This study provides new mechanisms for identifying and estimating explosive bubbles in mixed-root panel autoregressions with a latent group structure. A postclustering approach is employed that combines k-means clustering with right-tailed panel-data testing. Uniform consistency of the k-means algorithm is established. Pivotal null limit distributions of the tests are introduced. A new method is proposed to consistently estimate the number of groups. Monte Carlo simulations show that the proposed methods perform well in finite samples; and empirical applications of the proposed methods identify bubbles in the U.S. and Chinese housing markets and the U.S. stock market.
This study provides new mechanisms for identifying and estimating explosive bubbles in mixed-root panel autoregressions with a latent group structure. A post-clustering approach is employed that combines a recursive k-means clustering algorithm with panel-data test statistics for testing the presence of explosive roots in time series trajectories. Uniform consistency of the k-means clustering algorithm is established, showing that the post-clustering estimate is asymptotically equivalent to the oracle counterpart that uses the true group identities. Based on the estimated group membership, right-tailed self-normalized t-tests and coefficient-based J-tests, each with pivotal limit distributions, are introduced to detect the explosive roots. The usual Information Criterion (IC) for selecting the correct number of groups is found to be inconsistent and a new method that combines IC with a Hausman-type specification test is proposed that consistently estimates the true number of groups. Extensive Monte Carlo simulations provide strong evidence that in finite samples, the recursive k-means clustering algorithm can correctly recover latent group membership in data of this type and the proposed post-clustering panel-data tests lead to substantial power gains compared with the time series approach. The proposed methods are used to identify bubble behavior in US and Chinese housing markets, and the US stock market, leading to new findings concerning speculative behavior in these markets.
This paper explores predictive regression models with stochastic unit root (STUR) components and robust inference procedures that encompass a wide class of persistent and time-varying stochastically nonstationary regressors. The paper extends the mechanism of endogenously generated instrumentation known as IVX, showing that these methods remain valid for short and long-horizon predictive regressions in which the predictors have STUR and local STUR (LSTUR) generating mechanisms. Both mean regression and quantile regression methods are considered. The asymptotic distributions of the IVX estimators are new and require some new methods in their derivation. The distributions are compared to previous results and, as in earlier work, lead to pivotal limit distributions for Wald testing procedures that remain robust for both single and multiple regressors with various degrees of persistence and stochastic and fixed local departures from unit roots. Numerical experiments corroborate the asymptotic theory, and IVX testing shows good power and size control. The IVX methods are illustrated in an empirical application to evaluate the predictive capability of economic fundamentals in forecasting S\&P 500 excess returns.