Generalized full matching and extrapolation of the results from a large-scale voter mobilization experiment

Fredrik Sävje; Michael J. Higgins; Jasjeet S. Sekhon

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arXiv · 1703.03882

Generalized full matching and extrapolation of the results from a large-scale voter mobilization experiment

Fredrik Sävje·Michael J. Higgins·Jasjeet S. Sekhon

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Abstract

Matching is an important tool in causal inference. The method provides a conceptually straightforward way to make groups of units comparable on observed characteristics. The use of the method is, however, limited to situations where the study design is fairly simple and the sample is moderately sized. We illustrate the issue by revisiting a large-scale voter mobilization experiment that took place in Michigan for the 2006 election. We ask what the causal effects would have been if the treatments in the experiment were scaled up to the full population. Matching could help us answer this question, but no existing matching method can accommodate the six treatment arms and the 6,762,701 observations involved in the study. To offer a solution this and similar empirical problems, we introduce a generalization of the full matching method and an associated algorithm. The method can be used with any number of treatment conditions, and it is shown to produce near-optimal matchings. The worst case maximum within-group dissimilarity is no worse than four times the optimal solution, and simulation results indicate that its performance is considerably closer to the optimal solution on average. Despite its performance, the algorithm is fast and uses little memory. It terminates, on average, in linearithmic time using linear space. This enables investigators to construct well-performing matchings within minutes even in complex studies with samples of several million units.

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Fredrik Sävje, Michael J. Higgins, Jasjeet S. Sekhon. 2017-03-11. Generalized full matching and extrapolation of the results from a large-scale voter mobilization experiment. https://arxiv.org/abs/1703.03882

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