= Matching
{disambiguate=statistics}
{wiki}
= Matching in causal inference
{synonym}
<Matching (statistics)> constructs comparisons between units receiving different <treatments> but having similar pretreatment <covariates>. Similarity can be measured directly on selected <covariates> or through a <propensity score>. The design specifies the <distance>, allowed discrepancies, number of controls per treated unit and whether a control can be reused.
With one distinct control matched to each of $n_T$ treated units, a simple estimator is
$$
\widehat\tau_{\rm match}=\frac1{n_T}\sum_{i=1}^{n_T}(Y_{i,T}-Y_{i,C}).
$$
This averages differences in the represented treated population. Dropping unmatched treated units changes that population, and reusing controls induces dependence between pair differences. <Caliper matching> explicitly limits allowed discrepancies.
<Matching (statistics)> seeks <covariate balance>; it does not create a <randomized controlled trial>. Identifying a <causal effect> still requires <conditional exchangeability> given the matched pretreatment <covariates>, adequate <positivity>, and <consistency in causal inference>. Unmeasured determinants of assignment and outcome can remain different even when measured <covariates> are well balanced. Conditioning on a <causal mediator> or inducing <collider bias> is not repaired by calling the procedure <matching (statistics)>.
Back to article page
