Life, Limb and Bumper Trade‐offs Calculable from Road Accident Models: An Empirical Multimoment Portfolio Analysis and Life Asset Pricing Model (LAPM)

Abstract

The paper provides an empirical trade‐off analysis among the first three moments of road accident frequencies, and it is demonstrated that road drivers can be understood as behaving with respect to road accidents as investors trading among the various moments of the return of a financial asset, as they attach utility to at least three moments of the accident probability in conformity with Allais’s view. The method effectively proposes an empirical Life Asset Pricing Model (LAPM), i.e. a revealed preference alternative, derived directly from driver behaviour on the road itself, to the less direct human capital and willingness‐to‐pay approaches to the valuation of human life, termed ‘value of a statistical life’, in road risk analyses. The analysis, which is applicable in principle to any accident regression model, but performed here with two Demand for Road Use, Accidents and their Gravity (DRAG)‐type aggregate time series models, respectively, for Quebec, Canada, and western Germany, shows amazing similarities in the estimated rates of substitution among accidents of various severity levels within each region, as well as amazing dissimilarities between the regions in the asymmetry of the sample distributions pertaining to bodily injury accidents. For Quebec, where the fully documented model in official use has a long history of successful explanation and forecasting of the number and severity of road accidents, the rates of substitution among the accident frequencies of different categories imply that official Canadian human live valuations used in network accounts are too low (and the computed social cost recovery of roads too high), and that there exists a market for drivers willing to pay more for reduced driving risks than is assumed by road authorities on their behalf.

Notes

1. The note expanded here as an article has not been circulated separately from the paper by Blum and Gaudry (2000). Resulting draft versions of that paper (CRT‐99‐07) from May 1999 and August 1999 yielded a final manuscript (W. P. No. 2000‐11, Bureau d’économie théorique et appliquée, Université Louis Pasteur, Strasbourg), published in Gaudry and Lassarre (2000, pp. 67–96). A first version of this article was produced for the Bioteaux Committee (Boiteaux and Baumstark, 2001).

2. This paragraph and the intuitive presentation below are drawn essentially from the comments of one anonymous referee, to whom the author is grateful.

3. The ability to perceive at least the first three moments of a distribution is a much weaker assumption than required by the ability, shown in recent tests (Griffiths and Tenenbaum, 2006), according to which the implicit statistical model underlying perception is extremely close to reality to the point that cognitive judgement correctly identifies, even from unique observations, distributions such as the Gauss, Poisson, Erlang and Power Function laws.

4. Some rare models deal with the median of the explained variable.

5. It would be nice to consider a continuous loss function, but to do this one would need to know the trade‐offs that are the very subject of analysis among accident categories expressed in different numéraires or units.

6. The author thanks an anonymous referee for this suggestion.

7. Liem et al. (2000) is downloadable from the Analytical Methods page of Agora Jules Dupuit (http://www.ajd.umontreal.ca) (see Gaudry, 1984/2002).

8. This distinction does not depend on whether the random residual is assumed to be Gaussian or Poisson distributed, as incorrectly implied in a previous version of this paper and in Gaudry (2000), where the author stated that marginal trade‐offs between the first and second moments that differed from 1 implied a rejection of the Poisson model: the trade‐offs being measured are on the systematic (on the regression component) part of the model, not on the error terms. The author thanks the first anonymous referee for pointing out that our remark on the Poisson was inconsistent with the approach developed here and was itself an example of the confusion mentioned in this paragraph.

9. TRIO is downloadable from the Quantitative Methods page of the Agora Jules Dupuit website (see note 7).

10. See note 7.