Extraordinary Solution in the Flood-Garber Model of Financial Crises

概要

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The Flood-Garber equation in a classical model of financial crises has an extraordinary solution which gives an exponential increase of the shadow exchange rate e_g(t). In the Flood and Garber model, the shadow exchange rate e_g(t) is assumed as a linear function in t, so that the collapse time t_c can be predicted by using observed quantities at t < t_c. However, such the assumption cannot be justified at all, so that in general we cannot predict the collapse time t_c. In the present paper, it is pointed out that this problem originates in a more fundamental property of the differential equation: a solution of an n-th order differential equation inevitably contains n integration constants, which are fixed only by boundary conditions (initial conditions); since the behavior of e_g(t) is unknown for t < t_c, we cannot use boundary conditions at t < t_c, but we can use only those at t ≥ t_c; this means that the boundary condition at t=t_c is incompetent to predict the collapse time t_c.
静岡県立大学の論文
2003-10-15