Kernel-Based Indirect Inference

Abstract

The class of parametric dynamic latent variable models is becoming increasingly popular in finance and economics. Latent factor models, switching regimes models, stochastic volatility models, and dynamic disequilibrium models are only a few examples of this class of model. Inference in this class may be difficult since the computation of the likelihood function requires integrating out the unobservable components and calculating very high dimensional integrals. We propose an estimation procedure that could be applied to any dynamic latent model. The approach is based on the indirect inference principle and, in order to capture the dynamic features of these models, the binding functions are conditional expectations of functions of the endogenous variables given their past values. These conditional expectations are estimated by a nonparametric kernel-based approach. Unlike the indirect inference method, no optimization step is involved in the computation of the binding function and the approach is useful when no convenient auxiliary model is available. In spite of the nonparametric feature of the approach, the estimator is consistent and its convergence rate may be arbitrarily close to the classical parametric one. Moreover, a scoring method to select the best binding functions is proposed. Finally, some Monte Carlo experiments for factor ARCH and GARCH models show the feasibility of the approach.