A Theory of Statistical Inference for Matching Methods in Applied Causal Research

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A Theory of Statistical Inference for Matching Methods in Applied Causal Research

Abstract:

To reduce model dependence and bias in causal inference, researchers usually use matching as a data preprocessing step, after which they apply whatever statistical model and uncertainty estimators they would have without matching. Unfortunately, this approach is appropriate in finite samples only under exact matching, which is usually infeasible, or approximate matching only under asymptotic theory if large enough sample sizes are available, but even then requires unfamiliar specialized point and variance estimators. Instead of attempting to change common practices, we show how those analyzing certain specific (but extremely common) types of data can instead appeal to a much easier version of existing theory. This alternative theory is substantively plausible, requires no asymptotic theory, and is simple to understand. Its core conceptualizes continuous variables as having natural breakpoints, which are common in applications (e.g., high school or college degrees in years of education, a governmental poverty level in income, or phase transitions in temperature). The theory allows binary, multicategory, and continuous treatment variables from the outset and straightforward extensions for imperfect treatment assignment and different versions of treatments.

Last updated on 01/09/2016