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20 - Inference for General Causal Estimands

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
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Summary

INTRODUCTION

Much of the discussion in the fourth part of the book focused on an average treatment effect as the causal estimand of primary interest. Although this is an important case, many of the analyses extend to other causal estimands in a conceptually straightforward manner. In this chapter we discuss some examples of other estimands, and show how some of the earlier analyses apply with other estimands.

In many cases concerning causal questions, average effects are the most obviously interesting objects. Sometimes the focus is on average effects after taking some transformation of the outcome, possibly involving pre-treatment variables, but this does not lead to any conceptual problems or operational difficulties when applying the analyses from the previous chapters. In other cases, however, the causal estimands are conceptually distinct from average treatment effects. This includes situations where the average effect is just one of the objects of interest, as well as settings where the primary object is not an average effect. For example, policy makers may be interested in the effect of a new program on specific parts of the distribution of outcomes. In a labor market training program, policy makers may be less interested in the effect of the program on relatively high-earning individuals, instead being more concerned about the effect on the left tail of the distribution. In that case, differences between quantiles of the two potential out-come distributions may be more interesting estimands. Alternatively, policy makers may be interested in the effect of a new program on inequality in outcomes, say, through the effect of the treatment on the variance or the inter-quartile range of the distribution of outcomes.

The approach to estimation and inference that is the focus here is model-based imputation, which has a number of conceptual advantages relative to other approaches. The most important one is that once the missing potential outcomes are imputed, any causal estimand of the type we consider can be directly calculated.

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Publisher: Cambridge University Press
Print publication year: 2015

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