Skip to main content Accessibility help
×
Hostname: page-component-7c8c6479df-995ml Total loading time: 0 Render date: 2024-03-19T05:43:44.601Z Has data issue: false hasContentIssue false

17 - Subclassification on the Propensity Score

from PART IV - REGULAR ASSIGNMENT MECHANISMS: ANALYSIS

Published online by Cambridge University Press:  05 May 2015

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

Summary

INTRODUCTION

In this chapter we discuss a method for estimating causal effects given a regular assignment mechanism, based on subclassification on the estimated propensity score. We also refer to this method as blocking or stratification.

Given the assumptions of individualistic assigment and unconfoundedness, the definition of the propensity score in Chapter 3 implies that the super-population propensity score equals the conditional probability of receiving the treatment given the observed covariates. As shown in Chapter 12, the propensity score is a member of a class of functions of the covariates, collectively called balancing scores, that share an important property: within subpopulations with the same value of a balancing score, the super-population distribution of the covariates is identical in the treated and control subpopulations. This, in turn, was shown to imply that, under the assumption of super-population unconfoundedness, systematic biases in comparisons of outcomes for treated and control units associated with observed covariates can be eliminated entirely by adjusting solely for differences between treated and control units on a balancing score. The practical relevance of this result stems from the fact that a balancing score may be of lower dimension than the original covariates. (By definition, the covariates themselves form a balancing score, but one that has no dimension reduction.) When a balancing score is of lower dimension than the full set of covariates, adjustments for differences in this balancing score may be easier to implement than adjusting for differences in all covariates, because it avoids high-dimensional considerations. Within the class of balancing scores, the propensity score, as well as strictly monotonic transformations of it (such as the linearized propensity score or log odds ratio), have a special place. All balancing scores b(x) satisfy the property that if for two covariate values x and x′, b(x′) = b(x′), then it must be the case that e(x) = e(x′).

Type
Chapter
Information
Publisher: Cambridge University Press
Print publication year: 2015

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Save book to Kindle

To save this book to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

Available formats
×