What determines the optimal mix of public and private insurance?

Giuseppe Bertola, Winfried Koeniger 29 April 2011

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In all economies, both public policies and private contracts provide insurance. Government-sponsored social insurance programmes cover many health, employment and disability risks. Households can also insure partially against these and other risks in private markets by buying explicit state-contingent insurance or by accumulating wealth.

Insurance is costly and reduces incentives

These insurance schemes cannot and should not cover risk perfectly, for two reasons.

  • The first is that individuals should be rewarded for their effort to increase the mean and reduce the variance of their own (and aggregate) income and welfare. Since it is not generally possible to observe the relevant actions and their impact on the probability distributions of outcomes, insurance reduces incentives to exert effort.
  • The second is that providing insurance is costly. Public insurance administration and private insurance provision do not just transfer resources from lucky to unlucky individuals, they also absorb a substantial proportion of receipts. In Figures 1 and 2 below we plot available data on the cost of private and public insurance. Operating and administration expenses are widely diverse across OECD countries. On average, production of private non-life insurance costs about one-third of claims, and the administration of taxes absorbs 1% of net revenues.

Figure 1. 

Figure 2. 

The scope for public insurance schemes

Given that insurance is provided both by public insurance programmes and private contracts, at least two important questions immediately arise. What is the optimal mix of public and private-sector insurance provision, and can public tax and transfer schemes be designed so as to improve the trade-off between the benefits of insurance and its costs in terms of effort incentives and administrative expenses?

One can make substantial progress towards answering these questions by building on insights from the classic insurance literature (Pauly 1974) and the new dynamic public finance literature (Kocherlakota 2010). These strands of research have emphasised that public insurance provision is constrained not only because individual effort, which prevents adverse outcomes, is not observable but also because individuals' private transactions that shelter them from risk are not observable. It is generally possible to enter into multiple private insurance contracts, all of which contribute to reducing welfare fluctuations. Cumulative coverage can be limited for specific risks, such as theft and fire, but access to many independently provided insurance contracts implies that insurance prices do not account appropriately for the incentive effects of the additionally purchased insurance. Competitive insurance providers sell the additional insurance unit at a price that does not condition on the total amount of coverage, so insurance coverage is excessive in equilibrium.

For the provision of public insurance, the presence of hidden financial transactions poses a subtle and important problem. Portfolios of private assets, especially when they are contingent on individual risk realisations, can offset not only the effects of random shocks, but also those of public insurance schemes. If financial transactions are hidden and frictionless, public policy is completely powerless to address incentive issues.

In reality, neither the government nor the private-sector firms can fully observe all the private insurance transactions of households, due to data protection laws and the sheer cost of collecting data on all relevant household transactions. While private trade may be hidden, however, it is not costless. Focusing on the shape of the relevant costs, it is possible to explain why private and public insurance coexist, and to characterise their interaction. If the production cost structure of private insurance contracts implies increasing marginal costs, then the amount of private insurance is not only smaller, although still excessive in decentralised equilibrium, but is also manipulable by public transfers (see Bertola and Koeniger 2010). Whenever the equilibrium price of private insurance contracts depends on the depth of the market in terms of the total traded amount, they are not fully crowded out by public contingent transfers. Thus, public policy can influence an equilibrium that, in the presence of hidden insurance transactions, is generally inefficient.

The optimal insurance mix depends on transaction costs and preservation of incentives

In theory, the optimal mix of public and private insurance depends on the size and, especially, the shape of both public and private transaction costs. As decreasing-returns private production reduces the total cost of insurance operations, public transfers may be positively correlated with privately provided insurance. Since hidden private insurance is excessive, however, public transfers may reduce it, in order to improve effort incentives.

In practice, these mechanisms may explain the widely diverse levels and compositions of insurance across countries and time. The structural features that determine the character of information asymmetries and the shape of transaction costs in turn depend on institutional and technological factors. While entry barriers and market power are likely to restrict the volume of financial transactions, information pooling and lender competition may deepen financial markets.

Although very little empirical information is available to quantify the relevant effects, the qualitative insights are important for various policy areas. In all countries, private health insurance complements public health insurance schemes, and public old-age pensions complement private asset accumulation. In Nordic countries and elsewhere, the “Ghent” system sees unions administering unemployment insurance alongside government bodies. In such situations, and whenever multiple insurance providers are not perfectly informed about individual financial situations, the optimal mix of insurance has to strike a balance between the overall costs and benefits of insurance as well as the preservation of work incentives.

References

Bertola, Giuseppe and Winfried Koeniger (2010), “Public and Private Insurance with Costly Transactions”, CEPR Discussion Paper 8062.

Brown, Jeffrey R and Amy Finkelstein (2007), “Why is the Market for Long-Term Care Insurance so small?”, Journal of Public Economics, 91:1967-1991.

Kocherlakota, Narayana R (2010), The New Dynamic Public Finance (Toulouse Lectures in Economics), Princeton University Press.

OECD (2004), Tax Administration in OECD Countries: Comparative Information Series, OECD.

Pauly, Mark V (1974), “Overinsurance and Public Provision of Insurance: The Roles of Moral Hazard and Adverse Selection”, Quarterly Journal of Economics, 88:44-62.

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Topics:  Financial markets Labour markets

Tags:  insurance

Professore ordinario, Università di Torino; CEPR Research Fellow

Professor of Economics, University of St. Gallen; Research Fellow, Center for Financial Studies and IZA; Research Affiliate, CEPR

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