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Inference with "Difference in Differences" with a Small Number of Policy Changes

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  • Timothy G. Conley

    (Booth School of Business, University of Chicago)

  • Christopher R. Taber

    (University of Wisconsin-–Madison)

Abstract

In difference-in-differences applications, identification of the key parameter often arises from changes in policy by a small number of groups. In contrast, typical inference assumes that the number of groups changing policy is large. We present an alternative inference approach for a small (finite) number of policy changers, using information from a large sample of nonchanging groups. Treatment effect point estimators are not consistent, but we can consistently estimate their asymptotic distribution under any point null hypothesis about the treatment. Thus, treatment point estimators can be used as test statistics, and confidence intervals can be constructed using test statistic inversion. © 2011 The President and Fellows of Harvard College and the Massachusetts Institute of Technology.

Suggested Citation

  • Timothy G. Conley & Christopher R. Taber, 2011. "Inference with "Difference in Differences" with a Small Number of Policy Changes," The Review of Economics and Statistics, MIT Press, vol. 93(1), pages 113-125, February.
    • Handle: RePEc:tpr:restat:v:93:y:2011:i:1:p:113-125
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    1. Dynarski, Susan, 2000. "Hope for Whom? Financial Aid for the Middle Class and Its Impact on College Attendance," National Tax Journal, National Tax Association;National Tax Journal, vol. 53(3), pages 629-662, September.
    2. Matzkin, Rosa L., 1986. "Restrictions of economic theory in nonparametric methods," Handbook of Econometrics, in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 42, pages 2523-2558, Elsevier.
    3. Card, David & Krueger, Alan B, 1994. "Minimum Wages and Employment: A Case Study of the Fast-Food Industry in New Jersey and Pennsylvania," American Economic Review, American Economic Association, vol. 84(4), pages 772-793, September.
    4. Jonathan Gruber & Phillip Levine & Douglas Staiger, 1999. "Abortion Legalization and Child Living Circumstances: Who is the "Marginal Child"?," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 114(1), pages 263-291.
    5. David Card, 1990. "The Impact of the Mariel Boatlift on the Miami Labor Market," ILR Review, Cornell University, ILR School, vol. 43(2), pages 245-257, January.
    6. Angrist, Joshua D. & Krueger, Alan B., 1999. "Empirical strategies in labor economics," Handbook of Labor Economics, in: O. Ashenfelter & D. Card (ed.), Handbook of Labor Economics, edition 1, volume 3, chapter 23, pages 1277-1366, Elsevier.
    7. Amemiya, Takeshi, 1978. "A Note on a Random Coefficients Model," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 19(3), pages 793-796, October.
    8. Gary Chamberlain, 1980. "Analysis of Covariance with Qualitative Data," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 47(1), pages 225-238.
    9. Anderson, Patricia M. & Meyer, Bruce D., 2000. "The effects of the unemployment insurance payroll tax on wages, employment, claims and denials," Journal of Public Economics, Elsevier, vol. 78(1-2), pages 81-106, October.
    10. Susan Athey & Guido W. Imbens, 2006. "Identification and Inference in Nonlinear Difference-in-Differences Models," Econometrica, Econometric Society, vol. 74(2), pages 431-497, March.
    11. Newey, Whitney K. & McFadden, Daniel, 1986. "Large sample estimation and hypothesis testing," Handbook of Econometrics, in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 36, pages 2111-2245, Elsevier.
    12. Susan Dynarski, 2004. "The New Merit Aid," NBER Chapters, in: College Choices: The Economics of Where to Go, When to Go, and How to Pay For It, pages 63-100, National Bureau of Economic Research, Inc.
    13. Gary T. Henry & Ross Rubenstein, 2002. "Paying for grades: Impact of merit-based financial aid on educational quality," Journal of Policy Analysis and Management, John Wiley & Sons, Ltd., vol. 21(1), pages 93-109.
    14. Stephen G. Donald & Kevin Lang, 2007. "Inference with Difference-in-Differences and Other Panel Data," The Review of Economics and Statistics, MIT Press, vol. 89(2), pages 221-233, May.
    15. Gallant, A Ronald & Nychka, Douglas W, 1987. "Semi-nonparametric Maximum Likelihood Estimation," Econometrica, Econometric Society, vol. 55(2), pages 363-390, March.
    16. Marianne Bertrand & Esther Duflo & Sendhil Mullainathan, 2004. "How Much Should We Trust Differences-In-Differences Estimates?," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 119(1), pages 249-275.
    17. Meyer, Bruce D, 1995. "Natural and Quasi-experiments in Economics," Journal of Business & Economic Statistics, American Statistical Association, vol. 13(2), pages 151-161, April.
    18. Christopher M. Cornwell & David B. Mustard & Deepa Sridhar, 2005. "The Enrollment Effects of Merit-Based Financial Aid: Evidence from Georgia's HOPE Scholarship," HEW 0501002, University Library of Munich, Germany.
    19. Moulton, Brent R, 1990. "An Illustration of a Pitfall in Estimating the Effects of Aggregate Variables on Micro Unit," The Review of Economics and Statistics, MIT Press, vol. 72(2), pages 334-338, May.
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