Prices for Road Accident Externalities when Insurance Companies Have Market Power

Prices for Road Accident Externalities when Insurance Companies Have Market Power


M Dementieva, E T Verhoef, VU Amsterdam, NL


This paper concerns interactions between actors on the car insurance market, and the corresponding influence of large decision makers (insurance companies and government) on each other as well as on drivers' incentives, and thus on road safety.


Road accidents account for a large share of the social costs of road transport, and consist of medical cost, production loss, human losses, property damage, settlement costs and costs due to congestion. Practice shows that efficient control over the insurance markets along with an upgrade of road structure, and further development of social education and corresponding legislative acts can substantially improve road safety outcomes due to modification of road users' attitudes and behavior. In this paper, we study the efficiency of unregulated and regulated (through public pricing) insurance markets, taking into account the interactions with the market for road trips, and the market power that insurance companies normally possess. The key stone of the analysis is the accident externalities that individual road users impose on one another via their presence on the road and driving strategies, and the way insurance companies count it setting their premiums. Within the economic literature on externalities in transport, aviation and private road regulation are well-known fields of study.

Although the resulting social and monopolistic optimum insurance premiums that we will derive have close resemblance to the tolls in corresponding models of traffic congestion, the situation becomes more complex in a symmetric duopoly, as each of the companies has to take into account not only its own clients' but also the rival's customers' behavior, and the externalities they induce.

In contrast to the case of private congestion pricing, where a private firm internalizes (congestion) externalities that its customers impose on one another, a company on an insurance market partially internalizes externalities imposed on other companies' customers as well, because these need to be partially compensated in case of an accident.

Pigouvian and other parametrically viewed taxation rules are standard tools to control and eliminate negative externalities, however, they do not work when acting agents are so big that they can actually affect the level of these taxes (and are aware of this), and restrict their activity in such a manner that it would lead to individually optimal level. An alternative to this ``classical" approach is to introduce a so-called "manipulable" taxation rule, which would depend on the agent activity. Then the agent is forced to maximize social surplus along with its own profit. In this paper we construct such taxation rules for companies on a car insurance market. In order to do so, we develop equilibrium models that allow assessing the design and impact of second-best policy instruments for traffic regulation on safety externalities.

We analyze a three-level hierarchical insurance system, with government on the top; insurance companies in the middle; and atomistic drivers as the lowest level actors. We assume that the players are equally aware of the expected (monetary and non-monetary) accident costs, which are functions of exogenous speed and endogenous distance driven. To reflect that in reality not all costs of accidents are compensated, we introduce an exogenous percentage coverage of accident costs. Namely, the government sets the mandatory liability parameter, and insurance companies may also offer a casco insurance. Taking these into account, companies choose their insurance premiums, and then drivers react by choosing their kilometrage. The insurer of a guilty side covers the victim's costs caused by the accident according to the legislative acts provided by government. Further costs may be covered by extra insurances.

For simplicity we consider bilateral accidents (collisions of two cars) only. In line with laws in majority of countries, we assume that liability insurance that covers the third party loss (both physical injury and damage to property), is obligatory and there is an option to choose a voluntary general insurance (also known as casco) for one's own risks. All the cars and the drivers are identical in the model. Consistent with the symmetry of the road users, drivers involved in an accident are assumed to be equally guilty in expected terms. Expected costs of an accident may include material damage of the parties, medical claims and loss due to possible disability or death We will not distinguish these components explicitly.

Numerical analysis lets to complete the study with comparative statics analysis of relative efficiency of equilibria under different types of market equilibrium and regulation.


Association for European Transport