Re: st: Propensity scoring using -teffects- in Stata 13; puzzling features, documentation issues,

["David M. Drukker" <ddrukker@stata.com>]

Mike Lacy <Michael.Lacy@colostate.edu> had several questions about the
matching estimators implemented in -teffects-.

Essentially, Mike asked why the implemented matching estimators assume
matching with replacement and why all observations that share a distance are
included.  The short answer is that Abadie and Imbens(2006, 2011) used these
assumptions among others to produce their results.

Here are some details about these questions.

Abadie and Imbens have already written a detailed answer to Mike's first
question.  Abadie and Imbens (2006, page 240) make the following argument

        "We focus on matching with replacement, allowing each unit to be
        used as a match more than once.  Matching with replacement produces
        matches of higher quality than matching with replacement by
        increasing the set of possible matches. (As we show below, inexact
        matches generate bias in matching estimators.  Therefore, expanding
        the set of possible matches will tend to produce smaller biases.)
        In addition, matching with replacement has the advantage that it
        allows us to consider estimators that match all units, treated as
        well as controls, so that the estimand is identical to the
        population average treatment effect."

Mike's second question is essentially, why do the implemented estimators
include all the observations whose distances are tied.  A technical
discussion of ties is given in Abadie et al (2004, page 293).  There are two
arguments for including all the tied observations.  First, following from
the quote above, including all the ties provides a more precise estimator.
Second, without more information there is no way to choose which of the
observations that share a given distance should be included and which should
be excluded.

Mike also found a problem with the documentation.  Mike correctly noted that
there are places in the documentation in which the -caliper- option is
described incorrectly as a minimum distance, when in fact it is a maximum
distance.  The job of the -caliper()- option is to exclude observations that
are too far away, so it is clearly a maximum distance.  (We thank Mike for
finding this problem and we will fix it.)

Finally, Mike noted that the documentation for the -generate()- option
refers to

        "generate variables containing the row indices of the nearest
        neighbors"

while
        "row index" means "observation number in the dataset prior to
        execution of the -teffects-.

Again, we thank Mike for finding this problem in our documentation.  We will
get it fixed.

I hope that these explanations help.

  Best,
  David
  ddrukker@stata.com


References
----------

Abadie, Alberto, David Drukker, Jane Leber Herr, and Guido W. Imbens.  2004.
"Implementing matching estimators for average treatment effects in Stata."
Stata Journal 4: 290-311.

Abadie, Alberto, and Guido W. Imbens. 2006. "Large sample properties of
matching estimators for average treatment effects." Econometrica 74, no.  1:
235-267.

Abadie, Alberto, and Guido W. Imbens. 2011. "Bias-corrected matching
estimators for average treatment effects." Journal of Business & Economic
Statistics 29, no. 1.

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