Misspecification Tests for Log-Normal and Over-Dispersed Poisson Chain-Ladder Models

Jonas Harnau
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Jonas Harnau: Department of Economics, University of Oxford & Oriel College, Oxford OX1 4EW, UK

Risks, 2018, vol. 6, issue 2, 1-25

Abstract: 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 illustrate 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 derived for large cell mean asymptotics which hold the number of cells fixed. 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 (search for similar items in EconPapers)
JEL-codes: C G0 G1 G2 G3 K2 M2 M4 (search for similar items in EconPapers)
Date: 2018
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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