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Partial Identification of Discrete Counterfactual Distributions with Sequential Update of Information

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  • Stefan Boes

    (Socioeconomic Institute, University of Zurich)

Abstract

The credibility of standard instrumental variables assumptions is often under dispute. This paper imposes weak monotonicity in order to gain information on counterfactual outcomes, but avoids independence or exclusion restrictions. The outcome process is assumed to be sequentially ordered, building up and depending on the information level of agents. The potential outcome distribution is assumed to weakly increase (or decrease) with the instrument, conditional on the continuation up to a certain stage. As a general result, the counterfactual distributions can only be bounded, but the derived bounds are informative compared to the no-assumptions bounds thus justifying the instrumental variables terminology. The construction of bounds is illustrated in two data examples.

Suggested Citation

  • Stefan Boes, 2009. "Partial Identification of Discrete Counterfactual Distributions with Sequential Update of Information," SOI - Working Papers 0918, Socioeconomic Institute - University of Zurich.
    • Handle: RePEc:soz:wpaper:0918
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    References listed on IDEAS

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    1. Manski, Charles F, 1990. "Nonparametric Bounds on Treatment Effects," American Economic Review, American Economic Association, vol. 80(2), pages 319-323, May.
    2. Flavio Cunha & James J. Heckman & Salvador Navarro, 2007. "The Identification And Economic Content Of Ordered Choice Models With Stochastic Thresholds," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 48(4), pages 1273-1309, November.
    3. Pedro Carneiro & Karsten T. Hansen & James J. Heckman, 2003. "Estimating Distributions of Treatment Effects with an Application to the Returns to Schooling and Measurement of the Effects of Uncertainty on College," NBER Working Papers 9546, National Bureau of Economic Research, Inc.
    4. James J. Heckman & Edward Vytlacil, 2005. "Structural Equations, Treatment Effects, and Econometric Policy Evaluation," Econometrica, Econometric Society, vol. 73(3), pages 669-738, May.
    5. Gary S. Becker & H. Gregg Lewis, 1974. "Interaction between Quantity and Quality of Children," NBER Chapters, in: Economics of the Family: Marriage, Children, and Human Capital, pages 81-90, National Bureau of Economic Research, Inc.
    6. Michael Lechner, 2008. "Matching estimation of dynamic treatment models: Some practical issues," Advances in Econometrics, in: Modelling and Evaluating Treatment Effects in Econometrics, pages 289-333, Emerald Group Publishing Limited.
    7. Kreider, Brent & Pepper, John V., 2007. "Disability and Employment: Reevaluating the Evidence in Light of Reporting Errors," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 432-441, June.
    8. Heckman, James J. & Navarro, Salvador, 2007. "Dynamic discrete choice and dynamic treatment effects," Journal of Econometrics, Elsevier, vol. 136(2), pages 341-396, February.
    9. Carneiro, Pedro & Hansen, Karsten T. & Heckman, James J., 2003. "Estimating Distributions of Treatment Effects with an Application to the Returns to Schooling and Measurement of the Effects of Uncertainty on College Choice," IZA Discussion Papers 767, Institute of Labor Economics (IZA).
    10. Massimiliano Bratti, 2003. "Labour force participation and marital fertility of Italian women: The role of education," Journal of Population Economics, Springer;European Society for Population Economics, vol. 16(3), pages 525-554, August.
    11. Takeshi Amemiya, 1975. "Qualitative Response Models," NBER Chapters, in: Annals of Economic and Social Measurement, Volume 4, number 3, pages 363-372, National Bureau of Economic Research, Inc.
    12. Zhang, Junsen, 1994. "Socioeconomic Determinants of Fertility in Hebei Province, China: An Application of the Sequential Logit Model," Economic Development and Cultural Change, University of Chicago Press, vol. 43(1), pages 67-90, October.
    13. Stefan Boes, 2013. "Nonparametric analysis of treatment effects in ordered response models," Empirical Economics, Springer, vol. 44(1), pages 81-109, February.
    14. Heckman, James J & Honore, Bo E, 1990. "The Empirical Content of the Roy Model," Econometrica, Econometric Society, vol. 58(5), pages 1121-1149, September.
    15. Manski, Charles F., 2000. "Identification problems and decisions under ambiguity: Empirical analysis of treatment response and normative analysis of treatment choice," Journal of Econometrics, Elsevier, vol. 95(2), pages 415-442, April.
    16. Pedro Carneiro & Karsten T. Hansen & James J. Heckman, 2003. "2001 Lawrence R. Klein Lecture Estimating Distributions of Treatment Effects with an Application to the Returns to Schooling and Measurement of the Effects of Uncertainty on College Choice," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 44(2), pages 361-422, May.
    17. Judith Blake, 1974. "Can we believe recent data on birth expectations in the United States?," Demography, Springer;Population Association of America (PAA), vol. 11(1), pages 25-44, February.
    18. Boulier, Bryan L & Rosenzweig, Mark R, 1984. "Schooling, Search, and Spouse Selection: Testing Economic Theories of Marriage and Household Behavior," Journal of Political Economy, University of Chicago Press, vol. 92(4), pages 712-732, August.
    19. David Lam & Suzanne Duryea, 1999. "Effects of Schooling on Fertility, Labor Supply, and Investments in Children, with Evidence from Brazil," Journal of Human Resources, University of Wisconsin Press, vol. 34(1), pages 160-192.
    20. Imbens, Guido W & Angrist, Joshua D, 1994. "Identification and Estimation of Local Average Treatment Effects," Econometrica, Econometric Society, vol. 62(2), pages 467-475, March.
    21. Michael Lechner & Ruth Miquel, 2010. "Identification of the effects of dynamic treatments by sequential conditional independence assumptions," Empirical Economics, Springer, vol. 39(1), pages 111-137, August.
    22. Rosenzweig, Mark R & Schultz, T Paul, 1985. "The Demand for and Supply of Births: Fertility and Its Life Cycle Consequences," American Economic Review, American Economic Association, vol. 75(5), pages 992-1015, December.
    23. Charles F. Manski & John V. Pepper, 2000. "Monotone Instrumental Variables, with an Application to the Returns to Schooling," Econometrica, Econometric Society, vol. 68(4), pages 997-1012, July.
    24. Pollak, R.A. & Watkins, S.C., 1993. "Cultural and Economic Approaches to Fertility : A Proper Marriage or a Mesalliance?," Discussion Papers in Economics at the University of Washington 93-11, Department of Economics at the University of Washington.
    25. Sander, William, 1992. "The effect of women's schooling on fertility," Economics Letters, Elsevier, vol. 40(2), pages 229-233, October.
    26. Charles F. Manski & John V. Pepper, 2009. "More on monotone instrumental variables," Econometrics Journal, Royal Economic Society, vol. 12(s1), pages 200-216, January.
    27. James J. Heckman, 2001. "Micro Data, Heterogeneity, and the Evaluation of Public Policy: Nobel Lecture," Journal of Political Economy, University of Chicago Press, vol. 109(4), pages 673-748, August.
    28. Basu, Alaka Malwade, 2002. "Why does Education Lead to Lower Fertility? A Critical Review of Some of the Possibilities," World Development, Elsevier, vol. 30(10), pages 1779-1790, October.
    29. Abbring, Jaap H. & Heckman, James J., 2007. "Econometric Evaluation of Social Programs, Part III: Distributional Treatment Effects, Dynamic Treatment Effects, Dynamic Discrete Choice, and General Equilibrium Policy Evaluation," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 72, Elsevier.
    30. Heckman, James J & Willis, Robert J, 1977. "A Beta-logistic Model for the Analysis of Sequential Labor Force Participation by Married Women," Journal of Political Economy, University of Chicago Press, vol. 85(1), pages 27-58, February.
    31. Flavio Cunha & James J. Heckman & Salvador Navarro, 2007. "The Identification & Economic Content of Ordered Choice Models with Stochastic Thresholds," Working Papers 200726, Geary Institute, University College Dublin.
    32. Lancaster,Tony, 1992. "The Econometric Analysis of Transition Data," Cambridge Books, Cambridge University Press, number 9780521437899, October.
    33. Lechner, Michael, 2009. "Sequential Causal Models for the Evaluation of Labor Market Programs," Journal of Business & Economic Statistics, American Statistical Association, vol. 27, pages 71-83.
    34. Azeem Shaikh & Edward Vytlacil, 2005. "Threshold Crossing Models and Bounds on Treatment Effects: A Nonparametric Analysis," NBER Technical Working Papers 0307, National Bureau of Economic Research, Inc.
    35. Kahn, Lawrence M & Morimune, Kimio, 1979. "Unions and Employment Stability: A Sequential Logit Approach," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 20(1), pages 217-235, February.
    36. A. D. Roy, 1951. "Some Thoughts On The Distribution Of Earnings," Oxford Economic Papers, Oxford University Press, vol. 3(2), pages 135-146.
    37. Jaap H. Abbring & Gerard J. van den Berg, 2003. "The Nonparametric Identification of Treatment Effects in Duration Models," Econometrica, Econometric Society, vol. 71(5), pages 1491-1517, September.
    38. Joshua D. Angrist & Guido W. Imbens & D.B. Rubin, 1993. "Identification of Causal Effects Using Instrumental Variables," NBER Technical Working Papers 0136, National Bureau of Economic Research, Inc.
    39. Cheng, Benjamin S. & Nwachukwu, Savior L. S., 1997. "The effect of education on fertility in Taiwan: A time series analysis," Economics Letters, Elsevier, vol. 56(1), pages 95-99, September.
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    Cited by:

    1. Stefan Boes, 2009. "Bounds on Counterfactual Distributions Under Semi-Monotonicity Constraints," SOI - Working Papers 0920, Socioeconomic Institute - University of Zurich.

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    More about this item

    Keywords

    nonparametric bounds; treatment effects; endogeneity; binary choice; monotone instrumental variables; policy evaluation;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C25 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions; Probabilities
    • C35 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions

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