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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\u2010dimensional 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.<\/jats:p>","DOI":"10.3982\/ecta18979","type":"journal-article","created":{"date-parts":[[2023,1,24]],"date-time":"2023-01-24T09:27:41Z","timestamp":1674552461000},"page":"299-327","source":"Crossref","is-referenced-by-count":15,"title":["Inference for Large\u2010Scale Linear Systems With Known Coefficients"],"prefix":"10.3982","volume":"91","author":[{"given":"Zheng","family":"Fang","sequence":"first","affiliation":[{"name":"Department of Economics, Emory University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Andres","family":"Santos","sequence":"additional","affiliation":[{"name":"Department of Economics, UCLA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Azeem M.","family":"Shaikh","sequence":"additional","affiliation":[{"name":"Department of Economics, University of Chicago"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Alexander","family":"Torgovitsky","sequence":"additional","affiliation":[{"name":"Department of Economics, University of Chicago"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"2359","published-online":{"date-parts":[[2023]]},"reference":[{"key":"ecta200515-bib-0001","volume-title":"Infinite Dimensional Analysis\u2014a Hitchhiker's Guide","author":"Aliprantis","year":"2006"},{"issue":"1","key":"ecta200515-bib-0002","doi-asserted-by":"crossref","first-page":"119","DOI":"10.1111\/1468-0262.00271","volume":"78","author":"Andrews","year":"2010","journal-title":"Econometrica"},{"key":"ecta200515-bib-0003","doi-asserted-by":"crossref","unstructured":"Andrews, Isaiah, Jonathan Roth, and Ariel Pakes (2019): \u201cInference for Linear Conditional Moment Inequalities,\u201d Technical Report, NBER.","DOI":"10.3386\/w26374"},{"issue":"430","key":"ecta200515-bib-0004","doi-asserted-by":"crossref","first-page":"431","DOI":"10.1080\/01621459.1995.10476535","volume":"90","author":"Angrist","year":"1995","journal-title":"Journal of the American statistical Association"},{"issue":"4","key":"ecta200515-bib-0005","doi-asserted-by":"crossref","first-page":"979","DOI":"10.2307\/2937954","volume":"106","author":"Angrist","year":"1991","journal-title":"The Quarterly Journal of Economics"},{"key":"ecta200515-bib-0006","doi-asserted-by":"crossref","unstructured":"Bai, Yuehao, Andres Santos, and Azeem Shaikh (2019): \u201cA Practical Method for Testing Many Moment Inequalities,\u201d Working Paper, (2019-116), University of Chicago.","DOI":"10.2139\/ssrn.3454610"},{"key":"ecta200515-bib-0007","unstructured":"Bai, Yuehao, Azeem M. 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