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 post-Keynesian 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 profit-earning 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 profit-earning 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 mid-1950s, 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 wisdom² 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 profit-earning 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 profit-earning 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 comparative-statics issues for speculation via the general equilibrium contingent claims model and standard economic reasoning.  The standard format provides individuals with production functions, preferences, time-distributed endowments, etc., and specifies the available market range.  Economists then pose comparative-statics 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 comparative-statics, 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 market-clearing 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 Marshall-Lerner 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 Marshall-Lerner condition is met when long run export volume increases so much that the actual balance of trade increases.

    Williamson (1972) restates the Marshall-Lerner stability condition as follows.  Let  = the trade balance at time t, defined in foreign-exchange 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 dollar-mark exchange rate decreases from $0.62 to $0.55 per Deutsche Mark (DM).  Having already executed American import contracts, Germany will have an inelastic short-run 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, long-run German demand for United States exports.  Thus the Marshall-Lerner stability criterion states that the total volume decrease, perhaps down to $4 billion 31 DM 7.28 billion, will more than offset the short-run price gain:  (10.909 - 9.677) + (7.28 - 9.677) < 0.

    The Marshall-Lerner 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  Marshall-Lerner 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, second-order difference equation,

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,

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

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

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,

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

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