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Linear Model IV Estimation When Instruments Are Many or Weak

Michael P. Murray

Abstract

Economists rely frequently on instrumental variables estimation to overcome biases that endogenous explanatory variables cause in ordinary least squares estimation. However, traditional instrumental variables estimators, such as two-stage least squares and limited information maximum likelihood estimation, can suffer persistent estimator biases and size-of-test biases in even very large samples if the instruments used are large in number or are only weakly correlated with an endogenous explanatory variable. This paper reviews strategies for grappling with weak instruments and with large numbers of instruments in linear regression models.


Corresponding author: Michael P. Murray, Department of Economics, Bates College, Lewiston, ME 04240, USA, E-mail:

Acknowledgments

Daron Acemoglu, Isaiah Andrews, Josh Angrist, Jerry Hausman, Jim Heckman, Simon Johnson, Peter Kennedy, Emily Marshall, Marcelo Moreira, Daniel Riera-Chricton, Carl Schwinn, Paul Shea, Nathan Tefft and Motohiro Yogo provided helpful comments on drafts of this work. Two anonymous referees and the editor, Jack Porter, improved the final version. I am grateful to Vaibhav Bajpai for able research assistance. All errors are mine alone.

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Published Online: 2016-2-25
Published in Print: 2017-1-1

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