Matching for Balance, Pairing for Heterogeneity in an Observational Study of the Effectiveness of For-Profit and Not-For-Profit High Schools in Chile

By José R. Zubizarreta, R. Paredes, Paul R. Rosenbaum. 2014

136 citations recorded by the source corpus.

Conventionally, the construction of a pair-matched sample selects treated and control units and pairs them in a single step with a view to balancing observed covariates $\mathbf{x}$ and reducing the heterogeneity or dispersion of treated-minus-control response differences, $Y$. In contrast, the method of cardinality matching developed here first selects the maximum number of units subject to covariate balance constraints and, with a balanced sample for $\mathbf{x}$ in hand, then separately pairs the units to minimize heterogeneity in $Y$. Reduced heterogeneity of pair differences in responses $Y$ is known to reduce sensitivity to unmeasured biases, so one might hope that cardinality matching would succeed at both tasks, balancing $\mathbf{x}$, stabilizing $Y$. We use cardinality matching in an observational study of the effectiveness of for-profit and not-for-profit private high schools in Chile - a controversial subject in Chile - focusing on students who were in government run primary schools in 2004 but then switched to private high schools. By pairing to minimize heterogeneity in a cardinality match that has balanced covariates, a meaningful reduction in sensitivity to unmeasured biases is obtained.

Subfields: Education, Statistics and Probability

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Citations in the corpus

FLAME: A Fast Large-scale Almost Matching Exactly Approach to Causal Inference (2017, methodology): “…match assignments, some newer matching schemes use mixed integer programming, which is a ﬂexible framework that can accommodate linear balance constraints (Zubizarreta, 2012; Zubizarreta et al., 2014; Keele and Zubizarreta, 2014; Resa and Zubizarreta, 2016; Noor-E-Alam and Rudin, 2015b,a).”
Hypothesis Tests That Are Robust to Choice of Matching Method (2018, methodology): “For these types of problems, modern discrete optimization techniques have rarely been used, though there is one recent precedent in the literature for matched pairs, namely the line of work by Zubizarreta (2012), Zubizarreta et al. (2013, 2014).”
Evaluation of subset matching methods and forms of covariate balance (2016, methodology): “The second method is optimal cardinality matching or, simply, cardinality matching [9].”
Optimal Multilevel Matching in Clustered Observational Studies: A Case Study of the Effectiveness of Private Schools Under a Large-Scale Voucher System (2014, methodology): “As we discuss, our strategy is optimal in the sense that it minimizes the total sum of covariate distances between matched pairs of units (when implemented with optimal matching; Rosenbaum 1989), or that it maximizes size of the pair-matched sample that balances covariates as required by the investi”
Adaptive Hyper-box Matching for Interpretable Individualized Treatment Effect Estimation (2020, methodology): “MIPs have previously been used for causal inference in order to accomodate linear balance constraints on the covariates (Zubizarreta 2012; Zubizarreta et al. 2014; Morucci et al. 2018).”
Matching for Balance (2019, methodology): “Extending the formulation in Zubizarreta et al. (2014), we write these methods as follows max.”
MALTS: Matching After Learning to Stretch (2018, methodology): “A flexible setup for producing high quality matches is the optimal matching literature [20], which started with network flow algorithms and has evolved to use integer programming to produce matches that are constrained in user-defined ways [13, 14, 16, 17, 19, 28, 29].”
Optimal Multilevel Matching in Clustered Observational Studies: A Case Study of the School Voucher System in Chile (2014, methodology): “Unlike these matching methods, cardinality matching uses the original covariates to match units and directly balance their covariate distributions (Zubizarreta et al. 2014).”
Imposing Minimax and Quantile Constraints on Optimal Matching in Observational Studies (2017, methodology): “This is illustrated in an observational study in education by Zubizarreta, Paredes, and Rosenbaum (2014), where matching balanced many covariates, but pairs were made homogenous on the variables most predictive ofYi.”