Ruling Out Unstable Bubbles

A positive stock market bubble takes hold because investors expect the stock price to continue increasing, even though the price of the stock exceeds its fundamental value, as defined by the expected present value of dividends.

Similarly, a negative stock market bubble takes hold because investors expect the stock price to continue falling, although the price of the stock falls short of its fundamental value, as defined by the expected present value of dividends. As long as investors continue divesting in the stock, the price falls, and the expectations of investors are validated. Hence, a negative bubble may take hold as a self-fulfilling prophecy.

Negative bubbles can be ruled out more easily than positive bubbles. If stocks can be disposed of freely, the price of the stock cannot become negative. But negative bubble implies that the price of the stock will tend to minus infinity. This is ruled out by the free disposal condition; hence, a negative bubble can be ruled out.

Ruling out positive stock market bubbles is more tricky. If there are substitutes for the stock at a finite price, then a positive bubble can be ruled out as well, because in a positive bubble, the price of the stock will tend to infinity, and investors will stop buying the stock, turning instead to lower-valued stocks. In addition, in a positive bubble, shareholders in a listed stock will have a strong incentive to issue more stock at higher prices, which will also tend to eventually depress the price of the stock and rule out positive bubbles. Hence, one would only expect positive bubbles in markets where fundamentals are hard to ascertain, stocks are in short supply, and they do not have close substitutes.

Many of the incidents that have historically been recorded as positive bubbles, such as the tulip mania that crashed in 1637, or the South Sea bubble that crashed in 1720, involved such assets.⁷

A positive inflation bubble may take hold because households and firms expect the level of prices to continue increasing, even though the price level exceeds its fundamental value defined by the path of the money supply. As long as they continue to reduce their money holdings to buy goods, the price level increases, and the expectations of households and firms are validated. Hence, an inflation bubble may take hold as a self-fulfilling prophecy.

Similarly a negative inflation bubble (or deflation bubble) may take hold, because households and firms expect the level of prices to continue falling, even though the price level falls short of its fundamental value, as defined by the path of the money supply. As long as they continue to increase their money holdings and refrain from buying goods, the price level declines, and so the expectations of households and firms are validated. Hence, a deflation bubble may also take hold as a self-fulfilling prophecy.

However, inflation and deflation bubbles have more difficulty gaining traction than do stock market bubbles. Negative inflation bubbles can be ruled out by the fact that the price level cannot become negative. Positive inflation bubbles can be ruled out by the existence of substitutes for money, such as precious metals and other real assets.

The arguments analyzed so far for ruling out bubbles are partial equilibrium arguments. Tirole [1982, 1985] and Weil [1987a] have examined this issue in a general equilibrium context. Their conclusions suggest that whether bubbles can develop on real assets in general equilibrium models depends on whether agents have finite or infinite horizons. They conclude that bubbles on real assets can be ruled out in economies in which agents have infinite horizons.

The logic of the argument, as expounded by Tirole [1982], is that negative bubbles on real assets can be ruled out because then all individuals will want to buy and keep the asset forever, because its market price will exceed its fundamental price. However, in such a case, there will be excess demand for the asset, and the negative bubble cannot be an equilibrium. In the case of a positive bubble, if short selling occurs, there will be excess supply of the asset, and the positive bubble cannot be an equilibrium. Even without short selling, all agents will plan to sell the asset after a period of time. Hence, a positive bubble cannot be an equilibrium, because the anticipation of its collapse will rule out the bubble in advance. Hence, only in economies where new agents enter the market, such as in OLG models, can a bubble possibly exist. Even for OLG models, Tirole [1985] and Weil [1987a] prove that bubbles can be ruled out, with the exception of the case of dynamic inefficiency.

A large empirical literature, starting with Flood and Garber [1980], Shiller [1981], and others, has concentrated on testing for the existence of inflation and stock market bubbles, with generally mixed results.⁸

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