CAUTION Accounting Identity Handle with Care

About three years ago, early in my blogging career, I wrote a series of blog posts (most or all aimed at Scott Sumner) criticizing him for an argument in a blog post about the inefficacy of fiscal stimulus that relied on the definitional equality of savings and investment. Here’s the statement I found objectionable.

Wren-Lewis seems to be . . . making a simple logical error (which is common among Keynesians.)  He equates “spending” with “consumption.”  But the part of income not “spent” is saved, which means it’s spent on investment projects.  Remember that S=I, indeed saving is defined as the resources put into investment projects.  So the tax on consumers will reduce their ability to save and invest.

I’m not going to quote any further from that discussion. If you’re interested here are links to the posts that I wrote (here, here, here, here, here, and this one in which I made an argument so obviously false that, in my embarrassment, I felt like giving up blogging, and this one in which I managed to undo, at least partially, the damage of the self-inflicted wound). But, probably out of exhaustion, that discussion came to an inconclusive end, and Scott and I went on with our lives with no hard feelings.

Well, in a recent post, Scott has again invoked the savings-equals-investment identity, so I am going to have to lodge another protest, even though I thought that, aside from his unfortunate reference to the savings-investment identity, his post made a lot of sense. So I am going to raise the issue one more time – we have had three years to get over our last discussion – hoping that I can now convince Scott to stop using accounting identities to make causal statements.

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

In the standard national income accounting, gross domestic income equals gross domestic output.  In the simplest model of all (with no government or trade) you have the following identity:

NGDI = C + S = C + I = NGDP  (it also applies to RGDI and RGDP)

Because these two variables are identical, any model that explains one will, ipso facto, explain the other.

There is a lot of ground to cover in these few lines. First of all, there are actually three relevant variables — income, output, and expenditure – not just two. Second aggregate income is not really the same thing as consumption and savings. Aggregate income is constituted by the aggregate earnings of all factors of production. However, an accounting identity assures us that all factor incomes accruing to factors of production, which are all ultimately owned by the households providing services to business firms, must be disposed of either by being spent on consumption or by being saved. Aggregate expenditure is different from aggregate income; expenditure is constituted not by the earnings of households, but by their spending on consumption and by the spending of businesses on investment, the purchase of durable equipment not physically embodied in output sold to households or other businesses. Aggregate expenditure is very close to but not identical with aggregate output. They can differ, because not all output is sold, some of it being retained within the firm as work in progress or as inventory. However, in an equilibrium situation in which variables were unchanging, aggregate income, expenditure and output would all be equal.

The equality of these three variables can be thought of as a condition of macroeconomic equilibrium. When a macroeconomic system is not in equilibrium, aggregate factor incomes are not equal to aggregate expenditure or to aggregate output. The inequality between factor incomes and expenditure induces further adjustments in spending and earnings ultimately leading to an equilibrium in which equality between those variables is restored.

So what Scott should have said is that because NGDI and NGDP are equal in equilibrium, any model that explains one will, ipso facto, explain the other, because the equality between the two is the condition for finding a solution to the model. It therefore follows that savings and investment are absolutely not the same thing. Savings is the portion of household earnings from providing factor services that is not spent on consumption. Investment is what business firms spend on plant and equipment. The two magnitudes are obviously not the same, and they do not have to be equal. However, equality between savings and investment is, like the equality between income and expenditure, a condition for macroeconomic equilibrium. In an economy not in equilibrium, savings does not equal investment. But the inequality between savings and investment induces adjustments that, in a stable macroeconomic system, move the economy toward equilibrium. Back to Scott:

Nonetheless, I think if we focus on NGDI we are more likely to be able to think clearly about macro issues.  Consider the recent comment left by Doug:

Regarding Investment, changes in private investment are the single biggest dynamic in the business cycle. While I may be 1/4 the size of C in terms of the contribution to spending, it is 6x more volatile. The economy doesn’t slip into recession because of a fluctuation in Consumption. Changes in Investment drive AD.

This is probably how most people look at things, but in my view it’s highly misleading. Monetary policy drives AD, and AD drives investment. This is easier to explain if we think in terms of NGDI, not NGDP.  Tight money reduces NGDI.  That means the sum of nominal consumption and nominal saving must fall, by the amount that NGDI declines.  What about real income?  If wages are sticky, then as NGDI declines, hours worked will fall, and real income will decline.

So far we have no reason to assume that C or S will fall at a different rate than NGDI. But if real income falls for temporary reasons (the business cycle), then the public will typically smooth consumption.  Thus if NGDP falls by 4%, consumption might fall by 2% while saving might fall by something like 10%.  This is a prediction of the permanent income hypothesis.  And of course if saving falls much more sharply than gross income, investment will also decline sharply, because savings is exactly equal to investment.

First, I observe that consumption smoothing and the permanent-income hypothesis are irrelevant to the discussion, because Scott does not explain where any of his hypothetical numbers come from or how they are related. Based on commenter Doug’s suggestion that savings is ¼ the size of consumption, one could surmise that a 4% reduction in NGDP and a 2% reduction in consumption imply a marginal propensity to consumer of 0.4. Suppose that consumption did not change at all (consumption smoothing to the max), then savings, bearing the entire burden of adjustment, would fall through the floor. What would that imply for the new equilibrium of NGDI? In the standard Keynesian model, a zero marginal propensity to consume would imply a smaller effect on NGDP from a given shock than you get with an MPC of 0.4.

It seems to me that Scott is simply positing numbers and performing calculations independently of any model, and then tells us that the numbers have to to be what he says they are because of an accounting identity. That does not seem like an assertion not an argument, or, maybe like reasoning from a price change. Scott is trying to make an inference about how the world operates from an accounting identity between two magnitudes. The problem is that the two magnitudes are variables in an economic model, and their values are determined by the interaction of all the variables in the model. Just because you can solve the model mathematically by using the equality of two variables as an equilibrium condition does not entitle you to posit a change in one and then conclude that the other must change by the same amount. You have to show how the numbers you have posited are derived from the model.

If two variables are really identical, rather than just being equal in equilibrium, then they are literally the same thing, and you can’t draw any inference about the real world from the fact that they are equal, there being no possible state of the world in which they are not equal. It is only because savings and investment are not the same thing, and because in some states of the world they are not equal, that we can make any empirical statement about what the world is like when savings and investment are equal. Back to Scott:

This is where Keynesian economics has caused endless confusion.  Keynesians don’t deny that (ex post) less saving leads to less investment, but they think this claim is misleading, because (they claim) an attempt by the public to save less will boost NGDP, and this will lead to more investment (and more realized saving.)  In their model when the public attempts to save less (ex ante), it may well end up saving more (ex post.)

I agree that Keynesian economics has caused a lot of confusion about savings and investment, largely because Keynes, who, as a philosopher and a mathematician, should have known better, tied himself into knots by insisting that savings and investment are identical, while at the same time saying that their equality was brought about, not by variations in the rate of interest, but by variations in income. Hawtrey, Robertson, and Haberler, among others, pointed out the confusion, but Keynes never seemed to grasp the point. Textbook treatments of national-income accounting and the simple Keynesian cross still don’t seem to have figured this out. But despite his disdain for Keynesian economics, Scott still has to figure it out, too. The best place to start is Richard Lipsey’s classic article “The Foundations of the Theory of National Income: An Analysis of Some Fundamental Errors” (a gated link is available here).

Scott begins by sayings that Keynesians don’t deny that (ex post) less saving leads to less investment. I don’t understand that assertion at all; Keynesians believe that a desired increase in savings, if desired savings exceeded investment, leads to a decrease in income that reduces saving. But the abortive attempt to increase savings has no effect on investment unless you posit an investment function (AKA an accelerator) that includes income as an independent variable. The accelerator was later added to the basic Keynesian model Hicks and others in order to generate cyclical fluctuations in income and employment, but non-Keynesians like Ralph Hawtrey had discussed the accelerator model long before Keynes wrote the General Theory. Scott then contradicts himself in the next sentence by saying that Keynesians believe that by attempting to save less, the public may wind up saving more. Again this result relies on the assumption of an accelerator-type investment function, which is a non-Keynesian assumption. In the basic Keynesian model investment is determined by entrepreneurial expectations. An increase (decrease) in thrift will be self-defeating, because in the new equilibrium income will have fallen (risen) sufficiently to reduce (increase) savings back to the fixed amount of investment entrepreneurs planned to undertake, entrepreneurial expectations being held fixed over the relevant time period.

I more or less agree with the rest of Scott’s post, but Scott seems to have the same knee-jerk negative reaction to Keynes and Keynesians that I have to Friedman and Friedmanians. Maybe it’s time for both of us to lighten up a bit. Anyway in honor of Scott’s recent appoint to the Ralph Hawtrey Chair of Monetary Policy at the Mercatus Center at George Mason University, I will just close with this quotation from Ralph Hawtrey’s review of the General Theory (chapter 7 of Hawtrey’s Capital and Employment) about Keynes’s treatment of savings and investment as identically equal.

[A]n essential step in [Keynes’s] train of reasoning is the proposition that investment and saving are necessarily equal. That proposition Mr. Keynes never really establishes; he evades the necessity doing so by defining investment and saving as different names for the same thing. He so defines income to be the same thing as output, and therefore, if investment is the excess of output over consumption, and saving is the excess of income over consumption, the two are identical. Identity so established cannot prove anything. The idea that a tendency for investment and saving to become different has to be counteracted by an expansion or contraction of the total of incomes is an absurdity; such a tendency cannot strain the economic system, it can only strain Mr. Keynes’s vocabulary.

17 Responses to “CAUTION Accounting Identity Handle with Care”


  1. 1 Frank Restly February 11, 2015 at 7:53 pm

    David,

    I am presuming that Scott is also using savings (S) and investment (I) as flows. I think it was Steve Keen and Richard Koo who brought up that balance sheets (Savings and Investment as levels) also matter.

    And so even if we are in an equilibrium period of flows, we could be in a disequilibrium in balance sheets. An example of this would be a period of rapid technological change where inventories of previously produced goods become obsolete and worthless in rapid fashion.

  2. 2 Kenneth Duda February 11, 2015 at 11:51 pm

    David, thank you for this post. I have long been confused by the “savings = investment” assertion. If I sell my labor and receive cash, I can stuff the cash in a mattress. I feel like I have saved, but I have not invested. Your post gives my feeling a theoretical foundation, that in fact savings and investment are only the same in equilibrium, and as long as the public is increasing cash stored in mattresses, I imagine we have not reached equilibrium.

    Anyway, thanks for the post.

    -Ken

    Kenneth Duda
    Menlo Park, CA

  3. 3 Nick Edmonds February 12, 2015 at 2:05 am

    I’m not sure I like the idea that savings and investment are only equal in equilibrum. Suitably defined (e.g. with investment to include change in inventories), they must always be equal. Allowing for planned savings and planned investment to differ is better.

    But I don’t think we have to contemplate the possibility of an inequality to draw conclusions. Even with equilibrium and with perfect foresight, the Keynesian direction of causation is maintained because of the co-ordination issue. We just need to note that an increased propensity to save is quite consistent with no change in the actual amount of saving.

  4. 4 Rob Rawlings February 12, 2015 at 7:28 am

    I am imagining a simplistic .version of a Keynesian model something like this:

    – Each period businesses make expenditures investment of size I
    – This I becomes income for others in the economy
    – This income is multiplied up by rounds of consumption spending (and matching income) to become C

    This simple model guarantees that S and I are not just accounting identities but will be kept in equilibrium by processes inherent in the model . If I changes then the multiplier drives high/lower C. If the consumption function changes then this likewise leads to changes in C. The dynamics of the model keep S and I aligned at all time

    Am I way off base ?

    I can see that you could build more complex Keynesian-type models where producers of consumer goods keep stocks of inventories, and then you could have I and S diverging in monetary terms (but would be brought back into line again by including inventory accumulation in I). In this situation the equilibrating process would be more complex that in the simple version but drive more-or-less the same “Keynesian” results.

  5. 5 Rob Rawlings February 12, 2015 at 7:30 am

    “Each period businesses make expenditures investment of size I” should be “Each period businesses make investment expenditures of size I”

  6. 6 David Glasner February 12, 2015 at 12:21 pm

    Frank, I don’t see how savings and investment are anything but flows. You can think of savings as the change in assets held by households, and investment as the change in the physical assets held by business firms.

    Ken, You’re welcome. I think that there could be an equilbrium in which all savings was put into cash inside mattresses, but it wouldn’t be a very pleasant one.

    Nick, Your “suitable” definition turns the equilbrium condition, which must be capable of violation if it is to have any empirical content, into a truism. The distinction between planned and unplanned investment was introduced as a way to get around the inconsistency between an inviolable accounting identity and an empirically meaningful equilibrium condition, but it is not a very good way of doing so. The assumption that the difference between planned investment and planned savings corresponds to unplanned change in inventories is not, as textbooks claim, deducible from the model itself.

    Rob, You are thinking of an instantaneous multiplier which implicitly excludes the possibility of disequilibrium, the adjustment path from one equilibrium to another being suppressed. If instead you specify a model with an explicit lag structure, say, consumption this period being determined by income last period, and work out the adjustment period by period, you will see that savings and investment are not equal during the adjustment process, and there need be no unplanned inventory changes to guarantee that the alleged identity between savings and investment is satisfied. Lipsey works this all out in his wonderful paper, which is truly a must read.

  7. 7 Frank Restly February 12, 2015 at 1:42 pm

    David,

    “Frank, I don’t see how savings and investment are anything but flows. You can think of savings as the change in assets held by households, and investment as the change in the physical assets held by business firms.”

    You are simplifying. Does the change in the value of the assets happen because a transaction has taken place – I bought / sold some assets or does the change in the value of assets happen by another cause (depreciation / destruction, failing / increasing market demand, etc.)?

    The federal reserve in its Z1 report tracks both.
    Found here – http://www.federalreserve.gov/releases/z1/current/)

    I believe the Bureau of Economic analysis also monitors levels as well with their National Income and Product Account monitoring here:
    http://www.bea.gov/national/nipaweb/Nipa-Frb.asp?Freq=Qtr

    Simple question – do you consider a house, stocks, bonds, etc. as part of your savings? Does it have the same value as when you bought it? If the market value of those assets rise / fall, does that have an effect on future spending / saving decisions?

    The “equilibrium” condition for any transaction is a fleeting instant in time. After that brief instant in time when both the value of savings and the value of investment are equal (buyer and seller reach agreement), they immediately diverge.

  8. 8 Rob Rawlings February 12, 2015 at 4:07 pm

    Re “Rob, You are thinking of an instantaneous multiplier which implicitly excludes the possibility of disequilibrium”

    Well, I see that the adjustment process would be iterative and during it I may not equal S (for instance , if animal spirits lead to an increase in I then the immediate effect, before the multiplier kicks in , would be leave to I > S). But if nothing else changes the multiplier process will eventually lead to equilibrium and S = I. This would be true even in an economy with no inventories at all.

    Or as you say:

    “However, equality between savings and investment is, like the equality between income and expenditure, a condition for macroeconomic equilibrium. In an economy not in equilibrium, savings does not equal investment. But the inequality between savings and investment induces adjustments that, in a stable macroeconomic system, move the economy toward equilibrium”

  9. 9 Mark February 13, 2015 at 9:32 am

    False equivalence alert: While you dispute Friedman’s importance pertaining to some ideas ascribed to him, I haven’t seen you attack an idea just because it was his (or ascribed to him, or claimed by him, or judged useful by him…). This is not the same as the knee-jerk allergic reaction in some corners against anything that could be dubbed ‘Keynesian’, as nice as your diplomatic ploy here may seem. (Note that I do not dispute that ideological anti-Friedman positions exist, though.)

  10. 10 David Glasner February 13, 2015 at 11:48 am

    Frank, I plead guilty to simplifying. In the simple income expenditure model, prices are held fixed, so that any change in assets represents real accumulation of assets by households or by businesses. Changes in the value of assets raise issues that I was not addressing. Net accumulation of durable assets by households are properly considered a form of saving net of depreciation (which can be thought of as a form of consumption).

    Rob, The exercise is based on adjustment to given savings and investment functions, so a change in animal spirits is, by assumption, excluded within the terms of the exercise.

    Mark, Caught me red-handed.

  11. 11 Rob Rawlings February 13, 2015 at 6:08 pm

    David,

    Re: “The exercise is based on adjustment to given savings and investment functions, so a change in animal spirits is, by assumption, excluded within the terms of the exercise”

    But in your post you say “In the basic Keynesian model investment is determined by entrepreneurial expectations”.

    What is the difference between “entrepreneurial expectations” and “animal spirits”?

  12. 12 Matt Molewski February 14, 2015 at 12:15 am

    This whole post reminds me of the monumental headache reading the General Theory was: On the one hand, Keynes was saying that economies fell into states of underemploment due to there not being enough investment to soak up deficiencies in consumption; but then on the other, that savings necessarily equaled investment, which implied that there could never be a situation where supply did not equal demand. It was only later that I had some of that confusion cleared up for me by drawing the distinction between economies in equilibrium and out of it, where income moved to bring the two variables into equality, but, prior to that, I just had to kind of ignore that oddity, and appreciate Keynes’ masterful skewering of the classical contention that interest rates alone regulated the two. It seems that a lot of people found themselves struggling with that same issue, and clearly it’s very easy to end up with your foot in your mouth trying to parse the language. Honestly, I think it’s enough to say that if businesses don’t expect a return on their investments above the rate of interest, they won’t expand employment and incomes won’t grow: It’s intuitively pleasing and hard to argue with, and it’s what’s at the heart of Keynes’ theory. And as for those who would follow up by saying that falling prices would bring spending back up, I liked Hyman Minksy’s answer to that: “In a world with complicated financial usages, if there is a road to full employment by way of the Patinkin real-balance effect, it may well go by way of hell.”

  13. 13 JKH March 7, 2015 at 9:11 am

    “Aggregate expenditure is different from aggregate income; expenditure is constituted not by the earnings of households, but by their spending on consumption and by the spending of businesses on investment, the purchase of durable equipment not physically embodied in output sold to households or other businesses. Aggregate expenditure is very close to but not identical with aggregate output. They can differ, because not all output is sold, some of it being retained within the firm as work in progress or as inventory. However, in an equilibrium situation in which variables were unchanging, aggregate income, expenditure and output would all be equal.

    The equality of these three variables can be thought of as a condition of macroeconomic equilibrium. When a macroeconomic system is not in equilibrium, aggregate factor incomes are not equal to aggregate expenditure or to aggregate output. The inequality between factor incomes and expenditure induces further adjustments in spending and earnings ultimately leading to an equilibrium.”

    Wow. The start of this is right. But the rest is wrong IMO.

    First, that expenditure is different from income must be a trivial observation of reality. It is the quantity of each that is equivalent. I can’t believe that the distinction between a physical difference and a quantitative equivalence is part of this debate.

    Inventory is not an issue in the equivalence. Inventory accumulation (which is an investment) requires expenditure every bit as much as new fixed investment. If inventories increase, investment has increased. Something was spent to increase those inventories.

    Finally, I’m equally startled that you identity an association of inventory accumulation with (what is really not) a discrepancy between expenditure and income as an event of disequilibrium.

  14. 14 David Glasner March 11, 2015 at 4:55 pm

    Rob, I am not sure how exactly to describe the difference between animal spirits and entrepreneurial expectations. I think that they are pretty close. Perhaps one possible distinction would be to say that with given expectations of future prices, animal spirits refers to a willingness to undertake the risk that expectations are wrong. The more intense animal spirits the less the profit margin required by entrepreneurs to accept the risk associated with an investment projected, based on expectations, to yield a profit of a given amount.

    Matt, I think that Keynes went too far in denying that the rate of interest performs any equilibrating role in the allocation of capital and investment, but I think you do a good job in your comment of identifying what was problematic in his own explanation of why it is income that adjusts to equate savings and investment.

    JKH, The quantity of expenditure and income may or may not be equal, depending on the method of calculation. Is inventory valued at cost or at expected selling price? Are you saying that the rule adopted for valuing inventory is irrelevant to whether expenditure matches income when inventory accumulation takes place?


  1. 1 There's no point in arguing over definitions, by Scott Sumner - Citizens News Trackback on February 14, 2015 at 3:52 pm
  2. 2 Savings and Investment Aren’t the Same Thing and There’s No Good Reason to Define them as Such | Uneasy Money Trackback on February 17, 2015 at 12:19 pm
  3. 3 Resolving the Glasner-Sumner Dispute | The Everyday Economist Trackback on February 19, 2015 at 10:03 am

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About Me

David Glasner
Washington, DC

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

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