Random recursive partitioning: a matching method for the estimation of the average treatment effect

In this paper we introduce the Random Recursive Partitioning (RRP) method. This method generates a proximity matrix which can be used in applications like average treatment effect estimation in observational studies. RRP is a Monte Carlo method that randomly generates non-empty recursive partitions of the data and evaluates the proximity between two observations as the empirical frequency they fall in a same cell of these random partitions over all the replications. From the proximity matrix it is possible to derive both graphical and analytical tools to evaluate the extent of the common support between two datasets. The RRP method is ``honest'' in that it does not match observations ``at any cost'': if two datasets are separated, the method clearly states it. This method is affine under invariant transformation of the data and hence it is an equal percent bias reduction (EPBR) method when data come from ellipsoidal and symmetric distributions. Average treatment effect estimators derived from the proximity matrix seem to be competitive compared to more commonly used methods (like, e.g., Mahalanobis full match with calipers within propensity scores) even outside the hypotheses leading to EPBR. RRP method does not require a particular structure of the data and for this reason it can be applied when distances like Mahalanobis or Euclidean are not suitable. As a method working on the original data (i.e. on a multidimensional space instead of a one dimensional measure), RRP is affected by the curse of dimensionality when the number of continuous covariates is too high. Asymptotic properties as well as the behaviour of the RRP method under different data distributions are explored using Monte Carlo methods.