PROCEEDINGS May 15, 16, 17, 18, 2005 - Casualty Actuarial Society

250 WHEN CAN ACCIDENT YEARS BE REGARDED AS DEVELOPMENT YEARS?A further important consequence of this property is that parametersin the two directions can take the roles of both a leveland a ratio.We know within ourselves that the two directions are fundamentallydifferent, both in general appearance of their trends andin spirit. The development year direction tends to have a smoothrun-off shape, where the incremental losses tend to increase initiallyto a peak somewhere in the first few developments andthen smoothly decrease in the tail, while the accident years tendto have quite a different pattern. Yet the model itself makes nosuch distinction–it does not contain important information wealready know about claims payments (i.e., the structure in lossdata).Indeed, the chain ladder model, being a two-way cross classificationmodel (as has been recognized by numerous authors),not only fails to distinguish between accident years and developmentyears, it ignores the relationships between years withineither category.Consider the two plots of logs of paid data against developmentyear in Figure 5. Can you tell which one is the real data?Most practitioners will instantly (and correctly) guess that thelower plot is the real one. We know that paid data often has astrong pattern to its runoff–that nearby development periodstend to be more alike than ones further away, and further, weusually observe smooth trends relating them.Clearly the accident and development labels mean something,and you can’t arbitrarily relabel them without affecting the informationin the data. The observations in development year 3 donot just tend to be closer to each other than to observations fromother columns, they also tend to be more like the observations indevelopment years 2 and 4 than they are like observations fromcolumns further away. In a two-way cross-classification model,we can arbitrarily rearrange the group labels within both factors,and even interchange the factors without changing the fit. If the