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Non-parametric adjustment for covariates when estimating a treatment effect

Författare: Eva Cantoni, Och Xavier de Luna, Och

Publicerad i: Journal of Non Parametric Statistics 2006, vol. 18, iss. 2, pp. 227-244

Sammanfattning av Working paper 2004:9

We consider a non-parametric model for estimating the e ect 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 e ect is then obtained by taking the
di erence between the two tted regression functions. This paper proposes a
back tting algorithm which uses all the data for the two above-mentioned nonparametric
regression. We give theoretical results showing that the resulting
estimator of the treatment e ect can have lower nite 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
back tting estimator. When more than one covariate is observed our back tting
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
back tting estimator in a several covariate situation with data on a training
program for individuals having faced social and economic problems.
Keywords: Analysis of covariance, Back tting algorithm, Linear smoothers,
Propensity score.
JEL: C14

We consider a non-parametric model for estimating the e ffect 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 eff ect is then obtained by taking the diff erence between the two fitted regression functions. This paper proposes a backfi tting algorithm which uses all the data for the two above-mentioned nonparametric regression. We give theoretical results showing that the resulting estimator of the treatment effect can have lower fi nite 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 backfi tting estimator. When more than one covariate is observed our backfi tting 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 back fitting estimator in a several covariate situation with data on a training program for individuals having faced social and economic problems.

Keywords: Analysis of covariance, Backfi tting algorithm, Linear smoothers, Propensity score.
JEL: C14

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