Difference in differences say random assignment to

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Difference-in-Differences Say random assignment to treatment and control groups, like in a medical experiment One can then simply compare the change in outcomes across the treatment and control groups to estimate the treatment effect For time 1,2, groups A, B (y 2,B – y 2,A ) - (y 1,B – y 1,A ), or equivalently (y 2,B – y 1,B ) - (y 2,A y 1,A ), is the difference-in-differences Fall 2008 under Econometrics Prof. Keunkwan Ryu 5
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Difference-in-Differences (cont) A regression framework using time and treatment dummy variables can calculate this difference-in-difference as well Consider the model: C:control group T:treatment group d2 : a dummy variable for the second time period y = β 0 + δ 0 d2+ β 1 dT + δ 1 d2·dT +otherfactors Fall 2008 under Econometrics Prof. Keunkwan Ryu 6
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will be the difference-in-diffrences Fall 2008 under Econometrics Prof. Keunkwan Ryu 7 Before After After-Before Control β 0 β 0 + δ 0 δ 0 Treatment β 0 + β 1 β 0 + δ 0 + β 1 + δ 1 δ 0 + δ 1 Treatment-Control β 1 β 1 + δ 1 δ 0 TABLE 13.3 Illustration of the Difference-in-Differsnces Estimator ) ( ) ( ˆ , 1 , 1 , 2 , 2 1 C T C T y y y y - - - = δ 1 ˆ δ
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Difference-in-Differences (cont) When don’t truly have random assignment, the regression form becomes very useful
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