Interpretable Almost-Matching Exactly with Instrumental Variables

Abstract

<p>We aim to create the highest possible quality of treatment-control matches for categorical data in the potential outcomes framework. </p><p>The method proposed in this work aims to match units on a weighted Hamming distance, taking into account the relative importance of the covariates; To match units on as many relevant variables as possible, the algorithm creates a hierarchy of covariate combinations on which to match (similar to downward closure), in the process solving an optimization problem for each unit in order to construct the optimal matches. The algorithm uses a single dynamic program to solve all of the units' optimization problems simultaneously. Notable advantages of our method over existing matching procedures are its high-quality interpretable matches, versatility in handling different data distributions that may have irrelevant variables, and ability to handle missing data by matching on as many available covariates as possible. We also adapt the matching framework by using instrumental variables (IV) to the presence of observed categorical confounding that breaks the randomness assumptions and propose an approximate algorithm which speedily generates high-quality interpretable solutions.We show that our algorithms construct better matches than other existing methods on simulated datasets, produce interesting results in applications to crime intervention and political canvassing.</p>