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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.

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.

A Keynesian Postscript on the Bright and Shining, Dearly Beloved, Depression of 1920-21

In his latest blog post Paul Krugman drew my attention to Keynes’s essay The Great Slump of 1930. In describing the enormity of the 1930 slump, Keynes properly compared the severity of the 1930 slump with the 1920-21 episode, noting that the price decline in 1920-21 was of a similar magnitude to that of 1930. James Grant, in his book on the Greatest Depression, argues that the Greatest Depression was so outstanding, because, in contrast to the Great Depression, there was no attempt by the government in 1920-21 to cushion the blow. Instead, the powers that be just stood back and let the devil take the hindmost.

Keynes had a different take on the difference between the Greatest Depression and the Great Depression:

First of all, the extreme violence of the slump is to be noticed. In the three leading industrial countries of the world—the United States, Great Britain, and Germany—10,000,000 workers stand idle. There is scarcely an important industry anywhere earning enough profit to make it expand—which is the test of progress. At the same time, in the countries of primary production the output of mining and of agriculture is selling, in the case of almost every important commodity, at a price which, for many or for the majority of producers, does not cover its cost. In 1921, when prices fell as heavily, the fall was from a boom level at which producers were making abnormal profits; and there is no example in modern history of so great and rapid a fall of prices from a normal figure as has occurred in the past year. Hence the magnitude of the catastrophe.

In diagnosing what went wrong in the Great Depression, Keynes largely, though not entirely, missed the most important cause of the catastrophe, the appreciation of gold caused by the attempt to restore an international gold standard without a means by which to control the monetary demand for gold of the world’s central banks — most notoriously, the insane Bank of France. Keynes should have paid more attention to Hawtrey and Cassel than he did. But Keynes was absolutely on target in explaining why the world more easily absorbed and recovered from a 40% deflation in 1920-21 than it was able to do in 1929-33.

Making Sense of the Phillips Curve

In a comment on my previous post about supposedly vertical long run Phillips Curve, Richard Lipsey mentioned a paper he presented a couple of years ago at the History of Economics Society Meeting: “The Phillips Curve and the Tyranny of an Assumed Unique Macro Equilibrium.” In a subsequent comment, Richard also posted the abstract to his paper. The paper provides a succinct yet fascinating overview of the evolution macroeconomists’ interpretations of the Phillips curve since Phillips published his paper almost 60 years ago.

The two key points that I take away from Richard’s discussion are the following. 1) A key microeconomic assumption underlying the Keynesian model is that over a broad range of outputs, most firms are operating under conditions of constant short-run marginal cost, because in the short run firms keep the capital labor ratio fixed, varying their usage of capital along with the amount of labor utilized. With a fixed capital-labor ration, marginal cost is flat. In the usual textbook version, the short-run marginal cost is rising because of a declining capital-labor ratio, requiring an increasing number of workers to wring out successive equal increments of output from a fixed amount of capital. Given flat marginal cost, firms respond to changes in demand by varying output but not price until they hit a capacity bottleneck.

The second point, a straightforward implication of the first, is that there are multiple equilibria for such an economy, each equilibrium corresponding to a different level of total demand, with a price level more or less determined by costs, at any rate until total output approaches the limits of its capacity.

Thus, early on, the Phillips Curve was thought to be relatively flat, with little effect on inflation unless unemployment was forced down below some very low level. The key question was how far unemployment could be pushed down before significant inflationary pressure would begin to emerge. Doctrinaire Keynesians advocated driving unemployment down as low as possible, while skeptics argued that significant inflationary pressure would begin to emerge even at higher rates of unemployment, so that a prudent policy would be to operate at a level of unemployment sufficiently high to keep inflationary pressures in check.

Lipsey allows that, in the 1960s, the view that the Phillips Curve presented a menu of alternative combinations of unemployment and inflation from which policymakers could choose did take hold, acknowledging that he himself expressed such a view in a 1965 paper (“Structural and Deficient Demand Unemployment Reconsidered” in Employment Policy and the Labor Market edited by Arthur Ross), “inflationary points on the Phillips Curve represent[ing] disequilibrium points that had to be maintained by monetary policy that perpetuated the disequilibrium by suitable increases in the rate of monetary expansion.” It was this version of the Phillips Curve that was effectively attacked by Friedman and Phelps, who replaced it with a version in which the equilibrium rate of unemployment is uniquely determined by real factors, the natural rate of unemployment, any deviation from the natural rate resulting in a series of adjustments in inflation and expected inflation that would restore the natural rate of unemployment.

Sometime in the 1960s the Phillips curve came to be thought of as providing a stable trade-off between inflation and unemployment. When Lipsey did adopt this trade-off version, as for example Lipsey (1965), inflationary points on the Phillips curve represented disequilibrium points that had to be maintained by monetary policy that perpetuated the disequilibrium by suitable increases in the rate of monetary expansion. In the new Classical interpretation that began with Edmund Phelps (1967), Milton Friedman (1968) and Lucas and Rapping (1969), each point was an equilibrium point because demands and supplies of agents were shifted from their full-information locations when they misinterpreted the price signals. There was, however, only one full-information equilibrium of income, Y*, and unemployment, U*.

The Friedman-Phelps argument was made as inflation rose significantly in the late 1960s, and the mild 1969-70 recession reduce inflation by only a smidgen, setting the stage for Nixon’s imposition of his disastrous wage and price controls in 1971 combined with a loosening of monetary policy by a compliant Arthur Burns as part of Nixon’s 1972 reelection strategy. When the hangover to the 1972 monetary binge was combined with a quadrupling of oil prices by OPEC in late 1973, the result was a simultaneous increase in inflation and unemployment – stagflation — a combination widely perceived as a decisive refutation of Keynesian theory. To cope with that theoretical conundrum, the Keynesian model was expanded to incorporate the determination of the price level by deriving an aggregate supply and aggregate demand curve in price-level/output space.

Lipsey acknowledges a crucial misstep in constructing the Aggregate Demand/Aggregate Supply framework: assuming a unique macroeconomic equilibrium, an assumption that implied the existence of a unique natural rate of unemployment. Keynesians won the battle, providing a perfectly respectable theoretical explanation for stagflation, but, in doing so, they lost the war to Friedman, paving the way for the malign ascendancy of New Classical economics, with which New Keynesian economics became an effective collaborator. Whether the collaboration was willing or unwilling is unclear and unimportant; by assuming a unique equilibrium, New Keynesians gave up the game.

I was so intent in showing that this AD-AS construction provided a simple Keynesian explanation of stagflation, contrary to the accusation of the New Classical economists that stagflation provided a conclusive refutation of Keynesian economics that I paid too little attention to the enormous importance of the new assumption introduced into Keynesian models. The addition of an expectations-augmented Philips curve, negatively sloped in the short run but vertical in the long run, produced a unique macro equilibrium that would be reached whatever macroeconomic policy was adopted.

Lipsey does not want to go back to the old Keynesian paradigm; he prefers a third approach that can be traced back to, among others, Joseph Schumpeter in which the economy is viewed “as constantly evolving under the impact of endogenously generated technological change.” Such technological change can be vaguely foreseen, but also gives rise to genuine surprises. The course of economic development is not predetermined, but path-dependent. History matters.

I suggest that the explanation of the current behaviour of inflation, output and unemployment in modern industrial economies is provided not by any EWD [equilibrium with deviations] theory but by evolutionary theories. These build on the obvious observation that technological change is continual in modern economies (decade by decade at least since 1760), but uneven (tending to come in spurts), and path dependent (because, among other reasons, knowledge is cumulative with one advance enabling another). These changes are generated endogenously by private-sector, profit-seeking agents competing in terms of new products, new processes and new forms of organisation, and by public sector activities in such places as universities and government research laboratories. They continually alter the structure of the economy, causing waves of serially correlated investment expenditure that are a major cause of cycles, as well as driving the long-term growth that continually transforms our economic, social and political structures. In their important book As Time Goes By, Freeman and Louça (2001) trace these processes as they have operated since the beginnings of the First Industrial Revolution.

A critical distinction in all such theories is between risk, which is easily handled in neoclassical economics, and uncertainty, which is largely ignored in it except to pay it lip service. In risky situations, agents with the same objective function and identical knowledge will chose the same alternative: the one that maximizes the expected value of their profits or utility. This gives rise to unique predictable behaviour of agents acting under specified conditions. In contrast in uncertain situations, two identically situated and motivated agents can, and observably do, choose different alternatives — as for example when different firms all looking for the same technological breakthrough chose different lines of R&D — and there is no way to tell in advance of knowing the results which is the better choice. Importantly, agents typically make R&D decisions under conditions of genuine uncertainty. No one knows if a direction of technological investigation will go up a blind alley or open onto a rich field of applications until funds are spend investigating the route. Sometimes trivial expenses produce results of great value while major expenses produce nothing of value. Since there is no way to decide in advance which of two alternative actions with respect to invention or innovation is the best one until the results are known, there is no unique line of behaviour that maximises agents’ expected profits. Thus agents are better understood as groping into an uncertain future in a purposeful, profit- or utility-seeking manner, rather than as maximizing their profits or utility.

This is certainly the right way to think about how economies evolve over time, but I would just add that even if one stays within the more restricted framework of Walrasian general equilibrium, there is simply no persuasive theoretical reason to assume that there is a unique equilibrium or that an economy will necessarily arrive at that equilibrium no matter how long we wait. I have discussed this point several times before most recently here. The assumption that there is a natural rate of unemployment “ground out,” as Milton Friedman put it so awkwardly, “by the Walrasian system of general equilibrium equations” simply lacks any theoretical foundation. Even in a static model in which knowledge and technology were not evolving, the natural rate of unemployment is a will o the wisp.

Because there is no unique static equilibrium in the evolutionary world in which history matters, no adjustment mechanism is required to maintain it. Instead, the constantly changing economy can exist over a wide range of income, employment and unemployment values, without behaving as it would if its inflation rate were determined by an expectations-augmented Phillips curve or any similar construct centred on unique general equilibrium values of Y and U. Thus there is no stable long-run vertical Phillips curve or aggregate supply curve.

Instead of the Phillips curve there is a band as shown in Figure 4 [See below]. Its midpoint is at the expected rate of inflation. If the central bank has a credible inflation target that it sticks to, the expected rate will be that target rate, shown as πe in the figure. The actual rate will vary around the expected rate depending on a number of influences such as changes in productivity, the price of oil and food, but not significantly on variations in U or Y. At either end of this band, there may be something closer to a conventional Phillips curve with prices and wages falling in the face of a major depression and rising in the face of a major boom financed by monetary expansion. Also, the whole band will be shifted by anything that changes the expected rate of inflation.

phillips_lipsey

Lipsey concludes as follows:

So we seem to have gone full circle from early Keynesian view in which there was no unique level of income to which the economy was inevitably drawn, through a simple Phillips curve with its implied trade off, to an expectations-augmented Phillips curve (or any of its more modern equivalents) with its associated unique level of national income, and finally back to the early non-unique Keynesian view in which policy makers had an option as to the average pressure of aggregate demand at which the economy could be operated.

“Perhaps [then] Keynesians were too hasty in following the New Classical economists in accepting the view that follows from static [and all EWD] models that stable rates of wage and price inflation are poised on the razor’s edge of a unique NAIRU and its accompanying Y*. The alternative does not require a long term Phillips curve trade off, nor does it deny the possibility of accelerating inflations of the kind that have bedevilled many third world countries. It is merely states that industrialised economies with low expected inflation rates may be less precisely responsive than current theory assumes because they are subject to many lags and inertias, and are operating in an ever-changing and uncertain world of endogenous technological change, which has no unique long term static equilibrium. If so, the economy may not be similar to the smoothly functioning mechanical world of Newtonian mechanics but rather to the imperfectly evolving world of evolutionary biology. The Phillips relation then changes from being a precise curve to being a band within which various combinations of inflation and unemployment are possible but outside of which inflation tends to accelerate or decelerate. Perhaps then the great [pre-Phillips curve] debates of the 1940s and early 1950s that assumed that there was a range within which the economy could be run with varying pressures of demand, and varying amounts of unemployment and inflation[ary pressure], were not as silly as they were made to seem when both Keynesian and New Classical economists accepted the assumption of a perfectly inelastic, one-dimensional, long run Phillips curve located at a unique equilibrium Y* and NAIRU.” (Lipsey, “The Phillips Curve,” In Famous Figures and Diagrams in Economics, edited by Mark Blaug and Peter Lloyd, p. 389)


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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