The Excluded Variable Problem in Nonrandomized Control Group Designs

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Abstract
A solution to the problem of specification error due to excluded variables in statistical models of treatment effects in nonrandomized (nonequivalent) control group designs is presented. The solution relies upon longitudinal observation involving at least two pre tests. The assumptions of a single equation probit model for selection bias, structural invariance, and a first order autoregressive pattern are sufficient to identify the model and treatment effect—with one overidentifying restriction. The estimate of the treatment effect is adjusted for an unmeasured variable that influences both the dependent variable and the selection of cases into treatment and control groups. A small simulation suggests that the use of a ML estimation program such as LISREL, which assumes multivariate normality and linearity, may provide reasonable estimates of treatment effects.