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Robust Estimation with Nonrandom Measurement Error and Weak Instruments

Published online by Cambridge University Press:  04 January 2017

Timm Betz*
Department of Political Science, University of Michigan, Ann Arbor e-mail:


Two common problems in applications of two-stage least squares (2SLS) are nonrandom measurement error in the endogenous variable and weak instruments. In the presence of nonrandom measurement error, 2SLS yields inconsistent estimates. In the presence of weak instruments, confidence intervals and p-values can be severely misleading. This article introduces a rank-based estimator, grounded in randomization inference, which addresses both problems within a unified framework. Monte Carlo studies illustrate the deficiencies of 2SLS and the virtues of the rank-based estimator in terms of bias and efficiency. A replication of a study of the effect of economic shocks on democratic transitions demonstrates the practical implications of accounting for nonrandom measurement error and weak instruments.

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Copyright © The Author 2013. Published by Oxford University Press on behalf of the Society for Political Methodology 

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Ahmed, Faisal Z. 2012. The perils of unearned foreign income: Aid, remittances, and government corruption. American Political Science Review 106: 146–65.Google Scholar
Andrews, Bound, and Stock, James H. 2005. Discussion Paper No. 1530. Inference with weak instruments. New Haven, CT: Yale University, Cowles Foundation for Research in Economics.Google Scholar
Andrews, Donald W.K., Moreira, Marcelo J., and Stock, James H. 2007. Performance of conditional Wald tests in IV regression with weak instruments. Journal of Econometrics 139: 116–32.Google Scholar
Angrist, Joshua D., Imbens, Guido W., and Rubin, Donald B. 1996. Identification of causal effects using instrumental variables. Journal of the American Statistical Association 91: 444–55.Google Scholar
Angrist, Joshua D., and Pischke, Jörn-Steffen. 2009. Mostly harmless econometrics: An empiricist's companion. Princeton, NJ: Princeton University Press.Google Scholar
Bound, John, Jaeger, David A., and Baker, Regina M. 1995. Problems with instrumental variables estimation when the correlation between the instruments and the endogeneous explanatory variable is weak. Journal of the American Statistical Association 90: 443–50.Google Scholar
Brückner, Markus, and Ciccone, Antonio. 2011. Rain and the democratic window of opportunity. Econometrica 79: 923–47.Google Scholar
Ciccone, Antonio. 2011. Economic shocks and civil conflict: A comment. American Economic Journal: Applied Economics 3: 215–27.Google Scholar
Coakley, Clint W., and Hettmansperger, Thomas P. 1994. The maximum resistance of tests. Australian Journal of Statistics 36: 225–33.Google Scholar
Conover, W. J. 1999. Practical Nonparametric Statistics. New York: John Wiley & Sons.Google Scholar
Croux, Christophe, and Dehon, Catherine. 2010. Influence functions of the Spearman and Kendall correlation measures. Statistical Methods & Applications 19: 497515.Google Scholar
Deaton, Angus. 2005. Measuring poverty in a growing world (or measuring growth in a poor world). Review of Economics and Statistics 87: 119.CrossRefGoogle Scholar
Desmarais, Bruce A., and Harden, Jeffrey J. 2012. Comparing partial likelihood and robust estimation methods for the Cox regression model. Political Analysis 20: 113–35.CrossRefGoogle Scholar
Hájek, Jaroslav, and Sidak, Zbynek. 1967. Theory of Rank Tests. New York: Academic Press.Google Scholar
Hansen, Ben B., and Bowers, Jake. 2009. Attributing effects to a cluster-randomized get-out-the-vote campaign. Journal of the American Statistical Association 104: 873–85.Google Scholar
Hodges, J. L., and Lehmann, E. L. 1963. Estimates of location based on rank tests. Annals of Mathematical Statistics 34: 598611.CrossRefGoogle Scholar
Holland, Paul W. 1986. Statistics and causal inference. Journal of the American Statistical Association 81: 945–60.Google Scholar
Honoré, Bo E., and Hu, Luojia. 2004. On the performance of some robust instrumental variables estimators. Journal of Business and Economic Statistics 22: 3039.Google Scholar
Huber, Peter J., and Ronchetti, Elvezio. 2009. Robust statistics. Hoboken, NJ: Wiley.Google Scholar
Hug, Simon. 2010. The effect of misclassifications in probit models: Monte Carlo simulations and applications. Political Analysis 18: 78102.Google Scholar
Imbens, Guido W., and Rosenbaum, Paul R. 2005. Robust, accurate confidence intervals with a weak instrument: Quarter of birth and education. Journal of the Royal Statistical Society: Series A 168: 109–26.Google Scholar
Keele, Luke, McConnaughy, Corrine, and White, Ismail. 2012. Strengthening the experimenters toolbox: Statistical estimation of internal validity. American Journal of Political Science 56: 484–99.Google Scholar
Kerner, Andrew, and Lawrence, Jane. Forthcoming. What's the risk? Bilateral investment treaties, political risk, and fixed capital accumulation. British Journal of Political Science.Google Scholar
Lehmann, E. L. 1975. Nonparametrics: Statistical methods based on ranks. San Francisco: Holden-Day.Google Scholar
Marshall, Monty G., and Jaggers, Keith. 2006. Polity IV dataset. College Park, MD: Center for International Development and Conflict Management, University of Maryland.Google Scholar
Mebane, Walter R. Jr, and Sekhon, Jasjeet S. 2004. Robust estimation and outlier detection for overdispersed multinomial models of count data. American Political Science Review 48: 392411.Google Scholar
Miguel, Edward, Satyanath, Shanker, and Sergenti, Ernest. 2004. Economic shocks and civil conflict: An instrumental variables approach. Journal of Political Economy 112: 725–53.Google Scholar
Rosenbaum, Paul R. 1996. Comment on Angrist and Krueger. Journal of the American Statistical Association 91: 465–68.Google Scholar
Rosenbaum, Paul R. 2002. Observational Studies. New York: Springer.CrossRefGoogle Scholar
Rubin, Donald B. 1974. Estimating causal effects of treatments in randomized and nonrandomized studies. Journal of Educational Psychology 56: 688701.Google Scholar
Sovey, Allison J., and Green, Donald P. 2011. Instrumental variables estimation in political science: A readers' guide. American Journal of Political Science 55: 188200.Google Scholar
Staiger, Douglas O., and Stock, James H. 1997. Instrumental variables regression with weak instruments. Econometrica 65: 557–86.Google Scholar
Stock, James H., Wright, Jonathan H., and Yogo, Motohiro. 2002. A survey of weak instruments and weak identification in generalized method of moments. Journal of Business and Economic Statistics 20: 518–29.Google Scholar
Wand, Jonathan N., Shotts, Kenneth W., Sekhon, Jasjeet S., Mebane, Walter R. Jr, Herron, Michael C., and Brady, Henry E. 2001. The butterfly did it: The aberrant vote for Buchanan in Palm Beach County, Florida. American Political Science Review 95: 793810.CrossRefGoogle Scholar
Western, Bruce. 1995. Concepts and suggestions for robust regression analysis. American Journal of Political Science 39: 786817.Google Scholar