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# How Coarsening Simplifies Matching-Based Causal Inference Theory

The simplicity and power of matching methods have made them an increasingly popular approach to causal inference in observational data. Existing theories that justify these techniques are well developed but either require exact matching, which is usually infeasible in practice, or sacrifice some simplicity via asymptotic theory, specialized bias corrections, and novel variance estimators; and extensions to approximate matching with multicategory treatments have not yet appeared. As an additional option for researchers, we show how conceptualizing continuous variables as having logical breakpoints (such as phase transitions when measuring temperature or high school or college degrees in years of education) is both natural substantively and can be used in some applications to construct a relatively simple theory of causal inference. The result is a finite sample theory that is simple to understand and easy to implement by using matching to preprocess the data, after which one can use whatever method would have been applied without matching. The theoretical simplicity also allows for binary, multicategory, and continuous treatment variables from the start and for extensions to valid inference under imperfect treatment assignment. In applications where the existing theory of matching is difficult to apply, the new approach added to the existing toolkit may help some researchers in these situations make valid causal inferences, or at least better understand why they cannot.

Stefano M. Iacus is associate professor in Probability and Mathematical Statistics at the Department of Economics, Management and Quantitative Methods, University of Milan, former member of the R Core Team (2001-2014) for the development of the R statistical environment and co-founder of the SpinfOff company of the University of Milan called Voices from the Blogs. His field of interests include causal inference, inference for stochastic differential equations, numerical finance, sentiment analysis and computational statistics. He is author of three monographs and several academic papers in the above mentioned fields.

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