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Conditioning on the Probability of Selection to Control Selection Bias

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  • Joshua D. Angrist

Abstract

Problems of sample selection arise in the analysis of both experimental and non-experimental data. In clinical trials to evaluate the impact of an intervention on health and mortality, treatment assignment is typically nonrandom in a sample of survivors even if the original assignment is random. Similarly, randomized training interventions like National Supported Work (NSW) are not necessarily randomly assigned in the sample of working men. A non- experimental version of this problem involves the use of instrumental variables (IV) to estimate behavioral relationships. A sample selection rule that is related to the instruments can induce correlation between the instruments and unobserved outcomes, possibly invalidating the use of conventional IV techniques in the selected sample. This paper shows that conditioning on the probability of selection given the instruments can provide a solution to the selection problem as long as the relationship between instruments and selection status satisfies a simple monotonicity condition. A latent index structure is not required for this result, which is motivated as an extension of earlier work on the propensity score. The conditioning approach to selection problems is illustrated using instrumental variables techniques to estimate the returns to schooling in a sample with positive earnings.

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Bibliographic Info

Paper provided by National Bureau of Economic Research, Inc in its series NBER Technical Working Papers with number 0181.

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Date of creation: Jun 1995
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Publication status: published as "Conditional independence in sample selection models" Economics Letters, Volume 54, Issue 2, February 1997, Pages 103-112
Handle: RePEc:nbr:nberte:0181

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  1. Olsen, Randall J, 1982. "Distributional Tests for Selectivity Bias and a More Robust Likelihood Estimator," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 23(1), pages 223-40, February.
  2. Joshua D. Angrist & Guido W. Imbens, 1995. "Average Causal Response with Variable Treatment Intensity," NBER Technical Working Papers, National Bureau of Economic Research, Inc 0127, National Bureau of Economic Research, Inc.
  3. Little, Roderick J A, 1985. "A Note about Models for Selectivity Bias," Econometrica, Econometric Society, Econometric Society, vol. 53(6), pages 1469-74, November.
  4. Joshua Angrist & Alan Krueger, 1990. "Does Compulsory School Attendance Affect Schooling and Earnings?," Working Papers, Princeton University, Department of Economics, Industrial Relations Section. 653, Princeton University, Department of Economics, Industrial Relations Section..
  5. J.D. Angrist & Guido W. Imbens & D.B. Rubin, 1993. "Identification of Causal Effects Using Instrumental Variables," NBER Technical Working Papers, National Bureau of Economic Research, Inc 0136, National Bureau of Economic Research, Inc.
  6. Joshua D. Angrist & Alan B. Krueger, 1990. "The Effect of Age at School Entry on Educational Attainment: An Application of Instrumental Variables with Moments from Two Samples," NBER Working Papers 3571, National Bureau of Economic Research, Inc.
  7. Heckman, James J, 1974. "Shadow Prices, Market Wages, and Labor Supply," Econometrica, Econometric Society, Econometric Society, vol. 42(4), pages 679-94, July.
  8. Ashenfelter, Orley & Ham, John, 1979. "Education, Unemployment, and Earnings," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 87(5), pages S99-116, October.
  9. Ham, John C & LaLonde, Robert J, 1996. "The Effect of Sample Selection and Initial Conditions in Duration Models: Evidence from Experimental Data on Training," Econometrica, Econometric Society, Econometric Society, vol. 64(1), pages 175-205, January.
  10. Lee, Lung-Fei, 1982. "Some Approaches to the Correction of Selectivity Bias," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 49(3), pages 355-72, July.
  11. Gronau, Reuben, 1974. "Wage Comparisons-A Selectivity Bias," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 82(6), pages 1119-43, Nov.-Dec..
  12. Chamberlain, Gary, 1986. "Asymptotic efficiency in semi-parametric models with censoring," Journal of Econometrics, Elsevier, Elsevier, vol. 32(2), pages 189-218, July.
  13. 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, Econometric Society, vol. 55(4), pages 765-99, July.
  14. David Card, 1994. "Earnings, Schooling, and Ability Revisited," NBER Working Papers 4832, National Bureau of Economic Research, Inc.
  15. Olsen, Randall J, 1980. "A Least Squares Correction for Selectivity Bias," Econometrica, Econometric Society, Econometric Society, vol. 48(7), pages 1815-20, November.
  16. repec:fth:prinin:331 is not listed on IDEAS
  17. Ahn, Hyungtaik & Powell, James L., 1993. "Semiparametric estimation of censored selection models with a nonparametric selection mechanism," Journal of Econometrics, Elsevier, Elsevier, vol. 58(1-2), pages 3-29, July.
  18. Jacob Mincer, 1991. "Education and Unemployment," NBER Working Papers 3838, National Bureau of Economic Research, Inc.
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