Poorly Measured Confounders Are More Useful on the Left Than on the Right
Researchers frequently test identifying assumptions in regression based research designs (which include instrumental variables or difference-in-differences models) by adding additional control variables on the right hand side of the regression. If such additions do not affect the coefficient of interest (much) a study is presumed to be reliable. We caution that such invariance may result from the fact that the observed variables used in such robustness checks are often poor measures of the potential underlying confounders. In this case, a more powerful test of the identifying assumption is to put the variable on the left hand side of the candidate regression. We provide derivations for the estimators and test statistics involved, as well as power calculations, which can help applied researchers interpret their findings. We illustrate these results in the context of various strategies which have been suggested to identify the returns to schooling.
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References listed on IDEAS
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- Joseph G. Altonji & Todd E. Elder & Christopher R. Taber, 2005.
"Selection on Observed and Unobserved Variables: Assessing the Effectiveness of Catholic Schools,"
Journal of Political Economy,
University of Chicago Press, vol. 113(1), pages 151-184, February.
- Joseph G. Altonji & Todd E. Elder & Christopher R. Taber, 2000. "Selection on Observed and Unobserved Variables: Assessing the Effectiveness of Catholic Schools," NBER Working Papers 7831, National Bureau of Economic Research, Inc.
- Joshua D. Angrist & Jörn-Steffen Pischke, 2009. "Mostly Harmless Econometrics: An Empiricist's Companion," Economics Books, Princeton University Press, edition 1, number 8769.
- Anderson, Michael L., 2008. "Multiple Inference and Gender Differences in the Effects of Early Intervention: A Reevaluation of the Abecedarian, Perry Preschool, and Early Training Projects," Journal of the American Statistical Association, American Statistical Association, vol. 103(484), pages 1481-1495.
- Matias Cattaneo & Michael Jansson & Whitney K. Newey, 2017. "Inference in linear regression models with many covariates and heteroskedasticity," CeMMAP working papers CWP03/17, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
- MacKinnon, James G. & White, Halbert, 1985. "Some heteroskedasticity-consistent covariance matrix estimators with improved finite sample properties," Journal of Econometrics, Elsevier, vol. 29(3), pages 305-325, September.
- James G. MacKinnon & Halbert White, 1983. "Some Heteroskedasticity Consistent Covariance Matrix Estimators with Improved Finite Sample Properties," Working Papers 537, Queen's University, Department of Economics.
- Card, David, 2001. "Estimating the Return to Schooling: Progress on Some Persistent Econometric Problems," Econometrica, Econometric Society, vol. 69(5), pages 1127-1160, September.
- David Card, 2000. "Estimating the Return to Schooling: Progress on Some Persistent Econometric Problems," NBER Working Papers 7769, National Bureau of Economic Research, Inc.
- Griliches, Zvi, 1977. "Estimating the Returns to Schooling: Some Econometric Problems," Econometrica, Econometric Society, vol. 45(1), pages 1-22, January. Full references (including those not matched with items on IDEAS)
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