Identifying Common and Idiosyncratic Explosive Behaviors in the Large Dimensional Factor Model with an Application to U.S. State-Level House Prices

This study applies the date-stamping methodologies for explosive behaviors proposed in the seminal work of Phillips, P. C. B., and J. Yu. (2011. “Dating the Timeline of Financial Bubbles during the Subprime Crisis.” Quantitative Economics 2 (3): 455–91), Phillips, P. C. B., S. Shi, and J. Yu. (2015a. “Testing for Multiple Bubbles: Historical Episodes of Exuberance and Collapse in the S&P 500.” International Economic Review 56 (4): 1043–78), and Phillips, P. C. B., S. Shi, and J. Yu. (2015b. “Testing for Multiple Bubbles: Limit Theory of Real Time Detectors.” International Economic Review 56 (4): 1079–134) to a large dimensional factor model. To this end, we compare two methods of identifying common and idiosyncratic components: the Panel Analysis of Nonstationarity in Idiosyncratic and Common Components (PANIC) method by Bai, J., and S. Ng. (2004. “A Panic Attack on Unit Roots and Cointegration.” Econometrica 72 (4): 1127–77) and the Cross-Sectional regression (CS) method by Yamamoto, Y., and T. Horie. (2022. “A Cross-Sectional Method for Right-Tailed PANIC Tests under a Moderately Local to Unity Framework.” Econometric Theory (forthcoming)). We show that, when the explosive behavior lies only in the common component, the origination and termination dates are precisely estimated by either method. However, when the explosive behaviors exist in idiosyncratic components, only the CS method can detect them. We apply our method to the U.S. state-level real house price indices. We find that the 2000s boom was driven by not only the national bubble factors but also local components, while the 2010s onward expansion is dominated by the effect of national components.