Simple Adaptive Size-Exact Testing for Full-Vector and Subvector Inference in Moment Inequality Models
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We propose a simple test for moment inequalities that has exact size in normal models with known variance and has uniformly asymptotically exact size under asymptotic normality. The test compares the quasi-likelihood ratio statistic to a chi-squared critical value, where the degree of freedom is the rank of the inequalities that are active in finite samples. The test requires no simulation and thus is computationally fast and especially suitable for constructing confidence sets for parameters by test inversion. It uses no tuning parameter for moment selection and yet still adapts to the slackness of the moment inequalities. Furthermore, we show how the test can be easily adapted to inference on subvectors in the common empirical setting of conditional moment inequalities with nuisance parameters entering linearly. User-friendly Matlab code to implement the test is provided.
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We can test both testable implications using estimators DID^n,bal_l',l' of δ^n,bal_l,l', through a joint equality test for the first testable implication, and a multivariate inequality test for the second one.
“We can test both testable implications using estimators DID n,bal ℓ ′ ,ℓ ′ of δ n,bal ℓ,ℓ ′ , through a joint equality test for the first testable implication, and a multivariate inequality test for the second one (see, e.g., Cox and Shi, 2023, for a recent and simple proposal).”
From Difference-in-Differences Estimators of Intertemporal Treatment Effects (2026) · cites this paper as Cox and Shi, 2023
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- Authors
- Cox, G., & Shi, X.
- Affiliations
- National University of Singapore (SG)
- University of Wisconsin–Madison (US)
- Corresponding author
- Cox, Gregory
- ORCID
- Shi, Xiaoxia
- Venue
- The Review of Economic Studies
- Publisher
- Oxford University Press (OUP)
- Published
- 2022-03-15
- Volume
- 90
- Issue
- 1
- Pages
- 201-228
- ISSN
- 0034-6527 (ISSN-L)
- 1467-937X
- OpenAlex
- W3065003916
- Cited by
- 48
- References
- 78
- Citations by year
- 2026: 5 · 2025: 7 · 2024: 8 · 2023: 9 · 2022: 9 · 2021: 5 · 2020: 2 · 2019: 2 · 2018: 1
- FWCI
- 6.13
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Licence
- academic.oup.com/journals/pages/open_access/funder_policies/chorus/standard_publication_model (vor)
- Locations
- The Review of Economic Studies (publishedVersion)
- RePEc: Research Papers in Economics (submittedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Inference
- Physical Sciences › Mathematics › Statistics and Probability › Advanced Causal Inference Techniques
- Social Sciences › Economics, Econometrics and Finance › Economics and Econometrics › Spatial and Panel Data Analysis
- Keywords
- quasi-likelihood ratio test, confidence regions, nuisance parameters, asymptotic normality, moment selection, finite-sample inference
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
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