RATIONAL BUBBLES IN THE STOCK MARKET: ACCOUNTING FOR THE U.S. STOCK‐PRICE VOLATILITY

I. INTRODUCTION Many economists believe that stock prices are too volatile to be attributed to market fundamentals. In his seminal paper, Shiller [1981] reports that over the past century U.S. stock prices are five to thirteen times more volatile than can be justified by new information about future dividends. Research conducted by LeRoy and Porter [1981], independent of Shiller, also shows that the variability of actual stock price movements is too large to be explained by the present value of future earnings. While Shiller's methodology was heavily criticized by subsequent researchers because of his assumption of stationarity in stock price and dividends and the small-sample bias of his estimators, his results on the excess volatility of stock prices have not been reversed. Since the failure of the simple present-value model, economists have devoted a substantial amount of effort to seeking alternative model specifications to explain stock price volatility. One approach is to relax the assumption of a constant discount rate and allow investors to be risk averse, while maintaining the notion that stock prices are exclusively determined by the so-called market fundamentals. Variable discount rate specifications, however, provide only marginal support for the model in explaining stock price volatility. See, for example, Campbell and Shiller [1988a; 1988b] and West [1987; 1988]. Another approach that economists have taken to explain the data is to incorporate speculative bubbles into the model. Economists characterize rational asset bubbles as those generated by extraneous events or rumors and driven by self-fulfilling expectations. One implication of a rational bubble is that once a bubble is initiated, it will grow, in expectation, at a rate equal to the rate of discount and will eventually explode. The existence of speculative bubbles in financial markets has brought about heated debates and no consensus has been reached on whether bubbles are consistent with the rationality assumption on theoretical grounds.(2) Empirically, partly due to the lack of power of testing procedures, general specification tests for stock market bubbles yield mixed results. For example, Rappoport and White [1993; 1994] and West [1987] reject the null hypothesis of no bubbles, while Dezhbakhsh and Demirguc-Kunt [1990] and Diba and Grossman [1988b] report the opposite results. Flood and Garber [1980], Hamilton and Whiteman [1985] and Hamilton [1986] criticize these bubble tests on the grounds that bubbles are observationally equivalent to regime changes in market fundamentals which are unobserved by the econometrician. Furthermore, Evans [1991] points out that tests for bubbles based on investigating the stationarity properties of stock prices and dividends are flawed. He demonstrates by Monte-Carlo simulations that an important class of rational bubbles cannot be detected by these tests even though the bubbles are explosive. Froot and Obstfeld [1991] propose a particular type of bubble, called the intrinsic bubble. Unlike the bubbles traditionally defined, an intrinsic bubble depends exclusively on market fundamentals and not on extraneous events. They find significant evidence of such a bubble and demonstrate that incorporating an intrinsic bubble into the simple presentvalue model helps account for the long-run variability of the U.S. stock data. The intrinsic bubble specified by Froot and Obstfeld is unstable and implies an explosive price-dividend ratio.3 Furthermore, as their bubble is a deterministic function of dividends, once the bubble gets started, it will never burst as long as dividends remain positive. Froot and Obstfeld impose the free-disposal constraint on stock prices and allow only positive bubbles. Intuitively, however, it is difficult to imagine a situation in which market participants should always overvalue securities. In practice, tests for intrinsic bubbles are easily implemented only when dividends are assumed to follow a very simple process, for example, a geometric random walk. …