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How Much Should We Trust Differences-in-Differences Estimates?

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  • Marianne Bertrand
  • Esther Duflo
  • Sendhil Mullainathan

Abstract

Most papers that employ Differences-in-Differences estimation (DD) use many years of data and focus on serially correlated outcomes but ignore that the resulting standard errors are inconsistent. To illustrate the severity of this issue, we randomly generate placebo laws in state-level data on female wages from the Current Population Survey. For each law, we use OLS to compute the DD estimate of its "effect" as well as the standard error of this estimate. These conventional DD standard errors severely understate the standard deviation of the estimators: we find an "effect" significant at the 5 percent level for up to 45 percent of the placebo interventions. We use Monte Carlo simulations to investigate how well existing methods help solve this problem. Econometric corrections that place a specific parametric form on the time-series process do not perform well. Bootstrap (taking into account the autocorrelation of the data) works well when the number of states is large enough. Two corrections based on asymptotic approximation of the variance-covariance matrix work well for moderate numbers of states and one correction that collapses the time series information into a "pre"- and "post"-period and explicitly takes into account the effective sample size works well even for small numbers of states. © 2004 the President and Fellows of Harvard College and the Massachusetts Institute of Technology

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Bibliographic Info

Article provided by MIT Press in its journal The Quarterly Journal of Economics.

Volume (Year): 119 (2004)
Issue (Month): 1 (February)
Pages: 249-275

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Handle: RePEc:tpr:qjecon:v:119:y:2004:i:1:p:249-275

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  1. Alberto Abadie, 2005. "Semiparametric Difference-in-Differences Estimators," Review of Economic Studies, Oxford University Press, vol. 72(1), pages 1-19.
  2. Whitney K. Newey & Kenneth D. West, 1986. "A Simple, Positive Semi-Definite, Heteroskedasticity and AutocorrelationConsistent Covariance Matrix," NBER Technical Working Papers 0055, National Bureau of Economic Research, Inc.
  3. 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.
  4. MaCurdy, Thomas E., 1982. "The use of time series processes to model the error structure of earnings in a longitudinal data analysis," Journal of Econometrics, Elsevier, vol. 18(1), pages 83-114, January.
  5. Gary Solon, 1984. "Estimating Autocorrelations in Fixed-Effects Models," NBER Technical Working Papers 0032, National Bureau of Economic Research, Inc.
  6. Nickell, Stephen J, 1981. "Biases in Dynamic Models with Fixed Effects," Econometrica, Econometric Society, vol. 49(6), pages 1417-26, November.
  7. 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.
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