A1687
Title: Truncation-adjusted maximum likelihood for Weibull duration models
Authors: Tobias Jansen - University of Cologne (Germany) [presenting]
Dominik Wied - University of Cologne (Germany)
Abstract: Duration data subject to left truncation arise when entry into an observation window is conditioned on survival. Maximum likelihood estimation based on the unconditional density ignores this selection mechanism and yields inconsistent estimators. A truncation-adjusted maximum likelihood estimator for Weibull duration models is developed under double truncation induced by a uniform entry mechanism. A selection probability $\alpha_\theta$ generalizes the closed-form exponential case to arbitrary Weibull shape and is evaluated by numerical quadrature. Identification is established via an injectivity argument based on the linear independence of Weibull log-density components on the observation region, dispensing with the memorylessness assumption used in the exponential case. Consistency and asymptotic normality follow from standard M-estimator arguments. Truncation contracts both information curvature and score variance without offsetting, so the sandwich form does not reduce to the inverse information. A feasible plug-in estimator based on a numerical Jacobian and outer-product score delivers valid inference. Monte Carlo simulations across truncation severities and Weibull shape regimes confirm bias reduction and near-nominal coverage relative to the naive maximum likelihood benchmark. An empirical application to German firm insolvency data quantifies the hazard shape and the magnitude of the truncation correction.
