Bayesian estimation and comparison of conditional moment models. (16th December 2021)

• Record Type: Journal Article
• Authors: Chib, Siddhartha; Shin, Minchul; Simoni, Anna
• Is Part Of: Journal of the Royal Statistical Society. Volume 84:Number 3(2022)
• Page Start: 740
• Page End: 764
• Publication Date: 2021-12-16
• Subjects: Bayesian inference -- Bernstein–von Mises theorem -- conditional moment restrictions -- exponentially tilted empirical likelihood -- marginal likelihood -- misspecification -- posterior consistency; Statistics -- Periodicals; Great Britain -- Statistics -- Periodicals; 519.2
• DOI: 10.1111/rssb.12484
• Languages: English
• ISSNs: 1369-7412

Abstract

Abstract: We consider the Bayesian analysis of models in which the unknown distribution of the outcomes is specified up to a set of conditional moment restrictions. The non‐parametric exponentially tilted empirical likelihood 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). For any given sample size, results are robust to the number of expanded moments. We derive Bernstein–von Mises theorems for the behaviour of the posterior distribution under both correct and incorrect specification of the conditional moments, subject to growth rate conditions (slower under misspecification) on the number of approximating functions. A large‐sample theory for comparing different conditional moment models is also developed. The central result is that the marginal likelihood criterion selects the model that is less misspecified. We also introduce sparsity‐based model search for high‐dimensional conditioning variables, and provide efficient Markov chain Monte Carlo computations for high‐dimensional parameters. Along with clarifying examples, the framework is illustrated with real data applications to risk‐factor determination in finance, and causal inference under conditional ignorability.