What is the impact of duplicate coverage on the demand for health care in Germany?

Duplicate coverage involves those individuals who hold public health insurance, and purchase additional private coverage. Using data from the German Institute for Economic Research, we try to investigate the impact of duplicate coverage on the demand for healthcare (measured in number of visits to doctors). Given the simultaneity of the choices to take out additional private health insurance coverage, we estimate a negative binomial model to measure this impact. We also estimate a a Full Information Maximun Loglikelihood (FIML), known as Endogenous Switching Poisson Count Model and we compare these results with the standard maximum log likelihood (ML) estimators of the negative binomial model. The Results show that, there is a positive difference on the level of health services demanded when there is a duplicate coverage. We found also that there is evidence to think that in Germany there is a feedback between duplicate coverage and the demand of health services.