A Panel Clustering Approach to Analyzing Bubble Behavior

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