The Singularity of the Information Matrix of the Mixed Proportional Hazard Model
Elbers and Ridder (1982) identify the Mixed Proportional Hazard model by assuming that the heterogeneity has finite mean. Under this assumption, the information matrix of the MPH model may be singular. Moreover, the finite mean assumption cannot be tested. This paper proposes a new identification condition that ensures non-singularity of the information bound. This implies that there can exist estimators that converge at rate root N. As an illustration, we apply our identifying assumption to the Transformation model of Horowitz (1996). In particular, we assume that the baseline hazard is constant near t=0 but make no no parametric assumptions are imposed for other values of t. We then derive an estimator for the scale normalization that converges at rate root N.