Working Papers

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

New draft now available

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 adequately to 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 establish that the associated 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 a New Keynesian model with a zero lower bound on the nominal interest rate. After accounting for the zero lower bound, I find that the slope of the Phillips Curve is 0.076, which is less than 1/3 of typical estimates from linearized models. This suggests a strong decoupling of inflation from the output gap and larger real effects of unanticipated changes in interest rates in post Great Recession data.

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.



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