Inference with "Difference in Differences" with a Small Number of Policy Changes
Difference in differences methods have become very popular in applied work. This paper provides a new method for inference in these models when there are a small number of policy changes. This situation occurs in many implementations of these estimators. Identification of the key parameter typically arises when a group "changes" some particular policy. The asymptotic approximations that are typically employed assume that the number of cross sectional groups, N, times the number of time periods, T, is large. However, even when N or T is large, the number of actual policy changes observed in the data is often very small. In this case, we argue that point estimators of treatment effects should not be thought of as being consistent and that the standard methods that researchers use to perform inference in these models are not appropriate. We develop an alternative approach to inference under the assumption that there are a finite number of policy changes in the data, using asymptotic approximations as the number of non-changing groups gets large. In this situation we cannot obtain a consistent point estimator for the key treatment effect parameter. However, we can consistently estimate the finite-sample distribution of the treatment effect estimator, up to the unknown parameter itself. This allows us to perform hypothesis tests and construct confidence intervals. For expositional and motivational purposes, we focus on the difference in differences case, but our approach should be appropriate more generally in treatment effect models which employ a large number of controls, but a small number of treatments. We demonstrate the use of the approach by analyzing the effect of college merit aide programs on college attendance. We show that in some cases the standard approach can give misleading results.
|Date of creation:||Jul 2005|
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- 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 772-93, September.
- David Card & Alan B. Krueger, 1993. "Minimum Wages and Employment: A Case Study of the Fast Food Industry in New Jersey and Pennsylvania," NBER Working Papers 4509, National Bureau of Economic Research, Inc.
- 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
- 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, EconWPA.
- Dynarski, Susan, 2000.
"Hope for Whom? Financial Aid for the Middle Class and Its Impact on College Attendance,"
National Tax Journal,
National Tax Association, vol. 53(n. 3), pages 629-62, September.
- Susan Dynarski, 2000. "Hope for Whom? Financial Aid for the Middle Class and Its Impact on College Attendance," NBER Working Papers 7756, National Bureau of Economic Research, Inc.
- Gallant, A Ronald & Nychka, Douglas W, 1987. "Semi-nonparametric Maximum Likelihood Estimation," Econometrica, Econometric Society, vol. 55(2), pages 363-90, March.
- 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.
- Gary Chamberlain, 1980. "Analysis of Covariance with Qualitative Data," Review of Economic Studies, Oxford University Press, vol. 47(1), pages 225-238.
- 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.
- 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.
- 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 334-38, May.
- 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.
- 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.
- 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.
- David Card, 1989.
"The Impact of the Mariel Boatlift on the Miami Labor Market,"
NBER Working Papers
3069, National Bureau of Economic Research, Inc.
- 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.
- Meyer, Bruce D, 1995.
"Natural and Quasi-experiments in Economics,"
Journal of Business & Economic Statistics,
American Statistical Association, vol. 13(2), pages 151-61, April.
- Dynarski, Susan, 2004.
"The New Merit Aid,"
Working Paper Series
rwp04-009, Harvard University, John F. Kennedy School of Government.
- 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.
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