Title PageRational and Irrational BubblesCarnegie Mellon University andKeynote address for the Federal Reserve Bank of Chicago -Rational and Non-Rational BubblesRational bubblesNon-Rational BubblesAn alternative modelPolicy implicationsReferencesTitle PageRational and Irrational Bubblesby Allan H. MeltzerCarnegie Mellon University andthe American Enterprise InstituteKeynote address for the Federal Reserve Bank of Chicago -World Bank Conference onAsset Price BubblesChicago, April 23, 20020Rational and Non-Rational Bubblesby Allan H. MeltzerCarnegie Mellon University andthe American Enterprise InstituteThe subject of this conference is an esoteric issue in rational expectations, general equilibrium modeling. The issue arises because it is not possible to show that models of this kind converge to a unique, stationary equilibrium or dynamic equilibrium path. There are potentially multiple equilibria, and among them are some in which prices of assets or output do not converge to finite values. Prices can explode. A technical reason why a model may have bubble solutions is that there may not be an infinitely lived rational decision-maker who breaks the bubble.We have all heard of the German, Hungarian, and other hyperinflations studied by Cagan (1956) and subsequently by many others. The price level explodes upward in his model, as it didin practice. As long as the Reichsbank, or other central banks, allowed the money stock to accelerate, the price level accelerated. Indeed, this is the point of Cagan's model, and its success in explaining hyperinflations is evidence that there was not a bubble in these cases.The first lesson about bubbles is that all explosive movements are not bubbles. It was entirely rational for people to observe the Reichsbank's monetary acceleration and conclude that the price level would accelerate also as a systematic response to monetary acceleration.Economists use different definitions of "bubble" in their analytic work. The common element is that asset or output prices increase at a rate that is greater than can be explained by market fundamentals. Kindleberger (1992). Or, a price is above its fundamental value today only because investors believe it will be higher tomorrow. The equilibrium of these models is a rational expectations equilibrium.Popular use of "bubble" shares with economic usage the emphasis on anticipations. However, the Japanese stock market in the late 1980s, and the U.S. stock markets in 1929 and 1999-2000 are usually described as driven by irrational, or non-rational, anticipations. Alan  I am indebted to Bennett McCallum and Kevin Hassett for several helpful discussions.1Greenspan used the term "irrational exuberance" to describe what he thought had driven stock prices. A recent Wall Street Journal article about the dollar quotes a market participant. "Another rate cut by the Fed … will help a slight recovery of the dollar, but will not reverse the view that the dollar bubble has been pricked." McCarthy (2001). Robert Shiller's (2000) much-discussed book develops this line of reasoning, as did Charles Kindleberger (1978) and many others earlier. I discuss these two meanings separately because each raises some different issues.One problem with almost any bubble explanation of asset prices is the difference in the behavior of buyers and sellers. If buyers are rationally or irrationally exuberant, how can we characterize sellers? More on that later.Rational bubblesThe standard model of asset prices values the asset as the present value of the stream of dividends that the owner expects to receive. Strictly speaking, the horizon must be infinite but, much of the literature discusses bubbles that collapse within a finite period. In the standard assetprice model, the only systematic force driving asset prices is the expected dividend stream.1 If prices conform to this expectation, the rational expectations equilibria are said to be driven by fundamentals.Many other rational expectations equilibria are possible in principle. These equilibria depend on expectations that are unrelated to the dividend stream, or other fundamentals. They are called "bubble solutions," or bubbles. To preserve a rational expectations solution, the value of the bubble expected today must equal the discounted value of next period's anticipated value and be independent of fundamentals. By iterated substitution today's value depends on all future bubble values discounted to the present. Thus the price today has two parts, the contributions of the systematic and bubble components.At this stage in the development of economic theory, we must regard the rational bubble hypothesis as devoid of empirical content, or empty. The main reasons are that we do not observe expectations, and we cannot exclude other, entirely rational, non-bubble, alternative explanations of prices. I believe it is for these reasons that attempts to test the rational bubble hypothesis have not produced compelling evidence. Peter Garber (1990) casts doubt on some 1 Tomorrow's price depends on expected one-period dividends plus the expected capital gain. The latter depends on expected future dividends and gains. Repeated substitution yields a formula in which today's price depends on the entire future dividend stream.2major past bubbles, including the famous tulip mania in the 18th century and the Mississippi and South Sea bubbles. After reviewing the evidence from empirical tests, Flood and Hodrick (1990,p. 99) conclude that "current empirical tests for bubbles do not successfully establish the case that bubbles exist in asset prices." And the strict version of the bubble hypothesis does not pass the eyeball test: We do not observe asset prices that become infinite. Long before an infinite value is reached, the asset value would exceed expected GDP, hardly a rational outcome. FurtherPaul Weller (1992, p. 272) points to another problem. The theory "provides no clue" about the conditions initiating or terminating bubbles.One reason that a bubble hypothesis is difficult, if not impossible, to test is that expectations are measured relative to some maintained hypothesis and, with rational expectations, exploit all of the information that is relevant according to the maintained hypothesis. Bubble phenomena are what remains unexplained by the hypothesis. In this sense, bubbles are a name assigned to phenomena that may be explained by an alternative