Many social experiments are run in multiple waves, or are replications of earlier social experiments. In principle, the sampling design can be modified in later stages or replications to allow for more efficient estimation of causal effects. We consider the design of a two-stage experiment for...

The semiparametric efficiency bound of the mixed proportional hazard model is derived. The density factors in such a way that there exists a complete sufficient statistic for the individual heterogeneity. The efficient score is shown to be the difference between the score in the parametric...

The role of propensity score in the efficient estimation of the average treatment effects is examined. If the treatment is ignorable given some observed characteristics, it is shown that the propensity score is ancillary for estimation of the average treatment effects but not for estimation of...

This paper investigates a simple dynamic linear panel regression model with both fixed effects and time effects. Using “large n and large T”asymptotics, we approximate the distribution of the fixed effect estimator of the autoregressive parameter in the dynamic linear panel model and derive...