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Selection on Observed and Unobserved Variables: Assessing the Effectiveness of Catholic Schools

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  • Joseph G. Altonji
  • Todd E. Elder
  • Christopher R. Taber

Abstract

We develop estimation methods that use the amount of selection on the observables in a model as a guide to the amount of selection on the unobservables. We show that if the observed variables are a random subset of a large number of factors that influence the endogenous variable and the outcome of interest, then the relationship between the index of observables that determines the endogenous variable and the index that determines the outcome will be the same as the relationship between the indices of unobservables that determine the two variables. In some circumstances this fact may be used to identify the effect of the endogenous variable. We also propose an informal way to assess selectivity bias based on measuring the ratio of selection on unobservables to selection on observables that would be required if one is to attribute the entire effect of the endogenous variable to selection bias. We use our methods to estimate the effect of attending a Catholic high school on a variety of outcomes. Our main conclusion is that Catholic high schools substantially increase the probability of graduating from high school and, more tentatively, college attendance. We do not find much evidence for an effect on test scores.

Suggested Citation

  • Joseph G. Altonji & Todd E. Elder & Christopher R. Taber, 2000. "Selection on Observed and Unobserved Variables: Assessing the Effectiveness of Catholic Schools," NBER Working Papers 7831, National Bureau of Economic Research, Inc.
  • Handle: RePEc:nbr:nberwo:7831
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    References listed on IDEAS

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    1. Stephen V. Cameron & James J. Heckman, 1998. "Life Cycle Schooling and Dynamic Selection Bias: Models and Evidence for Five Cohorts of American Males," Journal of Political Economy, University of Chicago Press, vol. 106(2), pages 262-333, April.
    2. Stephen V. Cameron & Christopher Taber, 2004. "Estimation of Educational Borrowing Constraints Using Returns to Schooling," Journal of Political Economy, University of Chicago Press, vol. 112(1), pages 132-182, February.
    3. Sims,Christopher A. (ed.), 1994. "Advances in Econometrics," Cambridge Books, Cambridge University Press, number 9780521444606.
    4. Poterba, James M & Venti, Steven F & Wise, David A, 1994. "Targeted Retirement Saving and the Net Worth of Elderly Americans," American Economic Review, American Economic Association, vol. 84(2), pages 180-185, May.
    5. Kevin M. Murphy & Robert H. Topel, 1990. "Efficiency Wages Reconsidered: Theory and Evidence," Palgrave Macmillan Books, in: Yoram Weiss & Gideon Fishelson (ed.), Advances in the Theory and Measurement of Unemployment, chapter 8, pages 204-240, Palgrave Macmillan.
    6. Joseph G. Altonji & Todd E. Elder & Christopher R. Taber, 2002. "An Evaluation of Instrumental Variable Strategies for Estimating the Effects of Catholic Schools," NBER Working Papers 9358, National Bureau of Economic Research, Inc.
    7. Currie, Janet & Thomas, Duncan, 1995. "Does Head Start Make a Difference?," American Economic Review, American Economic Association, vol. 85(3), pages 341-364, June.
    8. William N. Evans & Robert M. Schwab, 1995. "Finishing High School and Starting College: Do Catholic Schools Make a Difference?," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 110(4), pages 941-974.
    9. Christopher Jepsen, 2003. "The Effectiveness of Catholic Primary Schooling," Journal of Human Resources, University of Wisconsin Press, vol. 38(4).
    10. Heckman, James J, 1990. "Varieties of Selection Bias," American Economic Review, American Economic Association, vol. 80(2), pages 313-318, May.
    11. repec:eme:rlepps:v:18:y:1999:i:1999:p:115-140 is not listed on IDEAS
    12. Sims,Christopher A. (ed.), 1994. "Advances in Econometrics," Cambridge Books, Cambridge University Press, number 9780521444590.
    13. Charles F. Manski, 1989. "Anatomy of the Selection Problem," Journal of Human Resources, University of Wisconsin Press, vol. 24(3), pages 343-360.
    14. Bronars, Stephen G & Grogger, Jeff, 1994. "The Economic Consequences of Unwed Motherhood: Using Twin Births as a Natural Experiment," American Economic Review, American Economic Association, vol. 84(5), pages 1141-1156, December.
    15. 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.
    16. Stephen V. Cameron & James J. Heckman, 1998. "Life Cycle Schooling and Dynamic Selection Bias: Models and Evidence for Five Cohorts," NBER Working Papers 6385, National Bureau of Economic Research, Inc.
    17. Witte, John F., 1992. "Private school versus public school achievement: Are there findings that should affect the educational choice debate?," Economics of Education Review, Elsevier, vol. 11(4), pages 371-394, December.
    18. Derek Neal, 1998. "What have we learned about the benefits of private schooling?," Economic Policy Review, Federal Reserve Bank of New York, vol. 4(Mar), pages 79-86.
    19. Eric M. Engen & William G. Gale & John Karl Scholz, 1996. "The Illusory Effects of Saving Incentives on Saving," Journal of Economic Perspectives, American Economic Association, vol. 10(4), pages 113-138, Fall.
    20. Richard J. Murnane, 1984. "A Review Essay-Comparisons of Public and Private Schools: Lessons from the Uproar," Journal of Human Resources, University of Wisconsin Press, vol. 19(2), pages 263-277.
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    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • I2 - Health, Education, and Welfare - - Education

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