment reduction, notwithstanding the dynamic operation of the MPS in reverse.

  32. 32 Rob Rawlings April 2, 2015 at 8:21 pm

    JKH,

    Just to let you know that I am still reading and trying to follow along.

    You logic sees to be: Investment spending will always lead to income that cannot be consumed since investment spending by definition does not generate consumer goods. So investment always equals savings.

    Likewise consumption spending, as it can be seen as spending from previously accumulated savings, will always be both dis-savings and dis-investment.

    So applying this logic to David’s model:

    In year 1 there will be 100 of I and S and no consumption so Y= 100
    In year 2 there will again be 100 I and S, but people will spend 90% of the 100 they earned (saved) in year 1 so Y= 190
    Y will then multiply up with people always spending 90% of the previous year Y until we reach an equilibrium of y=$1000, which is David’s staring point (and he brings Y forward a year).

    Then from equilibrium people decide they want to consume only 80% of the previous years Y, which then causes Y to multiply down to the new equilibrium of Y=500.

    David defines S as “Y-C” (where Y is E from the previous period) and based on that definition he uses dY/dt = 0 I = S as an equilibrium condition.

    Using (my interpretation of ) your version of David’s model, you could rename David’s S as a new variable called UY (Unspent Income = Last Years Y – this years C) , and draw the conclusion that in equilibrium dY/dt = 0 I = UY.

    Is above correct ?

  33. 33 JKH April 3, 2015 at 9:34 am

    Rob R.

    Thanks for following and your question.

    I’m attempting to put together a comment that compares David’s approach with more conventional accounting.

    There are a lot of moving pieces, so that’s going to take longer than I had first anticipated.

    At this point I hope to have that done no later than sometime on Monday.

    I think it will be effective for me to look at your comment more closely after I’m done with that. And I’ll try and respond then.

  34. 34 pliu412 April 5, 2015 at 9:46 am

    Dear
    I fully agreed that these accounting identities are faulty :
    1. GDI = C + I = C+ S = GDP
    2. GDP = C + I + G + (X – M) = GDI = C + S + T (used in MMR and MMT)

    But the NIPA foundation is really based on these accounting identities:
    1. GDP = C + I + NX (net exports)
    = C + S – NR (net income receipts from foreign)

    2 S – I = NX + NR = balance of current account

    Most people missed the meaning and definition of saving S in NIPA, which is “non-consumed” spending from income. Investment (I) is not considered as consumed spending.

    In NIPA accounting, saving S just measures the return of investments (both domestic and foreign) while investment I measures the cost of investment.

    Detailed NIPA accounts and the relationships of accounting items are here
    http://www.bea.gov/national/pdf/nipa_primer.pdf.

  35. 35 pliu412 April 5, 2015 at 10:53 am

    JKH and Bob R.

    I believe that we are using different definitions and meanings of S(savings) in the discussions. In my previous post, I referred to one pdf file about USA NIPA T economic accounting methodology for your reference.

    In economic accounting, sector T-accounting tables 2, 3 and 4 (public, business and personal) define a balance item called sector saving.

    LHS = “consumed” spending items + saving
    RHS = income items

    Please note that investments are not recorded in “consumed” spending items in table. Sector investments and savings are compared in domestic capital account table 6.

  36. 36 pliu412 April 5, 2015 at 1:07 pm

    The meanings of negative saving numbers (S < 0) and (S – I) < 0 in NIPA accounts Note that: S(saving) is used to measure the RETURN of investment. I is used to measure the COST of investment and it must be non-negative number.

    (a) S < 0
    Sector saving S can be a negative number in NIPA accounts since it is defined as sector income less "consumed" spending items. In USA, government saving is often a negative number. Sector ROI (Return of Investment) has not yet cover sector CFC (Consumption of Fixed Capital).

    (b) S-I < 0
    Gross saving (total ROI from public and private sectors) has not yet cover domestic investment (I)

    Since S and balance of current account can be negative numbers, "S=I" is described in NIPA investment and saving account (table 6 in NIPA guide) by this way: RHS = LHS

    RHS = net domestic saving + CFC = gross domestic saving(S)
    LHS = gross domestic investment (I) + balance of current account (NX+NR)

    Thus, the confusion of "S=I" comes from following sources from incorrectly using the NIA accounting items.

    1. The definition of S.
    In NIPA, I is not considered as "consumed" spending since S is a
    smart way to measure RO(I)

    2. The definition of I
    In NIPA, I is used to measure gross domestic investment

    3. NIPA T-accounting is based on money flow conservation laws, not
    based on supply-demand equilibrium cross. In temporal logic (http://en.wikipedia.org/wiki/Temporal_logic), the accounting identities mean "ALL" operator: ALL t such that LHS(t) = RHS(t) in NIPA T-accounts

    Note that, the supply-demand equilibrium cross is based on "EXIST" or "FUTURE" operator. IMO, behavioral and equilibrium math equations in current economic models make axiomatic economic theorems for "mechanizing" human economic behaviors. This is the problem of our economic models, far from reality.

  37. 37 JKH April 6, 2015 at 9:01 am

    2.3

    This is my comment discussing how standard accounting works for the lag model presented in the post.

    There are 2 aspects to the discussion – the structure of the economic scenario and model with lagged payments of income, and the accounting.

    The scenario is that an economy produces output with corresponding expenditure E but delays the payment of income Y until the next accounting period.

    I’m going to refer to standard accounting for Y as Y and the methodology used in the post as LGY (i.e. “Lipsey – Glasner income” ).

    Then:

    E ( t ) = Y ( t )

    E ( t ) = LGY ( t +1)

    Standard accounting recognizes income in the time period in which it is earned.

    LGY accounting recognizes income in the time period in which it is paid in cash.

    Consider the point in table 1 where the MPC propensity factor drops from .9 to .8.

    The economy starts to contact.

    In the first iteration, E is 900 ( 100 I + 800 C ) but LGY is 1000. 

    Household saving is shown to be 200.

    Here is how standard accounting handles that:

    First, a real world example. Suppose a US corporation listed on a stock exchange reports its financial results at the end of each calendar quarter. And suppose it pays its employees once a month. But for each month’s work it pays them at the start of the next month.

    Then there is no way that this corporation would report it’s December 31 financial results without showing a liability on its balance sheet for the employee compensation earned in December but not yet paid by December 31.

    Otherwise, it would be omitting an effective debt for what it still owed its employees, and it would be mistating it’s book equity position – it’s net worth as a corporation.  Regulators and shareholders would not tolerate that.

    In effect, the employees have loaned the corporation one months salary until that loan is repaid in the next accounting period.

    This is precisely what is happening at the macro level in the LGY lag example.

    So the standard national income accounting would show E = Y = 900, with a business liability of 900 at the end of the period. Households would have a corresponding financial asset of 900.

    Back at the beginning of that same period, business repaid the prior period liability of 1000 to households. But they received cash revenue of 900 during the period. So as the post says, business cash would have declined by 100 during the period. 

    This component of 100 when received by households is part of a loan repayment in effect. This does not constitute a component of standard income accounting Y or S for households. This sort of thing is captured In flow of funds accounting.

    Just as LGY is the delayed payment of Y earned in the previous period, LGS overstates S by the difference between LGY and Y.

    For example, when E is 900, LGY is 1000 and Y is 900. LGS is 200 while S is 100.

    So under regular accounting, this systematic LG overstatement reflects the cash repayment of a loan – not the differential receipt of income and saving.

    And another way of describing this is that households earn Y of 900 and get paid in the same period in the form of a non-cash financial asset of 900, which is in effect a loan to business for the amount of cash that business owes to households for the income the latter have already earned. That loan is repaid in the next period.

    Loans and loan repayments are not part of standard income accounting. They are captured in balance sheet and flow of funds accounting. These three essential accounting tools taken together constitute a comprehensive, coherent treatment for financial accounting – micro and macro.

    There are several ironies in the comparison of LG accounting with standard accounting.

    First, using standard accounting in no way impedes the analysis of cash flow lags. In fact, this is the reason for seperate balance sheet and flow of funds accounting – so as not to conflate cash flow anaysis with the earning of income when there are clear separations between the earning of income and the cash payments to the recipients of that income. The 3 part framework is precise in its treatment of such situations.

    Second, in the scenario constructed for the post, there is no logical connection between a delayed income payment of 1000 and a decision to ramp down consumption propensity. Why would one choose to consume less because an income payment is systematically late? If that was the case, one would ramp down consumption every time a payment was delayed. But every such payment is delayed in this model. Changes in consumption propensity cannot logically be a systematic function of a systematic lag – or consumption propensity would systematically approach 0, which is obviously nonsensical.

    Third, my earlier example of a corporation that delayed an income payment from December until January is a stretch on reality. Corporations have no valid reason to play such cash management games that span accounting periods. They must account for legitimate liabilities that are outstanding when proceeding to the next accounting period.

    Shorter term intra period lags may still exist – as within a one month income payment cycle. But again, so what? There cannot be systemic behavior to reduce consumption propensity due to systematic lags. Moreover, a lot of people get paid every 2 weeks. But that is not even the relevant point. Standard accounting handles any of these issues even at the level of internal management accounting accruals between external financial reporting dates.

    Just a closing note on some loose ends in the description  of the LG model. I’m not suggesting that there are errors in the construction of the model itself, but there are a few aspects that are omitted from the description that I think are interesting. This is where the correct accounting helps illuminate how a model like this works.

    First, this is essentially a flow of funds model. I will explain more what I mean by this, but it cuts to the core as to why a hybrid income accounting paradigm such as that determined according to the LG income and saving definitions is simply inadequate in revealing how even a lag model such as this works.

    In the context of the LG lag model, the essential missing pieces are the opening and closing balance sheets for each of business and households, and the period flow of funds that connects those balance sheets. I will not attempt to construct complete balance sheets. That would be too time consuming and would necessarily involve hypothetical assumptions to fill in the missing pieces. But I can suggest several pieces of the puzzle that would be critical to the completion of such balance sheets and why this is also critical to understanding the operation and implications of this lag model.

    The declining business cash balance is noted in the post. This is due to the difference between E and LGY for each period. Business revenue is less than the lagged income payment to households.

    But from a flow of funds perspective, it is likely that the business sector ends up holding most if not all of the investment goods that are produced on its own balance sheet (one exception could be new residential housing). Yet all income is assumed to be paid to households. This could be resolved with a flow of funds assumption that business issues new debt or equity each period in order to finance new investment. Such transactions have no primary income or saving effect in a regular accounting context. That would still leave the 100 saving component with households. But the flow of funds story would be tightened up from what is presented in the post. The neat thing about completing such a flow of funds connection for the regular 100 investment component of saving is that the residual component of LGS can then be captured coherently as a net cash transfer from business to households each period. This is the piece that results in the decline in the business cash balance as presented in table 1. This is the difference between E and LGY. That periodic although declining cash drain on business is then matched to a corresponding increase in household cash balances at the same time.

    Second, the scenario presented is a fundamentally interesting story about a very peculiar flow of funds pattern when explained in terms of standard accounting, with balance sheets, incomes, and the flow of funds each more clearly delineated. I have said that E and Y are the same for each period in this model under standard income accounting. This is correct. And that business pays a net cash flow to households in period in respect of the difference between revenue E and the repayment of an outstanding liability for LGY, where LGY is the same as the previous period’s Y. And this is correct. The result is that there is a multi-period net flow of funds from businesses to households, due to the combination of the payment lag and the time it takes to make the transition to the new lower consumption propensity level. And this is a fact under the assumptions of the model.

    The very interesting thing about this model is that if we move back the timing of each LGY payment and make it a prior period payment of Y instead – which is exactly the same amount by definition – then there is no net transference of cash from the business sector to the household sector over time. So one can ask – how can such a mere shifting of exactly the same payments produce such a very different net flow of funds outcome over time in this LG constructed economy? What is going on here? Why should the world end up in a different state when all of the payments that are made over time appear to be the same in the fullness of time?

    The answer has to do with the inherent cyclicality of the LG lag model. When the economy is contracting and as it finds a new equilibrium in response to a consumption propensity downward shock, the business sector transfers funds to the household sector until a new equilibrium is found. When the economy is expanding in response to a consumption propensity upward shock, the same phenomenon will happen with the amount of the recurring liability increasing instead of decreasing until a new equilibrium is found. In this latter case, households will transfer cash back to business until the new equilibrium is found. This will happen for example in the case of a reversal of the contraction depicted in table 1 of the post. The economy would expand and business cash would increase from 500 to 1000. The delay in the payment of income to households would be a cash inflow to business, because E would exceed LPY during the expansionary transition.

    One could then note at this point that there are liquidity constraints on the behavior of both businesses and households in these types of LG economic cycles. In a downturn, business must have a cash balance sufficient to fund the cash transfer to households, as per table 1. And in an upturn households likewise must have sufficient cash to transfer to business. If course, a banking sector can be helpful here.

    To make a long story short, cash gets transferred back and forth depending on the stage of the cycle. So the net cumulative cash flow effect of the lag structure is contained in the long run because  of this.

    This all happens regardless of whether one chooses LG accounting or standard accounting. The particular pattern depicted in the LG model is captured easily using standard accounting, where E = Y at all times and where the funds transference is interpreted for what it is – a flow of funds in the recurring repayment of a type of liability incurred because of a systematic delay in paying income that has already been earned.

  38. 38 JKH April 6, 2015 at 9:17 am

    David,

    I think I’ve probably responded implicitly in my last 3 comments to a number of points you raised in your most recent response to me.

    But I think I’ll let the dust settle a bit now and then circle back to that in a few days time to see what I might add.

  39. 39 David Glasner April 6, 2015 at 9:44 am

    JKH, Thanks for your responses. I will try to read through them all carefully, which I have not been able to do yet, and reply to you withing the next two or three days.

  40. 40 JKH April 7, 2015 at 3:49 am

    Rob R.

    A number of elements you included in your last comment seem right to me.  It’s a difficult subject to parse in total. I’ve tried to translate David’s model to standard accounting, so a fair bit of what I think about that is included in my last lengthy comment.

    I hope reasonable types can agree that accounting does not determine behavior. There are certainly examples where smart people make the mistake of forcing behavioral conclusions from identities. I think that is rare when it happens in the case of professional economists, although it does seem to happen on occasion (witness Krugman’s 2009 offensive on Chicago). I think that is one of David’s points in the more general sense beyond that.

    But it’s quite a different thing and I believe prudent thing to insist that the various pieces of a given puzzle must add up to the whole result – and nothing but the result. If something is assumed to occur that leads to a contradiction in how other known pieces of the puzzle need to fit with that contention – and that failure is captured in the breach of an accounting identity – well that is fair game in terms of emphasizing the importance of accounting. We can’t talk about economics without talking about numbers, and what are numbers in economics if not accounting? I think there are too many straw man denial arguments when it comes to the importance of accounting for economics.

    I can’t emphasize enough how important it is that income accounting is only one leg of a 3 part framework. Historically, the US Flow of Funds accounts published quarterly arguably have been more important than national income accounting in understanding how the the performance of the US economy is captured from an accounting perspective. In fact, national income accounting is actually embedded in flow of funds accounting – because income statements are traverses between balance sheets (but importantly they account for only part of the traverse).

    Returning to the focus of the post, my main point is that standard accounting can capture the kind of cash flow lag that is of interest. So I don’t see that this standard accounting, which includes national income accounting as a subset, is an impediment to this kind of modelling.

    I’m just not sure about the importance of this idea of lags.  Lags exist, but how consequential are they for the economy as a whole? The stock of money is important for allowing things to happen within any period of time. As I suggested in my comment, the very existence of assets and liabilities is a type of bridge over choppy income and cash flow patterns.

  41. 41 JKH April 7, 2015 at 4:35 am

    The Krugman post I’ve referred to several times:

    http://krugman.blogs.nytimes.com/2009/01/27/a-dark-age-of-macroeconomics-wonkish/?_r=0

    “What’s so mind-boggling about this is that it commits one of the most basic fallacies in economics — interpreting an accounting identity as a behavioral relationship.”

  42. 42 pliu412 April 7, 2015 at 9:20 am

    David and JKH,
    SD(Statistical Discrepancy) and ID(Instrument Discrepancy) are included in NIPA/FOF. If included, the actual T-accounting identities are

    (a) NGDP = NGDI + SD
    (b) S – I = (A – L) – ID for each sector, A: assets L: liabilities
    (c) S – I = Balance of current account – ID = Net Foreign Assets Purchased

    I believe that SD is LGY lag. JKH provides a good explanation with different accounting methods.

    IMHO, for (S-I) analysis, it will be more useful to analyze the corresponding financial structures (A-L) than the statistical discrepancy (SD) by using artificial behavioral and equilibrium equations,

  43. 43 pliu412 April 7, 2015 at 9:28 am

    Accounting identity (c) in previous post should be
    S-I = Balance of Current account – SD = Net Foreign Assets Purchased – ID

  44. 44 JKH April 7, 2015 at 1:26 pm

    pliu412,

    Fair enough point on statistical discrepancies and the like. The challenge of collecting consistent empirical data on all this must be a nightmare.

    But the challenge of looking for conceptual convergence is tough slogging too. I tend to put the first type of challenge on hold when wading into the second. 

  45. 45 JKH April 8, 2015 at 2:35 am

    2.3 revision

    I want to modify my earlier explanation of business and household cash positions. The central theme remains unchanged.

    Suppose the economy is in equilibrium at E = Y = 100.

    Consider 2 scenarios:

    a) Suppose households start out each period with a cash balance of 1000. They use this cash to fund E of 1000 during the period, which reduces their cash balance to 0. Then they get paid in cash at the end of the period for income earned during the period, which returns their cash balance to 1000. The cycle starts again.

    b) Same scenario except they get paid their income at the start of the next period. As described before, there is a household non-cash asset of 1000 at the end of the current period representing income earned but not yet paid in cash, which is subsequently paid in cash at the start of the next period, at which point the cash balance returns to 1000. The cycle starts again.

    Now assume a reduced propensity to consume kicks in. The only change is that the amount of the household starting cash balance required to fund E is less than before.

    For example, only 900 of the starting 1000 cash is needed to fund E when E drops to 900.

    So instead of being a cash transfer of 100 from business to households, that 100 difference is the amount of unused cash that remains continuously on the books of households for the entire period.

    Similarly, there is no cumulative transfer of 500 cash from business to households. When the economy reaches it’s new equilibrium at an E that is lower by 500, there is unused household cash of 500 for the entire time of each period.

    Similarly, business cash assumed to start out also at 1000 in the scenario as first presented in the post does not decline to 500 over time. Business starts out with that cash balance in each period, and is paid E at the beginning of the period. Whether it pays out Y = E at the end of the period or at the start of the next period (repaying an end of period liability in the second case) makes no difference to the cash balance of business at the point where households start each E cycle. Business cash increases during the period by the amount of E and then returns back to the same originally assumed 1000 starting balance after paying out income Y = E in cash.

    That is the revised explanation for economic contraction mode.

    In an expansion mode, households need enough starting cash to prefund any prospective higher level of E. So if E expands from 500 to 1000, they will need a cash balance of 1000. Business will see their cash balances rise by an increasing amount during each period as the economy expands, but balances return to 1000 with each cash payment of income to households, just as before. Again, there will be no net transfer of cash balances between business and households.

    In fact, under the simple types of scenarios generally assumed, business requires no starting cash balance at all, whereas households require the maximum prospective level of E as a cash balance (other things equal).

    All of that is quite a revision to the explanation of some of the cash management details. But the rest of the story is the same, and standard accounting when applied correctly works it out.

    Like I said, there are a lot of moving parts. The 3 part accounting framework provides checks and balances in this regard. I wouldn’t have caught this if it had not occurred to me that a cumulative transfer of cash in one case but not the other must result in different balance sheet equity positions, other things equal. And that simply can’t happen just because of a change in the timing of a cash payment for the same amount of income earned.

    I’ve written this correction out quickly in case of continuing reader interest.

  46. 46 JKH April 8, 2015 at 4:12 am

    Above starting out should be:

    ” Suppose the economy is in equilibrium at E = Y = 1000. “

  47. 47 pliu412 April 8, 2015 at 10:04 am

    David,
    I make corrections on accounting identities for your reference.

    (a) E(t) ≡ C(t) + I(t) (LG accounting identity)
    => E(t) ≡ C(t) + I(t) + NX(t) (NIPA accounting identity)

    (b) Y(t) ≡ C(t) + S(t) (LG accounting identity)
    => Y(t) ≡ C(t) + S(t) – NR(t) (NIPA accounting identity)

    Y(t) = E(t) (LG behavioral assumption)
    => Y(t) ≡ E(t) (NIPA accounting identity)

    You can define S = Y – C + NR(net income receipts from foreign) or I = E-C- NX(net exports), but you cannot use the same C in both E and Y equations by counting different combinations of consumption (NX may not be equal to – NR in NIPA accounting).

    E(t) must be equal to Y(t). For individual sector, S may not be equal to I, but for closed or whole world economy, S=I. Sector S-I Balance Accounting Identity:

    NX+NR ≡ (S-I) + (GS-GI)

    GS=government saving,
    GI=Government investment
    S= private saving,
    I= private investment.

    The widely-misused one: (X-M) = (S-I) + (T-G).

    Second, when we have defined savings and investment so that they can be unequal, but define their equality to be a condition of equilibrium, we can write the following dynamic relationships characterizing the system:
    dY/dt = 0 I = S
    dY/dt > 0 I > S
    dY/dt < 0 I < S

  48. 48 JKH April 8, 2015 at 11:52 am

    The model in this post excludes government and foreign sectors as a matter of deliberate simplification – to illustrate the point of the post in the most effective way, I presume. And it is very effective in that way. Extension to the other two sectors involves no fundamental complication in that context.

  49. 49 pliu412 April 8, 2015 at 4:09 pm

    JKH,

    For 2-sector closed economy, NIPA accounting identities will be
    (a) Households T-account (Y ≡ E):
    E ≡ C + S

    (b) Business T-account (BY ≡ BE)
    BE ≡ BC + BS

    (c) Capital T-account (Savings ≡ Investment)
    Savings ≡ S +BS
    Investment ≡ I +BI

    This I-S balance can be derived from (a) and (b) based on flow conservation laws: total expenditure E+BE must be equal to C+I+BC+BI

    Thus individual sector savings may not be equal to its sector investment as David observed, but total savings = total investment, and (S – I)+(BS – BI)= 0. Note that NIPA accounting trick:

    S is defined as Y – C in (a) and BS is defined as BY – BC in (b)

  50. 50 pliu412 April 8, 2015 at 4:34 pm

    Note that
    Y is not equal to C + S, and BY is also not equal to BC+ BS although Y = E and BY = BE in T-accounts.

  51. 51 pliu412 April 8, 2015 at 4:49 pm

    Sorry a minor mistake in previous sentence
    It should be:
    Either Y or E is not equal to C + I. Either BY or BE is also not equal to BC + BI.

  52. 52 JKH April 8, 2015 at 5:15 pm

    pliu412,

    Try S = HS + BS

    etc.

    it avoids conflating symbolic stuff

    NIPA would provide an institutional decomposition of the generic C + I = C + S, if it were done for 2 sector model

    This really is not an issue

  53. 53 JKH April 8, 2015 at 5:32 pm

    Maybe a clearer way to say it is that C + I = C + S is really a one sector model – the private sector.

    There’s no law that says businesses can’t save within that – and a two (sub)sector model can portray that.

  54. 54 pliu412 April 8, 2015 at 9:11 pm

    C + I = C + S only if it is for “closed” economy, and S/I/C aggregated from all sectors.

    The equation will not be a NIPA accounting identity if I is for one sector, and S = BS+HS

  55. 55 JKH April 9, 2015 at 2:33 am

    I said it was assumed closed earlier

  56. 56 JKH April 9, 2015 at 2:36 am

    and I said “etc.”

  57. 57 JKH April 9, 2015 at 2:39 am

    along the lines of 2 + 2 =

  58. 58 pliu412 April 9, 2015 at 8:41 am

    Just clarify some common confusions.

    Textbook teaching on “S=I” makes an implicit assumption that balance of current account (= NX+NR) is used either as foreign sector investment added to I or as minus foreign sector saving subtracted from S.

    These terms: foreign investment and savings, are not defined formally in NIPA. In NIPA domestic capital T-account:

    S = public saving + household saving + business saving
    I = public investment + household investment + business investment
    balance item of capital account (S – I) = NX+NR

    Textbook teaching on “capital account + current account = 0” really means
    “balance of capital account = balance of current account” in NIPA.

    Accounting identities are temporal logic assertions on time-series data, and are truth statements for all past/future time periods.

    Equilibrium and behavior equations are assumptions like dogma or axioms in math systems without proof. The equations may be true for specific group behaviors at particular time period. They are not general and are often not true.

    Equation “S=I” has different meanings depending on the view as an accounting identity or as an equilibrium/behavior equation. This view determines the more accurate equation form, and how the form is derived or assumed axiomatically. Similarly, equation “MV = PQ” has a different form and meaning if considered as an accounting identity.

  59. 59 JKH April 9, 2015 at 11:11 am

    Very good comment

    But if you want to complete a model like this to other/all sectors (and I don’t understand why you’re introducing the foreign sector asymmetrically to the exclusion of government) I think the cleanest way is through the following sector financial balances equation:

    I = S + (T – G) + (M – E)

    which says that domestic investment is funded by domestic private sector saving, the government budget surplus, and the capital account surplus

    NIPA gets adapted however it’s adapted; it is just an institutional decomposition of a functional tautology

  60. 60 pliu412 April 9, 2015 at 1:33 pm

    Fed NIPA/Z.1 FOF report actually follow SNA2008 and IMF BOP conventions.

    The financial balance equation “I = S + (T – G) + (M – E)” is mentioned in many places such as MR, MMT, …

    But the precise accounting identity should be

    I ≡ S + (GS – GI) + (M – E) + (IP – IR)

    I = private investment
    S = private saving
    GS = government saving
    GI = government investment
    IP = income payments to foreign
    IR = income receipts from foreign
    NX = (E – M) (net export)
    NR = (IR – IP) (net income receipts)

    There are few discrepancies.
    (a) government budget surplus(+)/deficit(-) = GS – GI
    G does not cover all government expenditures and only covers the
    spending counted as GDP calculation from government sector.
    G = Government Consumption(GC) + Government Investment(GI)

    Thus, T – G is not equal to budget surplus(+)/deficit(-). We need
    to subtract government non-G spending such as transfer payment, interest payments, etc.

    Government budget surplus(+)/deficit(-) = T – G – non-G = GS – GI which is consistent with private sector S – I

    (b) Current account surplus (+)/deficit(-) = E – M + IR – IP = NX + NR

    Foreign T-account (Receipts ≡ Payments)
    Receipts = E + IR
    Payments = M + IP + balance_of_current_account

    Note that capital account outflow (+)/inflow(-) = current account surplus(+)/deficit(-). E and M do not covers earnings from FDI investment, wages receipts/payments from/to foreign. As G, E and M only cover import’s payments and export’s receipts counted as GDP calculation.

  61. 61 Ramanan April 10, 2015 at 12:15 am

    pliu412,

    Your equations seem right and its not the trade balance which enters the sectoral balances identity but the current account balance and correct definitions are needed for what is meant by “G” such as government purchases of goods and services is counted in GDP by expenditure but the one in the sectoral balances is slightly different.

    However, I don’t see how your points are related to the issues raised here. Any place where such technicalities make a difference in the discuession?

  62. 62 pliu412 April 10, 2015 at 12:29 pm

    Ramanan,

    Here is the contrast.

    (A) E/Y part
    In NIPA T-accounting:
    each sector E(t) = Y(t), All sectors in total E(t)=Y(t)

    In L_G Model:
    Each sector E(t) may not be equal to Y(t), Thus, all sectors in total E(t)
    may not be equal to Y(t) as well. Sector or Total E(t) = Y(t) only in
    equilibrium.

    Note that “E(t) = Y(t)” is used as behavior equation in L_G model.
    Thus this equation may not be true for all time periods. You can
    see Table 1 data. For periods -1 and -2, they are equal. For periods 0, 1, and 2, they are not equal

    (B) S/I part:
    In NIPA T-accounting:
    Each sector S(t) may not be equal to I (t), All sectors in total S(t) = I(t)
    Each sector S(t) is defined as sector Y(t) – sector consumed spending

    In L_G Model
    Each sector S(t) may not be equal to I (t), All sectors in total S(t) may not be equal to I(t) . Sector or Total S(t) = I(t) only in equilibrium.
    Household and business Saving S(t) are defined differently.

    NIPA accounting identities can explain S-I dynamic behaviors adequately without need of equilibrium and behaviors equations. Table 1 data would not happen in NIPA.


  1. 1 JKH on the Keynesian Cross and Accounting Identities | Uneasy Money Trackback on April 14, 2015 at 7:15 pm

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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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