Against Savings

Abstract. The notion of savings in economics has a variety of mutually incompatible meanings. This paper goes through these various meanings and argues that, for the sake of clarity, it can and should be replaced with more precise terms. The paper then offers an “augmented” loanable funds model. Unlike the standard model, which depicts unintermediated lending, our model 1) does not identify the supply of loanable funds with “savings”, and 2) explicitly connects the banking sector to the supply of money with something more theoretically robust than a simple money multiplier. The resulting construction clarifies the relationship between the markets for money and credit, and is more faithful to the image of banks as creators of credit, while still retaining the pedagogical simplicity of the original loanable funds model.

The demand for money is satisfied in overwhelming part by private bank liabilities (Harwick & Burns 2016). Despite this fact, the traditional exposition of monetary theory, embodied in the textbook diagrams for real and nominal money supply and demand (M_S/M_D), leaves little room for banking. Similarly, the canonical diagrammatic model of banking, the loanable funds model, has the disadvantages 1) that it is mostly unconnected to M_S/M_D, and 2) that it lends itself to a naïve interpretation where banks are direct intermediaries of loanable funds. Students and economists whose mental model of saving has been shaped by these devices are liable to make certain classes of errors in modeling relationships among economic agents and sectors.

This paper, in contrast, advances a simple diagrammatic exposition of the supply and demand for money and credit, one in which banking is central, and which remains faithful to the image of banks as constrained in the medium run by deposited loanable funds, but free in the short run to generate credit ad hoc.

The following sections critique various definitions of “savings” as an economic aggregate, argue that the ambiguity between physical and monetary magnitudes vitiates many uses of the term, and suggest more suitable existing terms that can serve all the various and mutually incompatible purposes to which savings is now put. The third section advances an alternative model of the market for loanable funds, designed with bank lending in mind and without the use of a savings aggregate. The paper concludes with some avenues for the further development and extension of the model.

1. Physical Savings: The Problem of Ricardian-Realism

The classical political economists thought of savings with what I will call a “Ricardian”¹ or “realist” conception of the economy, one which – while theoretically problematic in many respects – still forms the intuitive basis of the notoion of saving in many expositions. As an analytical method, Ricardianism views monetary relationships as isomorphic to some underlying pattern of barter relationships. Money, in other words, is a “veil” over this set of relationships. With the additional assumption of homogenous product, this allows pure Ricardian models to conduct analysis in physical rather than monetary magnitudes.

The conventional wisdom was articulated by John Stuart Mill (1848, p. 488), but continues to be quoted approvingly (e.g. by Friedman & Schwarz [1963, p. 696]):

There cannot, in short, be intrinsically a more insignificant thing, in the economy of society, than money; except in the character of a contrivance for sparing time and labour. It is a machine for doing quickly and commodiously, what would be done, though less quickly and commodiously, without it: and like many other kinds of machinery, it only exerts a distinct and independent influence of its own when it gets out of order.

A pure Ricardian economy denotes its income and output in terms of a homogenous good – say, corn – which economic agents can choose either to consume or save. In such an economy, a stock of wealth for investment can only be amassed if the investor either abstains from consumption himself, or solicits a loan from someone else who has abstained from consumption. Ricardian saving, therefore, represents a definite stock of saved-up output which can then be used in the production of further output.

This is the premise of the wage-fund doctrine, first developed in the same work by Mill (1848), and that formed the core of the dominant theories of business cycles and economic growth until the early 20th century (e.g. Strigl 1934). Corn that is not consumed can be re-planted, and in this way saving is supposed to lead to economic growth. More modern moneyless neoclassical growth models such as Solow (1956) and its successors, still a staple of contemporary macroeconomic textbooks, are formally very similar: growth hinges on the accumulation of a homogenous K with diminishing marginal product,² and saving is defined as the excess of income over consumption. The interest rate is determined entirely by real factors, and is identical to the marginal productivity of capital in equilibrium. Units are generally left unspecified, but given the lack of money in these models, a physical interpretation seems most likely.

The chief advantage of Ricardianism, and one reason for its persistent intuitive appeal, is its usefulness in combating mercantilist fallacies. As the classical political economists emphasized, real goods in one form or another, rather than money as such, is what economic agents care about in the last resort. In addition, there is a great deal of evidence and theory to suggest that an economy’s capacity to produce real goods is more or less invariant in the long run to the behavior of the money stock (Friedman 1977). It makes some sense, therefore, to center the analysis directly on real goods, rather than on money, which can be a capricious yardstick for real goods. Any beneficial effects of nominal or balance sheet operations seem like the chimerical “free lunch”, getting something out of nothing. Ricardians tend, therefore, to be skeptical of nominal operations, preferring to ascribe real fluctuations to real causes.

There are, however, two crucial disanalogies between an individual laying aside idle funds and an economy laying aside idle resources that are elided in Ricardian analysis: first, the wage-fund model collapses the difference between the individual and system-wide perspectives on the act of saving (cf. Yeager 1982), and second, it collapses saving and investment into a single action.

On the first point, saving is a clearly meaningful concept for an individual, who faces a tradeoff in the use of his funds between present purchases and future purchases. He may, therefore, let some portion of his funds idle (from his own perspective) for spending in the future rather than spending them today. He may decide to hold these in more or less liquid form, but in normal circumstances the funds will be available for later use in whatever form he holds them. From a system-wide perspective, however, the situation is different. To an approximation (and barring recession), resources that are produced get used. Idle resources are a pathology to be avoided.³ For the system as a whole, the tradeoff is not between some consumption now and a greater amount of consumption later, but between production in one line versus another. To literally lay aside resources in a Ricardian manner for future consumption would be unnecessary and economically wasteful. What is necessary, rather, is the use (not the laying aside) of productive goods for the production of further investment and consumer goods, in ways that facilitate a growing stream of ultimate consumables. Investment is clearly involved, but from a system-wide perspective, the role of saving is at best secondary.

In addition to the individual and system-level perspectives, the Ricardian view of saving conflates monetary and physical magnitudes, or funds and resources. The impossibility of certain classes of economically meaningful physical aggregates was demonstrated during the controversy in the 1960s about whether capital (K) in the production function should refer to a physical or a monetary magnitude (Hodgson 2014), though particular difficulties with the approach had been recognized for decades by that point. The issues here are exactly identical. The Ricardian logic comes through in a “representative good” model, where heterogeneity is abstracted away or ignored. But to operationalize such a model, there is in general no way to sum quantities of diverse physical goods into an aggregate like “capital” or (in our case) “savings” in light of changes over time in the patterns of valuation of those goods. Money magnitudes, imperfect as they may be, are in general the only economically meaningful way to aggregate diverse goods.

The wage-fund and neoclassical growth models, however, become much less straightforward to interprtet if we take aggregate savings to be a fund of accumulated purchasing power rather than a stock of accumulated productive resources. Why should such a fund have a nonzero marginal productivity? It clearly requires a separate act of investment in productive resources. But then the important causal process is not the laying aside (saving) at all, but the investment.

One could, of course, argue that the individual act of laying aside idle funds in a monetary economy facilitates exactly this. To what extent and under what conditions this is true is discussed in the following section.

2. The Loanable Funds Model of Monetary Saving

The loanable funds model is a model of saving in monetary terms developed by Robertson (1933; 1934) and Ohlin (1937) which has, with some modification, persisted to the present day as the basic tool for introducing the banking and financial systems in economics.

Figure 1. The traditional loanable funds diagram on the left, and its use in the comparative statics of a credit expansion on the right.

The model as developed by Ohlin and Robertson conceptualized savings as the unintermediated purchase of corporate bonds on the open market, though with the assumption that bank finance could be assimilated unproblematically to that basic framework. Later uses of the diagram introduced banks explicitly as middlemen between corporate bond issuers and ultimate savers (e.g. Kohn 1982), or as the repositories of savings in their own right (e.g. Garrison 2001; 2004).

The model is therefore most straightforwardly applicable to bond markets,⁴ but there are a number of merits in its application to bank lending as well. Most importantly, in the comparative statics version, the channel of monetary adjustment is correctly identified as entering through financial markets, rather than a presumptive “helicopter drop” as in Friedman (1969) and most subsequent models of monetary expansion.⁵ The “liquidity effect” whereby the interest rate falls after a monetary expansion is easy to see. The long-run adjustment as the price level rises can be shown equivalently by an outward shift of the nominal demand for loanable funds or an inward shift of the real supply of loanable funds.

Nevertheless, the shift in the interpretation of the diagram from the determination of the bond rate to the determination of the bank loan rate has brought with it a number of conceptual difficulties which have so far been dimly perceived. The notion of savings implicit in the traditional loanable funds diagram – a stock or a flow of non-consumption that can be intermediated into investment projects – is an important component of several distinct post-Ricardian macroeconomic traditions. I will suggest, however, that even in an explicitly monetary form it obscures more than it illuminates, first of all because the term’s long history has given it a number of mutually incompatible meanings that are frequently conflated, and second, because each particular meaning brings essentially distinct magnitudes under the same head, presumably in order to maintain continuity with Ricardian usage.

This continuity, unfortunately, has burdened macroeconomic discourse across its many subfields with a concept without clear correspondence to any economically significant magnitude – or, worse, a correspondence to many such magnitudes. This section, therefore, attempts to distinguish among the various mutually incompatible meanings of the term in a rough chronological order, and argues that any work done by “savings” in any of these frames may be done more satisfactorily by other, more precise terms.

2.1. Savings as Non-Consumption versus Specific Demand

One example of the ambiguity of savings is the early and persistent debate over loanable funds versus liquidity preference theories of interest rate determination, which hinged on whether saving has an effect on the rate of interest.

Keynes (1937), in his exposition of liquidity-preference theory, had been using a Ricardian-type definition – savings as non-consumption of real income – and concluded that it had little bearing on the rate of interest. Non-consumption by itself, of course, has no effect on the price or quantity of lending, and in this sense he was surely correct. Robertson and Ohlin, however, had in mind something like “the demand for bonds”⁶ (or at least took non-consumption to imply an increase in the demand for bonds) – and in this sense they were surely correct that this demand is a crucial determinant of the bond rate of interest. As Snippe (1985) argues, “Keynes confused Robertson’s analysis of the impact of saving behaviour by assuming that the loanable funds theory was based on his own concept of saving.”

In a one-good Ricardian economy, non-consumption is equivalent by definition to investment in the capital good, which grows on its own. In a multi-good monetary economy, however, the two definitions are no longer coincident. Non-consumption of monetary income may or may not be spent on bonds, and there is no a priori reason to assume that changes in the demand for money balances pass entirely into the bond market, as opposed to various goods markets. Indeed, in the context of this debate, an increase in saving could refer to an increment or a decrement in the demand for money balances, depending on whether we define it as non-consumption or a specific demand for bonds. This surely matters for any causal chain in which savings is a link.

The confusion was compounded with the extension of these conceptions of savings to the determination of bank credit. When money balances are held as bank liabilities, it appears at a first glance that non-consumption really is equivalent to a demand for financial assets after all, excepting some hopefully minuscule fraction of “dead” savings held as base money. This is not tenable. As the following subsections show, it is more difficult to assimilate bank finance to “savings” in the sense of aggregate non-consumption than it is to assimilate bond finance to the suggested exposition in Section 3.⁷

2.2. The Loan and Deposit Rates of Interest

In the first place, a model of bank lending – unlike a model of a bond market – must specify two interest rates rather than one: i_L, the loan rate paid by borrowers to the bank, and i_D, the deposit rate paid by the bank to depositors. The supply of loanable funds increases in both, for independent reasons.

The supply of loanable funds increases in i_D because the bank can attract depositors and loosen its own budget constraint, in a process analogous to the Robertson-Ohlin loanable funds model. The upward slope in i_L, however, is not captured at all by the loanable funds model, and is unique to the process of bank lending: namely, a higher loan rate implies a higher opportunity cost for reserves, leading the bank to choose a lower reserve ratio.

To see this latter effect, compare the marginal cost conditions that characterize bank lending and bond purchase. In the latter – as in the loanable funds diagram – the lender must acquire liquid assets (deposited funds) in order to exchange them for illiquid assets (loans). The loan takes place entirely on the asset side of the balance sheet, and the relevant marginal cost of balance sheet expansion is the cost of attracting reserves, which can be done by adjusting the interest rate on deposits. Its cost function, therefore, is

(1) C_i(i_D) = i_DD(i_D)

where i_D is the deposit rate, and D is the quantity of deposits, which is a function of the deposit rate.

In a fractional reserve bank, by contrast, the bank marks up both its assets and its liabilities. Attracting deposits is not a precondition of lending funds, and the relevant marginal cost of balance sheet expansion is the expected liquidity cost of an increase in outstanding liabilities. Its cost function, therefore, is

(2) C_L(R/D) = Q(R/D)

where Q is defined as the integral of the left tail of the probability distribution function for reserve losses greater than reserves R, conditional on a reserve ratio R/D.⁸ Intuitively, liquidity risk rises as the bank chooses a lower reserve ratio. R, in turn, is a function of i_L for a given D: the bank may choose a higher risk of illiquidity in response to particularly enticing investment projects. And the smaller the quantity of reserves, the larger the loan portfolio for a given quantity of deposits, hence the upward slope in i_L.

Under perfect competition, i_D = i_L – S, where S reflects the cost of intermediation to the bank. If the two rates are functionally related, then the label on the LF diagram’s vertical axis is a matter of indifference, which appears to be the reason for its uncritical application to bank lending. However, the important point here is that the supply of loanable funds slopes upward even if the loan rate and the deposit rate are completely independent. This will be the case if, for example, i_D is fixed at zero, as in the model that follows, as well as over much of the history of U.S. banking.

A “quantity of savings” in the context of bank lending must refer to the supply of loanable funds as a function of i_D, for a constant i_L. The situation faced by banks, however, is nearly the reverse: a balance sheet whose size depends primarily on i_L, and a minimally variable i_D. For banks, therefore – as opposed to nonbank financial intermediaries – a supply curve for loanable funds derived primarily from liquidity considerations is impossible to identify with a quantity of savings.

2.3. Forced Saving, Normative Ricardianism, and the Comparative Statics of Credit Expansion

Ohlin and Robertson themselves were committed to a view that, though the quantity of loanable funds is a monetary rather than a physical magnitude, money was nevertheless a veil over more interesting “real” relationships. Nevertheless, the loanable funds construct has found use in various models of the business cycle, many of which feature nominal shocks.

It is in this context that normative Ricardianism arises, as opposed to the descriptive Ricardianism of the classical and neoclassical economists. Even if money is not in fact a veil, what classical analysis indicates is that it ought to be: the more closely an economy comports with Ricardian mechanics, the better. In particular, the normative Ricardian believes, because an economy’s wealth consists in goods and not money, it follows prima facie that any beneficial effect of nominal operations must be chimerical. The irreducible scarcity of physical goods, therefore, ought to be reflected in “hard” money on the side of the central bank, and the proscription of balance sheet operations on the side of private banks.⁹ Ricardian logic of this type underlies a great deal of support for narrow banking, as well as other opposition to fractional-reserve banking from a variety of economic perspectives (on which see Burns & Harwick 2017).

It was under such a paradigm that “forced saving” entered the economic lexicon, around the time that economists were beginning to move away from pure Ricardian models (e.g. in Hayek 1933).¹⁰ Credit expansion through the banking system finances new investment beyond the stock of accumulated savings, which must be covered by a diminution in the purchasing power of the community, i.e. by forced saving, the situation described in the second panel of Fig. 1. Even in an analysis that allows for the possibility of non-Ricardian operations, the desirability of those operations is still very much suspect: “forced” saving is something distinct from normal (i.e. Ricardian) saving. Barring forced saving, savings must still be accumulated over time by refraining from consumption. The normative question, then, is something like identifying the monetary policy that maximizes Ricardian relative to forced saving.

The problem with normative Ricardianism is that, in a proper money economy, investment does not depend on anyone’s deliberate laying aside either of resources or of funds, a supposed abstention that Schumpeter (1954: 1114) called “entirely imaginary”. All it requires is the purchasing power to bid away resources into investment use.¹¹ This purchasing power can be amassed by abstaining from consumption, as in the Ricardian scenario – either one’s own (internal financing) or others’ (debt issue, provided the debt is acquired by consumers and not the financial sector). However, the more usual scenario is to solicit a loan from the bank. In a banked money economy, the bank creates the funds ex nihilo, marking up its assets and its liabilities and transferring those liabilities to the borrower to spend. It is not a transfer of Ricardian saving from one party to another.

“Forced saving”, in other words, has always been the normal course of investment in a banked and monetized economy, with the response of the price level determined by the rule implicit in the monetary regime. The appearance of more favorable investment opportunities, given a constant monetary base and demand for money, will tend to raise prices of consumer goods as resources are bid away into investment uses, at least in the short run.¹²

Similarly, whether saving results in a “paradox of thrift” depends, first, on the form in which savings are held, and second, on the response of the broad money supply. The typical story of non-consumption being intermediated into investment is a special case, the situation necessary to ensure price level stability (and to avoid the paradox of thrift) with a constant total money supply: non-spending on the consumer side is then picked up one-for-one by spending on the investment side. Needless to say, theory based on this single case has little relevance in a world with an elastic money supply predominantly issued by banks in response to investment opportunities.

One important implication regards the dynamics of business cycles. To the extent that investment and consumption compete for the same resources, the diminution in consumption required for investment is not – as in the saving-led growth story – an exogenous backward shift in the demand for consumables (implying a fall in their price), but rather an endogenous backward shift in the supply of consumables (implying a rise in their price) as investment goods compete for their factors. Such a dynamic does indeed seem to characterize investment booms, a fact which is often – and likely spuriously – blamed on contemporaneous monetary expansion by the central bank.

There is, strictly speaking, never such a thing as a shortage of savings. What is scarce in the financing of productive capital projects is generally not accumulated funds or resources, but rather system-wide trust. Unlike in a Ricardian economy, where balance sheet operations are ruled out and lending must indeed be made out of accumulated funds, it is trust (and its obverse, trustworthiness) – which is to say, the expectation of real return – that enables a mere balance sheet operation to become an effective loan in a multi-tiered monetary system. To the extent that the bank’s liability-holders trust the bank to maintain the value of its liabilities (i.e. to redeem them at par in more basic money), the bank may finance prospectively profitable investments. I as an individual may similarly mark up my own balance sheet to any degree I wish, but the recipient of my loan cannot then spend it unless the community has sufficient trust in my ability and willingness to maintain their value, whether this is vouchsafed by my own accumulated wealth or my acumen in making profitable loans.¹³ Without such trust, lending can only be done out of accumulated assets.

Restricting lending to accumulated assets, as a full-reserve bank must do, is a way of guaranteeing credibility where the trust in balance sheet operations is lacking, whether for institutional reasons or a lack of productive investment opportunities. It is precisely this trust that characterizes a modern financialized economy, and which normative Ricardians cannot conceive. A systemwide lack of accumulated resources may indeed limit the trust that system can support, but this is a specific case of the more general phenomenon, and not likely a significant one in real-world crises of trust in the financial system. By the same token it is true that confidence in any particular bank is related to its stock of reserves and assets, and it is this stock in the aggregate that is sometimes meant by “savings”. But the supply of cash deposited at the bank itself depends on confidence in the bank. Indeed, the variable portion of this supply is nothing other than the demand for the bank’s liabilities, which depends entirely on confidence in the bank.

For this reason, it would be more apt to describe the determinants of the interest rate as the supply of profitable investments (rather than the demand for loanable funds), limited by the trust of liability holders in the issuing institutions (rather than savings). What matters for the interest rate is not time preference, as would be true in a Ricardian frame, but the riskiness of investment. This risk can come from any number of places. The borrower may default or abscond. The investor may die before enjoying his return. It is not, therefore, apt to think of a “risk-free” interest rate, determined by time preference, with a risk premium added on top. Rather, interest rates – including those on supposedly “risk-free” assets – reflect the risk inevitable in deferred consumption. From here a “liquidity premium” may be subtracted, hence the willingness to hold zero-return cash rather than positive-return government bonds, despite the two having the same risk. The slow development of institutions to support credible promises by governments and banking institutions over the past several centuries has brought with it a corresponding dramatic diminution in interest rates, which cannot plausibly be attributed to the increased farsightedness of the moderns over the ancients. One must imagine, in the limit, that a perfectly credible entity borrowing from immortal agents could always do so at zero interest¹⁴ – and in this sense, perhaps time preference was never anything more than risk aversion at all.

It is not, therefore, the case that “if [macromonetary] institutions are functioning properly . . . a dollar of new saving, a dollar not spent on purchasing final goods and services, allows for a dollar’s purchase of capital goods” (Buchanan 1993). Bank lending does not “funnel” funds from consumption uses to investment, as if the funds themselves rather than the trust underlying them were the scarce object. And while normative Ricardianism’s suspicion of banking has largely waned in mainstream circles, the analytical tools still used have seen only marginal adjustment to this new understanding. For this reason, in contrast to the Ricardian-realist framework, a set of more fundamentally “nominalist” tools – which deny both the descriptive validity and the normative desirability of reducing money relations to a barter pattern¹⁵ – is needed.

2.4. Savings as a Balance Sheet Constraint

One more view of savings bears mention, one sophisticated enough to sidestep many of the aforementioned issues. This view acknowledges both the impossibility of a physical aggregate and the gratuitousness of bank credit at the margin, but deemphasizes the latter and attempts to salvage Ricardian language by treating savings primarily as a determinate constraint on banks’ balance sheet expansion. Again, Ricardian language serves a prophylactic purpose, this time against “needs of trade” doctrines, or even more radically, the idea that the nominal money stock is determined passively by the demand for money, and therefore that monetary policy is generally impotent.

Selgin (1988, ch. 4), for example, interprets the stock of savings as the public’s willingness to hold circulating bank liabilities, rather than to spend them or hold base money (“dead” savings). This makes some sense in light of his argument that the public’s demand for a bank’s liabilities limits the quantity of those liabilities it can maintain in circulation (ibid., ch. 3). In short, the bank maintains some level of “precautionary reserves” given a gross volume of clearings in order to keep the risk of failing to meet its regular redemption obligations at some acceptably low level. Unwanted liabilities are returned for redemption via the clearing mechanism and impinge on the bank’s reserves. In order to maintain its precautionary reserves, therefore, the bank’s quantity of issues is determinate. If we suppose that the public’s holdings of base money are negligible, this strict relationship between demand for liabilities and the bank’s capacity to issue credit renders intelligible the idea of a determinate quantity of savings.

There are both semantic and substantiative issues here. Semantically, a specific demand – this time for bank liabilities rather than bonds – is again preferable to “savings”, which still suggests a nonspecific non-consumption. The composition of the demand for money is supposedly something entirely different from the supply of savings. And yet, a monetary system in which bank liabilities circulate as money means that non-consumption, either as a stock or as a flow, cannot be identified with the provision of funds to a bank. If this is the case, “saving” is superfluous.

More substiantiatively, the identification of the demand for bank liabilities with the supply of loanable funds assumes not only a constant risk schedule for the bank, but a constant preference on the risk schedule.¹⁶ Such an assumption is untenable: facing particularly enticing investment prospects, a bank may on the margin decide that the risk of lowering its precautionary reserves is worth the expected return.¹⁷ Without such a constant risk preference, the supply of loanable funds is a function of the demand for bank liabilities, but it is not identical with the demand for bank liabilities. Nor can their identity serve as a normative ideal unless we are willing to stipulate some objectively “correct” level of acceptable risk for the bank, bounded both from above and below and invariant to the alternative uses for its precautionary reserves. As Tobin (1963) argued,

There is more to the determination of the volume of bank deposits than the arithmetic of reserve supplies and reserve ratios. The redundant reserves of the thirties [and, one might add, of today] are a dramatic reminder that economic opportunities sometimes prevail over reserve calculations. But the significance of that experience is not correctly appreciated if it is regarded simply as an aberration from a normal state of affairs in which banks are fully “loaned up” and total deposits are tightly linked to the volume of reserves. . . . The use to which commercial banks put the reserves made available to the system is an economic variable depending on lending opportunities and interest rates.

3. An Alternative Model

Taking these points together, what is needed is a model of the loanable funds market in which 1) the supply of bank liabilities constitutes the major portion of the money supply, and 2) the supply of credit rests on banks’ optimizing decisions, and is not identified with a stock of savings. Ideally this model would also retain the virtues of 1) market constraints on the creation of credit, 2) determination of the interest rate on the basis of market behavior, and 3) simple graphical exposition. Such a model is offered in this section.

The demand for money, quite simply, is the demand for the services of money, namely as a medium of exchange and a store of value. The demand for credit, on the other hand, is the demand for present funds against future funds, the relative price between these being the interest rate. Most of the former demand is satisfied by holding private circulating liabilities, for example, bank deposits. The opportunity cost of holding these liabilities can be expressed in terms of base money, for which the bank liability is redeemable at a fixed rate. The vertical axis in Figure 2, therefore, is the price of the liability in terms of base money.

To simplify the model, we assume 1) that the real demand for cash balances is constant, and 2) that consumer demand for media of exchange is entirely satisfied by bank liabilities – in other words, that banks hold the entire stock of high-powered money. The demand for bank liabilities is therefore equivalent to the non-bank demand for money, and divided by the price level, is fixed. Our demand function is then

(3) D = α/P_D

where D is the quantity of bank liabilities, and P_D is the price of a bank liability in terms of the unit of account.The price of liabilities will be the inverse of the price level (P_D = 1/P), so (1) can also be expressed as D/P=α – i.e. that the real demand for the services of money (D/P) is equivalent to a constant α.

The bank stands ready to buy and sell any quantity of liabilities for $1 each. So long as the bank is solvent, therefore, the supply curve is simply

(4) P_D = 1

Figure 2. The demand for and supply of circulating bank liabilities

Equilibrium in the market for bank liabilities is indicated by the intersection of supply and demand, where D = α. This bears some resemblance to the traditional Ms/Md diagram, though with the supply curve horizontal rather than vertical, the difference being that the supply of bank money is not a choice variable either for an individual bank or the banking system as the supply of base money is for the central bank.

The bank’s liabilities may be thought of as deposits, though the bank will not pay interest on them. The analytical effect of (and the reason for) this assumption is to focus attention on the behavior of the bank and away from the decisions of consumers – that is, to focus on the supply of loanable funds as a function of the loan rate i_L rather than the deposit rate i_D. The latter might indeed be incorporated into this model by making the demand for bank liabilities an increasing function of the deposit rate, as in the traditional exposition. However, empirically, the public’s demand elasticity for bank liabilities with respect to bank credibility is relatively low, especially since the establishment of deposit insurance. Actual deposit rates for checking accounts were fixed at zero in the U.S. from 1933 with Regulation Q until its repeal in 2010,¹⁸ and have been negligible since. Realistically, therefore, the deposit rate is not a powerful tool for taking in new funds.

This inelasticity does not, however, consign the bank to pass up the opportunity. Independently of its upward slope in i_D, the prospect of higher returns will induce banks to lower reserve ratios and take on more illiquidity risk at the margin. In other words, the money multiplier is endogenous to the interest rate. A parametric money multiplier is appropriate on the assumption of binding reserve requirements, as was approximately the case when the theory was being developed. But since the 1990s, reserve requirements in most of the developed world have either been abolished, or rendered irrelevant due to retail sweeps (Anderson & Rasche 2001). Especially since the ballooning of excess reserves following three rounds of quantitative easing, the assumption of binding reserve requirements is difficult to justify.

We may, therefore, think of the primary constraint on bank lending – not as a quantity of “savings” – but as the credibility of its promises to repay at the current margin of lending. A series of good investment opportunities will raise the credibility of the bank’s promises to repay on the basis of those opportunities for any given reserve ratio. Even if this induces no additional demand for its liabilities, the bank is now more credible at any given reserve ratio. It can therefore afford to exploit the opportunity without increasing its illiquidity risk. Alternatively, a series of risky-but-high-return opportunities may make an increase in the illiquidity risk worthwhile. The effect is the same, and in neither case depends on changes in the rate or quantity of savings.

The model is defined with an additional three equations:

(5) F = F(i)

(6) F = D – R

(7) π = iF – Q(R/D)

(5) is the demand function for loanable funds, assumed to slope downward in the interest rate. (6), which connects the markets for money and credit, is simply the balance sheet condition rearranged: assets (reserves R + loanable funds F) equal liabilities (D). (7) is the profit condition for the bank, with Q being expected liquidity costs for a given reserve ratio as in (2). For a given R, Q will be rising in D at an increasing rate (i.e. Q_D > 0 and Q_DD > 0). Maximizing (7) subject to (6) results in the supply curve of loanable funds,

(8) i = Q_D

Suppose the expected profitability of prospective projects rises – i.e. F(i) shifts outward. In order to maximize profits, the bank will increase F and D in order to draw down its reserve ratio and increase Q_D. Per (6), F has an upper bound of D, which in turn is determined by (3). If D is vertical in i, therefore, (8) will be drawn such that F=0 when i=0 (when the opportunity cost of reserves is zero), and F approaches D asymptotically as i approaches infinity.

Figure 3. The supply and demand for loanable funds

Because the bank does not pay interest on its liabilities, it cannot attract more depositors as the interest rate rises, at least in the short run with which our model is concerned. For this reason, the supply of loanable funds in our diagram is not a “savings” curve, as in the traditional loanable funds diagram. Rather, it derives entirely from the decisions of the bank on the quantity of loans, with a given demand for liabilities. The dotted line D in figure 4, however, may be interpreted as conceptually equivalent to the supply of loanable funds in the canonical diagram, where the demand for bank deposits is a function of the interest paid on them. If we were to reintroduce a positive deposit rate into this model, (7) would become π = iF – Q(R/D) – i_DD, and the dotted line D would slope upward, with the actual supply curve continuing to approach it asymptotically from the origin as the loan rate rises.¹⁹

It is important to note that if the bank goes to zero reserves – if it is under no obligation to redeem – gratuitous credit means there is no limit to the expansion of its balance sheet, provided it does not thereby lose the trust of its liability holders.²⁰ In the more realistic case of a predictable stochastic flow of redemption demands (and thus a determinate Q), the redemption promise keeps the supply of liabilities horizontal with respect to price regardless of how low reserves in fact go, so long as R > 0. The quantity of liabilities as determined in that market is the limit of the bank’s ability to acquire interest-earning assets.

3.1. Implications

Consider the comparative static exercise of representing an increase in the demand for bank liabilities, i.e. a rise in α. At the posted price of $1, more people desire to hold bank liabilities than previously. The bank’s volume of clearings falls, allowing it to issue more loans without exposing itself to greater liquidity risk. Per (6), D rises on the liability side, and R on the asset side, and the upper bound on loanable funds (the dotted line in Figure 4) shifts out. The bank draws down its reserves and expands credit, stretching the supply curve out horizontally.

Figure 4. An increase in the demand for bank liabilities. The exogenous shift in demand in the left graph ramifies to an increase in supply in the right graph.

An increase in the demand for credit, however, does not redound the other way, to an increase in the supply of bank liabilities. In this case, we have an increase in the interest rate, but as the demand to hold bank liabilities is unchanged, the bank is not able to issue more liabilities except in the immediate run.

Compared to the traditional LF diagram, the present model also provides a more causally coherent model of negative loanable funds supply shocks. In the traditional comparative statics, a backward shift in the supply of loanable funds (i.e. a decrease in the saving schedule) typically results from an increase in time preference, i.e. by an increase in the demand for present goods compared to future goods. By contrast, our reformulation attributes the same shift to a fall in confidence in a particular institution or the system as a whole, a shock with a great deal more descriptive validity in a business cycle situation. Rather than a spontaneous bout of imprudence, the shock is better thought of as a loss of confidence: consumers decrease their demand for less liquid redeemable assets, forcing the institution in question to raise its interest rates and shrink its balance sheet in order to defend the value of its liabilities.

The exposition in two markets clears up another ambiguity inherent in the traditional loanable funds diagram, namely, two distinct senses in which the interest rate might be said to be the “price of money”: (1) insofar as store of value services can be bought in interest-bearing instruments rather than non-interest-bearing cash or bank liabilities, the interest rate on the former is part of the opportunity cost of holding the latter, and (2) the interest rate is the rental price of money over time. The first pertains to the market for bank liabilities; we ignore it on the basis of bank liabilities serving a unique medium of exchange function. These services are, at some margin, worth the foregoing both of interest and consumption that might otherwise be procured with those balances. The interest elasticity of the demand for bank liabilities, therefore, is likely to be low. The second properly pertains to the market for loanable funds, irrespective of the demand for currency. It is the failure to distinguish between these two markets that so vitiated the Real Bills Doctrine early in the development of monetary theory.

4. Conclusion and Future Research

The model presented in this paper is deliberately highly stylized. There are a great number of situations the model is silent on, for the simple reason that it is intended as a clean replacement for the traditional LF construct, and the traditional LF construct is also silent on all these issues. That such situations are ignored in this model should not, therefore, suggest that they are unimportant. Nevertheless, the current model is better-suited for extension in various directions than the unreconstructed loanable funds model. Here I suggest several extensions that would give it the analytical sophistication to tackle many of the same questions as a traditional DSGE model, and indeed – with its explicit model of the monetary and financial sectors – give it an advantage.

Most importantly, a richer model would endogenize price level changes. Such a model would have the potential to replace not only the LF construct, but also the traditional money supply/demand construct. The latter is limited by ignoring the banking system except through a mechanical money multiplier in the background. To unify a model of the banking system with a model of the broader money supply into a simple set of diagrams would be an important pedagogical achievement.

Second, the present model has focused on bank financing to the exclusion of bond financing, the reverse of the canonical LF model. Though we have argued that the latter presents fewer difficulties for the the present model than the former does for the canonical model, integrating an explicit model of the choice between bond issue and bank finance would be valuable. In addition, banks themselves have an array of financing options available richer than presented in this model. Future progress could account for secondary markets for bank loans, which do place banks in the role of a more “pure” intermediary. This would be important, for example, in modeling the 2008 housing crisis, for which the repackaging and reselling of mortgages on secondary markets was an important precipitate.

Third, the structure of substitutability and liquidity in modern financial markets is highly complex. This makes a simple model involving only two layers of the credit structure difficult to operationalize without arbitrary decisions as to what counts as “money” and what does not. In order to capture movements in the substitutability, the liquidity, and the “moneyness” of various assets across the business cycle (cf. Harwick 2018a), the model would have to stipulate a utility function for money-holders, perhaps along the lines of Barnett (1980). This would also, as Barnett (2016) argues, improve the structural stability of the underlying parameters.

Fourth, dynamics will be important for work applying this model to the business cycle. In conjunction with endogenizing the price level, if the adjustment of prices takes time, then short-run output will be endogenous. This is especially relevant to the dynamics of deflationary recessions. This will necessitate an explicit goods market in the model, either a continuum of goods or some representative good.

Finally, while the payment of interest on deposits has not been a significant factor in the U.S. for many decades now, in order to truly subsume the traditional LF model, the payment of interest on deposits can be allowed to vary with the interest rate, allowing for some endogeneity in the demand for bank liabilities against both goods and base money. While empirically plausible parameters will not likely alter the qualitative results, a breakdown of the relevance of increased deposits versus declining reserve ratios for the upward slope of the supply curve for loanable funds would be a useful study. Implicit interest payments in the form of “free” services rendered may also increase the quantitative significance of the former.

While the basics of the operation of the banking system are well-understood among monetary and macroeconomists, the introductory constructions remain mired in an outmoded analytical frame. For this reason many nonspecialists never advance beyond an overly simplistic and distorted view of a modern banking system. There is, of course, an inevitable tradeoff between realism and simplicity. However, simplifying assumptions like a constant money supply or a constant money multiplier, and analytical steps like the separation of money from credit or the identification of the supply of credit with a stock of savings, are viable only in the absence of comparably simple constructions that do not make such assumptions or steps.

Such a model has been offered in this paper, with the goal of minimal complexity and maximal perspicuity. By making banking analytically central, rather than an addition to a core of otherwise complete monetary theory, it also aims for maximal extensibility and descriptive accuracy given the aforementioned constraints – an approach I hope will be vindicated by the fruitfulness of future development along these lines.

Footnotes

1. The term “Ricardian” has been used in this sense by Lachmann (1958) and Buchanan (1958).
2. Catch-up growth, at least, as steady-state growth is driven by “technology” in Solow (1956) once capital accumulation has reached the point where depreciation just offsets it. Further changes in saving have a level effect in the long-run, but not a growth effect.
3. Per Hutt (1939, ch. 3), planned inventories are not “idle” in this sense.
4. The financing of corporate investment through the issue of bonds on the open market is relatively more common in the U.S. compared to the solicitation of a bank loan than elsewhere due to restrictions on bank branching that persisted into the 20th century (Bordo et al. 2015), so the dominance of the U.S. in the development of economic theory during that time may explain why this has appeared to generations of economists as a natural prototype for saving and investment.
5. Harwick (2018b) discusses the importance of the distinction.
6. This usage is usual in the international trade literature, where the notion of a country’s savings maps nicely onto its financial account. And indeed, in the typical Mundell-Fleming model, the balance of payments and the rate of interest are closely linked, despite its “Keynesian” heritage.
7. Indeed, Patinkin (1961) suggests that both have an equivalent effect on the equilibrium volume of spending, bank finance by increasing the quantity of money, and bond finance by increasing the degree of substitutability between bonds and money. In more modern terms, a broad and economically meaningful monetary aggregate may be increased equally well by an increase in the quantity of one component or by the partial monetization of a new component (Barnett 1980).
8. Q=p(O-R) φ(O|R/D)dO, where O is the outflow of reserves, φ is the probability density function over O conditional on R/D, and p is the cost of illiquidity for a given shortfall (White 1999: 57; 1989: 42).
9. This was the position of the Currency School in England, for example, who understood that price-specie flow mechanism was a negligible factor in the equilibration of international trade imbalances compared to the expansion and contraction of bank balance sheets (Eichengreen 1995: 47), and yet “looked to a hypothetical purely metallic currency system operating in Humean fashion” (White 1995: 116) as a normative ideal. A great deal of opposition to fractional reserve banking, which renders the broader money stock a function of bank balance sheets, is based on a similar intuition.
10. Though see Garrison (2004) on the contemporaneous debate surrounding the appropriateness and various uses of the term.
11. This appears to be Keynes’ (1937) point when he argues that savings will always keep pace with investment. Defining savings as non-consumption (or the excess of income over consumption), it is true almost by definition that any investment implies that those resources have been bid away from consumption uses. Though Keynes himself still speaks – perhaps inaptly – of a “supply of savings”, there is a long post-Keynesian tradition of treating S=I as an accounting identity (see, e.g., Lindner [2015] for a derivation).
12. This case should be distinguished from an increase in real GDP, which all else equal will be deflationary. The appearance of favorable investment opportunities is an expectation of a future increase in real GDP; however, the present effect is an increase in the broader money stock.
13. See Murphy (1978) for an instructive historical example, and a discussion of the trust necessary to keep payments going and avoid a deflationary deleveraging during the several nationwide bank closures in Ireland in the 1960s and 70s.
14. This is a sufficient, but not a necessary condition for zero or even negative interest rates: a sufficiently broad and severe decline in expected future incomes may also render investment in unprofitable ventures the least bad option, hence negative interest rates
15. Nominalism in this basic sense should be distinguished from what I’ll call hyper-nominalism, which denies entirely the the conceptual validity of real (as opposed to nominal) variables. This is Mehrling’s (1999) accusation when he argues that “Inflation was difficult for Minsky to understand because of the thoroughgoing nominalism of his thought. . . . In Minsky, there is no margin along which the ‘real’ value of money might be established.” (quoted in White [2015])
16. Or, alternatively, a vertical risk-preference schedule with respect to alternative investments.
17. Friedman and Schwartz (1963: 178; 541; 616; 695) document actual and potential behavior of this sort on the part of U.S. banks at various historical episodes.
18. Though see Startz (1979) on implicit interest on deposits, which finds them a much blunter instrument than explicit interest. Allen (1983) finds no significant implicit interest at all.
19. Strictly speaking, in order to avoid conflating the loan and the deposit rates, we would need another equation i = i_D + S explicitly describing the spread between the loan and deposit rates.
20. This is the position that fiat-issuing central banks find themselves in. Legal tender laws also prevent the demand for their currency from falling to zero. As this renders the model indeterminate for a profit-maximizing banking system, however (cf. Gurley and Shaw 1960, ch. 7), we consider only competitive private banks on the background assumption of a non-profit-maximizing central bank.