Estimating Causal Effects with Experimental Data. Some Basic Terminology. Start with example where X is binary (though simple to generalize): X=0 is control group X=1 is treatment group Causal effect sometimes called treatment effect
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LOGWAGE | Coef. Std. Err. t
BLACK | -.1673813 .0066708 -25.09
NO_HS | -.2138331 .0077192 -27.70
SOMECOLL | .1104148 .0049139 22.47
COLLEGE | .4660205 .0048839 95.42
AGE | .0704488 .0008552 82.38
AGESQUARED | -.0007227 .0000101 -71.41
_cons | 1.088116 .0172715 63.00
Proposition 2.3If εand X are independent the OLS formula for the standard errors will be consistent even if the variance of ε differs across individuals.
. reg y x, robust
(y1i-y0i )=(γ1- γ0 )’Wi+u1i-u0i
Proposition 2.6 regressionThe IV estimate for the heterogeneous treatment case is a consistent estimate of:where:the difference in the probability of treatment for individual i when in treatment and control group