arXiv 13 Dec 2012 · Statistics — Methodology · 8 citations (OpenAlex)
arXiv:1212.3267 · PDF · DOI · OpenAlex · Extracted main text
We provide a comprehensive semi-parametric study of Bayesian partially identified econometric models. While the existing literature on Bayesian partial identification has mostly focused on the structural parameter, our primary focus is on Bayesian credible sets (BCS's) of the unknown identified set and the posterior distribution of its support function. We construct a (two-sided) BCS based on the support function of the identified set. We prove the Bernstein-von Mises theorem for the posterior distribution of the support function. This powerful result in turn infers that, while the BCS and the frequentist confidence set for the partially identified parameter are asymptotically different, our constructed BCS for the identified set has an asymptotically correct frequentist coverage probability. Importantly, we illustrate that the constructed BCS for the identified set does not require a prior on the structural parameter. It can be computed efficiently for subset inference, especially when the target of interest is a sub-vector of the partially identified parameter, where projecting to a low-dimensional subset is often required. Hence, the proposed methods are useful in many applications. The Bayesian partial identification literature has been assuming a known parametric likelihood function. However, econometric models usually only identify a set of moment inequalities, and therefore using an incorrect likelihood function may result in misleading inferences. In contrast, with a nonparametric prior on the unknown likelihood function, our proposed Bayesian procedure only requires a set of moment conditions, and can efficiently make inference about both the partially identified parameter and its identified set. This makes it widely applicable in general moment inequality models. Finally, the proposed method is illustrated in a financial asset pricing problem.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Florens, J.P. and Simoni, A (2011) Bayesian identification and partial identification self | 0.405 | 1 | 1 | 100% |
| 2 | Ghosh, J.K. and Ramamoorthi, R.V (2003) Bayesian Nonparametrics. Springer-Verlag | 0.405 | 1 | 1 | 100% |
| 3 | Milgrom, P. and Segal, I (2002) Envelope theorems for arbitrary choice sets | 0.405 | 1 | 1 | 100% |
| 4 | van der Vaart, A.W (2002) Semiparametric Statistics | 0.405 | 1 | 1 | 100% |
| 5 | Sethuraman, J (1994) A constructive definition of the Dirichlet prior | 0.000 | 1 | 1 | 0% |
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