Rational Bubbles: Too Many to be True?

Issues that arise in the practical implementation of the Phillips, Wu, and Yu (2011) and Phillips, Shi, and Yu (2015a) recursive procedures for identifying and dating explosive bubbles in time-series data are considered. It is argued that the standard practice of using conventional levels of significance for critical values involved in the algorithms that locate the origination and termination dates of explosive episodes lead to false discoveries of explosiveness with large probability. In addition, the use of critical values for right-tailed unit-root tests obtained under the assumption of a drift whose magnitude depends on the sample size and becomes negligible in large samples result in over-rejection of the unit-root hypothesis when, as in many financial time series, the drift effect is non-negligible relatively to the stochastic trend. The magnitude of these difficulties is quantified via simulations, using artificial data whose stochastic properties reflect closely those of real-world time series such as asset prices and dividends. The findings offer a potential explanation for the relatively large number of apparent explosive episodes that are often reported in applied work. An empirical illustration involving monthly data on U.S. real stock prices and real dividends is also discussed.