Additional x s can be added to the regression to

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Additional x ’s can be added to the regression to control for differences across the treatment and control groups Sometimes referred to as a “natural experiment” especially when a policy change is being analyzed Fall 2008 under Econometrics Prof. Keunkwan Ryu 8
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Two-Period Panel Data It’s possible to use a panel just like pooled cross-sections, but can do more than that Panel data can be used to address some kinds of omitted variable bias If can think of the omitted variables as being fixed over time, then can model as having a composite error Fall 2008 under Econometrics Prof. Keunkwan Ryu 9
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Unobserved Fixed Effects Suppose the population model is y it = β 0 + δ 0 d2 t + β 1 x it1 +…+ β k x itk + a i + u it Here we have added a time-constant component to the error, υ it = a i + u it If a i is correlated with the x ’s, OLS will be biased, since we a i is part of the error term With panel data, we can difference-out the unobserved fixed effect Fall 2008 under Econometrics Prof. Keunkwan Ryu 10
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First-differences We can subtract one period from the other, to obtain y i = δ 0 + β 1 x i1 +…+ β k x ik + u i This model has no correlation between the x ’s and the error term, so no bias
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