Inference for Large-Scale Linear Systems with Known Coefficients

Zheng Fang (), Andres Santos (), Azeem Shaikh and Alexander Torgovitsky
Additional contact information
Zheng Fang: Texas A&M University - Department of Economics
Andres Santos: University of California, Los Angeles - Department of Economics

No 2020-134, Working Papers from Becker Friedman Institute for Research In Economics

Abstract: This paper considers the problem of testing whether there exists a non-negative solution to a possibly under-determined system of linear equations with known coefficients. This hypothesis testing problem arises naturally in a number of settings, including random coefficient, treatment effect, and discrete choice models, as well as a class of linear programming problems. As a first contribution, we obtain a novel geometric characterization of the null hypothesis in terms of identified parameters satisfying an infinite set of inequality restrictions. Using this characterization, we devise a test that requires solving only linear programs for its implementation, and thus remains computationally feasible in the high-dimensional applications that motivate our analysis. The asymptotic size of the proposed test is shown to equal at most the nominal level uniformly over a large class of distributions that permits the number of linear equations to grow with the sample size.

Keywords: Linear programming; linear inequalities; moment inequalities; random coefficients; partial identification; exchangeable bootstrap; uniform inference (search for similar items in EconPapers)
Pages: 66 pages
Date: 2020
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Citations: View citations in EconPapers (3)

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https://repec.bfi.uchicago.edu/RePEc/pdfs/BFI_WP_2020134.pdf (application/pdf)

Related works:
Journal Article: Inference for Large‐Scale Linear Systems With Known Coefficients (2023)
Working Paper: Inference for Large-Scale Linear Systems with Known Coefficients (2021)
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