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A recursive test procedure is suggested that provides a mechanism for testing explosive behavior, date stamping the origination and collapse of economic exuberance, and providing valid confidence intervals for explosive growth rates. The method involves the recursive implementation of a right-side unit root test and a sup test, both of which are easy to use in practical applications, and some new limit theory for mildly explosive processes. The test procedure is shown to have discriminatory power in detecting periodically collapsing bubbles, thereby overcoming a weakness in earlier applications of unit root tests for economic bubbles. An empirical application to the Nasdaq stock price index in the 1990s provides confirmation of explosiveness and date stamps the origination of financial exuberance to mid-1995, prior to the famous remark in December 1996 by Alan Greenspan about irrational exuberance in the financial market, thereby giving the remark empirical content. How do we know when irrational exuberance has unduly escalated asset values? (Alan Greenspan, 1996) Experience can be a powerful teacher. The rise and fall of internet stocks, which created and then destroyed 8 trillion of shareholder wealth, has led a new generation of economists to acknowledge that bubbles can occur. (Alan Krueger, 2005)
Phillips et al. (Tue,) studied this question.