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

39 Pages Posted: 23 Mar 2002  

Marianne Bertrand

University of Chicago - Booth School of Business; National Bureau of Economic Research (NBER); Centre for Economic Policy Research (CEPR)

Esther Duflo

Massachusetts Institute of Technology (MIT) - Department of Economics; Abdul Latif Jameel Poverty Action Lab (J-PAL); National Bureau of Economic Research (NBER); Centre for Economic Policy Research (CEPR); Bureau for Research and Economic Analysis of Development (BREAD)

Sendhil Mullainathan

Harvard University - Department of Economics; National Bureau of Economic Research (NBER)

Multiple version iconThere are 2 versions of this paper

Date Written: March 2002

Abstract

Most Difference-in-Difference (DD) papers rely on many years of data and focus on serially correlated outcomes. Yet almost all these papers ignore the bias in the estimated standard errors that serial correlation introduce4s. This is especially troubling because the independent variable of interest in DD estimation (e.g., the passage of law) is itself very serially correlated, which will exacerbate the bias in standard errors. 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 for this estimate. The standard errors are severely biased: with about 20 years of data, DD estimation finds an 'effect' significant at the 5% level of up to 45% of the placebo laws. Two very simple techniques can solve this problem for large sample sizes. The first technique consists in collapsing the data and ignoring the time-series variation altogether; the second technique is to estimate standard errors while allowing for an arbitrary covariance structure between time periods. We also suggest a third technique, based on randomization inference testing methods, which works well irrespective of sample size. This technique uses the empirical distribution of estimated effects for placebo laws to form the test distribution.

Suggested Citation

Bertrand, Marianne and Duflo, Esther and Mullainathan, Sendhil, How Much Should We Trust Differences-in-Differences Estimates? (March 2002). NBER Working Paper No. w8841. Available at SSRN: https://ssrn.com/abstract=305064

Marianne Bertrand (Contact Author)

University of Chicago - Booth School of Business ( email )

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HOME PAGE: http://gsbwww.uchicago.edu/fac/marianne.bertrand/vita/cv_0604.pdf

National Bureau of Economic Research (NBER) ( email )

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Centre for Economic Policy Research (CEPR)

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Esther Duflo

Massachusetts Institute of Technology (MIT) - Department of Economics ( email )

50 Memorial Drive
Room E52-544
Cambridge, MA 02139
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617-253-6915 (Fax)

Abdul Latif Jameel Poverty Action Lab (J-PAL) ( email )

Cambridge, MA
United States

HOME PAGE: http://www.povertyactionlab.org/

National Bureau of Economic Research (NBER)

1050 Massachusetts Avenue
Cambridge, MA 02138
United States

Centre for Economic Policy Research (CEPR)

77 Bastwick Street
London, EC1V 3PZ
United Kingdom

Bureau for Research and Economic Analysis of Development (BREAD) ( email )

Duke University
Durham, NC 90097
United States

Sendhil Mullainathan

Harvard University - Department of Economics ( email )

Littauer Center
Cambridge, MA 02138
United States
617-496-2720 (Phone)
617-495-7730 (Fax)

National Bureau of Economic Research (NBER) ( email )

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United States
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617-876-2742 (Fax)

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