The Simple Geometry of Correlated Regressors and IV Corrections
DOI:
https://doi.org/10.6000/1929-6029.2016.05.03.4Keywords:
Omitted variable bias (OVB), classical measurement error (CME), simultaneous equation models (SEM), instrumental variables, orthogonal projectionsAbstract
In medical research, frequently other important determinants, correlated with the key treatment variable, are omitted from the analysis. This omission yields biased and inconsistent estimates. For example, leaving out correlated (with, say, ) determinants of Y from regressions yield biased estimates of key parameters (say ). Instrumental variable estimation solves this problem by constructing similar triangles to retrieve consistent estimates. This article illustrates the geometry of correlated regressor bias, and the simple IV geometric solution.
References
RJ, William GJ. Satisfaction with Low Back Pain Care. The Spine Journal 2008; 8(3): 510-21. http://dx.doi.org/10.1016/j.spinee.2007.04.006 DOI: https://doi.org/10.1016/j.spinee.2007.04.006
Angrist JD, Jorn-Steffen P. Mostly Harmless Econometrics. (Princeton University Press, 2009). DOI: https://doi.org/10.1515/9781400829828
Parentea P, Santos S. A cautionary note on tests of overidentifying restrictions. Economics Letters, 115 (2), 314-317. http://dx.doi.org/10.1016/j.econlet.2011.12.047 DOI: https://doi.org/10.1016/j.econlet.2011.12.047
Butler RJ. The FIRE Project: Econometric Applications for Finance, Insurance and Risk Management online book, with taped lectures and auxiliary material 2016: https://sites.google.com/site/fireeconometrics/
Chen Y, Becky AB. Use of instrumental variable in prescription drug research with observational data: a systematic review. Journal of Clinical Epidemiology 2011; 4(6): 687-700. http://dx.doi.org/10.1016/j.jclinepi.2010.09.006 DOI: https://doi.org/10.1016/j.jclinepi.2010.09.006
Didelez V, Nuala S. Mendelian randomization as an instrumental variable approach to causal inference. Stat Methods Med Res 2007; 16(4): 309-330. http://dx.doi.org/10.1177/0962280206077743 DOI: https://doi.org/10.1177/0962280206077743
Martens EP, Pestman WR, de Boer A, Belitser SV, Klungel OH. Instrumental Variables: Application and Limitations. Epidemiology 2006; 17(3): 260-267. http://dx.doi.org/10.1097/01.ede.0000215160.88317.cb DOI: https://doi.org/10.1097/01.ede.0000215160.88317.cb
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Copyright (c) 2016 Richard J. Butler
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