Avoiding the Pitfalls: Can Regime-Switching Tests Detect Bubbles?
Work on testing for bubbles has caused much debate, much of which has focussed on methodology. Monte Carlo simulations reported in Evans (1991) showed that standard tests for unit roots and cointegration frequently reject the presence of bubbles even when such bubbles are present by construction. Evans referred to this problem as the pitfall of testing for bubbles.
Since Evans' note, new tests for rational speculative bubbles that rely on regime-switching have been proposed. Van Norden and Schaller (1993) and van Norden (1996) use a switching regression to look for a time-varying relationship between returns and deviations from an approximate fundamental price. Hall and Sola (1993) and Funke, Hall and Sola (1994) test whether asset prices seem to switch between explosive growth and stationary behaviour.
Our paper reports on Monte Carlo experiments using Evans' data-generating process to gauge the performance of these two kinds of regime-switching tests. The experiments rely heavily on certain new, fast and robust programs developed at the Bank of Canada for the estimation of switching regression models that make Monte Carlo studies of such estimators practical. We find that for some (but not all) parameter values, regime-switching tests have a significant amount of power to detect periodically collapsing bubbles. We also compare and contrast the performance of the two different regime-switching tests.