Elie Tamer, Christopher D. Walker
arXiv 26 Aug 2026 · Econometrics
arXiv:2608.25814 · PDF · Extracted main text
This paper proposes a nonparametric Bayesian inference framework for partially identified discrete response models. The key observation is that these models map a reduced-form conditional choice probability to an identified set. Consequently, nonparametric Bayesian inference for the conditional probability mass function leads to Bayesian inference for the identified set. The inference framework nests conditional moment inequalities and linear systems with unknown coefficients as special cases. Importantly, our proposal does not require converting conditional moments into unconditional moments or discretizing covariates. We show that the posterior is consistent for the true identified set when the model is correctly specified, show that the posterior can consistently detect model misspecification, and show posterior consistency for a pseudo-identified set that is valid under misspecification. We also verify the assumptions for a class of priors based on Gaussian processes that we use to implement our proposal. These priors offer similar flexibility to frequentist partial identification methods, and are computationally attractive because posterior sampling can be performed in closed-form. We also show that many of the ideas in this paper extend to continuous responses and aggregated discrete responses (e.g., market shares).
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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 | Manski, Charles F and Tamer, Elie (2002) Inference on regressions with interval data on a regressor or outcome self | 1.000 | 5 | 3 | 100% |
| 2 | Victor Chernozhukov and Han Hong and Elie Tamer (2007) Estimation and Confidence Regions for Parameter Sets in Econometric Models self | 0.941 | 6 | 3 | 83% |
| 3 | Shi, Xiaoxia and Shum, Matthew and Song, Wei (2018) Estimating semi-parametric panel multinomial choice models using cyclic monotonicity | 0.928 | 4 | 3 | 100% |
| 4 | Khan, SHAKEEB and Ponomareva, Maria and Tamer, ELIE (2023) Identification of dynamic binary response models self | 0.920 | 9 | 4 | 78% |
| 5 | Christopher D. Walker (2026) Semiparametric Bayesian Inference for a Conditional Moment Equality Model self | 0.894 | 7 | 4 | 71% |
| 6 | Aad van der Vaart and Harry van Zanten (2011) Information Rates of Nonparametric Gaussian Process Methods | 0.843 | 4 | 3 | 75% |
| 7 | Polson, Nicholas G and Scott, James G and Windle, Jesse (2013) Bayesian inference for logistic models using Pólya–Gamma latent variables | 0.843 | 5 | 4 | 60% |
| 8 | A. W. van der Vaart and J. H. van Zanten (2008) Rates of contraction of posterior distributions based on Gaussian process priors | 0.843 | 5 | 3 | 60% |
| 9 | Pakes, Ariel and Porter, Jack R and Shepard, Mark and Calder-Wang, S… (2021) Unobserved heterogeneity, state dependence, and health plan choices | 0.811 | 4 | 2 | 100% |
| 10 | Andrews, Donald W. K. and Shi, Xiaoxia (2013) Inference Based on Conditional Moment Inequalities | 0.737 | 3 | 2 | 100% |
Showing the top 10 of 134 scored citations.