Matching for Causal Inference Without Balance Checking

39 Pages Posted: 28 Jun 2008

See all articles by Stefano Maria Iacus

Stefano Maria Iacus

University of Milan - Department of Economics, Business and Statistics

Gary King

Harvard University

Giuseppe Porro

University of Trieste

Date Written: June 26, 2008


We address a major discrepancy in matching methods for causal inference in observational data. Since these data are typically plentiful, the goal of matching is to reduce bias and only secondarily to keep variance low. However, most matching methods seem designed for the opposite problem, guaranteeing sample size ex ante but limiting bias by controlling for covariates through reductions in the imbalance between treated and control groups only ex post and only sometimes. (The resulting practical difficulty may explain why many published applications do not check whether imbalance was reduced and so may not even be decreasing bias.) We introduce a new class of Monotonic Imbalance Bounding (MIB) matching methods that enables one to choose a fixed level of maximum imbalance, or to reduce maximum imbalance for one variable without changing it for the others. We then discuss a specific MIB method called Coarsened Exact Matching (CEM) which, unlike most existing approaches, also explicitly bounds through ex ante user choice both the degree of model dependence and the causal effect estimation error, eliminates the need for a separate procedure to restrict data to common support, meets the congruence principle, is approximately invariant to measurement error, works well with modern methods of imputation for missing data, is computationally efficient even with massive data sets, and is easy to understand and use. This method can improve causal inferences in a wide range of applications, and may be preferred for simplicity of use even when it is possible to design superior methods for particular problems. We also make available open source software which implements all our suggestions.

Suggested Citation

Iacus, Stefano Maria and King, Gary and Porro, Giuseppe, Matching for Causal Inference Without Balance Checking (June 26, 2008). Available at SSRN: or

Stefano Maria Iacus

University of Milan - Department of Economics, Business and Statistics ( email )

Via Conservatorio 7
Milano, 20122
+390250321461 (Phone)
+3950321505 (Fax)


Gary King (Contact Author)

Harvard University ( email )

1737 Cambridge St.
Institute for Quantitative Social Science
Cambridge, MA 02138
United States
617-500-7570 (Phone)


Giuseppe Porro

University of Trieste ( email )

Piazzale Europa 1
Trieste, Trieste 34100

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