We consider a non-parametric model for estimating the effect of a binary treatment on an outcome variable while adjusting for an observed covariate. A naive procedure consists in performing two separate non-parametric regression of the response on the covariate: one with the treated individuals and the other with the untreated. The treatment effect is then obtained by taking the difference between the two fitted regression functions. This paper proposes a backfitting algorithm which uses all the data for the two above-mentioned non-parametric regression. We give theoretical results showing that the resulting estimator of the treatment effect can have lower finite sample variance. This improvement may be achieved at the cost of a larger bias. However, in a simulation study we observe that mean squared error is lowest for the proposed backfitting estimator. When more than one covariate is observed our backfitting estimator can still be applied by using the propensity score (probability of being treated for a given setup of the covariates). We illustrate the use of the backfitting estimator in a several covariate situation with data on a training program for individuals having faced social and economic problems.
Analysis of covariance backfitting algorithm linear smoothers propensity score