JKH on the Keynesian Cross and Accounting Identities

Since beginning this series of posts about accounting identities and their role in the simple Keynesian model, I have received a lot of comments from various commenters, but none has been more persistent, penetrating, and patient in his criticisms than JKH, and I have to say that he has forced me to think very carefully, more carefully than I had ever done before, about my objections to forcing the basic Keynesian model to conform to the standard national income accounting identities. So, although we have not (yet?) reached common ground about how to understand the simple Keynesian model, I can say that my own understanding of how the model works (or doesn’t) is clearer than it was when the series started, so I am grateful to JKH for engaging me in this discussion, even though it has gone on a lot longer than I expected, or really wanted, it to.

In response to my previous post in the series, JKH offered a lengthy critical response. Finding his response difficult to understand and confusing, I wrote a rejoinder that prompted JKH to write a series of further comments. Being preoccupied with a couple of other posts and life in general, I was unable to respond to JKH until now. Given the delay in my response, I decided to respond to JKH in a separate post. I start with JKH’s explanation of how an increase in investment spending is accounted for.

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.

No one says that investment expenditure will not generate an equivalent amount of income; what is questionable is whether the income accrues to factors of production instantaneously. JKH maintains that cost accounting ensures that the accrual is instantaneous, but the recording of a bookkeeping entry is not the same as the receipt of income by households, whose consumption and savings decisions are the key determinant of income adjustments in the Keynesian model. See the tacit assumption in the sentence immediately following.

Consider the effect at the moment the income is fully accrued to the factors of production – before anything else happens.

I understand this to mean that income accrues to factors of production the instant expenditure is booked by the manufacturer of the investment goods; otherwise, I don’t understand why this occurs “before anything else happens.” In a numerical example, JKH posits an increase in investment spending of 100, which triggers added production of 100. For purposes of this discussion, I stipulate that there is no lag between expenditure and output, but I don’t accept that income must accrue to workers and owners of the firm instantaneously as output occurs. Most workers are paid per unit of time, wages being an hourly rate based on the number of hours credited per pay period, and salaries being a fixed amount per pay period. So there is no immediate and direct relationship between worker input into the production process and the remuneration received. The additional production associated with the added investment expenditure and production may or may not be associated with any additional payments to labor depending on how much slack capacity is available to firms and on how the remuneration of workers employed in producing the investment goods is determined.

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.

Since it is quite conceivable (especially if there is unused capacity available to the firm) that producing new investment goods will not change the total remuneration received by (or owed to) workers in the current period, all additional revenue collected by the firm accruing entirely to the owners of the firm, revenue that might not be included in the next scheduled dividend payment by the firm to shareholders, I am not persuaded that it is unreasonable to assume that there is a lag between expenditure on goods and services and the accrual of income to factors of production. At any rate, whether the firm’s revenue is instantaneously transmuted into household income does not seem to be a question that can be answered in only one way.

What the macroeconomy “must” do is an interesting question, but in the basic Keynesian model, income is earned by households, and it is households, not an abstraction called the macroeconomy, that decide how much to consume and how much to save out of their income. So, in the Keynesian model, regardless of the accounting identities, the relevant saving activity – the saving activity specified by the marginal propensity to save — is the saving of households. That doesn’t mean that the model cannot be extended or reconstructed to allow for saving to be carried out by business firms or by other entities, but that is not how the model, at its most basic level, is set up.

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.

I understand these two sentences to be an implicit concession that the basic Keynesian model is not being presented in the way it is normally presented in textbooks, a concession that accords with my view that the basic Keynesian model does not always dovetail with the national income identities. Lipsey and I say: don’t impose the accounting identities on the Keynesian model when they are at odds; JKH says reconfigure the basic Keynesian model so that it is consistent with the accounting identities. Where JKH and I may perhaps agree is that the standard textbook story about the adjustment process following a change in spending parameters, in which unintended inventory accumulation corresponding to the frustration of individual plans plays a central role, does not follow from the basic Keynesian model.

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.

It must be the case, if you define income and expenditure to be identical. If you define them so that they are not identical, which seems both possible and reasonable, then savings and investment are also not identical.

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.

Yes, that’s fine if income does accrue simultaneously with expenditure, but that depends on how one chooses to define and measure income, and I don’t feel obligated to adopt the standard accounting definition under all circumstances. (And is it really the case that only one way of defining income is countenanced by accountants?) At any rate, in my first iteration of the lagged model, I specified the lag so that income was earned by households at the end of the period with consumption becoming a function of income in the preceding period. In that setup, the accounting identities were indeed satisfied. However, even with the lag specified that way, the main features of the adjustment process stressed in textbook treatments – frustrated plans, and involuntary inventory accumulation or decumulation – were absent.

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 production 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.

There is no logical problem here given the definitional imputation of income to households in the initial period before any payments to households have actually been made. However, the model has to be reinterpreted so that household consumption and savings decisions are a function of income earned in the previous period.

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.

That is fine, but to get that result, you have to amend the basic Keynesian model or make consumption a function the previous period’s income, which is consistent with what I showed in my first iteration of the lagged model. But that iteration also showed that savings has a somewhat different meaning from the meaning usually attached to the term, saving or dissaving corresponding to a passive accumulation of funds associated with income exceeding or falling short of what it was expected to be in a given period.

JKH followed up this comment with another one explaining how, within the basic Keynesian model, a change in investment (or in some other expenditure parameter) causes a sequence of adjustments from the old equilibrium to a new equilibrium.

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).

Actually, it is clear that being off the 45-degree line is not a matter of possibility in any causal or behavioral sense, but is simply a matter of how income and expenditure are defined. With income and expenditure suitably defined, income need not equal expenditure. As just shown, if one wants to define income and expenditure so that they are equal at all times, a temporal adjustment process can be derived if current consumption is made a function of income in the previous period (presumably with an implicit behavioral assumption that households expect to earn the same income in the current period that they earned in the previous period). The adjustment can be easily portrayed in the familiar Keynesian cross, provided that the lag is incorporated into the diagram by measuring E(t) on the vertical axis and measures Y(t-1) on the horizontal axis. The 45-degree line then represents the equilibrium condition that E(t) = Y(t-1), which implies (given the implicit behavioral assumption) that actual income equals expected income or that income is unchanged period to period. Obviously, in this setup, the economy can be off the 45-degree line. Following a change in investment, an adjustment process moves from the old expenditure line to the new one continuing in stepwise fashion from the new expenditure line to the 45-degree line and back in successive periods converging on the point of intersection between the new expenditure line and the 45-degree line.

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.

There is no such “plan” in the model, because no one foresees where the adjustment is leading; households assume in each period that their income will be what it was in the previous period, and firms produce exactly what consumers demand without change in inventories. However, all expenditure planned at the beginning of each period is executed (every household remaining on its planned expenditure curve), but households wind up earning less than expected in each period. Suitably amended, I consider this statement to be consistent with Lipsey’s critique of standard textbook expositions of the Keynesian cross adjustment process wherein the adjustment to a new equilibrium is driven by the frustration of plans.

Finally, some brief responses to JKH’s comments on handling lags.

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” ).


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. . . .

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. . . .

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

The corporation will properly list a liability on its balance sheet for wages not yet paid. This may be a “loan in effect,” but employees don’t receive an IOU for the unpaid wages because the wages are not yet due. I am no tax expert, but I am guessing that a liability to pay taxes on the wages owed to, but not yet received by, employees is incurred until the wages are paid, notwithstanding whatever liability is recorded on the books of the corporation. A worker employed in 2014, but not paid until 2015, will owe taxes on his 2015, not 2014, tax return. A “loan in effect” is not the same as an actual payment.

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.

The “financial asset” in question is a fiction. There is a claim, but the claim at the end of the period has not fallen due, so it represents a claim to an expected future payment. I expect to get a royalty check next month, for copies of my book sold last year. I don’t consider that I have received income until the check arrives from my publisher, regardless of how the publisher chooses to record its liability to me on its books. And I will not pay any tax on books sold in 2014 until 2016 when I file my 2015 tax return. And I certainly did not consider the expected royalties as income last year when the books were sold. In fact, I don’t know — and never will — when in 2014 the books were sold.

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.

That is certainly a possible interpretation of the assumptions being made, but obviously there are alternative interpretations that are completely consistent with workings of the basic Keynesian model.

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.

Again, I observe that “payments in effect” are being created to avoid working with and measuring actual payments as they take place. I have no problem with such “payments in effect,” but that does not mean that the the magnitudes of interest can be measured in only one way.

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 separate balance sheet and flow of funds accounting – so as not to conflate cash flow analysis 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.

Not sure where the irony is. In any event, I don’t see how the 3 part framework adds anything to our understanding of the Keynesian model.

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.

This seems to be a misunderstanding of what I wrote. I never suggested that the lag between expenditure and income is connected (logically or otherwise) to the reduction in the marginal propensity to consume. A lag is necessary for there to be a sequential rather than an instantaneous adjustment process to a parameter change in the model, such as a reduced marginal propensity to consume. There is no other connection.

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.

I never suggested that corporations are playing a game. Wage payments, royalty and dividend payments are made according to fixed schedules, which may not coincide with the relevant time period for measuring economic activity. Fiscal years and calendar years do not always coincide.

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.

I never suggested that the propensity to consume is related to the lag structure in the model. The propensity to consume determines the equilibrium; the lag structure determines the sequence of adjustments, following a change in a spending parameter, from one equilibrium to another.

PS I apologize for this excessively long — even by my long-winded and verbose standards — post.


15 Responses to “JKH on the Keynesian Cross and Accounting Identities”

  1. 1 Thomas Aubrey April 15, 2015 at 12:10 am

    “No one says that investment expenditure will not generate an equivalent amount of income; what is questionable is whether the income accrues to factors of production instantaneously.”

    Based on my own experience of having turned around a number of failing businesses and then successfully built up two others I’d like to understand what happens when the investment doesn’t work out as planned and has to be written off completely? How can income accrue to the factors of production?


  2. 2 JKH April 15, 2015 at 4:26 am

    Thomas Aubrey,

    Your question is directed to David, but I would answer it this way:

    Suppose for example firm X manufactures a capital good and sells it to firm Y for the latter’s use in some other production process.

    The price that firm Y pays for the capital good covers the cost of firm X’s paying income to the factors of production (labor and capital) for that good. That is how the investment expenditure generates equivalent income.

    (It can be helpful to visualize “vertical integration” of various similar processes upstream to the final production of the capital good, as X probably bought some capital goods manufactured by other firms as inputs to its own production process, and then added value to make the final product.)

    Now suppose firm Y starts to use the capital good in its own production process but finds it can’t make good use of it and has to write it off. At the margin, that is a loss, which is negative income. That negative income will accrue to capital as a factor of production.

    At the level of the firm, it is an income loss that gets reflected on the balance sheet as a write-down in the book value of equity.

    At the level of the household, it may also be reflected in a drop in the stock price if the firm is not owned directly by the household.

    So the round trip in this example is that income accrued to the factors of production in the making of the capital good, but it was reversed out in the writing off of the value of capital good in its final use. Capital is the factor that directly absorbs the cost of that reversal.

    Capital as the residual factor of production absorbs both positive and negative income events.


  3. 3 JKH April 15, 2015 at 4:28 am

    Thanks for doing this David.

    I’ll take a few days to put together something that attempts to clarify several points from my perspective, including a few thoughts carried over from earlier discussion. I realize you’ve spent more time on this than you originally planned, so I’ll try to make it a summary type of comment.


  4. 4 Thomas Aubrey April 15, 2015 at 5:17 am

    “Capital is the factor that directly absorbs the cost of that reversal.”

    It’s mostly clearer now, but if I have written off that asset how can a capital asset absorb negative income when it is effectively worthless? Ie Doesn’t the firm itself absorb the reversal rather than capital asset?


  5. 5 JKH April 15, 2015 at 6:31 am

    “How can a capital asset absorb negative income…?”

    Good point – it’s always possible to be clearer on these things.

    The firm has real capital on the left hand said of its balance sheet – the capital good – and financial capital on the right hand side of its balance sheet – debt and equity.

    The left hand side is written down to 0. The equity portion of the right hand side is written down by the same amount. (Households have an ultimate claim on the value of equity in one form or another.)

    Perhaps it’s not right to refer to the financial form of capital as the factor of production. I tend to do that myself because the ultimate income streams are paid to labor and financial capital. Financial capital is a sort of representation of real capital in a monetary economy.


  6. 6 pliu412 April 15, 2015 at 8:07 am

    I formalize NIPA T-accounting in a simple algebraic system to illustrate the relationships of total and sector S and I for your comments to compare discrepancy from your model.

    The basic accounting identities record the basic production money flows
    “my spending item in one sector must be equal to sum of accrued new income from ALL sectors for any time of periods.

    Otherwise, our economic data is inconsistency.

    Sector income may not be equal to sector expenditure, but a balance item is added(or better description: operationally defined) to make sector E = Y in each sector T-accounting.

    In Keynesian model, saving HS or BS (households or business) is operationally defined as sector income less consumed spending. They are the balance items in NIPA T-accounting.

    There are many derived accounting identities. For example,

    total sector “S = I” can be DERIVED (not defined) from basic accounting identities in the following way.

    HE = HC + HS
    HS is the balance item, defined as (HY – HC)

    BE = BC + BS
    BS is the balance item, defined as (BY – BC)

    The derivation process for S = I is as follows:

    Total spending (from C and I) = HC+ BC+ HI + BI
    Total spending (from HE and BE) = HE + BE = HC +HS + BC + BS

    Thus, HI+BI = HS+ BS by removing consumption items
    I = S
    (BS- BI) + (HS – HI) = 0

    One sector investment must not be equal to sector saving. But they must be balanced in one of three forms shown above. Keynesian “cross” is actually
    total S-I conservation law . It is always true for all past or future time periods at 45-degree line for total S (=BS+HS) and total sector I (HI+BI).

    Individual sector BS/HS and BI/HI may be crossed at 45-degree line. But they must be balance to 0. It is also It is always true for all past or future time periods.


  7. 7 pliu412 April 15, 2015 at 11:10 am

    David and JKH,

    I pointed a critical place for your attention.
    In NIPA accounting, column E(t) in your TABLE 1 will be defined as
    E(t) = C(t) + S(t) (not as C(t) + I(t) in your definition). S(t) is defined as Y(t)-C(t), which is same as yours. The term definition sequence in NIPA: Y, C S, then E. Sector E(t) does not record the actual expenditure, which is C(t) + I(t)

    As you correctly observed, there is a difference between S(t) and I (t) in each sector. But all sectors differences must be added up to be zero. That is
    sum (S(t)-I(t)) = 0.


  8. 8 Jamie April 18, 2015 at 3:35 am

    JKH and you appear to be talking at cross purposes in some of this debate. Hopefully, this comment might explain some of the problem.

    There are two separate methods of accounting: accruals accounting and cash accounting. JKH is talking about accruals accounting. You are talking about cash accounting. Under accruals accounting, income and expenditure are recorded when the good or service is provided. Under cash accounting, income and expenditure are recorded when payment is made for the good or service. The rules for who can use each type are defined by government as they have major implications for tax calculations and audit / transparency. They are not open for redefinition by economists.

    All large and medium-sized businesses must use accruals accounting. All limited liability companies must use accruals accounting. Many governments have moved from cash accounting to accruals accounting over the last twenty to thirty years. The UK government definitely now uses accruals accounting. The IMF says that the US government does too [see box 1 on page 2 of link below] although I also found a few articles which appear to contradict the US position. I can’t imagine that the IMF is wrong here. Maybe the US government still uses cash accounting for budgeting but accruals accounting for actuals?

    Click to access tnm0902.pdf

    Small businesses are allowed to use cash accounting. However, the rules are very rigid. The size limit in the UK is a turnover of £82,000. This probably means mostly one person businesses providing simple services such as home decorating and gardening.


    Individuals who complete a standard personal tax return use cash accounting.

    Here is just one example where the advantages of accruals accounting are obvious for any organisation involved in long or complex contracts either as a customer or as a supplier. Imagine an IT business which has a contract to develop a bespoke computer system for a client. The project will last a year – spanning six months in one financial year and six months in another. The terms of the contract state that the business will be paid only on delivery of the new system. This means that, in the first financial year, the business has six months of expenditure but no payment from its client. Under cash accounting, it would make a very large loss. Under accruals accounting, it can book half of its expected income and make a small profit. In the second financial year, the business has a further six months of expenditure followed by a payment which will cover the full year’s expenditure plus profit. Under cash accounting, that would lead to a very large profit. Under accruals accounting, the business would make a further small profit. Under cash accounting, the business would post a very large loss followed by a very large profit. This would have major implications not only for taxation but also for the business’s share price. Under accruals accounting, both income and profit are smoothed across the two financial years leading to a more consistent tax profile and share price.

    At a microeconomic level, the fact that some actors use accruals accounting and others use cash accounting is of no consequence. Each actor is responsible for their own accounts. As long as each actor’s accounts are internally consistent there is no problem.

    At a macro level, however, it is a different story. Inconsistent accounting methods between actors could cause problems. Economists like to say that ‘one person’s expenditure is another person’s income’. However, if your publisher uses accruals accounting and you use cash accounting then this can lead to one period where the publisher has expenditure but you have no income followed by another period where you have income but your publisher has no expenditure.

    This type of anomaly presents economists with a challenge in compiling national accounts and another challenge in determining whether these anomalies result in significant deviations from accounting identities. It’s up to you what judgement you make.

    However, in your model where households work for businesses and where macro data is compiled on a month by month basis, it is likely that the vast majority of wages will be paid in the same period as the employing businesses accrue the benefits of the related labour. This would not be the case if macro data were compiled on a day by day basis or if workers were considered as suppliers rather than employees (as per your book publishing example where your payments are delayed).

    In summary, I’d suggest that accruals accounting is probably the best way to think of accounting at the macro level. Your example about your payments from your publisher is a good one. However, it is an exception rather than the rule. Your point would be far more significant if /when governments use cash accounting to buy goods and services from businesses which use accruals accounting. My key point is that the starting point for this analysis needs to be observation of the real world accounting practices and not economists’ models. If the real world changes e.g. when governments moved to accruals accounting then economists may need to change their thinking in response. Also, simple real world examples, like your publishing example, can be used to highlight deficiencies and inconsistencies in economists’ thinking.


  9. 9 JKH April 19, 2015 at 8:52 am


    A distraction of events has made it difficult for me to add a further comment as soon as I would have liked.

    I would still prefer to do this for completeness (to that point). There may not be much new to add, but a fresh shot at it might be helpful in expressing some of the ideas. But this may be a week or more away.

    I think Jamie’s comment above is constructive.

    I have attempted to describe things in more generic accounting language such as “income”, “sources and uses of funds” (flow of funds at the macro level) and balance sheet. I avoided the terminology distinction of accrual accounting versus cash accounting. For one thing, another distinction exists in the form of accrual accounting versus market to market accounting. This has become a rather nightmarishly complicated regulatory issue for banks especially over the past 15 years or so.

    The general “law” of income accounting is that income is recognized when it is earned (“accrued”) – not when it is paid in cash. This is the basis for both corporate and national income accounting. This corresponds to Jamie’s use of the term “accrual”. Additional information including cash flow lag patterns that may be of interest in behavioral modelling can be gleaned by considering opening and closing balance sheets and the flow of funds for the period in question – alongside income accounting.

    I think cash accounting or cash flow accounting occurs in two different general contexts – as a primary income accounting approach for some less sophisticated entities (with minimal if any external reporting requirements), and as information that is supplementary to the standard (accrual) income accounting approach in the case of more sophisticated entities. In that context I would think the bulk of US GDP is reflected directly or indirectly in standard income accounting terms on the books of sophisticated business reporting entities.


  10. 10 pliu412 April 23, 2015 at 10:59 am

    David, JKH, and Jamie,
    Problem in LG model is not in different accounting methods. NIPA already recognizes it as statistical discrepancy. The problem is really in bathtubs analogy with leakage as saving concept by using behavioral and equilibrium equations.

    The semantics of two sector savings in NIPA are as follows
    (a) Household savings(HS) measure the total contributed investments to household from both household and business sectors (HI1 + BI1)

    (b) Business savings(BS) measure the total contributed investments to business from both household and business sectors (i.e. HI2 + BI2).

    (c) Household Investment spending HI must be equal to HI1 + HI2 independent of accounting methods and investment behaviors.

    (d) Business Investment spending BI must be equal to BI1 + BI2 independent of accounting methods and investment behaviors.

    To be correct in LG model, S(t)= Y – C, The variables C, Y, and S must refer to household sector only (i.e. excluding business sector). Similarly, the business savings (BS) should be defined as business income (BY) – business consumption(BC). In LG model, the relationships of business/household savings to business/household investments are messed up.

    According to NIPA saving concept, total S=I must be preserved in economy for all time of periods, independent of sector equilibrium (BS=BI or HS=HI). However, in 2-sector case, if one sector is in equilibrium, then another sector must be in equilibrium as well.

    The chart for 4-sector (S-I) + statistical discrepancy = 0 is shown below


  11. 12 JKH April 24, 2015 at 4:20 am


    Here is my “summing up” comment. There is probably not a whole lot new here, but I hope the overall description adds to some understanding of how I am viewing this. I’ve not made all the points I might have made regarding the detailed dynamic of your type of lag model. But I think this is enough for now.

    The “stripped down” two sector model for national expenditure and income is:

    E = C + I
    Y = C + S

    E = Y
    And by derivation
    I = S

    This version excludes government and foreign sectors but is sufficient to illustrate the measurement relationship between expenditure and income.

    I think your core question relates to whether E = Y is the only possibility for the relationship between expenditure and income. And because I = S is a derivation of that, you question that as well.

    As preliminary, I strongly agree that I and S are not the same “thing”.

    C appears in duplicate in the equation, whereas I and S are separate symbols. Income valued at a quantity C equals expenditure on output valued at C. Much if not all of this activity appears as a direct application of income earned by households to expenditure by households. That direct association is the rationale for duplicate symbols in my view.

    Investment I undertaken by business is separate from saving S by households. Financial intermediation between physically separate investment and saving serves to make the required connection between the two. That separation is why I and S are different “things” in my view.

    While I don’t particularly care for barter economy thought experiments, it may be illustrative in this case. In a fantasy barter economy, where non-services income is distributed in quanta of real goods, investment I could represent both expenditure on investment and income earned in the form of investment goods. There is a rationale in that case for a duplicate symbol I for both expenditure and income. The same reasoning would holding in that world for a duplicate symbol C. But a barter economy of any complexity becomes difficult even to imagine.

    Whether or not this explanation is the best one, I think we agree that I and S are different “things”.

    The Lipsey/Glasner “list of caveats” seems to revolve around the observation that two different actors in the economy cannot plan for different things as if they were the same thing. But I think this is assuming a conclusion based on an erroneous assumption. The critical aspect is not that they are two different things, but that they inevitably have the same measure using standard income accounting. This is not just a matter of definition at the macro level. It is a matter of accounting construction at the micro level. This is what I meant in my earlier comment about proceeding one accounting entry at a time. Accounting obviously does not drive behavior. But the opposite is true. Accounting tracks and is a representation of the economic consequence of behavior.

    E = Y and S = I in measure because they are forced to be equal due to the mechanics of income accounting. The value of output and expenditure on output is reflected in the income earned by the factors of production (notwithstanding the timing of the payment of that income). Equivalence in measure is forced one step at a time and at all times by double entry bookkeeping that corresponds to the income accounting principle.

    S = I is a statement of measurement equivalence – not substantial equivalence. $ 100 saved from income or $ 100 held in the form of a bank deposit are not the same thing as a $ 100 real investment, but they are equal in measure.

    I suggested earlier that an inter-period lag in the payment of income resulted in effective financial asset for households. This is not a marketable financial asset, but it is a financial claim just as much as a business receivable. The same reasoning holds as in the case of interest accrued on a bond but not yet paid. For example, there is no difference to the net worth of the household as reflected on the balance sheet between the effect of a scheduled interest payment of $1,000 on the first day of a new accounting period and a scheduled compensation payment of $ 1,000 on the same date. Both have been earned in the previous income period.

    Tax accounting is not always the same as standard income accounting, but consistency holds in large part. For example, tax authorities will not allow the deferral of a compounded interest payment payable on maturity on a 5 year fixed income investment held in a taxable account. That income has to be recognized as it is earned and accrued. Tax authorities won’t allow the strategic deferral of tax outside of designated tax shelter vehicles. There may be exceptions where tax benefits or costs are calculated on a basis that is a special purpose overlay to standard income accounting that is still used to report income.

    It seems that the Lipsey-Glasner thesis drives from the fact that I and S are different “things” in order to assert that households cannot be planning the same “thing” in saving from income as business is planning with investing. On that basis, it is suggested that I and S should not be necessarily be treated as being “the same” identically – in models and in model accounting. I disagree with the premise. The issue is not one of an equation of things. It is one of an equation of values. And it is a consequence of standard income accounting that business and households plan different things that must have the same realized value, even if that realized outcome is not apparent to either one when planning. The fact that neither one “knows” that the value of what it is planning can only end up being the same as that realized in the outcome of the other’s planning is irrelevant to the inevitable result. The decisions that are made and the accounting for those decisions ensures that these values are equivalent at all stages of the implementation of their respective plans. This is double entry bookkeeping under standard income accounting, a point I have attempted to make and demonstrate in various comments through this series. It is not an easy point to demonstrate, because it is fundamental to the comprehensive construction of double entry bookkeeping for income accounting and how that construction creates a record of realized economic activity.

    For example, my decision not to get a haircut increases my saving but reduces my barber’s revenue and income – relative to the counterfactual of getting a haircut. Because it reduces the barber’s income, it reduces his saving (other things equal). The barber’s dissaving offsets my saving. That all gets reflected as differential accounting entries on small business and household income statements and balance sheets. My decision not to buy a lawnmower from Home Depot gets reflected as an increase in my saving and (following inventory adjustment) one less lawnmower manufactured and ordered by Home Depot, relative to the counterfactual. The drop in output gets reflected in less income paid to factors of production and the same amount of reduced saving (other things equal). These events can be reflected as differential accounting entries for the factual and the counterfactual. American Airline’s decision not to order a new aircraft from Airbus or Boeing similarly gets reflected as a reduction in investment goods produced by the manufacturer and a reduction in income paid to the factors of production and income saved by the economy, relative to the counterfactual. Again, differential accounting entries will track all of this. It is in the sense of such examples that I made the earlier comment that the economy proceeds one accounting entry at a time. It is not that accounting drives behavior, but that behavior gets reflected in accounting – one step at a time. The time period for such measurement can be collapsed in theory to the point of a single economic transaction. All economic transactions can be represented using double entry bookkeeping and standard income accounting. There will be an income statement and an opening and closing balance sheet for that time period. More than just the macro derivation/definition of S = I, this equation holds at all times through double bookkeeping entry one step at a time.

    Returning again to the higher level question of the equivalence of E and Y: from the equation it appears that I and S are equivalent in measure provided that E and S are equivalent in measure. It seems to me that both the parent equation and the derivation are quite logical. C and I are classifications covering the full scope of expenditure in the simple version of the equation. This expenditure is done at a price that covers the cost of income paid to the factors of production, including the cost of equity capital. The difference between C and I classifications is largely a difference of the time required for the full consumption of the output. C is consumed within the current accounting period – or at least is presumed that way for simplicity of classification. I is consumed over a number of accounting periods (as gradual depreciation in the value of capital goods). The value of C disappears by the end of the current accounting period. The value of I diminishes over multiple accounting periods. The amount of income C used to acquire consumer goods is equal to the expenditure on consumer goods. The amount of income S used for saving from income must be equal to the expenditure on an equivalent amount of investment goods. This follows from the reasonable calculation that E = Y and expenditure C is matched by income C.

    Regarding lags in the payment of income: the process of income accrual typically involves a lag between the time the accrual starts and the time the income is paid. Part IV in the series defines the timing of income according to the timing of its payment, so that Y (t) = E (t – 1). When E declines because of a drop in MPC, Y lags such that Y > E and saving results. My suggestion is that there is an outstanding liability for the payment of income at the end of a period when income has been accrued but not paid. That is how the accounts square under the standard definition where Y (t) = E (t). You have questioned whether such a liability should really be treated as a household asset. I would suggest that if there is a meaningful delay in the payment of income already earned, a banker would be interested in that information for purposes of credit analysis, and would treat that contracted payment as a receivable – which is a type of financial asset.

    Here are some simple cases again on the capital income side of things:

    Suppose a bank holds a bond that pays interest semi-annually. Banks report their financial results on a quarterly basis. In most cases, the time period between interest payments on such a bond will span three different financial reporting periods. The bank doesn’t get paid in cash for interest earned until the semi-annual coupon payment date. But the bank will definitely record interest earned on that bond in each period on a proportionate time-owned basis. If the semi-annual coupon date is in the middle of a financial reporting period, the bank will record income earned roughly in proportions of ¼, ½, and ¼ in respect of dividing up the distribution of income earned over 3 different accounting periods.

    The earlier mentioned household asset example: suppose a household owns a bank term deposit with a term to maturity of 5 years but where the interest payments compound to a single payment made at maturity. If that bond is held in a taxable account, income must be recognized as it accrues each year and income recognition and tax liability cannot be deferred for 5 years.

    The analogy with the payment of regular wages should be apparent. If there is an accounting period lag between the earning of wages and their payment in cash, the employer will record a liability in respect of wages due. In fact, this is not a typical circumstance, because employers tend to pay their employees in the month in which the income was earned, thereby avoiding such lags and corresponding accounting reconciliation and the need to show such liabilities on the balance sheet. Firms tend to pay cash to their employees within the accounting period over which the workers have earned their income, even if that payment occurs at the end of the accounting period. Will that lag still have an effect on behavior? Perhaps. Is it necessary to revise income accounting to reflect that in a behavioral model? I don’t see why that should be the case. The issue of cash flow lags should not be problematic for the adaptation of income accounting in the context of the Keynesian framework – particularly since there are other accounting tools such as flow of funds and balance sheet analysis whose purpose is to deal with such issues.

    That accounting identities do not determine behavior should be uncontroversial. As should be the point that saving is not the same thing as investment. Those are things that I’m in 100 per cent agreement on. What I disagree with is the implication of this observation for accounting.

    Lipsey-Glasner accounting fits the behavior you describe. In doing so, you have not suggested that accounting determines behavior. Nor have I. You have changed the accounting to better explain in your view the observation of behavior. What I am saying is that this is not necessary. While we agree that any kind of accounting cannot explain behavior, we disagree on whether standard accounting is misleading in its observation of behavior.

    I think your suggestion that standard income accounting is insufficient to the task is mistaken in the sense that it implies that income accounting is intended to be sufficient in the first place. It is not. Income accounting does not capture certain cash flow lags. But such lags are captured in standard flow of funds and balance sheet accounting – and those modes of accounting are intended as complements to income accounting in capturing the full scope of financial behavior. Income accounting alone is necessary but not sufficient in this context. If one wishes to explain behavior in light of cash flow timing mismatches, this can be done by supplementing standard income accounting with flow of funds and balance sheet accounting. I see no reason why the dynamics of your models can’t be captured by standard measurement framework.

    Accounting is used to explain observation de facto. But it is also useful in explaining conceivable observation in the future. That again does not explain the causality that moves us from today to tomorrow – it just confirms whether a particular expected or contingently expected observation for tomorrow’s outcome is in fact possible. It is a confirmation that things that are foreseen for tomorrow will add up under accounting treatment that is the same tomorrow as it is today.

    Regarding several specific points in this latest post:

    “I don’t accept that income must accrue to workers and owners of the firm instantaneously as output occurs. Most workers are paid per unit of time, wages being an hourly rate based on the number of hours credited per pay period, and salaries being a fixed amount per pay period. So there is no immediate and direct relationship between worker input into the production process and the remuneration received.”

    Again, standard accounting records income as it is earned – not when it is paid in cash. So while I agree there is no immediate relationship between input and remuneration received in cash, there is definitely a relationship between input and income earned. The issue of lags is one of cash flow mismatches. That is arguably a legitimate issue for economic behavior. But it does not need to be framed with an adjustment in income accounting treatment.

    “The additional production associated with the added investment expenditure and production may or may not be associated with any additional payments to labor…”

    That’s fine, but if it’s not, then it must be associated with additional payments made or payments due to capital and/or additional payments for cost of goods sold (which by regress reduce to payments to upstream factors of production).

    “So, in the Keynesian model, regardless of the accounting identities, the relevant saving activity – the saving activity specified by the marginal propensity to save — is the saving of households.”

    I’m puzzled by the apparent concern over the distribution of saving as between business and households. I don’t see it as a substantial issue in the design or assumptions of a particular model. A Keynesian model should be easily adaptable to any distribution of income or saving between business and households and the definition of MPC. If there is a basic assumption about what these things mean in a standard model (e.g. no business earnings, or no business retained earnings), fine. But adaptation to other distributions should be relatively easy. The only thing that matters is a consistent definition for what is meant by MPC, given the income distribution assumptions included in the model. In a given model, one has to decide which sectors are assumed to earn income. And then one has to make assumptions about the MPC consistent with that. If MPC is a strict function of household income, fine. But then it is necessary to ensure that such a calibration is consistent with whatever assumption is made about whether business does or doesn’t earn income and if it does earn income whether it does or doesn’t retain income as saving. Presumably such permutations of potential patterns of sector income and saving patterns will be reflected consistently in a well-defined MPC function with consistent scope. I see no issue here other than the consistency of assumptions for a given model.

    (As a sidebar to that paragraph, I’m also slightly puzzled by a strict assumption that business doesn’t purchase C goods. That doesn’t seem to correspond to real world situations. Even if the only C goods that business purchases are pizza for a late night working session, this will be captured as a business expense and not a household expenditure.)

    “I understand these two sentences to be an implicit concession that the basic Keynesian model is not being presented in the way it is normally presented in textbooks, a concession that accords with my view that the basic Keynesian model does not always dovetail with the national income identities.”

    I disagree with the second half of this assertion. My point is that the textbook presentation of the algebra of the multiplier misses the accounting connections that I described in my comment. The full saving effect is present in accounting terms as soon as the investment injection is realized. The MPS effect that ripples out from that includes saving at the microeconomic level – but it also includes equal and offsetting microeconomic dissaving – with a zero net contribution to macroeconomic saving. On the other hand, the net consumption expansion is effective at both microeconomic and macroeconomic levels.

    This connection between the algebra and the accounting does not negate the core logic of the Keynesian multiplier or the Keynesian cross. It is a point of algebraic/accounting interpretation and reconciliation – not one that disputes the ultimate multiplier effect. The investment injection has a consumption multiplier effect as described by the algebra, but there is no macroeconomic saving accompanying the consumption multiplier fallout in its various stages. The typical algebraic depiction is microeconomic, but is not comprehensively microeconomic and therefore it is not macroeconomic.

    “However, the model has to be reinterpreted so that household consumption and savings decisions are a function of income earned in the previous period.”

    I see no serious difficulty with the model you have set up as one of lagged response to prior period expenditure (prior period income according to standard definition) – whether or not one elects to change the standard income definition to one that corresponds to a cash flow lag in the payment of that income. I just don’t believe that standard income accounting is something that impedes the formulation and analysis of such a model.

    “As just shown, if one wants to define income and expenditure so that they are equal at all times, a temporal adjustment process can be derived if current consumption is made a function of income in the previous period (presumably with an implicit behavioral assumption that households expect to earn the same income in the current period that they earned in the previous period). The adjustment can be easily portrayed in the familiar Keynesian cross, provided that the lag is incorporated into the diagram by measuring E (t) on the vertical axis and measures Y (t-1) on the horizontal axis.”

    I agree with the first part of this in how I would see the functional relationship as framed in standard accounting terms. But I see no need for a horizontal axis translation in the geometric representation of the Keynesian cross.

    E and Y are equal, so the set of realizable outcomes lies on the 45 degree line with E and Y as the axes. Then, as the economy contracts, the (Y, E) point rolls down the 45 degree line. This is what I described and is what corresponds to standard income accounting. Yes, under standard accounting, current period consumption becomes a function of previous period Y (and E). But such a function just moves the (Y, E) point in the current period down from where it was in the previous period. That does not require a resetting of the horizontal axis. If the axes instead depicted the cash payment of expenditure and the cash receipt of income, that might fit with some sort of axis adjustment as you suggest. But those types of axes refer to cash flow – not income earned. If expenditure and income decline over time as a function of the previous period’s standard expenditure and income, the economy just iterates down the 45 degree line. That’s the propagation effect of a drop in the marginal propensity to consume. I see no problem with this. Somebody who is spending less is may disappoint the plans of somebody else who think their income is going to be unchanged. But that’s what happens under the assumptions. The behavioral function is what it is – the 45 degree equivalence of income and expenditure shouldn’t interfere with it. The fact that incomes may turn out at the end of the period not as expected at the beginning of the period is not problematic for the satisfaction of accounting identities over the period. If one wants to add to this by allowing for the assumption of lags between income earned and cash paid out in wages – that’s fine. But this should not be an issue for income (earned) accounting – only for cash flow accounting.

    “There is no such “plan” in the model, because no one foresees where the adjustment is leading; households assume in each period that their income will be what it was in the previous period, and firms produce exactly what consumers demand without change in inventories.”

    If households want to assume their income won’t change – fine. That is the current plan. And if somebody’s income drops unexpectedly, they may have to revise their plan. I think that is implied in my use of the word “discrete”. Plans evolve according to new facts (Keynes anyone?). And the emergence of declining incomes over the accounting period presents new facts. If my barber’s income declines because my haircut MPC drops, the economy shrinks relative to the counterfactual. Both those things can be represented as differential accounting entries relative to the counterfactual. This can all occur rolling down the 45 degree line (obviously without the involvement of investment adjustment in this example), in discrete steps, maintaining the relevant accounting identity.

    Accounting is a numerical record of economic transactions. This is the case for business, government, and foreign sectors and it is easily adaptable to the household sector. Household accounting is calculable even when households don’t do it. So I see accounting as being substantial in the observation of economic events, in the most granular way. It is in that sense that the economy proceeds one accounting transaction at a time. I think the “algebra of accounting” is as important to economics as the geometry of supply and demand diagrams or the differential calculus of DSGE models.

    Regarding inventories – textbooks sometimes describe the gap between the economy’s current point on the 45 degree line and the drop down point to a new lower non-equilibrium aggregate demand or expenditure planning line as being “filled” by unplanned inventories. If that new line represents the “plan”, then its implementation commences one transaction at a time – meaning one less purchase of C at a time and one more addition to inventories at a time, at first. As that happens, C declines but inventory investment I increases. So assuming that dynamic alone, the economy remains at the same point, but the composition of C and I changes. So yes there is inventory accumulation in this stage, but it is only vaguely related to the drop down distance from the 45 degree line to the aggregate demand line. The relevant point is that the economy will only proceed toward a new equilibrium that is the intersection of the 45 degree line with the new aggregate demand line by traversing directly down the 45 degree line. And the economy must contract in order for that happen. That does not happen in conjunction with inventory accumulation alone. It happens when the previous order flow, now counterfactual, begins to contract, as a response to unplanned inventory accumulation. That moves the economy in steps down the 45 degree line. And it will only find a new equilibrium with a new combination of new levels of consumption and investment, including the new equilibrium level of the flow of net inventory investment accumulation (as part of economic growth), which will also be lower than the previous flow level, other things equal.

    Here is a nuance on the core theme that I agree with in part – as expressed in an earlier post from the series:

    “To compare the relationship between savings and investment to the relationship between purchases and sales is clearly not valid. The definition of the activity called “purchasing” is that a commodity or a service is transferred from a seller to a buyer. Similarly the definition of the activity called “selling” is that a commodity is transferred to a buyer from a seller. The reciprocity between purchasing and selling is inherent in the definition of either activity. But the definition of “saving” does not immediately tell us anything about the activity called “investing.”

    Yes, they are different things. But they have the same measure according to standard income accounting. So what is being planned by one side is the measure of an outcome that must end up being the same as the measure of the outcome from the other side. These identical outcomes should not preclude analysis of the effect of cash flow lags on behavior using a complete accounting framework that includes income statements, balance sheets and flow of funds statements.


  12. 13 Egmont Kakarot-Handtke June 6, 2015 at 1:23 pm

    Tricky business
    Comment on ‘JKH on the Keynesian Cross and Accounting Identities’

    “What a tricky business this all is! In his Treatise on Money, Mr. Keynes told the world that savings and investment are only equal in conditions of equilibrium; that an excess of investment over saving means rising prices, and vice versa. In his General Theory, he told us that saving and investment are always equal, and that this is a mere identity or truism, without significance for the determination of prices. As far as I can make out, there are relevant and important senses in which all these statements are each of them right and each of them wrong.” (Hicks, 1939, p. 184)

    Many senses make no sense at all, but inconclusiveness is the inevitable outcome of every economic discussion. This is no coincidence. Economists do not solve problems, they are the problem. Inconclusiveness and vagueness is the survival strategy of the scientific incompetent.

    “Another thing I must point out is that you cannot prove a vague theory wrong.” (Feynman, 1992, p. 158)

    This conveniently prolongs the shelf-life of crappy theories. The I=S debate is a case in point.

    Keynes messed up the basics of macro with this faulty syllogism: “Income = value of output = consumption + investment. Saving = income – consumption. Therefore saving = investment.” (1973, p. 63)

    Since theories have an architectonic structure it is clear that if there is a fault in the formal foundations the whole superstructure is faulty. Actually, the defect in Keynes’s two-liner is in the premise income = value of output. This equality holds — see the formal proof in (2011) — only in the case of zero profit in both the consumption and investment good industry. Is it necessary to add that zero profit models never had and never will have a counterpart in the real world?

    Keynes’s conceptual problems started with profit.

    “His Collected Writings show that he wrestled to solve the Profit Puzzle up till the semi-final versions of his GT but in the end he gave up and discarded the draft chapter dealing with it.” (Tómasson and Bezemer, 2010, p. 12)

    This failure kicked off the chain reaction of errors/mistakes because when profit is not correctly defined, income is not correctly defined, and then saving is not correctly defined. By consequence, all I=S models, including IS-LM, are methodologically defective. The mistake has also been carried over to accounting (2012). Since the days when Keynes wrote down his faulty syllogism the representative economist did not realize the elementary logical blunder.

    “In fact, the history of every science, including that of economics, teaches us that the elementary is the hotbed of the errors that count most.” (Georgescu-Roegen, 1970, p. 9)

    To sum up: All I=S models are false and absolutely unacceptable. This is not a matter of taste or choice or wish-wash but of conceptual logic. The correct relationship reads Qre=I-S, that is, the business sector’s investment expenditures are NEVER equal to the household sector’s saving and their difference is ALWAYS equal to the business sector’s retained profit. This has already been figured out by a very smart Frenchman, Nobel Laureate Maurice Allais.

    “Autrement dit l’investissement n’est pas égal à l’épargne spontanée, mais à l’épargne spontanée augmenté du revenue non distribué des entreprises ….” (Allais, 1993, p. 69), see also (2011, fn. 4)

    Let there be no inconclusiveness and vagueness: the somewhat moronic I=S debate ended in 1993 at the latest. More than 75 years after the General Theory it is high time for a general intellectual upswing. After endless drivel perhaps JKH could give an example.

    Egmont Kakarot-Handtke

    Allais, M. (1993). Les Fondements Comptable de la Macro-Économie. Paris: Presses Universitaires de France, 2nd edition.
    Feynman, R. P. (1992). The Character of Physical Law. London: Penguin.
    Georgescu-Roegen, N. (1970). The Economics of Production. American Economic Review, Papers and Proceedings, 60(2): 1–9. URL http://www.jstor.org/stable/1815777.
    Hicks, J. R. (1939). Value and Capital. Oxford: Clarendon Press, 2nd edition.
    Kakarot-Handtke, E. (2011a). Keynes’s Missing Axioms. SSRN Working Paper Series, 1841408: 1–33. URL http://ssrn.com/abstract=1841408.
    Kakarot-Handtke, E. (2011b). Why Post Keynesianism is Not Yet a Science. SSRN Working Paper Series, 1966438: 1–20. URL http://ssrn.com/abstract=1966438.
    Kakarot-Handtke, E. (2012). The Common Error of Common Sense: An Essential Rectification of the Accounting Approach. SSRN Working Paper Series, 2124415: 1–23. URL http://ssrn.com/abstract=2124415.
    Keynes, J. M. (1973). The General Theory of Employment Interest and Money. The Collected Writings of John Maynard Keynes Vol. VII. London, Basingstoke: Macmillan. (1936).
    Tómasson, G., and Bezemer, D. J. (2010). What is the Source of Profit and
    Interest? A Classical Conundrum Reconsidered. MPRA Paper, 20557: 1–34. URL http://mpra.ub.uni-muenchen.de/20557/.


  13. 14 JF June 11, 2015 at 6:04 am

    And none of this mentions the plain fact that the Investment Injection that jkh employs could have been financed by bank-money or endogenous money – created new money – not from saved money.

    At least this commentary seems to highlight key points stemming from NIPA identities and early theorists; that is Savings does not equal Investment – as a matter of language they are different terms/words with different meanings (when used outside NIPA accounting). Thank goodness.

    The lack of understanding about where new money comes from is something that economists are also missing (in addition to the points raised by Egmont K-H). Keynes may have intuited here, why else would he note that govts could employ buried cash they just print – though somewhat mocking of gold-mining, he understood it seems to me that some entities were doing just printing-money, so to speak. It seems to me that his consumption theories are the most correct, a society and even a single household who drops their consumption significantly is not in a good condition, one that may need remarkable changes to recover toward normal senses of this. So take into account Net Wealth and endogenous money and we might get more understanding of economics and alleviate confusions about personal savings versus Investment Potential (I try never to use the term National Savings – it is a made up conception, misused by rent-seekers to capture policies of use to their group).

    This is so very important – misundertandings here have led to national policies where capital formation and Investment concerns/needs are somehow tied to calculations of household savings and used to signal fears about society’s Investment and the workings of capitalism. This has misleadingly resulted in tax burdens predominantly falling on flows in 12-month periods (I wonder what Keynes would say about 20% VATs?), differential tax favoratism for capital and Investment, and confusion about what to do about economic policy related to household savings (which people need to have but not as capital-stock).


  14. 15 JF June 11, 2015 at 8:27 am

    Sorry this thread stopped, and hope that there is a return to this.

    I also mentioned Net Worth as being outside these identity equations. But this is real (huge magnitude for the US, around $85 Trillion).

    So the scenario to start jkh off is to consider the owner of a business who wants to expand because of some idea they have. Last year, this owner was bequeathed an income-unproductive but beautiful lake property by a favorite uncle. The owner goes to the bank and offers to put the title of this land down as collateral for a loan at 4% in order to finance the 18-month return to profitability predicts as a result in part of the loan. The bank agrees as they can see that they can get their money either way, and this owner is convincing about managerial abilities, returns, and markets.

    Say it is $1 M, when the bank enters this amount electronically into a depository account for the owner tied to a lending-contract, where does the administering bank get the money when demands are subsequently made against this account?

    You got it, they find the money from all the flows occurring at the bank at the time of demand, but they do not have it when they set up the account or don’t need to have it sitting on the ‘saved-money’ schedule of their books (and they can’t use a depositor’s money as this is a liability of the bank; you simply can’t lend liabilities).

    So in this scenario, a very apt one, not an exaggerated one really, wealth is converted to Investment via a bank loan established with bank-money, ex nihilo. Interest payments are treated as an expense of the business, while depreciation is also used to offset the costs the owner bears on his/her household Net Worth (to reflect the use of the new stuff being purchased with the new money). A good deal for this owner of the business pans out.

    Yes, this Investment starts the flow of income accounting, but this flow- accounting ignores the Net Worth position to begin with and bank-money.

    Is this bequeathed land accounted for as National Savings this year, not under NIPA (in fact it would be picked up as a consumption negative from property taxation). The property isn’t sold in this scenario, so no new mark-to-market capital gain is picked up.

    It seems clear to me that economists, in particular, need to speak out more plainly here so policy makers and the public and their media are much better informed.

    BEA might be helpful here if they publish a new term, and stop referring to this 12-month, flow-accounting identity as National Savings (certainly not without mentioning at all times that this term has little to nothing to do with the huge Net Wealth of US residents or with the fact that banks can create Investment funds at any time, in any amount having little to do with this term). I’d prefer they come up with a new term.

    How about Avoided Consumption in Year (ACY, instead of calling it National Savings or Savings). See what I am getting at here, in terms of the policital economy rationalizations that stem from this simple term and its misuse)?


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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.

My new book Studies in the History of Monetary Theory: Controversies and Clarifications has been published by Palgrave Macmillan

Follow me on Twitter @david_glasner


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