Computational Aspects of Nonparametric Simulation Estimation

Abstract

This paper develops a nonparametric estimator for structural equilibrium models that combines numerical solution techniques for nonlinear rational expectations models with nonparametric statistical techniques for characterizing the dynamic properties of time series data. The estimator uses the the score function from a nonparametric estimate of the law of motion of the observed data to define a GMM criterion function. In effect, it forces the economic model to generate simulated data so as to match a nonparametric estimate of the conditional density of the observed data. It differs from other simulated method of moments estimators in using the nonparametric density estimate, thereby allowing the data to dictate what features of the data are important for the structural model to match. The components of the scoring function characterize important kinds of nonlinearity in the data, including properties such as nonnormality and stochastic volatility.

The nonparametric density estimate is obtained using the Gallant-Tauchen seminonparametric (SNP) model. The simulated data that solve the economic model are obtained using Marcet’s method of parameterized expectations. The paper gives a detailed description of the method of parameterized expectations applied to an equilibrium monetary model. It shows that the choice of the specification of the Euler equations and the manner of testing convergence have large effects on the rate of convergence of the solution procedure. It also reviews several optimization algorithms for minimizing the GMM objective function. The Nelder-Mead simplex method is found to be far more successful than others for our estimation problem.