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Unformatted text preview: Econ 139: Introduction to Econometrics Andrew Sweeting 1 Department of Economics Duke University Spring 2011 Econ 139 Handout 13 (Duke) Treatment E/ects Spring 2011 1 ¡ 52 Estimating Treatment E/ects Economists and social scientists are often interested in seeing how a population responds to a treatment or program. Clinical trials are the obvious example, but others include the e/ectiveness of job training programs, the impact of a minimum wage, and the e/ect of school vouchers. Program evaluation concerns estimating the e/ect of such programs, policies, and interventions (i.e. treatments ). Call the treatment X i and its outcome Y i Y i = β + β 1 X i + u i where X i is the treatment level & u i is the error. Econ 139 Handout 13 (Duke) Treatment E/ects Spring 2011 2 ¡ 52 Estimating Treatment E/ects Ideally, we&d like to compare the same individual with and without treatment, but this is clearly impossible. An alternative is to run a randomized experiment. How? Construct a random sample of n individuals and assign treatment X i = X to a randomly selected subset of them (the treatment group) and keep the remaining subset as a control (the control group). select n unemployed people, give some job training to a random subsample and compare employment outcomes. select n kids, give school vouchers to a random subsample and compare education outcomes. select n sick people, give a new drug to a random subsample and compare health outcomes. Econ 139 Handout 13 (Duke) Treatment E/ects Spring 2011 3 ¡ 52 Estimating Treatment E/ects If the treatment is randomly assigned, X i will be uncorrelated with the omitted variables by construction . Why? Random assignment means that X i is independent of any other variables that impact Y , so E ( u i j X i ) = . The causal e/ect of the treatment ( aka the treatment e/ect) is simply the di/erence in conditional expectations E ( Y i j X i = x ) & E ( Y i j X i = ) In many cases, the treatment is binary, so we can replace X with a binary variable G indicating whether or not the individual received the treatment. We will focus on this case from now on. Econ 139 Handout 13 (Duke) Treatment E/ects Spring 2011 4 ¡ 52 Estimating Treatment E/ects In an ideal randomized experiment, the causal e/ect can be estimated using OLS on the regression model Y i = β + β 1 G i + u i (1) where G is a binary variable indicating that i received the treatment. ˆ β 1 is called the di/erences estimator since it is the di/erence between the sample average outcome of the treatment group and the sample average outcome of the control group. Since an ideal randomized experiment eliminates any correlation between G i and u i , the di/erences estimator is unbiased and consistent....
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This note was uploaded on 08/03/2011 for the course ECON 139 taught by Professor Alessandrotarozzi during the Spring '08 term at Duke.
 Spring '08
 ALESSANDROTAROZZI
 Econometrics

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