The Efficiency Bound of the Mixed Proportional Hazard Model.

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 direction and its conditional expectation given the sufficient statistic. Applying this result to the single-spell Weibull mixed proportional hazard model, it is shown that its information matrix is singular and there cannot exist any [square root]n-consistent estimator sequence. The information of the multi-spell Weibull mixed proportional hazard model is shown to be nonsingular in general. Copyright 1994 by The Review of Economic Studies Limited.