Rational Speculative Bubbles

Flood and Garber (1982) show that price bubbles can arise in models in which the current market price depends on expected future price changes. Under rational expectations, such models tend not to yield a unique expression of agents' expectations. The indeterminacy arises out of trying to solve for two endogenous variables40 from one equilibrium market condition. As a result, arbitrary, self-fulfilling expectations of price changes may drive actual price changes independently of market fundamentals, causing price bubbles. The fundamentals are described by the precise model of market operation. Some models preclude rational bubbles and others do not; consequently it is not possible to prove that they exist at the theoretical level. They observe that empirical work attempting to identify bubbles has turned up mixed results and is, therefore, inconclusive.

They also note that the previous literature has attributed runs and panics to mass hysteria rather than to rational behaviour. Salent and Henderson (1978) regard runs as predictable events, however. They are regarded as events which terminate price fixing schemes. The viability of such schemes requires the economic agents running them to hold stocks and stand ready to buy and sell at a fixed price. If other agents perceive the scheme to be temporary and expect prices to rise, yielding a capital gain, they will draw down the stock backing the scheme. If stocks are depleted entirely in one final discrete withdrawal, then a run has occurred. Flood and Garber note that systemic bank collapses are the most famous examples of runs. Banks fix the price of deposits in terms of government currency and hold reserves of the currency as backing. If a capital loss on deposits is feared, then depositors deplete the bank's reserves forcing the bank to cease fixing the price of its deposits. Similarly, currency crises are associated with runs on government foreign exchange reserves which are held to fix the price of the domestic currency against other currencies.

Following the rational expectations (RE) revolution in the mid-1970s, it was a widely held view, Blan chard and Watson (1982) observe, that asset prices must reflect market fundamentals in the sense of depending on information on current and expected future returns on assets. Deviations from market fundamentals were viewed as evidence of irrationality. Market participants, however, often believe that fundamentals are only part of what determines the price of a security.

Extraneous events will influence asset prices if other participants believe they will do so, and crowd psychology becomes an important determinant. Meltzer (1982) suggests that the two views can be reconciled if rational expectations under risk is replaced by decision-making and expectations formation under uncertainty, since under uncertainty extraneous events or shocks can cause fundamental and sudden reappraisals of expected future returns.

Blanchard and Watson (1982) demonstrate that economists have overstated their case because rationality in behaviour and expectations formation does not prevent asset prices from deviating from fundamentals or rational bubbles occurring. They observe that there is little doubt that most large historical bubbles, such as those investigated by Kindleberger (1978), contained elements of irrationality and that such bubbles are much harder to deal with theoretically. They therefore concentrate on the analysis of rational bubbles. Their model assumes maximising behaviour, RE and continuous market clearing and implies that, given private information and information revealed by prices, assets are voluntarily held and there is no incentive to reallocate portfolios. With additional assumptions, including common and current information sets, the efficient market or no arbitrage condition can be derived from it. Their model is typical of a class in which expectations of future variables affect current decisions and does not have a unique solution. As a result the market price can deviate from the present value of the asset, without violating the no arbitrage condition. If a deviation occurs, the structure of the model implies that it can be expected to grow over time and constitute a bubble. Using examples they show that the bubble can take various forms. They also demonstrate that bubbles can occur even when agents are risk-averse and are no longer assumed to have identical information sets. They are not, however, able to make much progress on such issues as whether differential information permits a wider class of bubbles or whether some aspects of real world bubbles involve differential information. They also note that, while the efficient market condition itself does not preclude bubbles, there may be other conditions imposed institutionally or from market clearing, or implicit in rationality that rule them out.

Further, standard analysis assumes that bubbles themselves do not affect market fundamentals, but Blanchard and Watson feel this is unlikely. The rise in price associated with bubbles may well encourage an increase in the supply of assets affected. When the bubble bursts, prices will fall below the pre-bubble level because of the increased supply. Additionally, a price bubble in one asset will increase its price relative to other assets not subject to bubbles, and this will lead to portfolio redistribution. It should be noted that this may be a mechanism by which non-speculators are drawn into speculation because if they do not redistribute their portfolios, their relative returns will decline.

Because of the potential for real effects, it is important to ascertain whether bubbles are theoretical constructs of little relevance or whether they are witnessed frequently in the real world. Blanchard and Watson therefore turn to a review of the empirical literature. They observe that testing for bubbles is not easy because rational bubbles can follow many types of process. They show that certain bubbles will violate the variance bounds implied by a certain class of RE models and present empirical evidence that demonstrates such violations. They note that irrational bubbles would also cause such violations. Runs and tails tests are suggested when only price data is available, but it is demonstrated that such tests have low power.

Despite Blanchard and Watson's misgivings, Garbade (1982) argues strongly that bubbles are unlikely to occur in the New York Stock Exchange (NYSE). This is attributed largely to the Fed's margin requirements, which limit the amount of credit that can be used to purchase stocks. The margin requirements were introduced for the specific purpose of inhibiting speculative bubbles following the 1929 crash. (See Galbraith (1954, Ch. X) for further discussion.) In addition the Securities and Exchange Commission (SEC) has encouraged the provision of broader and more detailed information, and empirical evidence implies that stock prices are efficient in the sense of reflecting publicly available information, Garbade observes. Greater and more accurate information, he believes, should reduce the likelihood of bubbles. Empirically, he finds little evidence of bubbles. The stock market should demonstrate a run of increases as the bubble builds and a run of decreases as it collapses. On average, he finds a stock price increase is equally likely to be followed by another increase or a fall. It is implicit in Garbade's discussion that the 1929 crash could have been the collapse of a bubble and that this prompted the Fed to introduce margin requirements in 1934 to inhibit the development of bubbles in the future. The NYSE crash of October 1987 is also viewed by many analysts as the bursting of a bubble. It is argued that stock prices lost touch with fundamentals in the speculative bubble that preceded the crash.

Santoni (1987) notes that the 1924-9 NYSE bull market is widely accepted to have been a speculative bubble42 and that the same theory of stock market price formation has been used to describe the 1982-7 bull market. They are normally regarded as irrational rather than rational bubbles. He challenges the view that these events were speculative bubbles, arguing instead that stock prices reflected fundamentals in each period and presenting empirical support for his hypothesis. He accepts that current stock prices depend on forecasts of future outcomes and the expected returns derived from them, which are subject to changes as new information becomes available and which do not depend on current dividends observed. Consequently, relatively small changes in forecasts can lead to large changes in the fundamental price. Fundamentals cannot be observed directly, however, and proxies must be used that are believed to provide information on fundamentals, though they can only give a rough guide to the behaviour of fundamentals. When the market crashed in October 1987, commentators pointed to the proxies and claimed that stock prices were overvalued prior to the crash. An alternative explanation, he notes, is that the proxies gave a misleading impression of the fundamentals.

To examine the proposition that stock prices in the 1920s and 1980s were driven by factors extraneous to fundamentals, it is necessary to derive alternative hypotheses from the competing theories and test them. Santoni considers three different hypotheses:

1. The efficient market hypothesis.

2. The irrational bubble hypothesis.

3. The rational bubble hypothesis.

The efficient market or no arbitrage hypothesis assumes that stock prices are determined in efficient markets so that relevant known information is reflected in them. Prices change only in response to new information, which cannot be predicted ahead of arrival and is just as likely to be good or bad. If it is correct that past information on price changes contains no useful information about future changes, then the observed changes in stock prices should be uncorrected, and price changes should exhibit no long sequence of successive changes that are greater or less than the median change for the sample. This proposition should hold even if the level of prices appears to drift up or down. The fact that prices drifted up in both bull markets does not imply that price changes are correlated or that market participants were able to predict future changes by observing past changes. The irrational bubble hypothesis argues that self-feeding expectations drive up prices. Fundamentals are regarded as largely irrelevant. Stocks are bought in the belief that they can be sold at a higher price in the future for capital gain. Extrapolating from past price rises, speculators expect the rise to continue.44 The hypothesis implies that there are times when past changes matter. There should therefore be positive correlation in past sequences of price changes and long runs of positive changes that exceed the median change for the sample period, Santoni argues. The rational bubble hypothesis also postulates that there will be occasions when stock prices deviate from the fundamental price and that deviations will tend to persist and explode leading to bubbles that cannot be negative. Santoni concludes that the efficient markets hypothesis implies that stock price changes should follow a random walk while both the rational and irrational bubble hypotheses imply that stock price changes should not follow a random walk but should instead be positively serially correlated.

Despite the growing literature on rational bubbles, Santoni is concerned about the absence of a well specified theory. Following Brunner and Meltzer (1987), he argues that a complete theory of bubbles should identify their cause in terms of phenomena that can be observed, separately from the bubbles themselves. On occasions when a bubble was observed then so too would be the causal event. This would allow a direct test of the theory and could explain why bubbles are observed on some occasions and not on others. In the case of irrational bubbles, the unusual behaviour is attributed to euphoria and manias, which do not identify the cause of the bubble but merely give it another name, he argues. Brunner and Meltzer (1987) go further and argue that bubbles are inconsistent with the rational exploitation of information invoked by the analysis demonstrating their existence. It is clear that they are criticizing the rational bubble literature. Their argument may well be true for rational bubble models which assume a risky environment, although Blanchard and Watson (1982) were unable to prove that RE prevents bubbles. It is not so clear that it applies to the so-called irrational bubble hypothesis which, as Meltzer (1982) observed, is more likely to hold in an environment of uncertainty. Kindleberger (1978) in fact attempts to identify events that generated fundamental re-evaluations of expectations of future returns leading to bubbles and also tries to identify events that lead to their bursting. The irrational bubble and FIH literature is much richer because it attempts to explain the creation and bursting of bubbles and provides some insight into how to prevent them in the future by regulating the financial system. The rational bubble literature, which attributes crashes to bursting bubbles without adequately explaining why they burst, is of little help to the policy-maker.

Santoni (1987) concludes with an examination of the evidence to see if it supports the efficient markets or the bubbles hypotheses. He uses samples of more than 400 observations from each of two periods, the 1920s and the 1980s. In each period there was rapid price advance. Autocorrelation coefficients were estimated for price changes, and the Box-Pierce test was applied, but no significant autocorrelation was evident. The data was, therefore, consistent with the efficient market hypothesis. The upward drift was undeniable but at the time, he argues, it was not something that investors could have bet on with confidence. He also applied the runs test, which Blanchard and Watson noted has low power, and this too rejected the bubble hypotheses.

Despite these results, and others like them, the so-called upward price drift in these periods remains a cause for concern to some economists.

The price levels, rather than changes, were clearly positively correlated, and a trend term would have contributed strongly to any equation explaining price levels without lagged price terms. It may be that this is the important feature, implicit in calling such periods bull markets, and that the random walk in price changes can be readily explained. For example, speculators could, and probably did, bet on the medium-term rise in the trend price. But because of diverse expectations, which might be the result of non-homogeneous information and differing perceptions, speculators might take profits periodically and refinance their positions. It is after all the rising price levels that deliver the capital gains. A detailed analysis of the behaviour of speculators during the bull markets appears to be called for. In this case daily fluctuations in prices would not necessarily lead speculators to assume that the medium-term trend had altered. Further, if the stock prices were not overvalued, why did they drop so precipitously in 1929 and 1987? If the no arbitrage hypothesis holds, how was it possible that the government bond markets got so out of line with the equity markets prior to the 1987 crash? It is also notable that regardless of whether or not stock markets are subject to bubbles, other markets seem to demonstrate speculative behaviour consistent with the bubble hypothesis. This is particularly true of the property market, possibly as a result of the long gestation periods and potential for oversupply. There are numerous examples of property market bubbles and crashes,46 the most recent being the Texan crisis of the mid-1980s, which led the largest bank holding company in the state, First Republic Bank, to seek a capital injection from the FDIC in March 1988 and left many office blocks empty.

Recent literature on rational bubbles has not confined itself to stock market prices. It has also featured applications to the analysis of exchange rates, which many analysts believe have shown excessive short-run fluctuations and sustained periods of misalignment, neither of which are consistent with the fundamentals. Brunner and Meltzer (1987) argue that neither the efficient asset market approach of the 1970s nor the theories based on balance of payments fundamentals that preceded them can explain the exchange rate behaviour observed in the post-1973 floating exchange rate period. The natural approach in the 1980s was to return to the analytical framework of the efficient markets approach and extend it. This resulted in the literature on bubbles and sunspots. As in asset markets, the theories of bubbles in exchange markets exploit the non-uniqueness of solutions in RE equilibria. Standard RE models relate the exchange rate (yt) to fundamentals (f), which are determined by a linear combination of exogenous variables. But yt = ft + bt will also be a solution where bt follows a possible stochastic time path imposed on the system. The bubble term (bt) is determined by extrinsic information and refers neither directly nor indirectly to any observable phenomena.

The choice of extrinsic information is entirely arbitrary and is difficult to reconcile with the rationality and information postulates used in the analysis, Brunner and Meltzer argue. The basic model provides a continuance of convergent equilibrium paths while the supplementary, and arbitrary, specification of information extrinsic to the basic model determines the specific path taken by the exchange rate. They find this unsatisfactory because it offers no explanation of the volatility of exchange rates or the serially noncorrelated changes in exchange rates discovered in empirical analysis. The problem arises, they argue, from attempting to explain phenomena crucially conditioned by a pervasive uncertainty with an analysis incorporating RE that assumes that the probability distribution of shocks is known and, therefore, that risk rather than uncertainty prevails.

Previous attempts to explain exchange rates in terms of purchasing power parity (PPP),47 which postulate rational expectations in the context of complete and homogeneous information among agents, also eliminate all manifestations of the pervasive uncertainty. They argue that, with such an analysis, an explanation of volatility is inaccessible. Singleton (1987) examines the consequences of replacing complete and homogeneous information among agents with imperfect and heterogeneous information. This captures some of the dimensions of uncertainty and radically changes the implications. It allows for much greater volatility than standard exchange rate models but fails to settle the remaining major question: the integration of the observed random walk behaviour of exchange rate changes into the analysis. If, as seems undeniable, speculators are present in the exchange markets, then the explanation could lie in non-homogeneous information and perceptions among agents and the tendency for individual agents to take profits periodically and refinance positions, as a method of hedging, as outlined earlier.

Singleton (1987) provides a critical review of the burgeoning literature on the potential importance of speculative bubbles and sunspots for explaining the time series behaviour of exchange rates. He expresses doubts about such explanations of exchange rate behaviour and argues that speculation has not had a stabilising effect in exchange markets as previously argued by proponents of floating exchange rates. (See, for example, Friedman 1953, pp. 157-203.) Singleton notes that bubble and sunspot models adopt fairly simple, and inadequate, specifications of the interplay between and the information of agents by commonly imposing current and homogeneous information and assuming that the distribution of shocks is known. This, as Brunner and Meltzer (1987) observed, eliminates uncertainty in the sense of Knight (1921). There is a strange incoherence in models that imply that past price changes are no guide to future price changes and yet future shocks will follow the distribution of past shocks. These bubble and sunspot models abstract entirely from the dynamics introduced by incomplete information and heterogeneous beliefs and/or information, he observes. The rejection of the PPP and economic fundamentals theories, based on balance of payments analysis, has led to the development of bubbles and sunspot theories; but, he argues, changes in fundamentals can easily generate exchange rate behaviour that resembles a rational bubble.

Agents may believe, with time-varying degrees of confidence, that major changes in the stochastic processes governing fundamental economic variables, such as the money stock or income, may occur in the future. It is unlikely that all the fundamentals are observed by econometricians conducting empirical analysis, and consequently there may appear to be bubbles in the misspecified models being investigated. With the addition of some of the features of uncertainty, this misspecification explanation of broad swings in exchange rates can be extended to explain their short-term volatility, Singleton argues. If agents believe that changes in the environment will occur with some small probability, then misspecifying the model by ignoring this possibility may lead to an underestimation of volatility. He argues that the probability attached to such events is also likely to change over time, adding to the swings.

Further, incorporating nonlinearities into the model will create a much more important role for informational problems. To illustrate this point, he extends his basic model to include risk aversion. He also demonstrates that reducing the information available to agents can increase volatility relative to the full current information model. When he allows risk aversion to vary across agents, volatility also increases. Singleton demonstrates in addition that by altering the information structure so that shocks and real variables are observed at discrete time intervals while trading in continuous, current and past shocks can have persistent effects on exchange rates, which again become more volatile. Heterogeneous information further magnifies the reaction of the exchange rate to shocks. He argues that it is likely that some traders will be more interested in hedging, importers and exporters for example, while others may take uncovered, speculative positions. With imperfect competition of this sort, volatility may be further increased.

Singleton's examples employ models in which PPP holds. He concludes that to develop an alternative fundamental interpretation of the dollar's appreciation up to 1985, which is generally regarded as an overvalued position, it is necessary to identify credible sources of uncertainty which, when combined with risk aversion, explain the appreciation. One source of uncertainty might have been the growing budget deficit which could have led to a rise in the real rate of interest, and he considers others as well. He argues that a fundamentalist explanation of the dollar appreciation cannot be easily dismissed while doubts remain about the correct specification of current PPP-related models. He concludes that volatile exchange rates do not constitute evidence of inefficient trading or justify central bank exchange intervention. Rather they reflect decision-making in an uncertain environment which may be enhanced by uncertainty about future government policies leading to medium-term swings and increased day-to-day movements in exchange rates. This implies that these features of exchange rate movement could be reduced if the uncertainty regarding future government policies, especially those relating directly to exchange rates, was removed and policy rules were announced instead.

Singleton therefore rejects bubbles and argues that correctly specified models of the fundamentals will be able to explain medium-term movements in exchange rates and their short-term volatility under uncertainty. The latter is approximated by relaxing the current and homogeneous information assumption while the medium-term movements are attributed to omitted variables, including government policy stances, whose future evolution is also uncertain. While some of the medium-term movements may be explicable by omitted variables, the perception that they have frequently led to sustained misalignments is hard to dispel. This implies that better-specified models of the fundamentals may not be sufficient, and irrational bubbles based on speculative euphoria, which are more likely to occur under uncertainty than risk (as Meltzer (1982) observed), may still be present. The problem may be that the so-called fundamentals are not immutable in the complex social organisation48 we call the economy but depend themselves on the interaction of the perceptions of the economic agents at a specific time. The fashions and myths evident in dominant economic doctrines at various times and their tendency to change over time, perhaps even cyclically, may be a reflection of this problem. It is also highly likely that individual economic agents hold perceptions of the set of fundamental variables and their future evolution, and attach weights to them that vary at least as much as those infamously held by members of the economic profession.

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