The Treatment Effect, the Cross Difference, and the Interaction Term in Nonlinear “Difference-in-Differences” Models
I demonstrate that Ai and Norton’s (2003) point about cross differences is not relevant for the estimation of the treatment effect in nonlinear “difference-in-differences” models such as probit, logit or tobit, because the cross difference is not equal to the treatment effect, which is the parameter of interest. In a nonlinear “difference-in-differences” model, the treatment effect is the cross difference of the conditional expectation of the observed outcome minus the cross difference of the conditional expectation of the potential outcome without treatment. Unlike in the linear model, the latter cross difference is not zero in the nonlinear model. It follows that the sign of the treatment effect in a nonlinear “difference-in-differences” model with a strictly monotonic transformation function is equal to the sign of the coefficient of the interaction term of the time and treatment group indicators. The treatment effect is simply the incremental effect of the coefficient of the interaction term.
(This abstract was borrowed from another version of this item.)
|Date of creation:||2010|
|Contact details of provider:|| Postal: 12, place du Panthéon, 75230 Paris Cedex 05|
Phone: (33) 1 44 41 89 61 (66)
Fax: (33) 1 40 51 81 30
Web page: http://ermes.u-paris2.fr/
More information through EDIRC
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Joshua Angrist & Alan Krueger, 1998.
"Empirical Strategies in Labor Economics,"
98-7, Massachusetts Institute of Technology (MIT), Department of Economics.
- Richard Blundell & Monica Costa Dias, 2009.
"Alternative Approaches to Evaluation in Empirical Microeconomics,"
Journal of Human Resources,
University of Wisconsin Press, vol. 44(3).
- Richard Blundell & Monica Costa Dias, 2002. "Alternative approaches to evaluation in empirical microeconomics," CeMMAP working papers CWP10/02, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
- Richard Blundell & Monica Costa Dias, 2008. "Alternative approaches to evaluation in empirical microeconomics," CeMMAP working papers CWP26/08, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
- Richard Blundell & Mónica Costa Dias, 2008. "Alternative Approaches to Evaluation in Empirical Microeconomics," CEF.UP Working Papers 0805, Universidade do Porto, Faculdade de Economia do Porto.
- Blundell, Richard & Costa Dias, Monica, 2008. "Alternative Approaches to Evaluation in Empirical Microeconomics," IZA Discussion Papers 3800, Institute for the Study of Labor (IZA).
- Susan Athey & Guido W. Imbens, 2006.
"Identification and Inference in Nonlinear Difference-in-Differences Models,"
Econometric Society, vol. 74(2), pages 431-497, 03.
- Susan Athey & Guido Imbens, 2003. "Identification and Inference in Nonlinear Difference-in-Differences Models," Levine's Working Paper Archive 506439000000000079, David K. Levine.
- Susan Athey & Guido W. Imbens, 2002. "Identification and Inference in Nonlinear Difference-In-Differences Models," NBER Technical Working Papers 0280, National Bureau of Economic Research, Inc.
- Heckman, James J. & Lalonde, Robert J. & Smith, Jeffrey A., 1999. "The economics and econometrics of active labor market programs," Handbook of Labor Economics, in: O. Ashenfelter & D. Card (ed.), Handbook of Labor Economics, edition 1, volume 3, chapter 31, pages 1865-2097 Elsevier.
- 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.
- Marianne Bertrand & Esther Duflo & Sendhil Mullainathan, 2002. "How Much Should We Trust Differences-in-Differences Estimates?," NBER Working Papers 8841, National Bureau of Economic Research, Inc.
- 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.
- 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.
- Michael Lechner, 2010. "The Estimation of Causal Effects by Difference-in-Difference Methods," University of St. Gallen Department of Economics working paper series 2010 2010-28, Department of Economics, University of St. Gallen, revised Oct 2011.
- Ai, Chunrong & Norton, Edward C., 2003. "Interaction terms in logit and probit models," Economics Letters, Elsevier, vol. 80(1), pages 123-129, July.
When requesting a correction, please mention this item's handle: RePEc:erm:papers:1004. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: ()
If references are entirely missing, you can add them using this form.