IDEAS home Printed from https://ideas.repec.org/p/cla/levarc/506439000000000079.html
   My bibliography  Save this paper

Identification and Inference in Nonlinear Difference-in-Differences Models

Author

Listed:
  • Susan Athey
  • Guido Imbens

Abstract

This paper develops a generalization of the widely used difference-in-differences method for evaluating the effects of policy changes. We propose a model that allows the control and treatment groups to have different average benefits from the treatment. The assumptions of the proposed model are invariant to the scaling of the outcome. We provide conditions under which the model is nonparametrically identified and propose an estimator that can be applied using either repeated cross section or panel data. Our approach provides an estimate of the entire counterfactual distribution of outcomes that would have been experienced by the treatment group in the absence of the treatment and likewise for the untreated group in the presence of the treatment. Thus, it enables the evaluation of policy interventions according to criteria such as a mean-variance trade-off. We also propose methods for inference, showing that our estimator for the average treatment effect is root-N consistent and asymptotically normal. We consider extensions to allow for covariates, discrete dependent variables, and multiple groups and time periods. Copyright The Econometric Society 2006.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Susan Athey & Guido Imbens, 2003. "Identification and Inference in Nonlinear Difference-in-Differences Models," Levine's Working Paper Archive 506439000000000079, David K. Levine.
  • Handle: RePEc:cla:levarc:506439000000000079
    as

    Download full text from publisher

    File URL: http://www.dklevine.com/archive/refs4506439000000000079.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. 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.
    2. repec:fth:prinin:315 is not listed on IDEAS
    3. Esther Duflo, 2001. "Schooling and Labor Market Consequences of School Construction in Indonesia: Evidence from an Unusual Policy Experiment," American Economic Review, American Economic Association, vol. 91(4), pages 795-813, September.
    4. Manski, Charles F., 1992. "Identification Problems In The Social Sciences," SSRI Workshop Series 292716, University of Wisconsin-Madison, Social Systems Research Institute.
    5. Alberto Abadie & Joshua Angrist & Guido Imbens, 2002. "Instrumental Variables Estimates of the Effect of Subsidized Training on the Quantiles of Trainee Earnings," Econometrica, Econometric Society, vol. 70(1), pages 91-117, January.
    6. Richard Blundell & Amanda Gosling & Hidehiko Ichimura & Costas Meghir, 2007. "Changes in the Distribution of Male and Female Wages Accounting for Employment Composition Using Bounds," Econometrica, Econometric Society, vol. 75(2), pages 323-363, March.
    7. James J. Heckman & Jeffrey Smith & Nancy Clements, 1997. "Making The Most Out Of Programme Evaluations and Social Experiments: Accounting For Heterogeneity in Programme Impacts," Review of Economic Studies, Oxford University Press, vol. 64(4), pages 487-535.
    8. Aimee Chin, 2005. "Long-Run Labor Market Effects of Japanese American Internment during World War II on Working-Age Male Internees," Journal of Labor Economics, University of Chicago Press, vol. 23(3), pages 491-526, July.
    9. Nada Eissa & Jeffrey B. Liebman, 1996. "Labor Supply Response to the Earned Income Tax Credit," The Quarterly Journal of Economics, Oxford University Press, vol. 111(2), pages 605-637.
    10. 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.
    11. Richard Blundell & Alan Duncan & Costas Meghir, 1998. "Estimating Labor Supply Responses Using Tax Reforms," Econometrica, Econometric Society, vol. 66(4), pages 827-862, July.
    12. Laureano Escudero & M. Ortuño & V. Campos & Reinhardt Euler & Michael Jünger, 1996. "Discussion," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 4(1), pages 54-64, June.
    13. Keisuke Hirano & Guido W. Imbens & Geert Ridder, 2003. "Efficient Estimation of Average Treatment Effects Using the Estimated Propensity Score," Econometrica, Econometric Society, vol. 71(4), pages 1161-1189, July.
    14. Jonathan Gruber & Brigitte C. Madrian, 1993. "Limited Insurance Portability and Job Mobility: The Effects of Public Policy on Job-Lock," NBER Working Papers 4479, National Bureau of Economic Research, Inc.
    15. Jinyong Hahn, 1998. "On the Role of the Propensity Score in Efficient Semiparametric Estimation of Average Treatment Effects," Econometrica, Econometric Society, vol. 66(2), pages 315-332, March.
    16. Nicole M. Fortin & Thomas Lemieux, 1998. "Rank Regressions, Wage Distributions, and the Gender Gap," Journal of Human Resources, University of Wisconsin Press, vol. 33(3), pages 610-643.
    17. Richard Blundell & Monica Costa Dias & Costas Meghir & John Van Reenen, 2001. "Evaluating the employment impact of a mandatory job search assistance program," IFS Working Papers W01/20, Institute for Fiscal Studies.
    18. Heckman, James J & Payner, Brook S, 1989. "Determining the Impact of Federal Antidiscrimination Policy on the Economic Status of Blacks: A Study of South Carolina," American Economic Review, American Economic Association, vol. 79(1), pages 138-177, March.
    19. David Card & Alan Krueger, 1993. "Minimum Wages and Employment: A Case Study of the Fast Food Industry in New Jersey and Pennsylvania," Working Papers 694, Princeton University, Department of Economics, Industrial Relations Section..
    20. Orley Ashenfelter & Michael Greenstone, 2004. "Using Mandated Speed Limits to Measure the Value of a Statistical Life," Journal of Political Economy, University of Chicago Press, vol. 112(S1), pages 226-267, February.
    21. Lechner, Michael, 1999. "Earnings and Employment Effects of Continuous Off-the-Job Training in East Germany after Unification," Journal of Business & Economic Statistics, American Statistical Association, vol. 17(1), pages 74-90, January.
    22. Alan B. Krueger, 1999. "Experimental Estimates of Education Production Functions," The Quarterly Journal of Economics, Oxford University Press, vol. 114(2), pages 497-532.
    23. Juhn, Chinhui & Murphy, Kevin M & Pierce, Brooks, 1993. "Wage Inequality and the Rise in Returns to Skill," Journal of Political Economy, University of Chicago Press, vol. 101(3), pages 410-442, June.
    24. Ashenfelter, Orley & Card, David, 1985. "Using the Longitudinal Structure of Earnings to Estimate the Effect of Training Programs," The Review of Economics and Statistics, MIT Press, vol. 67(4), pages 648-660, November.
    25. Meyer, Bruce D & Viscusi, W Kip & Durbin, David L, 1995. "Workers' Compensation and Injury Duration: Evidence from a Natural Experiment," American Economic Review, American Economic Association, vol. 85(3), pages 322-340, June.
    26. Poterba, James M. & Venti, Steven F. & Wise, David A., 1995. "Do 401(k) contributions crowd out other personal saving?," Journal of Public Economics, Elsevier, vol. 58(1), pages 1-32, September.
    27. Marianne Bertrand & Esther Duflo & Sendhil Mullainathan, 2004. "How Much Should We Trust Differences-In-Differences Estimates?," The Quarterly Journal of Economics, Oxford University Press, vol. 119(1), pages 249-275.
    28. Robert J. LaLonde, 1995. "The Promise of Public Sector-Sponsored Training Programs," Journal of Economic Perspectives, American Economic Association, vol. 9(2), pages 149-168, Spring.
    29. Philip A. Haile & Elie Tamer, 2003. "Inference with an Incomplete Model of English Auctions," Journal of Political Economy, University of Chicago Press, vol. 111(1), pages 1-51, February.
    30. 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.
    31. Martin Feldstein & James M. Poterba, 1996. "Empirical Foundations of Household Taxation," NBER Books, National Bureau of Economic Research, Inc, number feld96-1, May.
    32. Manski, Charles F, 1990. "Nonparametric Bounds on Treatment Effects," American Economic Review, American Economic Association, vol. 80(2), pages 319-323, May.
    33. Susan Athey & Scott Stern, 2002. "The Impact of Information Technology on Emergency Health Care Outcomes," RAND Journal of Economics, The RAND Corporation, vol. 33(3), pages 399-432, Autumn.
    34. Charles F. Manski & Elie Tamer, 2002. "Inference on Regressions with Interval Data on a Regressor or Outcome," Econometrica, Econometric Society, vol. 70(2), pages 519-546, March.
    35. Joseph G. Altonji & Rosa L. Matzkin, 2001. "Panel Data Estimators for Nonseparable Models with Endogenous Regressors," NBER Technical Working Papers 0267, National Bureau of Economic Research, Inc.
    36. 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.
    37. Rajeev H. Dehejia & Sadek Wahba, 1998. "Causal Effects in Non-Experimental Studies: Re-Evaluating the Evaluation of Training Programs," NBER Working Papers 6586, National Bureau of Economic Research, Inc.
    38. Besley, Timothy & Case, Anne, 2000. "Unnatural Experiments? Estimating the Incidence of Endogenous Policies," Economic Journal, Royal Economic Society, vol. 110(467), pages 672-694, November.
    39. Victor Chernozhukov & Christian Hansen, 2005. "An IV Model of Quantile Treatment Effects," Econometrica, Econometric Society, vol. 73(1), pages 245-261, January.
    40. Heckman, James J. & Robb, Richard Jr., 1985. "Alternative methods for evaluating the impact of interventions : An overview," Journal of Econometrics, Elsevier, vol. 30(1-2), pages 239-267.
    41. Guido W. Imbens & Donald B. Rubin, 1997. "Estimating Outcome Distributions for Compliers in Instrumental Variables Models," Review of Economic Studies, Oxford University Press, vol. 64(4), pages 555-574.
    42. Abadie A., 2002. "Bootstrap Tests for Distributional Treatment Effects in Instrumental Variable Models," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 284-292, March.
    43. James J. Heckman & Hidehiko Ichimura & Petra Todd, 1998. "Matching As An Econometric Evaluation Estimator," Review of Economic Studies, Oxford University Press, vol. 65(2), pages 261-294.
    44. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Guido W. Imbens & Jeffrey M. Wooldridge, 2009. "Recent Developments in the Econometrics of Program Evaluation," Journal of Economic Literature, American Economic Association, vol. 47(1), pages 5-86, March.
    2. Alberto Abadie & Guido W. Imbens, 2002. "Simple and Bias-Corrected Matching Estimators for Average Treatment Effects," NBER Technical Working Papers 0283, National Bureau of Economic Research, Inc.
    3. Sergio Firpo, 2007. "Efficient Semiparametric Estimation of Quantile Treatment Effects," Econometrica, Econometric Society, vol. 75(1), pages 259-276, January.
    4. James J. Heckman, 2008. "The Principles Underlying Evaluation Estimators with an Application to Matching," Annals of Economics and Statistics, GENES, issue 91-92, pages 9-73.
    5. van der Klaauw, Bas, 2014. "From micro data to causality: Forty years of empirical labor economics," Labour Economics, Elsevier, vol. 30(C), pages 88-97.
    6. Lechner, Michael, 2011. "The Estimation of Causal Effects by Difference-in-Difference Methods," Foundations and Trends(R) in Econometrics, now publishers, vol. 4(3), pages 165-224, November.
    7. Heckman, James J., 2010. "The Assumptions Underlying Evaluation Estimators," Brazilian Review of Econometrics, Sociedade Brasileira de Econometria - SBE, vol. 30(2), December.
    8. Richard Blundell & Monica Costa Dias, 2009. "Alternative Approaches to Evaluation in Empirical Microeconomics," Journal of Human Resources, University of Wisconsin Press, vol. 44(3).
    9. Jones A.M & Rice N, 2009. "Econometric Evaluation of Health Policies," Health, Econometrics and Data Group (HEDG) Working Papers 09/09, HEDG, c/o Department of Economics, University of York.
    10. Zongwu Cai & Ying Fang & Ming Lin & Shengfang Tang, 2020. "Inferences for Partially Conditional Quantile Treatment Effect Model," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 202005, University of Kansas, Department of Economics, revised Feb 2020.
    11. C de Chaisemartin & X D’HaultfŒuille, 2018. "Fuzzy Differences-in-Differences," Review of Economic Studies, Oxford University Press, vol. 85(2), pages 999-1028.
    12. A. Smith, Jeffrey & E. Todd, Petra, 2005. "Does matching overcome LaLonde's critique of nonexperimental estimators?," Journal of Econometrics, Elsevier, vol. 125(1-2), pages 305-353.
    13. Markus Frölich, 2004. "Programme Evaluation with Multiple Treatments," Journal of Economic Surveys, Wiley Blackwell, vol. 18(2), pages 181-224, April.
    14. Peter Hull & Michal Kolesár & Christopher Walters, 2022. "Labor by design: contributions of David Card, Joshua Angrist, and Guido Imbens," Scandinavian Journal of Economics, Wiley Blackwell, vol. 124(3), pages 603-645, July.
    15. Dmitry Arkhangelsky & Guido Imbens, 2023. "Causal Models for Longitudinal and Panel Data: A Survey," Papers 2311.15458, arXiv.org.
    16. Guido W. Imbens, 2004. "Nonparametric Estimation of Average Treatment Effects Under Exogeneity: A Review," The Review of Economics and Statistics, MIT Press, vol. 86(1), pages 4-29, February.
    17. Pedro H. C. Sant'Anna, 2016. "Program Evaluation with Right-Censored Data," Papers 1604.02642, arXiv.org.
    18. Shengfang Tang & Zongwu Cai & Ying Fang & Ming Lin, 2020. "A New Quantile Treatment Effect Model for Studying Smoking Effect on Birth Weight During Mother's Pregnancy," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 202003, University of Kansas, Department of Economics, revised Feb 2020.
    19. Dionysia Lambiri & Alessandra Faggian & Neil Wrigley, 2017. "Linked-trip effects of ‘town-centre-first' era foodstore development: An assessment using difference-in-differences," Environment and Planning B, , vol. 44(1), pages 160-179, January.
    20. Lechner, Michael, 2004. "Sequential Matching Estimation of Dynamic Causal Models," IZA Discussion Papers 1042, Institute of Labor Economics (IZA).

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:cla:levarc:506439000000000079. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: David K. Levine (email available below). General contact details of provider: http://www.dklevine.com/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.