A0152
Title: Gumbel-type copulas as model for truncation dependence
Authors: Rafael Weissbach - University of Rostock (Germany) [presenting]
Anne-Marie Toparkus - Universität Rostock (Germany)
Abstract: For panel data, the dependence between the lifespan of the individual and its age at study entry is studied because the latter is equivalent to the birthdate, and independence implies the death hazard is stationary. Model dependence is studied with the Gumbel-type copulas in order to answer two questions. First, how can independence be tested? Second, is the hazard constant with age? The first question is considered parametric; the log-likelihood can be derived from standard results for point processes, and the unobserved sample size can be profiled. The asymptotic distribution of the test statistic is a mixture of a two-dimensional and a one-dimensional normal distribution. The second question is considered to be nonparametric, and a two-dimensional Kolmogorov-Smirnov goodness-of-fit test has a composite hypothesis when the unknown true parameter is replaced by its estimator. In cases of double truncation, the compactness of the truncation region allows the test statistic to be computed using common methods for the bivariate uniform case. In a generalized version of the test, truncation dependence is enabled with a copula. It is also outlined what to do when additional censoring arises e.g., because of the lack of early birthdates or when death is missing due to a loss in follow-up. Econometric examples of both questions are for 55,000 lifespans of German enterprises that ended between 2013-2015 and are compared with Japanese results.
