Solvability of perturbation solutions in DSGE models

Hong Lan and Alexander Meyer-Gohde

Journal of Economic Dynamics and Control, 2014, vol. 45, issue C, 366-388

Abstract: We prove that the undetermined Taylor series coefficients of local approximations to the policy function of arbitrary order in a wide class of discrete time dynamic stochastic general equilibrium (DSGE) models are solvable by standard DSGE perturbation methods under regularity and saddle point stability assumptions on first order approximations. Extending the approach to nonstationary models, we provide necessary and sufficient conditions for solvability, as well as an example in the neoclassical growth model where solvability fails. Finally, we eliminate the assumption of solvability needed for the local existence theorem of perturbation solutions, complete the proof that the policy function is invariant to first order changes in risk, and attribute the loss of numerical accuracy in progressively higher order terms to the compounding of errors from the first order transition matrix.

Keywords: Perturbation; DSGE; Nonlinear; Sylvester equations; Solvability; Bézout׳s theorem (search for similar items in EconPapers)
JEL-codes: C61 C63 E17 (search for similar items in EconPapers)
Date: 2014
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (13)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:dyncon:v:45:y:2014:i:c:p:366-388

DOI: 10.1016/j.jedc.2014.06.005

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