Introduction to economic theory of bubbles

This is an introduction to the special section on the economic theory of bubbles. © 2014 Elsevier B.V. All rights reserved. Asset markets around the world are very volatile. Two most important asset markets are the stock market and the housing market. Fig. 1 presents the US and the Japanese real stock market indices (S&P 500 and Nikkei 225).1 This figure shows that the US stock market experienced a persistent boom from 1990 through 2000 and price indices more than doubled. Themarket went down by about a half from the peak of December 1999 to early 2003. It then came back reaching a peak in January 2007, followed by a crash to the bottom in March 2009. Between this short period, the stock market lost more than 50%. Since then the stock market gradually recovered. The Japan’s stock market experienced a persistent boom until December 1989, rose by about 500% from early 1970. After that the stock market crashed and never came back with prices below a half of the peak. Fig. 2 shows the US and the Japanese real housing prices, price– income ratios, and price–rent ratios.2 This figure shows that the US ✩ I would like to thank Atsushi Kajii for useful comments. ∗ Correspondence to: Department of Economics, Boston University, 270 Bay State Road, Boston, MA 02215, USA. Tel.: +1 617 353 6675; fax: +1 617 353 4449. E-mail addresses:[email protected], [email protected]. 1 The monthly real S&P 500 stock price index is downloaded from Robert Shiller’s website: http://www.econ.yale.edu/shiller/data.htm. The monthly Nikkei 225 index is downloaded from Bloomberg. The real indices are deflated by the CPI data download from the OECD Main Economic Indicator Database. 2 The US nominal house price index is the all-transaction index from Federal Housing Finance Agency. The Japan’s nominal house price index is the nationwide urban land price index from the Japan Real Estate Institute. The real house price index is the nominal house price index deflated by the private consumption http://dx.doi.org/10.1016/j.jmateco.2014.06.002 0304-4068/© 2014 Elsevier B.V. All rights reserved. housingmarket experienced a persistent boom fromearly 1990s to December 2006 and increased by about 60% from the bottom to the peak in December 2006. It then dropped until September 2011 by about 40% from the peak. The Japan’s housing market experienced a persistent boom from January 1980 until the peak of February 1991 and increased by about 60%. It then dropped continually until October 2011, lost more than 50%. The price–income ratios and the price–rent ratios tracked the housing prices closely both in the US and Japan, indicating that the fundamental factors alone cannot explain the housing price dynamics. The boom and bust of the stock and housing markets have a large impact on the real economy. For example, it is widely believed that the recent Great Recession in the United States and the Japan’s lost decade were caused by the crash of the housing market. Thus understanding the high asset market volatility is important for both economists and policymakers. It turns out that this is a challenging task (Shiller, 1981). While there are many studies based on new classical theory, an important line of research is based on the idea that asset prices contain a bubble component in addition to the fundamental component. The growth of the bubble can help explain the asset market boom and the collapse of the bubble can help explain the asset market crash. deflator. The average real index in 2000 is normalized to 100. The price–income ratio is the ratio of the nominal house price index to the nominal per capita disposable income. The sample average is normalized to 100. The price–rental ratio is the ratio of the nominal house price index to the rent component of the consumer price index. The sample average is normalized to 100. All data are downloaded from http://www.econ.queensu.ca/files/other/House_Price_indices%20(OECD).xls. All series are quarterly and seasonally adjusted. J. Miao / Journal of Mathematical Economics 53 (2014) 130–136 131 Fig. 1. The monthly real S&P 500 indices and the Japan’s Nikkie 225 indices. Fig. 2. The real house prices, price–income ratios, and price–rent ratios for the US and Japan. This simple idea is intuitive and often talked about by the general public. It is also often mentioned by policymakers such as Ben Bernanke and Alan Greenspan.3 However, it has not entered 3 Bernanke wrote a research article with Mark Gertler on bubbles (Bernanke and Gertler, 1999). themainstream economics. Based onmy conversations withmany economists, most of them resist to accept the idea of asset bubbles. I think there might be two reasons. First, the current core of macroeconomics is the dynamic stochastic general equilibrium approach and the idea of asset bubbles belongs to the periphery (Caballero, 2010). Research on asset bubbles is hard to get published, especially in top journals. This discourages researchers from 132 J. Miao / Journal of Mathematical Economics 53 (2014) 130–136 working on this topic. Second, we do not know much about asset bubbles in economic theory. This topic is typically not taught in macroeconomics or microeconomics. There are many misunderstandings of some conceptual and theoretical issues. For example, some people often argue that the existence of bubbles implies that agents are irrational or there are arbitrage opportunities. There does exist a strand of literature on irrational bubbles (see, e.g., Shiller, 2005).4 However, I will confinemy discussions on models of rational bubbles. By ‘‘rational’’ I mean economic agents have rational expectations and maximize their utility. Moreover, markets are competitive and clear in equilibrium. The purpose of this special section is to promote theoretical research on rational asset bubbles. This section contains four papers that push the research frontier on this topic forward by studying infinite-horizonmodels. Before I discuss each of them, let me provide some background knowledge and a short review of the recent literature. Let me start with a standard two-period asset valuation equation. Suppose that there is no uncertainty and the asset’s gross required return is equal to a constant R. Let {Dt} denote the stream of bounded asset payoffs. Then the (ex-payoffs) asset price Pt satisfies