| Causal Inference With Non-Random/ Experimental Data |
| 2009-04-25 |
| In a model like y = Xb + e, we must have E(X'e) = 0 for unbiased and consistent estimates of b. This assumption fails in the presence of measurement error, simultaneous equations, omitted variables in X, or selection (of X) based
on unobserved or unobservable factors.
To control for this selection bias in observational data, one can use a variety of quasi-experimental approached to mitigate the selection bias, and stake a stronger claim towards a causal inference.
How valid is this approach?
A recent paper by William R. Shadish, M. H. Clark, and Peter M. Steiner published JASA (December 1, 2008, 103(484): 1334-1344.) based on "a randomized experiment comparing random and nonrandom assignments". Basically "In the randomized experiment, participants were randomly assigned to mathematics or vocabulary training; in the non-randomized experiment, participants chose their training." Given the self selection by students in the non-randomized experiment, the authors show that matching estimation using propensity scores, "reduced bias by about 58–96%, depending on the outcome measure and adjustment method". |
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