Estimation of Dynamic Models with Nonparametric Simulated Maximum Likelihood

We propose a simulated maximum likelihood estimator (SMLE) for general stochastic dynamic models based on nonparametric kernel methods. The method requires that, while the actual likelihood function cannot be written down, we can still simulate observations from the model. From the simulated observations, we estimate the unknown density of the model nonparametrically by kernel methods, and then obtain the SMLEs of the model parameters. Our method avoids the issue of non-identification arising from poor choice of auxiliary models in simulated methods of moments (SMM) or indirect inference. More importantly, our SMLEs achieve higher efficiency under weak regularity conditions. Finally, our method allows for potentially nonstationary processes, including time-inhomogeneous dynamics