29

Manfred f.M. Neumann

Manfred J. M. Neumann, a professor of economics at theUniversity of Bonn, Germany was a visiting scholar at theFederal Reserve Bank of St. Louis. Courtenay C. Stone mademany helpful comments on an earlier draft. Lora Holman andRichard 11 Jako provided research assistance.

TI1’1JWI.ONEY IS CERTAINLY one of the greatestinventions of mankind. As Brunner and Meltzer(1971) have noted, its vast social productivityarises from the enormous reduction in transac-tions and information costs that it provides byserving as a standardized medium of exchange.’Of course, these benefits, like those of any othergood or service, are not provided at zero cost.The revenue received from producing andmaintaining a nation’s money stock covers itsproduction costs and, perhaps) some profit aswell for its producers.

In monetary economics, the revenue frommoney creation is called “seigniorage.” Unfor-tunately, this term has been subject to a varietyof interpretations in the literature. After review-ing several traditional definitions, this article de-velops a new seigniorage measure, extendedmonetary seigniorage, and shows how it is dis-tributed between the Federal Reserve, memberbanks and the U.S. Treasury during the 1951-90

period. Then, it examines the relationship be-tween inflation and seigniorage during this peri-od and shows that this relationship is analogousto the well-known “i,affer curve” that relatestax rates and tax revenues: seigniorage in-creases as inflation rises until the inflation ratereaches about 7 percent; thereafter, inflationand seigniorage are inversely related. Indeed,for each percentage point rise in inflation above7 percent, the U.S. Treasury’s share of seig-niorage fell, on average, by $1.4 billion (meas-ured at 1982/84 consumer prices).

p%•,i%~4 i’i:1%I)~IIi~’I(1).r9t.~.~: :/T~:..)~

flFIiJI%~S(I)i~4i~;I~%T;IJ

CONCEPT

The term “seigniorage” dates back to the earlyMiddle Ages, when it was common for sover-eigns of many countries to finance some oftheir expenditures from the profits they earned

States:Seigniorage in the United

How Much Does theU. S. Government Make fromMoney Production?

1See Brunner and Meltzer (1971).

from the coinage of money. In the money litera-ture, seigniorage has often been used inter-changeably for either the total revenue or theprofit derived from money production andmaintenance. Of course, revenues and profitsare identical only if costs are zero. Althoughtheoretical analysis can be simplified by assum-ing that costs are zero, this assumption cannotbe maintained in empirical applications. Sincethis article focuses on the empirical issues as-sociated with seigniorage, the total revenue, costand profits associated with money productionmust be carefully distinguished and the relevantnotion of seigniorage must be clearly defined.

Tn the analysis that follows, seigniorage is de-fined as the revenue associated with moneyproduction and maintenance, rather than theresulting profit. Also, the focus is on the reve-nue accruing to the government and, therefore,on the creation of monetary base rather thanthe creation of deposits by private depositoryinstitutions.

Monetary theorists have used two main con-cepts of seigniorage in analyzing its relationshipto inflation. These concepts are termed “oppor-tunity cost seigniorage” and “monetary seig-niorage.”

/1//’ %...%..ISI lft?.U/nionfl/e

As its name indicates, opportunity cost seig-niorage defines seigniorage as the total “oppor-tunity costs” of money holders. It asks thequestion, What additional real income would in-dividuals have earned if they had held interest-earning assets instead of non-interest-earningmoney? The real interest earnings foregone byholding money are called its opportunity cost.

Real opportunity cost seigniorage (~~)is:

(1) s~,= rB/P,

where B denotes total base money holdings, r isthe representative nominal rate of return on as-sets other than base money and P is the con-sumer price level.

This concept of seigniorage has been used asan elegant tool of theoretical analysis.~Its ana-lytical attraction is that it derives the value of

seigniorage from the individuals’ valuation ofthe services of money. It does this by identify-ing seigniorage with the interest income that in-dividuals voluntarily forego by holding some oftheir wealth as money instead of as earning as-sets. This concept, however, presents someproblems when it is used for empirical studiesof seigniorage.

i’o make the concept of opportunity cost seig-niorage operational for empirical analysis, someactual nominal rate of return must be chosen asthe measure of the representative rate of return(r) in equation I. Estimates of seigniorage willdiffer widely depending on which rate ofreturn — for example, the federal funds rate,the average yield on government bonds or therate of return on stocks of, say, the computerindustry — is used. Thus, the problem is to de-termine a weighted average of observable assetreturns that meaningfully approximates the trueopportunity cost of money holders.

There is also a conceptual problem with usingthis definition of seigniorage: opportunity costseigniorage does not equal the monetary author-ity’s actual revenue from money creation.3 Be-cause the structure of the monetary authority’sportfolio differs markedly from the asset struc-ture preferred by private investors, opportunitycost seigniorage does not provide a measure ofthe gains to the monetary authority from moneycreation and maintenance.

/4

The concept of monetary seigniorage permitsa more straightforward and unambiguous em-pirical measurement. Monetary seigniorage (sc)is defined as the net change in base money out-standing (AB), deflated by the consumer pricelevel (P):

(2) s~= AB/P.

Monetary seigniorage measures the transactionvalue of non-monetary assets that money holderstrade in to the monetary authority to obtain thedesired increase in their base money balances(aB). Because the data necessary to calculate thismeasure are easily available, the concept of

25ee Bailey (1956), Johnson (1969), Auernheimer (1974)and Barro (1982).

3For a different view, see Gros (1989), p. 2. He interpretsequation 1 to represent ‘the interest savings the govern-ment obtains by being able to issue zero interest ratesecurities in the form of currency.” This interpretation,

however, is valid only if the nominal rate of return (r)equals the effective yield on government debt and operat-ing costs are zero.

31

monetary seigniorage has been widely used andmeasured by monetary economists.4

// //

Unfortunately, the traditional concept ofmonetary seigniorage does not provide a com-plete account of the government’s revenue frombase money provision. It abstracts from the ac-tual process of base money creation and, there-fore, neglects the fact that the total flow ofrevenue in addition depends on the asset struc-ture of the central bank.

The total flow of seigniorage to the govern-ment consists of two components. The first isthe real value of the non-monetary assets thatthe central bank receives from the public in ex-change for an increase in the monetary base.This is measured by the traditional concept ofmonetary seigniorage as defined above. The se-cond component is the interest earnings thecentral bank receives on its stocks of non-government debt.

Since domestic private and foreign debtorshave to service the debt held by the centralbank, there is a flow of seigniorage to govern-ment even if the public does not desire to in-crease its cash balances. It is important to note,however, that only the interest earnings onnon-government debt qualify. The Treasury’spayment of interest on its debt held by the cen-tral bank is an inside transaction between gov-ernment institutions that does not affect theresource transfer from the private moneyholders to government. Finally note that thecentral bank occasionally realizes capital gains(losses) by subsequently selling assets in theopen market at higher (lower) prices than it hadpurchased them.

To take these additional components of therevenue from base money production and main-tenance into account, let the interest rates onthe monetary authority’s holdings of privatedomestic debt (D) and official foreign debt (F) bedenoted by d and f, respectively, and unrealizedcapital gains by G1~Then, the extended mone-tary seigniorage, s~1,is:

(3) s~= s~+ (dD + fF + G5)/P.

Extended monetary seigniorage encompasses thetraditional measure of monetary seigniorage.The new concept provides the seigniorage meas-ure best suited for this study for two reasons.First, it directly measures the total real net flowof assets that the Federal Reserve System andU.S. Treasury receive from their monopoly overbase money production; second, it can readilybe computed from available data.

4 4

/1 1.J~.E~’1’../3.(1.1313~ ‘/.... r~J. •/.:4

An analysis of extended monetary seignioragein the United States can begin at either of twopoints: the “sources” side shows us how thegains were achieved, while the “uses” side tellsus who received the gains.

// . ~//~/•//4J

From the sources side, the extended monetaryseigniorage is shown by equation 3. In more de-tail, it can be written as:

(4) s\f = CAB + dD + fF + G5)/P

where B = C + RB + R~.

It is important to note that, in this analysis, themonetary base (B) is defined more broadly thanis usually the case. Here, official foreign depositsat the Federal Reserve System (RE) are added tothe usual monetary base components of curren-cy in circulation (C) and reserves of depositoryinstitutions (R8).

5 This expanded definition is ap-propriate because the Federal Reserve obtainsseigniorage from producing foreign deposits inprecisely the same way it does from producingdeposits for domestic depository institutions.

To develop the uses side of extended mone-tary seigniorage, two financial accounts are uti-lized: (1) the combined Federal Reserve-’I’reasury“monetary” balance sheet and (2) the incomestatement of the Federal Reserve System.

4See Friedman (1971), Calvo (1978), Fischer (1982), Dorn-busch (1988), Grilli (1989) and Klein and Neumann (1990).

foreign governments, and international organizations, likeIMF and World Bank; it excludes the Treasury’s ExchangeStabilization Fund.5’Foreign deposits” include the demand balances of for-

eign central banks, the Bank of International Settlements,

The U.S. monetary authorities’ combined bal-ance sheet can be written in first-differenceform to show the changes that have occurredover some specific time period as follows:

(5) AA~+ AD + AF + AC~+ AOA= AB + ARE, + AK.

The left-hand side of equation S describes thechanges in the Federal Reserve’s assets that sup-ply funds: outright purchases of U.S. Treasuryand federal agency obligations (AA~~),loans todepository institutions via the discount windowand government securities bought under repur-chase agreements (AD), the acquisition of gold,special drawing rights, and foreign exchange(AF), issuance of coin by the Treasury (ACe) andother Federal Reserve net assets (AOA).6

The right-hand side of equation S describesthe changes in the factors that absorb thesefunds: the monetary base (AB), deposits of theTreasury (ARG) and the Federal Reserve System’scapital accounts (AK)! Again, note that the mon-etary base definition used in this analysis in-cludes foreign deposits (R1,) held at the FederalReserve.

The Fed’s income statement is summarized inequation 6. The left-hand side describes theFed’s current income and expenses that giverise to its net revenue; the right-hand side ofequation 6 shows how the Fed’s net revenue isdistributed.

(6) dD + fF + aA1~,+ G5 + G~— OC~

= Y9+ YF.B + YGN

As noted earlier, d and f represent the inter-est rates that the Federal Reserve receives on itsloans to the domestic private sector and its in-ternational assets, respectively; similarly, “a”

denotes the average interest return it receiveson its portfolio of government securities boughtoutright.”

The next two terms are the “realized” profits(Ga) that the Fed receives from sales of its bondsand foreign assets at prices above those that itpaid for them, and the “unrealized” profits (G~,)that result from the Fed’s practice of markingthe prices of its foreign exchange holdings totheir market value. This accounting practicewas introduced in 1978; before foreign exchangeholdings were valued at historical rates.9

The term (OC~5)measures the current operat-ing costs or expenses of the Reserve Banks andthe Federal Reserve Board minus the fees andreimbursements that the System collects for theservices it sells to the banking industry, theTreasury and other government agencies. Theseservice fees and reimbursements are “nettedout” to remove receipts and expenses that arepresumably unrelated to the Federal ReserveSystem’s monetary authority role.

The right-hand side of equation 6 shows howthe Federal Reserve’s net revenue (Y) is distri-buted. The Fed pays its member banks statutorydividends (Y5) on their paid-in capital and usesan amount Y~5~which is equal to .SAK, to raisethe Reserve Banks’ surplus capital to the level ofits member banks’ paid-in capital. The remain-der of the System’s net income is transferred tothe U.S. Treasury under the heading of “In-terest on Federal Reserve notes” (Y~~).’°

Subtracting equation 6 from 5 and using theidentity that the current issuance of coin (ACe)equals the operating cost of the U.S. Mint (OC~1)plus the profit to the Treasury on the issuanceof coin (YGC) yields:

5ln contrast to their practice of valuing the domestic assetsat the original purchase price, the Federal Reserve Banksmark their foreign exchange holdings to the market. As aconsequence, reported changes in the stock of the Feder-al Reserve System’s international assets include net pur-chases at the actual transaction values (AF) and valuationgains (or losses) on the previous stock of these assets ifforeign currency prices have changed. Because thesevaluation changes do not directly increase or absorbreserves, they are not included in equation 5. Incorporat-ing them explicitly would simply introduce the same valueon both sides of equation 5 and, hence, they would be“netted out” of the analysis.

7% includes Treasury cash holdings.°TheFederal Reserve’s international assets include the na-tion’s gold stock on which it receives no interest earnings.

°MostEuropean central banks do not mark their foreign ex-change holdings to market values; instead, they evaluatetheir holdings at the lowest market price that occurredsince they were acquired. As a result, their income state-ments never show unrealized profits from their foreign ex-change holdings; however, they show unrealized losseswhenever the prices of foreign currencies fall below theiracquisition values.

WAs an historical aside, prior to 1933, the income transfer tothe U.S. Treasury was effected as a franchise tax basedon a provision of Section 7 of the Federal Reserve Act.This provision was repealed in 1933 to permit ReserveBanks to restore their surplus accounts, after they hadbeen cut to one-half by the enforced subscription to theFederal Deposit Insurance Corporation, founded in 1933.

(7) AB + dD + fF + GB

= (OCE, + OCM) + YEB + Y5+ (Y0~+ Y0~— aAEB — ARG)

+ A(AFR+ D + F + OA — K)

— G0,

where: B = C + R9 + RE, and

~GC = ACc — OCM,

YE,, = .SAK.

Dividing equation 7 through by the consumerprice level (P) and using the definition of ex-tended monetary seigniorage shown in equation 4yields:

(8) 5M = + 5~+ 5~+ S, +

where: s~= (OCEB + OCM)/P

SB =

= (Y0~.+ Y5~+ AAEB — aA7,, — ARG)/P,

5, = A(D + F + OA — .5K)/P and

s, = (—G3/P.

.~sioOF LiA~i..t~,~:ot~aMONO‘1711:9. V SFIC.N.IORAI7E

Equation 8 shows how the extended monetaryseigniorage in each period is used: (1) s~is thecost of providing the public’s desired real basemoney balances, including the costs associatedwith monetary policy and the Federal Reserve’scontribution to bank supervision, (2) memberbanks receive s,,, the statutory dividends, (3) thegovernment receives s, for spending purposes,(4) the Federal Reserve uses s, to increase itsportfolio of assets other than government debtand (5) the Fed uses s~to make up for book-losses resulting from adverse changes in assetprices.

It is useful to consider in detail the seignior-age distributed to the U.S. government, whichmay be termed “fiscal seigniorage.” Fiscal seig-niorage can be written in two different ways.

The first way, using the government’s budgetconstraint, is

(9a) s~= (G — T + aA, — AAQ)/P,

where (G — T) is the government’s primarybudget deficit or surplus and aA, is the govern-ment’s interest expenditure on its debt held out-side the System (A0). Equation 9a shows thatfiscal seigniorage is the portion of the govern-ment’s deficit that is not financed by borrowingfrom the public (AA0). This means that fiscalseigniorage contributes to the finance of theprimary budget deficit and of the interest ex-penditures on debt held by the public (outsidethe Federal Reserve System).

The second way of writing fiscal seigniorage,as shown in equation 8 above, is

(9b) s~= EYcc + (Yo,x — aAE,,) + A(AER — R5)]/P.

Equation 9b breaks down fiscal seigniorage intothree source components: the net revenue fromissuing coin (Y03, the net revenue receivedfrom the Federal Reserve (Yox -.- aA~,,),and thenet borrowing from Reserve Banks (AA~,,—ARG).’~

The treatment of net borrowing as a sourceof fiscal seigniorage is not an obvious one, sincethe Fed does not lend directly to the Treasury;instead it purchases Treasury securities in theopen market. From a purely technical point ofview, the Treasury receives the borrowed fundsfrom the public on the date of security issue,not from the Fed at the later date when thepublic resells the Securities to the FederalReserve.

The above treatment of borrowing can bejustified by the following considerations: First,from the economic point of view, what countsis not the first but the final placement of theTreasury securities. Thus, if the security dealersdo not hold but resell the Treasury securities toReserve Banks after a short duration, it is, infact, the Fed that supplies the borrowed fundsto the Treasury. At the same time, these trans-actions permit the security dealers to buy an-other load of new debt from the Treasury.Second, the bulk of the Federal Reserve’s pur-

‘1See Klein and Neumann (1990)‘2ln the theoretical literature, it is usually taken for granted

that the net revenue received from the Federal Reserve(Y0,, — aAE,,) cannot be negative since the governmentreceives back as part of the transfer (Y0 ,,) the interestpaid on its debt to the central bank (aA,,). This conclu-

sion, however, holds only if the costs of the monetaryauthority are assumed away. In the United States, for ex-ample, the Treasury’s interest payments to the Fed typical-ly exceed the Treasury’s income received as “interest onFederal Reserve notes.”

Figure 1Extended Monetary Seigniorage and Operating Cost(in 1982/84 Consumer Prices)Billions of dellars Billions of dollars35 _______ _______ ______ ______ _______ ______ 35

20

15

10

5

0

30

25

20

15

10

5

Operating Costs

0

5 —5

-— -——- -———- —- ~--~ -~-.

1951 52 54 56 55 60 62 64 66 68 70 72 74 76 78 80 82 84 86 88 1990

30

25

chases of Treasury securities is at the short-term end of the maturity spectrum. During the1980s, for example, 83 percent of the securitiespurchased had maturities of less than one year.For this large portion of newly acquired debt,the time difference between the public’s buyingand reselling plays no significant role in the em-pirical analysis below based on annual observa-tions. Third, some portion of new Treasurydebt issued with maturities exceeding one yearis also purchased by the Federal Reserve duringthe year of its issue. Finally, any approximationerror with respect to the annual time unit ceasesto play a role when annual average data for de-cades are examined below.

Figure 1 shows the magnitudes of the extend-ed monetary seigniorage (s,,) and the monetaryauthorities’ operating costs (se) as measured in1982/84 dollars, from 1951 to 1990. During the

past four decades, the annual real value of ex-tended monetary seigniorage has generally risen,while ranging over that period from —$6 billionin 1954 to $31 billion in 1986. As figure 1 indi-cates, a comparatively small portion of thisamount—only about 7 percent on average—wasused to cover the costs of producing the mone-tary base by the monetary authorities. Conse-quently, the government’s production of basemoney has resulted in sizable and rising netprofits, which are equal to the difference be-tween the two curves in figure 1.

This result is shown in somewhat differentform in table 1, which provides annual averagedata for each of the past four decades. Duringthe 1980s, the annual real net profit from basemoney production and maintenance averagedmore than $14 billion, while, during the l9SOs,it averaged $1 billion per year. The steepest in-crease in extended monetary seigniorage oc-curred in the 1960s, when it jumped to almost$10 billion annually, on average, up sharply

from its 1950’s level. About 80 percent of thisrise resulted from drastic increases in averagereserve requirements during the 1960s.

As table 1 shows, the average annual totaloperating costs of the monetary authorities in-creased by about 50 percent during the 1970sfrom its earlier levels. This rise primarilyreflects the Federal Reserve’s efforts to in-troduce a variety of services in the 1970s as-sociated with the payments mechanism. Themonetary seigniorage used for covering operat-ing costs fell in the 1980s when the Fed beganto charge explicitly for these services.”

Dividend payments to member banks on theirpaid-in capital (se), which run about $.I billionper year, and the System’s accounting losses onits holdings of foreign exchange (s,) represent

fairly negligible uses of the total monetary seig-niorage. As table I indicates, these accountingadjustments began in 1978, when the Fed start-ed valuing its foreign exchange holdings at cur-rent market prices.’4

During the 1980s, the Federal Reserve Systemaccounted an annual valuation gain on its for-eign exchange holdings averaging $380 million.This gain reflects the appreciation of theDeutschmark and yen against the dollar from1985 to 1987 and again in 1989/90. Occasionally,the Fed also realized profits on foreign ex-change holdings; they averaged $151 million peryear during the 1980s.

As in all countries, the bulk of the extendedmonetary seigniorage went to the government.l’he average annual flow of fiscal seigniorage

“For example, if the cost of priced services was added tothe operating costs for the 1980s, it would raise the figureshown by almost 75 percent.

“During the 1970s, the Fed’s realized (as opposed to ac-counting) losses on foreign exchange amounted to about$148 million per year in real terms. These losses resultedfrom foreign exchange intervention attempts to stem the

sharp decline in the value of the dollar during the 1970s.They appear, of course, on the sources side of the seig-niorage equation and, hence, reduce the total monetaryseigniorage collected; see equation 4.

Table 1The Uses of Extended Monetary Seiqntorage1

1951-60 1961-70 1971-80 1981-90Extended monetary

seigniorage 5M $1,555 $9,847 $14,373 $14,948

— Operating ~ 5c 454 695 1,039 7462

= Net profit 1,101 9,152 13,334 14,202

— Dividend payment tomember banks, s~ 67 100 101 96

— Book-loss on foreignexchange, 5L na. n-a. 23’ —379

— Investment in loans andforeign assets, s, —1,397

$2,431

— 1,159

$10,211

1,855

$11,355

3,283

$11,202= Fiscal seigniorage, s5

Memo:

Traditional monetaryseigniorage, 5~ $1,498 $9,683 $14,414 $13,945

Fiscal seigniorage aspercent of real federalon-budget spending tO% 2.8% 2.1% 1.6%

1Annual averages in millions of dollars, 1982/84 consumer prices.2Net of revenue from priced services ($501 million).‘Starting in 1978.

Table 2The Components of Fiscal Seigniorage’

...1!5160 196170 -- 1971-80 198190U S. government debt

bought outright by Fed 52,295 810.525 512.117 810.462

* Interest received or, FR-notes net of interestpaid to Fed —529 —541 — 1,233 455

Con issueo net ofoutlays of US Mint 591 428 1.092 587

— Change in Treasurysdeposits with Fed 74 —201 —621 —302

= Fiscal scigniorage $2,431 $10211 811.355 $11202

Memo-

Interest received on FR-notes $1671 85.214 810-189 $15954

Interest paio to FederalReserve $2,200 S 5.755 811.722 $15,499

‘Annual averages n miliions of dollars. 1982/84 consumer prices

rose from $2.4 billion during the 1950s to$11.2 billion in the 1980s. The dominating sourcecomponent of fiscal seigniorage is the outrightacquisition of government securities by the Fed.Just how important it is can be seen in table 2;for all practical purposes, it matches the total.

This observation underscores the fact that theseigniorage flow to government must not beidentified with the Fed’s payment to the Treasu-ry of “interest on Federal Reserve notes.” In ser-vicing the debt held by the Fed, the Treasurymakes interest payments of roughly the sameorder of magnitude as the Fed pays to the‘rreasury (see the bottom lines in table 2)13 In-deed, the Fed’s portfolio of U.S. governmentsecurities can be interpreted as an interest-freeloan to the Treasury.

While during the 1970s and the 1980s fiscalseigniorage amounted to 80 percent of mone-tary seigniorage collected, it even exceeded the

total flow during the 1950s and the 1960s. Howwas it possible that the government consumedmore seigniorage than was collected? The an-swer to that question is asset substitution infavor of U.S. government debt: for a given basemoney stock, the Fed can reduce its loans tothe banking sector or sell foreign assets and usethe proceeds for buying outright governmentdebt. For example, if the Fed replaces foreignassets worth $100 million with Treasury bills ofthe same amount, it foregoes foreign interestearnings of, say, $5 million. As a result, the cur-rent flow of fiscal seigniorage is increased by$95 million (see equation 9b).” To be sure, thisis a one-time effect. During subsequent periods,the flow of fiscal seigniorage will be smallerthan otherwise, because of the lost stream offoreign interest earnings.

As table 1 indicates, the observed differencesbetween the annual flows of monetary and fis-cal seigniorage are largely due to asset substitu-tion. During the 1950s and the 1960s, the Fed

“Barro (1982) was not aware of this, when he identified theinterest on Federal Reserve notes as the revenue frommoney creation. But note that Barro would be correct ifthe Fed, like the Deutsche Bundesbank, would mainly holdearning assets other than government debt.

“While the discussed transaction reduces the Fed’s interestearnings on foreign assets, it raises the interest earningson the portfolio of Treasury securities. But, as notedabove, this does not affect the net flow of fiscal seig-niorage.

raised the annual flow of fiscal seigniorage abovethe flow of extended monetary seigniorage byreplacing non-government debt worth morethan $1 billion each year, on average, with U.S.government securities. The reverse policy waschosen thereafter so that the annual flow offiscal seigniorage fell behind monetary seignior-age by an average of almost $4 billion duringthe 1980s.

While the continuous flow of fiscal seignioragehelps to finance the federal budget, it is a fairlysmall source of funds. On average, it contrib-uted about 2 percent to the finance of federalexpenditures over the past 40 years.

Sei,gnftji ag~ and InJlatimi

In the monetary economics literature, seig-niorage is often discussed and analyzed in termsof an “inflation tax,” a term that was coined byMilton Friedman (1953). This association reflectsthe fact that, other things the same, a nation’smonetary authorities can increase monetaryseigniorage by increasing the supply of basemoney relative to its demand. Because the re-sulting rising price level reduces the real valueof the public’s base money holdings, the publicwill demand more nominal base money balancesto make up for the price-level-induced decline inits real cash balances. As a result, the price riseproduces an increase in monetary seigniorage.

Extended monetary seigniorage, however, willnot rise in some fixed proportion to inflation;the demand for real cash balances is inverselyrelated to the rate of inflation. Hence, the in-crease in seigniorage associated with higher andhigher inflation becomes smaller and smaller;eventually, some inflation rate is reached atwhich monetary seigniorage is maximized.‘I’hereafter, higher inflation will reduce the levelof seigniorage as the inflation-induced effectdominates the price-level effect on the public’sdemand for real cash balances.

In sum, monetary theory predicts that seig-niorage rises with inflation but falls once the in-

flation rate has passed a certain threshold. Thus,the predicted relation resembles the shape ofthe Laffer curve in public finance wheie therevenue from the income tax first rises with theeffective tax rate but begins to decline once thedisincentive effect of too high a tax rate be-comes dominant.

Monetary theorists have applied profit-maxi-mizing conditions for a monetary authority togenerate the seigniorage-maximizing rate of in-flation.’~This concept, however, is unlikely toyield much insight in the actual behavior ofmonetary authorities. While, in history, mone-tary authorities of several countries have re-peatedly produced larger inflations in theattempt to accommodate fiscal problems, centralbanks, in general, are not profit-oriented organi-zations, and ascribing pi-ofit-maximizing motivesto them is misleading.”

Thus, instead of looking for some theoreticallyjustified story about inflation and the motives ofthe Federal Reserve System, we are better offby simply looking at the “stylized facts” aboutthe relationship between inflation and the ex-tended monetary seigniorage in the United States.Figure 2 provides one way of assessing this rela-tionship. The points in the diagram show therate of inflation and the associated monetaryseigniorage in each year from 1951 to 1990. Asexpected, the data reveal an initial positive rela-tionship between inflation and extended mone-tary seigniorage. As also expected, however, thispositive association slowly disappears, then be-comes negative for sufficiently high rates ofinflation. Thus, the empirical relationship resem-bles the shape of a Laffer curve.

The curve drawn in figure 2 shows the re-sults of estimating extended monetary seignior-age (sM) as a quadratic function of the rate ofinflation (it):

(10) s,~= a0 + a~n— a2n’ + e,

where e is a white-noise residual. The estimatedparameters imply that monetary seigniorage be-

“Consider the traditional concept of monetary seigniorage,as defined above by equation 2. It can be rewritten as:(a) s~,= (ABfB)(B/p).Next, assume a standard money demand function:(b) B/p = y exp[—A(r +where (y) is real income, (r) is the real rate of interest andn the inflation rate. Finally, assume a steady-state equilibri-

um in which y and rare constant. This implies: it = AB/B.Maximizing equation a subject to equation b yields theseigniorage-maximizing rate of inflation:(c) n°P~= 1/A.

“For a different view, see Toma (1982).

Figure 2Extended Monetary Seigniorage and Inflation(1982/84 Consumer Prices)Billions of dollars35 ________

30

25

20

15

10

5

0

—S

—10

Billions of dollars35

30

25

20

is

10

5

0

—5

—10

gins to decline once inflation exceeds a rate of7.9 percent.”

From the point of view of the U.S. govern-ment, fiscal seigniorage is more interesting thanmonetary seigniorage because the former meas-ures what the government actually receives forbudget finance. As figure 3 shows, fiscal seig-niorage is quite similarly related to the level ofinflation, except that it reaches a maximum atan inflation rate of 7.2 percent.’°

These estimates suggest that high inflation, atleast more than 7 percent or 8 percent peryear, has been less profitable for the U.S.

government when monetary or fiscal seig-niorage alone are considered. This is demon-strated in table 3, where average annualseigniorage flows are compared over differentinflation ranges. During the high inflation years,when inflation exceeded 9 percent annually, fis-cal seigniorage averaged 7.7 billion per year.This is about 5 percent lower than it averagedduring the low inflation years and even 45 per-cent lower than during the medium inflationyears.”

The government’s monopoly in issuing basemoney yields profits that facilitate its fiscal

IsEstimating equation 10 with a dummy for 1986 yields:a,, = —979 (—0.55), a, 4,325 (5.94), and a4 = 269(4.73), numbers in parantheses are t-values, R’ .62,DW = 1.52.

2OThe respective curve is computed from estimating equa-tion 10 with fiscal seigniorage as the dependent variable.Denoting the estimated parameters by b yields: b,, = 1,233(0.56), b, = 3,123 (3.51), b, = 217 (3.07), R’ = .28,DW = 1.88.

2lWhile it may be tempting, given the evidence presented intable 3, to conclude that the U.S. government shouldprefer inflation in the 4.6 percent to 9 percent annualrange, it would be a mistake to do so. First, there areother social (and governmental) gains from lower inflationthat are not examined here. Second, and perhaps morerelevant, the U.S. rate of inflation has been below 4.5 per-cent for 25 of the 40 years between 1951 and 1990.

—1.0 0.5 2.0 3.5 5.0 6.5 8.0 9.5 11.0 12.5 14.0

Percent

Figure 3Estimated Seigniorage and Inflation(in 1982/84 Consumer Prices)Billions of dollars BIllions of dollars20 20

15 15. Extended

Monetary Seigniorage

10 “~ 107

N

5 5/

/

0 0

—5—1.0 0,5 2.0 3.5 5.0 6.5 8.0 9.5 11.0 12.5 14.0

Percent

Table 3Seigniorage and Inflation’

Inflation range

—0.3 to 45% 46 to 9.0% 9 Ito 136%

Monetary seigniorage. s~, $8,056 $15 030 511.106

Fiscal seigniorage. s $8,096 $11. 117 S 7 685

Number of years 25 10 5

Average inflation rate 2.3% 6.2% 11 1%

1Annual averages in millions of dollars. 1982/84 consumer prIces

finance. This paper developed a new measure limits, governments are able to increase theirof monetary seigniorage and presented a frame-work for analyzing and measuring the totalseigniorage flow from base money productionand its allocation to various uses, including fis-cal finance, in the United States.

In addition, the paper analyzed the relation-ship between monetary and fiscal seigniorageand inflation in the United States from 1951 to1990. while it is well-known that, within certain

Auernheimer, Leonardo. “The Honest Government’s Guideto the Revenue from the Creation of Money:’ Journal of Ft-/it/cal Economy (May/June 1974), pp. 598-606.

Bailey, Martin J. “The Welfare Cost of Inflationary Finance’Journal of Pa//tica/ Economy (April 1956), pp. 93~110.

Barro, Robert J. “Measuring the Fed’s Revenue from MoneyCreation’ Econom/c Letters Vol. 10 (1982), pp. 327-32.

Brunner, Karl, and Allan H. Meltzer. “The Uses of Money:Money in the Theory of an Exchange Economy:’ AmericanEconomic Rev/ew (December 1971), pp. 784-805.

Calvo, Guillermo A. “Optimal Seigniorage from Money Crea-tion: An Analysis in Terms of the Optimum Balance of Pay-ments Deficit Problem,” Journa/ of Monetary Econom/cs(August 1978), pp. 503~17.

Dornbusch, Rudiger. “The European Monetary System, theDollar and the Yen,” in Francesco Giavazzi, Stefano Micos-si and Marcus Miller, eds., The European Monetary System,(Cambridge University Press, 1988).

Fischer, Stanley. “Seigniorage and the Case for a NationalMoney’ Journal of F~/itica/Economy (April 1982),pp. 295-3-la

seigniorage flows through higher inflation, thelimits to such actions are not as well-known.The evidence presented here suggests that theU.S. government’s fiscal seigniorage declineswhen the rate of inflation exceeds 7 percent. In-deed, in those years when inflation exceeded9 percent, the U.S. government’s fiscal seig-niorage fell short of the levels achieved whenU.S. inflation rates were less than 4.5 percent.

Friedman, Milton. “Discussion of the Inflationary Gap:’Essays in Pos/tive Economics (University of Chicago Press,1953).

_______- “Government Revenue from inflation,” .Journa/ ofPolitical Economy (July/August 1971), pp. 846-56.

Grilli, Vittorlo. “Seigniorage in Europe:’ in MarcelIo de Ceccoand Alberto Giovannini, eds., A European Central Sank?Perspectives on Monetary Unification after Ten Years of theEMS (Cambridge University Press, 1989).

Gros, Daniel. “Seigniorage in the EC: The Implications of theEMS and Financial Market Integration,” /MF Working Paper~ashington, D.C., January 23, 1989).

Johnson, Harry G. “A Note on Seigniorage and the SocialSaving from Substituting Credit for Commodity Money:’ inRobert A. Mundell and Alexander K. Swoboda, eds., Mone-tary Problems of the International Economy (University ofChicago Press, 1969).

Klein, Martin, and Manfred J.M. Neumann. “Seigniorage:What is It and Who Gets It?” I4&twirtschaftlichea Archiv(Heft 2/1990), pp. 205-21.

Toma, Mark. “Inflationary Bias of the Federal Reserve Sys-tem: A Bureaucratic Perspective:’ Journal of Monetary Eco-nomics (September 1982), pp. 163-90.