In his 1923 landmark article, Neyman introduced randomization-based
inference to estimate average treatment effects from experiments
under the completely randomized design. Under this framework,
Neyman considered the statistical estimation of the sample average
treatment effect and derived the variance of the standard estimator
using the treatment assignment mechanism as the sole basis of
inference. In this paper, I extend Neyman's analysis to randomized
experiments under the matched-pair design where experimental units
are paired based on their pre-treatment characteristics and the
randomization of treatment is subsequently conducted within each
matched pair. I study the variance identification for the standard
estimator of average treatment effects and analyze the relative
efficiency of the matched-pair design over the completely randomized
design. I also show how to empirically evaluate the relative
efficiency of the two designs using experimental data obtained under
the matched-pair design. My randomization-based analysis differs
from previous studies in that it avoids modeling and other
assumptions as much as possible. Finally, the analytical results
are illustrated with numerical and empirical examples.
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