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Commodity Money Inflation:
Theory and Evidence from France in 1350-1436
Nathan Sussman
The Hebrew University of Jerusalem
Joseph Zeira
The Hebrew University of Jerusalem and CEPR
August 2000
Abstract
This paper presents a theory of inflation in an economy with commodity money and
supports it by evidence from the inflationary episodes in France during the fourteenth
and fifteenth centuries. The paper shows that commodity money can be inflated
similarly to fiat money through repeated debasements, which act like devaluation.
Furthermore, as with fiat money, demand for commodity money falls with inflation.
Unlike fiat money, at high rates of inflation the demand for commodity money
becomes insensitive to inflation, since commodity money has intrinsic value in
addition to transactions, and thus losses from inflation are bounded. Finally, we show
that an anticipated stabilization reduces the demand for commodity money, which is
opposite to the effect of an anticipated standard stabilization on the demand for fiat
money. All the results of the model are supported by the data.
JEL Classification: E31, N13
Keywords: Inflation, commodity money, debasements, seignorage, stabilization.
Mailing Address:
Nathan Sussman
Department of Economics
Hebrew University of Jerusalem
Mt. Scopus
Jerusalem 91905
Israel
E-mail: [email protected]
Commodity Money Inflation:
Theory and Evidence from France in 1350-1436
1. Introduction
This paper describes and analyzes inflation in an economy with commodity money,
and compares it with fiat money inflation. The results are derived from a simple
model of commodity money and are supported by historical data on money and prices
in Medieval France, in the years 1350-1436. We show that there is much similarity
between inflation of commodity money and that of fiat money. First, commodity
money can be inflated by debasing the currency and inflation can be quite high.
Second, the demand for commodity money falls as inflation rises. We also find two
dissimilarities between the two types of money. The first is that due to the intrinsic
value of commodity money, its inflationary losses are bounded. As a result, when the
rate inflation is high, the demand for money becomes insensitive to inflation. The
second dissimilarity is that under commodity money the demand for money falls with
anticipation for stabilization, while it increases under fiat money.
The paper first shows how repeated debasements lead to inflation, which can
be rather high. In each new debasement the ruler issues a new coin with a lower
content of the precious commodity, which is silver in our historical example. The new
coin enters into circulation, the quantity of money increases and prices rise. The ruler
gains from such debasement since he collects seignorage from coins minted and
reminted. The main intuition behind this result is that the units of commodity money
are coins and not silver, and coins can have different contents of silver and thus
different values. We therefore assume that coins circulate by tale rather than by
1
weight. This assumption is supported by our data from France in 1350-1436. The data
show that debasements were frequent and substantial, that rates of inflation were quite
high and sometimes even very high, and that the volumes of minting and reminting
and of seignorage during debasements were substantial.1
The paper then analyzes the demand for commodity money. Inflation erodes
the value of money and operates as a tax on money holdings. Hence, if the public
expects higher inflation the demand for money is reduced. But losses to holders of
commodity money are bounded when inflation is high. This is due to the alternative
use of commodity money, which can be used to create new coins by reminting, and
even be converted, although at some cost, to silver. As a result, the demand for
commodity money in high inflation becomes insensitive to the rate of inflation.
Although we do not have observations on the demand for money in medieval
France, we do have data on minting volumes by the royal mints. The model enables us
to relate the demand for money to the volume of minting, in various stages of the
inflationary process. This enables us to perform empirical tests of the prediction of the
model. Our empirical analysis indeed shows that the negative effect of the rate of
inflation on the demand for money is strong at low rates of inflation and much weaker
at high rates of inflation.
Next we discuss the effect of an anticipated stabilization. A standard
stabilization of fiat money inflation consists mainly of stopping monetary expansion.
Hence, anticipating such stabilization reduces future expected costs of holding money
and therefore increases the demand for money. Under commodity money stabilization
requires issuing new coins with higher content of silver, since the process of inflation
1
Rolnick, Velde and Weber (1996) question this assumption and claim that coins did not circulate by
tale. We discuss this issue extensively in the paper.
2
has previously reduced the silver content of older coins by too much. During the
historical period we examine, many inflationary episodes ended with stabilizations
and always the silver content of coins increased at stabilization. Hence, in stabilization
old coins become either completely useless or go through silver extraction, which is a
very costly activity. Hence, stabilization is costly for money holders, and anticipation
of such stabilization reduces the demand for money rather than increases it.
This result is also supported by the data from French mints. We find that the
demand for money decreased prior to major anticipated stabilizations. We estimate the
probability of stabilization under rational learning and show that this probability had a
negative effect on the demand for money. It is important to note that this finding is
related not only to our theory of inflation, but is also evidence for rational learning by
the public on the probability of stabilization, which is an interesting result in itself.
This paper extends the existing literature on commodity money and connects it
to the mainstream literature on money and inflation. Recent important contributions to
the theory of commodity money are Li (1995), Sargent and Smith (1997), and Velde,
Weber and Wright (1997). These papers analyze the theory of commodity money, of
the types of coins in circulation and of debasements. Our paper offers three important
additions to this literature. First, it extends the analysis to a situation of repeated
debasements, namely of inflation, which to our best knowledge has never been done
before. Second, it turns from issues such as Gresham’s Law to the more applied and
more quantitative issue of the demand for money during inflation. That leads to our
third contribution to the literature, namely an empirical analysis of minting during
inflation, which supports the main results of our model.2 Our paper is also related to
2
Extending the analysis to issues of inflation comes at the cost of simplification. Instead of using search
or cash-in-advance models as the above papers, we use a model with utility from money.
3
other historical accounts of debasements. The closest is Sussman (1993) which deals
with the same historical episode, but there are many other historical episodes of
inflating commodity money by debasement, not only in France. A number of studies
examine similar episodes in early periods of modern Europe.3
The paper is organized as follows. It begins with historical background, then
discusses the theory, and finally presents the empirical results. Section 2 describes the
historical episode and the debasement process. Sections 3-6 present the theory of
commodity money inflation. Section 3 outlines the model, section 4 analyses minting
and prices, Section 5 studies inflation dynamics under debasements, and Section 6
studies the effect of expected stabilization. Section 7 presents the data and descriptive
statistics, and Section 8 describes the method and presents the results of the empirical
analysis. Section 9 concludes.
2. Historical background
During the French economic and commercial expansion of the thirteenth century,
there was a growing demand for a common medium of exchange to facilitate
commercial transactions. That development coincided with rulers’ efforts to reaffirm
their sovereignty by controlling the currency and raising seignorage revenues. They
achieved these objectives by establishing mints that charged seignorage for coining
private bullion into royal coins. By the end of the thirteenth century these mints were
gradually replacing private mints.
The royal mint system expanded throughout the fourteenth century and by
1415 there were 24 mints operating in France, requiring a relatively sophisticated
3
See Bordo (1986) for a survey, Gould (1970) for the Tudor debasement, Kindleberger (1991) for
debasements during the 30 years war; Miskimin (1984) for France; Motomura (1994) for Spain and
4
monitoring mechanism. A mint master operated each local mint. The central
administration encouraged the mint master to produce coins by paying him a given
percentage of the coins he struck. It also appointed royal officials to monitor the
various activities of this economic enterprise. Moreover, it required the mint to submit
random samples of coins for inspection in Paris. As a further reflection of the
influence and central control of the Parisian administration, the regional mint accounts
were written in the French of the court, whereas all other local fiscal accounts were
written in Latin or local dialects. This relatively well-organized and well-monitored
mint system gave the crown an instrument capable of effectively carrying out its
monetary policy.
Mints combined pure metal with base alloys to produce an alloy of a given
fineness and then cut it into coins. The coins' face value, denominated according to
prevailing unit of account, was not stamped on them but rather assigned by the crown.
The prevailing accounting system in France was the tournois system, based on the
denier tournois, the penny of Tours. In this system twelve deniers equaled one sou,
and twenty sous made up one livre. The livre tournois was the numeraire in the French
economy by which all commodities, silver and gold included, were valued. Royal
mints produced the following three types of coins: 1) full bodied gold coins of
denominations greater than one livre usually, 2) silver coins of 50 to 100 percent
fineness valued at fifteen, ten (the most popular), five and three deniers, and 3) petty
coins, containing less than 20 percent silver, valued at two, one and one half denier.
The money supply was generated primarily through minting of private bullion.
The monetary authority offered to exchange, at the ‘mint price’, any amount of bullion
(or foreign coins) in return for royal coins. Besides minting fresh bullion, the mint
Pamuk (1997) for the Ottoman empire.
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would also ‘remint’ older coins. Reminting occurred both in periods of ‘debasements’
and during currency reforms. A debasement was an act by the monetary authority of
lowering the silver content of the livre tournois, usually by issuing a new coin with the
same face value, but with smaller content of silver. As a result people could make
arbitrage profits from reminting their old coins into new ones, even if some of the
coins are paid to the ruler as seignorage. Also, recoinage was carried out, usually by
decree, during currency reforms. These reforms took place after periods of repeated
debasements or in response to the physical deterioration of the currency. We therefore
refer to them in the paper in the more modern term stabilization.
The objectives of medieval monetary authorities were similar to those of their
modern successors. Ordinarily, the monetary authority was concerned with managing
the money supply by responding to fluctuations in market prices of precious metals,
and by dealing with problems arising from wear and tear of coins in circulation. It also
addressed other concerns such as monitoring the mints, combating counterfeit and
maintaining the quality of royal coins through legislative and enforcement measures.
In periods of fiscal crisis the crown had an additional objective, namely to
increase seignorage revenues. This was achieved by debasing the currency, usually by
reducing the content of silver in the new coins issued. Hence, debasements generated
inflation by increasing the nominal value of bullion, as in modern devaluations. It also
increased the money supply through greater minting and reminting. During a
prolonged period of debasements, reminting increased significantly, as the mint price
rose frequently and induced reminting of older coins. This provided the crown with
seignorage revenues at times when inflationary expectations reduced the incentive to
sell fresh bullion to the mint.
6
One issue that emerges here is the circulation together of coins with various
levels of fineness. Reminting reduced the scope of this phenomenon but as long as
people did not remint all their coins, but only those with highest content of silver,
there was more than one coin in circulation. Could people distinguish between these
different coins? The answer is that they could, but only by help of experts, namely this
information was costly. While increases in face value or weight of coins were
transparent, changes in fineness were difficult to detect, as no information was
released to the public whether the change in mint price was due to change in fineness
or to seignorage rate or to both. In order to find fineness one needed to assay the coins,
which was an expert’s job.
We have historical evidence to the existence of moneychangers in medieval
Europe, who specialized in coin evaluation and exchange. They were usually expert
goldsmiths, either government agents or private entrepreneurs. Surviving archival
documents inform us about their operations. "Changers manuals," that served as
professional textbooks, describe in detail the procedures for essaying and evaluating
coins. Changers account books shed light on their actual activity and indirectly on
coin circulation in the regions they operated in. Surviving accounts show that the
changers were fully aware of the debasement process since they catalogued, in detail,
the coins from the various issues and determined their exchange rates with foreign and
with full bodied older coins. It is therefore plausible that changers were amongst the
first to observe debasement of coinage and that they acted as middlemen between the
public and the mint.
Costly information can explain both how different coins could circulate
together on the one hand and how people could know which coins to remint on the
other hand. If information is costly it is purchased only when the benefit is sufficiently
7
high. Thus individuals did not go to an expert before each transaction at the
marketplace and hence coins circulated by tale in the goods markets. But people did
go to an expert after a debasement to check which coins to remint.
The main period of fiscal crisis and debasement we explore in this paper is
during the Hundred Years War. The war between England and France, which began in
the 1330s and lasted with intervals until 1452, placed a heavy burden on government
finance. The fiscal resources at the disposal of the French monarchy were designed to
cover its regular expenses. Financing a war required additional resources on a grand
scale. The French crown resorted to raising seignorage revenues by means of debasing
the royal coinage primarily because seignorage was part of the traditional feudal rights
of the king. As such, the crown did not require the consent of the representative
assemblies for levying this tax. Other taxes were always contested, hard to obtain and
required extensive and lengthy bargaining to secure. Moreover, the collection costs
involving seignorage revenues were small and the flow of funds to the treasury timely.
The extent of debasement depended on the (mis)fortunes of war and on the
political bargaining power of the king. The Hundred Years War witnessed two periods
of extensive debasements: 1337-1360 and 1418-1436. The first was associated with
the outbreak of the war, the major French defeats at Crecy and Poitiers (when King
Jean II was captured by the English and held for ransom) and the onset of the Black
Death. The second period followed the defeat at Agincourt and the civil war between
the Armagnac and Burgundian factions.
3. The Model
Consider a small open economy in a discrete time framework. There are three goods
in the economy. The first is an aggregate consumption good. It is produced by labor
8
only and each unit of labor produces 1 unit of the physical good during each period.
The consumption good is assumed to be tradable. The second good is silver in the
form of bullion, which are also internationally traded. Silver can be lent or borrowed
in the world’s capital market at a world interest rate, which is assumed to be fixed and
equal to r. International price of the consumption good in terms of silver is 1. The
third good is money in the form of coins, which contain silver. Money is non-traded
internationally, but is the only legal tender within the economy. The price of silver in
terms of money is denoted Pt.
Money is issued by mints, who offer Qt coins for 1 unit of silver in period t.
We call Qt the ‘mint price’. The proportion of silver in coins, which are issued in
period t, is ft, which we call ‘fineness.’ We assume that all coins have the same weight
h, where 1 is the weight of one unit of silver.4 The overall amount of coins that can be
made of one unit of silver is 1/hft, but consumers who bring silver for minting get
fewer coins, since the government extracts seignorage from any minting by the mint.
We denote the rate of seignorage in period t by st. Hence:
(1)
Qt =
1
(1 − s t ) .
hf t
In this paper we consider situations where Qt is increased by the government, by
reduction of fineness. Such an increase is called ‘debasement’. More precisely, we
consider situations of repeated debasements for a long period of time, during which
the mint price rises significantly.
Mints issue new coins in exchange not only of silver bullions, but also in
exchange of old coins. Here we should distinguish between two cases. The first case
occurs during debasements, where the coins brought to the mint are turned to coins
4
Historically not all coins had the same weight, but we assume it for the sake of simplicity.
9
with lower fineness. We call this ‘reminting’. The second case occurs in a
stabilization, which follows a long period of successive debasements. In this case
coins are turned into coins with higher fineness, and we call it ‘recoinage.’ Of course,
the two types of exchange require different technologies, as reminting only requires
adding cheap metal to coins, while recoinage requires extraction of silver from old
coins before issuing new ones. Hence, recoinage is more costly than reminting. We
formally assume that recoinage costs x per one unit of extracted silver.
We next lay out the informational assumptions of the model. First, we assume,
for the sake of tractability, that mints operate at the beginning of each period before
trade in goods takes place, namely before payments by money are made. Our main
assumption is that all coins look alike for ordinary folks and cannot be distinguished
without help of experts, who are called ‘money changers.’ Such help is costly. To
simplify things we assume the following cost structure: in each period an individual
can obtain one evaluation of his coins for free, but additional evaluations are infinitely
costly. As a result, an individual chooses one time in each period to evaluate his coins.
We also assume that during a period many transactions take place and coins circulate
many times. As a result individuals cannot keep track of the composition of coins they
use and hold. Hence, their optimal strategy is to check coins at the beginning of each
period, in order to decide which coins should be reminted, which coins should be
turned into silver and which should be kept in circulation. During the period, when
goods are continuously traded, the set of coins changes, the information is lost and all
coins look alike. Hence, as a result of the law of large numbers, by the end of each
period the composition of coins held by each individual is the same as the
economy-wide composition.
10
We would like to further discuss our informational assumption that coins with
different fineness could not be distinguished in ordinary daily transactions, but only by
‘money changers’. In other words coins circulated by tale and not by weight, or not by
intrinsic value. This is a rather strong assumption, as pointed by Rolnick, Velde and
Weber (1996), since it means that agents repeatedly remint their old coins and thus
lose seignorage on these coins. We have three historical findings that support this
assumption. The first is the evidence on inflation in commodity prices during
debasement episodes, as documented in Sussman (1993). This means that coins were
used as numeraire in their face value, and commodities were not priced by silver, even
in times of repeated debasements. The second finding is that the volume of minting
and reminting was high during periods of debasements, as shown later in the paper,
and so was the volume of seignorage. Since it is not likely that mints coined only new
bullion, it is reasonable that much of their activity was reminting. The latter
conclusion is also supported by evidence from coin hoards of the time. These show
that during stable periods the public held a variety of coins from many vintages, but
hoards from periods of debasements contain mostly the newest vintages and almost no
‘old’ coins. This is evidence for circulation by tale and not by weight, since agents
would not mind holding old coins if they had circulated by weight.
We next describe individuals in the model economy. There is a continuum of
size one of consumers with infinite life horizon. Each supplies one unit of labor in
each period and thus produces 1 unit of good. For the sake of simplicity they are
assumed to be risk neutral. They derive utility from consumption and from money
holdings. This model therefore follows the tradition of money in the utility function,
which began with Sidrauski (1967), and follows the open economy version in
Obstfeld and Rogoff (1996, Ch. 8). Utility of individuals in time 0 is:
11
∞

 m 
U = ∑ (1 + ρ ) −t c t + v t  ,
t =0
 Pt 

(2)
where mt is the amount of money (coins) held by the individual at the beginning of
period t, after all transactions at the mint are completed, and v is concave. For the sake
of simplicity we assume that the subjective discount rate is equal to the interest rate,
i.e. ρ = r.
The government imposes no taxes and finances its activity by seignorage only.
In each period it sets both fineness ft and a seignorage rate st from minting new coins
and uses the seignorage revenues to finance its expenditures. We assume that these
expenditures are imports from abroad and hence the government must extract the
silver from the revenues domestic coins. The silver value of these revenues is
therefore: gt = hstntft(1-x) where nt is the amount of minting and reminting, namely of
production of new coins. An alternative assumption, that the government uses its
seignorage revenues for domestic purchases rather than imports would not change the
main results of the paper. Historically, the crown used seignorage income for both
types of purchases, but we need to set some assumptions in order to close the model.5
Finally, the government can also stabilize the currency. A stabilization consists of
replacing the old coins with new ones, which have higher fineness, namely reduce the
mint price Q and fix it at the new lower level thereafter.
We assume that all markets are perfectly competitive and that expectations are
rational. We first analyze a process of debasements and inflation, assuming all future
policies to be fully known in advance. In the next stage we add a possible stabilization
and allow for uncertainty with respect to the timing of the stabilization, which ends
the process of debasements.
12
4. Minting Decisions and Prices
We begin our analysis of equilibrium dynamics by looking at minting, reminting and
extraction decisions of agents. Remember that this decision is taken in the beginning
of the period, after the consumer takes the stock of money to the expert and learns
what coins he has. First, as long as the price of silver, which is also the price of the
consumption good Pt, is less than the mint price Qt, there is incentive for more
minting and the quantity of money increases. Second, reminting occurs for all coins
with sufficiently high fineness, namely if it can increase the number of coins.
Formally, all coins with fineness f such that
(3)
hfQt =
f
(1 − st ) ≥ 1
ft
are reminted. Note that fineness is non-increasing over time, namely f t ≤ f t −1 for all t,
and the inequality is strict when a debasement occurs. Hence, all coins from periods
prior to τ(t), where fτ(t)(1-st) < ft and fτ(t)-1(1-st) ≥ ft, are reminted in t, and fτ(t) is the
highest fineness held by agents. Consumers can also bring coins to the mint to
exchange with silver, as long as the value of extracted silver exceeds the number of
coins used. Hence, they extract the silver from coins of fineness fu if
(4)
Pt ≥
1 1
.
hf u 1 − x
The supply of money can therefore be described by a step function, as in figure
1. The amount of money mt,r is the amount after reminting and before bullion minting
or extraction take place. This amount does not depend on the price Pt, since reminting
does not depend on price, as seen in equation (3). The demand for money is the
5
The crown indeed listed in its accounts the silver value of its seignorage revenues.
13
demand of consumers only, as the government imports only. The demand for money is
proportional to the price level Pt and is presented in Figure 1 by a ray from the origin.
The equilibrium, which determines the equilibrium price level and the equilibrium
quantity of money is determined by the intersection of the supply step function and the
demand for money. The equilibrium price must, therefore, be within the following
range:
1 1
1
≥ Pt ≥ Qt =
(1 − s t ) .
hf t 1 − x
hf t
(5)
Figure 1 presents three possible equilibria. If the demand for money is small, as in D’,
coins are transformed to silver by extraction and mt=m’. If the demand for money is
large, as in D’’, bullions are minted into coins and mt=m’’. If the demand for money is
D, there is neither silver extraction nor silver minting and mt=mt,r.
Consider next the effect of debasement on equilibrium. A debasement
introduces a new coin with lower fineness. Hence it raises Qt and shifts some of the
supply curve upward. If the new fineness is low enough, so that ft falls below
fτ(t-1)(1-st), there is reminting, which shifts the whole supply curve to the right as well,
as it makes the upper step in the supply curve wider. Hence, a debasement tends to
raise the price. Clearly, there can be a debasement, which leaves the price unchanged,
if there is no reminting and if the previous price exceeds the new mint price. But if
debasements are repeated, they finally raise prices, since the equilibrium price exceeds
the mint price. Thus, repeated debasements lead to inflation, which is analyzed in the
next section.
When the authorities declare stabilization, all coins must be reminted and
hence the supply of money becomes infinitely elastic at the new mint price Qt. As a
result, the equilibrium price, in the case of stabilization, is equal to the mint price Qt.
14
5. Debasements and Inflation
In this section we consider the case of repeated debasements at a fixed rate π.
Consider the following monetary policy: the government collects seignorage at a fixed
rate, namely st = s, and it debases the currency every period at a fixed rate π, i.e.
(6)
Qt
f
= t −1 = 1 + π
Qt −1
ft
for all t.6 If the rate of debasement is fixed, there is a fixed number of types of coins
in circulation, which we denote by T. Every period a new coin is introduced and the
oldest coin is reminted. T is bounded by the following inequalities, which are derived
from (3):
(7)
1
≤ (1 + π ) T −1 (1 − s ) < 1 .
1+π
We next show that after a few debasements the price Pt becomes equal to the mint
price Qt. To see this note that the monetary dynamics are:
(8)
mt = mt −1 + nt −T [(1 + π ) T (1 − s ) − 1] + Qt et ,
where nt is the amount of coins minted in time t and et is the amount of bullion minted
into coins in t. If there is no minting of new bullion, we get from (8):
mt ≤ mt −1 [(1 + π ) T (1 − s )]
and the term in brackets is smaller than 1+π according to (7). Hence, if there is no
minting of new silver, the quantity of money grows at a rate lower than 1+π. This
cannot last long and hence after a few debasements there must be minting of new
6
Historically, the debasement episodes consisted not only of reduction in fineness, but often of
increased seignorage rates as well. In the theoretical part of the paper we treat inflation and seignorage
rates as independent. We return to this issue in the empirical part of the paper in Section 8.
15
silver. Note that silver is minted only if the equilibrium price equals the mint price, as
shown in Figure 1, and hence:
(9)
Pt = Qt ,
and this equality holds from then on. The intuition behind this result is simple. Since
the government uses the silver it gets as seignorage outside the economy, it reduces
the silver contents of coins continuously. Hence, consumers need to mint new bullion,
which they would not have done had the price of silver exceeded the mint price.7
In the rest of the section we focus on the steady state equilibrium. As we have
seen the rate of inflation at the steady state is π and the price is equal to the mint price.
We differentiate between two cases. In the first there is more than one type of coins in
circulation, i.e. T>1. In this case reminting is partial. In the second case the rate of
inflation is high so there is only one coin in circulation, i.e. T=1. In this case all former
coins are reminted.
5.1. Debasements with Partial Reminting
We next describe the steady state distribution of types of coins when the number of
types T is greater than 1.8 The quantity of coins of fineness ft-u for all 0 ≤ u ≤ T-1 is the
quantity of coins minted in period t-u, and is equal to
(10)
n t − u = mt
π
(1 + π ) −u ,
1 + π − (1 + π )1−T
where mt is the aggregate amount of money, which we derive next. Note that the
distribution of coins as described in (10) is both economy-wide and also holds for any
individual by end of trading period, due to high circulation of coins.
7
We should stress here that even if the government uses its seignorage revenues within the country and
as a result the equilibrium price is not always equal to the mint price, the main results of the model do
not change at all.
8
It can be shown that the distribution of coins converges to this steady state distribution.
16
The individual maximizes utility (2) with respect to the budget constraints. We
next calculate the marginal benefit and marginal cost of holding money in order to
find the demand for money. The marginal utility of real money balances is v′(mt / Pt ) .
In calculating the marginal cost of money the individual takes into consideration that
some coins will remain in circulation in next period and some will be reminted, thus
having different rates of return. Since the individual has no control over the
distribution of coins he will hold by end of period, he can only calculate the expected
marginal cost of holding money, based on the distribution (10). The marginal real cost
of holding coins, that will not be reminted next period, is due to inflation and loss of
interest, namely:
(11)
1−
1
1
.
1+ r 1+π
The marginal cost of holding coins, which will be reminted next period, is lower,
since reminting increases the number of coins, and is equal to:
(12)
1−
1 (1 + π ) T (1 − s )
,
1+ r
1+π
which is smaller than (11) due to (7). Given the distribution of coin types (10) we get
that the expected marginal cost of money is:
(13)
1−
1
1 1 − (1 + π )1−T + π (1 − s ) 

.
1+ r 1+π 
1 − (1 + π ) −T

Equating the marginal cost and marginal benefit of money yields the
equilibrium real balances in the economy, since only consumers hold money:
(14)
m
v ′ t
 Pt

1
1 1 − (1 + π )1−T + π (1 − s ) 
 = 1 −

.
1+ r 1+π 
1 − (1 + π ) −T


This equation shows that in equilibrium real balances (the demand for money) depend
both on the rate of inflation and on the rate of seignorage. Furthermore, the number of
17
coins in circulation T is an endogenous variable, which depends on these two
variables as well. In order to see how real balances depend on π and s in the reduced
form, consider the rates of debasement, at which the number of coins changes and
falls from T+1 to T. This rate is determined by the condition: (1 + π ) T (1 − s ) = 1 . At
this rate the marginal costs of all types of coins are equal and given by (11). Hence,
the equilibrium real balances are described by:
m
v ′ t
 Pt
(15)

r + π + rπ
 =
.
 (1 + r )(1 + π )
We, therefore, conclude that real balances depend negatively on the rate of inflation as
long as more than one type of coins circulates.
While equations (14) and (15) determine the equilibrium stock of money, our
data from Medieval France consists only of flows of minting, as reported by the
various mints. Luckily, our model enables us to easily find the flow of minting, which
depends on the demand for money and on the distribution of coin types. The amount
of minting n is therefore given by:
(16)
nt
mt
π
=
.
1−T
Pt 1 + π − (1 + π )
Pt
From this equation we see that inflation affects minting in three channels. First, the
overall demand for money m/P falls with inflation. Second, higher inflation reduces
the value of old coins more rapidly and that increases minting as shown in the first
term in the RHS of (16). This exerts a positive effect of inflation on minting. Third,
higher inflation reduces the number of coin types in circulation T and that also affects
minting positively. In order to consider the three effects together, consider again the
rate of inflation at which the number of coins falls from T+1 to T. At this rate minting
is equal to:
18
nt 1 π mt
=
.
Pt s 1 + π Pt
(17)
Hence, inflation affects minting in two ways: positively by reducing the number of
types of coins in circulation and negatively by reducing the demand for money. The
overall effect depends on the elasticity of the demand for money with respect to π.
Minting is negatively affected by π if this elasticity is greater than 1/(1+π).9 Minting is
also affect by the rate of seignorage, which has a negative effect.
5.2. Debasements with Full Reminting
We next examine the case where inflation is so high, that all the old coins are
reminted and there is only one coin in circulation, i.e. T=1. This case holds when
(1 + π )(1 − s ) > 1 .
(18)
In this case the marginal cost of money is given by (12), since all coins are reminted,
and is equal to:
1−
1− s
.
1+ r
Equating the marginal cost with the marginal benefit of money yields:
(19)
m
v ′ t
 Pt
 r+s
 =
.
 1+ r
Hence, the demand for money in this case does not depend on the rate of inflation but
on the rate of seignorage only.
This is a very surprising result, and it is unique for inflation in commodity
money. More precisely, it is a result of the intrinsic value of coins, namely of their
silver content, in addition to their transaction value. When the rate of inflation is high,
holders of commodity money can avoid some of the inflation tax by reminting. In
9
In our historical episode the effect of inflation on minting is negative, as shown in Section 8.
19
doing so they reduce their losses to the fixed seignorage only. As a result they can
hold more money and their demand becomes insensitive to the inflation rate. Note that
this strategy is not possible under fiat money.
The rate of inflation at which individuals begin to remint all their coins and at
which the demand for money depends only on the rate of seignorage is
(20)
π* =
s
.
1− s
When inflation exceeds π* and full reminting prevails, the real amount of minting is
equal to real balances described in (19), since all coins are new. Hence, when inflation
exceeds π* the amount of minting also depends on the rate of seignorage and not on
the rate of inflation. Section 8 presents some empirical evidence that supports this
theoretical result.
6. Debasements and Stabilization
In section 5 we describe a debasement process that goes on forever. This is a helpful
but not very realistic simplification. Rulers could not debase the currency forever by
bringing fineness as close as possible to zero, since at very low levels fineness
becomes indistinguishable from zero and commodity money loses all its value. This
level could not be reached and the public knew it as well. Indeed, our historical
records show that periods of repeated debasement, which reduced fineness to very low
levels, ended in stabilizations. Since such stabilization was anticipated it affected the
demand for money. In this section we add the effect of this anticipation to the analysis
and bring it closer to reality. We assume as above that there is a fixed rate of
debasement π and a fixed rate of seignorage s, and that the rate of debasement is so
high that agents remint all coins every period. We assume that the probability of
20
stabilization is positive, and denote this probability in period t by zt. Later on, we
make this probability endogenous as well.
We solve the model in two stages, after and before the stabilization takes
place. We first calculate the optimal value of utility from the stabilization on, when
the economy returns to full certainty and to full price stability. If stabilization occurs
in period t, then optimal utility V S depends on the accumulated amount of silver
bullion bt-1 and on the amount of real balances held, and is equal to
(21)

m  1+ r
m
1+ r
+ bt −1 (1 + r ) + t −1 (1 − s )(1 − x) − l * +
V S  bt −1 , t −1  =
v(l*)
Pt −1 
r
Pt −1
r

where l* is the amount of real balances after stabilization, which is determined by
(22)
v ′(l*) =
r
.
1+ r
Denote by V the optimal value of utility prior to the stabilization in period t.
Then the Bellman equation is:
(23)


m
m 
V  bt −1 , t −1  = max ct + v t
Pt −1 

 Pt

 z t +1 S  mt
 +
V  bt ,
Pt
 1+ r

 1 − z t +1  mt
 +
V  bt ,
Pt
 1+ r 

 

under the constraint:
(24)
ct = 1 +
mt −1
m
(1 + π )(1 − s ) + bt −1 (1 + r ) − bt − t .
Pt
Pt
Before we derive the first order conditions, note that due to the envelope theorem, the
partial derivatives of V are
(25)
Vb = 1 + r and Vl =
Pt −1
(1 + π )(1 − s ) .
Pt
The first order conditions of (23) are, therefore:
21
(26)
1=
1 − z t +1
z t +1
Vb ,
(1 + r ) +
1+ r
1+ r
which indeed fits (25), and:
(27)
z
1 − z t +1 Pt
m
v ′  = 1 − t +1 (1 − s )(1 − x) −
(1 + π )(1 − s ) .
1+ r
1 + r Pt +1
P
Hence, the demand for money falls as the probability of stabilization rises. We
next turn to find the rate of inflation. We prove that if the seignorage rate is high
enough, which has been the case in our historical episodes, price equals the mint price
Qt. The equilibrium price is affected by opposite demand and supply effects. On the
one hand demand for money is reduced as probability of stabilization increases. On
the other hand, if there is no minting of new bullion, money supply grows by
(1 + π )(1 − s ) − 1 according to (8), which is much lower than the rate of debasement π.
Hence, if the rate of seignorage s is sufficiently high there is always minting of new
bullion and the equilibrium price equals the mint price.10 Hence, the rate of inflation is
equal to π. Substituting in (27) yields:
(28)
m
v ′ t
 Pt
 r + s + (1 − s ) xz t +1
 =
.
1+ r

Hence, the demand for money depends both on the rate of seignorage and on the
probability of stabilization. This probability has a negative effect on the demand for
money, since agents wish to minimize the cost of recoinage, of converting debased
coins to good coins.
We next try to describe how the probability of stabilization evolves over time,
using a Bayesian learning process under very simple assumptions. Assume that the
public only knows that the process of debasement cannot go on to zero fineness, and
22
there is a minimum level of fineness f*. If the economy is expected to reach this
fineness in period T*, and there has been no stabilization until t, the probability of
stabilization is uniform, namely it is
(29)
z t +1 =
1
.
T * −t
Fineness falls at a rate π, and hence the time until T* can be deduced from
f * = f T * = f t (1 + π ) − (T *− t ) .
Hence, the probability of stabilization is
(30)
z t +1 =
1
log(1 + π )
.
=
T * −t log f t − log f *
The probability of stabilization, therefore, depends negatively on fineness. The lower
fineness is, the higher is the probability that the process of debasements ends soon.
This probability also depends positively on the rate of debasement.
Finally note that since only one coin circulates the amount of minting is equal
to the amount of money: nt = mt. Hence, minting depends negatively on the rate of
seignorage and negatively on the probability of stabilization. As debasement
continues, anticipation of stabilization rises, and hence minting is reduced. This is also
an explanation to the puzzle raised by Rolnick, Velde and Weber (1996), who find the
amount of minting to be too small given the rates of inflation in such situations.
7. Data and Descriptive Statistics
The data used in this paper is derived largely from original mint accounts found in the
national French archives and in the regional archive of the Isere at Grenoble11. These
10
Note that without this assumption the price would be higher than the mint price but the qualitative
results of the model would remain the same. This is therefore only a simplifying assumption.
11
For greater detail see Sussman (1997).
23
periodical accounts were submitted by the mints to the central monetary
administration in Paris and contained information about the characteristics of the
coins produced, the quantity minted, the costs, the seignorage revenues and the net
profit of the mint. Due to losses, fires and wars the extent of coverage of the
documents is not complete. We have data only for some of the mints and in many
cases there are gaps in the data for certain years. Notwithstanding, the data we have
allows us to assemble a data set that covers the major periods of debasements during
the 1350s and between 1415 and 1422 from 12 mints of varying importance and
geographical locations.
It is important to note that the data does not come in fixed periods of time but
rather in periods with varying lengths, since the frequency of submitting mint accounts
to the auditors in Paris was not uniform. The accounts cover periods as short as one
day to periods as long as fifteen months, and the average length of account is one
month. Accounting periods varied between mints and over time. Under normal
circumstances accounts were submitted every six months or annually. However,
during the debasement period, the accounts were submitted more frequently. This
phenomenon reflects the tighter fiscal control over the mints, which had to submit the
accounts and the profits on a more timely basis. Moreover, the accounts were usually
closed, under royal directive, following changes in any of the characteristics of the
coinage. In periods of debasement the changes were frequent and therefore the
accounts cover shorter periods. A further complication arises from the fact that royal
orders reached mints with varying delays, due to the large distances between the mints
and Paris, due to problems of travel in war zones and due to necessity to sometimes
pass through provincial administrative centers.
24
Although the data is in varying lengths of time, they cover continuos periods
of time for the 12 mints. Hence, they enable us to calculate the main variables and
how they evolve over time. The variables that are relevant for the model are mint
prices, rates of inflation, seignorage rates, and amounts of minting. The data are
pooled and allow us to draw some generalizations and to test the hypothesis derived
from our model.
We first present some descriptive features of the data on French debasements
in the years 1330-1436. The first debasement period was characterized by repeated
cycles of debasement and revaluation. The period from 1337 to 1354 witnessed 34
mild debasement cycles with relatively long periods of stable money (figure 2). The
period from 1354 to 1360 saw 51 rapid debasement cycles that reached
hyperinflationary magnitudes in 1360 (figure 3). The average increase in the nominal
value of silver during such a cycle was 200 percent and the average duration of a
debasement cycle was 400 days. The largest debasement cycle increased silver price
by 600 percent, and lasted only 116 days. The smallest cycle increased price by 66
percent. The shortest debasement cycle was 33 days during which the nominal value
of silver increased by a 100 percent. The period from 1417 to 1422 was characterized
by a prolonged process of debasement during which the nominal value of silver was
increased by 3500 percent without any attempt to stabilize the currency (figure 4),
milder debasements (average of 80 percent per cycle) followed until 1436 (figure 5).
This description of the dynamics of silver prices in this period shows that indeed the
government could inflate commodity money in high rates.
The debasements resulted in substantial minting and large government
revenues. While complete data for all the mints operating in France is lacking, the
data we found at the French archives allows us to assess the quantitative aspects of
25
these debasement episodes. Figure 6 shows the mint outputs of four major French
mints. The total mint output for the four mints in 1355 was about 75,000 marcs of
pure silver (20 tons) whereas the annual average of total minting in France in non
debasement years was 5,000 marcs. The revenues secured by the government were
also impressive: according to Maurice Rey, the 1419 seignorage revenues amounted to
six times ordinary royal revenues. Figures 7, 8 and 9 show, respectively, minting
levels and seignorage revenues at the mints of Rouen, Montpelier and the Dauphine
mints (Cremieu, Mirabel and Romans). The figures illustrate the high share of
seignorage revenues out of total minting. It is interesting to compare the experience of
Rouen (Figure 7) and Montpelier and (Figure 8). In 1356, following the capture of
King Jean by the English at Poitiers, the Estates of Languedoc (southern France) voted
to suspend debasement whereas the mints of the North continued to debase the
currency. In response, mint outputs and seignorage revenues in Montpelier started to
decline, while at Rouen they reached an all time high.
In the theoretical section of the paper we identify the price of silver with
commodity price. We further add assumptions that make the rate of inflation equal to
the rate of debasement, the rate of increase of mint price. It is interesting to examine
whether historical data can justify these assumptions. Unfortunately, high quality price
data for France are lacking. Nevertheless, reproducing in Table 1 data reported by
Sussman (1993) for the Dauphine, we see that grain prices followed the course of mint
prices whereas the price of gold followed the price of silver.
8. Empirical Analysis
Our model describes how the demand for commodity money and the amount of
minting are related to three main variables: the rate of inflation, the rate of seignorage
26
and the anticipated probability of stabilization, and how this relationship changes at
different levels of inflation. Since we do not have data on the quantities of money but
rather on the amounts of minting, we use this data to test the main conclusions of the
model. Namely we examine how minting depends on the rate of inflation, on the rate
of seignorage and on the probability of stabilization.
Before we describe the empirical analysis in detail we address the issue of the
correlation between the seignorage rate and the rate of inflation. We know from our
records that as inflation increased so did the rate of seignorage, as the ruler tried to
extract greater income from debasements. There is a clear positive correlation between
the rate of decline of fineness and the rise in seignorage rate. We have calculated these
correlations for various mints and they are not so high, namely less than 0.5. Hence,
the two variables, inflation and seignorage are related but can still be used as
explanatory variables in regression analysis.
Our empirical analysis has two parts. In the first part we examine a basic
equation, of minting as a function of the rate of inflation and the rate of seignorage,
and excluding for the meanwhile the probability of stabilization. We estimate this
basic equation considering two cases, that of low inflation and partial reminting and
that of high inflation and full reminting. Our hypothesis is that the effect of the rate of
inflation is weaker at higher rates of inflation. In the second part of the analysis we
estimate a measure of the expected probability of stabilization based on the model and
add this measure to the minting equation as a third variable. Our hypothesis in this
case is that minting is negatively related to the probability of stabilization.
Our regression estimates are based on a panel of data pooled from 12 mints
that includes the debasements episodes described above. As discussed above, due to
the varying lengths of mint accounts, the quantities of minting are from periods of
27
time of different lengths. In order to account for that and to normalize the minting data
we added the length of the account period as an additional explanatory variable to the
regressions.
The results of the first part of the analysis are presented in Table 2.
Regressions I and II in this table confirm the main hypothesis of our model, as
described by equation (18). We find that minting is negatively affected by both the
seignorage rate and the annual inflation rate. We then proceed to test whether the
effects of inflation and seignorage differ under low and high inflation rates. We
examine the effect of inflation on minting at rates below and above 50%. Remember
that according to equation (23) reminting is full above π* = s/(1-s). During the period
when inflation was bellow 50% the average seignorage rate was 27% with a
maximum of 50% which roughly corresponds to the inflation rate calculated from the
model. When inflation exceeded 50% the seignorage rate was higher at 37% on
average and with a maximum rate of 75%! Indeed, equations III and IV in Table 2
show that the effect of inflation is much larger and more significant than the effect of
seignorage in levels of inflation below 50 percent. However, as shown in equations V
and VI in Table 2, at higher inflation rates - around 100% - with complete reminting,
we find that the effect of the seignorage rate dominates that of inflation, and that the
effect of inflation even becomes zero and insignificant.
In the second part of our empirical analysis we add a third explanatory
variable, namely the probability of stabilization. Following is an explanation of how
this probability is estimated. In every period t we know the actual duration until
stabilization, i.e. t − t , where t is the actual date of stabilization. Expected duration
until stabilization is equal to (T*-t)/2 under the assumption of uniform distribution,
but it is also equal to the expectation of t − t . Hence, we can write:
28
(31)
t −t =
log f t − log f *
T * −t
+ ε t ,t =
+ ε t ,t .
2
2 log(1 + π t )
We therefore estimate a regression of the actual time to stabilization on two
explanatory variables: the logarithms of fineness and of the rate of inflation. The
estimated equation yields the probability of stabilization as a function of these two
variables. This regression is presented in Table 3 and it indeed shows that the time to
stabilization decreases with inflation and increases with fineness. Therefore, the
probability of stabilization rises with inflation and is negatively related to fineness.
After estimating the probability of stabilization as described above, we add
this probability as an explanatory variable to the minting equation. This is presented in
Table 4, which shows that this probability has a significant negative effect on minting,
beyond that of the seignorage rate and of inflation. Note that this result is in contrast
to the effect of expected stabilization in an economy with fiat money, in which
anticipated stabilization increases the demand for money. Here it reduces it. As
mentioned above, this result can resolve what Rolnick, Velde and Weber (1996)
present as an empirical puzzle. They claim that the amount of minting during
debasements is too small to justify circulation by tale. We show that if we take into
consideration the probability of stabilization, it can account for smaller demand for
commodity money and for less minting during the last phases of debasement episodes.
9. Summary and Conclusions
In this paper we show that inflation and even high inflation is possible under a
commodity money regime. Inflation can exist in such a regime because people prefer
to use coins rather than the commodity itself. Thus, if the commodity (silver) content
in coins is reduced continuously, inflation occurs. The possibility of high inflation due
29
to debasements is shown not only in a model, but also demonstrated by a hundred
years of frequent debasements in medieval France. Therefore the historical commodity
money regime was quite similar to the more modern fiat money regime and for a
similar reason, namely that people prefer money for transactions over other assets.
Despite this basic similarity between commodity money and fiat money, we
observe two main differences between the two. Under commodity money the demand
for money falls less when inflation becomes high. This is because coins still retain
some intrinsic alternative value and can be used for reminting. Another important
difference is with respect to demand for money when stabilization is anticipated.
While under fiat money this increases the demand for money, under commodity
money such a stabilization requires coin holders to recoin their money at a substantial
cost, thereby reducing the demand for money when stabilization is anticipated.
We test for these two results using data found in French archives and are able
to corroborate them. Though we do not have direct data on the demand for money, but
rather on minting, we show that minting behaves as indicated by our model, namely
that it declines with inflation in low inflation environment and becomes less affected
by inflation when the rates are high. Furthermore, we are able to show that minting
declines with the increase in the probability of expected stabilization.
Our model, findings and conclusions are not limited to France during the
Hundred Years War. There were numerous periods of debasements in Europe in the
early modern period, in the Low Countries, Spain, England, in Italian city states, in
Germany and in the Ottoman Empire. Though French data are perhaps the most
extensive and of the highest quality, we believe that our approach can be used to
explain similar episodes in other countries and over a large period of time,
characterized by the use of commodity money.
30
In this paper we assume that agents demand royal coins and trade them at face
value. It could be interesting to question this very assumption itself. Is it due to the
public good aspect of royal coinage? Are there economies of scale in their use? Why
do people use coins at face value even when inflation is very high and seignorage rate
is high as well? These are questions, which we do not address, but they are raised by
our story and they are relevant for understanding the role of money not only in the past
but in the present as well.
31
References
Bordo, Michael D., “Money, Deflation and Seignorage in the Fifteenth Century: A
Review Essay” Journal of Monetary Economics; 18(3), November 1986, pages
337-46.
Gould, John D., The Great Debasement (Oxford, 1970).
Kindleberger, Charles P. “The Economic Crisis of 1619 to 1623,” Journal of
Economic History; 51(1), March 1991, pages 149-75.
Li, Yiting, “Commodity Money under Private Information,” Journal of Monetary
Economics, 36(3), December 1995, pages 573-92.
Miskimin, Harry A., Money and Power in Fifteenth Century France (New Haven,
1984).
Motomura, Akira, “The Best and Worst of Currencies: Seignorage and Currency
Policy in Spain, 1597-1650,” Journal of Economic History; 54(1), March
1994, pages 104-27.
Obstfeld,
Maurice,
and
Kenneth
Rogoff,
Foundations
of
International
Macroeconomics, MIT Press, Cambridge MA, 1996.
Pamuk, Sevket, “In the Absence of Domestic Currency: Debased European Coinage in
the Seventeenth-Century Ottoman Empire” Journal of Economic History;
57(2), June 1997, pages 345-66.
Rolnick, Arthur J.; Velde, François R.; Weber, Warren E, “The Debasement Puzzle:
An Essay on Medieval Monetary History” Journal of Economic History; 56(4),
December 1996, pages 789-808.
Sargent, Thomas J., and Bruce D. Smith, “Coinage, Debasements, and Gresham’s
Laws,” Economic Theory, 10 (1997), pages 198-226.
Sidrauski, Miguel, “Rational Choice and Patterns of Growth in a Monetary
32
Economy,” American Economic Review, 57, May 1967, pages 534-544.
Sussman, Nathan, “Debasements, Royal Revenues, and Inflation in France during the
Hundred Years' War, 1415-1422” Journal of Economic History; 53(1), March
1993, pages 44-70.
Velde, François R., Warren E. Weber, and Randall Wright, “A Model of Commodity
Money, With Applications to Gresham’s Law and the Debasement Puzzle,”
Federal Reserve Bank of Minneapolis, Research Department Staff Report 215,
July 1997.
33
Table 1
Annual Price Changes In The Dauphine, 1418-1422
Year
Silver:
Mint Par
1418
1419
1420
1421
1422
Cumulative
:
Gold:
Grain:
Mint Price Gold Price Wheat Price
50%
33%
50%
167%
200%
13%
56%
43%
75%
100%
22%
45%
88%
100%
233%
50%
40%
-40%
100%
200%
2300%
775%
2122%
656%
Source: Sussman (1993)
34
Table 2
Dependent
variable
Method
Constant
Seignorage rate
Inflation
Length of
account*
R2
D.W.
N
Mint output*
Mint output*
I
Random Effects
5.35
(2.36)
-0.77
(-2.55)
-0.28
(-3.74)
0.57
(15.82)
0.5
1.62
539
II
Common
5.50
(22.68)
-1.01
(-3.58)
-0.17
(-2.27)
0.52
(13.76)
0.70
1.38
539
Mint output*
Mint output*
Mint output*
Mint output*
Inflation < 50%
III
Fixed effects
Inflation < 50%
IV
Common effect
6.06
(11.38)
-0.07
(-0.12)
-1.32
(-4.19)
0.55
(7.59)
0.87
1.59
107
Inflation < 100%
V
Fixed effects
Inflation < 100%
VI
Common effect
5.00
(15.3)
-1.76
(-4.85)
0.312
(1.88)
0.53
(12.22)
0.80
1.24
342
-0.94
(-1.57)
-0.88
(-2.43)
0.53
(7.06)
0.97
1.96
107
Notes: t-values in parenthesis
* - denotes log of variable.
All Regressions estimated using GLS procedure with cross section weights.
35
-0.79
(-2.16)
0.07
(0.44)
0.60
(14.6)
0.90
1.57
342
Table 3
Number of days
to stabilization
Fixed effects
-85.26
(-3.78)
238.55
(10.65)
0.47
0.4553
506
Method
Inflation*
Fineness*
R2
D.W.
N
Notes: t-values in parenthesis
* - denotes log of variable.
All Regressions estimated using GLS procedure with cross section weights.
36
Table 4
Dependent
variable
Method
Seignorage rate
Inflation
Expected
Stabilization*
Length of
account*
R2
N
D.W.
Mint output*
Mint output*
I
Fixed Effects
-0.72
(-2.11)
-0.26
(-3.13)
-0.18
(-2.20)
0.57
(15.10)
0.67
488
1.74
II
Fixed effects
-0.71
(-2.05)
-0.29
(-3.78)
0.60
(16.6)
0.641
488
1.71
Notes:
t-values in parenthesis
Probability of stabilization is the inverse of the expected number of days left to the
date of stabilization, as derived from Table 3.
* - denotes log of variable.
All Regressions estimated using GLS procedure with cross section weights.
37
Pt
(1 − x ) −1
hf t
D’
D
(1 − x ) −1
hf τ ( t )
D’’
S
Qt
mt,r
m’
Figure 1
38
mt
m’’
Figure 2
Cumulative debasement rate
France: 1337-1354
400%
300%
200%
100%
0%
Aug-35
Apr-38
Jan-41
Oct-43
Jul-46
Apr-49
Jan-52
Oct-54
Figure 3
Cumulative debasement rate
France 1353-1360
600%
500%
400%
300%
200%
100%
0%
May-53
Oct-54
Feb-56
Jun-57
39
Nov-58
Mar-60
Aug-61
Figure 4
Cumulative debasement rate
France: 1412-1422
6000%
5000%
4000%
3000%
2000%
1000%
0%
Dec-10
Sep-13
Jun-16
Mar-19
Nov-21
Aug-24
Figure 5
Cumulative debasement rate
France: 1423-1436
250%
200%
150%
100%
50%
0%
Nov-21
Aug-24
May-27
Feb-30
40
Nov-32
Aug-35
Apr-38
Figure 6
Minting volumes: France 1350-1361
in marcs of pure silver
30000
25000
20000
15000
10000
5000
0
1350
1352
Montpellier
1354
1356
Toulouse
1358
Troyes
1360
Rouen
Figure 7
Debasement Minting
Rouen: 1354-1361
25000
25
20000
20
15000
15
10000
10
5000
5
0
0
1354
1355 1356
1357
Marcs minted
net revenues in pure silver
41
1358 1359
1360 1361
Mint Price -livres
Figure 8
Debasement Minting
Montpellier: 1354-1361
10000
12
11
8000
10
6000
9
8
4000
7
2000
6
0
5
1354
1355
1356
1357
marcs minted
net revenues in pure silver
1358
1359
1360
1361
mint price - livres
Figure 9
Debasement Minting
Dauphine: 1417-1422
30000
80
70
25000
Marcs
50
15000
40
30
10000
Livres tournois
60
20000
20
5000
10
0
0
1417
Mint price - livres
1418
1419
Marcs minted
42
1420
1421
1422
Net revenues in pure silver