Computing second-order-accurate solutions for rational expectation models using linear solution methods

Lombardo, Giovanni; Sutherland, Alan

doi:10.1016/j.jedc.2005.10.004

Cited by 60 publications

(58 citation statements)

References 13 publications

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“…al. (2008), Lombardo and Sutherland (2007), and Schmitt-Grohe and Uribe (2004)-this paper shows that one can easily solve and analyze this class of models to the second order. In particular, I use the recent perturbation approach of Johnston, King, and Lie (2009).…”

Section: Introductionmentioning

confidence: 74%

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State-Dependent Pricing and Optimal Monetary Policy

Lie

2009

SSRN Journal

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This paper analyzes optimal monetary policy under precommitment in a state-dependent pricing (SDP) environment. Under SDP, monopolistically competitive …rms are allowed to endogenously change the timing of price adjustments. I show that this endogenous timing of price adjustment alters the tradeo¤ and the cost of in ‡ation variation faced by the monetary authority in comparison to the standard time-dependent pricing (TDP) assumption. In particular, it is desirable to let in ‡ation vary more under SDP. Despite the change in the policy tradeo¤, however, the optimal response under SDP to either a productivity or a government purchase shock under the timeless perspective (long-run) policy can still be characterized as an approximate price stability rule. Additionally, this paper studies the optimal policy start-up problem related to the cost of adopting the timeless perspective policy instead of the true Ramsey policy. The SDP assumption leads to di¤erent start-up dynamics compared to the dynamics under the TDP assumption in several important ways. In particular, the change in the policy tradeo¤ gives rise to much higher start-up in ‡ation under SDP. JEL Classi…cation: E31, E52, E61

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Section: Introductionmentioning

confidence: 74%

“…This state-dependence 2 2 The method here is related to several recent contributions on second-order approximations such as SchmittGrohe and Uribe (2004), Lombardo and Sutherland (2007), and Kim, et. al.…”

Section: Approximate Solutionsmentioning

confidence: 96%

State-Dependent Pricing and Optimal Monetary Policy

Lie

2009

SSRN Journal

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“…For completeness, the unpruned state-space system for the third-order approximation is given by (10) and (13). Lombardo and Sutherland (2007) pioneered the idea of separately keeping track of first-and second-order effects to solve for the second-order perturbation approximation of a DSGE model. Since the first circulation of our paper, Lombardo and Uhlig (2014) have presented an alternative derivation of our pruned state-space system, but only for models without interaction between the shocks and the state variables.…”

Section: As Shown Inmentioning

confidence: 99%

The Pruned State-Space System for Non-Linear DSGE Models: Theory and Empirical Applications

2013

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This article studies the pruned state-space system for higher-order perturbation approximations to dynamic stochastic general equilibrium (DSGE) models. We show the stability of the pruned approximation up to third order and provide closed-form expressions for first and second unconditional moments and impulse response functions. Our results introduce generalized method of moments (GMM) estimation and impulse-response matching for DSGE models approximated up to third order and provide a foundation for indirect inference and simulated method of moments (SMM). As an application, we consider a New Keynesian model with Epstein-Zin preferences and two novel feedback effects from long-term bonds to the real economy, allowing us to match the level and variability of the 10-year term premium in the U.S. with a low relative risk aversion of 5.

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“…See Kollmann (2004) and Lombardo and Sutherland (2007). (4) too is stable. The subsequent discussion assumes that the true DGP is given by the pruned system (3),(4).…”

Section: Pruningmentioning

confidence: 99%

“…1 Particle filters are slow computationally, which limits their use to small models. This paper develops a novel deterministic filter for estimating latent state variables of DSGE models that are solved using a second-order accurate approximation (as derived by Jin and Judd 2000, Sims 2000, Collard and Juillard 2001, Schmitt-Grohé and Uribe 2004, Kollmann 2004and Lombardo and Sutherland 2007. That approximation provides the most tractable non-linear solution technique for medium-scale models, and has thus widely been used in macroeconomics (see Kollmann 2002 andKollmann et al 2011 for detailed references).When simulating second-order approximated models, it is common to use the 'pruning' scheme of Kim et al (2008), under which second-order terms are replaced by products of the linearized solution.…”

Section: Introductionmentioning

confidence: 99%

Tractable Latent State Filtering for Non-Linear DSGE Models Using a Second-Order Approximation and Pruning

Kollmann

2014

Comput Econ

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This paper develops a novel approach for estimating latent state variables of Dynamic Stochastic General Equilibrium (DSGE) models that are solved using a second-order accurate approximation. I apply the Kalman filter to a state-space representation of the second-order solution based on the 'pruning' scheme of Kim et al. (J Econ Dyn Control 32:3397-3414, 2008). By contrast to particle filters, no stochastic simulations are needed for the deterministic filter here; the present method is thus much faster; in terms of estimation accuracy for latent states it is competitive with the standard particle filter. Use of the pruning scheme distinguishes the filter here from the deterministic Quadratic Kalman filter presented by Ivashchenko (Comput Econ, 43:71-82, 2014). The filter here performs well even in models with big shocks and high curvature. R. Kollmann (B)

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Computing second-order-accurate solutions for rational expectation models using linear solution methods

Abstract: In 2005 all ECB publications will feature a motif taken from the €50 banknote. WO R K I N G PA P E R S E R I E S N O. 4 8 7 / M AY 2 0 0 5

Cited by 60 publications

References 13 publications

State-Dependent Pricing and Optimal Monetary Policy

State-Dependent Pricing and Optimal Monetary Policy

The Pruned State-Space System for Non-Linear DSGE Models: Theory and Empirical Applications

Tractable Latent State Filtering for Non-Linear DSGE Models Using a Second-Order Approximation and Pruning

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