Bayesian Nonparametrics with Moment Conditions

• Activity Number: 373
• Type: Contributed
• Date/Time: Tuesday, August 11, 2015 : 10:30 AM to 12:20 PM
• Sponsor: Business and Economic Statistics Section
• Author(s): Reza Solgi* and Luke Bornn and Neil Shephard
• Companies: Harvard University and Harvard University and Harvard University
• Keywords: method of moments ; non-parametric Bayes ; empirical likelihood

Abstract

Much of modern econometrics and some of statistics is phrased in terms of moment conditions. However, if an individual used such conditions to make a personal decision they would need to embed these moments within an auxiliary model in order to make coherent Bayesian inference upon which a decision could be based. Here we show how to do this. We will typically work with informative priors about parameters which index the moment conditions while being entirely nonparametric about the rest of the auxiliary model. The moment conditions, which impose equality constraints on the parameters, cause the posterior distribution to be supported on a zero Lebesgue measure manifold in the full parameter space. In order to sample from the posterior we propose two MCMC simulation algorithms. The first algorithm draws samples from the marginal distribution of a "sufficient'' subset of the parameters. The second algorithm targets the posterior distribution in the full parameter space by using a proposal distribution supported on the manifold of feasible parameters. We subsequently verify and compare the effectiveness of these algorithms using both simulated and real data.