Fifth-order perturbation solution to DSGE models

Levintal, Oren

doi:10.1016/j.jedc.2017.04.007

Cited by 31 publications

(40 citation statements)

References 34 publications

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“…For all methods, the expected values of the Euler conditions are approximated by monomial rules with

2 n_{ε}

nodes (for

n_{ε}

shocks), and the convergence criterion is set at 10 −8 , as in Maliar and Maliar () . For comparability, the table reports also the results of perturbation solutions obtained by the algorithm described in Levintal (). The codes are written in MATLAB/MEX and run on a Dell computer with an Intel(R) Core(TM) i7‐5600U Processor and 16 GB RAM.…”

Section: Comparison To Other Projection Methodsmentioning

confidence: 99%

“…New features that have been introduced into these models generate nonlinearities that cannot be handled satisfactorily by standard perturbation solutions. 2 Examples include models with rare disasters (Fernández-Villaverde and Levintal, 2017), models with crisis equilibria that occur far from the steady state (Brunnermeier and Sannikov, 2014;Boissay et al, 2016), models with occasionally binding constraints 3 (Guerrieri and Iacoviello, 2015) and others. A common alternative to perturbation is projection (Judd, 1992), which is highly flexible and accurate.…”

Section: Introductionmentioning

confidence: 99%

“…By comparison, in perturbation the system is solved recursively, which is much easier; see Judd (1998). 7 To my knowledge, the first paper that applied the method at points other than the steady state is Levintal (2013), which is a preliminary version of the present article. After this paper circulated, Den Haan et al (2015) explored a similar approach and compared it to Coeurdacier et al (2011).…”

Section: Introductionmentioning

confidence: 99%

“…After this paper circulated, Den Haan et al (2015) explored a similar approach and compared it to Coeurdacier et al (2011). Fernández-Villaverde and Levintal (2017) and Barro et al (2017) employ the algorithm proposed in the present article to solve models with rare disasters. In particular, Barro et al (2017) solve the model at points that are extremely far away from the deterministic steady state.…”

Section: Introductionmentioning

confidence: 99%

“…In high-dimensional applications, we may have thousands of parameters in approximating functions, and the cost of computing derivatives may be prohibitive." Indeed, Fernández-Villaverde and Levintal (2017) document rapidly growing computational costs when the Newton method is used to compute a collocation solution.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Taylor Projection: A New Solution Method for Dynamic General Equilibrium Models

Levintal

2018

Int Economic Review

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This article presents a new solution method for dynamic equilibrium models. The solution is approximated by polynomials that zero the residual function and its derivatives at a given point x0. The algorithm is essentially a type of projection but is significantly faster, since the problem is highly sparse and can be easily solved by a Newton solver. The obtained solution is accurate locally in the neighborhood of x0. Importantly, a local solution can be obtained at any point of the state space. This makes it possible to solve models at points that are further away from the steady state.

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“…For all methods, the expected values of the Euler conditions are approximated by monomial rules with