Bayesian inference for partially identified smooth convex models

Liao, Yuan; Simoni, Anna

doi:10.1016/j.jeconom.2019.03.001

Cited by 12 publications

(9 citation statements)

References 54 publications

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“…For excellent overviews of frequentist and Bayesian inference for partially identified econometric models see Bontemps and Magnac (2017), Molinari (2020) and references therein. Most of the previous Bayesian literature is interested in constructing Bayesian proce-dures that provide asymptotically valid frequentist inferences for partially identified models, see for instance Liao and Jiang (2010), Gustafson (2010Gustafson ( , 2012, Moon and Schorfheide (2012), Norets and Tang (2013), Kline and Tamer (2016), Chen et al (2018), Liao and Simoni (2019) and Giacomini and Kitagawa (2021). They have proposed Bayesian or quasi-Bayesian approaches for constructing (asymptotically) valid frequentist confidence sets of the identified set.…”

Section: Initial Discussion Of Nonidentified Models Which Lay the Fou...mentioning

confidence: 99%

Revisiting identification concepts in Bayesian analysis

Florens¹,

Simoni²

2021

Preprint

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This paper studies the role played by identification in the Bayesian analysis of statistical and econometric models. First, for unidentified models we demonstrate that there are situations where the introduction of a non-degenerate prior distribution can make a parameter that is nonidentified in frequentist theory identified in Bayesian theory. In other situations, it is preferable to work with the unidentified model and construct a Markov Chain Monte Carlo (MCMC) algorithms for it instead of introducing identifying assumptions. Second, for partially identified models we demonstrate how to construct the prior and posterior distributions for the identified set parameter and how to conduct Bayesian analysis. Finally, for models that contain some parameters that are identified and others that are not we show that marginalizing out the identified parameter from the likelihood with respect to its conditional prior, given the nonidentified parameter, allows the data to be informative about the nonidentified and partially identified parameter. The paper provides examples and simulations that illustrate how to implement our techniques.

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Section: Initial Discussion Of Nonidentified Models Which Lay the Fou...mentioning

confidence: 99%

Revisiting identification concepts in Bayesian analysis

Florens¹,

Simoni²

2021

Preprint

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“…It is worth noting that previous Bayesian work on conditional moments, for example, Liao and Jiang (2011), Florens and Simoni (2012, 2016, Kato (2013), Chen, Christensen and Tamer (2018) and Liao and Simoni (2019), has little overlap with the discussion here. A major difference is that none of these papers adopt the fully Bayesian ETEL framework.…”

Section: Introductionmentioning

confidence: 89%

“…Our treatment also complements the papers on conditional moment models from a Bayesian viewpoint that are based on non-ETEL approaches and reflect other concerns. For instance, Liao and Jiang (2011), Simoni (2012, 2016), Kato (2013), Chen, Christensen and Tamer (2018) and Liao and Simoni (2019) allow the moment function to contain a non-parametric component that is estimated by a sieve type approximation method, or a Gaussian process prior, permitting the possibility that the non-parametric component is only partially identified, but within a quasi-Bayesian formulation based on a pseudo-likelihood. None of these papers tackles the problem of misspecification,…”

Section: Introductionmentioning

confidence: 99%

Bayesian Estimation and Comparison of Conditional Moment Models

Chib¹,

Shin²,

Simoni³

2019

Working Paper (Federal Reserve Bank of Philadelphia)

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We provide a Bayesian analysis of models in which the unknown distribution of the outcomes is specified up to a set of conditional moment restrictions. This analysis is based on the nonparametric exponentially tilted empirical likelihood (ETEL) function, which is constructed to satisfy a sequence of unconditional moments, obtained from the conditional moments by 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 also developed. The central result is that the marginal likelihood criterion selects the model that is less misspecified, that is, the model that is closer to the unknown true distribution in terms of the Kullback-Leibler divergence. Several examples are provided to illustrate the framework and results.

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“…This can be done, for instance, by applying the approaches considered in Giacomini et al (2018) and Giacomini et al (2019b), although we do not present them in this paper. Chen et al (2018), Kline and Tamer (2016), Liao and Simoni (2019), Moon and Schorfheide (2012), and Norets and Tang (2014) propose Bayesian approaches for drawing posterior inference for the identified set. To our knowledge, none of these proposals have been applied to the case where the identified set consists of isolated points.…”

Section: I1 Related Literaturementioning

confidence: 99%

Locally- but not globally-identified SVARs

Bacchiocchi¹,

Kitagawa²

2020

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This paper analyzes Structural Vector Autoregressions (SVARs) where identification of structural parameters holds locally but not globally. In this case there exists a set of isolated structural parameter points that are observationally equivalent under the imposed restrictions. Although the data do not inform us which observationally equivalent point should be selected, the common frequentist practice is to obtain one as a maximum likelihood estimate and perform impulse response analysis accordingly. For Bayesians, the lack of global identification translates to nonvanishing sensitivity of the posterior to the prior, and the multi-modal likelihood gives rise to computational challenges as posterior sampling algorithms can fail to explore all the modes. This paper overcomes these challenges by proposing novel estimation and inference procedures. We characterize a class of identifying restrictions that deliver local but non-global identification, and the resulting number of observationally equivalent parameter values. We propose algorithms to exhaustively compute all admissible structural parameter given reduced-form parameters and utilize them to sampling from the multi-modal posterior. In addition, viewing the set of observationally equivalent parameter points as the identified set, we develop Bayesian and frequentist procedures for inference on the corresponding set of impulse responses. An empirical example illustrates our proposal.

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Bayesian inference for partially identified smooth convex models

Cited by 12 publications

References 54 publications

Revisiting identification concepts in Bayesian analysis

Revisiting identification concepts in Bayesian analysis

Bayesian Estimation and Comparison of Conditional Moment Models

Locally- but not globally-identified SVARs

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