Title: Bayesian estimation and comparison of conditional moment models
Authors: Anna Simoni - CNRS - CREST (France) [presenting]
Siddhartha Chib - Washington University in Saint Louis (United States)
Minchul Shin - Federal Reserve Bank of Philadelphia (United States)
Abstract: The focus is on the Bayesian analysis of models in which the unknown distribution of the outcomes is specified up to a set of conditional moment restrictions. The nonparametric exponentially tilted empirical likelihood (ETEL) function is constructed to satisfy a sequence of unconditional moments based on an increasing (in sample size) vector of approximating functions (such as tensor splines based on the splines of each conditioning variable). The posterior distribution is shown to satisfy the Bernstein-von Mises theorem, subject to a growth rate condition on the number of approximating functions, even under misspecification of the conditional moments. A large-sample theory for comparing different conditional moment models is developed. The central result is that the marginal likelihood criterion selects the model that is less misspecified. Examples are provided to illustrate the framework and results.