Working Papers

The Discretization Filter: A Simple Way to Estimate Nonlinear State Space Models

New draft coming soon

Abstract: Existing methods for estimating nonlinear dynamic models are either too computationally complex to be of practical use, or rely on local approximations which often fail to adequately capture the nonlinear features of interest. I develop a new method, the discretization filter, for approximating the likelihood of nonlinear, non-Gaussian state space models. I apply results from the statistics literature on uniformly ergodic Markov chains to establish that the implied maximum likelihood estimator is strongly consistent, asymptotically normal, and asymptotically efficient. Through simulations I show that the discretization filter is orders of magnitude faster than alternative nonlinear techniques for the same level of approximation error and I provide practical guidelines for applied researchers. I apply my approach to estimate two models at the intersection of macroeconomics and finance: the Wu and Xia (2016) shadow rate term structure model, and the Gabaix (2012) asset pricing model of variable rare disasters. I provide the first estimates of the Gabaix model and show that the estimated model fails to identify the Great Recession as a disaster episode, suggesting the need to consider heterogeneity in the nature of disasters. My estimates of the Wu and Xia shadow rate indicate that unconventional monetary policy was more effective than previously thought.

Pockets of Predictability (with Lawrence Schmidt and Allan Timmermann)

Draft now available

Abstract: Return predictability in the U.S. stock market is local in time as short periods with significant predictability ('pockets') are interspersed with long periods with little or no evidence of return predictability. We document this empirically using a flexible non-parametric approach and explore possible explanations of this fi nding, including time-varying risk-premia. We fi nd that short-lived predictability pockets are inconsistent with a broad class of affine asset pricing models. Conversely, pockets of return predictability are more in line with a model with investors' incomplete learning about a highly persistent growth component in the underlying cash flow process which undergoes occasional regime shifts.

 

Publications

Discretizing Nonlinear, Non-Gaussian Stochastic Processes with Exact Conditional Moments (with Alexis Akira Toda)

Quantitative Economics, 2017

Abstract: Approximating stochastic processes by finite-state Markov chains is useful for reducing computational complexity when solving dynamic economic models. We provide a new method for accurately discretizing general Markov processes by matching low order moments of the conditional distributions using maximum entropy. In contrast to existing methods, our approach is not limited to linear Gaussian autoregressive processes. We apply our method to numerically solve asset pricing models with various underlying stochastic processes for the fundamentals, including a rare disasters model. Our method outperforms the solution accuracy of existing methods by orders of magnitude, while drastically simplifying the solution algorithm. The performance of our method is robust to parameters such as the number of grid points and the persistence of the process.

 

Works in Progress

Approximating and Estimating High-Dimensional State Space Models