Difference in Differences Lecture

Difference in Differences Lecture - Imbens/Wooldridge,...

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Imbens/Wooldridge, Lecture Notes 10, Summer ’07 What s New in Econometrics ? NBER , Summer 2007 Lecture 10 , Tuesday , July 31st , 4 . 30 - 5 . 30 pm Difference-in-Differences Estimation These notes provide an overview of standard difference-in-differences methods that have been used to study numerous policy questions. We consider some recent advances in Hansen (2007a,b) on issues of inference, focusing on what can be learned with various group/time period dimensions and serial independence in group-level shocks. Both the repeated cross sections and panel data cases are considered. We discuss recent work by Athey and Imbens (2006) on nonparametric approaches to difference-in-differences, and Abadie, Diamond, and Hainmueller (2007) on constructing synthetic control groups. 1 . Review of the Basic Methodology Since the work by Ashenfelter and Card (1985), the use of difference-in-differences methods has become very widespread. The simplest set up is one where outcomes are observed for two groups for two time periods. One of the groups is exposed to a treatment in the second period but not in the first period. The second group is not exposed to the treatment during either period. In the case where the same units within a group are observed in each time period, the average gain in the second (control) group is substracted from the average gain in the first (treatment) group. This removes biases in second period comparisons between the treatment and control group that could be the result from permanent differences between those groups, as well as biases from comparisons over time in the treatment group that could be the result of trends. We will treat the panel data case in Section 4. With repeated cross sections, we can write the model for a generic member of any of groups as y 0 1 dB 0 d 2 1 d 2 dB u (1.1) where y is the outcome of interest, d 2 is a dummy variable for the second time period. The dummy variable dB captures possible differences between the treatment and control groups prior to the policy change. The time period dummy, d 2, captures aggregate factors that would cause changes in y even in the absense of a policy change. The coefficient of interest, 1 , multiplies the interaction term, d 2 dB , which is the same as a dummy variable equal to one for those observations in the treatment group in the second period. The difference-in-differences estimate is ̂ 1 y ̄ B ,2 y ̄ B ,1 y ̄ A ,2 y ̄ A ,1 . (1.2) 1
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Imbens/Wooldridge, Lecture Notes 10, Summer ’07 Inference based on even moderate sample sizes in each of the four groups is straightforward, and is easily made robust to different group/time period variances in the regression framework. In some cases a more convincing analysis of a policy change is available by further
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Difference in Differences Lecture - Imbens/Wooldridge,...

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