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

Abstract

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)

Exchange Rates Dynamics with Long-Run Risk and Recursive Preferences

“…World growth W t g is a weighted average of US and ROW growth ( , ): (Adjemian et al (2014)). Simulations are based on the pruned state-space representation of the third-order accurate model solution (Kollmann (2005(Kollmann ( , 2013, Kim et al (2008), Andreasen et al (2013)). …”

Risk Sharing in a World Economy with Uncertainty Shocks

“…The Dynare toolbox is used for that purpose (Adjemian et al (2014)). I simulate the model and compute moments of endogenous variables using the pruned state-space representation of the third-order accurate model solution (Kollmann (2005(Kollmann ( , 2015a, Andreasen et al (2013)). …”

Sigma Point Filters for Dynamic Nonlinear Regime Switching Models

“…He finds in many of his experiments that the DDF is able to beat the Particle Filter and cites this as evidence that the Particle Filter has yet to converge with 500,000 particles. In a similar Monte Carlo experiment Kollmann (2015) tests the KalmanQ Filter, a Kalman Filter for pruned second order approximations of DSGE models, against a Particle Filter with 500,000 particles also using a simple DSGE model. He finds the KalmanQ Filter is able to beat the Particle Filter.…”

“…Andreasen (2013) shows with a simple DSGE model solved using both a second and third order perturbation method that the Divided Difference Filter provides more accurate results than the Particle Filter using 500,000 particles. Kollmann (2015) is also able to beat a Particle Filter that uses 500,000 particles with a deterministic Kalman Filter adapted for second order approximations in pruned state space (the KalmanQ Filter).…”