1.2 Basics of Experiments

GOVT 300 Geroge Mason University

Randomization of the treatment assignment (Randomly decide who gets the treatment and who does not)

helps ensure the groups are similar

there’s no preference for any type of unit to receive the treatment (or to not receive it)

As long as the sample is not too small, randomization of the

Treatment and control groups will be similar, on average

Treatment variable

Xi ∈ {0, 1} [1 if treated, 0 if not]

where X belongs to 0 or 1

Treatment group

Those units for which Xi = 1

Control group

Those units for which Xi = 0

n_T

number of units in the treatment group

n_C

number of units in the control group

Observed Outcome (Y_i)

the potiental outcome that is realized (depending on treatment status)

If a unit gets the treatment, then we observe their Potential Outcome Under Treatment

Yi = Yi(1) if Xi = 1

If a unit does not get the treatment, then we observe their Potential Outcome under control:

Yi = Yi(0) if Xi = 0

Average Outcome for the Treatment Group

Average Outcome for the Control Group

We use the average of Y_T to infer

the average of Y(1)

We use the average of Y_C to infer

the averge of Y(0)

(if groups are similar) the average of Y_C

is a good inferred counterfactual for the average of Y_T

Difference-in-Means estimator

(Average of Y_T) - (Average of Y_C)

When both groups are similar (when we randomize the treatment)

• the only systematic difference is the treatment

• thus, treatment and control groups serve as counterfactuals for each other

• thus, DiM allows us to infer SATE

Use DiM = the average of Y_T - the average of Y_C to infer

SATE = the average of Y(1) - the average of Y(0)

Use DiM = the average of Y_T - the average of Y_C to infer SATE = the average of Y(1) - the average of Y(0)

this inference is good as long as the groups are similar