# An optimization -based matching estimator : large and small sample properties

Tesis

##### Date

2014-12##### Metadata

Show full item record
Cómo citar
####

Rivera Cayupi, Jorge Enrique

Cómo citar

####
**An optimization -based matching estimator : large and small sample properties**

ï»¿

Compartir:

cargando...

Copiar

##### Author

##### Professor Guide

##### Abstract

This work proposes a novel matching estimator where weights and the choice of neighbors
used are endogenously determined by solving an optimization problem. The estimator is
non-parametric and is based on nding, for each unit that needs to be matched, sets of
observations such that a convex combination of their covariates has the same value of the
covariates as the unit to be matched, or with minimized distance between them. Since there
is generally more than one set per each unit, the method chooses the one with the closest
covariate values.
In this work we contribute to the matching literature by linking the choice of matches
and weights to the improvement of post-matching covariate balance in a simple way: an
optimization problem that optimizes individual covariate balance. It is worth mentioning
that the developed method is not an algorithm that iteratively checks covariate balance until
convergence. Instead, it incorporates an individual balance criterion in the objective function
that determines the weights used in each match. It can be written as a linear program that
allows us to use standard optimization techniques to solve the problem quickly. To aid
research, we provide a new R library called blopmatching.
Regarding asymptotic properties, we shows that our estimator of the ATE attains stan-
dard limit properties (consistency and normality), and it has a conditional bias that is
Op(N2=k). It worth mentioning that this order improves the order N1=k attained by the
NN-matching estimator. In fact, Op(N2=k) could be attained by the NN-matching estima-
tor in the only case in which the conditional expectation of the outcome variable is a linear
expression in covariates, a condition under which the conditional bias of our estimators is
as good as we want. Besides, even though the proposed estimator of the ATE is not
p
N-
consistent in general, we show that if the number of control units increases faster than the
number of treated units, then our matching estimator of the ATT attains the
p
N-consistency,
as its bias rate is better than the one attained by the NN-matching estimator.
Finally, as regards nite sample properties, we implement the proposed estimator to
data from the National Supported Work Demonstration nding an outstanding performance
even though when using alternative control groups from a non-experimental sample. In
addition, by performing Monte Carlo experiments with designs based on the related literature
that includes misspeci cation of the selection equation, we study its performance in nite
samples. We nd that our estimator provides good post-matching balance and performs
well in terms of bias and variance when compared to nearest neighbor matching estimators
(for both covariates and propensity score) and the normalized inverse probability weighting
estimator. Major improvements are observed when there is underspeci cation of the selection
equation for estimating the propensity score. Hence, our method gives researchers a new
alternative matching estimator that prevents the selection of an arbitrary number of neighbors
or the estimation of the propensity score.

##### General note

Tesis para optar al grado de Doctor en Economía

##### Identifier

URI: http://repositorio.uchile.cl/handle/2250/134485##### Collections

The following license files are associated with this item: