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Aggregation and the Estimated Effects of School Resources

  • Eric A. Hanushek
  • Steven G. Rivkin
  • Lori L. Taylor

This paper attempts to reconcile the contradictory findings in the debate over school resources and school effectiveness by highlighting the role of aggregation in the presence of omitted variables bias. While data aggregation for well-specified linear models yields unbiased parameter estimates, aggregation alters the magnitude of any omitted variables bias. In general, the theoretical impact of aggregation is ambiguous. In a very relevant special case where omitted variables relate to state differences in school policy, however, aggregation implies clear upward bias of estimated school resource effects. Analysis of High School and Beyond data provides strong evidence that aggregation inflates the coefficients on school resources. Moreover, the pattern of results is not consistent with an errors-in-variables explanation, the alternative explanation for the larger estimated impact with aggregate estimates. Since studies using aggregate data are much more likely to find positive school resource effects on achievement, these results provide further support to the view that additional expenditures alone are unlikely to improve student outcomes.

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File URL: http://www.nber.org/papers/w5548.pdf
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Paper provided by National Bureau of Economic Research, Inc in its series NBER Working Papers with number 5548.

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Date of creation: Apr 1996
Date of revision:
Publication status: published as Review of Economics and Statistics, 78(4), November 1996, pp.611-627.
Handle: RePEc:nbr:nberwo:5548
Note: LS
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  1. George E. Johnson & Frank P. Stafford, 1973. "Social Returns to Quantity and Quality of Schooling," Journal of Human Resources, University of Wisconsin Press, vol. 8(2), pages 139-155.
  2. Borjas, George J, 1987. "Self-Selection and the Earnings of Immigrants," American Economic Review, American Economic Association, vol. 77(4), pages 531-53, September.
  3. Bishop, John, 1992. "The impact of academic competencies on wages, unemployment, and job performance," Carnegie-Rochester Conference Series on Public Policy, Elsevier, vol. 37(1), pages 127-194, December.
  4. Hanushek, Eric A., 2006. "School Resources," Handbook of the Economics of Education, Elsevier.
  5. Pakes, Ariel, 1982. "On the Asymptotic Bias of Wald-Type Estimators of a Straight Line When Both Variables Are Subject to Error," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 23(2), pages 491-97, June.
  6. Summers, Anita A & Wolfe, Barbara L, 1977. "Do Schools Make a Difference?," American Economic Review, American Economic Association, vol. 67(4), pages 639-52, September.
  7. Moulton, Brent R., 1986. "Random group effects and the precision of regression estimates," Journal of Econometrics, Elsevier, vol. 32(3), pages 385-397, August.
  8. Charles M. Tiebout, 1956. "A Pure Theory of Local Expenditures," Journal of Political Economy, University of Chicago Press, vol. 64, pages 416.
  9. Swamy, P A V B, 1970. "Efficient Inference in a Random Coefficient Regression Model," Econometrica, Econometric Society, vol. 38(2), pages 311-23, March.
  10. Hanushek, E.A. & Rivkin, S.G., 1994. "Understanding the 20th Century Explosion in U.S. School Costs," RCER Working Papers 388, University of Rochester - Center for Economic Research (RCER).
  11. Betts, Julian R, 1995. "Does School Quality Matter? Evidence from the National Longitudinal Survey of Youth," The Review of Economics and Statistics, MIT Press, vol. 77(2), pages 231-50, May.
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