Existing methods for estimating nonlinear dynamic models are either highly computationally costly 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 in low‐dimensional settings and I provide practical guidelines for applied researchers. It is my hope that the method's simplicity will make the quantitative study of nonlinear models easier for and more accessible to 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.

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离散滤波器：一种估算非线性状态空间模型的简单方法

现有的用于估计非线性动态模型的方法要么在计算上非常昂贵，要么依赖于局部逼近，而局部逼近常常不足以捕获感兴趣的非线性特征。我开发了一种新的方法，即离散滤波器，用于近似非线性非高斯状态空间模型的可能性。我建立了关联的最大似然估计器，它是强一致的，渐近正态的和渐近有效的。通过仿真，我发现在低维设置中，对于相同水平的逼近误差，离散滤波器比替代非线性技术快几个数量级，并且为应用研究人员提供了实用指南。我希望该方法' 简单性将使非线性模型的定量研究更容易为应用研究人员所用。我采用我的方法来估计名义利率下限为零的新凯恩斯主义模型。在考虑了零下限之后，我发现菲利普斯曲线的斜率为0.076，小于线性模型的典型估计值的1/3。这表明通货膨胀与产出缺口之间的强烈脱钩，以及在大萧条过后，意料之外的利率变化带来的更大实际影响。