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Partial Identification and Sensitivity Analysis

  • Markus GanglEmail author
Chapter
Part of the Handbooks of Sociology and Social Research book series (HSSR)

Abstract

This chapter is concerned with methods of causal inference in the presence of unobserved confounders. Three classes of estimators are discussed, namely, local identification using instrumental variables, sensitivity analysis, and estimation of nonparametric bounds. In each case, the response to the core identification problem is to retreat from the standard focus on point identification of the average treatment effect, yet the three approaches characteristically differ in terms of alternative quantities of interest that are considered empirically estimable under more restrictive circumstances. The chapter develops the basic principles underlying the three classes of partial identification estimators and illustrates their empirical application with an analysis of earnings returns to education.

Keywords

Ordinary Little Square Instrumental Variable Average Treatment Effect Fixed Effect Ordinary Little Square Estimate 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgments

The GSOEP data have kindly been provided by the Deutsche Institut für Wirtschaftsforschung (DIW), Berlin. Of course, the DIW does not bear any responsibility for the uses made of the data, nor the inferences drawn by the author. I thank Stephen Morgan, Jan Brülle, and Fabian Ochsenfeld for helpful comments on an earlier draft of this chapter.

References

  1. Allison, P. D. (1994). Using panel data to estimate the effects of events. Sociological Methods & Research, 23, 174–199.CrossRefGoogle Scholar
  2. Angrist, J. D. (1990). Lifetime earnings and the Vietnam era draft lottery: Evidence from Social Security Administrative records. American Economic Review, 80, 313–335.Google Scholar
  3. Angrist, J. D. (2004). Treatment effect heterogeneity in theory and practice. Economic Journal, 114, C52–C83.CrossRefGoogle Scholar
  4. Angrist, J. D., & Evans, W. N. (1998). Children and their parents’ labor supply: Evidence from exogenous variation in family size. American Economic Review, 88, 450–477.Google Scholar
  5. Angrist, J. D., & Imbens, G. W. (1995). Two-stage least squares estimation of average causal effects in models with variable treatment intensity. Journal of the American Statistical Association, 90, 431–442.CrossRefGoogle Scholar
  6. Angrist, J. D., & Krueger, A. B. (2001). Instrumental variables and the search for identification: From supply and demand to natural experiments. Journal of Economic Perspectives, 15, 69–85.CrossRefGoogle Scholar
  7. Angrist, J. D., & Lavy, V. (1999). Using Maimonides’ rule to estimate the effect of class size on scholastic achievement. Quarterly Journal of Economics, 114, 533–575.CrossRefGoogle Scholar
  8. Angrist, J. D., & Pischke, J.-S. (2009). Mostly harmless econometrics. An empiricist’s companion. Princeton: Princeton University Press.Google Scholar
  9. Angrist, J. D., & Pischke, J.-S. (2010). The credibility revolution in empirical economics: How better research design is taking the con out of econometrics. Journal of Economic Perspectives, 24, 3–30.CrossRefGoogle Scholar
  10. Angrist, J. D., Imbens, G. W., & Rubin, D. B. (1996). Identification of causal effects using instrumental variables. Journal of the American Statistical Association, 91, 444–455.CrossRefGoogle Scholar
  11. Ashenfelter, O., & Rouse, C. (1998). Income, schooling, and ability: Evidence from a new sample of identical twins. Quarterly Journal of Economics, 113, 253–284.CrossRefGoogle Scholar
  12. Blau, P. M., & Duncan, O. D. (1967). The American occupational structure. New York: Free Press.Google Scholar
  13. Blundell, R., Gosling, A., Ichimura, H., & Meghir, C. (2007). Changes in the distribution of male and female wages accounting for employment composition using bounds. Econometrica, 75, 323–363.CrossRefGoogle Scholar
  14. Bound, J., Jaeger, D. A., & Baker, R. 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, 443–450.Google Scholar
  15. Card, D. (2001). Estimating the return to schooling: Progress on some persistent econometric problems. Econometrica, 69, 1127–1160.CrossRefGoogle Scholar
  16. DiPrete, T. A., & Gangl, M. (2004). Assessing bias in the estimation of causal effects: Rosenbaum bounds on matching estimators and instrumental variables estimation with imperfect instruments. Sociological Methodology, 34, 271–310.CrossRefGoogle Scholar
  17. Duncan, G. J., Jean Yeung, W., Brooks-Gunn, J., & Smith, J. R. (1998). How much does childhood poverty affect the life chances of children? American Sociological Review, 63, 406–423.CrossRefGoogle Scholar
  18. Frank, K. A. (2000). Impact of a confounding variable on a regression coefficient. Sociological Methods & Research, 29, 147–194.CrossRefGoogle Scholar
  19. Gangl, M. (2010). Causal inference in sociological research. Annual Review of Sociology, 36, 21–47.CrossRefGoogle Scholar
  20. Ganzeboom, H. B. G., & Treiman, D. J. (1996). Internationally comparable measures of occupational status for the 1988 international standard classification of occupations. Social Science Research, 25, 201–239.CrossRefGoogle Scholar
  21. Gastwirth, J. L., Krieger, A. M., & Rosenbaum, P. R. (1998). Dual and simultaneous sensitivity analysis for matched pairs. Biometrika, 85, 907–920.CrossRefGoogle Scholar
  22. Halaby, C. N. (2004). Panel models in sociological research: Theory into practice. Annual Review of Sociology, 30, 507–544.CrossRefGoogle Scholar
  23. Harding, D. J. (2003). Counterfactual models of neighborhood effects: The effect of neighborhood poverty on dropping out and teenage pregnancy. American Journal of Sociology, 109, 676–719.CrossRefGoogle Scholar
  24. Heckman, J. J. (1997). Instrumental variables: A study of implicit behavioral assumptions used in making program evaluations. Journal of Human Resources, 32, 441–462.CrossRefGoogle Scholar
  25. Heckman, J. J., & Urzúa, S. (2010). Comparing IV with structural models: What simple IV can and cannot identify. Journal of Econometrics, 156, 27–37.CrossRefGoogle Scholar
  26. Ichino, A., Mealli, F., & 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.CrossRefGoogle Scholar
  27. Imbens, G. W. (2003). Sensitivity to exogeneity assumptions in program evaluation. American Economic Review, 93, 126–132.CrossRefGoogle Scholar
  28. Imbens, G. W. (2010). Better LATE than nothing: Some comments on Deaton (2009) and Heckman and Urzua (2009). Journal of Economic Literature, 48, 399–423.CrossRefGoogle Scholar
  29. Imbens, G. W., & Angrist, J. D. (1994). Identification and estimation of local average treatment effects. Econometrica, 62, 467–475.CrossRefGoogle Scholar
  30. Imbens, G. W., & Rubin, D. B. (1997). Estimating outcome distributions for compliers in instrumental variables models. Review of Economic Studies, 64, 555–574.CrossRefGoogle Scholar
  31. Kirk, D. S. (2009). A natural experiment on residential change and recidivism: Lessons from Hurricane Katrina. American Sociological Review, 74, 484–505.CrossRefGoogle Scholar
  32. Lash, T. L., Fox, M. P., & Fink, A. K. (2009). Applying quantitative bias analysis to epidemiologic data. New York: Springer.CrossRefGoogle Scholar
  33. Lin, D. Y., Psaty, B. M., & Kronmal, R. A. (1998). Assessing the sensitivity of regression results to unmeasured confounders in observational studies. Biometrics, 54, 948–963.CrossRefGoogle Scholar
  34. Manski, C. F. (1995). Identification problems in the social sciences. Cambridge: Harvard University Press.Google Scholar
  35. Manski, C. F. (1997). Monotone treatment response. Econometrica, 65, 1311–1334.CrossRefGoogle Scholar
  36. Manski, C. F. (2003). Partial identification of probability distributions. New York: Springer.Google Scholar
  37. Manski, C. F. (2007). Identification for prediction and decision. Cambridge: Harvard University Press.Google Scholar
  38. Manski, C. F. (2011). Policy analysis with incredible certitude. Economic Journal, 121, F261–F289.CrossRefGoogle Scholar
  39. Manski, C. F., & Nagin, D. S. (1998). Bounding disagreements about treatment effects: A case study of sentencing and recidivism. Sociological Methodology, 28, 99–137.CrossRefGoogle Scholar
  40. Manski, C. F., & Pepper, J. V. (2000). Monotone instrumental variables: With an application to the returns to schooling. Econometrica, 68, 997–1010.CrossRefGoogle Scholar
  41. Manski, C. F., & Pepper, J. V. (2009). More on monotone instrumental variables. Econometrics Journal, 12, S200–S216.CrossRefGoogle Scholar
  42. Manski, C. F., Sandefur, G. D., McLanahan, S., & Powers, D. (1992). Alternative estimates of the effect of family structure during adolescence on high school graduation. Journal of the American Statistical Association, 87, 25–37.CrossRefGoogle Scholar
  43. Mauro, R. (1990). Understanding L.O.V.E. (left out variables error): A method for estimating the effects of omitted variables. Psychological Bulletin, 108, 314–329.CrossRefGoogle Scholar
  44. Morgan, S. L. (2005). On the edge of commitment: Educational attainment and race in the United States. Stanford: Stanford University Press.Google Scholar
  45. Morgan, S. L., & Winship, C. (2007). Counterfactuals and causal inference. Methods and principles for social research. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  46. Müller, W., & Karle, W. (1993). Social selection in educational systems in Europe. European Sociological Review, 9, 1–23.Google Scholar
  47. Pearl, J. (2009). Causality. Models, reasoning and inference (2nd ed.). Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  48. Robins, J. M. (1999). Association, causation, and marginal structural models. Synthese, 121, 151–179.CrossRefGoogle Scholar
  49. Rosenbaum, P. R. (2002). Observational studies (2nd ed.). New York: Springer.CrossRefGoogle Scholar
  50. Rosenbaum, P. R., & Rubin, D. B. (1983). Assessing sensitivity to an unobserved binary covariate in an observational study with binary outcome. Journal of the Royal Statistical Society B, 45, 212–218.Google Scholar
  51. Rosenzweig, M. R., & Wolpin, K. I. (2000). Natural ‘natural experiments’ in economics. Journal of Economic Literature, 38, 827–874.CrossRefGoogle Scholar
  52. Sharkey, P., & Elwert, F. (2011). The legacy of disadvantage: Multigenerational neighborhood effects on cognitive ability. American Journal of Sociology, 116, 1934–1981.CrossRefGoogle Scholar
  53. Staiger, D., & Stock, J. H. (1997). Instrumental variables regression with weak instruments. Econometrica, 65, 557–586.CrossRefGoogle Scholar
  54. Stock, J. H., & Yogo, M. (2005a). Asymptotic distributions of instrumental variables statistics with many weak instruments. In J. H. Stock & D. W. K. Andrews (Eds.), Identification and inference for econometric models: Essays in Honor of Thomas J. Rothenberg (pp. 109–120). Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  55. Stock, J., & Yogo, M. (2005b). Testing for weak instruments in linear IV regression. In J. H. Stock & D. W. K. Andrews (Eds.), Identification and inference for econometric models: Essays in Honor of Thomas J. Rothenberg (pp. 80–108). Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  56. VanderWeele, T. J. (2011). Sensitivity analysis for contagion effects in social networks. Sociological Methods & Research, 40, 240–255.CrossRefGoogle Scholar
  57. VanderWeele, T. J., & Arah, O. A. (2011). Bias formulas for sensitivity analysis of unmeasured confounding for general outcomes, treatments, and confounders. Epidemiology, 22, 42–52.CrossRefGoogle Scholar
  58. Wagner, G. G., Frick, J. R., & Schupp, J. (2007). The German Socio-Economic Panel Study (SOEP) – Scope, evolution and enhancements. Schmollers Jahrbuch, 127, 139–169.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Department of Social SciencesJ.W. Goethe University Frankfurt am MainFrankfurt am MainGermany
  2. 2.Department of SociologyUniversity of Wisconsin-MadisonMadisonUSA

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