From: Jens Reich, Seigniorage: On the Revenue from the Creation of Money (New York: Springer International Publishing, 2017), pp. 148, $109.99 (hardcover). ISBN: 9783319631233
DOI 10.1007/978-3-319-63124-0_5
Chapter 5
Seigniorage from Credit Currency
The purpose of this chapter is to demonstrate that the return from seigniorage and the economic laws governing the latter depend on the institutional currency supply framework. To do so, the modern framework for a fiat currency as presented in Chap. 3 was transferred to a commodity currency in Chap. 4. Now the modern framework is applied to a credit currency. This allows a comparison to be made between the economic laws governing the return from seigniorage and its optimality across different currency forms.
In a credit currency framework, the responsible authority, usually a public central bank, determines interest rates at which the currency can be borrowed and maintains these rates by accommodating the corresponding demand. An increasing number of economists have put forward analyses assuming a refinancing central bank. There are early contributors, like Wicksell (1898 or 1922), Keynes in his Treatise (Keynes 1930 [1971]), Hahn (1930), Hawtrey (1962), Davidson (1972), Black (1987), or Moore (1991). Recently many more contributions around this topic have been made. A (not always homogeneous) shift in assumptions or simply the assumption of a credit currency can be found in the work of New Keynesians (Woodford 2003), Post-Keynesians (Arestis and Sawyer 2008; Lavoie and Godley 2012), other economists (see Binswanger 2006; Emunds 2000; Gebauer 2004; Nautz 2000), and also central banks (Bank of Canada 2010; Bundesbank 2010, 2017; European Central Bank 2011). Surprisingly, almost all of these authors either omit the issue of seigniorage and so provide no analysis of it or revert to the standard assumption of a fiat currency.
Hence, it seems to be true what Keynes argued almost a century ago:
But although my field of study is one which is being lectured upon in every university in the world, there exists, extraordinarily enough, no printed treatise in any language—so far as I am aware—which deals systematically and thoroughly with the theory and facts of representative money [i.e. credit currency—JR] [1] as it exists in the modern world. (Keynes 1930, p. Xviii)
In contrast to a fiat currency, seigniorage stems from interest payments made by those demanding credit currency from the monetary authority (see, for instance, Deutsche Bundesbank 2010, p. 70). The monetary authorities supplying the currency receive the monetary seigniorage and, after allowing for costs, apply the net revenue, the fiscal seigniorage, to run the monetary system—hence to the government (the treasury). This is one of the tasks of this chapter: to transfer the contemporary framework to a credit currency (see Sect. 1), study the resulting laws governing the return from seigniorage (see Sect. 2), and finally consider the optimality considerations of cost-covering seigniorage (see Sect. 3). Hence, the chapter repeats the analysis carried out in Chaps. 3 and 4 but here assuming a credit currency.
5.1 The Framework
The purpose of this chapter is to extend the framework described in Chap. 3 to a credit currency regime. For a credit currency, the supply of currency depends on the interest rates which the central bank both wishes to sustain and is able to. Currency demand is, as above, assumed to depend positively on prices and negatively on the cost of acquiring and hoarding currency: the established interest rate in the money market, the currency, or the money rate of interest (i). The higher the central bank rate, the higher the cost of borrowing and the higher the opportunity cost of liquidity.
Usually the central bank distinguishes a main (iCB) and a marginal refinancing rate (iCB ). The marginal refinancing rate is usually a markup on the main refinancing rate. At this rate, central banks provide in principle unlimited amounts of currency (against security). For simplicity, the main and marginal refinancing rate may be referred to as “the central bank rate.” Positive balances on central banks’ accounts are usually paid a deposit rate close to the main refinancing rate for balances due to minimum reserve requirements and a varying deposit facility (iCB+) for balances beyond the minimum reserves. By controlling the central bank rate and the deposit rate, the central bank may more or less precisely determine the currency rate of interest. Put the other way around and slightly simplified, the supply of credit currency follows endogenously from the currency rate target pursued by the central bank [2]:
Fig. 5.1 Simplified supply and demand for a credit currency (Illustration based on this research)
Depending on the income from interest payments, the government can finance purchases of goods (AGp) and services (w‘G). The central bank supplies the currency (B) in the form of credit to the public and effectively charges the currency rate of interest. Hence, interest income depends on the currency rates of interest charged times the issued currency:
The value of a unit of currency is consequently determined by Eqs. (5.1) and (5.2), which can be written as:
As above, a figure can be drawn linking currency demand (B), prices (p), and the cost of holding the currency until the end of a certain period ((1+iB)p). This interdependence can be reduced to two dimensions. The simplified real supply of currency is a horizontal line given by the central bank lending rate, and real demand depends negatively on the currency rate of interest (Fig. 5.1).
In a less simplified version, the fact that the central bank charges several rates and also offers deposits should be taken into account. Interest payments on the deposits (iCB+) have to be deducted from the seigniorage revenue. The supply of credit currency is managed by controlling the currency rate of interest through the central bank’s lending and deposit rates. A more realistic representation is therefore given in Fig. 5.2.
The central bank deposit rate constitutes the lower and the central bank lending rate the upper bound of the currency rate of interest. Depending on central bank policy and alternative currency supplies, the currency rate of interest may vary between these rates. If there are no alternative currency supplies, the currency rate of interest will be close to the central bank’s lending rate. It gets even more complicated if the central bank charges different rates of interest on different forms of deposits, as is done by the ECB. (The latter discriminates between deposits for minimum reserves and for excess reserves.) The main issue with respect to seigniorage is the minimum reserve requirement. Under the assumptions made above (i.e., all currency is supplied as credit and all credit is renewed every period, the supply of currency is determined by the volume of loans granted by the central bank), positive balances may arise, but they are unlikely. A private entity would have to borrow from the central bank, and another entity which obtains the currency simply deposits this currency with the central bank. This is—in a pure credit currency framework—a net gain for the central bank. Interest payments on minimum reserve requirements increase the demand for currency and may, for a spread between the effective lending and deposit rate (on minimum reserves), increase seigniorage revenue. It will be assumed, as is the case in the EMU, that reserve requirements are not costly and hence can be neglected for the study of seigniorage at this point.
5.2 Seigniorage from Supplying a Credit Currency
Based on Eq. (5.2) with currency as numéraire ( pB ¼ 1), we can rewrite the seigniorage as
The monetary seigniorage for a credit currency (SK) is given as the interest payments on the stock of credit granted, the “real” amount of seigniorage by the interest on the supplied credit from the central bank divided by prices:
At first glance, this appears similar to the opportunity cost approach for a fiat currency. Even though the approaches might look similar regarding the formula, the institutional underpinnings are quite different. In the former case of a fiat currency, the interest rate is endogenous and the currency supply is exogenous. In the case of a credit currency, the central bank controls the central bank rate and the demand for currency is endogenous. Another difference is the choice of the interest rate. The rate of interest on government bonds used in the opportunity cost approach is replaced by the rate of interest charged by the central bank. The former ambiguity of estimating the “correct” rate of interest is avoided.
If currency demand is introduced to Eq. (5.5) in the same manner as above for a fiat and commodity currency, one gets
As with the negative relationship between currency demand and currency growth for the fiat currency, and the negative relationship between currency demand and the minting tax, a negative relationship between currency demand and the central bank rate is assumed. The first-order condition for the maximization of the seigniorage as a share of national income with respect to the central bank rate is similar to the calculations above:
The results are similar to those for a fiat and a commodity currency. The revenue from seigniorage is maximized for a currency rate of interest such that the elasticity with respect to the rate is minus one, which is the usual result for a monopolist. This holds true only if the interest rate has no effect on trade. If trade is influenced by the central bank rate, the revenue-maximizing condition is altered. The revenue-maximizing central bank rate can be obtained by rewriting Eq. (5.7):
For a Cagan-type demand function, the revenue-maximizing central bank rate depends solely on a constant and its impact on national income:
These results parallel the findings for the institutional monetary systems discussed above. The government faces a trade-off. The higher the central bank rate, the higher the return per unit of currency lent, but the lower the demand for currency. This can of course be represented graphically. Here the drawn curve represents the nominal return from seigniorage (see Fig. 5.3).
As before, a dishonest return exists. In a credit currency regime, a government may borrow directly from the central bank. A loan from the central bank which is actually going to be repaid does not necessarily increase seigniorage, because the additional interest payments to the central bank are a loss to the treasury. The additional supply of currency via public spending might reduce the public’s demand for borrowing currency. Thus, the government may replace some of the central bank’s borrowers. These borrowers might be supplied with currency which was borrowed by the government and which is consequently for the public a non-borrowed currency. The government pays interest to the central bank instead of private borrowers. By so doing, the government can reduce seigniorage by substituting for private borrowers of currency. This effect is changed if the government is not willing to repay the loans granted by the central bank. If it defaults on loans from the central bank, the government makes a gain and a loss from its operations. The avoided repayment of debt is a gain to the treasury and might be represented as dishonest seigniorage. The government issues credit currency and escapes from its repayment. (?) Such gains come with a loss of seigniorage to the central bank. For a given currency demand at a certain rate of interest, the government supplies non-borrowed reserves by defaulting on its debt owned by the central bank (?) and therefore reduces the amount of currency to be borrowed from the central bank—for constant currency demand (dotted line).
For a default exceeding the central bank’s revenue from seigniorage, the central bank’s equity reserves (which might have been accumulated in the past) are reduced. If there are no equity reserves, or the equity is depleted, the government has to raise funds by ordinary taxation and inject equity into the central bank to avoid its default (?). Alternatively, the central bank may offer to pay interest on excess reserves to sustain the central bank rate target. In this case, the government borrows indirectly from the public and the central bank services the interest payments.
However, the government is not forced to do so. A defaulting central bank is quite similar to a government printing currency on its own behalf. Where the central bank does not or cannot absorb the additional currency supplied, it loses control of the currency rate of interest. In other words, non-borrowed currency dominates the system. The government controls the stock of currency exogenously, and the currency rate of interest is determined by the market. In the latter case, the monetary system is altered. The currency supply is exogenously determined by government spending, and the economy therefore drifts into a fiat currency system.
This applies not only to a defaulting government but to every borrower. If currency is borrowed and spent and the debt becomes irredeemable, then the economy is supplied with non-borrowed reserves. This supply of non-borrowed reserves slowly pushes the credit currency regime toward a fiat currency regime. If the central bank takes measures to absorb the additional supply of non-borrowed reserves, it might require the central bank to run a deficit. In this case, the government has to cofinance the subsidies granted by the central bank to its creditors to whom the low central bank rate is granted. It was mentioned above that Ricardo and Wicksell objected to the possibility of permanently lowering the rate of interest below its natural level. For a commodity and a fiat currency regime, this might be true. In a credit currency regime, the government controls the central bank rate via the central bank. If the government is willing and able to subsidize a negative seigniorage, it is capable of lowering the central bank rate without creating inflation. This effect belongs to mixed monetary systems, i.e., a mixture of the ideal types analyzed so far. For private and government defaults, it will be dealt with in Sect. 6.2.
There is a second exception regarding a default in a credit currency regime, when the default is not limited to the government. In a credit currency system, there is the additional possibility, not so far addressed in the literature, of a default on central bank loans by private lenders. This issue will be addressed in Chap. 7.
5.3 Optimal Seigniorage for a Credit Currency
In this section, the optimality consideration of cost-covering seigniorage is transferred to a credit currency regime. It was already mentioned above that mainstream economists do not assume a credit currency, and the few economists who do so do not focus either on seigniorage or its optimal height. There is, however, an ongoing and unsettled debate regarding the “optimal” inflation target of central bank policy.
In this debate, the optimal inflation target is derived from cost-benefit analyses.
The difficulty in adding money to equilibrium models contributes to the heterogeneity in the assumptions and results of the model (see Sect. 2.3). Even within the modern core approach to macroeconomics, which usually adds in an ad hoc fashion a perfectly homogeneous and abstract aggregate of money to the model, there is no agreement on how money should be modeled. In neoclassical general equilibrium models, like contemporary dynamic stochastic general equilibrium (DSGE) models, money is “added” by postulating a demand function and an arbitrary supply of it by the government, for which money, by assumption, has a positive price (see Stiglitz and Greenwald 2003, pp. 3–4).
As a result, there is no generally accepted cost-benefit analysis of seigniorage.
Stephanie Schmitt-Grohe’s and Martin Uribe’s contribution to the third volume of the Handbook of Monetary Economics (Schmitt-Grohe and Uribe 2011) provides a good example of this. Even though they limit their analysis to a specific set of assumptions and models, they are forced to run a number of analyses. The assumptions they make lead to an outcome in which the results of these variations do not depart substantially from each other (see Schmitt-Grohe and Uribe 2011, p. 715).
Their results follow from the assumptions they have made in the first place. Their results, the costs of inflation, the benefits of increasing government debt, and the impact of currency growth on national trade, all of these intermediate results depend on the chosen framework and the way in which money is introduced into it.
Many economists stick closely to the original Friedman rule. They derive the Friedman rule or very low inflation targets, usually close to or below zero. An example of this line of argument can be found in Schmitt-Grohe and Uribe (2011).
As a result, they perceive a gap between the actual inflation targets of a central bank and the theoretically optimal inflation target. Inflation targets are all strictly positive. The lowest are around 2%. Many countries define a range somewhere between 2% and 8%. Only a few countries have (temporarily) departed from this range, aiming at higher rates, like Argentina, Belarus, Malawi, and Ukraine in 2016 (see Siklos 2008; Central Bank News 2016) (Table 5.1).
Central bankers place emphasis on arguments which yield higher targets. They highlight the costs of maintaining the currency system: “resource costs, associated functions, competitiveness, inventory costs, volume of regular (liquidity) traders, extent of exposure to informed insiders and risk of being caught by an unobservable shift in underlying value” (Goodhart 1989, p. 10). Beyond that, there are further issues.
First, there is seigniorage as a form of government revenue. Second, it is possible that the long-run Phillips curve is non-vertical at very low inflation rates. Third, there is the difficulty for monetary policy posed by a lower bound of zero on the nominal interest rate. Fourth, it is possible that measured inflation may overstate true inflation (Issing 2001, p. 190).
The third point has received some attention in the latest publications, which identify a trade-off between the inflation objective and macroeconomic stability (see Coenen et al. 2004; Reifschneider and Williams 2000). And even though central bankers like Bernanke have doubted that estimates of the optimal inflation target can be more than “a rough approximation,” such an estimate “likewise seems crucial to making good policy in the next few years” (see Bernanke 2004, p. 166).
The gap between inflation targets and the Friedman rule persists up until the present, leading central bankers having reaffirmed their target (see Weidman 2015; Yellen 2015).
Other economists have valued the benefit higher and the cost of inflation lower.
Krugman (1997), for instance, remarks, “one of the dirty little secrets of economic analysis is that even though inflation is universally regarded as a terrible scourge, efforts to measure its costs come up with embarrassingly small numbers.”
Blanchard, for instance, derived an optimal 4% target (Blanchard et al. 2010), and Rogoff even proposed up to 6% (Rogoff 2013).
From the perspective taken here, any discussion of an optimal rate of inflation should be seen in the context of an optimal seigniorage. Instead of a cost-benefit analysis, the cost-covering norm of optimal seigniorage is employed here (for the reasons, see in particular Sect. 2.3). The mutuality in the approaches mentioned is the assumption of a fiat currency. Hence, even though the existence of an interest rate or inflation targeting central bank is admitted, the assumption of a (paper) currency which is printed and spent is maintained. However, the supply of currency by means of crediting private entities, that is, the institutional organization of the credit currency supply, should explicitly be addressed.
5.3.1 Cost-Optimal Seigniorage for a Credit Currency
By analogy with Eq. (3.29), an optimal currency rate of interest can be derived if we can attribute to production and maintenance costs the direct costs for producing notes, replacing worn-out notes, and fixed costs for wages and salaries of central bank employees (ΆMG) :
This result yields an optimal interest rate, not an optimal rate of inflation. To derive an optimal rate of inflation, one has to make use of the Fisher equation and replace the currency rate of interest with the sum of the rate of inflation and the real rate of interest. Like Eq. (3.25), one gets
As a result, a targeted rate of inflation, e.g., like that of the European Central Bank of 2%, could be justified by referring to the costs of running and maintaining the currency system. In other words, a particular target rate can be justified on the basis of a cost-covering seigniorage, if the cost of producing and maintaining the currency relative to liquidity demand and trade exceeds the real interest rate by the targeted rate of inflation. If the cost of printing and maintaining the currency system is neglected, one is back to the Friedman rule. Hence, this result is not in contrast to the Friedman rule.
This is only part of the story. In another macroeconomic context, Stiglitz and Greenwald highlighted credit risk or in other words the probability of bankruptcy as an omitted variable. Reflecting on macroeconomics as taught before the publication of their book, they note:
There was a single, crucial variable that was omitted from the analysis: the probability of bankruptcy, the variable which we have argued, is at the center of all monetary analysis. If everyone always repaid their loans, then there would be little role for financial institutions.
Credit would be a trivial matter. It was understandable, perhaps, for economists who had been trained in macro-economics a quarter of a century ago to have failed to pay attention to that variable. Even today, the term ‘bankruptcy’ does not appear in the indices of most macro-economics textbooks. Yet, for policy makers the mistake is unforgivable. (Stiglitz and Greenwald 2003, p. 265)
Stiglitz and Greenwald do not apply this insight to the supply of a credit currency, but what is obvious can be demonstrated. The approach to an optimal (cost-covering) seigniorage depends crucially on the accounted costs of production, and this includes credit risk. For a theoretical approach, it is not necessary to determine the costs empirically but to ensure that all economically relevant categories of such costs are included. I argue here that attributing the cost of production and maintenance to the direct costs of issuing a unit of currency and the fixed costs of the monetary system misses an important category of costs arising for a credit currency: the credit risk and the losses from a default—in other words, expected losses. [3]
There is no reason why the cost of production of a “unit of currency,” for example, the cost of printing a paper note, should differ for a credit and fiat currency regime. Whether the fixed costs of maintaining the credit currency may or may not deviate from that of a fiat currency is debatable, but this is not crucial to the understanding of monetary systems. However, the lending operations of every bank are connected to risks, in particular default risk: the risk that a borrower goes bankrupt. Whatever the quality of the securities is, every private bank demands interest, partly to cover the risks incurred and partly to cover other costs. The same is true for central banks and central bank rates. Central banks face the risk (?) that their debtors will default, and hence they may be confronted with losses from their credit currency supply (Φ(B)). Indeed, central banks demand good security. Only the loss given default, not the risk of default, can be reduced by the central bank demanding good security prior to issuing currency. (?) As a result, the risk of default and the loss given default, that is, expected losses, have to be taken into account in the calculation of optimal seigniorage.
If the expected loss on a unit of currency is constant over all issued currency units, then the first derivative of the “risk function,” the marginal risk, is a constant:
This assumes that the expected loss does not depend on the size of the stock of issued currency. In a simplified example, where the central bank lends a certain sum to the public and the default probability on these loans times the loss in the event of default is 10% per unit of currency per annum of credit granted, and then the central bank would be required to demand a central bank rate of at least 10%. If the central bank demands a lower rate, it will, in case of an average default of 10%, run a deficit which the government has to cover by other means (for instance, through additional taxes).(?)
The optimal seigniorage has to be such that it permits the cost of production, maintenance cost, and expected losses to be covered. The same applies to the optimal bank rate and hence the established currency rate of interest. As a result, Eq. (5.11) becomes
As a result, Friedman’s claim of a zero interest rate does not apply for a credit currency, even if cost of production and maintenance costs ΆGM are neglected. The central bank rate charged has to cover expected losses. The cost-optimal seigniorage rule has therefore to be adapted for a credit currency even if other costs are—by analogy with a fiat currency—neglected. For a fiat currency, the interest rate on the fiat currency (iB*Chic) is, following the opportunity-cost-optimal seigniorage as expressed in Eq. (3.25), an interest rate of zero. For the credit currency, optimality requires a central bank rate (iB* ) which exceeds this rate by a markup to cover expected losses:
Even if all other costs are neglected, a positive central bank rate target is required by the credit currency version of the so-called Friedman rule. Depending on expected losses and the real interest rate, even a positive inflation target can be justified following the simple Fisher equation:
In case of very high expected losses, the optimal central bank rate might even be found on the decreasing section of the seigniorage revenue curve (Fig. 5.4).
In general it may be said that, with a credit currency, the targeted rate of inflation and the currency rate of interest have to be higher than in a fiat currency in order to cover expected losses from the supply of credit currency.
5.3.2 Systemic Risk, External Effects, and Central Bank Policy
The result of the previous subsection demonstrates that a central bank which targets a currency rate of zero, or at least below the rate necessary to cover expected losses, implicitly subsidizes either the banking industry or its customers. The bank’s finance costs are lower than would be necessary to cover the related costs of the credit currency supply. In other words, the private cost of acquiring currency differs from the social cost if the central bank violates cost-optimal seigniorage.
The central bank rate drives a wedge between the private marginal “production cost” of currency and the interest rate actually charged. A currency rate target below the optimal rate violates the optimum of cost-covering seigniorage and hence leaves a wedge between the private and the social cost of the production of currency. This creates by definition an external effect.
The biggest difference of such a violation, compared to the other monetary systems, is that it can be easily overlooked. Risks which might materialize in the future pile up throughout the system. The systematic mispricing of issued credit currency creates a systemic risk. This systemic risk is created by an external effect, cheap credit. But before the first lenders default, revenue from seigniorage might even appear to increase. If seigniorage is not cost-optimal in a credit currency regime, the government provides an indirect or hidden subsidy to the financial industry and its debtors. This subsidy is partly realized by the low cost of finance, owed to the low central bank rate. The most significant impact of this subsidy becomes apparent at the moment of crisis. If some or several borrowers default or are close to default, the government has to make a choice. If private banks default, the central bank may run a deficit. This deficit has to be covered from retained profits or tax payments. On the other hand, the government may try to avoid a default by using revenue from other taxes to support the “real” or “financial” economy. In both cases, the government cannot ignore the fact that the gap between private and social costs is not borne by those who benefited from the low central bank rate. Hence, the social costs remain uncovered and redistribution is instigated.
This external effect differs slightly from the one usually presented in textbooks.
One example may be enough to highlight the difference. In the usual presentation, an external effect is caused by direct and continuous damage to the environment, for instance, the atmospheric pollution caused by cars. Such external effects are defined here as direct external effects; they are directly connected to the use of the resource (air). One can see, measure, and smell the pollution caused by every single car while it is being driven. The external effect in the credit currency regime is not directly and continuously observable and is therefore rather similar to that of nuclear plants. Nuclear plants supply cheap electricity so long as they do not have to be insured against the full risk of a nuclear catastrophe. In Germany, for example, owners of nuclear plants benefit from a cap that limits their insurance premium in case of a nuclear worst case scenario. If the true costs exceed this cap, which is set at 500 million euros, there is an external effect. The owners of nuclear plants receive excess profits, or the clients benefit from cheap electricity. In either case, the external effect caused is not directly observable. With cars it is clear that those who do not drive cars share the burden of the air pollution without having the benefit of cheap car transportation. The burden shouldered by those not using cheap nuclear electricity appears invisible as long as there is no nuclear worst case scenario. Until then the burden shared is not obvious. Such external effects, which cannot be seen, smelt, or even precisely estimated until they arise, will be called indirect external effects. Ignoring this indirect external effect, it seems that requiring full insurance for the event of a nuclear worst case scenario only increases costs and causes disadvantages. Nonetheless, little attention is paid to the fact that by covering the external effect, the true costs of nuclear electricity production are paid by those using nuclear electricity. The same is true for credit currency regimes.
Central bank rates below the optimal rate seem to be a cost-free benefit for economic development. Requiring that the central bank raise its rate appears solely to be “costly.” This ignores the fact that a central bank rate set below its cost-covering level creates an external effect. It subsidizes the banks receiving cheap credit or their clients. Until the advent of the financial worst-case scenario for the economy, this indirect external effect is not apparent. Systemic risk is slowly piled up and the true costs are not realized until the bubble bursts. As with examples drawn from environmental economics, a low central bank rate brings about the overuse of resources: with the case of the nuclear plant, an overuse of electricity, and, in the case of the credit currency system, an overuse of credit. Risk mediation becomes risk creation.
In the tradition of welfare theory following Pigou and Ramsey, taxes should be applied to bring about such external effects. It was important to Ramsey (1927) that external costs are incorporated into private prices. This should be done without altering usual patterns of consumption, an idea later taken up by Phelps (1973). By the same reasoning, the cost-covering seigniorage for a credit currency should cover expected losses. Under the simple assumptions made here, the wedge or the “optimal tax” (seigniorage) covering direct and the indirect costs can easily be determined. If the expected loss is given by a constant (φ), the Friedman rule demands a minimum central bank rate at this level.
This situation can be outlined in a real supply and demand diagram for currency, similar to Fig. 5.5.
The real supply of currency is now a horizontal line. The central bank offers as much currency as demanded (against good collateral) to establish the desired currency rate. Following the Friedman rule for a fiat currency, the central bank would be required to maintain a zero currency rate, solely covering the direct cost of issuing currency, which has been assumed to be negligible, (BFS/p).
An optimal seigniorage requires avoiding negative seigniorage and coverage of the direct and the indirect costs of providing currency. Regarding the central bank rate, this situation requires a central bank rate which covers the expected losses of the central bank’s borrowers. The figure shows this as a red horizontal line.
This line is the supply curve assumed to cover the direct cost plus the related cost from the risk of default, (BKS/p). A cost-optimal seigniorage for a credit currency suggests a higher “price” for currency and a lower amount of real currency. (BK*/p), the amount of optimal currency supplied in a credit currency framework, is lower than the amount which would follow from the fiat currency Friedman rule, (BF*/p).
5.4 Summary
It was demonstrated in this chapter that the contemporary approach to seigniorage can be transferred to a credit currency. The framework developed bears some similarity to the opportunity cost approach, but it is quite different in its underlying theory. In the opportunity cost approach, seigniorage is estimated for a fiat currency by the opportunity cost of avoiding government debt. In the framework presented above, seigniorage derives from interest payments on borrowed credit currency.
By applying this framework to a credit currency, it was shown that a government faces a trade-off similar to that in debasing a commodity currency. Changes in central bank rates are costly to those who demanded currency in the past and who have to extend their credit at the rising currency rate of interest. The government increases its return per unit of currency, but the overall demand for currency is expected to fall for rising interest rates. This shows the direct link between a central bank’s monetary policy and seigniorage policy. These are indistinguishably intertwined.
Besides the honest return, it was shown that a government may obtain dishonest seigniorage by borrowing from its central bank and defaulting on these credits. This constitutes a supply of non-borrowed reserves, i.e., fiat currency. This procedure presents a gradual departure from a credit currency, and it will therefore be dealt with in Sect. 6.2.
The most remarkable results have been obtained for the analysis of an optimal seigniorage from a credit currency. First and foremost, it can be shown that the claims usually made about “optimal” rates of inflation are compatible with the theory of optimal seigniorage (see Sect. 3 but also Sect. 3.3). Optimal inflation targets are mostly discussed in terms of optimizing the costs and benefits of inflation. It is demonstrated that even in a purely cost-covering interpretation of optimality, a positive interest rate and rate of inflation follow if costs of production are considered. This result is identical to that of Chap. 3.
Second, a peculiarity of credit currency is highlighted. There are specific forms of cost—expected losses, which arise in the process of issuing credit currency.
These costs do not arise from the supply of fiat currency as there is no risk connected to its supply. In the supply of credit currency, however, expected losses have to be taken into account. They have to be considered in the applied seigniorage policy and optimal (in the sense of cost-covering) seigniorage and hence monetary policy. To be cost-covering the targeted currency rates have to cover expected losses from central banks’ lending operations. Hence, while the supply of fiat currency is judged “one of the few legitimate ‘free lunches’ economics has discovered in 200 years of trying” (Lucas 1987), this certainly does not apply to the supply of credit currency.
According to these findings, neither the positive inflation target of central banks nor the positive central bank rate has to concern those who adhere to the principle of a cost-covering seigniorage. Depending on central bank authorities’ judgment of expected losses (and other costs of production), the optimal central bank rate and the optimal rate of inflation are positive and they may exceed the real rate of interest. This resolves a puzzle in economic textbooks. It allows to reconcile the practical norms of central banks with the suggested optimal interest and inflation targeted by economic theory.
Third, the cost-covering seigniorage policy is in line with and suggested by welfare theory. For targeted currency rates below those optimal in the sense of cost-covering the private cost of production of currency are below the social cost of production. In other words, if the central bank charges a bank rate below the optimal rate, it creates an external effect and thereby subsidizes its debtors. In line with the usual results in welfare theory, an external effect creates a mispricing. In this case, interest rates are “too low,” that is, they do not cover the connected cost. Charged interest rates do not allow covering expected losses. In other words, by lowering the central bank rates below their optimum, the central bank creates an external effect and a mispricing which induces a systematic and hence systemic mispricing of credit risks. This mispricing of risks leads to the buildup of mispriced risks and hence creates the threat of financial crisis. From this perspective, the normative goal of a cost-covering seigniorage can be regarded as a result of general welfare theory.
Notes:
1 Keynes uses the term representative money where here the term credit currency is used. The bank money may represent no longer a private debt, as in the above definition, but a debt owing by the State. [. . .] A particular kind of bank money is then transferred into money proper—a species of money proper which we may call representative money (Keynes 1930, p. 5).
2 As a simplification, the currency rate is taken as the return to the central bank, even though the central bank may effectively charge different, higher rates, such as its main and marginal refinancing rate.
3 Expected losses are the product of the probability of default and the loss given default.
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