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Testing exclusion restrictions and additive separability in sample selection models

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  • Martin Huber
  • Giovanni Mellace

Abstract

Standard sample selection models with non-randomly censored outcomes assume (i) an exclusion restriction (i.e., a variable affecting selection, but not the outcome) and (ii) additive separability of the errors in the selection process. This paper proposes tests for the joint satisfaction of these assumptions by applying the approach of Huber and Mellace (Testing instrument validity for LATE identification based on inequality moment constraints, 2011 ) (for testing instrument validity under treatment endogeneity) to the sample selection framework. We show that the exclusion restriction and additive separability imply two testable inequality constraints that come from both point identifying and bounding the outcome distribution of the subpopulation that is always selected/observed. We apply the tests to two variables for which the exclusion restriction is frequently invoked in female wage regressions: non-wife/husband’s income and the number of (young) children. Considering eight empirical applications, our results suggest that the identifying assumptions are likely violated for the former variable, but cannot be refuted for the latter on statistical grounds. Copyright Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • Martin Huber & Giovanni Mellace, 2014. "Testing exclusion restrictions and additive separability in sample selection models," Empirical Economics, Springer, vol. 47(1), pages 75-92, August.
    • Handle: RePEc:spr:empeco:v:47:y:2014:i:1:p:75-92
    DOI: 10.1007/s00181-013-0742-1
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    as
    1. Chen, Le-Yu & Szroeter, Jerzy, 2014. "Testing multiple inequality hypotheses: A smoothed indicator approach," Journal of Econometrics, Elsevier, vol. 178(P3), pages 678-693.
    2. Constantine E. Frangakis & Donald B. Rubin, 2002. "Principal Stratification in Causal Inference," Biometrics, The International Biometric Society, vol. 58(1), pages 21-29, March.
    3. James J. Heckman, 1976. "The Common Structure of Statistical Models of Truncation, Sample Selection and Limited Dependent Variables and a Simple Estimator for Such Models," NBER Chapters, in: Annals of Economic and Social Measurement, Volume 5, number 4, pages 475-492, National Bureau of Economic Research, Inc.
    4. Whitney K. Newey, 2007. "NONPARAMETRIC CONTINUOUS/DISCRETE CHOICE MODELS," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 48(4), pages 1429-1439, November.
    5. Gary S. Becker, 1981. "A Treatise on the Family," NBER Books, National Bureau of Economic Research, Inc, number beck81-1, March.
    6. Angrist, Joshua D & Evans, William N, 1998. "Children and Their Parents' Labor Supply: Evidence from Exogenous Variation in Family Size," American Economic Review, American Economic Association, vol. 88(3), pages 450-477, June.
    7. Martin Huber & Giovanni Mellace, 2015. "Testing Instrument Validity for LATE Identification Based on Inequality Moment Constraints," The Review of Economics and Statistics, MIT Press, vol. 97(2), pages 398-411, May.
    8. 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.
    9. Richard Blundell & Amanda Gosling & Hidehiko Ichimura & Costas Meghir, 2007. "Changes in the Distribution of Male and Female Wages Accounting for Employment Composition Using Bounds," Econometrica, Econometric Society, vol. 75(2), pages 323-363, March.
    10. Fleisher, Belton M & Rhodes, George F, Jr, 1979. "Fertility, Women's Wage Rates, and Labor Supply," American Economic Review, American Economic Association, vol. 69(1), pages 14-24, March.
    11. Heckman, James, 2013. "Sample selection bias as a specification error," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 31(3), pages 129-137.
    12. Barnett,William A. & Powell,James & Tauchen,George E. (ed.), 1991. "Nonparametric and Semiparametric Methods in Econometrics and Statistics," Cambridge Books, Cambridge University Press, number 9780521424318.
    13. Philip Oreopoulos & Daniel Lang & Joshua Angrist, 2009. "Incentives and Services for College Achievement: Evidence from a Randomized Trial," American Economic Journal: Applied Economics, American Economic Association, vol. 1(1), pages 136-163, January.
    14. Horowitz, Joel L & Manski, Charles F, 1995. "Identification and Robustness with Contaminated and Corrupted Data," Econometrica, Econometric Society, vol. 63(2), pages 281-302, March.
    15. Mroz, Thomas A, 1987. "The Sensitivity of an Empirical Model of Married Women's Hours of Work to Economic and Statistical Assumptions," Econometrica, Econometric Society, vol. 55(4), pages 765-799, July.
    16. Whitney K. Newey, 2009. "Two-step series estimation of sample selection models," Econometrics Journal, Royal Economic Society, vol. 12(s1), pages 217-229, January.
    17. Heckman, James J, 1974. "Shadow Prices, Market Wages, and Labor Supply," Econometrica, Econometric Society, vol. 42(4), pages 679-694, July.
    18. Marcia M. A. Schafgans, 1998. "Ethnic wage differences in Malaysia: parametric and semiparametric estimation of the Chinese-Malay wage gap," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 13(5), pages 481-504.
    19. Zabel, Jeffrey E, 1993. "The Relationship between Hours of Work and Labor Force Participation in Four Models of Labor Supply Behavior," Journal of Labor Economics, University of Chicago Press, vol. 11(2), pages 387-416, April.
    20. Gallant, A Ronald & Nychka, Douglas W, 1987. "Semi-nonparametric Maximum Likelihood Estimation," Econometrica, Econometric Society, vol. 55(2), pages 363-390, March.
    21. Gronau, Reuben, 1974. "Wage Comparisons-A Selectivity Bias," Journal of Political Economy, University of Chicago Press, vol. 82(6), pages 1119-1143, Nov.-Dec..
    22. Horowitz, Joel L, 1992. "A Smoothed Maximum Score Estimator for the Binary Response Model," Econometrica, Econometric Society, vol. 60(3), pages 505-531, May.
    23. Crépon, Bruno, 2006. "Testing Exclusion Restrictions at Infinity in the Semiparametric Selection Model," IZA Discussion Papers 2035, Institute of Labor Economics (IZA).
    24. Joshua Angrist & Eric Bettinger & Michael Kremer, 2006. "Long-Term Educational Consequences of Secondary School Vouchers: Evidence from Administrative Records in Colombia," American Economic Review, American Economic Association, vol. 96(3), pages 847-862, June.
    25. Guido W. Imbens & Donald B. Rubin, 1997. "Estimating Outcome Distributions for Compliers in Instrumental Variables Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 64(4), pages 555-574.
    26. Mitali Das & Whitney K. Newey & Francis Vella, 2003. "Nonparametric Estimation of Sample Selection Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 70(1), pages 33-58.
    27. David S. Lee, 2009. "Training, Wages, and Sample Selection: Estimating Sharp Bounds on Treatment Effects," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 76(3), pages 1071-1102.
    28. Sheng‐Kai Chang, 2011. "Simulation estimation of two‐tiered dynamic panel Tobit models with an application to the labor supply of married women," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 26(5), pages 854-871, August.
    29. Casey B. Mulligan & Yona Rubinstein, 2008. "Selection, Investment, and Women's Relative Wages Over Time," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 123(3), pages 1061-1110.
    30. repec:mpr:mprres:2951 is not listed on IDEAS
    31. Edward Vytlacil, 2002. "Independence, Monotonicity, and Latent Index Models: An Equivalence Result," Econometrica, Econometric Society, vol. 70(1), pages 331-341, January.
    32. Barnett,William A. & Powell,James & Tauchen,George E. (ed.), 1991. "Nonparametric and Semiparametric Methods in Econometrics and Statistics," Cambridge Books, Cambridge University Press, number 9780521370905.
    33. Powell, James L., 1987. "Semiparametric Estimation Of Bivariate Latent Variable Models," SSRI Workshop Series 292689, University of Wisconsin-Madison, Social Systems Research Institute.
    34. Maria Fraga O. Martins, 2001. "Parametric and semiparametric estimation of sample selection models: an empirical application to the female labour force in Portugal," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 16(1), pages 23-39.
    35. Robert A. Nakosteen & Olle Westerlund & Michael A. Zimmer, 2004. "Marital Matching and Earnings: Evidence from the Unmarried Population in Sweden," Journal of Human Resources, University of Wisconsin Press, vol. 39(4).
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    More about this item

    Keywords

    Sample selection; Exclusion restriction; Additive separability; Monotonicity; Test ; C12; C15; C24; C26;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C24 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Truncated and Censored Models; Switching Regression Models; Threshold Regression Models
    • C26 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Instrumental Variables (IV) Estimation

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