Assessing Sensitivity to Unconfoundedness: Estimation and Inference

References

• Altonji, J. G., Elder, T. E., and Taber, C. R. (2005), “Selection on Observed and Unobserved Variables: Assessing the Effectiveness of Catholic Schools,” Journal of Political Economy, 113, 151–184. DOI: 10.1086/426036.
   Web of Science ®Google Scholar
• Altonji, J. G., Elder, T. E., and Taber, C. R. (2008): “Using Selection on Observed Variables to Assess Bias from Unobservables When Evaluating Swan-Ganz Catheterization,” American Economic Review P&P, 98, 345–350.
   Web of Science ®Google Scholar
• Athey, S., and Imbens, G. W. (2017), “The State of Applied Econometrics: Causality and Policy Evaluation,” Journal of Economic Perspectives, 31, 3–32. DOI: 10.1257/jep.31.2.3.
   PubMed Web of Science ®Google Scholar
• Caliendo, M., and Kopeinig, S. (2008), “Some Practical Guidance for the Implementation of Propensity Score Matching,” Journal of Economic Surveys, 22, 31–72. DOI: 10.1111/j.1467-6419.2007.00527.x.
   Web of Science ®Google Scholar
• Chernozhukov, V., Fernández-Val, I., and Kaji, T. (2017), “Extremal Quantile Regression,” in Handbook of Quantile Regression, eds. R. Koenker, V. Chernozhukov, X. He, and L. Peng, pp. 333–362, New York: Chapman and Hall/CRC.
   Google Scholar
• Cinelli, C., and Hazlett, C. (2020), “Making Sense of Sensitivity: Extending Omitted Variable Bias,” Journal of the Royal Statistical Society, Series B, 82, 39–67. DOI: 10.1111/rssb.12348.
   Google Scholar
• Dehejia, R. H., and Wahba, S. (1999), “Causal Effects in Nonexperimental Studies: Reevaluating the Evaluation of Training Programs,” Journal of the American Statistical Association, 94, 1053–1062. DOI: 10.1080/01621459.1999.10473858.
   Web of Science ®Google Scholar
• Fang, Z., and Santos, A. (2015), “Inference on Directionally Differentiable Functions,” working paper.
   Google Scholar
• Fang, Z., and Santos, A. (2019), “Inference on Directionally Differentiable Functions,” The Review of Economic Studies, 86, 377–412.
   Web of Science ®Google Scholar
• Fogarty, C. B. (2020), “Studentized Sensitivity Analysis for the Sample Average Treatment Effect in Paired Observational Studies,” Journal of the American Statistical Association, 115, 1518–1530. DOI: 10.1080/01621459.2019.1632072.
   Web of Science ®Google Scholar
• Fogarty, C. B., Shi, P., Mikkelsen, M. E., and Small, D. S. (2017), ““Randomization Inference and Sensitivity Analysis for Composite Null Hypotheses with Binary Outcomes in Matched Observational Studies,” Journal of the American Statistical Association, 112, 321–331. DOI: 10.1080/01621459.2016.1138865.
   Web of Science ®Google Scholar
• Fogarty, C. B., and Small, D. S. (2016), “Sensitivity Analysis for Multiple Comparisons in Matched Observational Studies through Quadratically Constrained Linear Programming,” Journal of the American Statistical Association, 111, 1820–1830. DOI: 10.1080/01621459.2015.1120675.
   Web of Science ®Google Scholar
• Heckman, J. J., LaLonde, R. J., and Smith, J. A. (1999), “The Economics and Econometrics of Active Labor Market Programs,” Handbook of Labor Economics, 3, 1865–2097.
   Google Scholar
• Heckman, J. J., and Smith, J. (1998), “Evaluating the Welfare State,” in Econometrics and Economic Theory in the 20th Century: The Ragnar Frisch Centennial Symposium (Vol. 31), ed. S. Strøm, pp. 241–318, Cambridge: Cambridge University Press.
   Google Scholar
• Hong, H., and Li, J. (2018), “The Numerical Delta Method,” Journal of Econometrics, 206, 379–394. DOI: 10.1016/j.jeconom.2018.06.007.
   Web of Science ®Google Scholar
• Hosman, C. A., Hansen, B. B., and Holland, P. W. (2010), “The Sensitivity of Linear Regression Coefficients’ Confidence Limits to the Omission of a Confounder,” The Annals of Applied Statistics, 4, 849–870. DOI: 10.1214/09-AOAS315.
   Web of Science ®Google Scholar
• Ichino, A., Mealli, F., and Nannicini, T. (2008), “From Temporary Help Jobs to Permanent Employment: What can we learn from Matching Estimators and their Sensitivity?” Journal of Applied Econometrics, 23, 305–327. DOI: 10.1002/jae.998.
   Web of Science ®Google Scholar
• Imbens, G. W. (2003), “Sensitivity to Exogeneity Assumptions in Program Evaluation,” American Economic Review P&P, 93, 126–132. DOI: 10.1257/000282803321946921.
   Web of Science ®Google Scholar
• Imbens, G. W. (2004), “Nonparametric Estimation of Average Treatment Effects under Exogeneity: A Review,” The Review of Economics and Statistics, 86, 4–29.
   Web of Science ®Google Scholar
• Imbens, G. W., and Rubin, D. B. (2015), Causal Inference for Statistics, Social, and Biomedical Sciences, New York: Cambridge University Press.
   Google Scholar
• Imbens, G. W., and Wooldridge, J. M. (2009), “Recent Developments in the Econometrics of Program Evaluation,” Journal of Economic Literature, 47, 5–86. DOI: 10.1257/jel.47.1.5.
   Web of Science ®Google Scholar
• Kallus, N., Mao, X., and Zhou, A. (2019), “Interval Estimation of Individual-Level Causal Effects under Unobserved Confounding,” in The 22nd International Conference on Artificial Intelligence and Statistics, pp. 2281–2290.
   Google Scholar
• Krauth, B. (2016), “Bounding a Linear Causal Effect using Relative Correlation Restrictions,” Journal of Econometric Methods, 5, 117–141. DOI: 10.1515/jem-2013-0013.
   Google Scholar
• LaLonde, R. J. (1986), “Evaluating the Econometric Evaluations of Training Programs with Experimental Data,” The American Economic Review, 76, 604–620.
   Web of Science ®Google Scholar
• Manpower Demonstration Research Corporation (MDRC). (1980), Summary and Findings of the National Supported Work Demonstration, Cambridge, MA: Ballinger Publishing Company.
   Google Scholar
• Manski, C. F. (1990), “Nonparametric Bounds on Treatment Effects,” American Economic Review P&P, 80, 319–323.
   Web of Science ®Google Scholar
• Masten, M. A., and Poirier, A. (2018), “Identification of Treatment Effects under Conditional Partial Independence,” Econometrica, 86, 317–351. DOI: 10.3982/ECTA14481.
   Web of Science ®Google Scholar
• Masten, M. A., and Poirier, A. (2020), “Inference on Breakdown Frontiers,” Quantitative Economics, 11, 41–111.
   Web of Science ®Google Scholar
• Oster, E. (2019), “Unobservable Selection and Coefficient Stability: Theory and Evidence,” Journal of Business & Economic Statistics, 37, 187–204. DOI: 10.1080/07350015.2016.1227711.
   Web of Science ®Google Scholar
• Robins, J. M., Rotnitzky, A., and Scharfstein, D. O. (2000), “Sensitivity Analysis for Selection Bias and Unmeasured Confounding in Missing Data and Causal Inference Models,” in Statistical models in Epidemiology, the Environment, and Clinical Trials, eds. M. Elizabeth Halloran and D. Berry, pp. 1–94, New York: Springer.
   Google Scholar
• Rosenbaum, P. R. (1984), “Conditional Permutation Tests and the Propensity Score in Observational Studies,” Journal of the American Statistical Association, 79, 565–574. DOI: 10.1080/01621459.1984.10478082.
   Web of Science ®Google Scholar
• Rosenbaum, P. R. (1987), “Sensitivity Analysis for Certain Permutation Inferences in Matched Observational Studies,” Biometrika, 74, 13–26.
   Web of Science ®Google Scholar
• Rosenbaum, P. R. (1988), “Sensitivity Analysis for Matching with Multiple Controls,” Biometrika, 75, 577–581.
   Web of Science ®Google Scholar
• Rosenbaum, P. R. (1991), “Sensitivity Analysis for Matched Case-Control Studies,” Biometrics, 47, 87–100.
   PubMed Web of Science ®Google Scholar
• Rosenbaum, P. R. (1995), Observational Studies, New York: Springer.
   Google Scholar
• Rosenbaum, P. R. (2018), “Sensitivity Analysis for Stratified Comparisons in an Observational Study of the Effect of Smoking on Homocysteine Levels,” The Annals of Applied Statistics, 12, 2312–2334.
   Web of Science ®Google Scholar
• Rosenbaum, P. R., and Rubin, D. B. (1983): “Assessing Sensitivity to an Unobserved Binary Covariate in an Observational Study with Binary Outcome,” Journal of the Royal Statistical Society, Series B, 45, 212–218. DOI: 10.1111/j.2517-6161.1983.tb01242.x.
   Google Scholar
• van der Vaart, A., and Wellner, J. (1996), Weak Convergence and Empirical Processes: With Applications to Statistics, New York: Springer.
   Google Scholar