{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,15]],"date-time":"2024-09-15T22:13:44Z","timestamp":1726438424933},"reference-count":33,"publisher":"Oxford University Press (OUP)","issue":"3","license":[{"start":{"date-parts":[[2021,12,16]],"date-time":"2021-12-16T00:00:00Z","timestamp":1639612800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2022,7,1]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>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\u2013von 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.<\/jats:p>","DOI":"10.1111\/rssb.12484","type":"journal-article","created":{"date-parts":[[2021,12,16]],"date-time":"2021-12-16T08:15:02Z","timestamp":1639642502000},"page":"740-764","source":"Crossref","is-referenced-by-count":2,"title":["Bayesian Estimation and Comparison of Conditional Moment Models"],"prefix":"10.1093","volume":"84","author":[{"given":"Siddhartha","family":"Chib","sequence":"first","affiliation":[{"name":"Olin Business School, Washington University in St. Louis , St. Louis , Missouri , USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Minchul","family":"Shin","sequence":"additional","affiliation":[{"name":"Federal Reserve Bank of Philadelphia , Philadelphia , Pennsylvania , USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Anna","family":"Simoni","sequence":"additional","affiliation":[{"name":"CREST, CNRS, \u00c9cole Polytechnique, ENSAE , Palaiseau , France"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2021,12,16]]},"reference":[{"issue":"6","key":"2023022408353924500_","doi-asserted-by":"crossref","first-page":"1795","DOI":"10.1111\/1468-0262.00470","article-title":"Efficient estimation of models with conditional moment restrictions containing unknown functions","volume":"71","author":"Ai","year":"2003","journal-title":"Econometrica"},{"issue":"1","key":"2023022408353924500_","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1016\/j.jeconom.2007.01.013","article-title":"Estimation of possibly misspecified semiparametric conditional moment restriction models with different conditioning variables","volume":"141","author":"Ai","year":"2007","journal-title":"Journal of Econometrics"},{"issue":"1","key":"2023022408353924500_","doi-asserted-by":"crossref","first-page":"206","DOI":"10.1214\/11-AOS921","article-title":"The semiparametric Bernstein-von Mises theorem","volume":"40","author":"Bickel","year":"2012","journal-title":"Annals of Statistics"},{"issue":"6","key":"2023022408353924500_","doi-asserted-by":"crossref","first-page":"797","DOI":"10.1017\/S0266466600166010","article-title":"Generalization of GMM to a continuum of moment conditions","volume":"16","author":"Carrasco","year":"2000","journal-title":"Econometric Theory"},{"issue":"3","key":"2023022408353924500_","doi-asserted-by":"crossref","first-page":"305","DOI":"10.1016\/0304-4076(87)90015-7","article-title":"Asymptotic efficiency in estimation with conditional moment restrictions","volume":"34","author":"Chamberlain","year":"1987","journal-title":"Journal of Econometrics"},{"issue":"6","key":"2023022408353924500_","doi-asserted-by":"crossref","first-page":"1965","DOI":"10.3982\/ECTA14525","article-title":"Monte Carlo confidence sets for identified sets","volume":"86","author":"Chen","year":"2018","journal-title":"Econometrica"},{"issue":"432","key":"2023022408353924500_","doi-asserted-by":"crossref","first-page":"1313","DOI":"10.1080\/01621459.1995.10476635","article-title":"Marginal likelihood from the Gibbs output","volume":"90","author":"Chib","year":"1995","journal-title":"Journal of the American Statistical Association"},{"issue":"4","key":"2023022408353924500_","doi-asserted-by":"crossref","first-page":"327","DOI":"10.1080\/00031305.1995.10476177","article-title":"Understanding the Metropolis-Hastings algorithm","volume":"49","author":"Chib","year":"1995","journal-title":"The American Statistician"},{"issue":"2","key":"2023022408353924500_","doi-asserted-by":"crossref","first-page":"322","DOI":"10.1016\/j.jeconom.2009.11.002","article-title":"Additive cubic spline regression with Dirichlet process mixture errors","volume":"156","author":"Chib","year":"2010","journal-title":"Journal of Econometrics"},{"issue":"453","key":"2023022408353924500_","doi-asserted-by":"crossref","first-page":"270","DOI":"10.1198\/016214501750332848","article-title":"Marginal likelihood from the Metropolis-Hastings output","volume":"96","author":"Chib","year":"2001","journal-title":"Journal of the American Statistical Association"},{"issue":"1","key":"2023022408353924500_","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1016\/j.jeconom.2009.08.003","article-title":"Tailored randomized block MCMC methods with application to DSGE models","volume":"155","author":"Chib","year":"2010","journal-title":"Journal of Econometrics"},{"key":"2023022408353924500_","doi-asserted-by":"crossref","first-page":"771","DOI":"10.1080\/07350015.2019.1573684","article-title":"Which factors are risk factors in asset pricing? 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