Variance identification and efficiency analysis in randomized experiments under the matched‐pair design

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.