Abstract
In this review, we present econometric and statistical methods for analyzing
randomized experiments. For basic experiments we stress randomization-based
inference as opposed to sampling-based inference. In randomization-based
inference, uncertainty in estimates arises naturally from the random assignment
of the treatments, rather than from hypothesized sampling from a large
population. We show how this perspective relates to regression analyses for
randomized experiments. We discuss the analyses of stratified, paired, and
clustered randomized experiments, and we stress the general efficiency gains
from stratification. We also discuss complications in randomized experiments
such as non-compliance. In the presence of non-compliance we contrast
intention-to-treat analyses with instrumental variables analyses allowing for
general treatment effect heterogeneity. We consider in detail estimation and
inference for heterogeneous treatment effects in settings with (possibly many)
covariates. These methods allow researchers to explore heterogeneity by
identifying subpopulations with different treatment effects while maintaining
the ability to construct valid confidence intervals. We also discuss optimal
assignment to treatment based on covariates in such settings. Finally, we
discuss estimation and inference in experiments in settings with interactions
between units, both in general network settings and in settings where the
population is partitioned into groups with all interactions contained within
these groups.
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