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Statistical verification of a natural "natural experiment": Tests and sensitivity checks for the sibling sex ratio instrument

  • Huber, Martin


This paper presents statistical evidence about the validity of the sibling sex ratio instrument proposed by Angrist and Evans (1998), a prominent natural “natural experiment” in the sense of Rosenzweig and Wolpin (2000). The sex ratio of the first two siblings is arguably randomly assigned and influences the probability of having a third child, which makes it a candidate instrument for fertility when estimating the effect of fertility on female labor supply. However, identification hinges on the satisfaction of the instrumental exclusion restriction and the monotonicity of fertility in the instrument, see Imbens and Angrist (1994). Using the methods of Kitagawa (2008), Huber and Mellace (2011a), and Huber and Mellace (2012), we for the first time verify the validity of the sibling sex ratio instrument by statistical hypothesis tests, which suggest that violations are small if not close to nonexistent. We also provide novel sensitivity checks to assess deviations from the exclusion restriction and/or monotonicity in the nonparametric local average treatment effect framework and find the negative labor supply effect of fertility to be robust to a plausible range of violations.

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Paper provided by University of St. Gallen, School of Economics and Political Science in its series Economics Working Paper Series with number 1219.

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Length: 43 pages
Date of creation: Aug 2012
Date of revision:
Handle: RePEc:usg:econwp:2012:19
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  1. repec:oup:restud:v:75:y:2008:i:4:p:1085-1120 is not listed on IDEAS
  2. Yoram Ben-Porath & Finis Welch, 1976. "Do Sex Preferences Really Matter?," The Quarterly Journal of Economics, Oxford University Press, vol. 90(2), pages 285-307.
  3. Jorg Stoye, 2009. "More on Confidence Intervals for Partially Identified Parameters," Econometrica, Econometric Society, vol. 77(4), pages 1299-1315, 07.
  4. 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 450-77, June.
  5. Martin Huber & Giovanni Mellace, 2010. "Sharp IV bounds on average treatment effects under endogeneity and noncompliance," University of St. Gallen Department of Economics working paper series 2010 2010-31, Department of Economics, University of St. Gallen.
  6. Hansen, Peter Reinhard, 2005. "A Test for Superior Predictive Ability," Journal of Business & Economic Statistics, American Statistical Association, vol. 23, pages 365-380, October.
  7. Donald, Stephen G. & Hsu, Yu-Chin, 2011. "A new test for linear inequality constraints when the variance–covariance matrix depends on the unknown parameters," Economics Letters, Elsevier, vol. 113(3), pages 241-243.
  8. Carlos A. Flores & Alfonso Flores-Lagunes, 2010. "Partial Identification of Local Average Treatment Effects with an Invalid Instrument," Working Papers 2010-24, University of Miami, Department of Economics.
  9. Aart Kraay, 2012. "Instrumental variables regressions with uncertain exclusion restrictions: a Bayesian approach," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 27(1), pages 108-128, 01.
  10. Aviv Nevo & Adam M. Rosen, 2008. "Identification with Imperfect Instruments," NBER Working Papers 14434, National Bureau of Economic Research, Inc.
  11. Goux, Dominique & Maurin, Eric, 2003. "The Effects of Overcrowded Housing on Children's Performance at School," CEPR Discussion Papers 3818, C.E.P.R. Discussion Papers.
  12. 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.
  13. Sebastian Galiani & Guillermo Cruces, 2005. "Fertility and Female Labor Supply in Latin America: New Causal Evidence," Working Papers 84, Universidad de San Andres, Departamento de Economia, revised Jun 2007.
  14. Michael P. Murray, 2006. "Avoiding Invalid Instruments and Coping with Weak Instruments," Journal of Economic Perspectives, American Economic Association, vol. 20(4), pages 111-132, Fall.
  15. repec:ese:iserwp:2001-19 is not listed on IDEAS
  16. Joshua Angrist, 1989. "Lifetime Earnings and the Vietnam Era Draft Lottery: Evidence from Social Security Administrative Records," Working Papers 631, Princeton University, Department of Economics, Industrial Relations Section..
  17. Orley Ashenfelter & Alan Krueger, 1992. "Estimates of the Economic Return to Schooling from a New Sample of Twins," Working Papers 683, Princeton University, Department of Economics, Industrial Relations Section..
  18. Steven D. Levitt, 1995. "Using Electoral Cycles in Police Hiring to Estimate the Effect of Policeon Crime," NBER Working Papers 4991, National Bureau of Economic Research, Inc.
  19. Lee, Jungmin, 2004. "Sibling Size and Investment in Children's Education: An Asian Instrument," IZA Discussion Papers 1323, Institute for the Study of Labor (IZA).
  20. Small, Dylan S., 2007. "Sensitivity Analysis for Instrumental Variables Regression With Overidentifying Restrictions," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 1049-1058, September.
  21. Guido W. Imbens & Donald B. Rubin, 1997. "Estimating Outcome Distributions for Compliers in Instrumental Variables Models," Review of Economic Studies, Oxford University Press, vol. 64(4), pages 555-574.
  22. Le-Yu Chen & Jerzy Szroeter, 2009. "Hypothesis testing of multiple inequalities: the method of constraint chaining," CeMMAP working papers CWP13/09, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  23. Jin‐young Choi & Myoung‐jae Lee, 2012. "Bounding endogenous regressor coefficients using moment inequalities and generalized instruments," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 66(2), pages 161-182, 05.
  24. Killingsworth, Mark R. & Heckman, James J., 1987. "Female labor supply: A survey," Handbook of Labor Economics, in: O. Ashenfelter & R. Layard (ed.), Handbook of Labor Economics, edition 1, volume 1, chapter 2, pages 103-204 Elsevier.
  25. Dalton Conley & Rebecca Glauber, 2005. "Parental Educational Investment and Children's Academic Risk: Estimates of the Impact of Sibship Size and Birth Order from Exogenous Variations in Fertility," NBER Working Papers 11302, National Bureau of Economic Research, Inc.
  26. Joshua Angrist & Victor Lavy & Analia Schlosser, 2010. "Multiple Experiments for the Causal Link between the Quantity and Quality of Children," Journal of Labor Economics, University of Chicago Press, vol. 28(4), pages 773-824, October.
  27. Angrist, Joshua D, 1990. "Lifetime Earnings and the Vietnam Era Draft Lottery: Evidence from Social Security Administrative Records: Errata," American Economic Review, American Economic Association, vol. 80(5), pages 1284-86, December.
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