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Abstract
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The second part of the state-of-the-art focuses on the development of the founders' double streams explaining single-outcome indicators (probability of accidents and fatalities, respectively) by fixed form regression, as outlined in the Part 1. Following Page (1997, pp. 67-122, 2001) and others, we use as turning point of the evolution of both aggregate and discrete approaches the DRAG-1 model of 1984, itself based on aggregate data, which introduced four key innovations in principle applicable to both streams.
The DRAG approach (i) decomposed losses (victims or damages) into a product of exposure, frequency and severity terms and formulated distinct explanations for all such terms; (ii) structured the decomposed problem as a system of simultaneous equations that included not only those three levels but a fourth one designed to explain driver behavior and make it endogenous; (iii) within each of the four principal levels, took into account sub-categories of severity the joint determination of which constituted a complete system of demand that brought numerous substitutions and complementarities into play; (iv) used for all specified equations flexible mathematical forms of the Box-Cox type applied to all regression variables. These forms were decisive in defining statistical correlations (signs included), upon which they themselves depended, and in justifying the initial breakdown into multiple risk dimensions by revealing the mathematical form appropriate for each level (exposure, frequency, and severity) of the decomposition.
Using these four critical dimensions, we summarize both aggregate and disaggregate model developments, classifying them notably with respect to number of risk outcome levels addressed, severity categories accounted for, mathematical form of their variables and number of classes of explanatory variables put to contribution. For aggregate models, we document evolution from early ones explaining a single damage category for one region to the latest explaining multiple damage categories for many regions, not forgetting intermediate cases. With respect to the disaggregate models, in addition to providing a classification with respect to the same four dimensions, we raise the specific problems of aggregation from individual to population values without which discrete analysis remains of limited relevance, giving disproportionate attention to the landmark by Bolduc et al., available for the first time in English in this issue. |