A. Colin Cameron 751correlative data summary to obtaining estimates of a causative effect, meaning mea-
sures of how an outcome changes in response to exogenous changes in a regressor.
The current microeconometrics toolkit contains many methods to do so.
The “treatment effects” or “natural experiment” approach seeks to measure cau-
sation by extending randomized experiment methods to observational data. This
major innovation in microeconometrics research uses a potential outcomes nota-
tion that differs from the simultaneous equations framework developed at the
Cowles Commission. Developments have also been made in other more traditional
methods to tease out causation, notably instrumental variables estimation, use of
panel data, and estimation of structural models.
14.5.1 Treatment effects
The treatment effects literature focuses on the simplest case of estimating the causal
effect of a binary regressor. A stereotypical example is to consider the impact on
earnings of participation in a training program. The terminology of a medical trial is
used. Enrollment in a training program is viewed as treatment, having no training
is viewed as control, and the objective is to estimate the causative effect of the
treatment on the outcome variable, earnings.
The ideal way to calculate this effect is to observe earnings for a person with
the training, observe earnings for the same person without training, and subtract.
But this is impossible. Instead the outcome is observed in only one state, while
the other state is a hypothetical unobserved value, called a potential outcome or
counterfactual.
The randomized experiment approach solves the inability to observe the counter-
factual by comparing average outcomes, rather than individual outcomes, for two
groups that are randomly assigned to either treatment or control. This approach
is used at times in the social sciences, in social experiments. But most economics
studies must instead rely on observational data.
The treatment effects literature seeks to extend the experimental approach to
nonrandomized settings. Again averages across groups are compared, but now
individuals select their treatment. Different assumptions about the nature of the
self-selection of treatment and data availability lead to different methods to com-
pute average effects of treatment. A key consideration is whether or not it is
reasonable to assume that self-selection can be controlled for using observed vari-
ables, or whether self-selection additionally depends on unobservables. The latter
case requires much stronger assumptions to make progress.
The following framework is used. The binary treatment variabledtakes value 1
if treatment is assigned and value 0 if untreated (a control). The observed outcome
of interestyis a continuous variable that then takes values:
yi={
y 1 i if treated(di= 1 )
y 0 i if control(di= 0 ).
(14.26)The individual treatment effect is defined to be:
αi=(y 1 i−y 0 i). (14.27)