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522 Chapter 13 Experiments and Quasi-Experiments

to middle-class students? This chapter discusses how such programs or policies can
be evaluated using experiments or quasi-experiments.

We begin in Section 13.1 by elaborating on the discussions in Chapters 1, 3,
and 4 of the estimation of causal effects using randomized controlled experiments.
In reality, actual experiments with human subjects encounter practical problems
that constitute threats to their internal and external validity; these threats and some
econometric tools for addressing them are discussed in Section 13.2. Section 13.3
analyzes an important randomized controlled experiment in which elementary stu-
dents were randomly assigned to different-sized classes in the state of Tennessee in
the late 1980s.

Section 13.4 turns to the estimation of causal effects using quasi-experiments.
Threats to the validity of quasi-experiments are discussed in Section 13.5. One issue
that arises in both experiments and quasi-experiments is that treatment effects can
differ from one member of the population to the next, and the matter of interpret-
ing the resulting estimates of causal effects when the population is heterogeneous
is taken up in Section 13.6.

13.1 Potential Outcomes, Causal Effects,

and Idealized Experiments

This section explains how the population mean of individual-level causal effects
can be estimated using a randomized controlled experiment and how data from
such an experiment can be analyzed using multiple regression analysis.

Potential Outcomes and the Average Causal Effect

Suppose that you are considering taking a drug for a medical condition, enrolling
in a job training program, or doing an optional econometrics problem set. It is
reasonable to ask, what are the benefits of doing so—receiving the treatment—for
me? You can imagine two hypothetical situations, one in which you receive the
treatment and one in which you do not. Under each hypothetical situation, there
would be a measurable outcome (the progress of the medical condition, getting a
job, your econometrics grade). The difference in these two potential outcomes
would be the causal effect, for you, of the treatment.

More generally, a potential outcome is the outcome for an individual under a
potential treatment. The causal effect for that individual is the difference in the
potential outcome if the treatment is received and the potential outcome if it is
not. In general, the causal effect can differ from one individual to the next. For