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On the Stock-Yogo Tables

Christopher Skeels and Frank Windmeijer ()

Bristol Economics Discussion Papers from Department of Economics, University of Bristol, UK

Abstract: A standard test for weak instruments compares the first-stage F-statistic to a table of critical values obtained by Stock and Yogo (2005) using simulations. We derive a closed-form solution for the expectation that determines these critical values. Inspection of this new result provides insights not available from simulation, and will allow software implementations to be generalized and improved. Of independent interest, our analysis makes contributions to the theory of confluent hypergeometric functions and the theory of ratios of quadratic forms in normal variables. A by-product of our developments is an expression for the distribution function of the non-central chi-squared distribution that we have not been able to find elsewhere in the literature. Finally, we explore the calculation of p-values for the first-stage F-statistic weak instruments test.

Keywords: Weak instruments; hypothesis testing; Stock-Yogo tables; hypergeometric functions; quadratic forms; p-values. (search for similar items in EconPapers)
JEL-codes: C12 C36 C46 C52 C65 C88 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-ecm
Date: 2016-11-09, Revised 2016-11-25
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Journal Article: On the Stock–Yogo Tables (2018) Downloads
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