Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Adam, K., & Billi, R. M. (2006). Optimal monetary policy under commitment with a zero bound on nominal interest rates. Journal of Money, Credit, and Banking, 38(7), 1877–1905. https://doi.org/10.1353/mcb.2006.0089.
Adam, K., & Billi, R. M. (2007). Discretionary monetary policy and the zero lower bound on nominal interest rates. Journal of Monetary Economics, 54(3), 728–752. https://doi.org/10.1016/j.jmoneco.2005.11.003.
Benhabib, J., Schmitt-Grohé, S., & Uribe, M. (2001). The perils of taylor rules. Journal of Economic Theory, 96(1–2), 40–69.
Blanchard, O., & Kahn, C. (1980). The solution of linear difference models under rational expectations. Econometrica: Journal of the Econometric Society, 48(5), 1305–1311.
Bullard, J. B. (2010). Seven faces of “the peril”. Review, Federal Reserve Bank of St. Louis, 92, 339–352.
Cochrane, J. (2007). Identification with Taylor rules: A critical review. NBER working paper .
Durrett, R. (2010). Probability: Theory and examples (4th ed., Vol. 31). Cambridge: Cambridge University Press.
Holden, T. D. (2016). Existence, uniqueness and computation of solutions to dynamic models with occasionally binding constraints, pp. 1–74. EconStor Preprints 127430, ZBW - Leibniz Information Centre for Economics.
Horn, R. A., & Johnson, C. R. (2013). Matrix analysis (2nd ed.). Cambridge: Cambridge University Press.
Jin, H., & Judd, K. (2002). Perturbation methods for general dynamic stochastic models. unpublished, Stanford University.
Kim, J., Kim, S., Schaumburg, E., & Sims, C. (2008). Calculating and using second-order accurate solutions of discrete time dynamic equilibrium models. Journal of Economic Dynamics and Control, 32(11), 3397–3414.
Klein, P. (2000). Using the generalized schur form to solve a multivariate linear rational expectations model. Journal of Economic Dynamics and Control, 24(10), 1405–1423.
Lan, H., & Meyer-Gohde, A. (2013). Solving DSGE models with a nonlinear moving average. Journal of Economic Dynamics and Control, 37(12), 2643–2667.
McCallum, B. (2009). Inflation determination with taylor rules: Is newkeynesian analysis critically flawed? Journal of Monetary Economics, 56(8), 1101–1108.
Mccallum, B. T. (2009). Indeterminacy from inflation forecast targeting: Problem or pseudo-problem? FRB Richmond Economic Quarterly, 95(1), 25–51.
Schmitt-Grohe, S., & Uribe, M. (2004). Solving dynamic general equilibrium models using a second-order approximation to the policy function. Journal of Economic Dynamics and Control, 28(4), 755–775.
Sims, C. (2002). Solving linear rational expectations models. Computational Economics, 20(1), 1–20.
Acknowledgements
This work was supported by the JST PRESTO program. I am grateful to the anonymous referees for their invaluable comments.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Tamura, T. Does a Unique Solution Exist for a Nonlinear Rational Expectation Equation with Zero Lower Bound?. Asia-Pac Financ Markets 27, 257–289 (2020). https://doi.org/10.1007/s10690-019-09293-1
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10690-019-09293-1
Keywords
- Nonlinear rational expectation model
- Functional equation
- Zero lower bound on interest rates
- Lyapunov functions