The purpose of this paper is to study bubbles solutions to
the Cagan hyperinflation models under rational expectations. Both the price and
exchange rate bubbles are considered. Specifications of the Cagan model under
rational expectations will be briefly described, in which the price and
exchange rate series are expressed in first-order linear difference equations.
The particular and the homogenous solutions to the Cagan model can then be
derived. The particular or fundamental solution characterizes a unique dynamic
movement of an underlying fundamental process. Several representations of the
fundamental solution will be explored. The homogenous or bubble solution is
non-unique in a rational expectations framework. Some examples of bubble
solution with different dynamic properties are specified. Also, examples of
bursting bubble specifications will be illustrated. It is concluded that the
problems of multiple solutions make indirect tests more attractive than direct
tests for bubble detection. In addition, the general solution, which is just
the sum of particular and homogenous solutions, will be discussed. Hence, the
bubble paths are characterized as any deviations of the general solution from
the fundamental solution when the model is specified correctly.
Author(s)details:-
Kai-Yin Woo
(Associate Professor)
Department of Economics and Finance, Hong Kong Shue Yan University, Hong
Kong.
Please See the book here :- https://doi.org/10.9734/bpi/mono/978-81-973195-8-7/CH2
