Difference in Differences Slides

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What’s New in Econometrics? Lecture 10 Difference-in-Differences Estimation Jeff Wooldridge NBER Summer Institute, 2007 1. Review of the Basic Methodology 2. How Should We View Uncertainty in DD Settings? 3. General Settings for DD Analysis: Multiple Groups and Time Periods 4. Individual-Level Panel Data 5. Semiparametric and Nonparametric Approaches 6. Synthetic Control Methods for Comparative Case Studies 1

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1 . Review of the Basic Methodology The standard case: 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 (panel data), 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 2
treatment group that could be the result of trends. With repeated cross sections, let A be the control group and B the treatment group. Write y 0 1 dB 0 d 2 1 d 2 dB u , (1) where y is the outcome of interest. The dummy dB captures possible differences between the treatment and control groups prior to the policy change. The dummy d 2 captures aggregate factors that would cause changes in y even in the absense of a policy change. The coefficient of interest is 1 . The difference-in-differences estimate is ̂ 1 y ̄ B ,2 y ̄ B ,1 y ̄ A ,2 y ̄ A ,1 . (2) 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 3

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variances in the regression framework. More convincing analysis sometimes available by refining the definition of treatment and control groups. Example: change in state health care policy aimed at elderly. Could use data only on people in the state with the policy change, both before and after the change, with the control group being people 55 to 65 (say) and and the treatment group being people over 65. This DD analysis assumes that the paths of health outcomes for the younger and older groups would not be systematically different in the absense of intervention. Instead, might use the over-65 population from another state as an additional control. Let dE be a dummy equal to one for someone over 65. 4
y 0 1 dB 2 dE 3 dB dE 0 d 2 1 d 2 dB 2 d 2 dE 3 d 2 dB dE u (3) The coefficient of interest is 3 , the coefficient on the triple interaction term, d 2 dB dE . The OLS estimate ̂ 3 can be expressed as follows: ̂ 3 y ̄ B , E ,2 y ̄ B , E ,1 y

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## This note was uploaded on 12/26/2011 for the course ECON 245a taught by Professor Staff during the Fall '08 term at UCSB.

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Difference in Differences Slides - Whats New in...

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