Introduction to economic theory of bubbles ✩
Introduction to economic theory of bubbles ✩
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2014
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通讯作者：
Jianjun Miao
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作者：
Jianjun Miao
这是对泡沫经济理论特别部分的介绍。©2014 Elsevier B.V.版权所有世界各地的资产市场都非常不稳定。两个最重要的资产市场是股票市场和房地产市场。图1显示了美国和日本的实际股票市场指数（标准普尔500指数和日经225指数）这一数字表明，从1990年到2000年，美国股市经历了持续的繁荣，价格指数增长了一倍多。从1999年12月的峰值到2003年初，市场下跌了大约一半。然后在2007年1月达到峰值，随后在2009年3月暴跌至谷底。在这短短的时间里，股市下跌了50%以上。此后，股市逐渐回升。直到1989年12月，日本股市经历了持续的繁荣，自1970年初以来上涨了约500%。在那之后，股市崩盘，再也没有跌到峰值的一半以下。图2显示了美国和日本的实际房价、房价收入比和房价租金比这张图显示了美国，我要感谢梶井诚司的有用评论。*通讯地址：波士顿大学经济系，美国马萨诸塞州波士顿湾州路270号。电话：+1 617 353 6675；传真：+1 617 353 4449。电子邮件地址：miaoj@bu.edu, jianjunmiao9@gmail.com。标准普尔500指数的月度实际股价指数可从罗伯特•席勒（Robert Shiller）的网站下载：http://www.econ.yale.edu/shiller/data.htm。每月的日经225指数是从彭博下载的。2美国名义房价指数是来自联邦住房金融局（Federal Housing Finance Agency）的所有交易指数。日本的名义房价指数是日本房地产研究所的全国城市地价指数。实际房价指数是扣除私人消费的名义房价指数http://dx.doi.org/10.1016/j.jmateco.2014.06.002 0304-4068/©2014 Elsevier B.V.版权所有。从1990年代初到2006年12月，房地产市场经历了持续的繁荣，从谷底到2006年12月的峰值增长了约60%。然后，直到2011年9月，它从峰值下跌了约40%。从1980年1月到1991年2月，日本房地产市场经历了持续的繁荣，增长了约60%。随后持续下跌，直到2011年10月，跌幅超过50%。在美国和日本，房价收入比和房价租金比与房价密切相关，表明仅靠基本面因素无法解释房价动态。股票和房地产市场的繁荣和萧条对实体经济有很大的影响。例如，人们普遍认为，最近发生在美国的大衰退和日本失去的十年是由房地产市场崩溃造成的。因此，理解资产市场的高波动性对经济学家和政策制定者都很重要。事实证明，这是一项具有挑战性的任务（Shiller, 1981）。虽然有许多基于新古典理论的研究，但一条重要的研究路线是基于资产价格除了基本面成分外还包含泡沫成分的观点。泡沫的增长可以帮助解释资产市场的繁荣，泡沫的破灭可以帮助解释资产市场的崩溃。平减指数。2000年的平均实际指数归一化为100。房价收入比是名义房价指数与名义人均可支配收入之比。样本平均值归一化为100。租售比是名义房价指数与消费者价格指数的租金成分之比。样本平均值归一化为100。所有数据从http://www.econ.queensu.ca/files/other/House_Price_indices%20(OECD).xls下载。所有系列都经过季度和季节调整。苗静/数理经济学报53 (2014)130-136 131每月实际标准普尔500指数和日本日经225指数。图2所示。美国和日本的实际房价、房价收入比和房价租金比。这个简单的想法是直观的，经常被公众谈论。伯南克（Ben Bernanke）和格林斯潘（Alan greenspan）等政策制定者也经常提到它。然而，它并没有进入伯南克（Bernanke）与马克·格特勒（Mark Gertler）合著的关于泡沫的研究文章（Bernanke and Gertler, 1999）。主流经济学。根据我与许多经济学家的谈话，他们中的大多数人都拒绝接受资产泡沫的观点。我认为可能有两个原因。首先，当前宏观经济学的核心是动态随机一般均衡方法，资产泡沫的思想属于外围（Caballero, 2010）。关于资产泡沫的研究很难发表，尤其是在顶级期刊上。这阻碍了来自132 J. Miao / Journal of Mathematical Economics 53(2014) 130-136的研究人员对这一主题的研究。第二，我们对经济理论中的资产泡沫了解不多。宏观经济学或微观经济学通常不教这个话题。在一些概念和理论问题上存在许多误解。例如，有些人经常认为，泡沫的存在意味着代理人是非理性的，或者存在套利机会。确实存在一些关于非理性泡沫的文献（例如，参见Shiller， 2005）然而，我将限制对理性泡沫模型的讨论。所谓“理性”，我指的是经济主体具有理性预期，并将其效用最大化。此外，市场是竞争性的，处于均衡状态。本专题旨在促进理性资产泡沫的理论研究。本节包含四篇论文，通过对无限水平模型的研究，推动了该主题的研究前沿。在我讨论它们之前，让我提供一些背景知识和对最近文献的简短回顾。让我从一个标准的两期资产估值方程开始。假设不存在不确定性，资产的总要求收益等于常数r，设{Dt}表示有界资产支付流。那么（除支付）资产价格Pt满足
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: miaoj@bu.edu, jianjunmiao9@gmail.com. 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