Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/217180 
Year of Publication: 
2019
Citation: 
[Journal:] Quantitative Economics [ISSN:] 1759-7331 [Volume:] 10 [Issue:] 4 [Publisher:] The Econometric Society [Place:] New Haven, CT [Year:] 2019 [Pages:] 1787-1824
Publisher: 
The Econometric Society, New Haven, CT
Abstract: 
This paper develops a general framework for conducting inference on the rank of an unknown matrix Π0. A defining feature of our setup is the null hypothesis of the form . The problem is of first-order importance because the previous literature focuses on by implicitly assuming away , which may lead to invalid rank tests due to overrejections. In particular, we show that limiting distributions of test statistics under may not stochastically dominate those under . A multiple test on the nulls , though valid, may be substantially conservative. We employ a testing statistic whose limiting distributions under are highly nonstandard due to the inherent irregular natures of the problem, and then construct bootstrap critical values that deliver size control and improved power. Since our procedure relies on a tuning parameter, a two-step procedure is designed to mitigate concerns on this nuisance. We additionally argue that our setup is also important for estimation. We illustrate the empirical relevance of our results through testing identification in linear IV models that allows for clustered data and inference on sorting dimensions in a two-sided matching model with transferrable utility.
Subjects: 
Matrix rank
bootstrap
two-step test
rank estimation
identification
matching dimension
JEL: 
C12
C15
Persistent Identifier of the first edition: 
Creative Commons License: 
cc-by-nc Logo
Document Type: 
Article

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