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Difference in Generalized-Differences with Panel Data: Effects of Moving from Private to Public School on Test Scores

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  • Myoung-jae Lee

    ()
    (Department of Economics, Korea University)

Abstract

Difference in differences (DD) relies on the key identifying condition that the untreated response variable would have grown equally across the control and treatment groups; i.e., the ¡®time effects¡¯ across the groups are the same. This condition can be rewritten as the ¡®group effects¡¯ across the time points being the same, with which this paper generalizes DD to difference in generalized-differences (DG). DG is indexed by a parameter ¥ç, and includes DD as a special case when ¥ç = 1. This makes it possible to use DG as a sensitivity analysis for DD by trying values of ¥ç other than one. Going further from sensitivity analysis, one may desire to fix ¥ç. For this, we provide a way to get a benchmark value of ¥ç using a dynamic panel data model for the control group. An empirical analysis is provided for the effects of moving from private to public school on test scores. In the empirical analysis, (i) DD magnitude is fairly sensitive to changes in ¥ç around one, but its statistical significance is not, (ii) ¥ç is significantly smaller than one in math score (and possibly in science score), and (iii) DG yields a significant negative effect of about 3-5% for reading score, but the effects are ambiguous or insignificant for the other scores. ¥ç being less than 1 means that, had the movers to public school stayed, the score gap between the movers and stayers would have narrowed. That is, the move to public school is likely to have been involuntary.

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File URL: http://econ.korea.ac.kr/~ri/WorkingPapers/W0721.pdf
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Bibliographic Info

Paper provided by Institute of Economic Research, Korea University in its series Discussion Paper Series with number 0721.

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Length: 30 pages
Date of creation: 2007
Date of revision:
Handle: RePEc:iek:wpaper:0721

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Keywords: treatment effect; difference in differences; panel data; private-school effect;

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  1. Myoung-jae Lee & Unto Häkkinen & Gunnar Rosenqvist, 2007. "Finding the best treatment under heavy censoring and hidden bias," Journal of the Royal Statistical Society Series A, Royal Statistical Society, Royal Statistical Society, vol. 170(1), pages 133-147.
  2. Cecilia Elena Rouse, 1998. "Private School Vouchers And Student Achievement: An Evaluation Of The Milwaukee Parental Choice Program," The Quarterly Journal of Economics, MIT Press, MIT Press, vol. 113(2), pages 553-602, May.
  3. Derek Neal, 2002. "How Vouchers Could Change the Market for Education," Journal of Economic Perspectives, American Economic Association, American Economic Association, vol. 16(4), pages 25-44, Fall.
  4. LaLonde, Robert J, 1986. "Evaluating the Econometric Evaluations of Training Programs with Experimental Data," American Economic Review, American Economic Association, American Economic Association, vol. 76(4), pages 604-20, September.
  5. Julie Berry Cullen & Brian A. Jacob & Steven Levitt, 2003. "The Effect of School Choice on Student Outcomes: Evidence from Randomized Lotteries," NBER Working Papers 10113, National Bureau of Economic Research, Inc.
  6. Guildo W. Imbens, 2003. "Sensitivity to Exogeneity Assumptions in Program Evaluation," American Economic Review, American Economic Association, American Economic Association, vol. 93(2), pages 126-132, May.
  7. Meyer, Bruce D, 1995. "Natural and Quasi-experiments in Economics," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 13(2), pages 151-61, April.
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