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This paper evaluates the accuracy of linear and nonlinear estimation methods for dynamic stochastic general equilibrium models. We generate a large sample of artificial datasets using a global solution to a nonlinear New Keynesian model with an occasionally binding zero lower bound (ZLB) constraint on the nominal interest rate. For each dataset, we estimate the nonlinear model--solved globally, accounting for the ZLB--and the linear analogue of the nonlinear model--solved locally, ignoring the ZLB--with a Metropolis-Hastings algorithm where the likelihood function is evaluated with a Kalman filter, unscented Kalman filter, or particle filter. In datasets that resemble the U.S. experience, the nonlinear model estimated with a particle filter is more accurate and has a higher marginal data density than the linear model estimated with a Kalman filter, as long as the measurement error variances in the particle filter are not too big. [ABSTRACT FROM AUTHOR]

We develop a sequential Monte Carlo (SMC) algorithm for Bayesian inference in vector autoregressions with stochastic volatility (VAR-SV). The algorithm builds particle approximations to the sequence of the model's posteriors, adapting the particles from one approximation to the next as the window of available data expands. The parallelizability of the algorithm's computations allows the adaptations to occur rapidly. Our particular algorithm exploits the ability to marginalize many parameters from the posterior analytically and embeds a known Markov chain Monte Carlo (MCMC) algorithm for the model as an effective mutation kernel for fighting particle degeneracy. We show that, relative to using MCMC alone, our algorithm increases the precision of inference while reducing computing time by an order of magnitude when estimating a mediumscale VAR-SV model. [ABSTRACT FROM AUTHOR]

In this paper, I consider forecasting from a reduced-form VAR under the zero lower bound (ZLB) for the short-term nominal interest rate. The ZLB constraint expands the number of states exponentially, making the exact computation of forecast moments infeasible. I develop a method that a) computes the exact moments for the fi rst n + 1 periods when n previous periods are tracked and b) approximates moments for the periods beyond n + 1 period using techniques for truncated normal distributions and approximations a la Kim (1994). In its simplest form, the algorithm tracks only the previous forecast period. The approximations become more accurate as additional previous periods are tracked at the cost of longer computational time, although when the method is tracking two or three previous periods, it is competitive with Monte Carlo simulation in terms computational time. I show that the algorithm produces satisfactory results for VAR systems with moderate to high persistence even when only one previous period is tracked. For very persistent VAR systems, however, tracking more periods is needed in order to obtain reliable approximations. I also show that the method is suitable for affine term-structure modeling, where the underlying state vector includes the short-term interest rate as in Taylor rules with inertia. [ABSTRACT FROM AUTHOR]

Vector autoregressions with Markov-switching parameters (MS-VARs) fit the data better than do their constant-parameter predecessors. However, Bayesian inference for MS-VARs with existing algorithms remains challenging. For our first contribution, we show that Sequential Monte Carlo (SMC) estimators accurately estimate Bayesian MS-VAR posteriors. Relative to multi-step, model-specific MCMC routines, SMC has the advantages of generality, parallelizability, and freedom from reliance on particular analytical relationships between prior and likelihood. For our second contribution, we use SMC's flexibility to demonstrate that the choice of prior drives the key empirical finding of Sims, Waggoner, and Zha (2008) as much as does the data. [ABSTRACT FROM AUTHOR]