SMU SOE Seminar (Jan 10, 2019): Improved Inference on the Rank of a Matrix

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TOPIC:

IMPROVED INFERENCE ON THE RANK OF A MATRIX

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 H0 : rank(π0) ≤ r. The problem is of first order importance because the previous literature focuses on H’0 : rank(π 0) = r by implicitly assuming away rank(π0) < r, which may lead to invalid rank tests due to over-rejections. In particular, we show that limiting distributions of test statistics under H’0 may not stochastically dominate those under rank(π 0) < r. A multiple test on the nulls rank(π 0) = 0,..., r, though valid, may be substantially conservative. We employ a testing statistic whose limiting distributions under H0 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. Keywords: Matrix rank, Bootstrap, Two-step test, Rank estimation, Identification, Matching dimension. Click here to view the paper. Click here to view the CV.
		PRESENTER Qihui Chen The Chinese University of Hong Kong, Shenzhen
		RESEARCH FIELDS Econometric Theory Applied Econometrics
		DATE: 10 January 2019 (Thursday)
		TIME: 4pm - 5.30pm
		VENUE: Meeting Room 5.1, Level 5 School of Economics Singapore Management University 90 Stamford Road Singapore 178903

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