Nonlinear interference and synchronization in housing, credit, and real activity cycles

Motivated by the coincidence of unexpected property price inflation, credit expansion and low interest rate in the U.S. market prior to the 2007 crisis, this paper investigates the interactions among the boom-bust cycles in the sector of housing, credit and real activities using a non-linear coupled oscillating system mode & mode locking model. Sometimes the linkages may not be strong enough for one cycle to drive another, but can be still strong enough to affect cycle's accelerator and cause a slight timing shift in the fluctuations in other sectors and bring about synchronization in a nonlinear way. The phenomenon behind this is called ëmode-lockingí. Using GDP, credit flow and housing price in U.S. market from 1976Q1 to 2011Q1, I first investigate the linear relationship among the three cycles using linear time series model vector autoregressive model. The results suggest that not all of the links are strong enough to result in causality relationship. In the next step, mode-locking model is employed based on Markov Chain Monte Carlo methods. The empirical results show that the three cycles nonlinearly interfere each other. Besides, due to the interactions, cyclesí amplitude is amplified, cyclesí phase is altered and in the end the three cycles synchronize. Moreover, monetary policy, such as interest rate, is also found to significantly nonlinear affect the three cycles. Given the significant interference, uniform monetary policy should be challenged. Monetary policy makers should be more aggressive in those markets with larger increase in the credit debt to avoid coincident large fluctuation in housing price, credit flow and GDP.