ＤＢＳ−１０−０１

On the Liquidation of Government Debt
under A Debt-Free Money System– Modeling the American Monetary Act –Kaoru Yamaguchi ∗Doshisha Business School
Doshisha University
Kyoto 602-8580, Japan
E-mail: kaoyamag@mail.doshisha.ac.jp

Abstract
Runaway accumulation of government debt in Japan under the recent ﬁnancial crises seems to deprive the government of its eﬀective policy discretion due to the burdens of debt repayment. This paper ﬁrst
examines that the government debt is structurally built in the current
macroeconomic system of money as debt which is founded by the Keynesian macroeconomic framework, and it is very costly to reduce it. Then, it
demonstrates how the government debt could be liquidated without cost
under an alternative macroeconomic system of debt-free money that is proposed by the American Monetary Act. Finally, it is posed that debt-freemacroeconomic system is far superior to the debt-burden current macroeconomic system in a sense that it can not only liquidate government debt
but also attain higher economic growth.

1

Introduction

Since 2004 I have been working on a step-by-step construction of macroeconomic models in [11], [12], [13] and [14] based on the method of accounting
system dynamics developed in [10]. This series of macroeconomic modelingwas completed in [15] with a follow-up analytical reﬁnement method of priceadjustment mechanism in [16].
While my macroeconomic modeling was advancing, the current world-wide
ﬁnancial crises were triggered by the bankruptcy of Lehman Brothers in September, 2008, and the US government has been forced to bail out the troubled ﬁnancial institutions with $800 billion out of taxpayers’ pockets, which in turncaused furious angers among American people.
∗ This paper is submitted to the 28th International Conference of the System Dynamics
Society, Seoul, Korea, July 25-29, 2010.

1

These ﬁnancial turmoils gave me, as a system dynamics researcher, a chance
to re-think about the eﬀectiveness of current macroeconomic system as a systemdesign, since system dynamics is a methodology to help design a better system
as Jay Forrester, founder of system dynamics, emphasized in 1961:
Labor turmoil, bankruptcy, inﬂation, economic collapse, politicalunrest, revolution, and war testify that we are not yet expert enoughin the design and management of social systems [1, p.1].

System of Money as Debt
Books such as [2] and [17] enlightened me as being an expert enough to understand that the currently dominant macroeconomic system has been founded on
the basis of money as debt. In the United States, this monetary framework was
instituted by the Federal Reserve Act in 1913, which allows the 100% privatelyowned Federal Reserve Board to play a role of the central bank and issue money.
Without exception almost all of macroeconomic textbooks such as [4], [5], [6],[3], which have been refereed to my modeling works, justify the current macroeconomic system without mentioning an alternative system, if any.
Speciﬁcally, the current macroeconomic system can be deﬁned as a system
of money as a debt in which government has no control over the issue of money,
except a small amount of metal coinage. Under the system only the central
bank has a control to issue money against debt borrowed by the government orcommercial banks. See [11] for a detailed process of creating money. Growing
economies constantly needs new issue of money to be put into circulation, andunder the current system it can only be fulﬁlled by the deﬁcit of government withinterest payment out of taxes. In other words, the government is systemicallyobliged to accumulate debt, as analyzed in [13].
Japanese government owns 55% of the shares of the central bank, that is,
the Bank of Japan, yet it has no control over the issue of money. Accordingly,
the government has to keep borrowing from the central bank with interest payment, though indirectly through the open market operations. In this sense, theJapanese macroeconomic system can also be said to be a system of money as
debt.
What’s wrong with this system? Nothing may be wrong if the system provides economic stability, full employment, fair income distribution and environmental sustainability. On the contrary, the system behaves oppositely, as
theoretically analyzed in my model in [15], and historically evidenced by theGreat Depression in 1929 and the recent ﬁnancial crises, to pick up some major
ones. Accordingly, seven reasons to abolish the system were articulated in [2],which seem convincing and hard to refute by rational economists. Due to thelimitation of space in this paper they are not quoted here, but the reader is
encouraged to investigate them in detail. Moreover, voices seem to be surfacing
increasingly in the Internet against the current monetary system as a fundamental cause of the recent ﬁnancial crises, speciﬁcally against the privately-owned

2and controlled central bank, that is, the Fed in the United States1 .
The current macroeconomic system has been structurally fabricated by theKeynesian economics, in which it is proposed that the additional government
expenditure can rescue the troubled economy from recession. Yet, it fails toanalyze why this ﬁscal policy is destined to accumulate government debt as
mentioned above. In fact, even though GDP gap is very huge in Japan, yet due
to the fear of runaway accumulation of debt, the government is very reluctant
to stimulate the economy and, in this sense, it seems to have totally lost thediscretion of public policies for the welfare of people even though production
capacities and workers have been sitting idle and ready to be called in service. In
other words, Keynesian ﬁscal policy cannot be applied to the troubled Keynesian
macroeconomy. Isn’t this an irony of the Keynesian theory? Macroeconomic
system of money as a debt seems to have fallen into the dead-end trap.
The ﬁrst objective of this paper is accordingly to reconﬁrm the fact that theaccumulation of the government debt is built in the Keynesian macroeconomic
system of money as debt.

System of Debt-Free Money
As a system dynamics modeler and designer, I have now to pose a question
if there exits an alternative macroeconomic system that helps escape from theabove dead-end trap of the current system? One of the answers seem tot bepresented in [17, Chap.24] and [18] as a macroeconomic system of debt-freemoney. This alternative system can be compactly deﬁned as having the following
three features:• Governmental control over the issue of money• Abolishment of credit creation• Constant inﬂow of money to sustain economic growth and welfare
Accordingly, the second objective of this paper is to construct a macroeconomic model which incorporates the above three features and examine if thisalternative system could help liquidate government debt or not. Before moving
on, let us take a closer look at these features in detail.
Governmental control over the issue of money
In macroeconomics, the amount of money to be issued by the central bank iscalled monetary base or high-powered money. In order for the government tocontrol the issue of money and monetary base, the American Monetary Act
suggests as follows:First, the Federal Reserve system becomes incorporated into the
U.S. Treasury. This nationalizes the money system, not the banking
1 For instance, http://www.themoneymasters.com and http://www.monetary.org.

3system. Banking is not a proper function of government, but control
and oversight of the money system must be done by government [18,p.12].
In Japan, the government owns 55% of the shares of the Bank of Japan. Accordingly, its incorporation to the government could be rather smoothly done,
though the government as its major shareholders is currently prohibited fromthe bank’s decision-making process by law. In Europe, two incorporation processes could be possible. First, EU member countries are politically integrated
into, say, the United States of Europe, which in turn establishes its own federal
European government and incorporate the current European Central Bank into
its branch. Or the ECB is once again disintegrated and incorporated into thegovernments of member countries, respectively.
Abolishment of credit creation
Credit can be created by the lending of commercial banks, and becomes a partof money supply, because it plays a role of means of exchange. See [11] for a
detailed analysis of credit creation. The credit creation has been called moneyout of nothing or money out of thin air by Keynes. It is made possible because
banks are required to hold only a fraction of deposits (with the central bank)and can lend the remaining larger portion. This system is called a fractional
reserve banking system. Heavily-criticized practice of leveraged investment that
led to the recent ﬁnancial crises is made possible by the credit creation. Undera debt-free money system, this fractional reserve banking system is abolished;that is, a fractional reserve ratio has to be 100%. The American Monetary Act
suggests as follows:
Second, the accounting privilege banks now have of creating money
through fractional reserve lending of their credit is stopped entirely,
once and for all. Banks remain private companies and are encouraged to act as intermediaries between their clients who want a returnon their savings and those clients willing to pay for borrowing thosesavings, but they may no longer create any part of the nation’s
money supply [18, p.12].
It will be worthwhile to clarify a position of money in an economy. Suppose
there exists N commodities in an economy. Under gold standard or commodity
money standard, one of the commodities becomes money against which theremaining N-1 commodities are exchanged. Hence, quantity of money is limitedby the production of gold or commodity money. Under a fractional reservebanking system, credit is created and used as low-powered money in addition
to monetary base or high-powered money. In other words, 2 types of money
are being used for the exchange of N commodities. Finally, under a systemof debt-free money, only the government-issued ﬁat money is used to exchange
for N commodities. Schematically, positions of money under diﬀerent monetarysystem is summarized as follows:4Gold or Commodity Money Standard(N - 1) + Gold
Fiat Money as Debt
N + Money + Credit(Deposits)
Debt-free Fiat Money
N + Money
Constant inﬂow of money
Growing economy demands for a growing amount of money as a means of exchange if monetary value is to be sustained. This can be easily veriﬁed from thefollowing quantity theory of money:
M V = P T = kP Y

(1)where M is money supply, V is a velocity of money, P is a price level, T is theamount of transaction, Y is real GDP, and k is a so-called Marshall’s k.
Assuming that V and k are constant, we have
Ṁ
Ṗ
Ẏ
=
+
(2)
M
P
Y
Thus, to sustain a monetary value by avoiding inﬂation or deﬂation, we haveto attain Ṗ /P = 0. This implies that Ṁ /M = Ẏ /Y ; that is, money has to beissued and put into circulation in accordance with the economic growth.
Under a system of money as debt, the injection of new money into circulation has only been carried out by the privately-controlled central bank at its
discretion and for its interest. Under a debt-free money system, two channels
for money injection becomes available. First, the government can directly distribute new money into circulation as an additional expenditure according to
its public policies supported by voters in the ﬁeld of infrastructures, education,
medical care, green technologies and environment. Second, the central bank,
now as a part of government, can make loans to commercial banks, free of interest, according to a guideline set by governmental growth strategies for theinterest and welfare of people.
As to the new issue of money, American Monetary Act suggest as follows:
Third, new money is introduced into circulation by government
spending it into circulation starting with the $2.2 trillion the engineers tell us is needed for infrastructure repair and renewal. In
addition, health care and education are included as human infrastructure. Everyone supports the infrastructure, but they worry how
to pay for it. That becomes possible with the passage of the American Monetary Act [18, p.12].

5

Battles to Control the Money System
Human history could be, in a sense, said to be a history of battles to control theissue of money; that is, the battles between a system of money as debt and asystem of debt-free money in our terminology here, or between interest-bearing
money and interest-free money.
Science of money, according to [17], was founded by Aristotle (384-322BC).
He viewed that “Money exists not by nature but by law(nomos)“ . His viewhas been supported through the church’s condemnation of usury up to the workby the philosopher George Berkeley2 in his 1735 book of questions “Querest”.
Neglecting his work, Adam Smith, father of economics, ended the battle bysupporting the Bank of England, founded in 1694, as a system of money as debt
in his book The Wealth of Nations in 1776.
This battle is summarized as Aristotle’s science of money vs. Adam
Smith’s metallic view of money. · · · Whether money should be tangible wealth and thereby be privately controlled to beneﬁt the wealthy(Smith), or be an abstract legal ﬁat power publicly controlled to promote the general welfare (Aristotle) [18, p.6].
In the United States, this battle was ﬁnalized when the Federal Reserve Act
was approved and system of money as debt has been introduced [2]. Since thenscience of money has been lost and economists showed no doubt on the role ofmoney as debt, including Keynes. The lost science has been reﬂected in many
macroeconomics textbooks, including the ones as brieﬂy mentioned above.
The dominance of current macroeconomic system is being challenged again
with the introduction of the American Monetary Act under the recent ﬁnancial
crises. As a system dynamics researcher and a professionally trained economist,
I’m of the opinion that it is a reclaiming process of the lost science of money toconstruct macroeconomic models which enable us to compare these two systems
and evaluate them impartially in terms of economics as a science.

2

The Macroeconomic System Revisited

For the comparative analysis of the two macroeconomic systems, the integrated
macroeconomic model developed in [13] is revisited in this paper. According
to the discussions above, the model is classiﬁed as a macroeconomic system ofmoney as debt, in which ﬁve macroeconomic sectors are assumed to play interdependent activities simultaneously; that is, producers, consumers, banks, government and the central bank. Figure 1 illustrates the overview of the macroeconomic system in this paper, and shows how these macroeconomic sectors
interact with one another and exchange goods and services for money. Foreign
sector is excluded from the model.
2 University of California at Berkeley, where I studied mathematical economics in late 70’s
and early 80’s, was named after the philosopher Berkeley.

6Central Bank

Money Supply

Banks
Loan

SavingWages & Dividens (Income)Consumer(Household)Consumption

Gross
Domestic
Products(GDP)

Production

Producer(Firm)

Labor & Capital

Investment(Housing)

National Wealth(Capital
Accumulation)

Investment (PP&E)

Public Services
Public Services

Investment (Public
Facilities)

Income Tax

Government

Corporate Tax

Figure 1: The Macroeconomic System Revisited

Production Function
To make our analysis simple enough without losing generality, the above integrated model is slightly revised such that labor market is excluded from themodel. This is also in accordance with my viewpoint that labor market shouldbe abolished from a market economy as a better economic system, which is
proposed as the MuRatopian economy in [9]3 . Accordingly, the Cobb-Douglas
production function needs to be replaced with the following production function
Y = Min(Yf ull , Y D ),(3)

in which full capacity output level Yf ull is speciﬁed as follows:1
Yf ull = eκt K,
θ

(4)

3 The MuRatopian economy is presented as an alternative system, beyond capitalist market
economy and planned socialist economy, suitable for the information age of the 21st century.
However, money system is missing in the economy, I admit. While writing this paper, I
become convinced that a debt-free money system should be indeed a monetary system of the
MuRaopian economy.

7where κ is an annual increase rate of technological progress, and θ is a capitaloutput ratio. Furthermore, the amount of desired output Y D is deﬁned as asum of the amount of inventory replacement and aggregate demand forecasting:Y D = (Desired Inventory − Inventory) + AD Forecasting.

(5)

The revised production function and the determination process of GDP are
illustrated in Figure 2.

Price Flexibility
Besides the simpliﬁcation of production function, two minor sophistications are
made to the model; that is, a price adjustment mechanism and a consumptionfunction. Based on [16] price adjustment mechanism is revised as follows. First,
price is adjusted according to the discrepancies between full capacity output
Yf ull and desired output Y D , which are called GDP gap. Price is also allowed
to adjust directly to the discrepancies between inventory Iinv and its desired∗
inventory Iinv
, which are called inventory gap here.
Hence, the adjusted equation can be described asdP∗= Ψ(Y D − Yf ull , Iinv
− Iinv ).
dt
Let us specify the equation as follows:dPP∗ − P=
dt
Delay Time

(6)

(7)

The desired price P ∗ is obtained asP∗ = (P∗
Iinv
Y(1 − ω) Yf ull
D + ωI
inv

)e

(8)

where ω, 0 ≤ ω ≤ 1, is a weight between production and inventory ratios, ande is an elasticity. Figure 3 illustrates the revised adjustment processes of priceand interest rate.

Consumption Function
Consumption, which was assumed to be determined by a constant marginal
propensity to consume in the previous integrated model, is now assumed to be
dependent on a relative price elasticity of consumption such thatc(P ) = (

c
P
P0

)e

(9)

where P0 is an initial price level and e is a price elasticity of consumption. As
price level goes up, marginal propensity to consume gets smaller. In this way,consumption is aﬀected by the relative size of prices and its elasticity.
8Figure 2: Production Function and the Determination of GDP

9

Technological
ChangeCapital-Output
Ratio

DesiredCapital-Output
Ratio<Interest Rate>

Interest
Sensitivity

Desired Capital(real)

Initial Capital(real)

Capital underConstruction

Change in AD
Forecasting

Net Investment(real)<Capital-Output
Ratio>

Time to Adjust
CapitalInvestment(real)<Price>Time to Adjust
Forecasting<Full Capacity
GDP>

Time to Adjust
Forecasting (Long-run)

Growth Rate

Growth Covertionto %Long-run
Production Gap<GDP (real)>

Production(-1)

Growth Unit

Growth Rate (%)

Government
Expenditure<Price>Consumption<Effect on
Consumption><Money as Public
Utility>

Government
Expenditure (real)<Investment(real)>

Consumption(real)<Price>Change in AD
Forecasting (Long-run)

Aggregate
DemandForecasting(Long-run)

Aggregate
Demand (real)

Gross Domestic
Expenditure (real)<Investment>

Normal Inventory
Coverage

Time to Adjust
Inventory

Sales (real)

DesiredInvestment (real)

CapitalCompletion

Construction
PeriodAggregate
DemandForecasting

DesiredInventory

Desired Inventory
Investment<Initial Inventory>

Inventory (real)

Capital (PP & E)
(real)<Excise Tax
Rate>

Exponenton
CapitalDepreciation(real)

Desired Output(real)

Depreciation
Rate

Full CapacityGDP

GDP (real)

Inventory
Investment

Figure 3: Price and Interest Rate Adjustment Processes

10<Desired
Inventory><Inventory (real)><Desired
Output (real)><Full Capacity
GDP>

Currency inCirculation

Weight ofInventory Ratio

Inventory
Ratio

Money
SupplyVelocity of
Money

Delay Time ofPrice Change

Effect on Price

Ratio Elasticity(Effect on Price)<Deposits (Banks)>

Production
Ratio<Vault Cash(Banks)><Cash (Government)><Cash (Producer)><Cash (Consumer)>

DesiredPrice

Change in Price

Supply of
Money(real)

Initial Pricelevel

Demand for
Money(real)

Price

Actual
Velocity of
Money

Money
Ratio

DesiredInterest Rate

InitialInterest
Rate

Interest Rate(nominal)

Inflation Rate

Price (-1)

Demandfor Money

Interest Rate

<Discount Rate>

Change inInterest Rate

Effect on
Interest Rate

Discount Rate
Change Time

Ratio Elasticity (Effecton Interest Rate)

Delay Time of Interest
Rate Change

Discount Rate
ChangeDemand for
Money by Banks

Demand for
Money by theGovernment

Demand for
Money by
Consumers

Demand for
Money by
Producers<Inflation Rate><Lending(Banks)><Payment by
Banks><Securities
purchased by
Banks><Cash out>

<Government
Expenditure><Interest paid by
the Government><Government Debt
Redemption><Cash Demand><Saving><Consumption><Income Tax><Dividends><Interest paidby Producer><DesiredInvestment><Payment by
Producer>Accordingly, the revised consumption function becomesC(P ) = C0 + c(P )Yd(10)

The consumption function thus revised has a feature of a downward-sloping
demand function, similar to a demand curve of of consumers at a microeconomic
level. This minor behavioral change, however, does not signiﬁcantly aﬀect thesystem structure of the model.

3

Macroeconomic System of Money as Debt

We are now in a position to describe some transactions by producers, consumers,
government, banks and the central bank under the current macroeconomic system of money as debt. They are basically the same as already explained in [13],and repeated here for the convenience of the reader.

Producers
Major transactions of producers are, as illustrated in Figure 4, summarized asfollows.
• Out of the GDP revenues producers pay excise tax, deduct the amount ofdepreciation, and pay wages to workers (consumers) and interests to thebanks. The remaining revenues become proﬁts before tax.
• They pay corporate tax to the government out of the proﬁts before tax.
• The remaining proﬁts after tax are paid to the shareholders (that is, consumers) as dividends.
• Producers are thus constantly in a state of cash ﬂow deﬁcits. To continue
new investment, therefore, they have to borrow money from banks andpay interest to the banks.

Consumers
Transactions of consumers are illustrated in Figure 5, some of which are summarized as follows.
• Consumers receive income as wages and dividends from producers.
• Financial assets of consumers consist of bank deposits and government
securities, against which they receive ﬁnancial income of interests frombanks and government. (No corporate shares are explicitly modeled.)• In addition to the income such as wages, interests, and dividends, consumers receive cash whenever previous securities are partly redeemed annually by the government.
11

Figure 4: Transactions of Producers

12<Lending(Banks)><New Capital
Shares>Cash
Flow<DesiredInvestment><Dividends><Producer Debt
Redemption><Interest paidby Producer>

Cash Flow Deficit(Producer)

Desired
Borrowing(Producer)

Direct Financing
Ratio

Cash Flow from
Financing Activities

Cash Flow from
Investing Activities

Cash Flow fromOperating Activities

DesiredFinancing<GDP(Revenues)>

Sales<Interest paid by
Producer><Producer Debt
Redemption><Investment><Payment by
Producer><Sales><Lending (Banks)>

New Capital
Shares<Dividends>

Inventory<Price><Sales (real)>

Financing
Activities

Cash (Producer)

Investing
Activities

Operating
Activities

Investment

DesiredInvestment

Capital(PP&E)<Price><DesiredInvestment(real)><Producer Debt
Redemption>
Distribution Ratioof Wages<Corporate Tax>

<Interest paidby Producer>

Depreciation

Dividends

Wages

Tax on Production

Excise Tax
Rate<Time for Fiscal
Policy>Producer Debt
Redemption

Producer
Debt Period

Change in Excise Rate

<Depreciation(real)><Corporate Tax>

<Wages><Initial Capital(real)>

Payment by
Producer<Tax on
Production>

Dividends Ratio

Retained Earnings(Producer)

Capital Shares

Debt (Producer)

Profits

Corporate
Tax

Corporate
Tax Rate

Profits
before Tax

GDP (Revenues)<Tax on
Production><Depreciation><Interest paidby Producer><Wages><New Capital
Shares><Price><GDP (real)>

Capital Shares
Newly Issued<Lending (Banks)>

Figure 5: Transactions of Consumer

13

<Gold
Certificates>

Money put into
Circulation<Income>

Disposable
Income<Interest Rate(nominal)>

Currency Ratio
Table

Cash
(Consumer)

Currency
Ratio

CashingTime

Cash
DemandSaving<Disposable
Income>Initial Deposits(Consumer)

Deposits(Consumer)

Marginal Propensity
to Consume

Consumption

Basic
Consumption

Income Tax

Initial Security
Holding Ratio
held by
Consumer<Government Debt
Redemption><Open Market
Purchase(Public Sale)>Government
Securities(Consumer)<Initial Capital
Shares>Shares(held by
Consumer)<Price><Initial Price level>

Security Holding Ratio
by Consumer

Securities soldby Consumer<Time for Fiscal Policy>

Change in Income Tax Rate

Price Elasticity
of Consumption

Securities purchased
by Consumer<Open Market Sale
(Public Purchase)><Government
Securities Newly
Issued>Financial
Investment(Shares)<Capital Shares
Newly Issued>

Effect on
Consumption

Government
Transfers

Income Tax
Rate

Lump-sum Taxes

Initial Gold heldby the Public

Consumer Equity

Distributed
IncomeIncomeDistribution
by Producers

Income<Gold Deposit><Interest paid by theGovernment (Consumer)><Interest paid byBanks (Consumer)><Dividends><Wages (Banks)><Wages><Depreciation><Interest paid by
Producer><Income><Corporate Tax><Dividends><Wages>• Out of these cash income as a whole, consumers pay income taxes, andthe remaining income becomes their disposal income.
• Out of their disposal income, they spend on consumption. The remaining
amount are either saved or spent to purchase government securities.

Government
Transactions of the government are illustrated in Figure 6, some of which aresummarized as follows.
• Government receives, as tax revenues, income taxes from consumers andcorporate taxes from producers as well as excise tax on production.
• Government spending consists of government expenditures and payments
to the consumers for its partial debt redemption and interests against its
securities.
• Government expenditures are assumed to be endogenously determinedby either the growth-dependent expenditures or tax revenue-dependent
expenditures.
• If spending exceeds tax revenues, government has to borrow cash frombanks and consumers by newly issuing government securities.

Banks
Transactions of banks are illustrated in Figure 7, some of which are summarized
as follows.
• Banks receive deposits from consumers, against which they pay interests.
• They are obliged to deposit a fraction of the deposits as the required reserves with the central bank (which is called a fractional banking system).
• Out of the remaining deposits loans are made to producers and banksreceive interests for which a prime rate is applied.
• Their retained earnings thus become interest receipts from producers lessinterest payment to consumers. Positive earning will be distributed amongbank workers as consumers.

14

Figure 6: Transactions of Government

15

Government
Deficit<Government
Securities Newly
Issued><Interest paid by theGovernment><Government Debt
Redemption><Tax Revenues>

Government
Borrowing

Cash (Government)

Government
Expenditure

SwitchBase Expenditure

Growth-dependent
Expenditure

Change in Government
Expenditure

Change in
Expenditure<Money as Public
Utility><Tax Revenues>

Time for Fiscal
PolicyPrimary
BalancePrimary Balance
Ratio

Interest paid by theGovernment (Consumer)

Interest paid by theGovernment (Banks)

Interest paid by theGovernment (Central Bank)

Revenue-dependent
Expenditure

Interest paid by theGovernment<Interest Rate(nominal)><Growth Rate><Interest paid by
the Government>

Primary Balance
Change TimePrimary Balance
ChangeGovernment Debt
Redemption

Government
Debt Period

Initial Debt
(Government)<Corporate Tax>

<Income Tax>

<Tax on
Production><Government
Deficit>

Initial Retained
Earnings (Government)

Tax Revenues

Government Securities
Newly Issued<GDP(Revenues)>

Initial Cash
(Government)

Retained Earnings(Government)

Debt (Government)

Debt-GDP ratio

Figure 7: Transactions of Banks

16

Desired
Borrowing(Banks)<Payment by
Banks>Cash Flow
Deficit(Banks)<Interest Income(Banks)><Producer Debt
Redemption><Securities soldby Banks><Deposits in><Borrowing(Banks)><Desired
Borrowing(Producer)><Securities
purchased by
Banks><Reserves
Deposits><Cash out>

Cash in

Vault Cash(Banks)Payment
by Banks<Desired
Borrowing(Producer)>

Lending (Banks)<Government Securities
Newly Issued>

Securities
purchased by
Banks

Reserves
AT<Excess
Reserves>

AdjustingReserves

Reserves
Deposits

Cash out<Deposits out>

<Banks Debt
Redemption>

Loan(Banks)Security Holding
Ratio by Banks

Government
Securities(Banks)<Producer Debt
Redemption><Government
Securities (CentralBank)><Switch(Seigniorage)>

Interest paid by
Banks(Consumer)

Banks Debt
Redemption

Wages (Banks)

Interest paidby Banks

Interest paid byBanks (Central
Bank)

Deposits out

Banks Debt
Period<Securities
purchased by
Consumer><Financial
Investment(Shares)><Cash
Demand><Government Debt
Redemption><Government
Securities (Consumer)>

Securities sold by
Banks<Open Market Sale
(Banks Purchase)>

RR Ratio Change Time

Debt
(Banks)Retained
Earnings(Banks)Profits (Banks)

Interest Income(Banks)<Loan (Banks)><Interest paid by theGovernment (Banks)><Interest paid byBanks>

Interest paid by
Producer

Prime Rate
Premium<Securities sold by
Consumer><Saving>

Prime Rate

Deposits in<Debt (Banks)>

Discount
Rate<Interest Rate(nominal)>

Deposits(Banks)Borrowing(Banks)<Lending(Central Bank)><Switch(Seigniorage)><Lending (Public
Money)>Net Deposits<Initial Required Reserve Ratio>

Excess Reserve
Ratio

Excess Reserves<Open Market Purchase(Banks Sale)>

Open Market
Operations

Reserves(Banks)RequiredReserves

RequiredReserve
Ratio

RR Ratio Change

Central Bank
In this revised model, the central bank plays an important role of issuing moneyor currency. Sources of its assets against which money is issued are simply
conﬁned to gold, discount loans and government securities. The central bankcan control the amount of money supply through the amount of monetary baseconsisting of currency outstanding and bank reserves. This monetary control
can be carried out through monetary policies such as a manipulation of required
reserve ratio and open market operations as well as direct control of lending to
the banks.
Transactions of the central bank are illustrated in Figure 8, some of which
are summarized as follows.
• The central bank issues money (historically gold certiﬁcates) against thegold deposited by the public.
• It can also issue money by accepting government securities through open
market operation, speciﬁcally by purchasing government securities fromthe public (consumers) and banks. Moreover, it can issue money by making discount loans to commercial banks. (These activities are sometimes
called creation of money out of nothing.)• It can similarly withdraw money by selling government securities to the
public (consumers) and banks, and through debt redemption by banks.
• Banks are required by law to reserve a certain fraction of deposits withthe central bank. By controlling this required reserve ratio, the central
bank can control the monetary base directly.
• The central bank can, thus, control the amount of money supply throughmonetary policies such as open market operations, reserve ratio and discount rate.
• Another powerful but hidden control method is through its direct inﬂuence
over the amount of discount loans to banks (known as window guidancein Japan.)4

System Behaviors of Money as Debt

Mostly Equilibria in the Real Sector
The revised model is now complete. It is a generic model, out of which diverse
macroeconomic behaviors will be generated. In this paper we only focus on an
equilibrium growth path of the macroeconomy. An equilibrium state is calleda full capacity aggregate demand equilibrium if the following three output anddemand levels are met:
Full Capacity GDP = Desired Output = Aggregate Demand
17

(11)

Figure 8: Transactions of Central Bank

18

<Government
Securities(Consumer)>Open Market
Purchase(Public Sale)

Open Market
Purchase

Securities
purchased byCentral Bank

Open Market
Purchase Time

Purchase Period

Open Market
Purchase Operation(temporary)Gold<Government
Securities (Banks)>

Open Market
Purchase(Banks Sale)

Securities
sold byCentral Bank

Open Market
Public Sales Rate

Sales Period

Open Market Sale Time

Open Market Sale
Operation (temporary)

Decrease in
Reserves

Monetary
Base

Notes Withdrown

Open Market Sale
(Banks Purchase)<Government Debt
Redemption><Open Market Sale
(Public Purchase)>

Open Market Sale
Operation (permanent)

Open Market Sale

Open Market Sale
(Public Purchase)

Initial Sequrity Holding
Ratio by Central Bank

Government
Securities(Central Bank)

Security Holding Ratio
by Central Bank

<Interest Income(Central Bank)><Banks Debt
Redemption>

Banks Debt Redemption(Central Bank)<Initial Gold heldby the Public><Government
Securities (Consumer)>

Discount Loan
(Central Bank)<Government
Securities (Banks)>

Lending(Central Bank)

Window
Guidance

Gold Deposit

Open Market
Purchase Operation(permanent)

Lending(Central Bank)(-1)

DesiredLending

Growth Rateof Credit<Government
Securities Newly
Issued>Lending
PeriodLending Time

Lending byCentral Bank

<Desired
Borrowing(Banks)>

Deposit Time

<Securities sold byCentral Bank> Gold Deposit by
the Public

Retained
Earnings(Central Bank)

Reserves(Central Bank)<Interest paid by theGovernment (CentralBank)>

Interest Income(Central Bank)<Interest paid byBanks (Central Bank)>

Increase in
Reserves<Open Market
Purchase (Banks Sale)><AdjustingReserves><Lending(Central Bank)><Open Market
Purchase (Public Sale)><Reserves
Deposits>

Notes Newly
Issued<Lending (Public
Money)>
Reserves by
Banks

Currency
Outstanding

Gold Certificates<Securities purchased
by Central Bank>If the economy is not in the equilibrium state, then actual GDP is determinedby
GDP = MIN (Full Capacity GDP, Desired Output )(12)
In other words, if desired output is greater than full capacity GDP, then actual
GDP is constrained by the production capacity, meanwhile in the opposite case,
GDP is determined by the amount of desired output which producers wish to
produce, leaving the capacity idle.
Does the equilibrium state, then, exist in the sense of full capacity aggregate
demand GDP? By trial and error, mostly equilibrium states are acquired when
price elasticity e is 1, and ω is 0.1, as illustrated in Figure 9.

Full Capacity GDP, real GDP and Aggregate Demand
600

DollarReal/Year

450
12

1 23

1 23

23

1

1 23

1 23

3

300
4

4

4

4

4

4

4

4

4

3

12

12 3

1 23

150
5

5

5

10

5

5

5

5

5

5

35

40

45

0
0

15

Full Capacity GDP : Equilibrium(as Debt)"GDP (real)" : Equilibrium(as Debt)"Aggregate Demand (real)" : Equilibrium(as Debt)"Consumption (real)" : Equilibrium(as Debt)"Investment (real)" : Equilibrium(as Debt)

20

25
30
Time (Year)
1

2
4

2

5

1
3

4

5

2

1
3

4

5

2

1
3

4

5

2

1
3

4

5

2

50

3

4

5

Figure 9: Mostly Equilibrium States
The reader may wonder why this is a state of mostly equilibria, because
growth rates and inﬂation rates are still ﬂuctuating as shown in Figure 10.
Speciﬁcally, growth rates ﬂuctuates between 1% and - 0.8%, and inﬂation rates
between 0.1% and - 0.2%. Our heart pulse rate, even of a healthy person,
ﬂuctuates between 60 and 70 per minute. Yet, this is a normal state. In a similar
fashion, it is reasonable to consider these ﬂuctuations as normal equilibrium
states.
In the previous paper [13], these equilibrium states are used as a benchmarking state for comparison, and examined various disequilibrium cases suchas ﬁx-price disequilibria, business cycles caused by inventory coverage and elastic price ﬂuctuation, and economic recession caused by credit crunch. Then it isanalyzed how these disequilibria may be ﬁxed toward equilibria through monetary and ﬁscal policies. For the purpose of this paper, our analysis is conﬁned
only to the case of liquidation of government debt.

19

Inflation Rate
0.002

0.007

0.001

1/Year

1/YearGrowth Rate
0.01

0.004

0.001

0

-0.001-0.002-0.002
0

5

10

15

20
25
30
Time (Year)

35

40

45

50

Growth Rate : Equilibrium

0

5

10

15

20
25
30
Time (Year)

35

40

45

50

Inflation Rate : Equilibrium

Figure 10: Growth and Inﬂation Rates of Mostly Equilibrium States

Money as Debt
For the attainment of mostly equilibria, enough amount of money has to be
put into circulation to avoid recessions caused by credit crunch as analyzed in[13]. Demand for money mainly comes from banks and producers. Banks are
assumed to make loans to producers as much as desired so long as their vault
cash is available. Thus, they are persistently in a state of shortage of cash aswell as producers. In the case of producers, they could borrow enough fund frombanks. From whom, then, should the banks borrow in case of cash shortage?
In a closed economic system, money has to be issued or created within thesystem. Under the current ﬁnancial system of money as debt, only the central
bank is endowed with a power to issue money within the system, and make loans
to the commercial banks directly and to the government indirectly throughthe open market operations. Commercial banks then create credits under afractional reserve banking system by making loans to producers and consumers.
These credits constitute a great portion of money supply. In this way, money
and credits are only crated when commercial banks and the government as wellas producers and consumers come to borrow at interest. If all debts are repaid,
money ceases to exit. This is an essence of a system of money as debt. This
process of creating money is known as money out of nothing.
Figure 11 indicates unconditional amount of annual discount loans and its
growth rate by the central bank at the request of desired borrowing by banks.
In other words, money has to be incessantly created and put into circulation inorder to sustain an economic growth under mostly equilibrium states. Roughly
speaking, a growth rate of credit creation by the central bank has to be inaverage equal to or slightly greater than the economic growth rate as suggestedby the right hand diagram of Figure 11.
In this way, the central bank begins to exert an enormous power over the
economy through its credit control. What happens if the central bank fails to
supply enough currency intentionally or unintentionally? An inﬂuential roleof the central bank which caused economic bubbles and the following burst
in Japan during 90’s is completely analyzed by Warner in [7] and [8]. Our
macroeconomic model might provide an analytical foundation to support his
new ﬁndings in the role of the central bank.

20

Growth Rate of Credit
0.4

45

0.2

Dmnl

Dollar/Year

Lending (Central Bank)
60

30

0

-0.2

15
-0.4
0

0
0

5

10

15

20
25
30
Time (Year)

35

40

45

5

10

15

20

50

25
30
Time (Year)

35

40

45

50

Growth Rate of Credit : Equilibrium
Growth Rate : Equilibrium"Lending (Central Bank)" : Equilibrium

Figure 11: Lending by the Central Bank and its Growth Rate

Government Debt
So long as the mostly equilibria are realized in the economy, through monetaryand ﬁscal policies in the days of recession, no macroeconomic problem seems
to exist. This is a positive side of Keynesian macroeconomic theory. Yet behind the full capacity aggregate demand growth path in Figure 9 government
debt continues to accumulate as the line 1 in the left diagram of Figure 12
illustrates. This is a negative side of the Keynesian theory. Yet most macroeconomic textbooks neglect or less emphasize this negative side, partly because
their macroeconomic frameworks cannot handle this negative side of the system
of money as debt.
Primary balance ratio is initially set to be one and balanced budget is assumed here; that is, government expenditure is set to be equal to tax revenues,
and no deﬁcit seems to arises. Why, then, does the government continue toaccumulate debt? Government deﬁcit is precisely deﬁned as
Debt (Government)

Debt-GDP ratio

800

1

2

1
1

600

1.5

1
1

1
1

200

12

12

12

1

2

2

1

2

2

2

2

2

2

2

2

2

40

45

1

1

1

1

1

1

Year

Dollar

400

12

0.5

12

12

1

2

2

1

1

1

1

2

1

1

1

1
1

2

2

2

2

2

2

2

2

0

0
0

5

10

15

"Debt (Government)" : Equilibrium(as Debt)"Debt (Government)" : Primary Balance=91%

20
25
30
Time (Year)
2

1

2

1

2

1

2

35
1

2

1

2

1

2

1

2

1

50
2

1

2

0

5

10

15

20
25
30
Time (Year)"Debt-GDP ratio" : Equilibrium(as Debt)"Debt-GDP ratio" : Primary Balance=91%

1
2

35
1

2

1
2

40
1

2

45
1

2

50

1
2

1
2

Figure 12: Accumulation of Government Debt and Debt-GDP Ratio

Deﬁcit = Tax Revenues - Expenditure - Debt Redemption - Interest(13)

Therefore, even if balanced budget is maintained, the government still has tokeep paying its debt redemption and interest. This is why it has to keep borrowing and accumulating its debt. Initial GDP in the model is obtained to be21

386, while government debt is initially set to be 200. Hence, the initial debtGDP ratio is around 0.52 year (similar to the current ratios among EU member
countries). Yet, the ratio continues to increase to 1.45 year at the year 50 in
the model as illustrated by the line 1 in the right diagram of Figure 12. Thisimplies the government debt becomes 1.45 years as high as the annual level ofGDP.
Can such a high debt be sustained? Absolutely no. Eventually this runaway
accumulation of government debt may cause nominal interest rate to increase,because the government may be forced to keep borrowing to pay higher interests,
which may eventually cause hyper-inﬂation4 .
Higher interest rates may in turn trigger a sudden drop of government security price, deteriorating values of ﬁnancial assets owned by banks, producers
and consumers. The devaluation of ﬁnancial assets may force some banks andproducers to go bankrupt eventually. In this way, another ﬁnancial crisis becomes inevitable and government is eventually destined to collapse as well. Thisis one of the hotly debated scenarios about the consequences of the rapidly accumulating debt in Japan, whose debt-GDP ratio in 2009 was 1.893 years; thehighest among OECD countries! Compared with this, debt-GDP ratios in themodel seem to be still modest.
Remarks: if this scenario of ﬁnancial breakdown due to the runaway accumulation of debt fails to be observed in the near future, still there exit somegood reasons to stop the accumulating debt. First, it continues to create unfair
income distribution in favor of bankers and ﬁnancial elite, causing ineﬃcient allocation of resources and economic performances, and eventually social turmoils
by the poor. Second, forced payment of interest forces the indebted producers
to continue incessant economic growth to the limit of environmental carrying
capacity, which eventually leads to the collapse of environment. In short, system
of money as debt is unsustainable as an economic system.

Liquidation of Government Debt
Let us now consider how to avoid such a ﬁnancial crisis and collapse. At the faceof the ﬁnancial crisis as discussed above, suppose that the government is forced
to reduce its debt-GDP ratio to less than 0.6 by the year 50, as required to all
EU members by the Maastricht treaty. To attain this goal, a primary balance
ratio has to be reduced to 0.91 in our economy. In other words, the government
has to make a strong commitment to repay its debt annually by the amount of
9 % of its tax revenues. Let us assume that this reduction is put into action
at the year 6. Under such a radical ﬁnancial reform, as illustrated by the line
2 in the right diagram of Figure 12, debt-GDP ratio will be reduced to around0.56, and the accumulation of debt will be eventually curved (line 2 in the left
diagram).
Even so, this radical ﬁnancial reform becomes very costly to the government
and its people as well. At the next year of the implementation of 9 % reduction
4 This feedback loop from the accumulating debt to the higher interest rate is not yet fully
incorporated in the model.

22

of a primary balance ratio, growth rate is forced to drop to minus 5 %, and theeconomy fails to sustain a full capacity aggregate demand equilibrium of line 1
as illustrated by the line 2 in Figure 13. Compared with the mostly equilibrium
path of line 1, debt-reducing path of line 2 causes business cycles.

GDP (real)
600
1

DollarReal/Year

500

1

1

400

12

12

12

1
2

1

12

12

12

1

12

1

2

12

2

40

45

2

2

2

300

200
0

5

10

15

20
25
30
35
Time (Year)
1
1
1"GDP (real)" : Equilibrium(as Debt)
222"GDP (real)" : Primary Balance=91%

1

1
2

50

1
2

2

Figure 13: Comparison of GDP paths

5

Macroeconomic System of Debt-Free Money

We are now in a position to implement the alternative macroeconomic system
discussed in the introduction, as proposed by the American Monetary Act, inwhich the central bank is incorporated into the government and a fractional reserve banking system is abolished. Let us call this new system a macroeconomic
system of debt-free money. Money issued in this new system plays a role of public utility of medium of exchange. Hence the newly incorporated institution may
be appropriately called the Public Money Administration in this paper.
Under this incorporation, transactions of the government, commercial banks
and the public money authority (formally the central bank) need to be revisedslightly. Let us start with the description of the revised transactions of thegovernment.

Government• Balanced budget is assumed to be maintained; that is, a primary balance
ratio is unitary. Yet the government may still incur deﬁcit due to the debt
redemption and interest payment.

23• Government now has the right to newly issue money whenever its deﬁcit
needs to be funded. The newly issued money becomes seigniorage inﬂow
of the government into its equity or retained earnings account.
• The newly issued money is simultaneously deposited with the reserve account of the Public Money Administration. It is also booked to its deposits
account of the government assets.
• Government could further issue money to ﬁll in GDP gap.
Revised transaction of the government is illustrated in Figure 14. Green stock
box of deposits is newly added to the assets.

Bankstransactions

of

banks

• Banks are now obliged to deposit a 100% fraction of the deposits as the required reserveswith the public money administration.

aresummarizedasfollows.

Required Reserve Ratio
3

1

3

3

23

3

23

23

2

23

3

23

23

2

0.75
2
Dmnl

Revised

0.5
2

0.25

• To meet the demand for loans
0from producers, banks are now
0
5
10
15
20
25
30
35
40
45
50
Time (Year)
allowed to borrow from thepublic money administration
free of interest; that is, former
Figure 15: Required Reserve Ratios
discount rate is now zero. Allocation of money to the banks
will be prioritized according to
the public policies of the government. (This constitutes a market-oriented
issue of new money. Alternatively, the government can also issue newmoney directly through its public policies to ﬁll in GDP gap as alreadydiscussed above.)2

123 123 12311

Required Reserve Ratio : Equilibrium(as Debt)
Required Reserve Ratio : Debt-Free(Gradual Fraction)
Required Reserve Ratio : Debt-Free(100% Fraction)

1

1

1

1

1

3

2

1

1

3

2

1

1

3

2

1

1

3

2

1

1

3

2

1

1

3

2

1

1

3

2

1

1

3

2

Line 1 in Figure 15 illustrates the original required reserve ratio of 5%. We
assume two diﬀerent ways of abolishing a fractional reserve banking system.
Line 2 shows that the 100% fraction is gradually attained in 10 years at theyear 25, starting from the year 10, meanwhile line 3 indicates that the 100%
fraction is attained immediately at the year 10.

Public Money Administration (Formerly Central Bank)
The central bank now becomes incorporated as one of the governmental organizations which is here called the Public Money Administration (PMA). Its
revised transactions become as follows.
24Figure 14: Transactions of Government

25<Interest paid by theGovernment><Government Debt
Redemption><Tax Revenues><Switch(Seigniorage)>

Government
CreditingGovernment
Borrowing

Deposits(Government)

Government
Deficit<Seigniorage><Government
Securities Newly
Issued>Cash (Government)

Base Expenditure

Growth-dependent
Expenditure

Change in Government
Expenditure

Change in
Expenditure<Money as Public
Utility><Tax Revenues>

Time for Fiscal
PolicyPrimary
BalancePrimary Balance
Ratio

Interest paid by theGovernment (Consumer)

Interest paid by theGovernment (Banks)

Interest paid by theGovernment (Central Bank)

Revenue-dependent
Expenditure

Government
Expenditure

SwitchInterest paid by theGovernment<Interest Rate(nominal)><Growth Rate><Interest paid by
the Government>

Primary Balance
Change TimePrimary Balance
ChangeGovernment Debt
Redemption

Government
Debt Period

Initial Debt
(Government)<Corporate Tax>

<Income Tax>

<Tax on
Production>

Money as Public
Utility<Government
Deficit>

Initial Retained
Earnings (Government)

Tax Revenues

Issue Duration

Issue Time

Seigniorage

Switch(Seigniorage)

Government Securities
Newly Issued<GDP(Revenues)>

Initial Cash
(Government)

Retained Earnings(Government)

Debt (Government)

Debt-GDP ratio• The PMA accepts newly issued money of the government as seigniorage
assets and enter the same amount into the government reserve account.
Under this transaction, the government needs not print hard currency,
instead it only sends digital ﬁgures of the new money to the PMA.
• When the government want to withdraw money from their reserve accounts at the PMA, the PMA could issue new money according to therequested amount. In this way, for a time being, former central bank noteand government money coexist in the market.
• With the new issue of money the PMA meets the demand for money bycommercial banks, free of interest, according to the guideline set by thegovernment public policies.
Under the revised transactions, open market operations of sales and purchases of government securities become ineﬀective, simply because government
debt gradually diminishes to zero. Furthermore, discount loan is replaced withinterest-free loan. This lending becomes a sort of open and public window guidance, which once led to the rapid economic growth after world war II in Japan[7]. Accordingly, interest incomes from discount loans and government securities
are reduced to be zero eventually. Transactions of the public money administration are illustrated in Figure 16. Green stock boxes of seigniorage assets andgovernment reserves are newly added.

6

System Behaviors of Debt-Free Money

Liquidation of Government Debt
Under this alternative macroeconomic system of debt-free money, the accumulated debt of the government gets gradually liquidated as demonstrated in Figure
17, which is the same as Figure 12 except that lines 3 and 4 are added here.
Recollect that line 1 was a benchmark debt of the mostly equilibria under thesystem of money as debt, while line 2 was the decreased debt when debt-ratio is
reduced under the same system. Now newly added line 3 indicates that the government debt continues to decline when a gradual fraction ratio is applied, whileline 4 shows a reduction of the government debt when 100% fraction is appliedat the year 10. Both lines coincide, meaning that the abolishment methods ofa fractional level do not aﬀect the liquidation of the government debt, because
banks are allowed to ﬁll in the enough amount of cash shortage by borrowing
from the PMA in the model.
Under the system of debt-free money, a higher GDP is attained, to oursurprise, than the one under the system of money as debt as illustrated bylines 3 & 4 in Figure 18. Moreover, it shows that the gradual abolishment of afractional reserve banking system (line 3) attains a higher GDP than the one bya sudden abolishment of 100% fraction at the year 10 (line 4). In either case,system of debt-free money can be said to be a far better system because of theaccomplishment of higher economic growth without inﬂation.
26

Figure 16: Transactions of the Public Money Administration

27

Growth Rateof Credit<Government
Securities(Consumer)>Open Market
Purchase(Public Sale)<Government
Securities Newly
Issued>Lending
PeriodOpen Market
Purchase

Securities
purchased byCentral Bank

Open Market
Purchase Time

Purchase Period

Open Market
Purchase Operation(temporary)Gold

Banks Debt Redemption(Central Bank)<Government
Securities (Banks)>

Open Market
Purchase(Banks Sale)

Securities
sold byCentral Bank

Open Market
Public Sales Rate

Sales Period

Open Market Sale Time

Open Market Sale
Operation (temporary)

Decrease in
Reserves

Monetary
Base

Notes Withdrown

Open Market Sale
(Banks Purchase)<Government Debt
Redemption><Open Market Sale
(Public Purchase)>

Open Market Sale
Operation (permanent)

Open Market Sale

Open Market Sale
(Public Purchase)

Initial Sequrity Holding
Ratio by Central Bank

Government
Securities(Central Bank)

Security Holding Ratio
by Central Bank

<Interest Income(Central Bank)><Banks Debt
Redemption>

Banks Debt Redemption(Public Money)<Initial Gold heldby the Public><Government
Securities (Consumer)>

Discount Loan
(Central Bank)<Switch(Seigniorage)>

Seigniorate
Assets<Government
Securities (Banks)>

Lending(Central Bank)

Window
Guidance

Open Market
Purchase Operation(permanent)

Lending(Central Bank)(-1)

DesiredLending

Lending (Public
Money)

Lending byCentral Bank

Lending Time

<Seigniorage>

Gold Deposit<Desired
Borrowing(Banks)>

Deposit Time

<Securities sold byCentral Bank> Gold Deposit by
the Public

Retained
Earnings(Central Bank)

Reserves(Central Bank)<Interest paid by theGovernment (CentralBank)>

Interest Income(Central Bank)<Interest paid byBanks (Central Bank)>

Increase in
Reserves<Open Market
Purchase (Banks Sale)><AdjustingReserves><Lending(Central Bank)><Open Market
Purchase (Public Sale)>Gold Certificates<Securities purchased
by Central Bank><Reserves
Deposits>

Notes Newly
Issued<Seigniorage><Lending (Public
Money)>
Reserves by
Banks

Currency
Outstanding<Government
Crediting>Reserves(Government)

Debt (Government)

Debt-GDP ratio

1,000

2
1

750

1
1

1.5

1

1
1
Year

Dollar

1
1

500

1

1

1

1
1

1
1

250

1

12

1

2

1

2

2

2

2

2

2

2

2

2

34

34

0

5

1

34

10

2

2

2

2

2

2

2

2

2

34

34

0

1

12

12

0.5

15

"Debt (Government)" : Equilibrium(as Debt)"Debt (Government)" : Primary Balance=91%"Debt (Government)" : Debt-Free(Gradual Fraction)"Debt (Government)" : Debt-Free(100% Fraction)

34

3

4

34

20
25
30
Time (Year)
1

2

1
3

4

2

1
3

2

4

34

35
1

3

2

4

34

1
3

34

40
2

4

1
3

2

4

50
1

3

34

0

34

45

0

5

10

34

15

"Debt-GDP ratio" : Equilibrium(as Debt)"Debt-GDP ratio" : Primary Balance=91%"Debt-GDP ratio" : Debt-Free(Gradual Fraction)"Debt-GDP ratio" : Debt-Free(100% Fraction)

2

4

34

34

34

34

20
25
30
Time (Year)
1

2

2

4

1
3

2

4

1
3

2

4

3

34

34

35

40

45

1

1

1

2

3

4

2

4

3

2

4

3

50
1

3

2

4

Figure 17: Liquidation of Government Debt and Debt-GDP Ratio

GDP (real)
600

3

3

525
DollarReal/Year3
3

34
12 34 12

375

34 12

34

341 2

1

34

1
1
12

12

1

1

4

34

450

4
4

2

2

2

2

2

300
0

5

10

15

"GDP (real)" : Equilibrium(as Debt)"GDP (real)" : Primary Balance=91%"GDP (real)" : Debt-Free(Gradual Fraction)"GDP (real)" : Debt-Free(100% Fraction)

1

20
25
30
Time (Year)
2

1
3

4

2

1
3

4

2

1
3

4

35
2

1
3

4

2

40
1
3

4

2

45
1
3

4

2

50
1
3

2

4

Figure 18: Comparison of GDP paths
In fact, left diagram in Figure 19 illustrates that price of line 3 increases
at maximum to 1.6% at the year 17, and inﬂation rate of line 3 in the right
diagram is constantly below 0.3% at maximum.

Inﬂation and GDP Gap
Persistent objection to the system of debt-free money has been that government,
once a free-hand power of issuing money is being endowed, tends to issue moremoney than necessary, which tends to bring about inﬂation eventually, though
history shows the opposite [17].
Theoretically, under the existence of GDP gap, increase in the government
expenditure by issuing new money would not cause inﬂation, but stimulate theeconomic growth instead. To examine this case, let us ﬁrst create a GDP gap
by changing the exponent of capital from 0.4 to 0.43 as illustrated by line 128

Inflation Rate

Price
0.02

1.013

3

34
1234

1

2

34

0.9750

3
4

1

1

1

2

3
41

3
41

41

3

2

3

3
4

2

2

2

0.01

1

1

1
4

4

1/Year

Dollar/DollarReal

1.051

0

12

2

2

3

34
341

41
3

1

0.9367

2

2

41

2
3

41

1

34

341

3

2

2

4

12
4

34

2

2

3

12

1

2

-0.01

2

0.8984
0

5

10

15

20
25
30
Time (Year)

Price : Equilibrium(as Debt)
Price : Primary Balance=91%
Price : Debt-Free(Gradual Fraction)
Price : Debt-Free(100% Fraction)

1
2

2

35

40

45

1

1

1

2
3

2
3

4

50

-0.02
0

1

2
3

4

2
3

4

3
4

5

10

Inflation Rate : Equilibrium(as Debt)
Inflation Rate : Primary Balance=91%
Inflation Rate : Debt-Free(Gradual Fraction)
Inflation Rate : Debt-Free(100% Fraction)

4

15

20
25
30
Time (Year)

1

1

2

2

4

1
3

2

4

1
3

2

4

35
1
3

2

4

40
1
3

2

4

45
1
3

2

4

50
1
3

2

4

Figure 19: Price Level and Inﬂation Ratein Figure 20, in which the GDP gap is observed between the year 5 and 10.
Faced with this recession, money as public utility is being newly issued by theamount of 23 for 10 years starting at the year 6. This corresponds to a continualinﬂow of money into circulation as proposed in the introduction. As a result
equilibrium is attained again as illustrated by line 2 in the left diagram, yet
inﬂation does not seem to appear as line 2 of the right diagram indicates.
Inflation Rate

GDP (real)

0.04

600

2
1
2
1

2
1
2
1

400

2
1

2
1

2
1

2
1

2
1

2
1

2

2

2

2
1

2
1

2
1

2
1

2
1

1

1/Year

DollarReal/Year

2
1

0.02

500

2
2
1

1

1

200
3

4

5
1

6

7
8
9
Time (Year)

1
2

2

-0.02
1

1

2

2
1

2

1

1

-0.04
1

2

2

300

0

1

2
1

2
1

"GDP (real)" : GDP Gap"GDP (real)" : GDP Gap1

1

2

0

1
2

1
2

10

1
2

11

1
2

12

1
2

13

1
2

14

1
2

15

0

2

Inflation Rate : GDP Gap
Inflation Rate : GDP Gap1

1
2

2

4

6
8
Time (Year)
1

1
2

1
2

10
1

2

12

1
2

1
2

14
1

2

1
2

2

Figure 20: No Inﬂation under GDP Gap
Inﬂation could occur only when government mismanages the money supply.
To examine this case, let us take a benchmark state attained by the gradualfraction equilibrium, then assume that the government increases its spendingby mistakenly issuing new money by the amount of 10 for 3 years, starting at
the year 10; that is, the government expenditure continues to increase to 74
from 64 for three years.
As being expected, the increase in the government expenditure under theequilibrium state surely causes inﬂation, 2% at the year 13, as illustrated byline 2 of the left diagram of Figure 21, followed by the deﬂation of -2% at theyear 17. To be worse, this inﬂation triggers economic recession of -6.6% at theyear 16 as illustrated by line 2 in the right diagram. Figure 22 shows businesscycles caused by the mismanagement of the increase in money supply when no
GDP gap exists.

29

Inflation Rate

Growth Rate (%)

0.04

10

2

0.02

2

5

12

1

12

2

1

1

12

12

1

1

1

2

12

2

Percent/Year

1/Year

0

1

12

2

2
12

0

1

12

12

1

12

1

1

12

12

2

12

2
2
12

1
1

1

1

2

2

2

-0.02

-5

-0.04

-10

2

0

5

10

Inflation Rate : Debt-Free(Gradual Fraction)
Inflation Rate : Inflation
2

15
2

20
25
30
Time (Year)
1

2

2

1

2

1

1

2

35
2

1

2

40
1

45
1

2

1

2

50
2

1

0

5

10

15

20
25
30
Time (Year)"Growth Rate (%)" : Debt-Free(Gradual Fraction)"Growth Rate (%)" : Inflation
2
2

2

2

2

1

2

1

35
1

2

2

1

40
1

2

2

45
1

2

1

50
2

1

2

Figure 21: Inﬂation under No GDP Gap

GDP (real)
600

1
1

2

2

1

525
DollarReal/Year

12
1

2

12

450

12

375

12

12

12

1

1

1

2

12

12
2

2

300
0

5

10

"GDP (real)" : Debt-Free(Gradual Fraction)"GDP (real)" : Inflation
2

15
2

20
25
30
Time (Year)
2

1

2

1

2

1

2

35
1

2

1

2

40
1

2

45
1

2

1

50
2

1

2

Figure 22: Business Cycles caused by Inﬂation under No GDP Gap

Maximum Tolerable Inﬂation
This could be a serious moral hazard lying under the system of debt-free money,
because the incumbent government tries to cling to the power by unnecessarily stimulating the economy in the years of election as history demonstrates.
Business cycle thus spawned is called political business cycle. “There is someevidence that such a political business cycle exits in the United States, and theFederal Reserve under the control of Congress or the president might make thecycle even more pronounced [6, p.353].” Proponents of the central bank takeadvantage of this cycle as an excuse for establishing the independence of thecentral bank from the intervention by the government. On the contrary, recent
ﬁnancial crises and runaway accumulation of government debt are caused, indeed, by the independence of the central bank under the system of money as
debt.

30

How can we avoid the political business cycle, then, without resorting to the
independence of the central bank? As a system dynamics researcher, I suggest
an introduction, by law, of a feedback loop of stabilizing monetary value which
forces a resignation of the government in case of higher inﬂation, or at least thehead of the Public Money Administration to step down.
How high inﬂation, then, can we be tolerant of? The American Monetary
Act stipulates the maximum interest rate of 8% per year, including all fees.
Because before 1980/1981, forty nine States had “anti-usury” laws
which limited normal interest rates to a maximum of between 6% and
10% p.a. (one state had 12%). The American Monetary Act takes
the middle of this range to represent a restoration of the interest
limits prevailing across the country prior to 1980/1981 [18, p.27].
From the following relation,
Nominal interest rate = Real interest rate + Inﬂation rate(14)

we have, for non-negative real interest rate ≥ 0,
Maximum Nominal interest rate (= 8%) ≥ Inﬂation rate

(15)

That is to say, the maximum tolerable inﬂation rate has to be not higher than
8% under the system of debt-free money. The success of the system depends
on the legalization of a forced step down of the government or the head of the
public money administration in case of the inﬂation rate higher than 8%.

Debt-free Monetary Policy
The role of the public money administration under the macroeconomic system ofdebt-free money is to maintain the monetary value, similar to the role assigned
to the central banks under the system of money as debt. Interest rate is nolonger controlled by the public money administration, and left to be determinedin the market. History shows that bubble and its burst have been caused by
the purposive manipulation of the interest rates such as overnight call rate andfederal fund rate by the privately-owned central bank for the beneﬁts of ﬁnancial
elite. In this sense, we will be ﬁnally freed from the control of the central bank.
Accordingly, the only tool to stabilize the monetary value is through the
public management of the amount of money in circulation. This could be carried out through the control of lending money to the banks and through theﬁscal policy. Speciﬁcally, in case of inﬂationary state, lending money to thebanks may be curbed, or the money in circulation could be sucked back byraising taxes or cutting government spending. In case of deﬂation, demand formoney by the banks would be weak, so that government has to take a strong
leadership by spending more than tax revenues with newly issued money. In
this way, complicated monetary policies such as the manipulation of required
reserve ratio, discount ratio, and open market operations under the system ofmoney as debt are no longer required.
31

Finally, it would be worth mentioning that system of debt-free money isecologically friendly to the environment, because forced payment of interest will
be replaced with interest-free money, and borrowers of money, mainly producers,
need not be driven into forced economic growth at the cost of environmental
destruction. System of debt-free money is indeed a system of sustainability.

7

Conclusion

This paper investigates how to liquidate runaway government debt under thecurrent ﬁnancial crises. First, the current system is identiﬁed as a macroeconomic system of money as debt, under which the accumulation of government
debt is built into the system by the Keynesian theory, and the reduction of debtGDP ratio is, it is demonstrated, very costly, triggering economic recessions andbusiness cycles.
Then the alternative system is suggested as the system of debt-free money,in which only the government can issue money, and the government debt, it
is shown, can to be gradually eliminated. Moreover, it turns out that higher
economic growth is simultaneously attained.
In this sense, the alternative macroeconomic system, from a viewpoint ofsystem design, seems to be worth being implemented if we wish to avoid accumulating government debt, unfair income distribution, repeated ﬁnancial crises,
war and environmental destruction.

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[18] Stephen
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34

Monetary
Institute,