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Econometrics 2018, 6(4), 44;

On the Stock–Yogo Tables

Department of Economics, The University of Melbourne, Parkville, 3010, Australia
Department of Economics and IEU, University of Bristol, Bristol, BS8 1TU, UK
Author to whom correspondence should be addressed.
Received: 31 March 2018 / Revised: 17 October 2018 / Accepted: 8 November 2018 / Published: 13 November 2018
(This article belongs to the Special Issue Celebrated Econometricians: Peter Phillips)
Full-Text   |   PDF [513 KB, uploaded 28 November 2018]   |  


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 from which these critical values are derived, as well as present some second-order asymptotic approximations that may be of value in the presence of multiple endogenous regressors. Inspection of this new result provides insights not available from simulation, and will allow software implementations to be generalised and improved. Finally, we explore the calculation of p-values for the first-stage F-statistic weak instruments test. View Full-Text
Keywords: weak instruments; hypothesis testing; Stock–Yogo tables; hypergeometric functions; quadratic forms; p-values weak instruments; hypothesis testing; Stock–Yogo tables; hypergeometric functions; quadratic forms; p-values

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Skeels, C.L.; Windmeijer, F. On the Stock–Yogo Tables. Econometrics 2018, 6, 44.

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