Demand Elasticity, Risk Classification and Loss Coverage: When Can Community Rating Work?

Abstract

This paper investigates the effects of high or low fair-premium demand elasticity in an insurance market where risk classification is restricted. The effects are represented by the equilibrium premium, and the risk-weighted insurance demand or “loss coverage”. High fair-premium demand elasticity leads to a collapse in loss coverage, with an equilibrium premium close to the risk of the higher-risk population. Low fair-premium demand elasticity leads to an equilibrium premium close to the risk of the lower-risk population, and high loss coverage – possibly higher than under more complete risk classification. The demand elasticity parameters which are required to generate a collapse in coverage in the model in this paper appear higher than the values for demand elasticity which have been estimated in several empirical studies of various insurance markets. This offers a possible explanation of why some insurance markets appear to operate reasonably well under community rating, without the collapse in coverage which insurance folklore suggests.

Insurance Loss Coverage Under Restricted Risk Classification: The Case of Iso-Elastic Demand

“…Thomas (2008Thomas ( , 2009 introduced the idea of 'loss coverage', namely the expected claims under a given premium rating scheme at equilibrium. It may be thought desirable, from a social policy point of view, for loss coverage to be as high as possible (depending on the nature of the undesired event).…”

“…This paper follows Thomas (2008Thomas ( , 2009) which illustrated the concept of loss coverage with simulations based on an exponential-power demand function suggested by De Jong & Ferris (2006). This demand function is very flexible, but also rather intractable.…”

“…This demand function is very flexible, but also rather intractable. Thus, Thomas (2008Thomas ( , 2009) did not give a full mathematical account of loss coverage. Here, we present a comprehensive mathematical analysis of equilibrium premia, adverse selection and loss coverage, based on a more tractable iso-elastic demand function.…”

“…We define τ i = d(µ i , µ i ) to be the "fair-premium demand" for insurance for risk-group i, which can be regarded as the proportion of risk-group i who buy insurance at an actuarially fair premium De Jong & Ferris (2006) suggested a "flexible but practical" exponential-power demand function, and this approach was also followed by Thomas (2008Thomas ( , 2009). However the exponential-power function, whilst very flexible, is also rather intractable.…”

“…That multiple equilibria can arise was demonstrated by Thomas (2009) using the exponential power demand function proposed by De Jong & Ferris (2006). Thus, for any choice of demand function, we must determine whether or not multiple equilibria can arise, and if they can, whether or not they are material.…”