S"T
1188 COPY 2
FACULTY WORKING
PAPER NO. 1188
The First Rational Bubbles: A New
Look at the Mississippi and South
Sea Schemes
Larry Neal
Eric Schubert
Commerce and Business Administration
Bureau of Economic and Business Research
University of Illinois, Urbana-Champaign
College of
BEBR
FACULTY WORKING PAPER NO. 1188
College of Commerce and Business Administration
University of Illinois at Urbana-Champaign
September, 1985
A New Look at the
The First Rational Bubbles:
Mississippi and South Sea Schemes
Larry Neal, Professor
Department of Economics
Eric Schubert
September 1985,
Comments Invited.
The authors acknowledge with gratitude helpful comments and criticisms
of earlier drafts by Professors P. G. M. Dickson, Robert Flood, Charles
Kindleberger and Eugene White as well as by participants in seminars at
the Cliometrics Conference at Miami University, Columbia University,
University of Chicago, University of Illinois, and Northwestern University
Research support was provided by the University of Illinois Research
Board, the Bureau of Economic and Business Research, and the National
Science Foundation (SES 83-09211).
,
Digitized by the Internet Archive
in
2011 with funding from
University of
Illinois
Urbana-Champaign
http://www.archive.org/details/firstrationalbub1188neal
ABSTRACT
This paper makes explicit the linkages between the Mississippi
Bubble in France, the South Sea Bubble in England as well
with the aftershocks in Amsterdam and Hamburg during the
years 1719 and 1720 by using semi-weekly exchange rate data
that were published regularly throughout this period.
These
have never been used before to analyze either the dynamics of
the two major bubbles or the linkages between them. We then
use daily price data for the Compagnie des Indes in France,
and the South Sea Company as well as the Bank of England
and East India Company in England select and estimate the
appropriate ARIMA models for different subperiods.
They suggest very strongly
portions of the Mississippi
Bubble may be rational bubbles although it is as likely they
manipulation of market fundamentals; that the
reflect the
South Sea Bubble was clearly a rational bubble but only for
South Sea stock and not for Bank of England or East India
Company stock; and that the Dutch bubbles were most likely
rational but broken more by monetary reforms in France and
reorganization of the South Sea Company in England than by
their internal dynamics.
that
are now to enter upon the year 1720; a year remarkable
beyond any other which can be pitched upon by historians for
romantic
projects,
proposals,
and
and
extraordinary
which,
national;
and
ought
undertakings, both private and
perpetual remembrance, not only as being what
to be had in
never had its
parallel, nor, it is to be hoped, ever will
We
...
...
may
serve for a perpetual
memento to the legislators and ministers ... never to leave it in
the power of any, hereafter, to hoodwink mankind into so
shameful and baneful an imposition on the credulity of the
people, thereby diverted from their lawful industry. (Adam
Anderson, Origin of Commerce, v. 3, pp. 91-2.)
hereafter;
The
and bust
it
Holland and Germany during the years 1719 and
in
were parts of the
1720
as
Mississippi Bubble in France, the South Sea Bubble in England,
and similar bubbles
The
likewise,
but,
international stock market speculative
first
The legacy of
in capitalist Europe.
Bubble
Act
of
1720
in
England
these episodes
limited
the
use
boom
was substantial.
of
joint
stock
corporations until well into the nineteenth century; the French collective
Law and
memory
of John
even
pronouncing the word 'bank' for 150 years thereafter;" 1 and, of
in
course, they gave
movements
us
the
in asset prices.
modern macroeconomics. 2
his
Banque Royale meant "there was hesitation
word "bubble" for describing purely speculative
These are the subject of a growing literature
It
is
in
useful to present and analyze as clearly as
possible these classic bubbles in light of this recent theoretical literature,
useful
1
2
not
only
for
Kindleberger (1984),
E.g.,
understanding
better
the
economic
history
of
the
p. 98.)
Blanchard and Watson (1982), Diba and Grossman (1983, 1984, and
and Garber (1982), Shiller (1984), Tirole (1982), and West (1984
1985), Flood
and 1985).
eighteenth
century
theory.
is
It
for
also
grasping
its
task of quantitative analysis
begun
just
Our
and theoretical understanding
4
available.
Bubble
same
in
aided by
is
modern economic
historians
to exploit.
results,
interpretation
economic
for
in a relatively pristine state.
the existence of extensive data resources that
have
significance
interesting for economic theory to observe the
intrinsically
on capital markets when they were
activities
The
but
of
presented in detail below, give a somewhat different
these
We regard
Protean
the
events
Mississippi
than
in
Bubble
the
France,
in
currently
literature
the
South Sea
England, and the later bubbles in the Netherlands as part of the
historical process.
economic game.
More accurately, each was
The game
in
each case was
of shares in a given joint-stock corporation.
will be described
to drive
The
a
replay of the same
up the nominal values
specific techniques used
below when discussing the Mississippi bubble since these
South Sea and Dutch bubbles.
The
were the same that were used
in the
game was confined by
one company (Compagnie des Indes) in the
3
fiat to
E.g., McCusker (1978); Mirowski
(1985b); Parsons (1974); Riley (1980).
(1981);
Neal
(1977),
(1983),
(1985a),
4
Lengthy works by Levasseur (1854), Harsin (1928, 1934, 1935), and most
recently, Faure (1977), have covered the Mississippi Bubble in detail.
The
best analytical treatments available to date in English are by Hamilton
(1936-37; 1967; 1969) and Minton (1975) is a useful narrative.
Carswell (1960), Scott (1910), and Dickson (1967) have discussed the South
Sea extensively: Carswell the often humorous socio-political aspects; Scott,
the dry but enlightening corporate and financial subtleties; and Dickson the
historical background as well as the technical specifics of stockjobbing in
the various subscriptions. All three accounts, in turn, rely very heavily on
Adam Anderson's discussion in his Origins of Commerce (1801).
case of France; in England
was
it
company
also concentrated on one
The game
South Sea Company) in practice as will be demonstrated below.
was finally dissipated when
companies
in the various
The
the actual
a
number of competing
provinces and cities of the Netherlands.
participants
and
"insiders"
was spread over
it
"outsiders".
game
each
can
divided
usefully
into
Insiders possessed superior information on
what
in
prospects of the
company
or
be
companies were and had earlier
access to information on changes in capital authorized
granted or not.
5
and privileges
to be
The most important information they had which was never
available to outsiders was about the actual
issued.
(the
number of shares
that
had been
Nevertheless, they had to share their superior information with the
outsiders since
question
they changed
when they
acted
the
upon
company
in
Moreover, insiders were subject
to
price
it.
of the stock
of
the
increasing constraints over the course of a bubble by their commitments to
political patrons
and
supporters..
Outsiders, in turn, could be divided usefully into "speculators" and
"suckers".
Speculators are the
most interesting participants in the game
from an economic viewpoint. By reacting
reasonably expect to
make money by buying any time during
long as they sold out before the collapse.
buy
5
in
alertly to price signals, they could
while prices were rising and
It
to sell out
the bubble so
would be rational for them
while prices were falling,
to
i.e.,
Scott (1910-12) makes this the focal point of his analysis of the South Sea
Bubble; Levasseur (1854) mentions it as a contributory factor but Faure
(1977) places more emphasis on it for the Mississippi case.
first to
make
the rise and then the fall of price greater than
We argue
otherwise.
were examples of
Of
this
course,
kind of "rational bubble."
any speculator could look
is
it
did
"rational bubble",
we enjoy today
bubble
had
of the actual course
actions affect
their
Did such speculators
become very wealthy.
prices
we would expect
as
and were they anything but randomly lucky?
who bought how much and when and
records of
the
rational, even smart, if he
not difficult to identify periods during which such
prescient speculators could have
actually exist,
would be
and South Sea bubbles
that at least the Mississippi
the benefit of the historical retrospect
of prices, and
it
But
stocks.
we do
possess
at
We
in
a
lack
what price for any of
evidence
of
reciprocal
price
fluctuations in the most important intervening asset available to speculators.
Its
price
movements can be used
game and
speculators entered each
This
is
"mark" when some very important
to
left
it.
the course of foreign exchange, which in this early period
proved remarkably responsive
to international capital flows.
By identifying
characteristic "signatures" in the course of exchange rates that
flows in
the
sophisticated
eighteenth
speculators
century,
entered
we can date within
and
left
the
mark
three
days when
games.
various
periods of play, in turn, correspond to periods of price accelerations
would be profitable
to
buy long while the periods of
periods of price decelerations
we have evidence
when
that at least
it
in
If
these
when
it
recess correspond to
would be profitable
some participants
capital
a
to sell short,
then
given bubble were
rational.
rational
This does not by any means imply that the bubble activity was
in
some
social
sense,
nor,
interestingly,
does
it
imply that
the
insiders themselves were rational in the strictest sense.
We draw
of
explicit linkages
between the two major stock market
1719-20 and the aftershocks in
crises
Amsterdam and Hamburg using semi-
weekly exchange rate data that were published regularly throughout
period.
These have never been used before
to
analyze either the dynamics
of the two major bubbles or the linkages between them.
Though
there has
been extensive study of the two bubbles individually, there has been
investigation of the links between them,
bubbles in the Netherlands.
6
6
bubble
and
the
less the links
little
with the later
So the data we present in the various charts
from both Paris and London represent
market
much
this
direct
a
linkages
unique overview of each stock
between
them.
The
ARMA
Scott and Carswell give subjective statements about the movement of the
speculation in Europe.
Kindleberger (1978; 1984) mentions briefly a
transmission of the speculative mania while Ashton (1959) does take a short
but close look at the transfer of capital between London, Paris, and
Amsterdam and the resulting effects on English exchange rates. Adam
Anderson, who was a clerk for the South Sea Company at the time, when
writing his account much later in the century mentioned the presence of
foreigners in both Paris and London during the height of each bubble. But
he drew only parallels between the two and made no explicit links.
(Anderson, v. 3, pp. 79-123.) John Law made an explicit comparison of the
two episodes in 1721, drawing conclusions very much to his favor, but never
addressed the issue of direct financial linkages between them. (Harsin, 1934,
v. 3, pp. 198-235.)
Luethy (1959) discusses the role of Geneva investors in
both bubbles. Sayous (1937; 1940) the role of Dutch investors in each and
the effect of the bubbles on the Netherlands; Groeneveld (1940) and Wilson
(1941) the role of Dutch investors in English funds during this period and
after.
Dickson (1967) does the most thorough job of making the links, but
he relies on contemporary newspaper reports of bullion shipments and
exchange rate movements for his quantitative data. While he reproduces
fortnightly prices of stocks from Castaing (p. 139) the only exchange rate he
gives is that on Amsterdam.
estimations for the daily price data from the Mississippi and South Sea cases
also represent the first empirical effort at characterizing the course of these
bubbles in terms of the events in the foreign exchanges.
The remainder of
the paper
is
divided into four sections.
it
to the
Mississippi
various bubble episodes.
The second
Bubble and the "system" of John
November 1720 when Law
left
to
part investigates the
Law from May
France incognito and
first
framework we use
describes the exchange rate data and the analytical
apply
The
in disgrace.
1719
until
The
third
section examines the South Sea bubble in the context of not only foreign
capital
movements but of
competing domestic
the existing English stock markets
securities.
The
final section extends the analysis to the
flows of foreign capital from England to Holland and
summer of 1720 and
in the
autumn
Hamburg
their return to their countries of origin.
as the
and the chief
Dutch bubbles broke,
the
in
This occurred
Law's system ended formally
France, and the English began to re-organize the South Sea Company.
in
The
legacy of French, English and Dutch bubbles was the continued disturbance
of the international
money markets
one might hope for, but in
this
into 1721.
None had
the
happy endings
paper we concentrate on the bubbles rather
than the aftermaths.
Parsons (1974) analyzes daily movements of stock prices on the London
Stock Exchange in terms of weak tests of market efficiency during the
South Sea Bubble but ignores the foreign exchanges or questions of rational
bubbles.
Using quotes from the Course of
the
Exchange of John Castaing for
information on exchange rates, gold, and stock prices, we can chart the
progress of
this
first
Our data
European-wide stock mania.
weekly quotes from the Course of
1719 through December 1720.
Mississippi Bubble starts,
the
The
Exchange covering
starting point
and the finishing point
is
is
a period
are
twice-
from April
one month before the
the end of the South Sea
and Amsterdam Bubbles and the trough of the ensuing financial collapse
in
England.
Since the dates on the Course of the Exchange are quoted in the
Old Style
(O.S.)
or Julian calendar, all dates listed
in
this
paper will be
based from this calendar, even though both Amsterdam and Paris were
using the
New
Shown
Style (N.S.), or Gregorian, calendar.
in Charts 1-3 are
four exchange rates (three of which are compared with intermittent quotes
from the Paris exchanges), and the price of
the
London on
livre
tournois
per
pence
sterling;
banco per three
rate, in schilling
are two
London on
the
livre tournois;
banco per pound
month usance
sterling.
of sustained rises or
rise or fall
Amsterdam
Amsterdam
rate
in
rate,
measured
and the London on Hamburg
Unless otherwise stated, these
rates.
While each exchange rate series has
sudden
rates are
Paris exchange rate, measured in French crowns or three
schellingen banco per pound sterling; the Paris on
in schellingen
The exchange
gold.
falls,
and
all
are
followed quickly by
its
peculiarities, all
show periods
marked by occasional
a
reversal.
A sudden
"blips"
—
a
appreciation
of a particular currency followed by a full depreciation back to the normal
exchange rate usually signaled a scramble for liquidity in the country of
Since short term liquid assets were few, the scramble would
that currency.
focus on existing
bills
That
of exchange.
is
any movement from
to say, for
one capital asset to another in any of the European countries at this time,
bills
of foreign exchange were the dominant intervention asset.
letters
rate
would revert
the
previous
period).
Thanks
of
posting
"signatures"
We
detail
to its
exchange
pace of business correspondence relative to
rates
semi-weekly
at
one of the
movement
in
"Ashton effect" since T.
statistical
indicators
of
S.
Ashton describes
financial
crises
in
it
the
While one sign of impending crises was often an
in
same thing occurred
the
foreign
exchanges,
in the
summer
a
sure
sign
of
an actual
Ashton notes that the
of 1914 when, briefly, there appeared to
be a flight from the dollar to the pound.
8
Exchange
currency in this period show characteristic
scramble for liquidity was this sudden appreciation.
rate following the
Royal
the
capital market disturbances occurred.
shall call this the
as
had been authorized, the exchange
currency and credit manipulations of this
series for each
eighteenth century. 8
adverse
the
to the sedate
when
bills
equilibrium level (which might, of course, not be
given
level
London, the time
in
as
from the country scrambling for liquidity had reached the merchant
correspondents abroad and fresh
the
As soon
A
depreciation in a
Ashton effect may overshoot the previous
currency's
rate, in
which
Ashton (1959), p. 113. Ashton gives credit, however, to Jacob Viner for
the explanation of this non-intuitive result.
case
we
This overshooting of the exchange rate
indicates a capital outflow.
it
will call the "Kindleberger effect".
the Ashton effect to state
whence they are coming
It
enables us in combination with
where foreign capital flows are going and from
at the
end of any particular speculative episode.
Kindleberger lays special emphasis on the destabilizing consequences of
speculative capital
illustrated his
movements from one financial center
argument with
bubbles through the late 1970s.
historical episodes dating
the spring of
fluctuations to come, but
of Law's system in
This
1719.
it
May
is
series in
is
Scott
that
"Paris
1,
we
first note a small
overlooked, given the violent
monopoly company for France, on the
London and Amsterdam
writes
easily
Chart
interesting that this coincides with the start
Law's existing Compagnie d'Occident.
left
from the 1719-20
1719 with the formation of the Compagnie des
Indes, the general trading
money
another and has
9
Examining the London-Paris
blip in
to
The
basis of
existing literature suggests that
for Paris in the late
summer
of 1719.
became the Mecca of speculators of Europe." 10
Carswell cites a report that 30,000 foreign speculators had entered Paris in
the fall of 1719.
slight
11
The graph of
appreciation of the livre in mid-August, but the increase
relative to the
background noise of the previous two months.
Kindleberger, (1978)
perspective.
10
li
the London-Paris exchange rate shows a
Scott,
I,
p.
Carswell,
403.
p.
101.
is
the best exegesis of his
argument
is
small
In September,
in the historical
at
the
height
of
the
capital
flow
to
Paris,
the
exchange rate actually
that
Law
depreciates!
The answer
to the
apparent paradox
is
through a systematic money inflation. (See
Table
rate started to depreciate in late October 1719
This depreciation was due to a slowing
1.)
fostered the
The
Paris exchange
and continued
down and
boom
to
March
1720.
reversal of the capital
inflow along with the continued increase in the issue of bank notes and
debasement of the
livre
by Law.
In late
November and
early
December
1719 one can find a sharp appreciation of the pound with respect to the
guilder and the livre.
Because of the suddenness of the movements, and the
sharp drop in the price of French stock, we infer that a fair number of
speculators took their profits and departed for England.
that 500 million livres in bullion
When
had been carried out
the share quotations for the
Law's target level of 10,000 livres
November
(O.
S.),
12
left Paris for
in late 1719.
estimates
12
Compagnie des Indes had reached
twenty-fold increase) in the middle of
the issuance during the next
worth of new shares stabilized the
market speculators
(a
Scott
price.
13
week of 30 million
livres
At the end of that week, stock
London.
Scott, p. 404.
13
new shares, "litres", issued but
His source, (Dutot, v. II,
billion livres worth.
pp. 257-8), on the other hand, only says "30 millions" without specifying
"titres" or "livres".
Dutot's summary of the total value of Compagnie des
Indes stock at the end of November, however, is only 4.782 billion livres.
this
Faure,
p.
269, says there were 30 million
would imply nearly 300
The number of new shares
issued in
mid-November, therefore, must have
been only 3,000; their approximate market value 30 million
livres.
11
Another
halted
to
On February
exit occurred in early February.
12,
Law
1720
dealings in stock, foreign exchange, and bank notes in an attempt
all
combat
inflation
and
The
speculation.
price
of
Mississippi
shares
At the same time, the English Parliament approved the South
plummeted.
Sea Company's proposal for funding a large part of the National Debt.
money
left
France and headed for England.
Popular pressure forced
February
So
Law
to
reopen the Paris stock market on
with the purchase and sale of unlimited quantities of shares
23,
priced at 9000 livres, and to re-open the offices where billets de banque
This restored the stock market boom, but
could be converted to silver.
now took
speculation
place in the paper currency, the billets de banque.
The
reaction of the Paris-London exchange rate at first was a case of the Ashton
As speculators could not convert
effect.
their shares of Mississippi stock
directly into specie but only into depreciating paper currency on the French
market, the uncertainty of the situation led to an appreciation of the livre
as
holders of
discount.
English
Once
of exchange on
bills
Paris sold
these
assets
at
a
the stock market in Paris reopened, the livre depreciated
sharply, signaling the exodus of speculators.
The
stock
market
gyrations
continued
domestic speculators until the middle of
desperation,
Law announced
save his system.
May
in
1720.
France
On May
a deflationary decree, again in
with
mostly
10, in a fit of
an attempt
Convertibility of bank notes to specie was to end.
official price of shares of the
Compagnie des Indes was dropped
to
to
The
8000
livres
with a target price of 5000 livres by December
French
exchange-rate
followed
appreciation
moved
by
as
sharp
a
had
it
in
In response, the
1.
with
February,
depreciation.
However,
13
May
through
initial
the
graph
London from
overstates the appreciation of the livre since the quotes in
May
an
20 are "at sight" instead of the customary usance of
Therefore, they incorporate the sight premium as well as any
two months.
Afterwards, the quotes were again at usance
appreciation during that week.
but the Kindleberger effect, or overshooting of the previous level for the
exchange
shows
rate,
speculators, French
profits or
up
clearly
nonetheless.
and/or foreigners,
left
Whether
the
remaining
France for England for more
whether the French nobility took their specie
to safer quarters,
this depreciation signals a capital outflow.
From
the deflationary decree in
May (which Law
lifted a
week
later,
again under public pressure) onward, currency debasements and increased
bank note
issues
resulted
bankruptcy of July 6
France from shares
in
(O.S.)
in the
continued depreciation of the
a
The
livre.
of the Banque Royale shifted speculation in
Compagnie des Indes
to billets
de banque which
declined in value until the exchange market in France closed in September
1720.
The sharp appreciation of
the livre in late September
was the
result
of more traditional bankers regaining power and causing a repatriation of
gold into France.
Turning
pick
out
the
to
Chart
2,
repercussions
the
Amsterdam-London exchange
of
the
rate,
French speculative movements
we can
as
the
13
relative importance of
inflows
capital
London and Amsterdam
France
to
or
as
destinations
shifts as either sources for
for
capital
outflows
from
Carswell has linked the speculative fever of the Mississippi and
France.
South Sea Bubbles only in
late spring of 1720:
Buying orders for South Sea stock poured into London from
Holland, 200,000 pistoles arriving in one consignment from
Amsterdam towards the end of April. 14
London that spring were coming a great many of those
who, only a few months before, had been crowding the rue
Quincampoix (French stock market). 15
And
to
Looking
the
at
Amsterdam-London exchange
rate
South Sea stock prices, however, we can see that an
came
speculators
to
England
in
March.
and the graph of
influx of foreign
Both the price of South Sea shares
and the English pound appreciated throughout the spring of 1720.
By
the
first
half
of
May
both South Sea stock and the London-
Amsterdam and London-Hamburg exchange
lull
before the next storm, however.
rates leveled off.
On May
This was the
20 the South Sea
Company
announced more conversions of debt, long-term and short-term annuities
375 pounds, and granted loans to aid buyers of additional stock.
appreciated sharply as foreigners entered the market.
capital inflows in the spring of 1720, the
summer.
14
15
This signals a reversal
Carswell, pp. 147-8.
Carswell,
p.
143.
pound began
at
The pound
After these large
to depreciate in the
of the capital flpw, first to Amsterdam,
then to Hamburg.
Carswell
"Amsterdam
Exchange was crowded from morning
One can explain
(in)
.... Others were on the
crop of native promotions
the
states
June and July saw
way
to
a
Hamburg, where
to night.
the sharp fluctuations that highlight this June-July
depreciation of the pound as temporary slowings in the capital outflow.
Two
The
events in the story of the South Sea Bubble seem to be responsible.
first
sharp
came
rise
as the result of another
South Sea stock sold between June 16 and
million pounds in stock at 1000.
June
group of subscriptions of
The company offered
22.
pumped
5
4.75 million
pounds into
the market, running the total to 11.4 million pounds since April.
The second
rise,
found
in early
may be due
to the
July,
is
This issue
not associated with an issuance of stock but
French connection.
The
price of South Sea stock
hovering around 850 or more and had not yet begun
While the bankruptcy of the Banque Royale on July 6
its
final
(O.S.) in
plummet.
France caused
both the pound and the guilder to appreciate relative to the livre,
that flight capital
was
it
appears
from France headed more toward London than toward
Amsterdam.
The timing of
by
illustrated
Hamburg
rates
the
in
the capital
convergence
June.
flows to Amsterdam and
of
the
Hamburg
are
London-Amsterdam and London-
The pound depreciated
relative
to
the
Dutch
schellingen banco while the pound fluctuated around the pre-bubble level
relative
16
to
the
German
Carswell, pp. 164-165.
schilling
banco.
This implies a capital outflow
15
directed toward Amsterdam.
as the
pound depreciated
In July the spread between the rates
widened
relative to the schilling banco, signalling a capital
flow increasingly headed towards Hamburg.
The sharp
August
This
is
produced
Company
Worried
money from
August
technicality the
18
the
by
insiders
real
the
their operations, the
which
tried to close
itself
from the
On September
last
24
the
the
pound
appreciated
was short-lived.
precariously
weak
and
of
The
a writ of scire
of South
price
legal
Sea stock
August through the middle of
money market.
gold
prices
from Holland
for the last three
mid-October as
in
plummeted.
months of the
faltered
year.
and
This
easing
remained
As can be seen on
price graph, a depreciated
bills
These
October and the
in
at this time.
The English financial system
gold prices indicate a sharp depreciation in
Scott, III, p. 323.
Sea
were draining
projects
money market came
and
sharply
Amsterdam exchange-gold
South
the
Sword Blade Bank suspended payments,
brief respite in the tight
arrival of 100,000 guineas in gold
17
had begun.
bubble that had occurred
movements reflected the collapse of the Dutch boom
the
rates in mid-
some of these companies on a
intensifying the scramble for cash in a tight
A
of
company invoked
violated.
half
directors
the
in
companies
other
that
company
dropped sharply
October.
Amsterdam and Hamburg
in
fall
unintentionally
themselves,
previously.
facias on
and
the Ashton effect, signalling the financial panic that
was
precious
rise
pound and high
of exchange and bank
notes,
A
respectively.
widening between
substantial
exchange rates on Amsterdam, over ten times higher
and usance
sight
in
October 1720 than
in 1723, indicates that interest rates in the international
money market were
very high.
II
There has recently been an interest
bubbles in asset prices.
set of
of
possibility
rational
Were the Mississippi and South Sea episodes
described rational bubbles or not?
West (1984, 1985) and
the
in
test for
If
we were
to
just
follow the example of
consistency of two separate estimates of the
parameters needed to calculate the expected present discounted value
of a given stock's dividend stream,
it
is
clear
we would find
the existence
of speculative bubbles in the prices of both Mississippi and South Sea stock.
This
is
clear
compared
from the
relative
stability
of dividends actually
to the volatility of the stock prices.
intended
like to
The evidence of contemporaries marveling
do here.
crowd psychology displayed
Exchange Alley
or
But West's techniques are not
bubble episodes within a limited time period as
to isolate rational
we would
in the
Kalverstraat
using these
is
certainly
bubbles
are
with
consistent
And
we have presented strengthens Kindleberger's
episodes as
primary examples of
international
at the
narrow confines of Rue Quincampoix or
behavior explanations recently revived by Shiller (1984).
rate evidence
paid out
disturbances
his
transmitted
thesis
the
crowd
the exchange
case (1978) for
that
most price
among two
centers that lead to irrational and overzealous trading in each.
or
more
17
But can the price movements also be explained by movements in
market fundamentals
as
Flood and Garber (1980, 1982) would argue?
It
is
even more true for the eighteenth century than the twentieth that we lack
data on the
quality and
forced
commonly
specified determinants of stock prices comparable in
frequency
some
improvise
to
advantage of the data
not
suggestive,
that available
to
alternative
we do
possess.
we
believe
definitive,
portions of the Mississippi Bubble
likely
they
reflect
the
may
We
for stock prices alone.
that
tests
While
they
the
will
take
results
suggest
very
are
maximum
will
only
strongly
be rational bubbles although
it
manipulation of market fundamentals; that
be
that
is
as
the
South Sea Bubble was clearly a rational bubble but only for South Sea stock
and not for Bank of England or East India Company stock; and that the
Dutch bubbles were most
reforms
in
likely
rational
but broken
more by monetary
France and reorganization of the South Sea Company in England
than by their internal dynamics.
Rational bubbles appear ultimately to depend upon the co-existence
for
a
brief
period
of
time
of
two distinct
classes
of
traders:
perhaps
distinguished by the quality of the information they hold, perhaps by their
attitude toward risk, perhaps by their time horizons.
these
elements can be
bubbles.
found
in
As we
shall see, all
both the South Sea and the Mississippi
But the two classes of traders operating in the same way but at
different times left their distinctive
in certain time periods.
mark on
the course of stock prices only
In the theoretical literature of bubbles, a bubble occurs
expected rate of change in the price of an asset
determining the current market price
18
is
There
.
is
when
the
an important factor
in
no question rates of
change in asset prices changed long enough and sharply enough
to
have
affected expectations of investors in both France and England in 1719 and
The
1720. (See Figures 4-5.)
real question
considered to be rational or not.
the
and
Mississippi
speculators
represent
the
t
=
t
Sea
cases
the
is
for
rational bubble that best fits
the
a discounted martingale.
fundamental
market
mobile
internationally
by
19
the
One can
following
20
=((l+r)/q)c
t
c
above
return
whether these bubbles can be
The type of
we have observed above
difference equation:
c
South
is
_j
+
with
z
probability
q;
probability
1-q;
t
with
z
t
E(z|I _j)
t
=
c
0;
= return above market fundamental;
r= period
discount.
The participants
the
next
period
speculative gain
18
if
if
see a capital gain
the
bubble
continues
the bubble bursts.
Flood and Garber,
p.
above the market
or
a
return
to
The longer the bubble
fundamental
zero
in
expected
lasts the
higher
275.
19
A martingale is a repeated series of bets where the stakes are raised after
each loss so that with a positive probability of winning on each bet, the
gambler may eventually win. The original term refers not to a bird, but to
piece of horse harness designed to keep the horse's head down while
running or pulling a load.
20
Blanchard and Watson, pp. 297-298.
19
gain must
the capital
be to
According
market crash.
compensate for the greater likelihood of
to Tirole (1982), a rational
horizon must meet two further stipulations.
a
bubble with a finite
Expectations must be myopic;
sequential traders only look at the expected trading options in this period
and the subsequent period.
Law
initiated,
and the South Sea directors
imitated, the practice of paying for stock subscriptions in monthly, later
changed
This had the desired effect of creating
to quarterly, installments.
precisely
this
kind of myopia by the
first
purchasers of the
stock
Second, there must be several "generations" of traders entering the
issues.
market.
21
was an
essential element in the capital expansion of both the
The device of
issuing several subscriptions of additional stock
Indes and the South Sea Company.
foreign
From
new
Compagnie des
This also created, as we noted on the
exchange graphs, successive "generations" of outside speculators.
the theoretical viewpoint, then, sufficient conditions appear to be in
place to warrant asking whether each episode was a rational bubble or not.
From
well.
a strictly historical viewpoint, the question
The South Sea episode
directors of the
company and
is
worth asking
clearly contained a swindle by a subset of the
the only disagreement
among
historians arises
over whether this was the primary element in the situation or not.
John
System of
controlled
remained
21
Tirole,
Law
directly
so
contained
such
many
the
of
a
fascinating question whether
p.
1170,
1175.
great
it
But the
mixture of elements and
conceivable
a
p.
as
policy
variables
it
has
could have worked in part or
Faure distinguishes two parts
with some minor modification.
sage,
and
le
very well
to
it:
plan fou and argues that the "wise plan" could have
if left
on
its
plan
worked
own.
summary
In our
le
of the System below
and analysis presented by Faure
(1977).
we
rely essentially on the data
Faure's study in turn rests heavily
on the previous work by Harsin, but supplements
it
with important new
data on the share prices of the Compagnie des Indes, exchange rates in Paris
on both Amsterdam and London, and the market values of bank notes issued
22
by the Banque Royale.
2 below.
These data are incorporated into Chart 4 and Table
All these studies emphasize, however, the singularity of the French
experience rather than, as
The
experience.
and
marvel,
we did above,
the linkages
role of foreigners in these accounts
rather
than
transmit
to
French
it
had
was
to
to the British
come
economic
to Paris
disturbances
elsewhere.
After a large-scale cancellation of government debt at the beginning
of the
Regency of Louis XV, the crown
interest on the
solutions,
brilliant
the
still
found
it
impossible to pay
remaining debt already discounted 75 percent.
Regent, the
Scottish
Banque generale,
Duke
financier, John
the
enterprises to come.
success
In
of
of
Orleans,
fell
May
Law.
In
which
laid
the
under
1716,
basis
Desperate for
the
sway of
Law founded
for
the
a
the
greater
August 1717 Law formed the Compagnie d'Occident
Faure also adds his own delightful appraisal of the high politics of the
era as acted out by principals possessing an amazing variety of sexual
idiosyncrasies!
21
which, like the South Sea
Company
in its original charter of 1711, took
some of the national debt for special overseas trading
over
Citizens
privileges.
and foreigners could exchange their holdings of government debt for stock
in
The
the company.
share,
was 100 million
below par
at
300
nominal capital, par value 500
original
The
livres.
In
livres.
livres
per
market value of the stock was
initial
December 1718 Law converted
the
Banque
generate into the Banque Royale whose notes, denominated in either gold ecus
or in silver livres
louis d'or
now became
the
was devalued relative
the preferred
medium
for tax payments.
to the livre so that
form of money for the public
Compagnie d'Occident was expanded
to hold.
the billets-livre
Also in
May
In the
summer
of 1719,
Law
The decrees of August
the System with a
1719 the
new
issue
put the remaining elements
Company
of the System into place, acquiring the right of the
and assuming the farm of the indirect
became
monopoly of trade with
to include the
India and China and was renamed the Compagnie des Indes with a
of 50,000 shares.
May, the
In
to
mint coins
taxes.
16-20, 1719 (O.S.) completed the formation of
bold step toward fiscal reform
—
the suppression and
reimbursement of the rentes and many of the offices that had been sold
the previous two decades in order to raise money.
place in billets de banque at the offices of the
to the
reimbursees as well as
either bearer shares in the
all
in
The reimbursement took
Company which had
to offer
other holders of existing government debt
Company with 4% annual dividends
de constitution de rente" which carried a
fixed
return of
reduced rate the government paid the Company on the debt
it
or "contrats
3%, the same
held.
Luethy
considers
flaw
the
fatal
new
issues of
this
System
the
in
since
reimbursements
the
mm
required large
believes the reimbursees
paper money.
would have used
Faure, on the other hand,
their billets de banque to purchase
one or the other of Company's obligations to avoid further depreciation of
Based on the increased revenues projected from the tax farm
their assets.
on indirect taxes now controlled by the Company for the next seven years
as
well
revenues from the monopoly of the mint, these obligations,
as
"actions rentieres" could
have been a very attractive, blue chip investment
that in effect the elimination of direct taxes, offices,
and the
rentes could
have been funded into the permanent capital stock of the Company. 24
was,
Law proceeded
capital
stock
September
(the
2, 17,
to
his plan
fourth,
and
fifth,
fou with three successive
and
sixth
petites filles, as they
gains.
The
to
buy them
livres,
24
Luethy,
I,
p.
317.
Faure, pp. 225-28.
Company on
each with a
the possessors of these
were popularly called, profited from
at existing
in
purchasing these new shares so they were
market value.
This meant they had to hope
for further capital gains on their shares in the
23
issues of
existing holders of government debt, however,
were not accorded any priority
forced
it
Since the first three issues of shares
had had face values of 500, 550, and 1,000
enormous capital
the
at a face value of 5,000 livres
promised dividend of four percent.
and
in
new
As
21 in 1719 (O.S.).
These shares were issued
meres, filles,
issues)
so
Company
if
they were to
23
regain some of the losses they had already suffered on government debts.
The
third step in Law's plan
was
to raise the
market value of the shares
to
10,000 livres, this in order to reduce the effective rate of interest to two
percent.
25
To
capital,
facilitate speculation, or
Law
in
his
view
to
mobilize the necessary
took the following steps:
1) he divided shares into fractions small
investors to be able to purchase them;
enough for modest
provided for installment payments, 10% per month, and
further provided the first two months could be deferred to
the third. This meant December and March were the months
of reckoning;
2)
3) provided loans from the Bank on the security of shares,
even if only partially paid for;
on December 19 (O.S.), opened an office for the
purchase and sale of shares in the Company;
4) starting
5) later
fixed the price of each share at 9,000 livres
26
All these steps can be seen as establishing the rules for a
object of which
to
10,000
is
livres.
to increase the price of shares of the
Did the price
in
fact
follow a
to be
from mid-July 1719
25
to the
the
Compagnie des Indes
discounted martingale
during a period that we believe outside speculators entered and
foreign exchange as their intervention asset?
game
left
using
The effective period turns out
end of November
(N.S.)
but Faure's daily
Faure, pp. 232-3. Faure cites a number of Law's writings from 1715 to
1724 in which he repeats this sacrosanct number of 2%.
26
Faure, pp. 233-234.
price data do not begin until August
Our empirical
1.
exercise
is
to take
the first differences of the natural log transforms of the daily price quotes
available in Faure, and then to search for a detectable time series pattern
that
significantly different
is
from white noise or
a
random walk.
This
equivalent to a weak test for market efficiency in the sense of Fama.
purposes
patterns should
there
is
market
claiming
of
yield (0,0)
such
efficiency,
autoregressive,
searches
for
time
is
For
series
moving average models —
i.e.,
only "white noise" or random, unpredictable movements in the price
This
changes.
is
what we hope
During the
bubbles.
movement,
preferably
bubbles,
to
find during periods before and after
however,
described
an
as
we should find
autoregressive
a
predictable
movement
with
This would be consistent with two or more classes of
positive coefficients.
traders anticipating further price increases with some probability greater
than zero.
It
may
also be consistent with a steady
growth process
in
market
fundamentals, but changes in market fundamentals during the brief periods
we
are
analyzing here are more
processes.
A
process, then,
likely
predictable pattern that
may
is
to
show up
as
best described as a
moving average
moving average
be consistent with a rational bubble, but
indicates instead an innovation in market fundamentals.
Taking the period from August
1,
1719 through
for prices of the second subscription of shares of the
(the so-called filles),
we find
that the best fitting
it
probably
27
November 29
(N.S.)
Compagnie d'Occident,
ARMA
model
is
a (5,0).
Moving average processes are generally found, for example, when ARMAs
are estimated on data series with missing entries, entry errors, or outliers.
25
This
with daily data but ignoring gaps that occurred frequently not only
is
regularly
for
holidays.
If
Sunday but
each
for
irregularly
also
and
religious
state
missing values for the holidays are filled in either by naive
extrapolation from the last quoted price or by linear interpolation in the
logarithms of the prices before and after the holidays, then a (0,2)
Checking for the
selected.
20, 1719 to
March
they
results,
separate
may
classes
of
1,
1720
indicate
traders
best
1720.
we found
to be a (0,0).
rational
that a
was
it
progress
in
during
we find when some allowance
is
28
If
made
and indirectly
directly
in
the market
the first
period
that
the
Compagnie d'Occident and
we prefer
its
collapse in Spring
"la folie
de Law. ..est
to take the (0,2)
ARMAs
for the missing observations during
holidays, however, then they indicate that
prices.
the
This would conform with Faure's judgement that
et raisonnante."
we take
If
bubble with as many as five
market ruled until the System began
une folie raisonnee
is
model on the run of prices from November
significant price rise took place in shares of the
that an efficient
ARMA
Law was
fundamentals
frequently intervening
to
create the rise in
This interpretation conforms more to the more traditional analyses
of Luethy and especially Levasseur.
Ill
Irrational bubbles are those in
its
28
which the relationship of an
asset to
market fundamental simply breaks down because of overzealous trading
Faure,
p.
233.
Kindleberger (1978)
or an unrealistic appraisal of the value of the stock.
view of market bubbles.
espouses this
economic
changes
system
the
Coupled with easy
enterprise.
In
perceived
credit, a
this
scenario a shock
of
profitability
boom
a
to other assets
a
madcap
schema
—
it.
These new
In
Kindleberger's analysis suggests a mania that spreads
shares in
of joint stock companies, real estate and
all sorts
The South Sea Bubble
of alternative assets.
variety
as if tailor
particular
knowledge of the market and thus add an element of
little
irrationality into
the
Speculation spreads to
ensues.
parts of the public that normally avoid playing the market.
entrants have
to
made
(by the
Mad
his
Hatter, of course).
our investigation of the South Sea
essentially the analysis
fits
we have adopted
Bubble,
and appraisal made by Dickson.
The motivation
for
the South Sea scheme was essentially the same as for the Mississippi Bubble
--
to
the
refinance the immense debts accumulated by the government during
A
War of
the Spanish Succession.
very similar.
government
promised
exchange,
In
debt
capital
in
And
the mechanics of the scheme were
exchange for their annuities, holders of the existing
were
offered
South
Two-thirds
gains.
response
new
to
directors of the South Sea
of
increasingly
Company.
Sea
the
annuity
attractive
These
Company
owners
terms
in turn
stock
which
made
the
by
the
offered
were divided into an
inner ring of prime movers privy to most of the details of each successive
29
Dickson, pp. 91-2.
Cf.
Hamilton
(1947).
27
stage of the
scheme and the remainder of the Directors who probably were
not.
The operations consisted of four new
made on April
of stock which
April 29, June 17, and August 24, 1720
14,
could be purchased for one-fifth
down (2nd and
issues
down
and 4th
(1st
(O.S.).
issues)
were
These
or one-tenth
3rd issues) with the balance due in equal installments spread
over 16 months (1st issue), 32 months (2nd issue), 54 months (3rd issue) or 36
months (4th
With the
issue).
the South Sea
Company
held by a purchaser.
30
According
to
--
The
May, and during June.
two
itself for the
occurred in three spurts
moving from Paris
last
to
issues, loans
could be obtained from
market value of the South Sea shares
Dickson, the
rise in price of the shares
the second half of March, the second half of
first
was due primarily
London, the second due
to foreigner speculation
to increased participation
by
Dutch investors and the beginning of loans by directors of the company on
security of South Sea stock, while the third was due to an
in
on
loans
verbally.
stock,
on
subscription
receipts
immense increase
and on subscriptions made
31
The same efficiency
test
used for the stock
of Law's
d'Occident was implemented for the major three English stocks
England, East India Company, and the South Sea
price data
from the Course of
30
Dickson, pp. 123-5.
31
Dickson, pp. 140-43.
the
Exchange.
The
Company —
Compagnie
— Bank
of
using the daily
results are listed in
Table
2.
The
best models are
found for each stock
in each of five separate sub-
The
periods that can be distinguished by exchange rate movements.
first is
the pre Bubble period for England, but the height of the Mississippi bubble
Both the South Sea stock and the Bank of England stock show
in France.
The next period,
evidence of disturbances but East India stock does not.
January 19
-
April
5,
continues to show nothing for East India stock while a
strong second order autoregressive process occurs for South Sea stock.
This
implies that different groups of market participants were using the same
information at different times
players for different
sets.
—
a
band wagon effect with different
This conforms
posits as necessary for a bubble period
market-rigging
performed
by
the
to
the type of situation Tirol
and with
inner
circle
portrayal of the
Scott's
of
South
Sea
Company
(No model was picked for the Bank of England stock since 2 1/2
directors.
weeks of observations are missing during the period they closed the transfer
books
to
pay dividends.)
In the following period,
which
is
regarded as the
height of the madness according to the historical accounts, neither East
India or
Bank of England
stock
showed anything but white noise and while
the South Sea stock continued to have a strong autoregressive
its
growth
rate,
it
fourth period that
was
is
movement
a first order, rather than second order, process.
taken as the
accounts, however, shows
lull
in
The
before the storm in the traditional
marked disturbances
for each stock.
The
post-
Bubble period shows continued disturbances for East India stock, perhaps
because the directors of that
Company now began
to
make
security of East India shares, but none for the South Sea
loans on the
Company
stock.
29
During
this period
everyone knew that a reorganization and settlement of
accounts would take place for the
Company
knew what
but no one
would
it
be until 1721.
Table
shows the best models and their estimated coefficients for
3
when
South Sea stock during various sub-periods of the Bubble period
The
exchange rate signatures occurred.
strongest bubble process appears to
be the period February 23 through June 15 in the sense that the coefficients
An anomaly
are highest in this period for both lagged terms.
May
the period February 23 to
when
16
the best model
is
does appear in
a (0,2) or
second
order moving average process rather than an autoregressive process.
explanation technically
MA
process as well as in the
lowest
order
AR
that the first order term
is
AR
very small in the
is
process and the selection technique takes the
model before
may
explanation economically
The
mixing
begins
it
in
MA
models.
The
be that in the early stages of the bubble the
second generation investors were more important for getting the bubble
The
underway.
game.
Their maneuvers
as shifts in
MA
as
to
accomplish this
process as an
AR
process.
AR
relatively constant, ranging
low
as
to get the "outsiders" into the
may
be seen in theoretical terms
market fundamentals — and therefore are as likely
second order term in the
is
were clearly trying
"insiders"
0.07
and
as
high
It
is
to create
an
interesting that the coefficient for the
processess estimated for the various subperiods
from
as
0.28 to 0.31, while the first order
0.21.
This appears
to
be
the
term
is
statistical
counterpart of the phenomenon reported by Dickson that the bubble kept
gathering
its
own momentum
so that the last
two
issues of stock
were not
at
the initiative of the inner ring of the directors so
the tremendous
demand
Our conclusion
by
strengthened
the
for
new
stock.
much
as their response to
32
that the bubble in South Sea stock
fact
despite
that
using
same
the
was rational
procedures
none was found for either
in
during, and after the South Sea bubble.
for
Company
identifying a rational bubble in Bank of England or East India
stock,
is
any of the five subperiods before,
While we have not examined prices
of other assets such as land or buildings, Dickson makes the interesting
observation that greatly inflated prices sometimes quoted for real assets
during the height of the bubble were generally for payment in South Sea
stock, implying that the price
would have been much
less if
payment were
AA
made
in
cash or bank deposits.
If
this
is
correct,
then
it
is
further
evidence that the South Sea bubble was a rational bubble and not a response
to
changes in market fundamentals.
IV
We have used
the entry
and
"speculators"
the
movements
exit of outsiders.
in the foreign
exchange rates
Although we distinguished
initially
to
mark
between
and "suckers" within the "outsider" category, implicitly we put
foreign outsiders into the speculator group and domestic outsiders into the
sucker group.
32
33
In
fact, of
Dickson, pp. 126-28.
Dickson,
p.
147.
course, foreigners
and natives could be either
31
speculators or suckers and, as the discussion of the Ashton effect above
demonstrated, both foreign and domestic speculators would find
convenient
to enter
and
bills
of exchange.
The dominant foreign group mentioned
extraordinarily shrewd in picking their
fact, English
Bubble.
Sea
Law
and
Irish investors
in
moments
London
the
New
the most
amazing example of
in
August 1720.
in late
all
34
role of
Hamilton (1967) gives
— John Law's
summer 1719
French
short sale of
at £-180,000 for delivery
This had to be covered in the summer of 1720 by buying
and
his
London banker
34
Luethy,
35
Luethy, pp. 294-5.
36
Hamilton, (1967), pp. 275-6.
p.
South
freely between London,
East India stock at nearly double the agreed sale price.
in this single bet
rate.
Luethy describes the
members of which moved
£100,000 of East India stock
a director of the
break the French exchange
World, and the Jacobite court in Paris. 35
details of
In
had remitted 20 millions pound
investors were active in the South Sea episode.
the Oglethorpe family,
to leave.
August 1779 and who was expelled by
the charge he
in order to
and
played an important role in the Mississippi
to Paris in
March 1720 under
sterling to
them with being
to enter
Luethy mentions the case of Jean Lambert,
Company who came
both bubbles
at the time in
and contemporary accounts credited
Dutch,
the
most
exit the capital markets of the eighteenth century
through the medium of foreign
were
it
291.
Law
lost a
failed by the end of 1720.
36
fortune
The depreciation of
the
summer
Hamburg
in the
Amsterdam and Hamburg exchange
rates in
of 1720 shows that speculators, whatever their nationality, first
money
took their
the
Amsterdam
to
in
June and increasingly headed toward
Groeneveld dates the
in July.
Netherlands on June
10,
first joint stock
1720 (May 30
company proposal
Another scheme was
O.S.).
presented in late July and the remainder after September 12
collapse of the South Sea bubble).
(i.e.,
after the
Although the Dutch schemes followed
as
hard upon the English bubble as the South Sea had followed the French,
this does
mean
not
invested at home.
the
all
Dutch withdrew
(N.S.)
37
of South Sea as well as other English
There are even orders dated the 10th and 13th of September
1720 from Portuguese Jews in Amsterdam, reputedly the shrewdest
speculators of
shares
from abroad and
Groenevelde gives many examples in the inventories of
Amsterdam bankruptcies of holdings
securities.
their funds
in
all,
authorizing Joseph Henriques Junior in London to buy
South
the
Sea
Company without
limit.
38
Nevertheless,
our
evidence from the exchanges indicates that in September and October 1720
the speculators
respite
in
the
went home
to
decline
the
of
London and
exchanges
Paris.
in
37
38
39
Groeneveld, pp. 79-80.
Groeneveld, pp. 124-5.
Dickson,
p.
151.
is
mid-October,
response to an effort by the Bank of England to
Amsterdam. 39
There
draw on
only one brief
apparently
its
in
debtors in
33
In sum, in all three episodes our
the importance of international
Kindleberger "signatures"
and
collapse.
in
exchange rate data have confirmed
movements of
capital
marked by Ashton-
dating periods of price explosion, stagnation,
The suspicions of Dickson and Kindleberger
were linked and that the stock mania was international
that the bubbles
in scope
appear
to
be verifiable by quantitative techniques, although Kindleberger's argument
was eventually irrational
that this
is
not supported.
individual bubbles
did
coincide
not
exchange rates for
that
the
A
in the sense of
final note of caution
may have had
becoming
a general
must be sounded.
Although the
significant periods of rationality, these
Given the disarray evident
or
even overlap.
all
three financial centers by the fall of 1720,
immediate
aftermath
of
the
bubbles
was
it
disruptive
economies of each country, although the longer run effects appear
been minimal and even beneficial.
bubbles
is
beyond the scope of
this
mania
in
is
to
to
the
clear
the
have
But a normative evaluation of the
paper and the limits of our data
set.
TABLE
1
ISSUE OF NOTES BY BANQUE ROYALE
FROM DECEMBER 1718 TO APRIL 1720
(IN MILLIONS OF LIVRES)
Date of commission
December
January
March
April
May
25, 1718
31, 1719
21, 1719
11,
1719
30, 1719
July 14, 1719
September 1, 1719
October 13, 1719
December
1719
1720
26,
March 15, 1720
March 25, 1720
April 20, 1720
18,
January
Notes added
Total note issue
18
18
20
38
59
110
160
381
501
621
981
1181
1481
21
51
50
221
120
120
360
200
300
437
362
2195
2557
Source: Harsin (1928)
Note: At the start of this period, there were an estimated one billion livres
country and 148 million livres in Banque Generate notes
outstanding.
in specie in the
35
TABLE 2
ESTIMATED ARMA MODELS FOR COMPAGNIE DES INDES
STOCK DURING THE MISSISSIPPI BUBBLE
Time Period
August
1
Version 2 2
Version
(n=78)
(n=103)
(n=103)
(5,0)
(0,2)
(0,2)
Version
1
l
3
3
to
November
29, 1719
All missing observations (each Sunday, plus all holidays) were simply
omitted, giving a compressed time series.
This may be a valid
representation if traders simply halted their expectations or if no new
information occurred on non-trading days.
The missing observations for holidays
setting each equal to the last observation.
The missing observations
were interpolated naively by
for holidays were interpolated linearly in logs.
TABLE 3
ESTIMATED ARIMA MODELS FOR BANK OF ENGLAND, EAST INDIA
AND SOUTH SEA COMPANIES DURING THE SOUTH SEA BUBBLE*
B of E 1
Time Period
Sept. 4
18, 1719
=
(n
65)
2
(0,3)
(0,0)
(0,1)
(-,-)
(0,0)
(2,0)
(0,0)
(0,0)
(1,0)
(0,3)
(0,2)
(0,2)
(-,-)
(0,5)
(0,0)
-
Apr. 5, 1720
(n = 67)
Apr. 20
SS Co.
-
Nov.
Jan. 19
EI Co.
-
June 22, 1720
(n = 55)
June 29 Aug. 31, 1720
(n = 55)
Sept. 4, 1720
-
Dec. 15, 1720
(n = 89)
The program searched
for the "best" AutoRegressive model up to 5 lags on
differences of the natural logarithms of the stock prices.
Then the
addition of Moving Average models up to 5 terms for each AR model were
first
The one
that minimized the expression:
log (sigma2(t)) + 2*t/n
where sigma2(n) is the sum of squared residuals for the given model, n
number of observations, and t is the sum of terms in the
and
models, was then selected as the best model. (Hannen and Rissanen (1982))
compared.
AR
is
MA
1
One missing observation for September 18, 1719 was set equal to previous
observation.
At this point there is a one time drop in price of Bank of
England stock; without this, the estimated
would be (0,0).
No
is run for the period of the bubble, Jan. 19 - April 5, 1720
or the post-bubble period, Sept. 4 - Dec. 15, 1720 since many observations
are missing (March 5 - March 23; Sept. 16 - 30) during these periods when
the transfer books were closed for payment of dividends.
There was a run on the Bank in the period June 29 - August. 31, 1720
(ARMA = (0,3)).
ARMA
ARMA
The
(2,0)
ARMA
ARMA
during the Jan.
5
-
April 20 phase had parameter
values of 0.097 and 0.313.
The
(1,0)
value of 0.48.
during April 20
to
June 22 phase had
a
parameter
37
TABLE
4
COMPARISON OF ARMA MODELS FOR SOUTH SEA
STOCK PRICE CHANGES IN DIFFERENT BUBBLE PERIODS
Time Period
Jan. 19
Best
Model
Estimated Coeffs.
-
Apr. 5, 1720
(n = 67)
1
(2,0)
[0.099, 0.31]
(0,2)
[0.095, 0.32]
(2,0)
[0.2, 0.31]
Feb. 23, 1720 4
June 22, 1720
(n = 103)
(2,0)
[0.21, 0.28]
July 5, 1720
5
Aug. 17, 1720
(n = 37)
(0,0)
Feb. 23, 1720 May 16, 1720 2
(n = 71)
Feb. 23, 1720 3
June
June 15, 1720
(n = 97)
•
The coefficients of the ARMAs were estimated with constant
suppressed. The exact likelihood method of Ansley (1979) was used.
1
term
Bubble period between exchange rate signatures.
2
Bubble period between exchange rate signatures. Linear interpolation of
natural logs for missing data on April 15, 18 and 19. When a (2,0)
process (a close second choice to the (0,2)) was estimated for this episode, its
parameters were:
[0.07, 0.29].
ARMA
3
Bubble period between exchange rate signatures. Linear interpolation of
natural logs for missing data on April 15, 18 and 19.
4
Bubble period from exchange rate signature to data break.
Linear
interpolation of natural logs for missing data on April 15, 18 and 19.
5
Post bubble period marked with exchange rate signatures.
When a (2,0)
process was estimated for this episode, its parameters were
ARMA
[-0.65, -.32].
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Eighteenth
CHART
1.
EXCHANGE RATES
AMSTEROAM
PARIS
PARIS
60
-
LONDON-
-
LONDON
-
AMSTERDAM
-
40
f\
30
-
20
-
w
I
W
'
or
S
9
-i
p*
1
3
D
—
*»
z
—
t/i
to
*j
-«
W
-J
—
i
a
mono
-I
T>
i/>
z r—
m
at
o
1
Lfl
—
*j
o»
1
1
o,
z
—
<
—
u
o
1
m n
n
«k*
o
-j
IZDX>X>ZZ(_t_l_
l
<
AJ
s
s
r>
—
•-
t/i
*J
t/l
—
(0
X
X
t/1
to
r
-<
-<
ns
o
1
B
1
m
c»
1720
1719
CHART la.
PARIS - LONDON
EXCHANGE RATE
PT PARIS
AT L0N00N
utaaaz zoo
-1
d
xt
r>
CI
C»
"»
1
1
1
1
1
1
1—
-i
1
1
1
1
1
r-
-i
1
1
—~T—
i
1
P
-«
t/»
1719
1
-D-fl-flJJDCCCCCC
z
z
U>
W
-J
o
720
tO
Nl
O*
1
r-
-»•-«
CHART
2.
EXCHANGE RATES
AMSTERDAM
-
LONDON
SCHELLJNGEN BANCO rt« PSUNO STERLING
HAMBURG
LONDON
SCHILLING 9ANCO PEA fOUNO STERLING
O
n
(0
1719
CHART
1720
3.
PRICE OF GOLD IN BARS
P0UN0S
-
SHILLINGS PER OUNCE
171 9
1
720
O
n
M
b>
CHART
2000
-
1750
-
IS00
-
4.
COMPflGNIE DES
INDES
STOCK PRICES
\
ACTIONS
SOUMISSIONS JULT 1?19
J
M
O
t—
x
/
J
too
i
i
;
-*»—#.
M
1719
CHART
U<
(0
1720
5.
BRITISH STOCK PRICES
EAST INDIA
BANK OF ENGLANO
SOUTH SEA
\
T»
-t
-»
s
M
1719
1720
U
<A
M