Contradiction Between Venter and Taylor

In the Venter paper we are told that the “Parametrized BF” model has twice the number of parameters as the Chain Ladder model. Namely that the BF model has 2n - 2 parameters and that the CL model as n -1 parameters where n is the number of accident years. But Taylor points out in section 3.2 that the Cross Classified model has 2n - 1 parameters and that the CL model effectively has the same number of parameters because conditioning on the loss to date serves as row parameter for each accident year. Venter is actually wrong in two ways because he gives the number of parameters for the BF model as 2n - 2 when in fact it should be 2n - 1 as in both Taylor and Shapland.

It seems to me that the CAS should release a study note that explains the contradictions between the different papers and clarifying which is correct. I still think the Venter paper is important because it does point out a lot of good ideas about testing the assumptions of the CL model, but it’s also a bit outdated, contradicting many of the more recent monographs.

Venter assumes we aren’t trying to predict the losses at the first evaluation point, so there’s only n-1 column parameters. Then there are n row parameters. Since we can scale all the parameters by a constant, the total number of parameters is 2*n-2.

2n - 1 vs 2n - 2 is actually a pretty minor difference that wasn’t the main point of my post. My main point is that the Chain Ladder model effectively has the same number of parameters as the Cross Classified model, namely 2n - 1, as pointed out in Taylor. This is because conditioning on the loss to date effectively acts as a row parameter for each AY. So Venter is wrong to assume that the Parametrized BF has more parameters than the CL model.

Oh yeah, I agree with that. Clark also has a similar discussion on the number of parameters. Since he uses 2 parameters to fit the development pattern, he says the Cape Cod method has 3 parameters and the LDF method has n+2 (one for each AY, and 2 for the curve fitting).