- Chatterjee, Indradeb and Hao, MingJie and Tapadar, Pradip and Thomas, R. Guy (2024). Can price collars increase insurance loss coverage?. Insurance: Mathematics and Economics.
Abstract: Loss coverage, defined as expected population losses compensated by insurance, is a public policy criterion for comparing different risk classification regimes. Using a model with two risk-groups (high and low) and iso-elastic demand, we compare loss coverage under three alternative regulatory regimes: (i) full risk-classification (ii) pooling (iii) a price collar, whereby each insurer is permitted to set any premiums, subject to a maximum ratio of its highest and lowest prices for different risks. Outcomes depend on the comparative demand elasticities of low and high risks. If low-risk elasticity is sufficiently low compared with high-risk elasticity, pooling is optimal; and if it is sufficiently high, full risk classification is optimal. For an intermediate region where the elasticities are not too far apart, a price collar is optimal, but only if both elasticities are greater than one. We give extensions of these results for more than two risk-groups. We also outline how they can be applied to other demand functions using the construct of arc elasticity.
- Chatterjee, Indradeb and Macdonald, Angus S. and Tapadar, Pradip and Thomas, R. Guy (2021). When is utilitarian welfare higher under insurance risk pooling?. Insurance: Mathematics and Economics.
Abstract: This paper considers the effect of bans on insurance risk classification on utilitarian social welfare. We consider two regimes: full risk classification, where insurers charge the actuarially fair premium for each risk, and pooling, where risk classification is banned and for institutional or regulatory reasons, insurers do not attempt to separate risk classes, but charge a common premium for all risks. For iso-elastic insurance demand, we derive sufficient conditions on higher and lower risks’ demand elasticities which ensure that utilitarian social welfare is higher under pooling than under full risk classification. Using the concept of arc elasticity of demand, we extend the results to a form applicable to more general demand functions. Empirical evidence suggests that the required elasticity conditions for social welfare to be increased by a ban may be realistic for some insurance markets.
- Hao, MingJie and Macdonald, Angus S. and Tapadar, Pradip and Thomas, R. Guy (2018). Insurance loss coverage and social welfare. Scandinavian Actuarial Journal.
Abstract: Restrictions on insurance risk classification may induce adverse selection, which is usually perceived as a bad outcome, both for insurers and for society. However, a social benefit of modest adverse selection is that it can lead to an increase in `loss coverage’, defined as expected losses compensated by insurance for the whole population. We reconcile the concept of loss coverage to a utilitarian concept of social welfare commonly found in economic literature on risk classification. For iso-elastic insurance demand, ranking risk classification schemes by (observable) loss coverage always gives the same ordering as ranking by (unobservable) social welfare.
Abstract: Insurers typically argue that regulatory limits on their ability to use genetic tests will induce ‘adverse selection’; they say that this has disadvantages not just for insurers, but also for society as a whole. I argue that, even on its own terms, this argument is often flawed. From the viewpoint of society as a whole, not all adverse selection is adverse. Limits on genetic discrimination that induce the right amount of adverse selection (but not too much adverse selection) can increase ‘loss coverage’, and so make insurance work better for society as a whole.
- Hao, MingJie and Macdonald, Angus S. and Tapadar, Pradip and Thomas, R. Guy (2018). Insurance loss coverage and demand elasticities. Insurance: Mathematics and Economics, 79. pp. 15-25.
Abstract: Restrictions on insurance risk classification may induce adverse selection, which is usually perceived as a bad outcome. We suggest a counter-argument to this perception in circumstances where modest levels of adverse selection lead to an increase in `loss coverage’, defined as expected losses compensated by insurance for the whole population. This happens if the shift in coverage towards higher risks under adverse selection more than offsets the fall in number of individuals insured. The possibility of this outcome depends on insurance demand elasticities for higher and lower risks. We state elasticity conditions which ensure that for any downward-sloping insurance demand functions, loss coverage when all risks are pooled at a common price is higher than under fully risk-differentiated prices. Empirical evidence suggests that these conditions may be realistic for some insurance markets.
- Hao, MingJie and Macdonald, Angus S. and Tapadar, Pradip and Thomas, R. Guy (2016). Insurance loss coverage under restricted risk classification: The case of iso-elastic demand, ASTIN Bulletin, 46 (2). pp. 265-291.
Abstract: This paper investigates equilibrium in an insurance market where risk classification is restricted. Insurance demand is characterised by an iso-elastic function with a single elasticity parameter. We characterise the equilibrium by three quantities: equilibrium premium; level of adverse selection (in the economist’s sense); and “loss coverage”, defined as the expected population losses compensated by insurance. We consider both equal elasticities for high and low risk-groups, and then different elasticities. In the equal elasticities case, adverse selection is always higher under pooling than under risk-differentiated premiums, while loss coverage first increases and then decreases with demand elasticity. We argue that loss coverage represents the efficacy of insurance for the whole population; and therefore that if demand elasticity is sufficiently low, adverse selection is not always a bad thing.
- Thomas, R. Guy (2009) Demand elasticity, risk classification and loss coverage: when can community rating work? ASTIN Bulletin, 39 (2). pp. 403-428.
Abstract: This paper investigates the effects of high or low fair-premium demand elasticity in an insurance market where risk classification is restricted. 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 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.
- Thomas, R. Guy (2008) Loss Coverage as a Public Policy Objective for Risk Classification Schemes, Journal of Risk and Insurance, 75 (4). pp. 997-1018.
Abstract: This article suggests that from a public policy perspective, some degree of adverse selection may be desirable in some insurance markets. The article suggests that a public policymaker should consider the criterion of “loss coverage,” and that in some markets a policymaker may wish to regulate risk classification with a view to increasing loss coverage. Either too much or too little risk classification may reduce loss coverage. The concept is explored by means of examples and formulaic and graphical interpretations. An application to the UK life insurance market is considered.