Profitable Destabilizing Speculation*

MICHAEL A. S. GUTH, Ph.D., J.D. 
Profitable Destabilizing Speculation*
Economists have sometimes conjectured that speculators
profit from buying low and selling high and thus tend to stabilize market
prices. Others contend that speculators
can earn profits and simultaneously destabilize markets. The possibility of profitable destabilizing
speculation (PDS) affects the operation of competitive markets under
uncertainty. For if speculators may
profitably destabilize, then clearly real world markets can be unstable. However, if destabilizing speculators
always lose money, then in a Darwinian sense they will fail to survive.
Our
present knowledge of the relation between speculative profits and stability
evolved from studies in international economics, price theory, finance, and
modern uncertainty theory. Although PDS
represents a sustainable, endogenous source for fluctuations and business
cycles, macroeconomic theorists (aside from the Chicago School) have largely
overlooked the debate. Yet analyzing
this conjecture will provide better understandings of the microfoundations of
macroeconomics under uncertainty.
Indeed many postKeynesian proponents of active fiscal and monetary
policies point out the need to counteract such endogenous, destabilizing market
forces.
This
chapter reexamines the literature on PDS, integrating various aspects of works
into the general theory of speculation.
While profitable destabilizing speculation has been theoretically
depicted, work in this area appears confusing and contradictory. Many of the early uncertainty theorists
employed arbitrary doctrines and primitive models which inadequately portrayed
a complex phenomenon like speculation.
Utilizing the benefit of hindsight and modern analytic techniques, we
aim to clarify and develop more formally some of the main themes of the
speculation and stability literature.
The text
proceeds as follows. Section 1 restates
the basic proposition that profitearning speculators stabilize markets. Since many theorists adopted different
speculation and stability definitions, Section 2 attempts to describe the
semantic controversy. Next, Section 3
reviews William Baumol's counterexamples, and the comments and criticisms they
elicited. Section 4 continues sorting
valid from invalid PDS counterexamples.
Section 5 discusses some representative empirical findings, and the
final section contains conclusions and a summary. The appendices derive results from Baumol's counterexamples,
which provide an excellent review for differential equation modeling in
economics, and a class of nonlinear excess demand counterexamples. Readers not interested in differential
equations and Hilbert spaces can skip the appendices without losing any
economic concepts.
1.1.
Speculation and Stability: The
Friedman Proposition
A number of economists have argued that
profitearning speculators stabilize markets.
The argument dates back at least to the Nineteenth Century, e.g., John
Stuart Mill advanced the notion in his Principles of Political Economy.^{1} Ross (1938) criticized Mill's notion and
offered a counter argument based on stock market fluctuations.
The
argument resurfaced in the mid1950s, when economists began debating the merits
of flexible exchange rates and the stability of a flexible regime as compared
with exchange rates pegged to the gold standard. Milton Friedman's contention that profitable speculation tends to
stabilize a market shook the conventional wisdom^{2} blaming
speculators for exchange rate instabilities during the 1920s and Great
Depression era. Supporting flexible
exchange regimes and a general free market philosophy, Friedman (1953) asserted
People
who argue that speculation is generally destabilizing seldom realize that this
is largely equivalent to saying that speculators lose money, since speculation
can be destabilizing in general only if speculators on the average sell when
the currency is low in price and buy when it is high....A warning is perhaps in
order that this is a simplified generalization on a complex problem. A full analysis encounters difficulties in
separating `speculative' from other transactions, defining precisely and
satisfactorily `destabilizing speculation' and taking account of the effects of
the mere existence of a system of flexible rates as contrasted with the effects
of actual speculative transactions under such a system. (Friedman (1953), pp. 175, 175n)
An extensive literature then grew out of the
question of whether profitearning speculators could destabilize markets and
whether proposed counterexamples had shortcomings that invalidated them.
1.2. The
Semantic Controversy
Originally, theorists, such as Friedman, based
their analysis on markets without speculation.
The theory asserted profitearning speculators' entry into such a market
would stabilize prices. With the development
of the modern uncertainty theory framework, we now know that attempting to
model a `nonspeculative' market is fruitless.
Chapter 3 illustrates why in an incomplete market, almost everyone is
forced to speculate, because claims are not available for their optimal
consumption bundle.
Modern
uncertainty theory solves comparativestatics issues for speculation via the
general equilibrium contingent claims model and standard economic
reasoning. The standard format provides
individuals with production functions, preferences, timedistributed
endowments, etc., and specifies the available market range. Economists then pose comparativestatics
questions: e.g., what happens if
preferences change?
Unfortunately,
economists have no universally accepted economic dynamics framework;
therefore, no prescribed methodology exists to address issues such as
stability, a dynamic concept.
Consequently, what theorists might consider unacceptable modern
uncertainty comparativestatics, e.g., arbitrarily specified speculative excess
demand functions, have frequently shed light on important dynamic stability
concepts. In Sections 3 and 4, counterexamples
are illustrated that employ these arbitrary methodologies; the text will thus
emphasize substance over technique. By
keeping an open mind, one may glean an idea or two from these earlier works
that can be transposed into a modern framework.
1.2.A.
Definitions of Speculation
The first step in reviewing specific examples of
PDS is to define our terminology. The
classic speculator definition focuses on the capital gains motive. A speculator buys (sells) goods under
uncertainty, with the intent to resell (repurchase) them after some anticipated
favorable price change. We must
emphasize that speculators transact in an uncertain environment. When traders profit from purchasing goods
and later reselling them at an a priori known price, the traders have
engaged in arbitrage not speculation.
Moreover, speculators traditionally receive no gain from consuming or
using these goods, lest speculation be confused with simple expected utility
maximization. Kaldor (1939)
characterized speculative sales or purchases as those motivated solely by
perceived capital gains.
Some
theorists maintain Kaldor's definition excludes `speculation' involved in
dynamic consumption or production plans.
For example, does a manufacturer `speculate' by postponing a required
input's purchase to realize an expected capital gain? We can clarify our speculation definition by introducing a legal per
se distinction. To meet the three
criteria for speculation per se, a person must (1) purchase (sell) a
good, (2) face price/profit uncertainty, and (3) transact primarily with a
capital gains motive. The manufacturer
above did not sell the desired input with the intent of later repurchasing it;
therefore, he did not speculate per se.
Put another way, he could not be charged with speculation per se,
since one of the three essential elements (purchase) is missing. He did `speculate' in the sense of
attempting to minimize his input costs over time, but this type of behavior
lies outside the definition.
The same
distinction holds for consumers who `speculate' by shopping at a particular
grocery store or who consider the potential resale value in their house and
automobile purchases. We can
distinguish between investors who consider a capital good's salvage value and
those primarily concerned with reselling the capital good at a profit. The latter group primarily purchases (sells)
to realize a capital gain, while the former group is not speculating per se. The more a house purchaser weighs the
capital gain potential of his investment, as opposed to wanting to capture the
benefits from living in a house, the more he acts like a speculator per se.
Consider
now an individual who has no intention ex ante to speculate, but finds
he can realize an ex post capital gain.
The third essential element of our definition  the capital gains motive
 does not influence the individual. An
ex post transactions focus potentially would include nonspeculative
capital gains as well, e.g., a Pigou effect.
Particularly
in the stock market, differentiating between ex ante and ex post
speculation would sometimes fail to include investors who speculated but did
not realize their ex post capital gains or losses. Most importantly, a speculation definition based
on ex post activity would deemphasize the crucial expectations and
motives that economists mean when they discuss speculative behavior.
Rather
than proceeding with a common speculation definition, from which theorists
might distinguish other market transactions, the profitable destabilizing
speculation literature at once began to quarrel over the ongoing problem of
defining `nonspeculators.' As we will
now proceed to demonstrate, the old `nonspeculator' semantic controversy
appears avoidable by defining speculation per se.
Friedman
[(1957) at p.269] suggested that `perhaps a nonspeculator can only safely be
defined (if this is done in terms of his demand curve) as one whose purchases
are directly influenced by current prices but not by past prices or price
trends.' Telser defended Friedman's
notion and added that nonspeculators derive profits from other sources.
What
distinguishes speculators from other traders in the market is that their
profits depend only on the price or price change of the commodity they
trade. Nonspeculators' profits are
determined not only by the price of the commodity traded on the organized
exchange but also by the prices of other related commodities. If the nonspeculators are hedgers, they can
make their profits almost independent of the price level itself. (Telser (1959), p.295)
Telser
illustrated his nonspeculator definition with a textile manufacturer purchasing
raw cotton and for whom cotton fabric and textile prices also determine his
profit level. To illustrate his `profit
from other sources' criterion, Telser chose an importer who profits from
decreases in exchange rates and shipping costs, in addition to the imported
commodity's price. Although the textile
manufacturer and importer meet Telser's criterion, they would be `foolish to
ignore price trends in their supply and demand decisions.' (Baumol (1959), p.302)
Upon
reexamination, we note that if Telser's importer purchases primarily with the
intent to resell at a gain, no matter where he may derive additional profits,
then he has engaged in speculation per se. Telser's `speculator' definition  an investor who solely profits
from exchange rate capital gains  is a convention frequently used in the
international economics literature.
However, in this chapter we will broadly apply the Friedman Proposition
across markets and will not add the sole profit motive limitation to the
elements of our per se definition.
Baumol
defined nonspeculators as the speculators' trading partners.
The
practical question which has lain behind the discussion is whether the entry
into a market of skillful professional speculators, people who have no
desire to hedge their holdings, can be stabilizing. Now it is clear the remaining participants in the market, the nonspeculators,
the people who would like to hedge, must in their own interests consider price
trends. For price changes must also
affect the values of nonspeculators' holdings and obligations unless in fact
they have succeeded in setting up perfect hedges, which in most markets is out
of the question. (Baumol (1959), p.302)
Baumol's
comment raises an interesting, though not widely understood, fact about
hedging. In futures market jargon,
imperfectly hedged contracts sometimes force hedgers to speculate per se
on the basis, the spread between the cash and futures prices. If the hedgers leave their hedge positions
in place and do not unwind them, then they will not speculate per se.
Consider
an elevator operator who buys _{} bushels of corn in
the period _{} cash market. Let _{} and _{} denote the period _{} cash and futures
prices. For simplicity, assume all
futures contracts in period _{} terminate in period _{}. The elevator
operator short hedges _{} bushels, where _{} In period _{}, the operator sells his corn and cancels his hedge by
purchasing _{} futures
contracts. Suppose the operator incurs
a storage cost of _{}dollars per bushel.
If _{} denotes his assets in
period _{}, then his assets in period _{} will be
_{}
We can rewrite this expression as
_{}
For any value of _{}, an increase in the period _{} basis raises _{}. Similarly, any
increase in the period _{} basis reduces _{}. Most hedgers would
rationally consider basis changes in formulating their strategies.
Only
those hedgers who intend to leave their hedges in place actually refrain from
speculating per se. In fact,
these hedgers are often prepared to accept a small capital loss as the cost of
locking in a known price. Clearly,
Baumol's comments refer to this type of hedger. Our analysis confirms these hedgers do not speculate per se,
but they are clearly influenced by spot and futures market prices.
To recap
this section, speculation per se involves purchases (sales) under
uncertainty with the intent to resell (repurchase). This operational definition should not be confused with the
layman's use of `speculate' to refer to simple guessing under uncertainty.
1.2.B.
Definitions of Stability
Defining stability and `destabilizing
speculation' is even more complex that the previous effort to define
speculation. Unlike speculation,
neither `stability' nor `instability' have most preferred definitions. This chapter therefore broadly interprets
the term `destabilize' to mean increasing price fluctuations' frequency,
volatility (here meaning explosiveness not the standard deviation as in option
pricing), or amplitude/variance.
In the
speculation and stability literature, economists supporting Friedman most
frequently interpreted stability to mean dampening the amplitude of
fluctuations; these authors commonly measured stability with the price's mean
squared standard deviation (MSSD). This
concept corresponds to a random sample's variance without any probability
connotation. Kemp (1963) and others
loosely term this measure the `variance' even though prices in their models may
contain no random element. Throughout
this chapter we call this measure the MSSD, so as not to confuse the reader with
the actual price variance in modern uncertainty economics.
Measuring
stability with the MSSD required theorists to determine the spread between the
MSSD with and without speculation.
Alternatively, the MSSD could be compared prior to and following a new
speculative group's entry. If the MSSD
increased with the new speculators, then theorists concluded the new group
destabilized market prices.
The MSSD
does not capture increases in the fluctuation's frequency.^{3} In criticizing Friedman's model of speculative
behavior, Baumol observed `while the Friedman argument takes account of the
levels of the variables it neglects their time derivatives, and the time path
is dependent on both.' (Baumol (1957),
p.264n) Friedman relied on amplitude,
i.e., `buy high and sell low,' to measure stability. Yet static measures of stability, such as the amplitude, fail to
capture destabilizing changes in the time derivative of prices.
Obst
(1967) suggested defining stability as dampening the deviations from any trend
line rather than exclusively its mean.
In Figure 1.1, the dotted lines indicate the impact of some speculative
trading on a price over time. These transactions would be regarded as
destabilizing, even though they are actually driving prices closer to their
mean.
Figure 1.1.
Trend Line Instability
Stability
can also be defined in terms of an equilibrium's existence or volatility. Kenen (1979) and others examined profitable
speculation's impact on the existence of a marketclearing price. A related stability definition examined
speculation's impact on generically unstable equilibria, e.g., in a Giffenesque
demand.
Finally,
within the international economics field, some economists evaluate exchange
rate stability based upon the MarshallLerner condition. In the short run, a balance of trade
deficit, ceteris paribus, would tend to increase a country's exchange
rate, defined as the units of domestic currency equal to one foreign currency
unit. An exchange rate increase would
tend, in the short run, to reduce the trade volume's export value and increase
its domestic currency import value.
However, in the long run, ceteris paribus, the increased exchange
rate would encourage other countries to import more goods and services from
that country, thus tending to raise its total trade volume. The MarshallLerner condition is met when
long run export volume increases so much that the actual balance of trade
increases.
Williamson
(1972) restates the MarshallLerner stability condition as follows. Let _{} = the trade balance
at time t, defined in foreignexchange terms; and _{} = the units of
foreign currency equal to one domestic currency unit. Depreciation of domestic currency implies _{} < 0. For simplicity if we write the trade balance
as a function of the present and preceding exchange rates, then _{}, with _{} _{} and _{}
[T]he
immediate effect of a revaluation is to improve the trade balance as a result
of price changes preceding volume changes, but the volume change comes through
in the next period and is sufficiently powerful to outweigh the price effect
(i.e., _{}). (Williamson (1972),
p.79)
A Numerical Example. Suppose
the dollarmark exchange rate decreases from $0.62 to $0.55 per Deutsche Mark
(DM). Having already executed American
import contracts, Germany will have an inelastic shortrun demand for American
dollars. If total German purchases
amount to 6 billion dollars, then the short run net effect of the change in the
exchange rates will increase the American goods' cost from approximately 9.677
billion DM to 10.909 billion DM. However,
Germany has a more elastic long run demand for American dollars. The dollar's appreciation will reduce, ceteris
paribus, longrun German demand for United States exports. Thus the MarshallLerner stability criterion
states that the total volume decrease, perhaps down to $4 billion _{}31
DM 7.28 billion, will more than offset the shortrun price gain: (10.909  9.677) + (7.28  9.677) < 0.
The
MarshallLerner stability condition can alternatively be shown to state that the
sum of domestic and foreign import demand elasticities must exceed unity. Thus stability requires that appreciation of
a given currency reduce world excess demand for that currency.
To close
this section on definitions of stability, we have identified at least four
separate criteria for judging destabilizing influences: increases in price fluctuations' 1) variance or amplitude; 2) frequency; 3) volatility, explosiveness, or nonequilibriating behavior; and 4) the
MarshallLerner condition for foreign exchange. The following sections will review the PDS
literature assuming each of these four stability definitions are appropriate
for applications or counterexamples.
1.3.
Speculation and Stability: The
Baumol Counterexamples
We begin studying the Friedman Proposition's
dynamic aspects by first reviewing William J. Baumol's (1957) counterexamples
based on a cyclical time path for prices.
He proposed that speculators could profit from buying after the price
trough and selling after the price peak.
The speculators would in fact purchase on the price upswing and sell on
the downswing, thus accelerating price swings and causing other instabilities.
Baumol
constructed three counterexamples, each with the same intuitive notion. He attempted to show that speculators can
destabilize even while buying low and selling high. Rather than explaining why speculators may behave as he suggests,
Baumol only assessed the destabilizing impact of such plausible speculative
behavior.
1.3.A.
Example 1: Baumol's Difference
Equation Model
In his first counterexample, Baumol delineated a
cyclical price path using a sinusoidal, secondorder difference equation,
_{} (1.1) 
where _{} and _{} are constants, with *_{}* < 1. For those readers who would like a brief
refresher on differential equations, Appendix A recasts this equation
into a more familiar sinusoidal form,
_{} (1.2) 
The price path completes a cycle every time _{} increases by 360°. The cycle has wavelength _{} and frequency f
= _{}/360. The price path
without Baumol's speculators follows equation (1.2), where the _{} = _{}.
When
Baumol's speculators enter the market  buying on the upswing and selling on
the downswing  they subsequently alter the market price expression to
_{} (1.3) 
Comparing (1.3) with (1.1), we find that with the
speculators' transactions, the _{} _{}, since the fraction _{} for _{} > 0. This relation implies that Baumol's proposed
speculation will increase the frequency of price fluctuations over time.
Second,
Baumol demonstrated that, depending on initial conditions, such speculation may
increase or decrease the cycle's amplitude.
We will focus on an instance where the speculators increase the
amplitude. Let _{} = 0 in both the
market with and without speculators and assume the same corresponding initial
prices. Then the sinusoidal equation
(1.2) evaluated at _{} = 0 reads
_{}
If the initial price rests at the mean price
level (_{}), then V = 0 and
_{}
which has amplitude 2_{}. For notational
convenience, denote the speculative price time path as
_{}
which has amplitude 2_{}. Suppose the curves
also coincide at the peak of the nonspeculative cycle: when _{} = 90, or _{} = 90/_{}. Evaluated at this
point,
_{}
or
_{} (1.4) 
since 0 < (_{}) < 1. Expression
(1.4) shows that the amplitude of the commodity's price with Baumol's speculators
exceeds the amplitude without these speculators. Intuitively, the two sine curves coincide at an initial value, _{}, and again at the peak of the nonspeculative curve, which
has a longer cycle. Thus the
speculative price curve must have already attained its peak and be moving
downward: it must have a higher peak
than the curve without Baumol's speculators.
1.3.B.
Example 2: Baumol's Differential
Equation Model
Again proposing the same speculative behavior,
Baumol constructed the differential equation model,
_{} (1.5) 
where _{} and _{} are positive
constants, and _{} is the second
derivative of price with respect to time.
Based on (1.5) the commodity's normal excess demand is
_{} (1.6) 
At the trough when the second derivative is
positive, excess demand will be low; similarly, excess demand will be high at
the peak. To incorporate the `buy on
the upswing, sell on the downswing' behavior, Baumol defined a speculative
excess demand by
_{} (1.7) 
with _{} > 0, _{} > 0, and _{} These speculators
have greatest excess demand with simultaneously low (_{}) and rising (_{}) prices. In
equilibrium, _{} and _{} must sum to zero:
_{}
and solving
for _{}
_{} (1.8) 
Baumol
then demonstrated a different destabilizing impact. Whereas for appropriate values of _{} the solution of (1.5)
has complex roots and therefore a sinusoidal time path, the roots of (1.8) also
include a positive real term given by
_{}
with _{} constants. Thus the price no longer fluctuates with
constant amplitude but will increase at a geometric rate. `[P]rofitable speculation has demonstrated
its destabilizing ability by (taking) the system from its position of delicate
constant amplitude balance into a time path of explosive fluctuation.' (Baumol (1957), p.269)
1.3.C.
Example 3: Baumol's `Real' Cycle
Model
In an effort to construct a counterexample in
which past prices or price trends did not affect nonspeculative excess demand,
Baumol developed a third model where `real' factors cause a cyclical price
path. In this model a commodity's
supply varies sinusoidally, perhaps due to seasonality or other market conditions,
expressed by _{} with constants _{}. In keeping with
Friedman's criterion, the nonspeculative excess demand depends only on the
current price: _{} where _{} and _{} are constants.
When
speculators then buy on the upswing and sell on the downswing, they transform the
price path from its cyclical pattern into an unstable, explosive one. As derived in Appendix B, the time
path of prices in the economy cum speculators has the solution
_{} _{}
where _{} are constants, and E,
W, and B are positive constants.
The real term creates a problem in Baumol's third model when the
speculators try to realize their profits.
In
the short run, the time path may still be cyclical....(but in the long run) the
time path of P will eventually approach _{}....In other words, speculators will continue to buy on the
rising market and, at least in terms of the value of their assets, this would
appear to be profitable. However, it is
clear that difficulties can arise if speculators try to cash in these profits
or if they run out of funds with which to continue their purchases. (Baumol (1957), p.270)
1.3.D.
Comments on Profit Realization and the Underlying Market
1.3.D.1.
Speculators Must Realize Their Profits. To derive PDS counterexamples,
Baumol had to prove that his speculators could in fact realize positive
profits. Lester Telser stated more
succinctly the problem with Baumol's third model: `...the latter two terms [in equation (1.9)] are sinusoidal with
constant amplitude. Thus the solution
is dominated by (_{}and, since _{} > 0), the price
rises indefinitely. I must emphasize
again that the price necessarily rises indefinitely.' (Telser (1959), p.301)
Similarly, if _{} < 0, the price
falls indefinitely. In Baumol's third
model, if all the speculators attempt to realize their profits the bubble will
burst.
Telser
also recapitulated Friedman's criticism that Baumol's nonspeculators actually
speculated, since past prices influenced their decisions. Current price and recent price trends are
shown in the righthand side of (1.1), thus contradicting Friedman's
independence assumption. `If nonspeculators
are not affected by past prices and if speculators have to realize their
profits then Baumol's counterexamples are unacceptable.' (Telser (1959), p.301)
Replying
to Telser, Baumol conceded that all the speculators could not realize their
profits in his third counterexample, or the speculative bubble would
burst. `Hence I must agree that it is
unreasonable to cite this as an example of destabilizing profitable
speculation.' (Baumol (1959),
p.301) However, Baumol maintained his
first two models had demonstrated PDS, even if price trends influenced the
underlying demand in them. More
important, Baumol noted that no one had disproved the central idea of buying on
an upswing and selling on a downswing.^{4}
Kemp
(1963) pointed out that Baumol was only constructing a counterexample, not a
general theory of speculation. Kemp considered
Telser's speculative bubble criticism irrelevant, since economists could view
Baumol's counterexample as PDS for a limited time interval before the bubble
collapses. Indeed most economists would
regard speculative transactions leading to bubble formation and destruction as
destabilizing influences. The Friedman
Proposition should govern even those speculators who derive profits at the
expense of other speculators.
1.3.D.2.
Friedman's Criteria Restated. Milton Friedman subsequently remained unconvinced
that Baumol, Kemp, and others had validly demonstrated PDS.
Speculators
can make fluctuations wider...only by selling net when prices would otherwise
be low and buying net when prices would otherwise be high. But this means that they sell at a lower
price than they buy and so make losses.
Our model therefore implicitly defines stabilizing speculation as
speculation yielding gains...and destabilizing speculation as speculation
yielding losses. (Friedman (1969),
p.287)
Friedman also restated the criteria necessary to
disprove his conjecture.
Consider
any market in operation. Suppose that
an additional set of transactions are made in the market by an additional group
of people whom we shall call `speculators' or `new speculators.' We shall then deal only with the question
whether this additional set of transactions increases the fluctuations in price
... By dealing this way with a change in the amount of speculation, we can avoid
the troublesome intellectual problem of defining zero speculation without any
loss in generality. We shall make one
further assumption ... that the activities of speculators do not affect the
quantities demanded and supplied by other participants in the market at each
current price. (Friedman, 1969,
pp.286287)
Superficially,
Friedman's assumptions lend support to Baumol's first two counterexamples. In light of Friedman's remarks, we might
interpret Baumol's speculators as `new speculators' in an existing speculative
market. However, Friedman maintained in
a footnote that Baumol had yet to propose an acceptable counterexample: `It will be clear that our assumptions rule
out the main case (Baumol) considered.
Baumol also considers a special case corresponding to our assumptions. His own conclusion is ambiguous but only
because in judging the profitability of speculation he does not require it to
be carried through to completion.' (Friedman (1969), p.287n)
The
price trend terms in Baumol's underlying market excess demand curve continue to
be the crux of the objections.
Originally, the model was criticized for depicting `nonspeculators' as
speculators. The models fail to meet
the restated criteria, because these same price trends show that the `new group
of speculators' have influenced the other market participants' demand, thus
violating Friedman's independence assumption.
Friedman's
independence assumption has proven to be the most controversial in the
literature. Krueger (1969), for
example, found the assumption implausible and limiting the Proposition's
scope. However, some economists
supported Friedman's assumptions.
The
traditional argument is predicated on the assumption that `real' (by which is
meant nonspeculative underlying demand and supply) forces dominate the market
and that speculative turnover is only a small part of the traded quantity,
which can consequently influence only the magnitude, not the direction, of
price changes. (Lipschitz and Otani
(1977), p.38)
From the Lipschitz and Otani summary, Baumol's
`nonspeculative' excess demand functions, which Friedman and others consider
speculative, cannot drive the cyclical price movements without violating
Friedman's criteria. Therefore, even
models examining `new speculative' effects must still distinguish between the speculators
and nonspeculators: the models must
assure that only real forces predominantly determine price movements.
If we
have correctly analyzed Friedman's restated criteria, then we once again face
the old conundrum of differentiating between speculators and
nonspeculators. We recommend avoiding
this difficulty by separating traders using the per se distinction. Considering price trends or past prices is
not equivalent to buying with the intent to resell.
1.4.
Categories of Counterexamples
1.4.A.
PreModern Depictions of PDS
Numerous authors have proposed counterexamples to
the Friedman Proposition; each author envisions his own market conditions that
create opportunities for profitable destabilizing speculation. The interested reader may want to contrast
some of the works in this section with the modern contingent claims example in
Section 1.4.B.
1.4.A.1.
PanicStricken Central Bank Counterexample. Stein
(1961) proposed a narrative counterexample concerning the vulnerability of a central
bank's foreign currency reserves to speculative attacks. Suppose a central bank purchases some
speculative group's supply of foreign currency (presumably for balance of trade
reasons). After acquiring the foreign
currency, the central bank becomes panicked over its depleted home currency
reserves and devalues it. Following the
devaluation, the speculators buy back the home currency at a profit. The speculators apparently profited at the
expense of exchange rate stability.
The
difficulty with Stein's counterexample is that when the central bank devalues
the home currency, it too speculates.
Stein's counterexample depicts a zerosum game: the private speculative gains equal the
central bank's (the public's) losses.
The central bank's reaction to the speculative sales, rather than the
speculators' activity, creates the opportunity for profits and destabilizes the
exchange rates.
Stein's
proposed counterexample is important in another respect. His work illustrated how profitearning
speculators may cause government policies to be reshaped in such a way as to
destabilize markets more than if the government did not intervene. In private correspondence, Professor
Friedman told me that, in retrospect, he perhaps envisioned such misguided
intervention when he included the qualifier `in general' in the Friedman
Proposition. Only coordinated and
concerted intervention by the G7 central banks has proven successful in fending
off speculative attacks on currency reserves.
1.4.A.2. Lagged
Trader Responses Counterexample. Williamson (1972) suggested a second counterexample
based on traders' lagged responses to exchange rate changes, the socalled
`Jcurve' reaction. Recall from the
discussion of the MarshallLerner condition in Section 1.3.B that a
country's currency appreciation would in the short run raise the value of that
country's exports; while in the long run, decreased foreign demand for that
country's goods and services would actually reduce its net trade balance.
Suppose
a country's period 0 exchange rate rests in equilibrium at _{}. In period 1 a group
of speculators begins selling, for whatever reason, domestic currency. The speculative transactions lower the
exchange rate to _{} and induce a balance
of payments deficit. Importers of that
country's goods and services have relatively inelastic shortrun demand, since
many of these orders have been fixed by legal contract. They will attempt to purchase the same
quantity of goods and services at the new high exchange rate prices. Thus foreign trading partners must purchase
these domestic goods with more units of foreign currency, which tends to
depress the value of their own currencies further.
However,
in period 2, Williamson's clever speculators realize that longterm forces will
eventually raise the country's exchange rate again. When the exchange rate drops to _{}, Williamson's speculators begin buying up the domestic
currency's commercial excess supply.
The longterm forces combine with the speculators' purchases to raise
the exchange rate to _{}
If
Williamson's proposed speculative behavior recurs, the exchange rate will
oscillate about its equilibrium moving from _{} to _{}. Speculators earn positive profits  buying low at _{} and selling high at _{}  yet their
actions destabilize the exchange rate.
Williamson's speculators exploit profits from traders who determined
their volume of exports and imports for nonspeculative reasons, based on
advanced legal contracts to trade or based on commitments from experience with
the equilibrium rate of _{}.
As Price
and Wood (1974) note, this general profitmaking opportunity relies on a
dichotomy in forecasting ability (or intelligence) among the profitearning
speculators and the other market participants.
These other traders cannot forecast when longterm influences will
affect the exchange rates as well as Williamson's speculative group. Levin (1983) extended Williamson's model to
a rational expectations framework and obtained results indicating that
unanticipated real disturbances can lead to overshooting. Furthermore, Levin found that capital
immobility may lead to exchange rate fluctuations around long run equilibrium
values due to exchange rate lags behind changes in the balance of trade.
Additional
work on the rational expectations theme by Canzoneri (1984) has shown that even
for unpegged exchange rates, if a speculator expects `other market
participants' to react to gold price fluctuations, then he too will consider
the price of gold in deciding his demand and supply quantities. When enough speculators behave this way,
then gold price changes will indeed affect the prevailing exchange rates, thus
fulfilling the speculators' destabilizing beliefs.
Under
the `new' macroeconomic approach, Canzoneri's policy prescription occasionally
may run counter to the present interventionist philosophy of leaning against
the wind.
If
the exchange rate rises above its long run equilibrium value it must be forced
down; an appreciation must be engineered.
`Rational' portfolio managers will foresee this appreciation and raise
their demand for money; the (real) supply of money must be increased to
accommodate this new demand. Put
another way, the monetary authority must accommodate the demand for money that
is consistent with the expected appreciation or depreciation that moves the
exchange rate in the desired direction.
(Canzoneri, 1984, p.76)
The correct policy may sometimes call for
accommodation: a currency depreciation
should be met with an increase in the money supply.
We
conclude from the work of Williamson (1972) and Price and Wood (1974) that
institutional constraints in the foreign exchange markets can permit profitable
destabilizing speculation. Speculators
in these works take an exchange rate out of equilibrium by selling their
carryover stock, and then later buy back when the exchange rate has fallen
still farther. Their actions cause the
exchange rate to oscillate around its long run equilibrium value while the
speculators earn profits. Moreover,
Canzoneri (1984) has shown that when enough speculators believe gold prices, or
other extrinsic factors, influence foreign exchange rates, their behavior leads
to a selffulfilling equilibrium.
1.4.A.3.
Giffenesque Good Counterexample. Kemp (1963) proposed a counterexample
based on excess demand for a Giffen good.
The `nonspeculative' excess demand is a function of current price `and
to embrace seasonal, trend, and purely random factors, time itself.' (Kemp (1963), p.185). Thus Kemp's nonspeculative demand has the
form, N[P(t),t].^{5}
Figure
1.2 shows the excess demand for a
typical Giffen good. _{} and _{} are stable
equilibria; _{} is an unstable
equilibrium. Suppose N(P)
depicts a market's excess demand, and the price rests at the equilibrium value _{}. Speculators enter
the market, begin buying up the commodity, and shift the market excess demand
from N(P) to N(P)+S.
Eventually, the price would settle at _{} However, the
speculators withdraw from the market when the price exceeds _{}. The excess demand
reverts back to N(P), but the price continues to rise until it reaches
equilibrium at _{}
Figure 1.2.
Kemp's (1963) Model
At this
point, Kemp's speculators now sell their inventory holdings, which they
purchased at prices less than or equal to _{} The speculators
enter the market as sellers on curve N(P)S. Again, it appears the price would settle at _{}. However, after the
price drops below _{}, the speculators withdraw from the market. The excess demand reverts back to N(P);
the price falls to _{}. In fact, the price
has now completed a cycle. Kemp's
speculators bought the commodities at prices below or equal to _{} and sold them at
prices above or equal to _{}: the speculators
profited. By shifting the N(P)
curve away from its _{} equilibrium, Kemp's
speculators also destabilized the market.
The
principal objection to Kemp's counterexample concerns the functioning of a
tâtonnement process. In general,
traders can only purchase and sell the commodity at the points _{}, and _{}. Kemp's speculators
seem to transact outside equilibrium, before the Walrasian auctioneer arrived
at a marketclearing price.
1.4.A.4.
Multiperiod BuyLow, SellHigh Counterexample. Consider
now a fourth counterexample with changing
preferences over time. Let _{} denote an element of
a speculative sales vector and _{} the corresponding
speculative transaction price. Define
the speculative profits by _{}_{} The MSSD for a
particular speculative transaction is
given by _{} where _{} is the average or
mean speculative transaction price. Let
_{} denote the MSSD
without the speculative transaction.
Suppose
market excess demand for some good across three periods is given by: N_{1} = P_{1}
 30  5Q_{1}, N_{2}
= P_{2}  40  5Q_{2}, N_{3} = P_{3}  50  2Q_{3},
where Q_{i} denotes the equilibrium quantity transacted in
period i. Market clearing requires
zero excess demand. Therefore, the
economy has equilibrium prices of P_{1} = 30, P_{2}
= 40, and P_{3} = 50.
The mean price is 40 and the _{} would equal 200/3.
If a
speculator buys 1 unit of the good in period 2 and sells it in period 3, the
new equilibrium prices would be P_{1} = 30, P_{2}
= 45, and P_{3} = 48. In
this case _{} = (48  45) > 0
and _{} 186/3 < _{}. Therefore, the
speculation is both profitable and stabilizing.
If the
speculator instead sells 1 unit in period 2 and repurchases it in period 3, the
equilibrium price vector will be (30, 35, 52). In this case _{}, but _{} = (35  52) <
0. Thus the destabilizing speculation
has also been unprofitable, just as the Friedman Proposition would predict. Note that the excess demand curves in this
illustration exhibit different slope intercepts (if plotted on pricequantity
axes) and different slopes, reflecting changes in demand elasticities.
Now
consider the following modification.
The excess demand for the good across the three periods is N_{1} = P_{1}
 30  5Q_{1}, N_{2} = P_{2}  40
 8Q_{2}, N_{3}
= P_{3}  50  1Q_{3}. Only the slopes in time periods 2 and 3 have changed. Therefore, P_{1} = 30, P_{2}
= 40, and P_{3} = 50 are still the market clearing prices, 40 is
still the mean, and _{} = 200/3. If a speculator buys 1 unit in period 2 and
sells it in period 3, the new equilibrium prices would be P_{1} = 30, P_{2}
= 48, and P_{3} = 49. In
this case _{} = (49  48) >
0, but _{} 229/3 > _{}. Thus we have shown
a counterexample in which speculation is profitable yet destabilizing.
1.4.A.5.
Class of Nonlinear Excess Demand Counterexamples. For
some twenty years, a theorem circulated in the speculation and stability
literature that models containing linear excess demand curves were sufficient
to validate the Friedman Proposition.
In contrast, nonlinear excess demand curve models were thought to
generate PDS counterexamples. This
proposed theoretical limitation began when Kemp suggested if `the
nonspeculative (excess) demand is linear in price and contains a component dependent
on time only, profitable speculation cannot fail to be stabilizing....' (Kemp (1963), p.189) Note that our multiperiod counterexample in
the preceding section immediately contradicts this assertion.
Farrel
(1966) followed Kemp's lead and emphasized Friedman's independence assumption.
In
the absence of transactions costs linearity (in price) of the nonspeculative
excess demand function is a sufficient condition for the validity of the basic
proposition...In markets where the independence assumption holds and
where transaction costs are large enough to cover actual departures from
linearity of the nonspeculative excess demand function, the basic proposition
holds. (Farrel (1966), p.192)
Since these assumptions  independence from past
speculative activity and price linearity  severely restricted his model,
Farrel concluded that his analysis had limited value. `But ... this paper will not have been wasted if it has persuaded
economists that our basic proposition is too strong to hold with any great
generality and that they should therefore seek to establish weaker propositions
concerning the properties of speculative markets.' (Farrel (1966), p.192)
Schimmler
(1967) simplified and unified Kemp's and Farrel's proofs using a Hilbert
space. Lien (1984) found an error in
these proofs that permitted us to generate the counterexample in Section
1.4.A.4. Lien showed that the linear
excess demand curve theorem is valid only when the slopes of the excess demand
curves do not change.
Schimmler
(1967) went on to develop an entire class of counterexamples based on
nonlinear excess demands.
Unfortunately, his class of models lack intuitive appeal, such as `buy
on the upswing, sell on the downswing.'
Given the nonlinear excess demand curves in Baumol's and Kemp's counterexamples,
it is not too difficult to imagine problems that these curves might create for
the Friedman Proposition. The
derivation would also distract the reader for several pages just to establish
the Hilbert space framework. Therefore,
we have placed the derivation of this class of counterexamples and the proof
of the linear excess demand curve theorem in Appendix C.
1.4.B.
Modern Uncertainty Theory Counterexample
Salant
(1974) proposed a counterexample incorporating speculative carryovers in
economies with stochastic endowments.
Only the speculator has carryover facilities. Consider a consumer's planning problem in a two good, two period
economy. The individual has known
current endowments of the two goods (_{}) and random future endowments _{} depending on whether
it rains, _{}, or shines, _{}. If the consumer had
carryover facilities, he might store part of his current endowment, _{} and _{}, for consumption in the next period. The consumer's present and future
consumption would then be _{} _{}
Suppose
the consumer expects rain with probability _{} and has a separable
utility function which permits us to write his expected utility as
_{}
_{}
where _{} and _{} are concave,
increasing functions, and _{} is a constant. The first order condition that emerges from
maximizing expected utility with respect to _{} is:
_{},
This expression describes the optimal quantity of
good _{} to carryover and the
second expression shows the consumer's indifference to good _{} carryovers. Therefore, treat good _{} as a numeraire and
set its price equal to one. The
consumer would then desire to equate his marginal utilities from present and
future consumption.
However,
suppose the consumer cannot carryover either good. Instead of treating consumption as a dynamic programming problem,
the consumer simply maximizes utility separately in each period. In period 1 the consumer maximizes utility
subject to an income constraint:
_{}
where _{} is the associated
Lagrange multiplier and Y is his income. The emerging optimality condition equates the marginal rate of
substitution with the price ratio, _{}
In
period 2 the individual again maximizes utility subject to an income
constraint:
_{}
with corresponding optimality condition _{} If the speculator
transports _{} of good X into
the next period and sells it, then in period 1 the price of X will be _{} Similarly, in period 2 the good X
price conditional on each state, rain or shine, will be _{} and _{} with
probabilities _{} and _{}, respectively. The
speculator expects to receive profits _{} given by
_{}
How does
speculative carryover affect the random period 2 price? If _{} the consumer's
inverse demand curve, _{}, is concave. Any
speculative carryover will always increase the price variance.^{6} With concave and therefore increasingly
steep demand, speculative carryover, _{}, widens the spread between good X's
conditional prices for each state of the world. See Figure 1.3. Thus for
any set of prices for which _{} > 0, speculative
carryover can increase some good's price variance.
Figure 1.3.
Concave Market Demand Curve
1.5. Brief
Empirical Overview on Destabilizing Speculation
1.5.A.
Econometric Tests
One of the first theoretical PDS counterexamples
contained the warning: `The effects of
profitable speculation on stability is in part an empirical question and ...
attempts to settle it by a priori arguments must somewhere resort to
fallacy.' (Baumol (1959), p.302) Although one might have expected the
empirical tests of Friedman's Proposition to employ data on stock market
speculation, the empirical work in this area has primarily used exchange rate
data. The empirical tests have yielded
inconclusive results. Frequently the
research confirms that a speculative group earned profits and simultaneously
stabilized prices. However, these
findings fail to disprove any of the counterexamples or theoretical
limitations to the Friedman Proposition.
Representative works on both sides of the Proposition include Arndt
(1968) and Kenen (1975).
Arndt's
study indicated that speculators in his sample from the Canadian foreign
exchange probably follow the logic in Friedman's Proposition. Arndt concludes, ``In a stable environment
... our theory predicts  and the data tentatively support this conclusion 
that speculators' expectations will be a slowly changing variable with
considerable inertia, and that speculative sales and purchases will have a
dampening effect on movements in the exchange rate.'' (Arndt, 1968, p.69)
On a
more ambiguous note, Kenen (1975), in examining speculation under different
exchange regimes, found no uniform data to support the conclusion that
profitearning speculators generally stabilize prices. `Although long lags and high elasticities
appear to amplify instability, we cannot conclude from (its profitability) that
speculation is indeed stabilizing.' (Kenen,
1975, p.134)
The
empirical work as a whole  as might be expected from the theoretical
difficulty in isolating when a speculative group has transacted  has not
provided conclusive evidence one way or the other for the validity of the Friedman
Proposition. Overall, one senses a
reluctance among the econometricians who examined this relationship to
categorize professional (and presumably profitable) speculation as a
stabilizing influence.
1.5.B.
General Comments on Foreign Exchange Rate Stability
In the opening paragraphs of this chapter we
pointed out that speculation must be profitable over time, or the losses from
speculative activity would be a selfcorrecting problem: the destabilizing speculators would fail to
survive in a Darwinian sense. It is of
some interest then to examine how speculation has generally been perceived to
influence the stability of foreign exchange markets. Exchange rate forecasters were initially optimistic that free
market speculation would attenuate exchange rate fluctuations.
In the
early 1970s when countries first adopted flexible exchange regimes, the initial
swings in exchange rate values were thought to be ``what one might expect
during a learning period, when speculators' views regarding longrun equilibrium
values are weakly held and substantial stimulus is therefore required to make
them act on them.'' (Whitman, 1975,
p.138)
After
many years experience with flexible regimes, the prevalent view shifted to some
disillusionment that the exchange rate mechanism may have inherent
instabilities spawned by professional speculation.
The
focus of attention then shifted to market imperfections, including
insufficiency of stabilizing speculation, as the cause of the volatility that
characterized real world exchange rates.
But, with the passage of time, an explanation of these imperfections as
temporary phenomena characteristic of a transition period became less and less
credible. (Whitman, 1984, p.300)
Economists
have thus recognized that professional (profitearning) speculation does not
necessarily stabilize foreign exchange markets, and at least some have
attributed enhanced volatility to this same speculation.
1.6.
Conclusions and Future Research
We have reexamined the proposition that speculators
buy low and sell high, and thus tend to stabilize market prices. Although this proposition dates back to the
Nineteenth Century, the proposition was given new life in the 1950s when Milton
Friedman endorsed it to support the adoption of flexible exchange rates. However, Friedman carefully restated the
proposition in terms of `new speculators' and the reaction of `other market
participants.' This restatement seemed
more closely tailored to real world conditions.
Baumol
challenged Friedman's assertion by proposing counterexamples that depict an
early portrayal of `overshooting.' The
gist of Baumol's counterexample is that (some fraction of) speculators wait
until after the trough and peak of a cycle, so that they wind up buying on the
upswing and selling on the downswing of the cycle.
Comments
on the technical features of Baumol's model raised questions about the
restrictions under which the Friedman Proposition would be valid. These criteria include minimal, if any,
effect on other market participants by the speculative group under
consideration. Baumol's work
illustrates one group of speculators profiting at the expense of another
speculative group, not unlike everyday transactions in capital and foreign exchange
markets.
The
international exchange markets have particular institutions that may yield
theoretical possibilities for profitable destabilizing speculation: intervention by monetary authorities,
`Jcurve' timedelayed reactions, and overshooting. The empirical literature has found evidence of both stabilizing
and destabilizing speculation without providing conclusive evidence of
speculation which is simultaneously destabilizing and profitable. Indeed some of the initial optimism for
flexible exchange regimes voiced by economic theorists and forecasters in the
1960s and early 1970s gave way to disillusionment in the wake of foreign
exchange instabilities under flexible rates.
The 30%
crash in the Dow Jones Industrial Average over October 16 19, 1987, has shown
that endogenous influences can cause greater instabilities in the market than
even external factors. Panic buying and
selling can lead to further panic, or trigger computerdriven program
trading. If such speculative behavior
were on the whole unprofitable, then it would not be expected to recur. Those speculators who panic and lose capital
would be part of a selfcorrecting problem.
Yet new constraints imposed to limit program trading, such as the New
York Stock Exchange's "uptick rule," show concern for this ongoing
form of destabilizing speculation. So
we are left with a proposition that has engendered valid theoretical
counterexamples and some anecdotal evidence to the contrary on inherent foreign
exchange instability and program trading.
Appendix A:
Outline of Baumol's Difference Equation Model
In his first counterexample, Baumol proposed
that some `nonspeculative' group creates a cyclical path for a commodity's
price over
time. To
represent the time path, Baumol constructed a sinusoidal secondorder
difference equation,
_{} (A.1) 
where _{} and _{} are constants, with *_{}* < 1. Applying the quadratic formula permits us to
recast this equation in a more familiar sinusoidal form. In the homogeneous equation,
_{}
let _{} = 1, _{} = 2_{}, and _{} = 1. Substituting these values into the formula
for the solution of a quadratic equation yields
_{}
and note _{}. Let _{} be some angle such
that _{} then
_{}
The general solution for _{} from this equation is
_{} _{}
_{}
_{}
_{}
_{}
Let _{} _{}, and R denote the mean price level. To derive the value of _{} in terms of _{} and _{} from equation (A.1),
set _{}, a constant, for all _{}. Substituting this
value into (A.1) yields
_{} and solving for _{} leads to _{}. Therefore _{} in equation (A.1) can
be expressed as
_{} (A.2)
This result clearly illustrates equation (A.1)'s
sinusoidal characteristics. We can
verify that _{} is the mean price
level by evaluating (A.2) at its peak, _{}, and at its trough, _{} _{}. These two prices
sum to 2_{}, and the mean price is therefore _{}.
Baumol
then constructs a `nonspeculative' or underlying excess demand from (A.1):
_{} (A.3) 
where _{} is a constant, and _{} is a positive
constant. Current price and recent
price trends, as evinced by the lagged prices in (A.3), influence Baumol's nonspeculative
excess demand.
Baumol
next specified a speculative excess demand function given by
_{} (A.4)
where C is a positive constant. If _{} is the price
immediately following a trough, then these speculators have positive excess
demand. Similarly, the speculators wish
to sell immediately after a peak.
In
equilibrium the speculative and nonspeculative excess demand functions must sum
to zero: _{} Summing equations
(A.3) and (A.4), expressed in period t, yields
_{}
And the solution for _{}207
is
_{} (A.5) 
Since
equations (A.5) and (A.1) have the same form, (A.5) is also sinusoidal. Furthermore, the price expression in (A.1)
must also solve (A.4), the speculative excess demand function. With this basic construction, Baumol then
illustrated that maximum speculative purchases immediately follow the
trough, while maximum
sales immediately follow the
peak. Consider (A.1) evaluated at
period _{}: _{} Substituting this
value of _{} into equation (A.4)
produces
_{}
Since _{} is a constant with *_{}* < 1, we may
rewrite the equation as _{} where _{} is a constant, and _{} is a positive
constant.
This
latter equation incorporates speculative sales after a peak and purchases
immediately following the trough `since it states essentially that speculative
excess demands fluctuate inversely with prices one period earlier (note
the time subscripts of _{} and _{}).' (Baumol (1957),
p.266). Baumol's speculators profit
from this activity, since the prices at which they sell exceed those at which
they purchase.
Appendix B:
Derivation of Baumol's `Real' Model's Solution
In equilibrium supply equals demand (_{}), so that _{}, and _{}, where _{} The equilibrium cum
speculation is the same as before, but nonspeculative excess demand is
represented by the difference between demand and supply: _{}, where _{} is expressed in
equation (1.8) from the second counterexample. Substituting for D and _{} in the latter
equation yields,
_{}
and solving for _{},
_{}
which can be rewritten as
_{}
where _{} are constants. This solution for _{} and the corresponding
value for _{} can again be
substituted into equation (1.10) to obtain the following thirdorder
differential equation:
_{} (B.1) 
Based on
this result Baumol asserts that the preceding equation has at least one real
root, which must be positive since the terms in equation (B.1) alternate in
sign. `It follows that the time path of
prices is changed by speculation from a cyclical pattern of constant amplitude
into an unstable, explosive movement.'
(Baumol (1957), pp. 269270)
We will
first derive the homogeneous solution for equation (B.1):
_{}
Let _{}, and substituting in the latter equation yields,
_{} Next, by dividing through by _{} and simplifying the
equation becomes
_{} = 0
_{} = 0
_{} = 0
_{} = 0,
with solutions _{} and _{}. Therefore, the
thirdorder differential equation has a solution
_{} (B.2) 
where _{} and _{} are constants.
Appendix C:
Schimmler's Hilbert Space Model.
Let _{} denote a speculative
excess demand vector and _{} the `nonspeculative'
or existing excess demand. Equilibrium
price vectors with and without this speculation are denoted by _{} and _{}, respectively.
Requiring the speculators to realize their profits implies that the
speculative transactions must sum to zero, or more formally, _{} where _{} is a vector of unity
elements.^{7} By convention,
speculative profits, _{} have a negative sign
to indicate that net sales are negative while purchases are positive.
The MSSD
for price vector P is denoted _{} _{} where _{} To measure
stability, define
_{} When _{} is positive, the
speculative activity has stabilized prices.
Friedman proposed that _{} implies _{}
Farrel
(1966) made the nonspeculative excess demand independent of the speculative
activity by assuming that the price spread, _{}, is a function of _{} alone: _{}. Schimmler (1967)
extended Farrel's results to temporal independence:
_{} (C.1)
This seemingly innocuous assumption turns out to
be pivotal to the analysis that follows.
It turns out that only linear excess demand schedules follow condition
(C.1).^{8}
Schimmler
denoted centralized vectors with an asterisk, e.g., _{} where _{} is the mean element
of _{}. Thus _{} _{}. Consider now the
inner product of _{} and _{}:
_{} = _{}
=
_{}
=
_{}
=
0.
Since _{} Schimmler maintained
_{} (C.2)
where _{} is some real valued
function. When _{} > 0, speculative
purchases increase the spread between _{} and _{}. As Schimmler noted,
equation (C.2) `shows the difference between _{} and _{} is a linear function
of _{} with temporally
independent slope and temporally independent constant term.' (Schimmler (1967), p.113).
Schimmler's
work also defined an entire class of counterexamples based on excess demand
curves that are nonlinear in price. We
begin by defining the product of T and c:
_{} = _{}
=
_{}
=
_{}
=
_{}
=
_{}
=
_{} (C.3)
=
_{} (C.4)
If _{} does not follow the
linear relationship in (C.2), then there exist two vectors _{} and _{}, such that _{} > 0 and c
< 0. Let _{} denote a vector
linearly independent from _{}. In the plane
spanned by _{} and _{}, the two halfplanes
_{} (C.5)
and
_{} (C.6)
have a nonempty intersection. A vector _{} can be selected from _{} so that
_{}
From the
definition of H(S) in (C.1), it follows that
_{}
Let _{} then _{} _{} can then be defined
by
_{}
Recall from (C.3) that
_{} = _{}
=
_{}
from the definition of the halfplane A in
(C.5). The speculative profits are
_{} = _{}
=
=
_{}
This latter expression is positive since _{} and thus the
properties of the halfplane B in (C.6) hold as well. Thus the speculation has been profitable and
destabilizing, or more succinctly _{} while _{}.
Notes
1. Mill
(reprinted 1921, at pp. 707708) stated,
`When a speculation in a commodity proves profitable to the speculators
as a body... their purchases make the price begin to rise sooner than it
otherwise would do, thus spreading the privation of the consumers over a longer
period, but mitigating it at the time of its greatest height...[I]t often
happens that speculative purchases are made in the expectation of some increase
of demand, or deficiency in supply, which after all does not occur, or not to
the extent which the speculators expected.
In that case the speculation, instead of moderating fluctuations, has
caused a fluctuation of price which otherwise would not have happened, or
aggravated one which would. But in that
case the speculation is a losing one...[A]nd though (speculative transactions)
are sometimes injurious to the public, by heightening the fluctuations which
their more usual office is to alleviate, yet whenever this happens the
speculators are the greatest losers.'
2. See,
e.g., Dulles (1929).
3. Kemp
illustrates this point more rigorously as follows. If the price follows a regular sine path, _{} the cycle has
period _{} and frequency _{}. The price has MSSD equal to _{} and note _{} Thus a change in the
amplitude _{} has no impact on the
MSSD.
4. The
literature has more frequently noted Baumol's concession than his defense of
this general theme of buying on the upswing and selling on the downswing. Compare Logue (1975), Glahe (1966), Krueger
(1969), Farrel (1966), Johnson (1976), and Telser (1981); with Kemp (1963),
Baumol (1965, pp.1731), and Eichengreen (1982).
5. Speculation,
as differentiated from arbitrage, only occurs under uncertainty. Modern uncertainty theorists would
explicitly define the variable adding randomness to a model, e.g., the state of
the world, not merely append uncertainty to the passage of time.
6. The only
instance where carryover would not increase the price
variance is if X^{r} = X^{s}.
7. Schimmler's model incorporates timedependent
variables expressed as vectors in the _{}dimensional
Euclidean space, _{}. Alternatively, his
model could be formulated with functions of time, such as Kemp (1963), using
measurable and Lebesgue squareintegrable functions in the Hilbert Space _{}. The scalar or inner
product _{} of the vectors _{} and _{} would thus be defined
by _{} in the _{} and by _{} in the _{}.
8. This point is due to Lien (1984).
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Arndt,
Sven W., (1968), `International Short Term Capital Movements: A Distributed Lag Model of Speculation in
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William J., (1957), `Speculation, Profitability, and Stability,' Review of
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Comment
I am
grateful to Michael Guth for his useful summary of the discussion, and for
providing me the opportunity to add a few words. More than thirty years have elapsed since I left the controversy
over the possibility that profitable speculation can be destabilizing. The length of that interval certainly
suggests obsolescence and reduces my qualifications for reentry into the
fray. Nevertheless, I remain convinced
that speculation need not always be stabilizing to be profitable, and that the
counterexamples I have supplied are perfectly legitimate.
Two comments may perhaps help the reader to
see why I am not moved by my critics.
The first deals primarily with the behavior of nonspeculators. Let me suggest that the critics struggled to
escape their trap through resort to semantics, but that, of course, will never do. They argued that my `nonspeculators' were
really speculators, because they were (subconsciously?) taking more than one
period's prices into account. This is
surely an odd requirement for someone to qualify as a nonspeculator. Is there any mentally competent adult buyer
or seller of anything who has never compared past and present prices? Yet, let me show that even with such a
tortured use of the word it is easy to reinterpret my models to contain only
two groups, one unambiguously composed of speculators and the other of persons
absolutely free of that taint.
For this purpose, assume that the second
group is made up entirely of persons who simply put cash into the market when
they happen to receive it, and withdraw it whenever they happen to need it for
exogenouslydetermined transactions purposes.
They put it into the market to avoid the expected interest or dividend
opportunity costs that would be incurred by keeping the money idle in the form
of cash between the date of its receipt and the day it will be spent. These totally passive investorsdisinvestors
are surely not `speculators' by any definition remotely related to standard use
of language, and their purchases and sales of securities are determined fully
from outside the model, with absolutely no consideration of any security
prices, past, future or even present.
Now suppose that the exogenous forces happen to lead to investments and
withdrawals whose time path would entail cyclical securityprice behavior in
the absence of speculator activity.
There you have my models, and my conclusions surely follow, exactly as
before.
Second, let me turn to a question that has
been raised about the postulated behavior of my speculators. Why do I assume that speculators sell just
after the downturn and buy just after the upturn? How can this assumption constitute a plausible element in
my counterexamples? Two reasons. First, in an uncertain world, if prices have
been rising monotonically, how else can a speculator (who, like the rest of us,
cannot really foresee the future) be guided systematically to select dates at
which he has some confidence that the expansion phase of the price cycle is
coming to an end? How else can that
person hope to judge when the market has hit bottom? Surely, it is not unreasonable to wait until prices actually show
some manifestation of the beginnings of a downturn or the start of an upturn.
There is another reason why this is not an
implausible story. For I have spoken to
some speculators, and they have told me that this is how they actually
behave. That is not to claim that all
speculators do so, or even that a substantial proportion do so always, but only
that the assumption seems to me far more plausible than the one implying that
speculators regularly manage to sell exactly at the top and buy just at the
bottom. In any case, since as Kemp
noted, my goal is just to provide counterexamples, it is hardly necessary for
me to offer a universallyaccurate depiction of speculator behavior.
W. J.
Baumol
C.V.
Starr Center for Applied Economics
New
York University
Comment
This
chapter shows that controversy still remains about whether speculation under
the floating exchange rate system is stabilizing or destabilizing. My own work on the subject (Journal of
International Economics, November 1983) dealt with the implications of the
Jcurve for the stability of floating exchange rates. The Jcurve is the empirical phenomenon in which a depreciation
of the home currency initially causes a trade deficit to widen because of the
immediate upward pressure on import prices with no initial impact on trade
volumes. The latter respond only with a
lag to the exchange rate movement.
Consequently, over time import volume declines and export volume
expands, and the trade deficit eventually begins to move in a desirable
direction. Ultimately, the depreciation
will cause the trade deficit to shrink, but the dynamic response of the trade
deficit resembles the letter J tilted sideways.
The implication of the Jcurve for floating exchange
rates should now be obvious. A
depreciation of the home currency initially causes the trade deficit to expand,
and one might then expect the currency to depreciate even further in response. In turn, the Jcurve reaction would produce
an even larger trade deficit and therefore a downward spiral of the
currency. In this scenario, the
floating exchange rate system becomes completely unstable. In my work on this subject, I introduced
speculators with perfect foresight into the system but allowed them to be risk
averse. Three conclusions emerged from
the analysis. First, speculators would
stabilize the floating exchange rate system, provided capital mobility is
sufficiently high (i.e., speculators are not too risk averse); second, unless
the degree of capital mobility exceeds an even higher critical level, exchange
rates will oscillate around their longrun equilibrium values; and third, a
real unanticipated disturbance will cause the exchange rate to overshoot its
longrun equilibrium level.
The first conclusion is the most important
one for this discussion, because it suggests that the Jcurve will not be a
source of instability for floating exchange rates provided speculation is
sufficiently sensitive to prospective exchange rate movements. In the limiting case, if speculators were
risk neutral, the exchange rate would be completely stabilized by
speculation. No cycles would
occur. Real disturbances would cause
the exchange rate to move immediately to its new long run equilibrium level.
These conclusions are very sanguine for the
stability of floating exchange rates in the presence of speculation. They suggest that the more speculation the
better and that the imposition of capital controls is likely to be a disruptive
element to a well functioning floating exchange rate system. Moreover, although this chapter shows that a
number of counterexamples have been developed in the literature suggesting
that destabilizing speculation can be profitable, many of them rest on
collusive behavior on the part of speculators or other unrealistic
assumptions. This suggests to me that
the Friedman proposition that speculation will be stabilizing in the long run
is a very plausible one, although the argument that professionals could feed
off of a revolving group of amateurs and that the group as a whole could be
destabilizing is also a plausible one to me.
Nor do these arguments tell us much about the possibility of speculative
bubbles. These questions can be
resolved only by considering empirical tests on speculation.
My own view is that we know very little
about the stabilizing or destabilizing nature of speculation from the current
body of empirical work. There is some
evidence [Froot and Frankel (1989) and Takagi (1991)] that speculators in the
major currencies may be very close to being risk neutral but that their
expectations may not be rational. To
the extent that speculators make systematic errors in their forecasts of future
exchange rates, this could have a destabilizing effect on exchange rates. The counterargument is that if speculators
form their expectations adaptively or regressively or with distributed lags, as
some evidence suggests [Frankel and Froot (1987)], these types of mechanisms
are stabilizing. Moreover, some
evidence suggests that speculators with shortterm horizons may be
destabilizing and those with longterm horizons may be stabilizing [Frankel and
Froot (1990)]. Finally, there is little
empirical evidence on the existence of speculative bubbles. These conclusions, however, are tentative
and require further empirical confirmation.
Jay
H. Levin
Department
of Economics
Wayne
State University
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Shinji, (1991), `Exchange Rate Expectations:
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*A condensed version of this
chapter was originally published in the Rivista Internazionale di Scienze
Economiche e Commerciali, Vol. 35:6, June 1988, pp. 523538. Permission of the Rivista Internazionale
to reprint this article is gratefully acknowledged.