Irrational Bubble Analysis Under Vector Autoregressive Model

Irrational Bubble Analysis Under Vector Autoregressive Model

We analyze the ‘irrational bubble’ of economy through the VAR (vector autoregressive) model in the context of cointegration. We define that a cointegration has an irrational bubble if the disequilibrium error arises from the past sustained equilibrium without unexpected disequilibrium error shock. A sufficient condition for a cointegration not to have an irrational bubble is that the disequilibrium error is completely described by its own AR (autoregressive) process. A test is suggested to check the irrational bubble, which may use the standard critical values of Johansen and standard F tests. A decomposition of nonstationary variable to the cointegration fundamental and adjustment error is also suggested. We found some evidences that there are irrational bubbles in the US (United States) real stock price after the 1950 and Yen/Dollar exchange rate after 1990. Further we found the magnitudes of bubbles are bigger after 1950 than before 1950.