A0208
Title: Left-truncated durations: Theoretical review and empirical applications
Authors: Rafael Weissbach - University of Rostock (Germany) [presenting]
Eric Scholz - University of Rostock (Germany)
Abstract: Left-truncated are statistical units in a panel data set when (i) Units born before the first wave belong to the population, (ii) Death of a population unit before the first wave is possible, and (iii) The birthdate of every observed unit is known if the model is not age-homogeneous. Filtrations model the missing data and enable circumventing the unknown number of truncated units by using conditional likelihood. Proving the martingale property of the process of counting events of interest after compensation enables the use of martingale limit theorems to derive standard errors and asymptotic normality. One has to invest in theorems with assumptions which can be verified. Theoretical results are for time-continuous and time-discrete durations. Applications are for human and business demography, namely from a panel of claims data by a German health insurance company and from panel data of the German Statistical Office on enterprise foundation and closure. It is found that after a stroke, with time measured in years, the intensity of dementia onset increases from 0.02 to 0.07, with the standard error of the difference being 0.00093. It is found that the life expectancy of German enterprises is 10 years, with a standard error of 0.015. Both models are asymptotically normal. Events after the last wave are right censored and taken into account as usual.
