Establish whether sample splitting is theoretically unnecessary

Determine whether the correlation between the estimated pseudo-distance and the network formation error terms vanishes asymptotically sufficiently rapidly to make sample splitting unnecessary for the proposed covariate-assisted local two-way fixed-effects network-imputation estimator.

Background

The theoretical analysis uses sample splitting to ensure independence between the pseudo-distance used for neighborhood selection and the error terms entering the local two-way fixed-effects regression. In the empirical implementation, however, sample splitting reduces the effective sample size and produces worse finite-sample performance than the full-sample procedure.

The authors state that it is reasonable to expect the dependence between the pseudo-distance and the regression errors to diminish as the sample size grows, but they do not formally establish this result. Consequently, whether the practically preferable full-sample procedure has the same asymptotic guarantees remains unresolved.