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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

dY/dt = 0 <=> I = S

dY/dt > 0 <=> I > S

dY/dt < 0 <=> I < S

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

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

Of Bathtubs, Drains, and Faucets

I was planning to write another installment in my series of posts on the savings-investment identity in which I have been working through and summarizing Richard Lipsey’s essay “The Foundations of the Theory of National Income.” Perhaps I will get to my next installment later this week. If not, then I hope to do so early next week. But it occurred to me that the best way to explain why saving is not identical to investment is by framing the discussion in terms of the familiar circular-flow schematic model of income and expenditure. The accompanying diagram is a typical representation of the circular-flow model, with a government sector (government spending and taxes) and a foreign sector (exports and imports) included in addition to just circular_flow_modelinvestment and saving.

As indicated by the arrows in the diagram, investment, government spending, and exports are added to the circular flow while savings, taxes and imports are withdrawn from the circular. In the conventional terminology, investment, government spending and exports are injections, and savings, taxes and imports are leakages. And, of course, a basic property of the model is that injections and leakages are equal. It is only in the simplest model, with no government and with no foreign sector, so that there is just one injection (investment) and one leakage (saving), in which the familiar equality between investment and savings holds.

So the question that I want to ask now is simply this: is the equality in the simple one-sector model between injections (investment) and leakages (savings) an equality that may or may not be true, or is it an identity that must necessarily be satisfied in all places and at all times?

Well, rather than try to argue this through in terms of abstract economic or accounting reasoning, let’s think about it in terms of a simple physical analogy, one that we could actually demonstrate for ourselves in our own homes. So think of a bathtub with some water in it. Depending on the size of the bathtub and the amount of water in the bathtub, the water will reach some uniform height in the bathtub. Let’s call that uniform water level an equilibrium. It’s an equilibrium, because if that’s all the water there is in the bathtub, and we don’t let any water out of the bathtub, and, for purposes of our little thought experiment, we ignore any evaporation, that water level will persist indefinitely, with no tendency to change. No water in, no water out, and you have a constant water level. In other words, with no injections and no leakages, the water level of the bathtub is stable; it does not change. The water level is in equilibrium.

But if you turn on the faucet and water starts to flow into the bathtub, the water level will start to rise. As long as water is being injected into the bathtub, the water level will keep rising, and the water level will not be in equilibrium. However, if you unplug the drain to the bathtub, water will start flowing out of the bathtub. What happens to the water level? That depends on whether water is leaking out of the bathtub through the drain faster than water is being injected into the bath tub through the faucet. If injections are greater than leakages, the water level will rise, and if leakages are greater than injections, the water level will fall. And if, by chance or design, injections are exactly equal to leakages, then the water level will be stable and back in equilibrium. Thus, the condition for a stable water level is that injections be exactly equal to leakages. When injections into, and leakages from, the bathtub are equal, the water level of the bathtub is in equilibrium. When injections are greater than leakages, the water level rises, and when leakages are greater than injections the water level falls.

I think all that is pretty elementary, and I am guessing that if you look in any textbook treatment of injections and leakages in the circular flow of income, you will find a similar story about the effect of a difference between injections and leakages on the level of income. (Check out the Wikipedia article on the circular flow of income, especially the section on equilibrium.)

So, if you believe that investment and savings are identically equal, please tell me whether you also believe that injections and leakages are identically equal. And if you do believe that injections and leakages are identically equal, please explain to me what the difference is between the circular-flow-of-income model with injections and leakages identically equal in equilibrium or out of equilibrium and the bathtub model in which the water level can change only insofar as injections and leakages are not equal.

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

In my previous post, I argued that an accounting identity, which tells us that two expressions are defined to be the same, must hold in every state of the world, and therefore could not be disproved by any conceivable observation. So if I define savings and investment (or income and expenditure) to be the same thing, I am simply restricting my semantic description of the world, I am not restricting in any way the set of observable states of the world that conform to my semantic convention. An accounting identity therefore has no empirical content, which means that the accounting identity between savings and investment cannot explain the process by which a macroeconomic model adjusts to a parametric change in the model, traversing from a pre-existing equilibrium with savings and investment being equal to a new equilibrium with savings and investment equal.

In his paper, “The Foundations of the Theory of National Income,” which I am attempting to summarize and explain in this series of posts, R. G. Lipsey provides a numerical example of such an adjustment path. And it will be instructive to follow that path in some detail. The key point about this model is the assumption that households decide how much to save and consume in the current period based on the disposable income received in the previous period. The assumption that all receipts of the business firms are paid out to owners and providers of factor services at the end of each period is a behavioral assumption (not an accounting identity) that rules out any change in the retained earnings held by firms. If firms were accumulating financial assets, then their payments to households would not match their receipts. The following simple model reflects a one-period lag (known as a Robertsonian lag) between household earnings and household consumption.

C(t) = aY(t-1) (behavioral assumption)

I(t) = I* (behavioral assumption)

E(t) ≡ C(t) + I(t) (accounting identity)

Y(t) ≡ C(t) + S(t) (accounting identity)

Y(t) = E(t) (behavioral assumption)

Y(t-1) = Y(t) (equilibrium condition)

Assume that the economy starts off with a = .9 and I(t) = 100. The system is easily solved for E = Y = 1000, with C = 900 and I = 100. Savings, which is the difference between Y and C, is 100, just equal to I. The definition of saving will have to be fleshed out further below. Now assume that there is a parametric change in a (the marginal propensity to consume) to .8 from .9. This change causes equilibrium income to fall from 1000 to 500. By assumption, investment is constant, so that in the new equilibrium saving remains equal to 100. The change in income is reflected in a drop in consumption from 900 to 400. But given the one-period lag between earnings and expenditure, we can follow how the system changes over time, moving closer and closer to the new equilibrium in each successive period, as shown in the following table.

Consider the following questions.

First, in the course of this period-by-period adjustment, will there be any unplanned investment?

Second, in this example, the parametric change — an increase in the propensity of households to save — may be described as an increase in planned savings by households. Planned investment is unchanged. With planned savings greater than planned investment, will the household plans to increase savings be frustrated (implying positive or negative unplanned savings) as alleged in proposition 3 in the list of erroneous propositions provided earlier in the first installment in this series (see appendix below).

The answer to the first question is: not necessarily. There is nothing to prevent us from assuming that all firms correctly anticipate the reduction in consumer demand, so that production falls along with consumption with no change in inventories. It is not necessary to assume that firms can foresee the future; it could be that all consumption is in the form of services, or that production is undertaken only in response to consumer orders. With inventories unchanged, there is no unplanned investment.

The answer to the second question is that it depends on what is meant by unplanned savings. Unplanned savings could mean that households wind up saving an amount other than the amount that they had intended to save at the beginning of the period; households intended to save 200 at the beginning of period 0, but because their income turned out to be only 900, instead of 1000, in period 0, household savings, under the accounting identity, is only 100 instead of 200. However, households intended to consume 800 in period 0, and that is the amount that they actually consumed. The only sense in which households did not execute their intended plans is that household income in period 0 was less than households had expected. Lipsey calls this a distinction between plans in the point sense, and plans in the schedule sense. In this scenario, while plans in the schedule sense are carried out, plans in the point sense are not, because households do not end up at the point on their consumption functions that they had expected to be on.

So the equilibrium condition above that income does not change from one period to the next can be restated as follows: the system is in equilibrium when planned savings equals realized savings. Planned savings is the unconsumed portion of households’ expected income, which is the income households earned in the previous period. The definition embodies a specific behavioral hypothesis about how households formulate their expectations of income in the future.

S_p_(t) ≡ Y(t-1) – C(t).

Realized savings is the unconsumed portion of households’ actual income in the current period. It can be written as

S_r_(t) ≡ Y(t) – C(t).

Or restated differently yet again, the equilibrium condition is that actual disposable income in period t equals expected disposable income in period t.

Let’s flesh out the behavioral assumptions behind this model in a bit more detail. Business firms disburse income to households (owners and providers of factor services) at the end of each period. Households decide how much to save and consume in the upcoming period after receiving their incomes from firms at the close of the previous period. Savings are in the form of bond purchases made at the start of the period. Based on the consumption and savings plans formulated by households at the start of the new period, firms decide how much output to produce and how much labor to hire to produce that output, firms immediately notifying households how many hours they will work in the upcoming period. However, households are committed to the consumption plans already made at the beginning of the period, so they must execute those plans even if the incomes earned during the period are less than anticipated.

In our example, by choosing to increase their savings to 200 through bond purchases at the beginning of the upcoming period, while reducing consumption from 900 to 800, households cause business firms to reduce output from 1000 to 900 (investment being unchanged), and to reduce employment (measured in terms of total hours worked) by 11.1%. After buying bonds equal to 200, households have 800 left in cash, with which they finance their purchases for the rest of the month. So it is not obvious that households were unable to execute any of their plans  during the period. However, at the end of the period, households receive only 900 in income from business firms, so although households did buy bonds equal to 200 at the start of the period, they carry over only 900 in cash into the next period, not 1000 as expected. Thus, realized savings are only 100 instead of 200, because household cash holding at the endo f the period turned out to be 100 less than expected. Nevertheless, it is difficult to identify any plan to save that was frustrated, inasmuch as households did purchase bonds equal to 200 at the beginning of the period, and did reduce consumption as planned. As Lipsey puts it:

[W]hether or not the actual real plans laid by households are frustrated depends on what plans households lay, i.e., it depends on our behaviour assumption, not on our definitions. If we assume that households make point plans about their bonds, and schedules plans about their transactions and precautionary balances, then no frustration of plans occurs.

If the statement quoted in (3) [see appendix below] is meant to have empirical content, it depends on a very specific hypothesis about households’ savings plans. These plans must be made in the point and not in the schedule sense, and the plans must include not only additions to the stock of income-earning assets, but also point-plans concerning transactions balances even though the household does not now know what level of transactions the balances will be required to facilitate. . . .

[W]e are now in a position to see what is wrong with statement (2), that actual savings must always equal actual investment, and statement (5), which draws the analogy with demand and supply analysis. Consider statement (2) first.

In the General Theory, Keynes stressed the fact that savings and investment decisions are made by different groups and that there is thus, no reason why planned investment should equal planned savings. [It has been argued] that, although plans can differ, actual realised saving must always be equal to actual realised investment, and, therefore, when planned savings does not equal planned investment, either the plans of savers, or of investors, must be frustrated. Of course, it is quite possible to define savings and investment so that they are the same thing, but it is a basic error to equate the magnitude so defined with the magnitude about which savers actually lay plans. Since ex post S and I as defined bear no relation to the magnitudes about which savers actually make plans, we can deduce nothing about what happens when ex ante S is not equal to ex ante I from the fact that we chose to use the terms ex post S and ex post I to refer to a single, and different, magnitude. The basic error arises from the assumption that households and firms make plans about the same magnitude when they are planning their savings and investment. The traditional theory defines investment as goods produced and not sold to households (= capital goods plus changes in inventories). According to our theory of the behaviour of firms, this is what firms do lay plans about: they plan to add so many capital goods and so many inventories to their existing holdings. The theory then says I ≡ S, and , thus, builds in the implicit assumption that households lay plans about the same magnitude. But according to the standard theory of household behaviour, they do not do so! Households, not subject to money illusion, are assumed to wish to lay aside a certain quantity of real purchasing power which is either used to increase the holdings of cash or used to purchase bonds. There is nothing in the standard theory of household behaviour that leads us to hypothesise that households care whether or not there exists – produced but unconsumed – a physical stock of goods which is the counterpart of the money they have laid aside. Indeed why should they? All they are assumed to care about is the potential real purchasing power of their savings, and this depends only on the amount of money saved, the present price level, and the expected future price level.

This is one of the keys to the whole present confusion: households lay plans about a magnitude that is different from the one that firms lay plans about. Firms plan to have produced and unconsumed a certain quantity of goods, while households plan to leave unspent a certain quantity of purchasing power. This means that it is quite possible for planned investment to differ from planned savings and to have both sets of plans fulfilled so that actual, realized investment differs from actual realized savings. [footnote: Now, of course, we mean by realised S and I the realised magnitudes about which firms and households are actually laying plans. This, of course, does not interfere with the statistician saying that realised savings is identical with realised investment since he refers to a different magnitude when he speaks of realised savings.]

Now consider another variation of the numerical example in Table 1. Instead of a change in the propensity to consume in period 0, assume instead that planned investment drops from 100 to 0. Starting with period -1, Table 2 displays the same initial equilibrium as in Table 1. Because we make a behavioral hypothesis that inventories do not change, planned and realized investment must be zero in period 0 and in all subsequent periods.

According to the national-income identities, savings must equal zero because investment is zero. But what is the actual behavior that corresponds to zero saving? In period 0, households carried over 1000 in cash from period -1. From that 1000, they used 100 to buy bonds and spent the remainder of their disposable incomes on consumption goods. So households planned to save 100 and consume 900, and it appears that they succeeded in executing their plans. But according to the national-income identities, they failed to execute their plan to save 100, and saved only 0, presumably because there were unintended savings of -100 that cancelled out the planned (and executed) savings of 100. So it appears that we have come up against something of a paradox. Here is Lipsey’s solution of the paradox.

[A]ny definitions are possible if consistently used, but this use of the word “unintended” has nothing to do with intended and unintended behaviour. To preserve the identity we must say that the plans of households were frustrated because a real counterpart of the saving they successfully made was not produced. We may say this if we wish, but the danger is that we will think we have said something about the world, and about the actual experiences of households. Indeed, a perusal of established textbooks shows that this confusion has occurred over and over again.

Thus, we conclude that, when we define investment as production not consumed, and savings as income [not consumed] . . . there is no reason why actual savings should not differ from actual investment.

Finally, what about the analogy between savings and investment in macro analysis and demand and supply in micro analysis as in erroneous statement (4) (see appendix)? If we write demand for some good as a function of the price of the good

D = D(p),

and write the supply of some good as a function of the price of the good

S = S(p),

then our equilibrium condition is simply D = S, where D represents desired purchases of the good, and S represents desired sales of the good. Because the act of selling logically entails the activity of purchasing, a purchase and a sale are merely different names for the same thing. So the plans of demanders to buy and the plans of suppliers to sell are plans about the same thing. The plans of demanders to buy and the plans of suppliers to sell cannot be fulfilled simultaneously unless there is an equilibrium in which demand equals supply. The difference between the microeconomic equilibrium in which demand equals supply and the macroeconomic equilibrium in which savings equals investment is that suppliers and demanders in a market are making plans about the same magnitude: sales (aka purchases) of a good. However,

in the national income case the two sets of real plans (savers’ and investors’) are laid about two different magnitudes. Thus the analogy often draw between the two theories in respect of plans and realized quantities is an incorrect one.

Appendix: List of Erroneous Propositions

1 The equilibrium of the basic Keynesian model is given by the intersection of the aggregate demand (i.e., expenditure) function and the 45-degree line representing the accounting identity EY.

2 Although people may try to save different amounts from what people try to invest, savings can’t be different from investment; realized (ex post) savings necessarily always equals realized (ex post) investment.

3 Out of equilibrium, planned savings do not equal planned investment, so it follows from (2) that someone’s plans are being disappointed, and there must be either unplanned savings or dissavings, or unplanned investment or disinvestment

4 The simultaneous fulfilment of the plans of savers and investors occurs only when income is at its equilibrium level just as the plans of buyers and sellers can be simultaneously fulfilled only at the equilibrium price.

5 Whenever savers (households) plan to save an amount different from what investors (business firms) plan to invest, a mechanism operates to ensure that realized savings remain equal to realized investment, despite the attempts of savers and investors to make it otherwise. Indeed, this mechanism is what causes dynamic change in the circular flow of income and expenditure.

6 Since the real world, unlike the simple textbook model, contains a very complex set of interactions, it is not easy to see how savings stay equal to investment even in the worst disequilibrium and the most rapid change.

7 The dynamic behavior of the Keynesian circular flow model in which disequilibrium implies unintended investment or disinvestment can be shown by moving upwards or downwards along the gap between the expenditure function and the 45-degree line in the basic Keynesian model.

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

In this installment of my series on Richard Lipsey’s essay “The Foundations of the Theory of National Income,” I am going to focus on a single issue: what inferences about reality are deducible from a definition about the meaning of the terms used in a scientific theory? In my first installment I listed seven common statements about the basic Keynesian income-expenditure model that are found in most textbooks. The first concerned the confusion between the equality of investment and saving (or between income and expenditure) as an equilibrium condition and a definitional identity. Interpreting the equality of savings and investment as an identity essentially means collapsing the entire model onto the 45-degree line and arbitrarily choosing some point on the 45-degree line as the solution of the model.

That nonsensical interpretation of the simple Keynesian cross is obviously unsatisfactory, so, in an effort to save both the definitional identity of savings and investment and the equality of investment and savings as an equilibrium condition, the textbooks have introduced a distinction between ex ante and ex post in which savings and investment are defined to be identically equal ex post, but planned (ex ante) savings may differ from planned (ex ante) investment, their equality being the condition for equilibrium.

Now, to be fair, it is perfectly legitimate to define an equilibrium in terms of plan consistency, and to say that the inconsistency of the plans occasions a process of readjustment in the plans, and that it is the readjustment in the plans which leads to a new equilibrium. The problem with the textbook treatment is that it draws factual inferences about the adjustment process to a disequilibrium in which planned saving is not equal to planned investment from the definitional identity between ex post savings and ex post investment. In particular, the typical textbook treatment infers that in a disequilibrium with planned savings not equal to planned investment, the adjustment process is characterized by unplanned positive or negative investment (inventory accumulation or decumulation) corresponding to the gap between planned savings and planned investment. Identifying a gap between planned saving and planned investment with unplanned inventory accumulation or decumulation, as textbook treatments of the income expenditure model typically do, is logically unfounded.

Again, I want to be careful, I am not saying that unplanned inventory accumulation or decumulation could not occur in response to a difference gap between planned savings and planned investment, or even that such unplanned inventory accumulation or decumulation is unlikely to occur. What I am saying is that the definitional identity between ex post savings and ex post investment does not imply that such inventory accumulation or decumulation takes place and certainly not that the amount by which inventories change is necessarily equal to the gap between planned savings and planned investment.

Richard Lipsey made the key point in his comment on my previous post:

The main issue in this whole discussion is, I think, can we use a definitional identity to rule out an imaginable state of the universe. The answer is “No”, which is why Keynes was wrong. The definitional identity of S ≡ I tells us nothing about what will happen if agents wish to save a different amount from what agents wish to invest.

Here is how Lipsey put it in his 1972 essay:

The error in this interpretation lies in the belief that the identity EY can tell us what can and cannot happen in the world. If it were possible that a definitional identity could rule out certain imaginable events, then such a definitional identity would be an informative statement having empirical content! If it is a genuine definitional identity (which follows from our use of words and is compatible with all states of the universe) then it is only telling us that we are using E and Y to refer to the same thing, and this statement no more allows us to place restrictions on what happens in the world than does the statement that we are not using E and Y to refer to the same thing.

Lipsey illustrated the problem using the simple Keynesian cross diagram. To make the discussion a bit easier to follow, I am going to refer to my own slightly altered version (using a specific numerical example) of the familiar diagram. Setting investment (I) equal to 100 and assuming the following consumption function

C = 25 + .5Y

We can easily solve for an equilibrium income of 250 corresponding to the intersection of the expenditure function with the 45-degree line.

lipsey_45_degreeWhat happens if we posit that the system is at a disequilibrium point, say Y = 400. The usual interpretation is that at Y = 400, planned (ex ante) investment is less than savings and planned (ex ante) expenditure is less than income. Because, actual (ex post) investment is identically equal to savings and because actual (ex post) expenditure is identically equal to income, unplanned investment must occur to guarantee that the investment-savings identity is satisfied. The amount of unplanned investment is shown on the graph as the vertical distance between the expenditure function (E(Y)) at Y = 400 and the 45-degree line at Y = 400. This distance is shown in my diagram as the vertical distance between the points a and b on the diagram, and it is easy to check that the distance corresponds to a value of 75.

So the basic textbook interpretation of the Keynesian cross is using the savings-investment identity to derive a proposition about the behavior of the economy in disequilibrium. It is saying that an economy in disequilibrium with planned investment less than planned savings adjusts to the disequilibrium through unplanned inventory accumulation (unplanned investment) that exactly matches the difference between planned saving and planned investment. But it is logically impossible for a verbal identity (between savings and investment) — an identity that can never be violated in any actual state of the world — to give us any information about what actually happens in the world, because whatever happens in the world, the identity will always be satisfied.

Recall erroneous propositions 2, 3 and 4, listed in part I of this series:

2 Although people may try to save different amounts from what people try to invest, savings can’t be different from investment; realized (ex post) savings necessarily always equals realized (ex post) investment.

3 Out of equilibrium, planned savings do not equal planned investment, so it follows from (2) that someone’s plans are being disappointed, and there must be either unplanned savings or dissavings, or unplanned investment or disinvestment

4 The simultaneous fulfilment of the plans of savers and investors occurs only when income is at its equilibrium level just as the plans of buyers and sellers can be simultaneously fulfilled only at the equilibrium price.

If realized (ex post) savings necessarily always equals realized (ex post) investment, that equality is the result of how we have chosen to define those terms, not because of people actually are behaving, e.g., by unwillingly accumulating inventories or failing to save as much as they had intended to. However people behave, the identity between savings and investment will be satisfied. And whether savers and investors are able to fulfill their plans or are unable to do so cannot possibly be inferred from a definition that says that savings and investment mean the same thing.

In several of his comments on my recent posts, Scott Sumner has cited the professional consensus that savings and investment are defined to be equal. I am not so sure that there is really a consensus on that point, because I don’t think that most economists have thought carefully about what the identity actually means. But even if there is a consensus that savings is identical to investment, no empirical implication follows from that definition. But typical textbook expositions, and I think even Scott himself when he is not being careful, do use the savings-investment identity to make inferences about what actually happens in the real world.

In the next installment, I will go through a numerical example that shows, based on a simple lagged adjustment between consumption and income (household consumption in this period being a function of income in the previous period), that planned savings and planned investment can be realized and unequal in the transition from one equilibrium to another.

PS I apologize for having been unable to respond to a number of comments to previous posts. I will try to respond in the next day or two.

Imagination and Identity

Before continuing my summary of the key points of Richard Lipsey’s important paper, “The Foundations of the Theory of National Income,” I want to clear up a point that the deliberately provocative title may have obscured. The accounting identities that I am singling out for criticism are the identities between income and expenditure (and output) and between savings and investment. It is true that, as Scott Sumner points out in a comment on my previous post, every theory has to define its terms in some way or another, so there is no point in asserting that a definition is wrong. Scott believes that I am a saying that it is wrong to define investment and savings as the same thing, but I am not saying that. I am saying that, in the context of the basic income-expenditure theory of national income, it makes the theory incoherent, so that there is a mismatch between the definition and the theory.

It is also true that sometimes identities follow directly from basic definitions. Such identities are like conservation laws in physics. For example, purchases must equal sales, because purchasing and selling are reciprocal activities; to assert that purchases are, or could be, unequal to sales would be self-contradictory. Keynes, when ridiculed by Hawtrey for asserting that a) savings and investment are equal by definition, and b) that the equality of savings and investment is achieved by variations in income, responded by comparing the equality of savings and investment to the equality of purchases and sales. Purchases are necessarily equal to sales, but prices adjust to achieve equality between desired purchases and desired sales.

The problem with Keynes’s response to Hawtrey is that to assert that purchases are unequal to sales is to misconstrue in a really fundamental way the meaning of the terms “purchase” and “sales.” But when it comes to national-income accounting, the identity of “investment” and “savings” does not follow immediately from the meaning of those terms. It must be derived from the meaning of two other terms: income and expenditure. So the question becomes whether the act of spending (i.e., expenditure) necessarily entails an immediate and corresponding accrual of income, in the same way that the act of purchasing necessarily entails the act of selling. To assert that expenditure and income are identical is then to assert that any expenditure necessarily and simultaneously entails a corresponding accrual of income.

Before pursuing this line of thought further, let’s just pause for a moment to recall the context for this discussion. We are talking about a fairly primitive model of an economy in which there are households that are units of consumption and providers of factor services. Households purchase consumption goods and provide factor services to business firms. Business firms are units of production that combine factor services provided by households with raw materials purchased from other business firms, and new or existing capital goods produced now or previously by other business firms, to produce raw materials, consumption goods, and capital goods. Raw materials and capital goods are sold to other business firms and consumption goods are sold to households. Business firms are owned by households, so profits earned by business firms are remitted, along with payments for factor services, to households. But although the flow of payments from households to business firms corresponds to a flow of payments from business firms to households, the two flows, which can be measured separately, are, at not identical, or at least not obviously so. When I bought a tall Starbucks coffee just now at a Barnes & Noble cafe, my purchase of $1.98 was exactly and necessarily matched by a sale by Barnes & Noble to the guy who writes for the Uneasy Money blog. But expenditure of $1.98 by the Uneasy Money blogger to Barnes & Noble did not trigger an immediate and corresponding flow of $1.98 to households from Barnes & Noble.

Now I grant that it is possible for income so to be defined that every act of expenditure involves a corresponding accrual of income to providers of factor services to the firm, and of profit to owners of the firm. But expenditure entails simultaneous accrual of income only by virtue of an imputation of income to providers of factor services and of profit to owners of firms. Mere imputation does not and cannot constitute an actual flow of payments by firms to households. The identity between purchases and sales is entailed by the definition of “purchase” and “sales,’ but the supposed identity between expenditure and income is entailed by nothing but an act of imagination. I am not criticizing imagination, which may often provide us with an excellent grasp of reality. But imagination, no matter how well attuned to reality, does not and cannot establish identity.

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

I have had occasion to make many references in the past to Richard Lipsey’s wonderful article “The Foundations of the Theory of National Income” which was included in the volume Essays in Honour of Lord Robbins. When some 40 years ago, while a grad student at UCLA, I luckily came upon Lipsey’s essay, it was a revelation to me, because it contradicted what I had been taught as an undergrad about the distinctions between planned (ex ante) investment and savings, and realized (ex post) investment and savings. Supposedly, planned investment and planned savings are equal only in equilibrium, but realized investment and savings are always equal. Lipsey explained why the ex ante/ex post distinction is both incorrect and misleading. In this post I want to begin to summarize some of the important points that Lipsey made in his essay.

Lipsey starts with a list of seven erroneous propositions commonly found in introductory and intermediate textbooks. Here they are (copied almost verbatim), grouped under three headings:

I The Static Model in Equilibrium

1 The equilibrium of the basic Keynesian model is given by the intersection of the aggregate demand (i.e., expenditure) function and the 45-degree line representing the accounting identity EY.

II The Static Model in Disequilibrium

2 Although people may try to save different amounts from what people try to invest, savings can’t be different from investment; realized (ex post) savings necessarily always equals realized (ex post) investment.

3 Out of equilibrium, planned savings do not equal planned investment, so it follows from (2) that someone’s plans are being disappointed, and there must be either unplanned savings or dissavings, or unplanned investment or disinvestment

4 The simultaneous fulfilment of the plans of savers and investors occurs only when income is at its equilibrium level just as the plans of buyers and sellers can be simultaneously fulfilled only at the equilibrium price.

III The Dynamic Behavior of the Model

5 Whenever savers (households) plan to save an amount different from what investors (business firms) plan to invest, a mechanism operates to ensure that realized savings remain equal to realized investment, despite the attempts of savers and investors to make it otherwise. Indeed, this mechanism is what causes dynamic change in the circular flow of income and expenditure.

6 Since the real world, unlike the simple textbook model, contains a very complex set of interactions, it is not easy to see how savings stay equal to investment even in the worst disequilibrium and the most rapid change.

7 The dynamic behavior of the Keynesian circular flow model in which disequilibrium implies unintended investment or disinvestment can be shown by moving upwards or downwards along the gap between the expenditure function and the 45-degree line in the basic Keynesian model.

Although some or all of these propositions are found in most standard textbook treatments of national income theory, every one of them is wrong.

Let’s look at proposition 1. It says that the equilibrium level of income and expenditure is determined algebraically by the following two relations: the expenditure (or aggregate demand) function:

E = E(Y) + A

and the expenditure-income accounting identity

E ≡ Y.

An accounting identity provides no independent information about the real world, because there is no possible state of the world in which the accounting identity does not hold. It therefore adds no new information not contained in the expenditure function. So the equilibrium level of income and expenditure must be determined on the basis of only the expenditure function. But if the expenditure function remains as is, it cannot be solved, because there are two unknowns and only one equation. To solve the equation we have to make a substitution based on the accounting identity E ≡ Y. Using that substitution, we can rewrite the expenditure function this way.

E = E(E) + A

If the expenditure function is linear, we can write it as follows:

E = bE + A,

which leads to the following solution:

E = A/(1 – b).

That solution tells us that expenditure is a particular number, but it is not a functional relationship between two variables representing a theory, however naïve, of household behavior; it simply asserts that E takes on a particular value.

Thus treating the equality of investment and savings as an identity turns the simply Keynesian theory into a nonsense theory.

The point could be restated slightly differently. If we treat the equality of investment and savings as an identity, then if we follow the usual convention and label the vertical axis as E, it is a matter of indifference whether we label the horizontal axis Y or E, because Y and E are not distinct, they are identical. However we choose to label the horizontal axis, the solution of the model must occur along the 45-degree line representing either E = Y or E = E, which are equivalent. Because, the equality between E and itself or between E and Y is necessarily satisfied at any value of E, we can arbitrarily choose whatever value of E we want, and we will have a solution.

So the only reasonable way to interpret the equality between investment and saving, so that you can derive a solution to the simple Keynesian model is to treat E and Y as distinct variables that may differ, but will always be equal when the economy is in equilibrium.

So the only coherent theory of income is

E = E(Y) + A

and, an equilibrium condition

E = Y.

E and Y do not represent the same thing, so it makes sense to state a theory of how E varies in relation to Y, and to find a solution to the model corresponding to an equilibrium in which E and Y are equal, though they are distinct and not necessarily equal.

But the limitation of this model is that it provides us with no information about how the model behaves when it is not in equilibrium, not being in equilibrium meaning that E and Y are not the equal. Note, however, that if we restrict ourselves to the model in equilibrium, it is legitimate to write EY, because the equality of E and Y is what defines equilibrium. But all the erroneous statements 2 through 7 listed above all refer to how the model.

The nonsensical implications of constructing a model of income in which expenditure is treated as a function of income while income and expenditure are defined to be identical has led to the widespread adoption of a distinction between planned (ex ante) investment and savings and realized (ex post) investment and savings. Using the ex ante/ex post distinction, textbooks usually say that in equilibrium planned investment equals planned savings, while in disequilibrium not all investment and savings plans are realized. The reasoning being that is that if planned saving exceeds planned investment, the necessity for realized savings to equal realized investment requires that there be unintended investment or unintended dissaving. In other words, the definitional identity between expenditure and income is being used to tell us whether investment plans are being executed as planned or being frustrated in the real world.

Question: How is it possible that an identity true by definition in all states of the world can have any empirical implications?

Answer: It’s not.

In my next installment in this series, I will go through Lipsey’s example showing how planned and realized saving can indeed exceed planned and realized investment over the disequilibrium adjustment induced by a reduction in planned investment relative to a pre-existing equilibrium.

UPDATE (2/21/2015]: In the second sentence of the paragraph beginning with the words “An accounting Identity provides,” I wrote: “It therefore adds information not contained in the expenditure function,” which, of course, is the exact opposite of what I meant to say. I should have written: “It therefore adds NO NEW information not contained in the expenditure function.” I have now inserted those two words into the text. Thanks to Richard Lipsey for catching that unfortunate mistake.

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

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

Economics textbooks define savings as being equal to investment:

S = I

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

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

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

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

GDI = C + S = C + I = GDP

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

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

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

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

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

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

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

Then Scott addresses my criticism:

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

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

Scott objects to this statement from my previous post:

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

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

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

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

Here is Scott’s response:

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

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

Scott then makes the following point.

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

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

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

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

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

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

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

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

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

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


About Me

David Glasner
Washington, DC

I am an economist at the Federal Trade Commission. Nothing that you read on this blog necessarily reflects the views of the FTC or the individual commissioners. Although I work at the FTC as an antitrust economist, most of my research and writing has been on monetary economics and policy and the history of monetary theory. 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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