Yuehao Bai, Kirill Ponomarev, Andres Santos, Azeem M. Shaikh, Max Tabord-Meehan, Alexander Torgovitsky
arXiv 27 Apr 2026 · Econometrics
arXiv:2604.24904 · PDF · DOI · OpenAlex · Extracted main text
This paper considers the problem of testing whether there exists a solution satisfying certain non-negativity constraints to a linear system of equations. Importantly and in contrast to some prior work, we allow all parameters in the system of equations, including the slope coefficients, to be unknown. For this reason, we describe the linear system as having unknown (as opposed to known) coefficients. This hypothesis testing problem arises naturally when constructing confidence sets for possibly partially identified parameters in the analysis of nonparametric instrumental variables models, treatment effect models, and random coefficient models, among other settings. To rule out certain instances in which the testing problem is impossible, in the sense that the power of any test will be bounded by its size, we begin our analysis by characterizing the closure of the null hypothesis with respect to the total variation distance. We then use this characterization to develop novel testing procedures based on sample-splitting. We establish the validity of our testing procedures under weak and interpretable conditions on the linear system. An important feature of these conditions is that they permit the dimensionality of the problem to grow rapidly with the sample size. A further attractive property of our tests is that they do not require simulation to compute suitable critical values. We illustrate the practical relevance of our theoretical results in a simulation study.
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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 | Cox, Gregory Fletcher and Shi, Xiaoxia and Shimizu, Yuya (2025) Testing Inequalities Linear in Nuisance Parameters | 1.000 | 9 | 4 | 100% |
| 2 | Goff, Leonard and Mbakop, Eric (2025) Inference on the value of a linear program | 1.000 | 9 | 4 | 100% |
| 3 | Freyberger, Joachim and Horowitz, Joel L (2015) Identification and shape restrictions in nonparametric instrumental variables estimation | 1.000 | 6 | 3 | 100% |
| 4 | Liu, Yiqi (2025) Synthetic Parallel Trends | 0.874 | 5 | 2 | 100% |
| 5 | Magnus, J.R. and Neudecker, H (2019) Matrix Differential Calculus with Applications in Statistics and Econometrics | 0.737 | 4 | 3 | 50% |
| 6 | Fang, Zheng and Santos, Andres and Shaikh, Azeem M and Torgovitsky,… (2023) Inference for Large-Scale Linear Systems With Known Coefficients self | 0.737 | 3 | 2 | 100% |
| 7 | Fox, Jeremy T and Kim, Kyoo Il and Ryan, Stephen P and Bajari, Patrick (2011) A simple estimator for the distribution of random coefficients | 0.737 | 3 | 2 | 100% |
| 8 | Mogstad, Magne and Santos, Andres and Torgovitsky, Alexander (2018) Using instrumental variables for inference about policy relevant treatment parameters self | 0.737 | 3 | 2 | 100% |
| 9 | Gu, Jiaying and Russell, Thomas M (2023) Partial Identification in Nonseparable Binary Response Models with Endogenous Regressors | 0.644 | 2 | 2 | 100% |
| 10 | Andrews, Isaiah and Roth, Jonathan and Pakes, Ariel (2023) Inference for Linear Conditional Moment Inequalities | 0.405 | 1 | 1 | 100% |
Showing the top 10 of 46 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | Testing the Solvability of Systems of Linear Inequalities | 0.405 | 1 | 1 |