The Statistical Methods For Evaluating Treatment Effects

This paper considers the statistical methods for evaluating the treatment ef-fects. In many social sciences such as economics, biology and medicine, the eval-uation problem of the treatment effect has been often concerned. The questioncomes from the concern about whether a new drug is effective or not. And then itis extended to many fields and has been widely applied, such as, the study for theeffect of a job training program and the effect of attaining a college degree. Sim-ple comparisons of program participants with non-participants often lead to theselection bias for the treatment effects. In a randomized trial, randomization elim-inates selection bias. However, a randomized trial often faces logistical diffculty,long duration, and potentially high cost of randomized trials. In many cases, suchtrials are impractical. Much of the research we do, therefore, attempts to exploitcheaper and more readily available sources of variation. We hope to find naturalor quasi-experiments that mimic a randomized trial by changing the variable ofinterest while other factors are kept balanced. Nevertheless, we take the positionthat a notional randomized trial is our benchmark. The quasi-randomized assign-ment is just the unconfoundedness in this paper. Under the unconfoundedness,the observational studies overcome selection bias. And with the assumption, manymethods such as the regression, matching and propensity score may be used toevaluate the average treatment effect.In this paper we consider the identification and estimation of the relative av-erage treatment effect in the presence of misclassification. Misclassification occurswhen a binary variable (the treatment indicator) is measured with error, that is,some units are reported to have received treatment when they actually have not,and vice versa. Misclassification describes any binary variable is mismeasured. Forexample, in a returns to schooling analysis the outcome could be wages, the bi-nary variable could be attaining a college degree, and misclassification could arise from school transcript reporting errors. Failure to account for misclassification isshown to result in bias in the estimated treatment effect. Therefore, consideringthe treatment effect with classification is interesting.An identifying assumption that overcomes this bias is the existence of aninstrument for the binary regressor. An example is relating wages to schoolingusing a distance to school instrument.We use the relative effect to evaluate the treatment effect. This is because insome settings the relative (or ratio) effect is more appropriate than the difference(or absolute) effect to evaluate the effects of treatments, which the relative effectcan evaluate the effects of treatment that the difference effect can not. Further,we present the nonlinear relationship between the true and mismeasured relativetreatment effects and show that attenuation bias can be caused on no account ofmisclassification. Then, to overcome this bias, we assume there exists an instrumentfor the true treatment And show that the true relative average treatment effectsare identified. Finally, we propose the estimator based on nonparametric methods.