2 mhbounds
1 Introduction
Matching has become a popular method to estimate average treatment effects. It is
based on the conditional independence or unconfoundedness assumption which states
that the researcher should observe all variables simultaneously influencing the partici-
pation decision and outcome variables. Clearly, this is a strong identifying assumption
and has to be justified case-by-case.1 Hence, checking the sensitivity of the estimated
results with respect to deviations from this identifying assumption becomes an increas-
ingly important topic in the applied evaluation literature.
If there are unobserved variables which simultaneously affect assignment into treat-
ment and the outcome variable, a ‘hidden bias’ might arise to which matching estimators
are not robust (Rosenbaum, 2002). Since it is not possible to estimate the magnitude
of selection bias with non-experimental data, we address this problem with the bound-
ing approach proposed by Rosenbaum (2002).2 The basic question to be answered is
whether or not inference about treatment effects may be altered by unobserved factors.
In other words, one wants to determine how strongly an unmeasured variable must
influence the selection process in order to undermine the implications of the matching
analysis. It should be noted that the bounding approach does not test the uncon-
foundedness assumption itself, because this would amount to testing that there are no
(unobserved) variables that influence the selection into treatment. Instead, Rosenbaum
bounds provide evidence on the degree to which any significance results hinge on this
untestable assumption. Clearly, if the results turn out to be very sensitive, the re-
searcher might have to think about the validity of his/her identifying assumption and
consider alternative estimation strategies. DiPrete and Gangl (2004) provide an ado-file
(rbounds) which allows the researcher to test sensitivity for continuous outcome vari-
ables, whereas our module mhbounds focusses on the case of binary outcome variables
(e.g. employment vs. unemployment), which are frequently used in the evaluation liter-
ature.3 Recent applications of this approach can be found in Aakvik (2001) or Caliendo,
Hujer and Thomsen (2005). We outline this approach briefly in Section 2, an extensive
discussion can be found in Rosenbaum (2002) and Aakvik (2001). Section 3 presents
the syntax and Section 4 the options of mhbounds. Finally, in Section 5 we illustrate
the module with some examples. It should be noted, that the aim of this paper is
not to present or discuss the estimation of treatment effects with matching estimators.
Instead we assume that the reader is familiar with this literature. Good overviews can
be found in Heckman, Ichimura, Smith and Todd (1998), Imbens (2004) or Smith and
Todd (2005). Stata programs to estimate treatments effects are provided by Becker and
Ichino (att*, 2002), Leuven and Sianesi (psmatch2, 2003) and Abadie et al. (nnmatch,
2004).
1. Caliendo and Kopeinig (2006) provide a survey of the necessary steps when implementing (propen-
sity score) matching methods.
2. See the paper by Ichino, Mealli, and Nannicini (2006) for a related approach and the ado-package
sensatt by Nannicini (2006) for an implementation in Stata.
3. Clearly, mhbounds is also applicable to binary transformations of the outcome variable in the case
of continuous outcomes.