A Simulation Analysis of Maximum Likelihood Estimation of Log-Rate Models with Gaussian Unobserved Heterogeneity

Francesca Michielin, University of Padua
Constantijn (Stan) Panis, RAND

This paper assesses the properties and the robustness of the Maximum Likelihood Estimator of mixed proportional hazard rate models when the unobserved heterogeneity components are assumed to have a normal, or a joint normal, distribution function additive on the log-hazard, and where duration dependence is given a flexible specification (piecewise continuous linear Gompertz). We undertake an extensive simulation/bootstrap analysis of a previous application in which migration and fertility transitions are modelled as interrelated processes. We investigate the properties of estimates for single spell - single process (out-migration), multiple spell - single process (the fertility process), and multiple processes (fertility and out-migration as interrelated processes). In most cases we find MLE to perform well - generally producing unbiased estimates. However, the analysis demonstrates under which circumstances large biases might arise. More specifically, this tends to happen in single spell models when the variance is small, and in models with multiple processes when the covariance is large and positive.

Presented in Session 77: Statistical Demography