On stability in generalized Schinasi’s macroeconomic model under fixed exchange rates

Abstract

A nonlinear dynamic macroeconomic model of a small open economy is constructed. The model is based on the IS-LM structure and generalizes the Schinasi’s model of a closed economy. Sufficient conditions for the existence of the equilibrium of the model are found and the question of its stability is analyzed.

On the bifurcation of limit cycles in a dynamic model of a small open economy

“…Remark 1 Sufficient conditions for the existence of an equilibrium E * (γ) = (Y * (γ), K * (γ), R * (γ), M * (γ)) were found in [5].…”

“…Definition 1 A triple (α 0 , β 0 , γ 0 ) of parameters α, β, γ is called the critical triple of model (5) if the matrix A = A(α 0 , β 0 , γ 0 ) has a pair of purely imaginary eigenvalues λ 1,2 = ±i ω, i 2 = −1, and the other two eigenvalues λ 3,4 have negative real parts.…”

“…Model (1) was introduced in [5]. It deals with a small open economy, which means that economic processes in this economy have negligible influence on the ones in the region with which it is connected through inter-regional trade and inter-regional capital movement (this region we call a foreign country).…”

“…The questions for the existence of an equilibrium of the model and its stability were investigated in [5].…”

“…Theorem 2 in this section recalls the main result from [5] on the stability of an equilibrium. Stable limit cycles can appear in the case of the linear approximation matrix of model (1) having at least one pair of purely imaginary eigenvalues with the others having negative real parts.…”