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In open economy models with incomplete asset markets the deterministic steady state depends on the initial conditions of the economy and the steady state is compatible with any level of international bond holdings. In a stochastic environment the linearized model generates non-stationary variables as international bond holdings follow a unit root process. Several modifications of the standard model have been proposed in order to induce stationarity among which are an endogenous discount factor (Uzawa-type preferences), a debt elastic interest rate premium or convex portfolio costs.
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