On the Stock-Yogo Tables

Christopher Skeels, Frank Windmeijer

Research output: Contribution to journalArticle (Academic Journal)peer-review

7 Citations (Scopus)
184 Downloads (Pure)


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
6 implementations to be generalised and improved. Finally, we explore the calculation of p-values for the first-stage F-statistic weak instruments test.
Original languageEnglish
Article number44
Number of pages23
Issue number4
Early online date13 Nov 2018
Publication statusPublished - Dec 2018

Structured keywords

  • ECON Econometrics
  • ECON CEPS Data


  • Hypergeometric functions
  • Hypothesis testing
  • p-values
  • Quadratic forms
  • Stock-Yogo tables
  • Weak instruments


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