Bootstrapping asset price bubbles Luciano Gutierrez Department of Economics and Woody Plant Ecosystems, University of Sassari, Via E. De Nicola 1, Italy abstract article info Article history: Accepted 15 July 2011 Keywords: Rational bubbles Bootstrap Nonstationary tests In this paper we propose a method that allows to test for asset price bubbles. The method is mainly based on a bootstrap methodology which helps to compute the finite sample probability distribution of the asymptotic tests which were recently proposed in Phillips et al. (2011) and Phillips and Yu (2009). We apply the method to the Nasdaq stock price index and Case-Shiller house price index. The results indicate that speculation was behind the upsurge in both asset prices. © 2011 Elsevier B.V. All rights reserved. 1. Introduction In the last two decades the world has experienced significant and persistent movements in asset prices and the recent financial turmoil in 2007–2009 has revitalized the dispute about the existence of asset bubbles. Basically, one view is that the asset prices reflect economic fundamentals; that is, an asset price such as a stock is always equal to the present discounted value of its dividends, see Garber (1990), Tirole (1982, 1985) among others. If this is the case, a bubble cannot be identified before it collapses. Interestingly the former chairman of the Federal Reserve Board Alan Greenspan took this line when he said that the Federal Reserve is not in a position to identify or fight bubbles before they collapse. 1 A second view basically identifies four major types of bubbles: rational or near rational bubbles, Shiller (1981) and LeRoy and Porter (1981), intrinsic bubbles, Froot and Obstfeld (1991), fads, Shiller (1984), and informational bubbles, Grossman and Stiglizt (1980). All the previous types of bubbles can be well represented by Stiglitz's famous definition: “[I]f the reason that the price is high today is only because investors believe that the selling price is high tomorrow – when ‘fundamental’ factors do not seem to justify such a price – then a bubble exists”, Stiglitz (1990). In other words, movements in asset prices can be based on self-fulfilling prophecies of market participants which do not depend on the fundamental values. In an effort to propose empirical methods to detect bubbles, a large number of papers have focused on rational bubbles. Asset prices will contain a rational bubble if investors are willing to pay more for the asset than they know is justified by the value of the discounted stream because they expect to sell it at a higher price in the future, making the current high price an equilibrium price. The variance bounds tests of Shiller (1981) and LeRoy and Porter (1981); West's test of bubbles (1987, 1988); the integration-cointegration based tests, Diba and Grossman (1988a, 1988b) and Evans' (1991) criticisms, have all addressed the problem of the econometric detection of asset price bubbles. In synthesis, the results from these studies show that asset price bubbles cannot be detected with a satisfactory degree of certainty. More recently, Phillips et al. (2011) and Phillips and Yu (2009) have proposed a forward recursive procedure that allows us to compute right-side unit root test for the null hypothesis of a nonstationary process against the alternative of the explosive process that usually characterizes a speculative bubble. The tests are based on the large sample asymptotic theory of mildly explosive processes provided in Phillips and Magdalinos (2009). Phillips et al. (2011) show that the procedure has discriminatory power in detecting periodically collaps- ing bubbles thereby overcoming Evans' (1991) criticisms. Further- more, the procedure provides consistent dating of the origin and collapse of speculative bubbles. In this paper we propose a bootstrap procedure that generates a large number of simulated values of the test statistics proposed in Phillips et al. (2011) and Phillips and Yu (2009) and allows us to compute their empirical distribution functions. Using the bootstrap distribution function we are able to compute the p-value of the test statistic for each observation, i.e. the probability under the null hypothesis of obtaining a test statistic at least as extreme as the one that was actually observed. Because the p-value will range from zero to one, using the bootstrap procedure we obtain a simple measure of the probability that the asset price is affected by a speculative bubble. In synthesis, the lower the p-value is the higher will be the probability that the asset is affected by a rational speculative bubble. Thus the objective of the model is to provide practitioners with a probability measure of the presence of an asset bubble. We apply the bootstrap procedure to the Nasdaq composite stock price index and Case-Shiller Economic Modelling 28 (2011) 2488–2493 1 Greenspan speech at a symposium on Economic Volatility, FRB Kansas City, Jackson Hole, Wyoming, August 30 2002. E-mail address: lgutierr@uniss.it. 0264-9993/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.econmod.2011.07.009 Contents lists available at SciVerse ScienceDirect Economic Modelling journal homepage: www.elsevier.com/locate/ecmod