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Author:Herbst, Edward 

Working Paper
Forward Guidance with Bayesian Learning and Estimation
Considerable attention has been devoted to evaluating the macroeconomic effectiveness of the Federal Reserve's communications about future policy rates (forward guidance) in light of the U.S. economy's long spell at the zero lower bound (ZLB). In this paper, we study whether forward guidance represented a shift in the systematic description of monetary policy by estimating a New Keynesian model using Bayesian techniques. In doing so, we take into account the uncertainty that agents have about policy regimes using an incomplete information setup in which they update their beliefs using Bayes rule (Bayesian learning). We document a systematic change in U.S. policymakers' reaction function during the ZLB episode (2009-2016) that called for a persistently lower policy rate than in other regimes (we call this the forward guidance regime). Our estimates suggest that private sector agents were slow to learn about this change in real time, which limited the effectiveness of t he forward guidance regime in stimulating economic activity and curbing disinflationary pressure. We also show that the incomplete information specification of the model fits economic outcomes over the economy's long spell at the ZLB better than the full information specification.
AUTHORS: Gust, Christopher J.; Lopez-Salido, J. David; Herbst, Edward
DATE: 2018-10-25

Working Paper
Estimating (Markov-Switching) VAR Models without Gibbs Sampling: A Sequential Monte Carlo Approach
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.
AUTHORS: Herbst, Edward; Bognanni, Mark
DATE: 2015-12-18

Working Paper
Using the \\"Chandrasekhar Recursions\\" for likelihood evaluation of DSGE models
In likelihood-based estimation of linearized Dynamic Stochastic General Equilibrium (DSGE) models, the evaluation of the Kalman Filter dominates the running time of the entire algorithm. In this paper, we revisit a set of simple recursions known as the "Chandrasekhar Recursions" developed by Morf (1974) and Morf, Sidhu, and Kalaith (1974) for evaluating the likelihood of a Linear Gaussian State Space System. We show that DSGE models are ideally suited for the use of these recursions, which work best when the number of states is much greater than the number of observables. In several examples, we show that there are substantial benefits to using the recursions, with likelihood evaluation up to five times faster. This gain is especially pronounced in light of the trivial implementation costs--no model modification is required. Moreover, the algorithm is complementary with other approaches.
AUTHORS: Herbst, Edward
DATE: 2012

Working Paper
The Empirical Implications of the Interest-Rate Lower Bound
Using Bayesian methods, we estimate a nonlinear DSGE model in which the interest-rate lower bound is occasionally binding. We quantify the size and nature of disturbances that pushed the U.S. economy to the lower bound in late 2008 as well as the contribution of the lower bound constraint to the resulting economic slump. We find that the interest-rate lower bound was a significant constraint on monetary policy that exacerbated the recession and inhibited the recovery, as our mean estimates imply that the zero lower bound (ZLB) accounted for about 30 percent of the sharp contraction in U.S. GDP that occurred in 2009 and an even larger fraction of the slow recovery that followed.
AUTHORS: Gust, Christopher J.; Lopez-Salido, J. David; Smith, Matthew E.; Herbst, Edward
DATE: 2012

Working Paper
Tempered Particle Filtering
The accuracy of particle filters for nonlinear state-space models crucially depends on the proposal distribution that mutates time t-1 particle values into time t values. In the widely-used bootstrap particle filter this distribution is generated by the state-transition equation. While straightforward to implement, the practical performance is often poor. We develop a self-tuning particle filter in which the proposal distribution is constructed adaptively through a sequence of Monte Carlo steps. Intuitively, we start from a measurement error distribution with an inflated variance, and then gradually reduce the variance to its nominal level in a sequence of steps that we call tempering. We show that the filter generates an unbiased and consistent approximation of the likelihood function. Holding the run time fixed, our filter is substantially more accurate in two DSGE model applications than the bootstrap particle filter.
AUTHORS: Schorfheide, Frank; Herbst, Edward
DATE: 2016-08-25

Working Paper
Sequential Monte Carlo sampling for DSGE models
We develop a sequential Monte Carlo (SMC) algorithm for estimating Bayesian dynamic stochastic general equilibrium (DSGE) models, wherein a particle approximation to the posterior is built iteratively through tempering the likelihood. Using three examples--an artificial state-space model, the Smets and Wouters (2007) model, and Schmitt-Grohe and Uribe's (2012) news shock model--we show that the SMC algorithm is better suited for multimodal and irregular posterior distributions than the widely-used random-walk Metropolis-Hastings algorithm. We find that a more diffuse prior for the Smets and Wouters (2007) model improves its marginal data density and that a slight modification of the prior for the news shock model leads to important changes in the posterior inference about the importance of news shocks for fluctuations in hours worked. Unlike standard Markov chain Monte Carlo (MCMC) techniques, the SMC algorithm is well suited for parallel computing.
AUTHORS: Schorfheide, Frank; Herbst, Edward
DATE: 2013

Working Paper
Evaluating DSGE model forecasts of comovements
This paper develops and applies tools to assess multivariate aspects of Bayesian Dynamic Stochastic General Equilibrium (DSGE) model forecasts and their ability to predict comovements among key macroeconomic variables. We construct posterior predictive checks to evaluate conditional and unconditional density forecasts, in addition to checks for root-mean-squared errors and event probabilities associated with these forecasts. The checks are implemented on a three-equation DSGE model as well as the Smets and Wouters (2007) model using real-time data. We find that the additional features incorporated into the Smets-Wouters model do not lead to a uniform improvement in the quality of density forecasts and prediction of comovements of output, inflation, and interest rates.
AUTHORS: Herbst, Edward; Schorfheide, Frank
DATE: 2012

Working Paper
Monetary Policy, Real Activity, and Credit Spreads : Evidence from Bayesian Proxy SVARs
This paper studies the interaction between monetary policy, financial markets, and the real economy. We develop a Bayesian framework to estimate proxy structural vector autoregressions (SVARs) in which monetary policy shocks are identified by exploiting the information contained in high frequency data. For the Great Moderation period, we find that monetary policy shocks are key drivers of fluctuations in industrial output and corporate credit spreads, explaining about 20 percent of the volatility of these variables. Central to this result is a systematic component of monetary policy characterized by a direct and economically significant reaction to changes in credit spreads. We show that the failure to account for this endogenous reaction induces an attenuation bias in the response of all variables to monetary shocks.
AUTHORS: Caldara, Dario; Herbst, Edward
DATE: 2016-05

Working Paper
Estimating (Markov-Switching) VAR Models without Gibbs Sampling: A Sequential Monte Carlo Approach
Vector autoregressions with Markov-switching parameters (MS-VARs) offer dramatically better data fit than their constant-parameter predecessors. However, computational complications, as well as negative results about the importance of switching in parameters other than shock variances, have caused MS-VARs to see only sparse usage. For our first contribution, we document the effectiveness of Sequential Monte Carlo (SMC) algorithms at estimating MSVAR posteriors. Relative to multi-step, model-specific MCMC routines, SMC has the advantages of being simpler to implement, readily parallelizable, and unconstrained by reliance on convenient relationships between prior and likelihood. For our second contribution, we exploit SMC?s flexibility to demonstrate that the use of priors with superior data fit alters inference about the presence of time variation in macroeconomic dynamics. Using the same data as Sims, Waggoner, and Zha (2008, we provide evidence of recurrent episodes characterized by a flat Phillips Curve.
AUTHORS: Herbst, Edward; Bognanni, Mark
DATE: 2014-11-12

Working Paper
Sequential Monte Carlo sampling for DSGE models
We develop a sequential Monte Carlo (SMC) algorithm for estimating Bayesian dynamic stochastic general equilibrium (DSGE) models, wherein a particle approximation to the posterior is built iteratively through tempering the likelihood. Using three examples consisting of an artificial state-space model, the Smets and Wouters (2007) model, and Schmitt-Grohe and Uribe's (2012) news shock model we show that the SMC algorithm is better suited for multi-modal and irregular posterior distributions than the widely-used random walk Metropolis-Hastings algorithm. Unlike standard Markov chain Monte Carlo (MCMC) techniques, the SMC algorithm is well suited for parallel computing.
AUTHORS: Herbst, Edward; Schorfheide, Frank
DATE: 2012

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