Misspecifi cation Tests for Chain-Ladder Models

Dec 2017 |

Authors: Jonas Harnau


Despite the widespread use of chain-ladder models, so far no theory was available to test for model specification. The popular over-dispersed Poisson model assumes that the over-dispersion is common across the data. A further assumption is that accident year effects do not vary across development years and vice versa. The log-normal chain-ladder model makes similar assumptions. We show that these assumptions can easily be tested and that similar tests can be used in both models. The tests can be implemented in a spreadsheet. We show the implementation in several empirical applications. While the results for the log-normal model are valid in finite samples, those for the over-dispersed Poisson model are asymptotic. We show in a simulation study that the finite sample performance is close to the asymptotic performance.

Keywords: Bartlett test; F-test; over-dispersed Poisson; log-normal

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