  A new matching method is proposed for the estimation of the average treatment
effect of social policy interventions (e.g., training programs or health care
measures). Given an outcome variable, a treatment and a set of pre-treatment
covariates, the method is based on the examination of random recursive
partitions of the space of covariates using regression trees. A regression tree
is grown either on the treated or on the untreated individuals {\it only} using
as response variable a random permutation of the indexes 1...$n$ ($n$ being the
number of units involved), while the indexes for the other group are predicted
using this tree. The procedure is replicated in order to rule out the effect of
specific permutations. The average treatment effect is estimated in each tree
by matching treated and untreated in the same terminal nodes. The final
estimator of the average treatment effect is obtained by averaging on all the
trees grown. The method does not require any specific model assumption apart
from the tree's complexity, which does not affect the estimator though. We show
that this method is either an instrument to check whether two samples can be
matched (by any method) and, when this is feasible, to obtain reliable
estimates of the average treatment effect. We further propose a graphical tool
to inspect the quality of the match. The method has been applied to the
National Supported Work Demonstration data, previously analyzed by Lalonde
(1986) and others.
