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Comparing principal stratification and selection models in parametric causal inference with nonignorable missingness


  • Mealli, Fabrizia
  • Pacini, Barbara


Two approaches for dealing with "endogenous selection" problems when estimating causal effects are considered. They are principal stratification and selection models. The main goal is to highlight similarities and differences between the two approaches, by investigating the different nature of their parametric hypotheses. The principal stratification approach focuses on information contained in specific subgroups of units. The aim is to produce valid inference conditional on such subgroups, without an a priori extension of the results to the whole population. Selection models, on the contrary, aim at estimating parameters that should be valid for the whole population, as if the data come from random sampling. A simulation study is conducted to show their different performances, with data generating processes coming from either approach. It is also argued that principal stratification is able to suggest alternative identification strategies not always easily translatable into assumptions of a selection model.

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  • Mealli, Fabrizia & Pacini, Barbara, 2008. "Comparing principal stratification and selection models in parametric causal inference with nonignorable missingness," Computational Statistics & Data Analysis, Elsevier, vol. 53(2), pages 507-516, December.
  • Handle: RePEc:eee:csdana:v:53:y:2008:i:2:p:507-516

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    References listed on IDEAS

    1. Donald B. Rubin, 2004. "Direct and Indirect Causal Effects via Potential Outcomes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 31(2), pages 161-170.
    2. Robinson, Peter M, 1988. "Root- N-Consistent Semiparametric Regression," Econometrica, Econometric Society, vol. 56(4), pages 931-954, July.
    3. Honore, Bo E. & Kyriazidou, Ekaterini & Udry, Christopher, 1997. "Estimation of Type 3 Tobit models using symmetric trimming and pairwise comparisons," Journal of Econometrics, Elsevier, vol. 76(1-2), pages 107-128.
    4. A. Mattei & F. Mealli, 2007. "Application of the Principal Stratification Approach to the Faenza Randomized Experiment on Breast Self-Examination," Biometrics, The International Biometric Society, vol. 63(2), pages 437-446, June.
    5. Olsen, Randall J, 1980. "A Least Squares Correction for Selectivity Bias," Econometrica, Econometric Society, vol. 48(7), pages 1815-1820, November.
    6. Little, Roderick J A, 1985. "A Note about Models for Selectivity Bias," Econometrica, Econometric Society, vol. 53(6), pages 1469-1474, November.
    7. Francis Vella, 1998. "Estimating Models with Sample Selection Bias: A Survey," Journal of Human Resources, University of Wisconsin Press, vol. 33(1), pages 127-169.
    8. Newey, Whitney K, 1990. "Semiparametric Efficiency Bounds," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 5(2), pages 99-135, April-Jun.
    9. Christofides, Louis N, et al, 2003. "Recent Two-Stage Sample Selection Procedures with an Application to the Gender Wage Gap," Journal of Business & Economic Statistics, American Statistical Association, vol. 21(3), pages 396-405, July.
    10. Heckman, James J, 1990. "Varieties of Selection Bias," American Economic Review, American Economic Association, vol. 80(2), pages 313-318, May.
    11. Lee, Lung-fei, 1994. "Semiparametric two-stage estimation of sample selection models subject to Tobit-type selection rules," Journal of Econometrics, Elsevier, vol. 61(2), pages 305-344, April.
    12. Barnard J. & Frangakis C.E. & Hill J.L. & Rubin D.B., 2003. "Principal Stratification Approach to Broken Randomized Experiments: A Case Study of School Choice Vouchers in New York City," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 299-323, January.
    13. Ahn, Hyungtaik & Powell, James L., 1993. "Semiparametric estimation of censored selection models with a nonparametric selection mechanism," Journal of Econometrics, Elsevier, vol. 58(1-2), pages 3-29, July.
    14. Lee, Lung-Fei, 1983. "Generalized Econometric Models with Selectivity," Econometrica, Econometric Society, vol. 51(2), pages 507-512, March.
    15. Li, Qi & Wooldridge, Jeffrey M., 2002. "Semiparametric Estimation Of Partially Linear Models For Dependent Data With Generated Regressors," Econometric Theory, Cambridge University Press, vol. 18(03), pages 625-645, June.
    16. Lung-Fei Lee, 1982. "Some Approaches to the Correction of Selectivity Bias," Review of Economic Studies, Oxford University Press, vol. 49(3), pages 355-372.
    17. Heckman, James J, 1974. "Shadow Prices, Market Wages, and Labor Supply," Econometrica, Econometric Society, vol. 42(4), pages 679-694, July.
    18. Edward Vytlacil, 2002. "Independence, Monotonicity, and Latent Index Models: An Equivalence Result," Econometrica, Econometric Society, vol. 70(1), pages 331-341, January.
    19. Pagan, Adrian & Vella, Frank, 1989. "Diagnostic Tests for Models Based on Individual Data: A Survey," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 4(S), pages 29-59, Supplemen.
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    Cited by:

    1. Martin Huber & Giovanni Mellace, 2015. "Sharp Bounds on Causal Effects under Sample Selection," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 77(1), pages 129-151, February.
    2. Marra, Giampiero & Wyszynski, Karol, 2016. "Semi-parametric copula sample selection models for count responses," Computational Statistics & Data Analysis, Elsevier, vol. 104(C), pages 110-129.
    3. Marra, Giampiero & Radice, Rosalba, 2013. "Estimation of a regression spline sample selection model," Computational Statistics & Data Analysis, Elsevier, vol. 61(C), pages 158-173.
    4. Zhichao Jiang & Peng Ding & Zhi Geng, 2016. "Principal causal effect identification and surrogate end point evaluation by multiple trials," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(4), pages 829-848, September.
    5. Giovanni Mellace & Roberto Rocci, 2011. "Principal Stratification in sample selection problems with non normal error terms," CEIS Research Paper 194, Tor Vergata University, CEIS, revised 02 May 2011.

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