Comments on GMM with Latent Variables
نویسندگان
چکیده
We consider classical and Bayesian estimation procedures implemented by means of a set of conditional moment conditions that depend on latent variables. The latent variables evolve according to a Markovian transition density. Two main classes of applications are: 1) GMM estimation with time-varying parameters; and 2) estimation of nonlinear Dynamic Stochastic General Equilibrium (DSGE) models. The key idea is to base inference on an approximate likelihood that depends on conditional moment conditions. Bayesian estimation using this approach has received previous attention. The Bayesian results, which exploit some differences between Bayesian and frequentist inference, are summarized. Two methods for extending the Bayesian results to frequentist inference are discussed: 1) a particle filter approach. and, 2) a nonparametric sieve approach. At the present state of development, the former holds the most promise.
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