Section_12 - Section 12 - Econ 140 GSI: Hedvig, Tarso,...

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Unformatted text preview: Section 12 - Econ 140 GSI: Hedvig, Tarso, Xiaoyu * 1 Experiments 1.1 Basic model Y i = + 1 X i + u i , where: Y i is the dependent variable X i is a treatment dummy * X i = 1 , if individual i was randomly included in the treatment group * X i = 0 , if individual i was randomly included in the control group u i is the error term * E [ u i | X i ] = 0 : conditional mean-zero assumption Treatment e ect : E [ Y i | X i = 1]- E [ Y i | X i = 0] = ( + 1 )- ( ) = 1 The OLS estimator b 1 from the regression of Y i on X i is then called the di erences estimator . * b 1 = Y treatment- Y control "Treatment e ect" means the causal e ect of a treatment on some outcome of interest in an ideal randomized controlled experiment. The term "causal e ect" comes from this setting. 1.2 General model What if the treatment and control groups di er in observable characteristics? Y i = + 1 X i + 2 W 1 i + ... + 1+ r W ri + u i W s are additional regressors representing observable characterisitcs of the treated entities. * Example: If the randomization occurs separately for each level of education and for each gender, then we must include these variables in our regression to estimate 1 . E [ u i | X i ,W 1 i ,...,W ri ] = E [ u i | W 1 i ,...,W ri ] : conditional mean-independence assumption * Interpretation: After conditioning on the observable characteristics, the treatment variable ( X i ) is uncorrelated with the error term ( consistency of the estimator de ned below). * If it holds, the coe cient on X i (variable of interest) will have a causal interpretation, but the coe cients on W 1 i ,...,W ri (control variables) will not! The OLS estimator b 1 from the regression of Y i on X i ,W 1 i ,...,W ri is then called the di erences estimator with additional regressors . * Many thanks to previous GSIs, Edson Severnini and Raymundo M. Campos-Vazquez, as this note is based on theirs. All errors are ours. 1 1.3 Basic model with panel data Y i = + 1 X i + u i Y i = Y after i- Y before i , which assumes that we have observations on the same subjects before and after the treatment (panel data). Treatment e ect : E [ Y i | X i = 1]- E [ Y i | X i = 0] = ( + 1 )- ( ) = 1 The OLS estimator b 1 from the regression of Y i on X i is then called the di erences-in-di erences estimator , because: b 1 = Y treatment- Y control = Y after- Y before treatment- Y after- Y before control We also can estimate the treatment e ect in this setting using an OLS regression on the following model: Y it = + 1 X i + 2 After t + 3 ( X i * After t ) + u it * X...
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This note was uploaded on 02/02/2012 for the course ECON 140 taught by Professor Duncan during the Spring '08 term at University of California, Berkeley.

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Section_12 - Section 12 - Econ 140 GSI: Hedvig, Tarso,...

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