EconBase
← All papers

Semiparametric Bayesian Inference for a Conditional Moment Equality Model

Christopher D. Walker

arXiv 21 Oct 2024 · Econometrics · 1 citations (OpenAlex)

arXiv:2410.16017 · PDF · DOI · OpenAlex · Extracted main text

Abstract

Conditional moment equality models are regularly encountered in empirical economics, yet they are difficult to estimate. These models map a conditional distribution of data to a structural parameter via the restriction that a conditional mean equals zero. Using this observation, I introduce a Bayesian inference framework in which an unknown conditional distribution is replaced with a nonparametric posterior, and structural parameter inference is then performed using an implied posterior. The method has the same flexibility as frequentist semiparametric estimators and does not require converting conditional moments to unconditional moments. Importantly, I prove a semiparametric Bernstein-von Mises theorem, providing conditions under which, in large samples, the posterior for the structural parameter is approximately normal, centered at an efficient estimator, and has variance equal to the Chamberlain (1987) semiparametric efficiency bound. As byproducts, I show that Bayesian uncertainty quantification methods are asymptotically optimal frequentist confidence sets and derive low-level sufficient conditions for Gaussian process priors. The latter sheds light on a key prior stability condition and relates to the numerical aspects of the paper in which these priors are used to predict the welfare effects of price changes.

Citation extraction

81
references
185
in-text mentions
81
distinct cited
2
self-citations
11,919
main-text words

appendix boundary found by appendix_command · 62% of the source is main text. Read the extracted text to check this.

Most heavily cited references

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.

ReferenceIntensityMentionsSectionsMain text
1Ai, Chunrong and Chen, Xiaohong (2003) Efficient Estimation of Models with Conditional Moment Restrictions Containing Unknown Functions1.00054100%
2Vincent Rivoirard and Judith Rousseau (2012) Bernstein–von Mises theorem for linear functionals of the density1.00053100%
3Chamberlain, Gary (1987) Asymptotic efficiency in estimation with conditional moment restrictions0.96419789%
4A. W. van der Vaart and J. H. van Zanten (2008) Rates of contraction of posterior distributions based on Gaussian process priors0.9285380%
5Whitney K. Newey (1993) 16 Efficient estimation of models with conditional moment restrictions0.92843100%
6Ismaël Castillo (2012) Semiparametric Bernstein-von Mises theorem and bias, illustrated with Gaussian process priors0.92843100%
7Castillo, Ismaël (2012) A semiparametric Bernstein–von Mises theorem for Gaussian process priors0.92843100%
8Newey, Whitney K (1990) Efficient instrumental variables estimation of nonlinear models0.92843100%
9Chib, Siddhartha and Shin, Minchul and Simoni, Anna (2022) Bayesian estimation and comparison of conditional moment models0.8947371%
10Ismaël Castillo and Judith Rousseau (2015) A Bernstein–von Mises theorem for smooth functionals in semiparametric models0.8749567%

Showing the top 10 of 81 scored citations.

Cited by, within the corpus

arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.

Citing paperIntensityMentionsSections
1Optimal Decision Rules when Payoffs are Partially Identified0.40511
2Generalized Bayes in Conditional Moment Restriction Models0.40511
3Nonparametric Bayesian Policy Learning0.40511