The full text on this page is automatically extracted from the file linked above and may contain errors and inconsistencies.
Vol. 34, No. 1
ECONOMIC REVIEW
1998 Quarter 1
Money
2
by James Madison
James Madison’s Monetary Economics
7
by Bruce D. Smith
Beneficial “Firm Runs”
by Stanley D. Longhofer
FEDERAL RESERVE BANK
OF CLEVELAND
21
2
http://clevelandfed.org/research/review/
Economic Review 1998 Q1
Money
by James Madison
Observations written 1 posterior to the circular
Address of Congress in September 1779, and
prior to their Act of March, 1780. 2
It has been taken for an axiom in all our reasonings on the subject of finance, that supposing the quantity and demand of things vendible
in a country to remain the same, their price will
vary according to the variation in the quantity
of the circulating medium; in other words, that
the value of money will be regulated by its
quantity. I shall submit to the judgment of the
public some considerations which determine
mine to reject the proposition as founded in
error. Should they be deemed not absolutely
conclusive, they seem at least to shew that it is
■ *This essay was originally published in two parts, in the December 19
and 22, 1791, issues of Philip Freneau’s National Gazette of Philadelphia.
The edited, annotated version reprinted here is taken from The Papers of
James Madison, vol. 1, 16 March 1751–16 December 1779, ed. William T.
Hutchinson and William M. E. Rachal (Chicago: University of Chicago
Press, 1962), pp. 302–10. The note referenced by a dagger (†) is James
Madison’s; the numbered notes are those of the University of Chicago
Press editors. This version of the essay is reprinted with the permission of
the University of Chicago Press. © 1962 by the University of Chicago. All
rights reserved.
James Madison was
president of the United
States from 1809 to 1817.*
liable to too many exceptions and restrictions
to be taken for granted as a fundamental truth.
If the circulating medium be of universal
value as specie, a local increase or decrease of
its quantity, will not, whilst a communication
subsists with other countries, produce a correspondent rise or fall in its value. The reason is
obvious. When a redundancy of universal
money prevails in any one country, the holders
of it know their interest too well to waste it in
extravagant prices, when it would be worth
so much more to them elsewhere. When a
deficiency happens, those who hold commodities, rather than part with them at an undervalue in one country, would carry them to
another. The variation of prices in these cases,
cannot therefore exceed the expence and
insurance of transportation.
Suppose a country totally unconnected with
Europe, or with any other country, to possess
specie in the same proportion to circulating
■ 1 The original manuscript of the essay is not known to be extant.
In the Tracy W. McGregor Library, University of Virginia, is a transcript of
about the first one-third of the article, which John C. Payne probably
copied from the newspaper version of it.
3
property that Europe does; prices there would
correspond with those in Europe. Suppose that
so much specie were thrown into circulation as
to make the quantity exceed the proportion of
Europe tenfold, without any change in commodities, or in the demand for them: as soon as
such an augmentation had produced its effect,
prices would rise tenfold; or which is the same
thing, money would be depreciated tenfold. In
this state of things, suppose again, that a free
and ready communication were opened
between this country and Europe, and that the
inhabitants of the former, were made sensible
of the value of their money in the latter; would
not its value among themselves immediately
cease to be regulated by its quantity, and
assimilate itself to the foreign value?
Mr. Hume in his discourse on the balance
of trade supposes, “that if four fifths of all the
money in Britain were annihilated in one night,
and the nation reduced to the same condition,
in this particular, as in the reigns of the Harrys
and Edwards, that the price of all labour and
commodities would sink in proportion, and
every thing be sold as cheap as in those ages:
That, again, if all the money in Britain were
multiplied fivefold in one night, a contrary
effect would follow.” This very ingenious writer
■ 2 Pledging on September 1, 1779, not to increase its $160 million
of outstanding bills of credit by more than 25 percent, and that only in
case of a dire emergency, the Continental Congress had John Jay draft a
“Circular Address” to the states (adopted September 13) exhorting them
to supply enough soldiers, money, and matériel to restore public credit
and advance the common cause. And yet, by March 18, 1780, the gloomy
situation obliged Congress to authorize the states to issue new bills of
credit and declare that the old continental issues would be redeemed at
only one-fortieth of their face value (Journals of the Continental Congress,
XV, 1052–62; XVI, 262–67). Although in the prefatory note Madison
declared that he wrote his essay during the six months intervening between
these two actions by Congress, he probably could have narrowed the time
to the period from late in December 1779 to early in March of the next year.
In his brief third-person autobiography, written long afterward, Madison
mentioned his election to Congress on December 14, 1779, and then
added: “To prepare himself for this service, he employed an unavoidable
detention from it in making himself acquainted with the state of Continental
affairs, and particularly that of the finances which, owing to the depreciation of the paper currency, was truly deplorable. The view he was led to
take of the evil, and its causes, was put on paper, now to be found in several periodical publications, particularly Freneau’s National Gazette.” By
“unavoidable detention” he most likely referred to his necessary preparations at Montpelier for his residence in Philadelphia and the heavy snow
which delayed his departure for that city until March 6, 1780, or for some
days after he had planned to begin the trip. The essay was printed as the
fourth in Madison’s series of seventeen politically tinged articles appearing
in Freneau’s newspaper late in President Washington’s first term. Even
though Madison may have revised his original manuscript before releasing
it for publication, it deals with a problem which was much less acute by
1791 than when he wrote the essay nearly twelve years earlier.
seems not to have considered that in the
reigns of the Harrys and Edwards, the state
of prices in the circumjacent nations corresponded with that of Britain; whereas in
both of his suppositions, it would be no less
than four fifths different. Imagine that such
a difference really existed, and remark the
consequence. Trade is at present carried on
between Britain and the rest of Europe, at a
profit of 15 or 20 per cent. Were that profit
raised to 400 per cent. would not their home
market, in case of such a fall of prices, be so
exhausted by exportation—and in case of
such a rise of prices, be so overstocked with
foreign commodities, as immediately to restore
the general equilibrium? Now, to borrow the
language of the same author, “the same causes
which would redress the inequality were it to
happen, must forever prevent it, without some
violent external operation.” 3
The situation of a country connected by
commercial intercourse with other countries,
may be compared to a single town or province
whose intercourse with other towns and
provinces results from political connection.
Will it be pretended that if the national currency were to be accumulated in a single
town or province, so as to exceed its due
proportion five or tenfold, a correspondent
depreciation would ensue, and every thing
be sold five or ten times as dear as in a neighboring town or province?
If the circulating medium be a municipal
one, as paper currency, still its value does not
depend on its quantity. It depends on the credit
of the state issuing it, and on the time of its
redemption; and is no otherwise affected by
the quantity, than as the quantity may be supposed to endanger or postpone the redemption.
That it depends in part on the credit of the
issuer, no one will deny. If the credit of the
issuer, therefore be perfectly unsuspected, the
time of redemption alone will regulate its value.
To support what is here advanced, it is sufficient to appeal to the nature of paper money. It
consists of bills or notes of obligation payable
in specie to the bearer, either on demand or at
a future day. Of the first kind is the paper currency of Britain, and hence its equivalence to
specie. Of the latter kind is the paper currency
of the United States, and hence its inferiority to
■ 3 Madison accurately reflects the thought, but does not always
quote the exact words, of David Hume in his Political Discourses
(Edinburgh, 1752), pp. 82–83.
4
specie. But if its being redeemable not on
demand but at a future day, be the cause of
its inferiority, the distance of that day, and
not its quantity, ought to be the measure of
that inferiority.
It has been shewn that the value of specie
does not fluctuate according to local fluctuations in its quantity. Great Britain, in which
there is such an immensity of circulating
paper, shews that the value of paper depends
as little on its quantity as that of specie, when
■ 4 The portion of the essay in the issue of the National Gazette
for December 19, 1791, ends here. The remainder is in the issue of
December 22, 1791.
■ † As the depreciation of our money has been ascribed to a wrong
cause, so, it may be remarked, have effects been ascribed to the depreciation, which result from other causes. Money is the instrument by which
men’s wants are supplied, and many who possess it will part with it for that
purpose, who would not gratify themselves at the expence of their visible
property. Many also may acquire it, who have no visible property. By
increasing the quantity of money therefore, you both increase the means
of spending, and stimulate the desire to spend; and if the objects desired
do not increase in proportion, their price must rise from the influence of
the greater demand for them. Should the objects in demand happen, at the
same juncture, as in the United States, to become scarcer, their prices must
rise in a double proportion.
It is by this influence of an augmentation of money on demand, that we
ought to account for that proportional level of money, in all countries,
which Mr. Hume attributes to its direct influence on prices. When an
augmentation of the national coin takes place, it may be supposed either,
1. not to augment demand at all; or, 2. to augment it so gradually that
a proportional increase of industry will supply the objects of it; or, 3. to
augment it so rapidly that the domestic market may prove inadequate,
whilst the taste for distinction natural to wealth, inspires, at the same time,
a preference for foreign luxuries. The first case can seldom happen. Were
it to happen, no change in prices, nor any efflux of money, would ensue;
unless indeed, it should be employed or loaned abroad. The superfluous
portion would be either hoarded or turned into plate. The second case can
occur only where the augmentation of money advances with a very slow
and equable pace; and would be attended neither with a rise of prices,
nor with a superfluity of money. The third is the only case, in which the
plenty of money would occasion it to overflow into other countries. The
insufficiency of the home market to satisfy the demand would be supplied
from such countries as might afford the articles in demand; and the money
would thus be drained off, till that and the demand excited by it, should
fall to a proper level, and a balance be thereby restored between exports
and imports.
The principle on which Mr. Hume’s theory, and that of Montesquieu’s
before him, is founded, is manifestly erroneous. He considers the money
in every country as the representative of the whole circulating property
and industry in the country; and thence concludes, that every variation
in its quantity must increase or lessen the portion which represents the
same portion of property and labor. The error lies in supposing, that
because money serves to measure the value of all things, it represents
and is equal in value to all things. The circulating property in every country,
according to its market rate, far exceeds the amount of its money. At Athens
oxen, at Rome sheep, were once used as a measure of the value of other
things. It will hardly be supposed, they were therefore equal in value to
all other things.
the paper represents specie payable on
demand. Let us suppose that the circulating
notes of Great Britain, instead of being payable
on demand, were to be redeemed at a future
day, at the end of one year for example, and
that no interest was due on them. If the same
assurance prevailed that at the end of the year
they would be equivalent to specie, as now prevails that they are every moment equivalent,
would any other effect result from such a
change, except that the notes would suffer a
depreciation equal to one year’s interest? They
would in that case represent, not the nominal
sum expressed on the face of them, but the sum
remaining after a deduction of one year’s interest. But if when they represent the full nominal
sum of specie, their circulation contributes no
more to depreciate them, than the circulation
of the specie itself would do; does it not follow,
that if they represented a sum of specie less
than the nominal inscription, their circulation
ought to depreciate them no more than so
much specie, if substituted, would depreciate
itself ? We may extend the time from one, to
five, or to twenty years; but we shall find no
other rule of depreciation than the loss of the
intermediate interest.
What has been here supposed with respect
to Great Britain has actually taken place in the
United States. Being engaged in a necessary
war without specie to defray the expence,
or to support paper emissions for that purpose
redeemable on demand, and being at the
same time unable to borrow, no resource was
left, but to emit bills of credit to be redeemed
in future. The inferiority of these bills to specie
was therefore incident to the very nature of
them. If they had been exchangeable on
demand for specie, they would have been
equivalent to it; as they were not exchangeable on demand, they were inferior to it. The
degree of their inferiority must consequently
be estimated by the time of their becoming
exchangeable for specie, that is the time of
their redemption.
To make it still more palpable that the
value of our currency does not depend on
its quantity, let us put the case, that Congress
had, during the first year of the war, emitted
five millions of dollars to be redeemed at the
end of ten years; that, during the second year
of the war, they had emitted ten millions
more, but with due security that the whole
fifteen millions should be redeemed in five
years; that, during the two succeeding years,
they had augmented the emissions to one hundred millions, but from the discovery of some
5
extraordinary sources of wealth, had been
able to engage for the redemption of the
whole sum in one year: it is asked, whether
the depreciation, under these circumstances,
would have increased as the quantity of
money increased—or whether on the contrary, the money would not have risen in
value, at every accession to its quantity? 4
It has indeed happened, that a progressive
depreciation of our currency has accompanied
its growing quantity; and to this is probably
owing in a great measure the prevalence of the
doctrine here opposed. When the fact however
is explained, it will be found to coincide perfectly with what has been said. Every one must
have taken notice that, in the emissions of Congress, no precise time has been stipulated for
their redemption, nor any specific provision
made for that purpose. A general promise entitling the bearer to so many dollars of metal as
the paper bills express, has been the only basis
of their credit. Every one therefore has been
left to his own conjectures as to the time the
redemption would be fulfilled; and as every
addition made to the quantity in circulation,
would naturally be supposed to remove to a
proportionally greater distance the redemption
of the whole mass, it could not happen otherwise than that every additional emission would
be followed by a further depreciation.
In like manner has the effect of a distrust
of public credit, the other source of depreciation, been erroneously imputed to the quantity
of money. The circumstances under which
our early emissions were made, could not
but strongly concur, with the futurity of their
redemption, to debase their value. The situation
of the United States resembled that of an individual engaged in an expensive undertaking,
carried on, for want of cash, with bonds and
notes secured on an estate to which his title
was disputed; and who had besides, a combination of enemies employing every artifice
to disparage that security. A train of sinister
events during the early stages of the war likewise contributed to increase the distrust of
the public ability to fulfill their engagements.
Before the depreciation arising from this cause
was removed by the success of our arms, and
our alliance with France, it had drawn so large
a quantity into circulation, that the quantity
itself soon after begat a distrust of the public
disposition to fulfill their engagements; as well
as new doubts, in timid minds, concerning
the issue of the contest. From that period, this
cause of depreciation has been incessantly
operating. It has first conduced to swell the
amount of necessary emissions, and from
that very amount has derived new force and
efficacy to itself. Thus, a further discredit of
our money has necessarily followed the augmentation of its quantity; but every one must
perceive, that it has not been the effect of the
quantity, considered in itself, but considered
as an omen of public bankruptcy. † 5
Whether the money of a country, then, be
gold and silver, or paper currency, it appears
that its value is not regulated by its quantity.
If it be the former, its value depends on the
general proportion of gold and silver, to
circulating property throughout all countries
having free inter communication. If the latter,
it depend[s] on the credit of the state issuing
it, and the time at which it is to become equal
to gold and silver.
Every circumstance which has been found
to accelerate the depreciation of our currency
naturally resolves itself into these general principles. The spirit of monopoly hath affected
it in no other way than by creating an artificial
scarcity of commodities wanted for public
use, the consequence of which has been an
increase of their price, and of the necessary
emissions. Now it is this increase of emissions
which has been shewn to lengthen the supposed period of their redemption, and to
foster suspicions of public credit. Monopolies
destroy the natural relation between money
and commodities; but it is by raising the
value of the latter, not by debasing that of
the former. Had our money been gold or
silver, the same prevalence of monopoly
would have had the same effect on prices
and expenditures; but these would not have
had the same effect on the value of money.
The depreciation of our money has been
charged on misconduct in the purchasing
departments: but this misconduct must have
operated in the same manner as the spirit of
monopoly. By unnecessarily raising the price
of articles required for public use, it has
swelled the amount of necessary emissions,
on which has depended the general opinion
concerning the time and the probability of
their redemption.
■ 5 Madison’s entire footnote is in italics in the National Gazette.
In the last paragraph of the footnote, he refers to Book XXII of Montesquieu’s De l’esprit des lois, first published in Geneva in 1748 and
soon thereafter translated into English. Madison’s daring in challenging
the correctness of this redoubtable authority is noted by Paul Merrill
Spurlin in his Montesquieu in America, 1760–1801 (Baton Rouge, La.,
1940), pp. 175–76.
6
The same remark may be applied to the
deficiency of imported commodities. The deficiency of these commodities has raised
the price of them; the rise of their price has
increased the emissions for purchasing them;
and with the increase of emissions, have
increased suspicions concerning their redemption. Those who consider the quantity of
money as the criterion of its value, compute
the intrinsic depreciation of our currency by
dividing the whole mass by the supposed
necessary medium of circulation. Thus supposing the medium necessary for the United States
to be 30,000,000 dollars, and the circulating
emissions to be 200,000,000 the intrinsic difference between paper and specie will be nearly
as 7 for 1. If its value depends on the time of
its redemption, as hath been above maintained,
the real difference will be found to be considerably less. Suppose the period necessary for its
redemption to be 18 years, as seems to be
understood by Congress; 100 dollars of paper
18 years hence will be equal in value to 100
dollars of specie; for at the end of that term,
100 dollars of specie may be demanded for
them. They must consequently at this time
be equal to as much specie as, with compound
interest, will amount, in that number of years,
to 100 dollars. If the interest of money be rated
at 5 per cent. this present sum of specie will be
about 41 1-2 dollars. Admit, however the use of
money to be worth 6 per cent. about 35 dollars
will then amount in 18 years to 100. 35 dollars
of specie therefore is at this time equal to 100
of paper; that is, the man who would exchange
his specie for paper at this discount, and lock it
in his desk for 18 years, would get 6 per cent.
for his money. The proportion of 100 to 35 is
less than 3 to 1. The intrinsic depreciation of
our money therefore, according to this rule of
computation, is less than 3 to 1; instead of 7 to
1, according to the rule espoused in the circular
address, 6 or 30 or 40 to 1, according to its currency in the market.
I shall conclude with observing, that if the
preceding principles and reasoning be just,
the plan on which our domestic loans have
been obtained, must have operated in a manner directly contrary to what was intended. A
loan-office certificate differs in nothing from
a common bill of credit, except in its higher
■ 6
See note 2.
denomination, and in the interest allowed
on it; and the interest is allowed, merely as
a compensation to the lender, for exchanging
a number of small bills, which being easily
transferable, are most convenient, for a single
one so large as not to be transferable in ordinary transactions. As the certificates, however,
do circulate in many of the more considerable
transactions, it may justly be questioned, even
on the supposition that the value of money
depended on its quantity, whether the advantage to the public from the exchange, would
justify the terms of it. But dismissing this consideration, I ask whether such loans do in any
shape, lessen the public debt, and thereby
render the discharge of it less suspected or
less remote? Do they give any new assurance
that a paper dollar will be one day equal to a
silver dollar, or do they shorten the distance of
that day? Far from it: The certificates constitute
a part of the public debt no less than the bills
of credit exchanged for them, and have an
equal claim to redemption within the general
period; nay, are to be paid off long before the
expiration of that period, with bills of credit,
which will thus return into the general mass,
to be redeemed along with it. Were these bills,
therefore, not to be taken out of circulation
at all, by means of the certificates, not only
the expence of offices for exchanging, reexchanging, and annually paying the interest,
would be avoided; but the whole sum of
interest would be saved, which must make
a formidable addition to the public emissions,
protract the period of their redemption, and
proportionally increase their depreciation. No
expedient could perhaps have been devised
more preposterous and unlucky. In order to
relieve public credit sinking under the weight
of an enormous debt, we invest new expenditures. In order to raise the value of our money,
which depends on the time of its redemption,
we have recourse to a measure which removes
its redemption to a more distant day. Instead
of paying off the capital to the public creditors,
we give them an enormous interest to change
the name of the bit of paper which expresses
the sum due to them; and think it a piece of
dexterity in finance, by emitting loan office
certificates, to elude the necessity of emitting
bills of credit.
7
James Madison’s
Monetary Economics
by Bruce D. Smith
Introduction
James Madison's essay, “Money” (pp. 2–6 as
reprinted here), considers issues that are as
timely and important today as they were when
it was first written. While his concern with an
eighteenth-century economy and his focus on
an ultimate return to a gold standard may seem
to relegate his writings to the history of economic thought, he was in fact wrestling with
questions that have been central to monetary
theory and policymaking for more than two
centuries. Even now, his way of framing these
issues creates a wonderful opportunity for
contrasting two fundamentally different views
of monetary policy’s role and function.
Madison, of course, wrote as a member of a
Revolutionary government that faced profound
fiscal and monetary policy problems. With no
■ 1 This figure, which refers to the period 1775–79, is from
Ferguson (1961, pp. 43–44). It contrasts markedly with the
fraction of expenditures financed through seignorage revenue
in any modern economy.
■ 2 See Ferguson (1961) and Nevins (1927, p. 481).
Bruce D. Smith is a professor of economics at
the University of Texas at
Austin. He thanks Jerry L.
Jordan and participants in
a seminar at the Federal
Reserve Bank of Cleveland
for their helpful comments.
established tax base and little ability to borrow
in the conventional “capital markets” of the
day, it confronted huge wartime expenditures
against a great power. With no alternative but
to run large deficits and monetize them, this
government accomplished the astounding feat
of financing 82 percent of its expenditures by
printing money. 1
Needless to say, this achievement had
its cost. The massive printing of money was
associated with a major inflation, which accelerated over time. In January 1777, $1.25 in
Continental currency could purchase $1.00
in gold, reflecting a relatively modest depreciation of 25 percent during the first year and a
half of the war. By January 1781, however,
$100 Continental was required to purchase
$1.00 in gold.
What was the source of this inflation? The
conventional answer—with which Madison
takes issue—is the quantity of money printed.
Madison (p. 6) makes a fairly standard guess
that puts the prewar money supply of the 13
colonies at $30,000,000. During the war, the
Federal government issued $226,000,000 in
Continental currency, and the states issued a
similar amount.2 Was this the “cause” of the
8
inflation? Or was it rather that the size of the
deficit, combined with the behavior of prices,
forced that much money to be printed? And
could such a large inflation have been averted?
In analyzing Madison’s response, it is important to note carefully how the wartime currency
was created. In 1775, the money supply of the
13 colonies consisted of paper printed by the
individual colonies plus gold and silver coin.3
Colonial governments did not redeem their
paper currencies in specie, but they did sometimes promise to do so in the future, and they
typically made taxes payable in either paper
money or specie, accepting paper at a fixed
rate in terms of specie. When the Continental
Congress began issuing its own money in 1775,
it followed the same system. Continental dollars
were not redeemable in gold or silver, but the
Congress promised postwar redemption of
paper into gold on a one-for-one basis, and it
also made paper money acceptable for taxes
on the same basis as coin.
Madison’s writings presumed that the government would honor its promise of a onefor-one redemption. While that faith eventually
proved unfounded,4 one could ask a counterfactual question: What would have happened
if the government’s promise of redemption had
been believed and had been honored?
This question is motivated by much more
than pure intellectual curiosity. Over and over
again, governments facing large wartime
expenditures have suspended gold standards,
issued then-irredeemable paper money, and
promised to resume gold convertibility at some
date after the war’s end. Some examples of particular importance in monetary history include
Britain during and after the Napoleonic Wars
and World War I and the United States during
and after the Civil War. In each case, there was
some wartime inflation, accompanied either by
contemporary or later historical debate over
whether “better”—that is, less inflationary—
policies were available. Invariably, there was
■ 3 See Smith (1988) and Rolnick, Smith, and Weber (1994) for a
discussion of this period.
■ 4 The ultimate redemption rate was 3 cents on the dollar
(Ferguson [1961]).
■ 5 For discussions of the quantity theory of money, see Friedman
(1956) and Lucas (1980). Also, while I will follow Madison in using the
term “money,” note that his arguments apply equally to any expansion in
the stock of government liabilities. Viewed from this perspective, Madison’s assertions are less obviously in conflict with the quantity theory than
they may first appear to be.
also a postwar deflation before resumption of
a gold standard. And indeed, there were substantial deflations in many parts of the United
States after the Revolution; in some places,
these were just as pronounced as wartime
inflation. For example, by 1786 prices in Pennsylvania had returned to their 1773 levels
(Bezanson [1951, p. 174]).
The fact that the policies followed by the
Revolutionary government—while no doubt
necessary for it—have been so widely adopted
elsewhere suggests that Madison’s concerns are
of interest in a far broader context than just that
of the Revolutionary War. In fact, he addressed
a number of issues that remain basic in monetary theory to this day, including:
i. To what extent is inflation determined
by money growth? Is this all that matters,
as is often asserted, or does it matter
almost not at all, as Madison argued?
ii. If money growth is not all that matters,
does the degree of inflation depend
on the nature of the government’s
promises about “backing” its money
in the future through gold redemption
or some other scheme?
iii. Madison’s argument about the lack of
inflation resulting from money growth
is not based on any commitment to
reduce the money stock at some future
date. Thus, he asserts that some future
redemption in gold—essentially, a commitment to future price-level stabilization
or “targeting”—is adequate to prevent
money growth from raising the price
level today. This seems in conflict with
the quantity theory of money, namely,
that inflation is always and everywhere a
monetary phenomenon.5 What is the theoretical foundation for Madison’s view?
iv. Wisdom that was, at least until recently,
“conventional” asserts that it is always
less inflationary to finance a deficit by
borrowing (issuing bonds) than by printing money. At the end of his essay, Madison denies the validity of this wisdom.
The first three of these issues relate to one
of the oldest debates in monetary economics:
Does a permanent increase in the money supply necessarily raise the price level? Most
adherents of the quantity theory would argue
that the answer is yes, and their viewpoint
currently prevails in the formulation of monetary policy. However, a competing school of
thought argues that permanent increases in
the money supply need not be inflationary
9
if accompanied by appropriate “backing” of
the newly created money. The modern intellectual foundations of this idea, which has
ancient antecedents,6 appear in Tobin (1963),
Wallace (1981), Sargent (1982), Sargent
and Wallace (1982), and Sargent and Smith
(1987a,b). Most of the backing discussed in
this literature assumes that increases in the
money supply are accompanied by government asset acquisitions of equal value; hence,
this reasoning can be applied in only a limited
way even to temporary deficit monetization.
Madison argues that the government can print
money to finance temporary deficits, backed
by a promise of future redemption (but not
retirement), and that the only resulting inflation
will be due to the delay in redemption. Moreover, he strongly denies that the behavior
of the price level should depend in any way
on the quantity of money printed, unless this
delays the time to redemption.7 He also asserts
that delays in future redemption put upward
pressure on the current price level.
The remainder of this article constitutes a
modern theoretical attempt to formalize and
evaluate Madison’s views. To a large extent,
my conclusions are favorable to his line of
argument. The commitment to a future redemption, which is little more than a pledge
to stabilize prices in the future, is enough to
break the link between money growth and
inflation. In addition, his assertion that delayed
redemption puts upward pressure on the price
level is also strongly supported. However,
the analysis does not suggest that price-level
behavior is fully independent of changes in the
money stock. In this respect, Madison seems to
have gone too far.
To be fair to him, a formal theoretical analysis should capture the main economic aspects
of his reasoning. I take these to be as follows:
i. Money is held primarily as an asset. If
it constitutes a future claim to specie, its
current value should be just the discounted present value of that claim.
■ 6 See Mints (1945) for a discussion of this idea, as well as
for criticisms.
■ 7 Note that one could also cast this as an increase in the stock
of outstanding government debt without affecting the market value of
the debt, unless it delayed the time to redemption.
■ 8 The model closely resembles that of Sargent and Wallace (1983).
ii. As a corollary, if other assets earn a
higher return than money, this happens
only because they involve some “inconvenience,” such as being issued in excessively large denominations.
iii. An alternative asset to money exists. The
real rate of interest on it is unaffected by
government policy (although it need not
always be held in positive quantities).
In the subsequent section, I build a model
incorporating these features and apply it to
some of the issues that concerned Madison. In
doing so, I gloss over some other issues that
he took up, but the concluding section offers
comments on them as well.
I. The Environment
To illustrate Madison’s points, I consider a twoperiod-lived, overlapping-generations model of
a particularly simple variety.8 At each date
t = 0, 1, ..., a set of N identical agents is born.
They are endowed in both periods with some
of a single perishable consumption good; let
wj ( j = 1, 2) denote the age j endowment of a
representative agent. I assume throughout that
w 1 > 0 and w 2 > 0.
In addition, agents have access to a
reversible linear technology which allows
one unit of current consumption to be converted into φ > 0 ounces of gold (and back
again, if desired). One possible interpretation
of the technology is that this is a small open
economy operating in a world on a gold standard, so that the consumption good can always
be bought or sold abroad at a fixed rate for
some amount of gold. Such an interpretation
would obviously be fairly appropriate to the
economy in which Madison lived.
Once obtained, gold can either be stored in
raw form or—if the domestic economy is on a
gold standard—it can be coined. In either
case, it depreciates at the rate δ ∈ (0,1).
Each young agent values age j consumption,
denoted cj , according to the (common) utility
function ln c1 + β ln c2 . Note that gold is then
not held by agents for its consumption value; it
is held—if at all—only as an asset.
It will be necessary in what follows to allow
for the possibility that agents born at certain
dates face a government-levied tax. Any direct
taxes that the government does levy are lumpsum in nature. I also assume that agents pay
these taxes (if at all) only when old.
The following notation will prove useful:
Suppose an agent, born at date t, pays a lump-
10
sum tax of τ t + 1 when old and faces a gross rate
of return on a single asset of rt + 1 between t
and t + 1. Then, let s (w1 ,w2 – τ t + 1,rt + 1 )
denote the savings function of this agent.
Given the assumed form of the utility function,
clearly
βw 1
w – τt + 1
.
(1) s (w 1, w 2 – τt + 1,rt +1) = 1 + β – (1 2+ β )r
t +1
I will assume that agents are willing to save,
even if they must do so by storing gold in raw
form; I therefore impose an assumption: 9
Assumption 1. s (w 1,w 2 ,1 – δ ) > 0.
II. The Government
The government that Madison contemplated
as he wrote had large wartime spending needs
and very limited powers of taxation. The result
was a massive government budget deficit that
was financed by printing paper money.
In Madison’s vision—which essentially
eventuated in practice—the war would be
followed by a period of peace accompanied
by a relatively balanced government budget,
or perhaps even one in surplus. During this
time, wartime paper money would continue
to circulate.10 After a transitional period, the
paper money would be retired, having been
converted into gold at some specified rate.
Thereafter, the economy would remain on a
gold standard, and Madison (as well as others)
probably envisioned a purely metallic currency
from that point onward.
In consonance with this scenario, I consider
a government confronting the following circumstances. For dates t = 0, 1, ..., T1, the government has a real per capita expenditure (and
deficit) level of g > 0.11 It finances expenditures solely by printing paper currency that is
not then redeemable, but that it promises to
convert into gold at some future date.
■ 9 Assumption 1 is equivalent to β w 1 (1 - δ ) > w 2.
■ 10 Of course, this did not happen after the Revolution, as the
phrase "not worth a Continental" indicates. However, a good deal of new
paper money was created, by both state and federal governments, from
1783 to 1789. For an overview of this period, see Rolnick, Smith, and
Weber (1994).
■ 11 As noted above, the Revolutionary government financed about
82 percent of its expenditures by printing money. Thus, the implied
abstraction from tax revenue is well founded.
During this period, the government confronts the budget constraint
(2) g = (Mt – Mt – 1 )/pt ; t = 0, ..., T1
where Mt is the stock of paper currency outstanding at t, and pt is the time t price level.
The initial money stock M – 1 is given as an
initial condition. For simplicity— and consistency with the realities of a Revolutionary
government—I set M – 1 = 0.
The government has no direct expenditures
for dates t > T1. I assume that for t = T1 + 1, ...,
T – 1, it engages in no activity whatsoever,
and neither adds to nor subtracts from the
existing stock of money. A gold standard has
not yet been established, and the money is
not yet redeemable. Thus, for t = T1, ..., T – 1,
Mt = MT holds. This corresponds to the transi1
tional period prior to establishment of a full
gold standard.
At date T, the government “calls in” the
existing stock of paper currency and replaces
it dollar for dollar with gold coins which it
mints—at its own expense—at that date.
Thereafter, it stands ready to coin freely any
gold brought to the mint by private agents.
The government coins gold dollars and establishes a mint ratio b stating the number of
ounces of gold in a newly minted gold dollar.
Any subsequent change in the money supply is
purely the result of minting and melting activity
by the private sector. There are no policyinduced changes in the money supply, nor is
there any further government expenditure. I
also assume that there is no uncertainty or lack
of commitment, so that the transitional dates
T1 and T are known in advance by everyone.
At T, the government must mint enough
new coins to redeem the existing money stock
and must raise some resources for this purpose.
Let nTg be the number of new gold coins, in
dollars, created by the government at T.
Clearly nTg = MT must hold. Moreover,
1
to mint nTg new gold dollars, the government
requires nTg (b/φ ) units of the consumption
good, which it obtains by levying a lumpsum tax on old agents at T. Since there is
no other taxation at any date, under the
policy described,
(3) τT = nTg (b/φ ) = MT (b/φ )
1
τt = 0; t ≠ T.
After date T – 1, the entire stock of money
consists of gold dollars. I assume that gold
11
coins circulate by weight,12 and I let Gt denote
the stock of gold dollars—by weight—at t.
As before, pt continues to denote the time t
price level.
(6) c 2t ≤ w 2 + mt (pt /pt + 1 )
+ (1 – δ )( gt /φ ).
The solution to this problem sets
III. The Behavior of Agents
(7) mt + gt = s (w 1,w 2,pt /pt + 1 )
In this section, I describe the behavior of agents
and
before, during, and after the implementation of
a gold standard.
(8) [(pt /pt + 1 ) – (1 – δ )]gt = 0.
The Paper Money Regime (t < T – 1)
For all t < T, paper currency is in circulation
(although the promise of ultimate redemption
is understood and believed). I also focus on the
situation where paper money is accepted voluntarily in exchange for private assets.13 Since
agents can choose between holding money and
holding raw gold as an asset,14 clearly money
will be held only if it earns a real return as
great as that on raw gold.15 The gross real
return on paper currency between t and t + 1
is given by pt /pt + 1, and the gross real return
on storage of raw gold is 1 – δ. Thus,
(4) pt /pt + 1 ≥ 1 – δ; t = 0, ..., T – 1
must hold.
Let gt denote the storage of raw gold by a
young agent at t, and let mt denote the accumulation of real balances. Then gt , mt , and a
consumption profile (c 1t ,c 2t ) are chosen to
maximize ln c 1t + β ln c 2t , subject to
(5) c 1t + mt + ( gt /φ ) ≤ w 1
and
Equation (8) asserts that, if the return on
money exceeds that on the storage of raw gold,
no raw gold will be stored.
The Transition (t = T – 1)
Young agents born at T – 1 will live through the
transition to a gold standard; when old, they
will bear the costs of this transition. They thus
bear the lump-sum tax, τ T ,when old.
In addition, when old, these agents will have
the opportunity to coin or melt gold. Let ntj be
the coinage (or melting, if negative) of gold by
a representative agent of age j ( j = 1,2) in
period t. Clearly this coinage can be nonzero
only for t ≥ T. Young agents born at T - 1
choose a level of real balances, m T – 1, a quantity of raw gold storage, g T - 1, a consumption
profile (c 1T – 1 ,c 2T – 1 ), and a minting/melting
strategy when old nT2 , to maximize ln c 1T – 1
+ β ln c 2T – 1 , subject to
(9) c 1T – 1 + m T – 1 + ( gT – 1 /φ ) ≤ w 1
and
(10) c 2T – 1 ≤ w 2 – τT + m T – 1 ( pT – 1 /pT )
+ (1 – δ )( gT – 1 /φ ) + nT2 [(1/pT ) – (b/φ )],
■ 12 I could assume equally well that coins circulate according to
their face value (“by tale”). Each outcome is an equilibrium, and it makes
no qualitative difference to the results which situation obtains. For a discussion of coins that circulate by tale, see Sargent and Smith (1997).
■ 13 In practice, during the Revolution, the army often seized what it
needed, offering a choice of paper liabilities or nothing in exchange.
Clearly here, when paper money was taken, it was not taken voluntarily.
Madison obviously conceived of a situation where agents take money for
goods of their own volition.
■ 14 And since there is no uncertainty.
■ 15 Parenthetically, Madison's argument implies that he regarded
money as an asset, earning a return competitive with that on relatively
close substitutes.
where the last term in (10) represents the profit
from using (b/φ ) units of resources to obtain
nT2 gold dollars, which then have a purchasing
power of nT2 /pT .
An absence of arbitrage opportunities
requires that
(11) pT = φ /b.
When (11) holds, as it must in equilibrium,
the total savings of a young agent at T – 1
must satisfy
(12) m T – 1 + gT – 1 = s(w 1,w 2 ,pT – 1 /pT ).
In addition, gT – 1 = 0 holds if pT – 1 /pT > 1 – δ.
12
A Gold Standard (t ≥ T )
For t ≥ T, the economy is on a gold standard.
No further taxes are levied, and all agents, old
and young, have the opportunity to mint and
melt coins at all dates. As before, agents can
select a level of real balances, m t (now held in
the form of gold coins), a quantity of raw gold
to store, g t , a consumption profile, (c 1t ,c 2t ),
and a minting/melting strategy, (n t2 ,n t2 ), to
maximize ln c 1t + β ln c 2t , subject to
(13) c 1t + m t + ( gt /φ ) ≤ w 1
+ n 1t [(1/p t ) – (b/φ )]
and
(14) c 2t ≤ w 2 + mt (1 – δ )( pt /pt + 1)
+ ( gt /φ )(1 – δ ) + n 2t + 1 [(1//pt + 1)
– (b/φ )].
The real balance term in (14) must now be
multiplied by 1 – δ , since gold coins circulate
by weight and depreciate at the rate δ .
As before, an absence of arbitrage opportunities associated with minting and melting
requires that
(15) pt = φ /b; t ≥ T.
In addition, the price stability revealed in (15)
implies that there is never any reason for agents
to store raw gold rather than hold gold coins.
Hence, without loss of generality, we can take
g t = 0; t ≥ T. Then, agents save entirely in the
form of gold, which earns a gross real return of
(1 – δ )( pt /pt + 1) = (1 – δ ), where the equality
follows from (15). Real balances per capita are
then given by
(16) mt = s (w1,w2 ,1 – δ ); t ≤ T.
IV. A General Equilibrium
For t ≥ T, it is clear what must happen in
equilibrium. Equation (15) gives the price
level. The nominal per capita gold stock at t,
Gt , must then obey
(17) Gt = pt s (w 1,w 2 ,1 – δ )
= (φ /b)s (w 1,w 2 ,1 – δ ); t ≥ T.
Since the nominal gold stock (in ounces) is
constant, private minting/melting in each
period must just replace the depreciated
gold stock:
(18) (n 1t + n t2 )/2 = δ Gt – 1 ; t ≥ T + 1.
In periods before the advent of the gold
standard, there is a much richer variety of possible equilibrium outcomes.16 Here I construct
an equilibrium having certain features and then
display the restrictions on parameters required
for those features to emerge. The equilibrium
features I consider are chosen for two reasons.
First, they seem illustrative of what Madison
had in mind. Second, for much of history,
economies have abandoned gold standards in
time of war and financed their deficits by printing paper money. With the cessation of hostilities, the government budget is roughly balanced (or even in surplus), although gold
convertibility is not immediately resumed. A
postwar deflation occurs during this period, terminating with the resumption of gold convertibility. Indeed, such a pattern was observed
through much of the United States following
both the Revolutionary War and the Civil War,
and in the United Kingdom after World War I.
For these reasons, I focus on equilibria which
display inflation for t = 0, 1, ..., T1, followed by
a deflation for t = T1 + 1, ..., T. This deflation
ends with conversion to a gold standard.
The Deflation ( t = T 1 + 1, ..., T )
In this section, I state conditions under which
there is an equilibrium satisfying
(19) pt ≥ pt
+ 1;
t = T1, ..., T – 1.
Note that (19) implies that no agent will wish to
store raw gold during the period in question.
At date T – 1, young agents understand that
they will be required to pay for the transition to
a gold standard. In addition, since they store
no gold when young, the time T – 1 equilibrium condition in the money market is that
(20) MT – 1 /pT – 1 = MT /pT – 1
1
= s (w 1,w 2 – τT , pT – 1 /pT ) = β w 1 /(1 + β )
– (w 2 – τT )/(1 + β )( pT – 1 /pT ).
■ 16 This is not to say that any given economy has multiple possible equilibrium outcomes. Rather, different economies may have equilibria that look quite different from one another.
13
Substituting (3) and (11) into (20), and solving
for MT /pT – 1 yields the equilibrium level of real
1
balances at T – 1:
The following proposition fully describes the
behavior of the price level during this deflation,
given the inherited money supply MT :
(21) MT /pT – 1 = w 1 – w 2 (φ /b)/β pT – 1 .
PROPOSITION 1. For t = T 1 + 1, ..., T – 1, the
price level satisfies
1
Equation (21) implies that the time T – 1 price
level is given by
1
(28) pt = (φ /b)(w 2 /βw 1)T – t
(22) pT – 1 = (MT /w 1) + (φ /b)(w 2 /β w 1).
+ MT {w 1–1 (w 2 /βw 1)T – (t + 1)
Notice that pT – 1 ≥ pT = (φ /b) holds iff
+ [(1+ β )/βw 1] [1 – (w 2 /βw 1)T – (t + 1)]
1
(23) MT
1
1
≥ (φ /b)[w 1 – (w 2 / β )]
= (φ /b)
5
1+β
β
÷ [1 – (w 2 /βw 1 )] }.
6 s (w ,w ,1)
1
2
is satisfied. Below I derive restrictions on parameters implying that (23) holds.
For t = T1 + 1, ..., T – 2, young agents will
experience no regime transitions and will bear
no taxation. In addition, (19) implies that they
will store no gold. Hence the equilibrium level
of real balances at these dates is given by
(24) Mt /pt = MT /pt = s (w 1,w 2 ,pt /pt + 1)
1
= βw 1/(1 + β ) – w 2
÷ (1 + β )( pt /pt + 1 ).
Equation (24) can be solved for pt in terms of
pt + 1; the implied solution is
(25) pt = MT [(1 + β )/βw 1] + (w 2 /βw 1)pt + 1;
1
t = T1 + 1, ..., T – 2.
Equations (22) and (25) describe the evolution
of the price level during the transitional period
prior to the establishment of a gold standard.
Equation (25) implies that pt ≥ pt + 1 is satisfied iff
(26) MT /pt + 1 ≥ βw 1/(1 + β ) – w 2 /(1 + β )
Proposition 1 is easily verified by a comparison
of equations (22), (25), and (28).
The Inflation ( t ≤ T 1)
It remains to describe the evolution of the
money supply and the price level during
the wartime period of positive government
expenditure, which was obviously the issue
that concerned Madison. In addition, he
believed that there was an alternative asset
to money that was relevant during this period,
that money and this other asset were closely
substitutable, and that government policy
could not influence the rate of return on the
alternative asset. Motivated by Madison’s thinking, I proceed as follows in this section: If
agents store raw gold, then gold competes
with money in agents’ portfolios. Moreover,
the return on gold, 1 – δ, is exogenously given.
Thus, if agents store gold at any date t ≤ T 1, this
serves the role of Madison’s alternative asset.
Of course, gold and paper money can both
be held voluntarily at t iff
(29) pt /pt + 1 = 1 – δ.
I now construct an equilibrium where (29)
holds for all t = 0, 1, ..., T 1 – 1. In addition,
raw gold is (at least potentially) stored at these
dates. I also impose
1
= s (w 1,w 2 ,1)
holds. Thus, by induction, if
(27) MT /pT
1
1+1
≥ s (w 1,w 2 ,1)
obtains, so does equation (19). Thus, (27) is
sufficient for a sustained postwar deflation to
be observed.
(30) pT > (1 – δ )pT
1
.
1+ 1
Equation (30) is consistent with inflation occurring between T 1 and T 1 + 1, but raw gold is not
stored between these periods. Allowing (29) to
be violated at t = T 1 eases the construction of
the desired equilibrium.
Equation (29) implies that
(31) pt = (1 – δ )T 1 – t pT ; t = 0, ..., T 1
1
14
In addition, the government budget constraint (2) requires the money supply to
evolve according to
requires that
(37) MT /pT
1
= s (w 1,w 2 , pT /pT
1
1+ 1
)
= βw 1/(1 + β )
(32) Mt = M t – 1 + gpt
= M t – 1+ g pT (1 – δ )T 1 – t; t ≤ T1,
– w 2 /(1 + β )( pT /pT
1
with M –1 = 0 given as an initial condition. The
following proposition then describes the evolution of the real and nominal money supplies:
PROPOSITION 2.
a) For t = 0, 1, ..., T1, the nominal money
supply satisfies
(33.a) Mt = M 0 + ( g /δ )(1 – δ )T 1 – t
× [1 – (1 – δ )t ]pT
1
1
).
1+ 1
Solving (37) for pT yields
1
(38) pT
= MT [(1+ β )/βw 1 ]
1
1
+ (w 2 /βw 1 )pT
1 +1
.
It is then immediate from (38), (25), and
proposition 1 that
(39) pT
= (φ /b)(w 2 /β w 1)T – T1
1
1
+ MT {w 1–1(w 2 /βw 1)T – (T1 + 1)
1
with
+ [(1+ β )/βw 1 ]
(33.b) M 0 = gp0 = g (1 – δ )T 1 pT .
1
× [1 – (w 2 /βw 1)T – (T1 + 1) ]
b) For t = 0, 1, ..., T1, the real money supply
satisfies
(34) Mt /pt = ( g /δ )[1 – (1 – δ )t
+ 1 ].
Equation (36) can be rewritten as
Part a of the proposition can be verified directly
by substituting (33.a) into (32). Part b is immediate from (31) and (33.b).
Of course, the construction of equilibrium
just undertaken is predicated on gold being
stored at all dates prior to T1 and on (30). Raw
gold is stored for t ≤ T1 – 1 if
(35) Mt /pt = ( g /δ )[1 – (1 – δ )t
+ 1]
/pT
1– 1
1
1
+ 1 ]p .
T1
Equations (39) and (40) then determine MT
1
and pT . Once those values have been
1
obtained, all other equilibrium price levels can
be deduced from (28) and (31).
It will now be useful to introduce some
notation. Define x by the relation
+ 1 ].
= ( g /δ )[1 – (1 – δ )T 1 ]
< s (w 1,w 2 ,1 – δ ).
(42) ψ1 ≡ s (w 1,w 2 ,x )(w 2 /βw 1)T – T 1
Also, in order for (30) to hold,
(36) MT /pT
1
A comparison of (36), (37), and (41) will indicate that x = pT /pT + 1 , and x is clearly an
1
1
exogenous variable. Condition (30) requires
that x > 1 – δ hold. In addition, define ψ1
and ψ2 by
is satisfied for all such dates. Clearly this condition is equivalent to
1– 1
(40) MT = ( g /δ )[1 – (1 – δ )T 1
(41) s (w 1,w 2 ,x ) ≡ ( g /δ )[1 – (1 – δ )T 1
< s (w 1,w 2 ,1 – δ )
(35′) MT
÷ [1 – (w 2 /βw 1 )].
= ( g /δ )[1 – (1 – δ )T 1
and
+ 1]
> s (w 1,w 2 ,1 – δ )
must obtain.
It remains to determine the price level and
money stock at time T 1. Since there is no raw
gold storage at T 1, money market clearing
(43) ψ2 ≡ ( β /w 2 ) ψ1{1 + [(1 + β )/β ]
× [( β w 1/w 2 ) T – (T1 + 1) – 1 ]
÷ [ 1 – (w 2 /βw 1 )]}.
15
The following result is then immediate:
PROPOSITION 3. Suppose that
(44) ψ1 ≥ (1 – ψ2 )(1 + β )s (w 1,w 2 ,1)/β > 0
Proposition 4, which is proved in appendix B,
asserts that parameter values can always be
chosen so that the construction of equilibrium
performed here is valid. In the next section, I
examine some properties of this equilibrium.
and
(45) g (1 – δ )T 1
–1
≥ w 2 [x – (1 – δ )]/(1 + β )x
V. Madison's Assertions
> δβ w 1/(1 + β ).
It is now possible to use the construction of
Then, an equilibrium satisfying (19), (29), and
(30) exists. This equilibrium has
(46) MT
1
= (φ /b) ψ1 /(1 – ψ2 )
and
(47) pT
1
= (φ /b)(w 2 /β w 1)T – T1 /(1 – ψ2 ).
The proof of proposition 3 appears in
appendix A. The first inequality in (44)
implies that (23) is satisfied and hence
that pT – 1 ≥ pT holds. The second inequality in (44) is required for MT > 0
1
and pT > 0 to hold. Finally, (45) implies
1
that (35), (36), x > 1 – δ , and (27) are satisfied. Satisfaction of (27), of course, implies that
pt ≥ pt + 1 holds for all t = T1 + 1, ..., T – 1.
It remains to describe conditions under
which the inequalities in (45) are satisfied.
These conditions are stated in the following:
PROPOSITION 4.
a) The relations in (44) hold iff
(48) [(w 1 + w 2 )/w 1](w 2 /βw 1 ) T – (T1 + 1)
> w 2 (x – 1)/x s (w 1,w 2 ,x )
≥ (w 2 /βw 1 ) T – (T1 + 1)
is satisfied.
b) Suppose that w 1, w 2 , β, T1 and T satisfy
βw 1 > w 2 , T ≥ T1 + 2, and
(49) 1/(1 + T1) > w 2 /βw 1 .
–
Then, there exists a nonempty interval, [x
– ,x–),
with x
iff x ∈ [x ,x ).
– > 1, such that (48) holds
– ), (1.a.) and– (45)
In addition, for all x ∈ [x
,x
–
hold if δ is sufficiently close to zero.
sections III and IV to investigate the validity of
some of Madison’s main assertions, which I
take to be as follows:
i. For a government following the kind of
policy outlined in section II, the simple
quantity theory of money fails, even
before the transition to a gold standard.
ii. That is, the rate of inflation and the
growth rate of the money stock are not
the same, and it is easy for the money
growth rate to substantially exceed the
inflation rate.
iii.i )More strongly, the behavior of the price
level is independent of the quantity of
money printed, so long as there is no
uncertainty about the date of transition to
a gold standard.
(i )While this may reflect my own reading,
iv.
Madison seems to suggest that the behavior of the price level does not depend
on the size of the government deficit, so
long as there is no uncertainty about T.
Anything that delays the transition to a
gold standard acts to raise prices, at least
up to date T 1.
I now investigate each of these propositions.
It is the case here that the rate of growth of
the money stock does exceed the rate of inflation in all periods prior to T. Indeed, in some
periods the difference can be quite substantial.
I now state the following result:
PROPOSITION 5. For all t < T, it is true that
Mt + 1 /M t > pt + 1 /pt holds.
Indeed,
a) for t ≤ T1 – 1,
(50) pt + 1/pt = (M t + 1/M t )[1 – (1 – δ )t
÷ [1 – (1 – δ )t
b) For t = T1, ..., T – 1,
+ 2]
+ 1]
< (M t + 1/M t ).
16
to a gold standard. Let T~(T)
denote the transition date in
the first (second) economy,
and let p~t (pt ) be the date t
price level in the first
(second) economy. Suppose
that T~ > T and x ≥ x– hold.
Then, p~t > pt for all t ≤ T 1.
(51) pt + 1/pt ≤ (1/x)(M t + 1/M t )
< M t + 1/Mt .
The proof of proposition 5 appears in appendix
C. For small values of δ, [1 – (1 – δ ) t + 1]
÷ [1 – (1 – δ )t + 2 ] is approximately equal to
(t + 1)/(t + 2). Thus, early in the period of
deficit finance, the price level can rise far
more slowly than the money supply. In
addition, since the money supply is constant
for t = T1, ..., T – 1, and since deflation
is under way during this time, the money
supply grows faster than the price level
here as well. Indeed, since x can be fairly
large, equation (51) implies that the difference
between the rate of inflation and the rate
of money creation can again be quite great.
Thus, Madison’s first assertion is borne out.
As is apparent from proposition 1 and
equation (31), however, the model supports
Madison’s second assertion less well. The
price level at all dates can be viewed as
depending—and, moreover, depending
proportionally—on MT . Since M –1 = 0,
1
MT is the total quantity of paper money
1
printed during the period of deficit finance.
The entire time path of prices, up to date
T, depends on MT , although the rate of
1
inflation does not.
Similarly, the analysis suggests that the
total size of the deficit financed through date
T1 affects the price level at all dates and the rate
of inflation/deflation at all dates t = T1, ..., T – 1.
However, it does not affect the rate of inflation
for t < T, which is simply 1/(1 – δ ). To see the
first point, notice from equations (41), (42), and
(43) that a higher government budget deficit
raises ψ 2 and hence—by equation (47)—
raises pT . From equation (41), an increase
1
in g also raises x; this clearly raises pT /pT + 1 ;
1
1
indeed, it raises pt /pt + 1 for all t = T1, ...,
T – 1. Thus, a larger deficit raises the price
level for all dates up to and including T1;
but a larger deflation also ensues when deficit
spending ceases.
It remains to investigate Madison's last assertion, namely, that a delay in the transition to
a gold standard implies a higher price level
for all t ≤ T 1. This is, in fact, accurate, as the
next proposition asserts. Its proof is given
in appendix D.
PROPOSITION 6. Consider two economies that
are identical in all respects
except their dates of transition
Thus, other things equal, a more rapid
movement to a gold standard implies less
upward pressure on the price level, exactly
as Madison argued. It is also easy to show
that it implies less money will be printed.
VI. Conclusion
Madison’s essay, “Money,” challenges the belief
in a necessary connection between money
growth and inflation that underlies much of the
quantity theory of money. He obviously considered the circumstances of a government that
was engaged in monetizing a temporary budget
deficit, issuing inconvertible paper money, and
promising to establish a gold standard and
redeem its paper currency at some future time.
If honored, as this (and Madison’s) analysis
assumes, such a promise would constitute a
type of future “backing” of money issues that
he thought would limit inflation and break the
connection between inflation and the rate of
money growth. Moreover, his concerns have
universal application; many other governments
at other times have confronted similar circumstances and conducted similar policies.
The model constructed here can—under
circumstances that have been described—
give rise to equilibria that mimic general observations about what occurs when governments
follow these kinds of policies. There is inflation during wars, but deflation begins when
the government’s wartime spending ceases.
This deflation permits resumption to begin
as scheduled, even if the government does
nothing to contract the money supply. The
latter point is of some interest: Friedman and
Schwartz (1963), for example, argue that it
was a purely “accidental” consequence of the
postwar deflation that the United States was
able to resume gold convertibility after the
Civil War and that very little active policy was
conducted to restore it. The analysis here,
however, suggests that resumption of convertibility was no accident.
17
I have argued that Madison's views have
much theoretical validity. Indeed, the kind
of policy he describes allows the inflation rate
to be very different from the rate of money
growth, and the time to redemption has potentially great importance in determining the
behavior of the price level. However, the
link between the behavior of the money
supply and the behavior of the price level
is not completely broken, as he asserts it
should be.
But why isn’t this link broken? Tobin
(1963), Wallace (1981), and Sargent and Smith
(1987a,b) describe circumstances under which
appropriately conducted increases in the
money supply—that is, increases which are
appropriately “backed”—have no price level
consequences. Madison’s policy backs current
money creation with a promise of future gold
redemption; here, this promise requires that the
government run future surpluses to raise the
resources required for redemption. Why don’t
these resources constitute the backing required
by Tobin, Wallace, and Sargent and Smith? The
answer is that Madison's scheme assigns the
redemption cost to a specific generation; that is,
it redistributes resources among generations.
This prevents the kind of policy he discusses
from being irrelevant to price-level behavior.
Madison’s analysis nonetheless raises a host
of fascinating issues which remain unaddressed
here. For example, is there an “optimal” speed
of transition to a gold standard? Mitchell (1897)
maintained that the United States took too
long to resume gold convertibility after the
Civil War; Keynes argued that Britain resumed
too quickly after World War I, causing an excessively large postwar deflation. An analysis of
the “correct” length of time to redemption
would definitely be interesting in light of these
discussions.
Madison also challenged the common notion
that borrowing to finance a deficit is less inflationary than monetizing the same deficit. His
particular concern was that the implied interest
payments on the government debt simply add
to the government’s financial burden, exacerbating inflation. The same concern is reflected in Sargent and Wallace’s (1981) work
on “unpleasant monetarist arithmetic,” which
describes conditions under which Madison’s
reservations are well founded. Indeed, the
Sargent–Wallace conditions can be weakened substantially, as shown by Bhattacharya,
Guzman, and Smith (1995).
However, Madison’s analysis of money
versus bond financing of a government
budget deficit raises an even subtler issue.
His final paragraph discusses government
bonds that bear interest only because their
large denominations make them costly to use
in many transactions. Adding this feature to
the others implicit in his description would
yield a model similar to that of Bryant and
Wallace (1979), in which bond finance is
always more inflationary than money finance
because it increases the costs of trade. However, Bryant and Wallace did not consider a
government confronting some of the other
conditions that concerned Madison. An integration of these considerations would also be
extremely interesting.
Appendix A
Proof of Proposition 3. Equations (46) and (47)
are immediate from the equilibrium conditions
(39) and (40), and from the definitions of ψ1
and ψ2. It then remains to verify that the solution sequence {pt } implied by (46), (47), (38),
(31), and (28) satisfies the maintained hypotheses of the construction. These hypotheses are
that equations (19), (29), and (30) are satisfied,
as are (35) and (36). Equation (29) is clearly
satisfied by construction for t ≤ T1 – 1.
The first equality in (44) implies that
(23) is satisfied; as noted in the text, satisfaction of (23) is equivalent to pT – 1 ≥ pT .
pT > (1 – δ )pT + 1 is equivalent to x >
1
1
1 – δ . Iff (27) is satisfied, pt ≥ pt + 1
holds for t = T1 + 1, ..., T – 1. In view
of (30), a sufficient condition for (27) is that
(A.1) (1 – δ )MT /pT
1
1
= (1 – δ )( g/δ )
× [1 – (1 – δ )T1 + 1]
= (1 – δ )s (w 1,w 2 ,x )
≥ s (w 1,w 2 ,1)
be satisfied. (A.1) is easily shown to be equivalent to the second inequality in (45). This
inequality also implies that x > 1 – δ . Thus,
the first inequality in (44) and the second
inequality in (45) imply that (19) and (30) are
satisfied.
As already noted, (36) holds iff x > 1 – δ ,
which is implied by the second inequality in
(44). Moreover, by the definition of x, (35′) is
equivalent to
18
(A.2) ( g /δ )[1 – (1 – δ )T 1
+1
– 1 + (1 – δ )T 1 ]
w 2 (x – 1)/x s (w 1,w 2 ,x )
(A.7) xlim
→∞
= g (1 – δ )T 1 ≥ s (w 1,w 2 ,x )
– s (w 1,w 2 ,1 – δ )
= w 2 [x – (1 – δ )] /(1 + β )(1 – δ )x.
But this is obviously the first inequality in (45),
establishing the proposition. ■
= (1 + β )w 2 /βw 1
are satisfied. Moreover, T ≥ T 1 + 2 implies that
lim w 2 (x – 1)/x s (w 1,w 2 ,x )
x →∞
> (w 2 /βw 1 ) T – (T1 + 1)
holds. Thus, the condition
Appendix B
(A.8) w 2 (x
– – 1)/x
– s (w 1,w 2 ,x
–)
≡ (w 2 /βw 1 ) T – (T1 + 1)
Proof of Proposition 4. The second inequality
in (44) obviously holds iff ψ2 < 1. It is easy
to verify that
has a solution x
– > 1. Likewise, if the
condition
(A.3) ψ2 ≡ [s (w 1,w 2 ,x )/s (w 1,w 2 ,1)]
(A.9) w 2 (x – 1)/x s (w 1,w 2 ,x )
× {1 – (w 2 /βw 1 ) T – (T1 + 1)
× [1 – s (w 1,w 2 ,1) /w 1]}.
Then, ψ2 < 1 holds iff
(A.4) [s (w 1,w 2 ,x ) – s (w 1,w 2 ,1)]
÷ s (w 1,w 2 ,x ) < [1 – s (w 1,w 2 ,1)/w 1]
× (w 2 /βw 1 ) T – (T1 + 1)
is satisfied. Rearranging terms in (A.4) yields
the first inequality in (48).
To obtain the second inequality in (48), note
that the first inequality in (44) holds iff
has a solution, let x– denote it. If (A.9) has no
solution, let x– = ∞. Then, the inequalities in
(48) are clearly satisfied iff x ∈ [x– , x– ).
It remains to show that δ can be selected to
satisfy (a.1) and (45). To begin, rewrite (45) as
(A.10) g (1 – δ )T 1 – 1 ≡ δ (1 – δ )T 1 – 1
× s (w 1,w 2 ,x )/[1 – (1 – δ )T 1 + 1 ]
≥ w 2 [x – (1 – δ )] /(1 + β )x
> δβw 1 /(1 + β ).
≥ s (w 1,w 2 ,1) – s (w 1,w 2 ,x )
Clearly, βw 1 > w 2 implies that, for δ near
zero, (a.1) and the second inequality in (A.10)
are satisfied. Moreover, the first inequality in
(A.10) can be written in the form
+ s (w 1,w 2 ,x )[1 – s (w 1,w 2 ,1)/w 1]
(A.11) δ (1 – δ )T 1 – 1/ [1 – (1 – δ )T 1 + 1 ]
(A.5) [ β /(1 + β )]s (w 1,w 2 ,x )(w 2 /βw 1 ) T – T1
× (w 2 /βw 1 ) T – T1 – 1.
Rearranging terms in (A.5) yields the second
inequality in (48).
To establish part (b) of the proposition,
notice that
(A.6) w 2 (x – 1)/x s (w 1,w 2 ,x )
= (1 + β )w 2 (x – 1)/βw 1 [x – (w 2 /βw 1 )].
and
= [(w 1 + w 2 )/w 1](w 2 /βw 1 ) T – (T1 + 1)
≥ (w 2 /βw 1 )[x – (1 – δ )]
÷ [x – (w 2 /βw 1 )].
For δ satisfying assumption 1 and for all x > 1,
we clearly have
(w 2 /βw 1 )[x – (1 – δ )] /[x – (w 2 /βw 1 )]
< (w 2 /βw 1 ).
19
(A.13) ψ2 ≡ ( g /δ )[1 – (1 – δ )T 1
Moreover, by L’Hopital’s rule,
+ 1]
lim δ (1 – δ )T 1 – 1/ [1 – (1 – δ )T 1 + 1 ]
× {w 1–1 (w 2 /βw 1)T – (T1 + 1)
= 1/(T 1 + 1).
+ [(1 + β )/βw 1 ][1 – (w 2 /βw 1)T – (T1 + 1)]
δ →0
Thus, condition (49) implies that, for all
x ∈ [x– , x– ), both inequalities in (45) are satisfied whenever δ is chosen sufficiently small. ■
÷ [1 – (w 2 /βw 1 )]},
respectively. Then,
Appendix C
(A.15) pT
a) For t ≤ T1 – 1, equation (50) follows immediately from (34). Moreover, by L’Hopital’s rule,
δ →0
1
= (φ /b)(w 2 /β w 1)T – T1 /(1 – ψ 2 )
~
hold, and p
T
Proof of Proposition 5.
lim [1 – (1 – δ ) t
1
~
= (φ /b)(w 2 /β w 1)T – T1 /(1 – ψ~2 )
~
(A.14) p
T
+ 1 ]/[1
– (1 – δ ) t
+ 2]
1
> pT iff
(A.16) (w 2 /β w 1
1
~
)T – T (1
– ψ 2 ) > 1 – ψ~2
is satisfied.
Now, straightforward manipulation establishes that
= (t + 1)/(t + 2).
Hence, the assertion in the text following the
proposition.
b) Equation (34), the definition of x, and
M t /pt = s (w 1,w 2 ,pt /pt + 1 ), t = T1, ..., T – 1,
imply that pT + 1 /pT = x = x (MT + 1 /MT ),
1
1
1
since the money supply is constant for all
t ≥ T1. Moreover, for t = T1 + 1, ..., T – 1, the
conditions pt + 1 ≤ pt and Mt /pt = MT /pt
1
= s (w 1,w 2 ,pt /pt + 1 ) are satisfied. Therefore,
Mt /pt ≥ Mt /pt – 1 ≥ ⋅⋅⋅ ≥ MT /pT =
1
1
s (w 1,w 2 ,x) must hold. It is then immediate
that, for all such t, pt /pt + 1 > x, and pt + 1 /pt
< (1/x )(Mt + 1 /Mt ) = 1/x obtain. ■
~
(A.17) (w 2 /β w 1)T – T ψ 2 = ψ~2 – ( g /δ )
× [1 – (1 – δ )T 1
+ 1 ][(1
+ β )/βw 1 ]
~
× [1 – (w 2 /βw 1)T – T ]/[1 – (w 2 /βw 1)].
Substituting (A.17) into (A.16) and rearranging
~ > p holds iff
terms, one obtains that p
T
T
1
1
~
(A.18) ψ~2 – (w 2 /βw 1)T – T ψ 2
= ( g /δ )[1 – (1 – δ )T 1
+ 1 ][(1
+ β )/βw 1 ]
~
× [1 – (w 2 /βw 1)T – T ]/[1 – (w 2 /βw 1)]
~
> 1 – (w 2 /βw 1) T – T .
When T~ > T obtains, (A.18) is equivalent to
Appendix D
(A.18′) ( g /δ )[1 – (1 – δ )T 1
Proof of Proposition 6. Define ψ~2 (ψ 2 ) by
(A.12) ψ~2 ≡ ( g /δ )[1 – (1 – δ )T 1
+ 1]
÷ [1 – (w 2 /βw 1 )]}
and
+ β )/βw 1 ]
÷ [1 – (w 2 /βw 1 )] ≡ s (w 1,w 2 ,x )
÷ s (w 1,w 2 ,1) > 1.
~
{w 1–1 (w 2 /βw 1)T – (T1 + 1)
+ [(1 + β )/βw 1 ][1 – (w 2 /βw 1
+ 1 ][(1
~
)T – (T1 + 1)]
Since x– > 1, (A.18′) clearly holds for all
x ≥ x– . ■
20
References
Bhattacharya, Joydeep, Mark Guzman,
and Bruce D. Smith. “Some Even More
Unpleasant Monetarist Arithmetic,” Canadian Journal of Economics, forthcoming.
Bryant, John, and Neil Wallace. “The Inefficiency of Interest-Bearing National Debt,”
Journal of Political Economy, vol. 87, no. 2
(April 1979), pp. 365-81.
Ferguson, E. James. The Power of the Purse:
A History of American Public Finance,
1776 –1790. Chapel Hill, N.C.: University
of North Carolina Press, 1961.
Friedman, Milton. “The Quantity Theory
of Money—A Restatement,” in Milton
Friedman, ed., Studies in the Quantity
Theory of Money. Chicago: University of
Chicago Press, 1956.
________, and Anna J. Schwartz.
A Monetary History of the United States,
1876 –1960. Princeton, N.J.: Princeton
University Press, 1963.
Lucas, Robert E., Jr. “Two Illustrations of
the Quantity Theory of Money,” American
Economic Review, vol. 70, no. 5 (December
1980), pp. 1005 –14.
Mints, Lloyd. A History of Banking Theory in
Great Britain and the United States. Chicago:
University of Chicago Press, 1945.
Mitchell, Wesley C. “Greenbacks and the
Cost of the Civil War,” Journal of Political
Economy, vol. 5 (March 1897), pp. 117–56.
Nevins, Allan. The American States during
and after the Revolution, 1775 –1789. New
York: Macmillan, 1924.
Rolnick, Arthur J., Bruce D. Smith, and
Warren E. Weber. “In Order to Form a
More Perfect Monetary Union,” Federal
Reserve Bank of Minneapolis, Quarterly
Review, vol. 17, no. 4 (Fall 1993), pp. 2–13.
Sargent, Thomas J. “The Ends of Four Big
Inflations,” in Robert E. Hall, ed., Inflation:
Causes and Effects, National Bureau of
Economic Research project report. Chicago:
University of Chicago Press, 1982.
________, and Neil Wallace. “Some Unpleasant Monetarist Arithmetic,” Federal Reserve
Bank of Minneapolis, Quarterly Review,
vol. 5, no. 3 (Fall 1981), pp. 1–17.
________, and ________. “A Model of
Commodity Money,” Journal of Monetary
Economics, vol. 12, no. 1 ( July 1983),
pp. 163–87.
________, and Bruce D. Smith. “Irrelevance
of Open Market Operations in Some
Economies with Government Currency
Being Dominated in Rate of Return,”
American Economic Review, vol. 77, no. 1
(March 1987a), pp. 78–92.
________, and ________. “The Irrelevance
of Government Foreign Exchange Operations,” in Elhanan Helpman, Assaf Razin,
and Efraim Sadka, eds., The Economic Effects
of the Government Budget. Cambridge,
Mass.: MIT Press, 1987b.
________, and ________. “Coinage, Debasements, and Gresham’s Laws,” Economic
Theory, vol. 10, no. 2 (August 1997),
pp. 197–226.
Tobin, James. “Commercial Banks as Creators
of Money,” in Deane Carson, ed., Banking
and Monetary Studies. Homewood, Ill.:
Irwin, Inc., 1963.
Wallace, Neil. “A Modigliani-Miller Theorem
for Open Market Operations,” American
Economic Review, vol. 71, no. 3 ( June 1981),
pp. 267–74.
21
Beneficial “Firm Runs”
by Stanley D. Longhofer
Introduction
Recent research in law and corporate finance
suggests that existing bankruptcy rules have
evolved to eliminate inefficiencies that result
when lenders rush to retrieve their assets from
a firm in financial distress. In contrast, firstcome, first-served (FCFS) rules, often considered a benchmark in the absence of other
bankruptcy rules, are commonly thought to be
inefficient because they reduce the value of the
defaulting firm’s assets. This, however, may not
always be the case. Moral hazard problems
associated with the choice of project may make
the act of running on a firm desirable, since it
can help align investment incentives.
This paper looks at the problem of an entrepreneur who must raise outside funds to finance one of two investment alternatives. One
of them is risky, and the bankruptcy costs expected to result from this project make it less
desirable socially than the alternative, riskless
project. Nevertheless, the firm is unable to commit to the less risky enterprise.
FCFS rules act to diminish this moral hazard
problem. I derive a mixed-strategy equilibrium
in which lenders monitor the firm with some
positive probability. When the firm is caught
Stanley D. Longhofer is an economist at the Federal Reserve Bank
of Cleveland. This article has
benefited from the comments and
suggestions of Richard Arnott,
Charles Calomiris, Charles Kahn,
Anne Villamil, and Andrew
Winton, as well as seminar participants at the University of Illinois,
the University of Strathclyde, the
Federal Reserve Bank of Cleveland, the University of Kansas,
and Northwestern University.
investing in the risky project, it is liquidated;
otherwise, it is allowed to continue. Although
this mixed-strategy equilibrium may exist under
both a FCFS rule and a proportionate priority
rule (PPR), I demonstrate that it is less likely to
exist under the PPR, and that when it does, the
FCFS equilibrium is Pareto superior.
The fact that lenders can run on the firm
when they observe that it has chosen the risky
project helps keep the firm honest. The FCFS
aspect of asset distribution keeps lenders from
wanting to free ride on the monitoring efforts of
others because the lenders who monitor are first
in line to receive their claim on the firm’s assets
and are thus likely to be paid in full. Lenders
who wait to observe the monitoring of others
are less likely to receive anything if the firm
goes under. This process is similar to that described in Calomiris and Kahn (1991), where
demandable debt is used to control the banker’s
moral hazard problem, while sequential service
prevents depositors from free riding on the
monitoring efforts of others.
The key idea here is that bankruptcy institutions should reward monitors when and only
when they have performed their duties. A similar argument has been made by Rajan and
Winton (1995), who analyze how the choice of
22
different priority and term structures in loan
contracts affects lenders’ incentives to monitor
the firm. They argue that information conditions determine which structures provide the
best monitoring incentives, meaning that the
firm’s capital structure can be used to achieve
outcomes that are not directly contractible. In
other words, ex ante efficiency is improved by
choosing a capital structure that properly rewards monitors. This paper differs from Rajan
and Winton, however, in that it focuses directly
on the structure of the bankruptcy institution,
outside of which private agents are not allowed to contract by law.
Although FCFS rules are beneficial in my
model, there are other factors I have ignored
that work in the opposite direction. Longhofer
and Peters (1997) examine the coordination
problem discussed above and show how lenders might fail to coordinate their liquidation
decisions, even when doing so would be a
Pareto-superior outcome. As a result, mandatory
bankruptcy procedures (which implicitly enforce a PPR) can be socially desirable, since
they enable lenders to coordinate in states of the
world where they would not otherwise do so.
In many respects, the work of Longhofer and
Peters represents the opposite side of this analysis. Notably, their paper assumes that FCFS rules
entail a deadweight social cost, while ignoring
the potential impact of such rules on a lender’s
monitoring incentives. This paper does exactly
the opposite, focusing on how FCFS rules can
ameliorate the firm’s moral hazard problem. A
more complete model would attempt to capture
both effects of a FCFS rule: the benefits associated with improved monitoring incentives and
the costs associated with inefficient default.
The next section summarizes traditional
bankruptcy analyses. Here, I outline some of
the standard arguments in favor of an alternative to a FCFS rule in bankruptcy law and question whether they are valid in all circumstances.
I then use this background to analyze other
studies of bankruptcy. I introduce my model in
section II and show that under certain conditions, a firm may be unable to obtain financing
because it cannot commit ex ante to a low-risk
project; possible solutions to this problem are
analyzed. In particular, I show that there exists
a mixed-strategy equilibrium in which the firm
is able to find lenders. Section III looks at the
effect different bankruptcy rules may have on
the equilibrium of this game. I show that a PPR
reduces lenders’ incentives to monitor the firm,
thus raising the social cost of these contracts.
I conclude in section IV, relegating all proofs to
the appendix.
I. Justifications
for PPRs
Most discussions of bankruptcy institutions start
with the assumption that a formal procedure is
needed for distributing an insolvent firm’s assets, and then focus on the specific form such a
procedure should take. It is not clear, however,
that this assumption is valid in all cases. To see
this, consider some of its standard justifications.
In the absence of bankruptcy laws, assets
are distributed to creditors in the order in
which they have staked their claims. Thus,
the first lender to request repayment is generally the first to receive it. Lenders who end
up last in line are paid last and quite possibly
receive nothing.1 For this reason, these default
bankruptcy proceedings are typically called
FCFS rules.
Traditional rationales for a more orderly
mechanism cite several potential problems with
FCFS rules. First, lenders may wish to protect
their position by expending excessive resources
to monitor the firm’s condition. If a lender does
not do this, the argument goes, he will certainly
be the last to know when the firm is about to
default, and consequently be the last in line to
collect his claim. Furthermore, since all lenders
are engaged in this monitoring, no one will get
a better place in line than he would if none of
them monitored, so these resources are spent in
vain. This game looks much like the classic prisoners’ dilemma, in which the Pareto-superior
outcome with no monitoring is not a Nash
equilibrium. It is argued that an orderly bankruptcy procedure allows lenders to avoid these
costs, making all of them better off.
A second argument against FCFS rules is the
classic “common pool” problem. Here, it is
claimed that in their rush to be paid, lenders
might reduce the total liquidation value of the
firm by separating assets that would be more
valuable together.2 An orderly liquidation, on
the other hand, would ensure that the firm’s
assets are put to their most productive uses,
maximizing their value to the creditors. Worse
yet, lenders might actually run too soon and
foreclose on illiquid but otherwise viable firms.
Again, formal bankruptcy rules should help
prevent these inefficient liquidations.
■ 1 This can be true even when some lenders insert seniority
covenants into their loan agreements. Once the first lender removes his
assets from the firm, a later lender’s seniority provision no longer carries
much benefit. Effectively, under a FCFS rule, lenders can assign seniority
to themselves ex post by being the first to request repayment.
■ 2 See Longhofer and Peters (1997).
23
Jackson (1986, p. 10) summarizes the intuition behind these arguments: “The basic
problem that bankruptcy law is designed to
handle ... is that the system of individual
creditor remedies may be bad for the creditors
as a group when there are not enough assets
to go around.”
With these (often implicit) assumptions, modern studies of bankruptcy rules investigate what
shape formal liquidation rules should take. For
example, many authors have looked at the relative efficiency of the absolute priority rule
(where the order of repayment is determined
ex ante by assigning each lender a priority level)
and PPRs.3 Under various assumptions, they all
conclude that these rules are inefficient with
regard to both the liquidation/continuation decision and the decision to make new investments.
Numerous other studies analyze Chapter 11 of
the Bankruptcy Code and show that, in general,
it does not provide efficient investment or liquidation incentives either. None of these studies,
however, examines the relative efficiency of various bankruptcy rules compared to the natural
default—FCFS rules—a necessary starting place
for bankruptcy analyses.
In addition, most models analyze the effects
of bankruptcy ex post. They begin with a firm
whose existing capital structure cannot meet its
current debt obligations. These models focus
on whether different bankruptcy rules provide
proper incentives so that creditors will foreclose
if and only if the firm is insolvent, and will
extend new credit to the firm for and only for
positive net present value projects. It is certainly
interesting to ask whether bankruptcy rules
provide for decisions that are efficient ex post.
But debt contracts are designed to resolve
ex ante uncertainty, and their efficiency must
therefore be measured from the viewpoint of
the initial contracting problem. The proper
question, then, is how different bankruptcy
rules affect the social cost of debt contracts
at the time they are written.
Boyes, Faith, and Wrase (1991) is one of only
a few papers that address both these issues.4 Its
authors compare the ex ante social cost of debt
contracts under PPRs and under FCFS rules,
concluding that the PPR found in Chapter 7 is
more efficient than FCFS rules, since it reduces
the cost of contracting. Their result depends on
their assumption that rushing to liquidate the
firm is costly, whereas formal bankruptcy proceedings are not. In a FCFS world, lenders must
pay to enter a queue to obtain the firm’s assets.
If they allow a firm to continue despite the fact
that its expected return is negative, they will
avoid these queuing costs some of the time
(when the firm does well). Thus, lenders have
an incentive to allow some firms with negative
net present value to continue.5
The model of Boyes, Faith, and Wrase differs
from this one in several important respects.
First, they assume that a FCFS rule is costlier to
implement than is a PPR.6 More important, in
my model the firm chooses between two different investment projects. This choice is the firm’s
private information, creating a moral hazard
problem that requires lenders to monitor the
firm. When there are many lenders, they may
wish to free ride on one another’s monitoring
efforts. I propose that FCFS rules can serve to
ameliorate this problem.
II. The Model
Consider a two-period world in which a riskneutral firm has the opportunity to invest in
one of two projects in period 0, either of which
will mature in period 2. The first, project B, has
a random return, paying xh in period 2 with
probability p and xl with probability (1 – p). In
contrast, project G is a safe project, returning
x– = pxh + (1 – p)xl in period 2 with certainty.7
Either project requires an investment of I
to undertake. Because the firm has no resources
of its own, it must borrow these funds from
outside investors. I assume the loan market is
composed of a large number of identical, riskneutral agents. In equilibrium, competition will
always drive down the interest rate, R, to ensure
that all lenders earn zero profits. Assume that x–
is high enough always to enable the firm with
the riskless project to make its promised payments in period 3. In contrast, I > xl , so that if
the firm chooses project B, it can meet its obligations only when the project is successful.
When the firm is unable to repay its loans,
default costs of d are incurred.
■ 3 See, for example, Bulow and Shoven (1978), White (1980, 1983),
and Gertner and Scharfstein (1991).
■ 4 See also Longhofer and Peters (1997).
■ 5 The authors also acknowledge that FCFS rules may result in
inefficient liquidations of firms that have a positive net present value and
claim that this further supports their argument that PPRs are more efficient.
They ignore, however, the possibility that these two effects may offset each
other, reducing the net inefficiency of FCFS rules.
■ 6 If they were to assume that both types of rules entailed the same
costs, their model would indicate a preference for FCFS rules, which involve these costs only a fraction of the time, rather than PPRs, which
always do.
■ 7 More generally, I could assume that G is second-order stochastic
dominant over B.
24
F I G U R E
from project B is p (xh – 2R). Because there are
deadweight costs associated with default, it is
certain that, if both projects were priced competitively, the firm would earn a higher expected return from project G. Nevertheless, it is
easy to show:
1
Sequence of Events
PROPOSITION 1. Given any fixed promised repayment R, the firm will
always choose to invest in
project B.
SOURCE: Author.
Assume that the choice of project is costlessly
observable by the firm. Outsiders, however,
must monitor the firm in period 1 in order to
discover its project choice. Let c denote the cost
of doing so. Although the results of this monitoring provide a perfect signal of the firm’s project choice, I assume that this information cannot
be verified in court, making it impossible for
contracts to depend on the choice of project.8
To analyze the effects of priority on the efficiency of financial contracting, I assume that
the firm must borrow from multiple lenders.9
For simplicity, assume that the firm borrows I /2
from each of two lenders. Figure 1 shows the
order of events in this economy.
This proposition implies that long-term debt
prevents the firm from credibly promising to
invest in the riskless project in equilibrium.
Once it receives the (relatively low) interest rate
associated with project G, it would like to go
ahead and invest in B, since it suffers none of
the losses associated with the project’s increased
variability. If long-term debt is the only option,
no lender will accept any interest rate below
RB*, and the firm will invest in project B.
This inability to commit to the riskless project
obviously entails social costs. Because lenders
earn zero profits in equilibrium, these costs can
be measured by comparing the profits the firm
would have earned had it been able to commit
to project G with those it earns from project B.
This ends up equaling the expected deadweight
default costs associated with project B: d (1 – p).
Short-term Debt
Long-term Debt
To finance either of these projects, the firm
could issue long-term debt—that is, debt that
comes due in period 2. On the basis of their
beliefs about the firm’s project choice, prospective lenders will demand a default premium
commensurate with that project’s anticipated
risk. If they believe the firm will choose to invest in the riskless project G, each lender will
simply charge the zero-profit interest rate,
RG* = I/2. On the other hand, if they anticipate
the firm will choose project B, each lender’s
expected return is
(1)
pR + (1 – p)
xl – d
– I ,
2
2
implying a zero-profit interest rate,
RB* = [I – (1 – p)(xl – d )]/2p; it is straightforward to verify that RB* > RG* .
Of course, the firm is concerned about the
interest rate it pays only to the extent that its
profits are affected. Given any promised payment, R, the firm’s period-2 profit from project
G is x– – 2R with certainty. In contrast, its profit
Is it possible to avoid such costs? One solution
to this moral hazard problem is a maturity mismatch with short-term debt.10 Suppose the firm
must make a payment to its lenders in period 1.
Since it has no revenues until period 2, it must
either default or convince the lenders to roll
over its debt. Before renewing the debt, however, lenders can monitor the firm and determine which project has been selected.
If lenders could credibly commit to monitoring the firm in period 1, short-term debt would
give the firm an incentive to invest in project G.
■ 8 If contracts could depend on the specific contract chosen, the
first–best outcome would occur, in which the firm always chooses project G.
■ 9 I do not formally motivate this assumption here. See Bolton
and Scharfstein (1996) for a formal model motivating the use of multiple
creditors.
■ 10 It would be formally identical if we continued to consider longterm contracts with covenants that allow lenders to demand repayment in
period 1. Note, however, that such covenants would not explicitly depend
on the choice of project, since we have assumed this choice is not verifiable
in court.
25
I assume, however, that such commitment is not
possible. As a result, once project G is chosen,
lenders no longer have any incentive to monitor
the firm. Of course, the firm can anticipate that
this will happen, and will once again choose
project B. Thus, the pure-strategy equilibrium is
the same with short- and long-term debt contracts; the firm chooses project B, while lenders
charge RB* and never monitor the firm.
Thus, to find an equilibrium in which the
firm invests in the riskless project, we must
focus on mixed strategies, in which the firm
chooses each of the projects with some positive probability, and lenders randomly monitor
this choice.
After financing is provided in period zero,
the firm must decide how often it will invest in
each of the two projects, and the bank must
decide how often it will monitor. Let π ∈ (0,1)
be the probability that the firm selects project
B, and α ∈ (0,1) be the probability that each
lender monitors the firm in period 1. Since I
am looking for a symmetric equilibrium, the
total probability that the firm is monitored is
1 – (1 – α) 2.11 Finally, let R denote the face
value of the debt owed to each lender, so that
the firm’s total debt is 2R.
Conditional on the results of its monitoring
in period 1, each lender must decide whether
to roll over its debt or to demand immediate
repayment of its loan. Assume that the firm has
no cash assets in period 1, so that it must be
liquidated whenever either lender demands
repayment, and that all debt contracts contain
cross-default clauses, stipulating that the loan is
in default whenever another creditor demands
early repayment of its debt. Let z be the postbankruptcy-cost, period-1 liquidation value
of the firm. I assume that z < I /2, so that this
value is insufficient to pay off either of the
firm’s creditors. Lenders who monitor the firm
are first in line for its assets when it is liquidated in period 1, since they are the first to be
aware that the firm has cheated. Thus, under
a FCFS rule, the firm’s assets, z, are distributed
only to lenders who actually monitor the firm;
since z < I /2, nothing remains for a nonmonitoring lender. In contrast, under the PPR,
each lender receives z/2 when the firm is
liquidated in period 1, whether it monitored
the firm or not.
Finally, if the firm is not liquidated in
period 1, its project matures and revenues are
received in period 3. If the firm’s project is successful, it pays off its lenders and keeps the balance of its revenues as profit; otherwise, it is
liquidated and its assets (xl – d ) are divided
equally between the two creditors.
Derivation of
an Equilibrium
Since we are looking for a symmetric, mixedstrategy Nash equilibrium, α and π must be
chosen so as to make the firm and the lenders,
respectively, willing to randomize. That is, each
lender’s probability of monitoring, α, must be
such that the firm earns the same expected
return regardless of which project it chooses:
(2)
x– – 2R = (1 – α)2 p (xh – 2R)
or
(3)
Ïp (xx ––2R2R)
–
α* = 1 –
.
h
Direct differentiation of α * shows that it is
increasing in R. In other words, the firm’s moral
hazard problem worsens as R gets larger, implying that more monitoring is required to keep
it indifferent between the two projects when
the interest rate is high.
Similarly, π must be chosen to ensure that
lenders are indifferent between monitoring and
not monitoring the firm. The competitive loan
market imposes the additional constraint that
each lender must earn zero expected profit. It
follows that π * and R * must be jointly chosen
to solve
(4)
3
4
(1 – π )R + π α z + (1 – α)λ 1 – c – I = 0
2
2
and
(5)
(1 – π )R
5
3
x –d
+ π αλ 2 + (1 – α) pR + (1 – p) l
2
46
– I = 0,
2
where λ 1 and λ 2 are a lender’s payoffs from
early liquidation when it is the only one to
monitor and when it does not monitor, respectively. These two payoffs depend on the bankruptcy rules in effect.
The intuition behind each of these expressions is clear. Equation (4) is a lender’s expected
return when it monitors the firm. If it discovers
that the firm selected the riskless project (which
happens with probability 1 – π ), it allows the
firm to continue until period 2 and receives its
■ 11 I focus on a symmetric equilibrium because of its analytical
tractability. The same basic conclusions would follow from a model in
which one lender was designated to monitor more frequently than the other.
26
promised payment R at that time. On the other
hand, if it finds that the firm chose project B, it
demands immediate repayment.12 If the other
lender also monitored (which happens with
probability α), the two lenders divide z equally.
On the other hand, if the other lender did not
monitor the firm, then the monitoring lender’s
payoff is λ 1 and depends on the bankruptcy
rule in effect. Under FCFS rules, the sole monitor is entitled to all of the firm’s liquidation
value, while these assets are divided equally
under a PPR. Thus, λ 1FCFS = z, and λ 1PPR = z/2.
Finally, note that the lender’s total costs in this
case include the monitoring expenses it incurs,
c, and its original investment in the firm, I/2.
A similar intuition is behind equation (5),
the lender’s expected return when it does
not monitor. With probability 1 – π , the firm
chooses the riskless project, and the lender
earns R with certainty. With probability π, the
firm chooses project B. With probability α ,
the other lender monitors the firm and
demands immediate repayment. In this last
case, the nonmonitoring lender receives λ 2 ,
where λ 2FCFS = 0 and λ 2PPR = z/2. On the other
hand, if neither lender monitors the firm, its
project is allowed to mature. With probability p,
the project succeeds, paying each lender R.
With probability 1 – p, it fails, and the two
lenders split xl – d between them. Finally, since
no monitoring costs are incurred in this case,
the interest rate must simply recoup the firm’s
investment, I/2.
Given this setup, we have the characterization of equilibrium in
PROPOSITION 2. The following strategies constitute a mixed-strategy,
sequential Nash equilibrium
with short-term debt:
a) The firm chooses project B with probability π * and project G with probability
1 – π *;
b) Each lender chooses to monitor the firm
with probability α * and refuses to renew
its loan only after observing the firm has
chosen project B; and
c) Lenders never liquidate the firm in period 1 when they do not monitor.
Proposition 2 tells us that short-term debt
may be one device for mitigating the firm’s
incentive to invest in the risky project, B, and
that it holds regardless of which bankruptcy
rules are in effect. The possibility that it might
be monitored and liquidated by one of its
lenders gives the firm an incentive to invest in
the safe project with some positive probability.
Since the deadweight costs of default associated
with project B are incurred less often, the firm’s
ex ante profits are higher.
III. The Relative
Efficiency of
Bankruptcy Rules
In the last section, I showed how short-term
debt with monitoring can be used to lessen a
firm’s moral hazard problem, improving the efficiency of financial contracting. In this section, I
focus on how the institutional structure used to
divide the assets of a financially distressed firm
can affect the efficiency of these contracts.
The equilibrium derived in the last section
was equally consistent with FCFS rules and
PPRs. My goal in this section is to show that this
mixed-strategy equilibrium is less likely to exist
under PPRs, and that when it does exist, the
total social cost of the contract will be higher
with PPRs. I do this by examining the interest
rate in the problem under each of these rules.
For a mixed-strategy equilibrium to exist, R *
and π * must jointly solve (4) and (5). In addition, the following conditions must be satisfied:
α * ∈ (0,1), π * ∈ (0,1), and R * ≤ x– /2.13
Because I have assumed that the loan market is perfectly competitive, it is straightforward
to measure the relative efficiency of bankruptcy
rules by calculating the difference between the
firm’s expected profits under each of them. Because α * is chosen to make the firm indifferent
between the two projects, the firm’s expected
profit is simply equal to
(6)
x– – 2R.
Expression (6) makes it clear that the preferred bankruptcy rule will be the one that minimizes the total face value of the firm’s debt.
I am now able to prove the primary result of
this paper:
PROPOSITION 3. The total face value of the
firm’s debt is lowest under the
FCFS rule, meaning that
social welfare is highest
under this bankruptcy rule.
■ 12 This is simply assumed in the formulation of expression (4) and
is formally proven in proposition 2.
■ 13 If this final condition is violated in any candidate equilibrium,
the firm will have no incentive to choose the riskless project (π * = 1),
giving the lender no incentive to monitor the firm. As the previous section
showed, this degenerates to the (inefficient) long-term debt solution.
27
F I G U R E
2
Advantage of FCFS Rules
SOURCE: Author.
Proposition 3 is illustrated in figure 2. Let π 1
be the locus of (π, R ) pairs that solve (4), and
π 2 the locus solving (5). The leftmost intersection of these loci is the equilibrium.14
When the firm is caught investing in project
B, a FCFS rule gives more to lenders who monitor than does a PPR. Thus, π 1FCFS is everywhere
above π 1PPR. Similarly, when the firm is caught
cheating, lenders who monitor have a higher
expected return under a PPR than under a FCFS
rule. Hence, π 2FCFS is everywhere below π 2PPR.
Together, these two facts imply that the first
intersection of the two curves under a PPR must
be to the right of their first intersection under a
FCFS rule. Consequently, the equilibrium under
a FCFS rule must entail a lower interest rate.
Proposition 3 affirms that, contrary to the
generally accepted view, a bankruptcy institution in which lenders may run on a firm in
default to collect their assets can actually be
socially preferred to an institution prohibiting
such runs. Essentially, PPRs encourage lenders
to free ride on the monitoring efforts of others,
since these rules give each lender—whether it
monitors or not—the same claim on the firm’s
assets. With FCFS rules, lenders have more incentive to monitor because they get first call on
the defaulting firm’s assets. This reduces the interest rate needed to give lenders zero expected profits, letting the firm earn a higher return.
Proposition 3 has an immediate corollary:
PROPOSITION 4. A mixed-strategy equilibrium
is less likely to exist under a
PPR than under a FCFS rule.
Proposition 4 implies that equilibrium under
PPRs is more likely to degenerate to the purestrategy, long-term debt equilibrium in which
the firm always invests in project B. To understand this proposition, note that the largest
value that R can take in any mixed-strategy
equilibrium is x– /2; for any larger R, the firm
would never choose to invest in project G,
since doing so would provide it with a negative
return. Basically, the shifts in π 1 and π 2 resulting from a move to a PPR make it less likely
that the intersection between these two curves
will occur within this relevant range.
To summarize, FCFS rules can be beneficial
for two reasons. First, socially desirable debt
contracts are more likely to be feasible under
FCFS rules than when PPRs govern default.
Second, the total cost of this debt is lower
under FCFS rules, increasing the firm’s ex ante
expected profit. In short, allowing lenders to
run on the firm can be beneficial because it
improves lenders’ monitoring incentives by
compensating them when, and only when, they
perform this socially desirable activity.
IV. Concluding
Thoughts
This paper questions the standard assumption
that preventing lenders from running on a firm
is always necessary in bankruptcy. In the
model presented here, a moral hazard problem
makes the act of monitoring a socially beneficial public good. As a result, the total cost of
debt contracting is reduced when the bankruptcy procedure compensates those lenders
who monitor a misbehaving firm. Allowing
creditors to run on a financially distressed firm
to retrieve their assets serves to implement just
such a compensation mechanism.
Lately, there has been extensive debate
about whether bankruptcy laws should be
reformed, and if so, how. One proposal receiving significant attention is by Aghion, Hart, and
Moore (1992).15 They suggest that each of a
■ 14 Since any such intersection provides lenders with zero expected
profit, the leftmost intersection results in the lowest possible interest rate
for the borrower, making it the equilibrium.
■ 15 See also Roe (1983) and Bebchuk (1988).
28
firm’s creditors should be given an option to
purchase the firm’s assets from more senior
claimants at the value of their claims. This system would guarantee that a distressed firm’s
assets end up with the individual or group that
values them most, and would ensure that economically viable firms will continue. While
this proposal would do much to eliminate the
ex post inefficiencies associated with modern
bankruptcy proceedings, it does not resolve
the basic concerns addressed in this paper.
Like the PPR I discuss above, their proposal
does not consider the impact a proper compensation scheme can have on the probability
that bankruptcy will occur in the first place.
The main point of this model with respect
to the debate over bankruptcy reform is that
policymakers should consider the impact of
bankruptcy rules not only on the distribution of
a financially distressed firm’s assets, but also on
the terms of debt contracts. It is this latter influence that has the largest effect on social welfare.
which must hold since c is positive. An analogous argument shows that the lender will
always want to liquidate the risky firm under
FCFS rules.
2) The lender’s expected return from allowing the riskless project to mature is R * > I/2 > z,
verifying that lenders will not force early liquidation in this case.
3) The most a lender can hope to earn from
liquidating a firm that it does not monitor is z,
which is (by assumption) less than I/2, the
expected return from allowing this firm’s project to mature (by expression [5]). Thus, lenders
will allow the firm’s project to mature in this
case as well. ■
Proof of Proposition 3. Solving (4) and (5) for π
as functions of R gives us
(8)
and
(9)
Appendix
Proof of Proposition 1. Holding the interest
rate constant, the difference between the
firm’s profit from project B and project G is
(1 – p)(2R – xl ). In any equilibrium, 2R ≥ I > xl ,
showing that this difference must be positive. ■
Proof of Proposition 2. R * and π * are defined
in the text so as to ensure that lenders are willing to randomize, and α * is defined to ensure
that the firm is willing to randomize. Thus, it remains to be shown only that 1) lenders will
liquidate the firm after monitoring and observing project B; 2) lenders will not liquidate after
monitoring and observing project G; and
3) lenders will not liquidate the firm in period 1
when they do not monitor.
1) Upon observing project G, the lender’s
expected return from liquidating the firm is z/2
under a PPR. Thus, for a lender to be willing to
liquidate a risky firm under a PPR, it must be
the case that
(7)
3
z > α z + 1 – α) pR + (1 – p) xl – d
2
2
2
R – c – I/2
π 1(R) = R – αz/2 – (1 – α)λ
1
π 2(R) =
R – I/2
.
R – αλ 2 – (1 – α)[pR + (1 – p)(x1 – d)/2]
The intersection of these two functions in
the positive orthant gives the (π, R) pairs that
simultaneously solve (4) and (5). If these curves
intersect more than once, the first such intersection is the candidate for equilibrium, since it
entails the lowest interest rate.
Now, π1(R) = 0 when R = I/2 + c, and
π2(R) = 0 when R = I/2. As R gets larger, each
of these must move into the positive orthant,
since π is a convex weight. As noted in the
text, λ 1 is smaller under a PPR than under a
FCFS rule. Thus, π1PPR minorizes π1FCFS.16 Similarly, λ 2 is larger under a PPR than under a
FCFS rule, implying that π2FCFS minorizes π2PPR.
This implies that the first intersection of π1PPR
and π2PPR must lie to the right of the first intersection of π1FCFS and π2FCFS (see figure 2). Compared to a FCFS rule, then, a PPR must entail a
higher interest rate. ■
4
*
= I/2 – (1 – π )R (by expression [5])
π
= z – c (by expression [4]),
2 π
■ 16 That is, for every R, π 1PPR (R ) , π 1FCFS (R ).
29
References
Aghion, Philippe, Oliver Hart, and John
Moore. “The Economics of Bankruptcy
Reform,” Journal of Law, Economics, and
Organization, vol. 8, no. 3 (October 1992),
pp. 523–46.
Bebchuk, Lucian Arye. “A New Approach to
Corporate Reorganizations,” Harvard Law Review, vol. 101, no. 4 (February 1988),
pp. 775–804.
Bolton, Patrick, and David S. Scharfstein.
“Optimal Debt Structure and the Number of
Creditors,” Journal of Political Economy,
vol. 104, no. 1 (February 1996), pp. 1–25.
Boyes, William J., Roger L. Faith, and
Jeffrey M. Wrase. “An Efficiency Theory of
Bankruptcy Rules” Arizona State University,
Working Paper No. 91–8, 1991.
Bulow, Jeremy I., and John B. Shoven.
“The Bankruptcy Decision,” Bell Journal of
Economics, vol. 9, no. 2 (Autumn 1978),
pp. 437–56.
Calomiris, Charles W., and Charles M.
Kahn. “The Role of Demandable Debt in
Structuring Optimal Banking Arrangements,”
American Economic Review, vol. 81, no. 3
( June 1991), pp. 497–513.
Gertner, Robert, and David S. Scharfstein.
“A Theory of Workouts and the Effects
of Reorganization Law,” Journal of
Finance, vol. 46, no. 4 (September 1991),
pp. 1189–222.
Jackson, Thomas H. The Logic and Limits of
Bankruptcy Law. Cambridge, Mass.: Harvard
University Press, 1986.
Longhofer, Stanley D., and Stephen R.
Peters. “Protection for Whom? Creditor Conflicts in Bankruptcy,” Federal Reserve Bank
of Cleveland, unpublished manuscript,
March 1997.
Rajan, Raghuram, and Andrew Winton.
“Covenants and Collateral as Incentives to
Monitor,” Journal of Finance, vol. 50, no. 4
(September 1995), pp. 1113–46.
Roe, Mark J. “Bankruptcy and Debt: A New
Model for Corporate Reorganization,”
Columbia Law Review, vol. 83 (April 1983),
pp. 527–602.
White, Michelle J. “Public Policy toward Bankruptcy: Me-First and Other Priority Rules,”
Bell Journal of Economics, vol. 11, no. 2
(Autumn 1980), pp. 550–64.
________. “Bankruptcy Costs and the New
Bankruptcy Code,” Journal of Finance,
vol. 38, no. 2 (May 1983), pp. 477–88.
@FedFRASER