Does a Unique Solution Exist for a Nonlinear Rational Expectation Equation with Zero Lower Bound?
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To formalize a nonlinear rational expectation model in macroeconomics as a functional equation, we investigate the existence of a unique solution. Assuming that the probability of large exogenous disturbance occurring is sufficiently small, we prove that a unique solution exists. This result provides a rigorous foundation for research on nonlinear rational expectation models as a natural extension of existing linear models.
KeywordsNonlinear rational expectation model Functional equation Zero lower bound on interest rates Lyapunov functions
This work was supported by the JST PRESTO program. I am grateful to the anonymous referees for their invaluable comments.
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