In paired experiments, the units included in the randomization, e.g. villages, are matched into pairs, and then one unit of each pair is randomly assigned to treatment. We conducted a survey of papers that used paired randomized experiments in economics. To estimate the treatment effect, researchers usually regress their outcome on a treatment indicator and pair fixed effects, and cluster standard errors at the unit-of-randomization level , namely, at the village level in our example . We show that the variance estimator in this regression may be severely downward biased: under constant treatment effect, its expectation is equal to 1/2 of the true variance. Using that variance estimator may lead researchers to substantially overreject the null of no treatment effect. Instead, we argue that researchers should cluster their standard errors at the pair level  .
In paired experiments, units are matched into pairs, and one unit of each pair is randomly assigned to treatment. To estimate the treatment effect, researchers often regress their outcome on a treatment indicator and pair fixed effects, clustering standard errors at the unit-of-randomization level . We show that the variance estimator in this regression may be severely downward biased: under constant treatment effect, its expectation equals 1/2 of the true variance. Instead, we show that researchers should cluster their standard errors at the pair level . Using simulations, we show that those results extend to stratified experiments with few units per strata .
R
the units included in the randomization, e.g. villages,
units
D
then
D
We conducted a survey of papers that used paired randomized experiments in economics.
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usually
often
R
and cluster
clustering
D
, namely, at the village level in our example
R
is equal to
equals
D
Using that variance estimator may lead researchers to substantially overreject the null of no treatment effect.
R
argue
show
A
. Using simulations, we show that those results extend to stratified experiments with few units per strata