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15 - Matching to Improve Balance in Covariate Distributions

from PART III - REGULAR ASSIGNMENT MECHANISMS: DESIGN

Published online by Cambridge University Press:  05 May 2015

Guido W. Imbens
Affiliation:
Stanford University, California
Donald B. Rubin
Affiliation:
Harvard University, Massachusetts
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Summary

INTRODUCTION

In observational studies, the researcher has no control over the assignment of the treatment to units. This lack of control makes such studies inherently more sensitive and controversial than evaluations based on randomized assignment, where biases can be eliminated automatically, at least in expectation, through design, and as a result, for example, p-values can be assigned to sharp null hypotheses without relying on additional assumptions. Nevertheless, even in observational studies, one can carry out what we like to call a design phase during which researchers can construct a sample such that, within this selected sample, inferences are more robust and credible. We refer to this as a design phase because, just like in the design phase of a randomized study, it precedes the phase of the study during which the outcome data are analyzed. In this design phase, researchers can select a sample where the treatment and control samples are more balanced than in the original full sample. Balance here refers to the similarity of the marginal (generally multivariate) covariate distributions in the two treatment arms. This balance is not to be confused with the covariate balance conditional on the true propensity score that we discussed in the previous chapter. The latter holds, in expectation, by definition.

An extreme case of imbalance occurs when the ranges of data values of the two covariate distributions by treatment differ, and as a result there are regions of covariate values that are observed in only one of the two treatment arms. More typical, even if the ranges of data values of the covariate distributions in the two treatment arms are identical, there may be substantial differences in the shapes of the covariate distributions by treatment status. In a completely randomized experiment, the two covariate distributions are exactly balanced, in expectation. In that case, many different estimators – for example, simple treatment-control average differences, covariance-adjusted average differences, as well as many different model-based methods – tend to give similar point estimates of causal effects when sample sizes are at least moderately large.

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Publisher: Cambridge University Press
Print publication year: 2015

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