Against Savings
Aug17
Money & Macro14

Against Savings

A Suggested Exposition of the Markets for Money and Credit

This paper is also available on SSRN as a PDF.

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 (MS/MD), 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 MS/MD, and 2) that it lends itself to a naïve interpretation where banks are direct intermediaries of loanable funds.

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 that drives the traditional loanable funds model – iterations whose very number indicates the appropriateness of more precise terminology – and suggests more suitable existing terms that can serve all the various and mutually incompatible purposes to which savings is now put. The third section advances a basic alternative loanable funds model, 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 conceptualized savings under the simplifying assumption of what I will call a “Ricardian” or “realist” conception of the economy.

Ricardianism has both a positive and a normative component. As an analytical method, it views monetary relationships as isomorphic to some underlying pattern of barter relationships. Money, in other words, is a “veil” over this set of relationships. In conjunction 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.

Ricardian saving represents a stock of saved-up “stuff” which may then be used in the production of further “stuff”. 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. There is, accordingly, a determinate amount of “saving” in the economy that can be intermediated toward investment projects. This is the premise of the basic wage-fund doctrine that formed the core of the dominant theories of business cycles and economic growth until the early 20th century (see e.g. Strigl 1934), and one that persists into the Neoclassical era through moneyless Solow-inspired models of growth that hinge on the accumulation of a homogenous K.

The wage-fund model, first developed in the same work by Mill (1848), is a stylized one-good economy (say, corn) where a consumer faces a choice between saving or consuming that good. Corn that is not consumed can be re-planted. In this way, saving is supposed to lead to economic growth. The interest rate, then, is determined entirely by real factors, and is identical to the marginal productivity of capital in equilibrium.

There are, however, two crucial disanalogies between an individual laying aside idle funds and an economy laying aside idle resources. In the first place, the wage-fund model elides the difference between the individual and system-wide perspectives on the act of saving (cf. Yeager 1982), and collapses saving and investment into a single action. 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. In whatever form he decides to hold his saving, the only questions for him are liquidity and return; they are available to him for use in the future.

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.1 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 this 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 unclear.

In addition to conflating individual and system-level perspectives, the Ricardian view of saving runs into the problem of monetary versus physical magnitudes, or funds versus resources. The impossibility of an economically meaningful physical aggregate was demonstrated during the controversy in the 1960s about whether capital (K) 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 model, however, becomes incomprehensible if we interpret aggregate savings, not as accumulated productive resources, but as accumulated purchasing power. Why should such a fund grow on its own? 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 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

Moving into the 20th century, Robertson (1933; 1934) and Ohlin (1937) developed a model of saving in monetary terms, a model which has – with some modification – persisted as the basic tool for introducing the banking and financial systems in economics.

Loanable Funds
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 they believed that bank finance could be assimilated to that basic framework. Later uses of the diagram introduced banks 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). It is with these latter uses that we are mainly concerned.

Applied to bank lending, the diagram has a number of merits. Most importantly, in the comparative statics version, the channel of monetary adjustment is correctly identified as entering through bank reserves, rather than a presumptive “helicopter drop”, as in Friedman (1969) and most subsequent models of monetary expansion.2 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 interest rate on unintermediated bonds to the determination of the bank loan rate has brought with it a number of conceptual difficulties which have so far been dimly perceived. Most importantly, the process of bank lending (where the bank marks up both its assets and its liabilities) differs fundamentally from unintermediated lending (where the lender exchanges one asset for another). This makes the supply curve for loanable funds impossible to identify with a quantity of savings, and implies a different logic for the upward slope of the supply of loanable funds.

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 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 its Ricardian heritage.

This continuity, unfortunately, has burdened macroeconomic discourse across its many subfields with a concept without a clear correspondence to any economically significant magnitude.3 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

A concrete example of the legacy of savings’ ambiguity 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 the 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” (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 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 proper one-good Ricardian economy, of course, non-consumption is equivalent by definition to investment in the capital good. 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, “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.

An open market for financial investment vehicles does look a great deal like the canonical loanable funds diagram. However, it overlooks the economically significant role of credit creation in bank finance.4 Subsequent uses of the loanable funds diagram have had in mind not bond finance, but bank credit, which introduces further confusion. When money balances are held as bank liabilities, it appears at a first glance that non-consumption really is a demand for financial assets after all. 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 the following section.

2.2. 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. This “monetized” analytical Ricardianism quickly fell out of fashion during the 1930s.

Nevertheless, in spite of its analytical difficulties, Ricardianism retained a strong intuitive appeal, particularly for its usefulness in combating mercantilist fallacies. 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 directly on real goods, rather than on money, which can be a capricious yardstick for real goods. Any positive effects of nominal or balance sheet operations seem like the chimerical “free lunch”, getting something out of nothing.

For this reason, even among those forced to admit the importance of money in economic analysis, Ricardianism persisted as a normative stance, which manifested as a skepticism of nominal (as opposed to real) movements or operations. Even if money is not in fact a veil, classical analysis indicates that it ought to be: the more closely an economy comports with Ricardian mechanics, the better. In particular, the normative Ricardian believes, implicitly or explicitly, that the irreducible scarcity of physical goods ought to be reflected in the proscription of balance sheet operations, which stretch the contingent scarcity of funds.5

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). 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 such a framework is an unwarranted suspicion of what is very much the normal process of financial intermediation through a banking system. In a proper money economy, investment does not depend on anyone’s deliberate laying aside either of resources or of funds. All it requires is the purchasing power to bid away resources into investment use. This purchasing power can be amassed by abstaining from consumption – i.e. internal financing – as in the Ricardian scenario. However, the more usual scenario is to solicit a loan from the bank. In a banked money economy, the bank creates the money ex nihilo, marking up its assets and its liabilities and transferring those liabilities to the borrower to spend, which bridges the gap between the present and the future. It is not a transfer of Ricardian saving from one party to another. Indeed, Ricardian saving is typically amassed – both by corporations (Lachmann 19856: 88) and consumers (Leijonhufvud 1973) – not for the purposes of investment, but as a buffer stock for unplanned emergency expenditures. Though prudent to maintain, such buffer stocks bear little on the question of economic growth.

“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.6

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) 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.7 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. Without such trust, lending can only be done out of accumulated assets.

Restricting lending to accumulated assets is a way of guaranteeing credibility where the trust in balance sheet operations is lacking. 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 base of assets, and it is this base in the aggregate that is sometimes meant by “savings”. But the supply of assets to 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 interest8 – 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 which, however unfortunately, sometimes runs into regulatory impediments. And while normative Ricardianism with its 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 pattern9 – is needed.

2.3. Savings as a Balance Sheet Constraint

A more sophisticated view of savings 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 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 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 entirely 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.10 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.11 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 criticisms 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 exposition. Such a model is offered in this section.

3.1. The Market for Money Balances

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. Most of this demand is satisfied by holding private circulating liabilities. 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 1, 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 fixed, 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

(1) L = α/PL

where L is the quantity of bank liabilities, and PL 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 (PL = 1/P), so (1) can also be expressed as L/P=α – i.e. that the real demand for the services of money (L/P) is equivalent to a constant α. All Greek letters are exogenous constants.

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

(2) PL = 1

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

Equilibrium in the market for bank liabilities is indicated by the intersection of the supply and demand curves, where L = α.

3.2. The Loanable Funds Market

The demand for credit, on the other hand, is the demand for present consumption against future consumption, the ratio between these being the interest rate. Before continuing, it will be worth saying a few words on the mechanics of credit in order to illuminate the setup of the next steps and distinguish from the traditional setup.

  1. As argued in the previous section, banks can create credit gratuitously. The initial act of credit creation is in most cases simply the exchange of IOUs created ex nihilo on the spot. The bank creates a balance of demand deposits, a present claim to base money, and uses it to buy a claim to future money from the borrower. The borrower may redeem his claims at any time; the bank redeems its claim after the maturity of the loan. This is, in principle, no greater power than any individual citizen has to issue claims on himself. The difference is that the bank must invest in sufficient trust and brand name capital in order for claims on it to circulate as currency. The claim, in other words, must be more or less perfectly credible if it is to substitute for the value upon which it is a claim. If its commitment to a horizontal supply curve is ever doubted, its liabilities must trade at a discount and cease to serve as money.
  2. The balance sheet must at all times be in balance as a matter of accounting: assets must equal liabilities plus equity. This holds as well for the first derivative of both sides; changes in assets must be offset by an equal change in liabilities. When a loan is made, both sides of the balance sheet rise by an equal dollar amount: the liability side by the amount lent, and the asset side by the present value of the borrower’s IOU. Until the borrower begins to spend his money, the loan is nothing more than a balance sheet operation. If the loan fails to be repaid, it impinges on equity. Going forward we stipulate constant equity in order 1) to focus on the pure intertemporal operation without regard to the question of default risk, and 2) to ignore equity entirely if we interpret the model as pertaining to changes in the balance sheet.
  3. Gratuitous credit creation does not mean unconstrained credit creation. The fact that a loan creates claims on the bank to base money means that the bank must take care to actually be able to redeem its liabilities on demand; failure to do so results in some outsize penalty (see (5)). Because the supply of liabilities is perfectly elastic – its price is pegged at $1 – credit creation by an individual bank does not in fact affect the supply of circulating liabilities for more than a short period of time: they are returned to the bank by other banks or at the teller. For this reason, the bank holds reserves of base money. Ordinarily the bank can get by holding a very small fraction of its outstanding liabilities in reserves; the rest it is free to loan out at interest. Just how small a fraction depends on the risk of illiquidity it is willing to bear. If reserves bear no interest, the opportunity cost of holding reserves will be the interest rate at which it might otherwise create loans that draw down those reserves.
Assets Liabilities
Reserves (R) $1,000 Deposits (L) $10,000
Loans (LF) $9,000

Figure 3. An example balance sheet with a reserve ratio (R/L) of 10%. Equity is ignored, but would appear on the liability side in a less stylized example.

The bank’s liabilities may be thought of as (private) banknotes or deposits, though for simplicity the bank will not pay interest on either. 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. As mentioned in the previous section, the supply of loanable funds in the traditional construction slopes upward for two analytically distinct reasons. First – and perhaps most obviously – a higher interest rate allows the bank to attract more depositors by paying interest on deposits. A stronger demand for bank liabilities allows the bank to hold more interest-bearing assets for a given risk preference. This is the main focus of the traditional exposition, which might be incorporated into this analysis by having the demand schedule for liabilities rise with the interest rate. 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. Realistically, therefore, the bank takes in negligible new “savings” in response to the new opportunity.

This inelasticity does not, however, consign the bank to pass up the opportunity. A second reason for the upward slope of the supply curve is that 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 “saving” – 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 saving.

The assumption of zero interest paid on deposits therefore gives our construction of the credit market an upward-sloping supply curve resulting only from the optimizing decisions of the bank on its reserve ratio, leaving consumer decisions strictly exogenous. The model is defined with an additional three equations:

(3) LF = LF(i)

(4) LF = L – R

(5) π = iLF – Q(R/L)

(3) is the demand function for loanable funds, assumed to slope downward in the interest rate. (4), which connects the markets for money and credit, is simply the balance sheet condition rearranged: assets (reserves R + loanable funds LF) equal liabilities (L). (5) is the profit condition for the bank, with Q being expected liquidity costs for a given reserve ratio.12 For a given R, Q will be rising in L at an increasing rate (i.e. QL > 0 and QLL > 0). Maximizing (5) subject to (4) results in the supply curve of loanable funds,

(6) i = QL

Suppose the expected profitability of prospective projects rises – i.e. LF(i) shifts outward. In order to maximize profits, the bank will increase LF and L in order to draw down its reserve ratio and increase QL. Per (4), LF is limited by L, which in turn is determined by (1). If L is vertical in i, therefore, (6) will be drawn such that LF=0 when i=0 (when the opportunity cost of reserves is zero), and LF approaches L asymptotically as i approaches infinity.


Figure 4. 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 L 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 interest on deposits into this model, the dotted line L would slope upward, with the actual supply curve continuing to approach it asymptotically from the origin as the interest rate rises.

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.13 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. The quantity of liabilities as determined in that market is the limit of the bank’s ability to acquire interest-earning assets.

3.3. 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 (3), L 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.

Comparative Statics
Figure 5. 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 LF 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 give it an advantage with an explicit model of the financial sector.

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, 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 2017a), 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. Per Hutt (1939, ch. 3), planned inventories are not “idle” in this sense.
  2. Harwick (2017b) discusses the importance of the distinction.
  3. The fact that there exist time series for aggregates with titles such as “gross private saving” does not by itself suggest the economic meaningfulness of those aggregates, as Barnett (1980) argues for summed monetary aggregates such as M2.
  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 early 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. 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.
  6. 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.
  7. 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 he still speaks inaptly of a “supply of savings”, there is a long Keynesian tradition of treating S=I as an accounting identity (see, e.g., Lindner [2015] for a derivation).
  8. 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
  9. 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])
  10. Or, alternatively, a vertical risk-preference schedule with respect to alternative investments.
  11. 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.
  12. Q is defined as the integral of the left tail of the probability distribution function for reserve losses greater than reserves: Q=p(O-R) φ(O|R/L)dO, where O is the outflow of reserves, φ is the probability density function over O conditional on R/L, and p is the cost of illiquidity for a given shortfall. See White (1999: 57; 1989: 42).
  13. 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, however, we consider only competitive private banks on the background assumption of a non-profit-maximizing central bank.

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BankingMoneyGeorge SelginJames TobinJohn Maynard KeynesLawrence WhitePerry Mehrling

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14 Comments

  • 1

    Peter

    Jul 28, 2016 at 17:31 | Reply

    It is an old story, semantics; are capital and savings funds, or do they refer to valuable production-goods. In order to organize and deploy the latter we need institutions that facilitate the former. Garrison is talking about real savings, the availability of resources to produce valuable goods and services and thus create value.

    • 1.1

      Cameron Harwick

      Jul 28, 2016 at 17:47

      I mostly agree – as you noticed, I’m thinking of this is in the same spirit as your work on capital and Duration. But if “capital” is irreducible to a physical aggregate, the same would seem to be true of “real savings”. If that doesn’t make sense to talk about as an aggregate, is there any sense in which it’s useful to talk about a stock of monetary “saving”, rather than the supply and/or demand of some classes of liabilities?

      “Capital” may or may not be worth replacing with some other term, given that it has the same Ricardian baggage. But any coherent notion of “saving” definitely has clearer and more precise alternatives.

    • 1.2

      Peter

      Jul 28, 2016 at 17:49

      Yes, true. Aggregates are a big problem. And Roger used them in his model for pedagogic purposes only. You are correct to say that there is a price to be paid. We now have to point out that aggregate non-consumption as a fund may be a necessary condition for economic growth, but it is in no way sufficient. For that one needs successful entrepreneurship at the micro level.

    • 1.3

      Cameron Harwick

      Jul 28, 2016 at 17:56

      Part of my discomfort too is that I’m not even sure what something like “aggregate non-consumption” means. Any economic good is more or less durable, and provides a shorter or longer stream of services. You *could* operationalize it as the holding of money balances (or something else), but then that has a rather different economic significance.

      You could interpret it as something like “don’t be wasteful” – but that’s more of an efficiency/inefficiency question than a saving/consumption question.

      Hm, there’s a thought – I wonder if part of the problem is that those two axes are being mixed up.

    • 1.4

      Peter

      Jul 28, 2016 at 18:26

      No, there is an objective measure of non-consumption. It is a monetary aggregate, it is a value. As Mises emphasized we use money to enable calculation and calibration. In an economy with capital markets, loanable funds facilitate the acquisition of productive resources by entrepreneurs. If people do not save, this cannot happen.

      And, another matter, it turns out that the only sensible way you can talk about time in investment is in terms of its duration in value terms. Physical durability has nothing directly to do with it. Savings allows for the ‘extending’ of production in the sense that it allows for projects for which you might have to wait longer on average to earn a dollar.

    • 1.5

      Cameron Harwick

      Jul 28, 2016 at 18:52

      I interpret what you said as: people save productive resources, and loanable funds enable entrepreneurs to buy them. Is that right? If so, I’m not sure why the emphasis is on “saving” those resources rather than “producing” them. If not, what’s the connection between monetary saving and the accumulation of productive resources? (Or does saving just assist in the acquisition of those resources?)

      What is the monetary measure of non-consumption – the entire money stock, the portion held as bank liabilities, or something else? In a monetary economy, I’m not sure why any of these should necessarily be the mirror image of consumption.

    • 1.6

      Peter

      Jul 28, 2016 at 21:41

      I don’t think that is a good interpretation of what I said. People save money – an option to consume an unspecified thing in the future. That enables other people to invest in resources – by borrowing the money.

      As long as things are valued in money they can be aggregated. In order for there to be loanable funds there has to be saving in the sense that people save – in money – what they do not consume. Do we really disagree about anything?

    • 1.7

      Cameron Harwick

      Jul 28, 2016 at 22:21

      Not sure yet if/how we disagree – I think it’s terminological now, but we’re getting close in any case. The problem I have with your formulation there is that entrepreneurs don’t borrow saved money; they borrow *new* money, created ex nihilo on the bank’s balance sheet. The demand for that bank’s liabilities (saving?) limits how much of that the bank can safely do, but even so saving in that sense is not the same thing as the quantity of loanable funds.

      See if this a more agreeable interpretation:

      1. Saving consists in money balances held rather than spent
      2. Saving has nothing to do with the *accumulation* of productive resources, but facilitates the *transfer* of those resources to entrepreneurs

      If this is the case, is there a difference between saving and the demand for money?

    • 1.8

      Peter

      Jul 28, 2016 at 22:42

      Whoa. I think this is hugely confusing. You are mixing two things. Saving and money creation.

      Saving is not the same thing as money balances. Putting money in a pension fund, in a mutual fund, buying and insurance premium, etc. all increase the amount of loanable funds. Financial intermediation is the key. It is a crucial part of the capital market. It is the essence of capitalism. It is only in a system with capital markets that the act of saving (broadly understood) can be separated from the act of investment, thus reaping the huge rewards of specialization in production. But investment cannot occur without saving.

      As for money creation if I put money in a commercial bank, does that increase loanable funds? Yes. Presumably banks decide on their loans on the basis of the average amount of deposits with them. For example using my commercial bank I do not actually save anything. By the end of the month my balance is zero. So the bank cannot loan out any of my money. But, presuming that the bank has it has a positive overall average balance from depositors, it will loan out money based on its expectations of withdrawals, keeping on hand a sufficient amount of reserves to meet withdrawals. Does then the act of depositing lead to the creation of money, so that entrepreneurs will be borrowing “new” money. Not unless my or anyone’s deposit is a net addition to the system. If I receive the money I deposit from someone else’s payment out of their account there is no net addition to reserves and no new money can be created. Thus, unless the Fed is injecting reserves into the system, no “new” money is created and my savings in any financial intermediary frees resources for entrepreneurs. If on the other hand it is the “new” money, from newly injected reserves, that is borrowed, then only the illusion of savings occurs and this precipitates a credit-induced cycle.

    • 1.9

      Cameron Harwick

      Jul 28, 2016 at 23:35

      Good point about investment funds actually loaning out literal savings. I’ll have to think about what that difference entails – I know Europe depends more on banks and the US on financial markets for investment, but my first-face intuition is that the process ought to be basically the same in its essentials as far as it involves money (or near-money) creation. After all, a corporation issuing shares is pretty much the same sort of balance sheet operation (though from the borrower’s perspective) as a bank issuing liabilities to make a loan.

  • 2

    George Selgin

    Aug 25, 2016 at 20:56 | Reply

    Cameron, to the extent that I can follow your argument, and especially the meaning you attach to the notion of “gratuitous” credit creation, I’m led to conclude that you have read my discussion of credit creation in TFB rather carelessly. In it I very carefully distinguish between “transfer” and “created” credit, noting that both are in fact “money” based, while only the last involves forced savings. Yet so far as I can tell, the distinction, which I regard as fundamental, is one you don’t recognize. (Peter Lewin, on the other had, seems to recognize and make use of a similar distinction in his remarks.)

    I also have grave doubts about the value of such grandiose exercises in economic revisionism as yours, which appear to have become even more de rigueur than ever among younger Austrian PhD holders and candidates, and their more sympathetic fellow-travelers. With so many working to deny the meaningfulness of the economics being done by others, who, prey tell, is planning to supply useful alternatives? So far as I can tell, viewing things at ground level at Cato, the answer is: no one at all!

    • 2.1

      Cameron Harwick

      Aug 25, 2016 at 21:41

      Hm, well, I did reread your section on transfer credit and created credit in TFB right before writing this. If I have been careless in doing so, I think it would help to know in practice how one would look at a given bank’s (or economy’s?) balance sheet and distinguish between the two.

      My impression was that there are two things necessary to make the distinction operational: 1) the reduction of abstinence to a single monetary value, and 2) a constant risk preference for the bank, as I argued above. I take your argument to be that the demand for bank liabilities serves purpose (1) – and though I might not find it helpful to identify that with “savings”, that’s just semantic. As for (2) – while it’s true, as you argue in TFB, that the demand for bank liabilities limits the bank’s ability to create credit, without a constant risk preference, I don’t see how there could be an objectively “correct” quantity of credit above which is recognizably created rather than transfer.

      If you do read this as an exercise in Austrian revisionism, I hope you read it in the same spirit of revisions to the Austrian canon such as your integration of monetary disequilibrium theory, or Prof. Lewin’s integration of the aftermath of the Cambridge capital controversy – both of which were extremely valuable (even grandiose) additions! My hope is that, by doing theory with an eye to making concepts both economically meaningful and practically operational, putting meaningful alternatives into practice will be more or less straightforward. From my own view, this is precisely what many of the younger Austrian PhD holders and candidates are working on.

  • 3

    Lorenzo from Oz

    Nov 02, 2017 at 1:17 | Reply

    I was particularly taken by your discussion of risk and time preference, as I have not been able to see what the latter did that could not be covered by the former.

    Have you read Tobin’s article on Commercial Banks as “Creators” of Money? It would seem to be very germane to your argument.
    http://cowles.yale.edu/sites/default/files/files/pub/d01/d0159.pdf

    • 3.1

      Cameron Harwick

      Nov 02, 2017 at 18:29

      Thanks! I’ll check out the Tobin paper. Someone recently recommended a paper by Leland Yeager to me which responds (not very convincingly, I think) to this Tobin piece, so it’ll be good to read Tobin’s full argument too.

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