Public and Private Insurance Cross country evidence and a model

Insurance provision di¤ers across developed countries both in terms of total amounts expended, and of whether it is supplied via public schemes or private contractual arrangements. We propose a model where insurance is limited by the need to elicit unobservable e¤ort; entails implementation costs that may di¤er for public and private entities; and tends to be more desirable when liquidity constraints reduce the scope of self-insurance. We characterize how the model’s parameters bear on the absolute (public and private) and relative (public vs. private) dimensions of insurance provision patterns, and seek support for our assumptions and modeling approach using data on the cost of public insurance administration and the actuarial fairness of private insurance markets. Università di Torino and CEPR. Queen Mary, University of London, and IZA. We thank Luigi Bocola for useful comments. This research is part of a project funded by Università di Torino (ex 60%). 1 1 Introduction Developed countries di¤er widely as to whether insurance is publicly provided or based on private contracts, and also di¤er in terms of total public and private insurance expenditures. Scandinavian countries rely much more on public than on private insurance; the di¤erence between public and private insurance expenditures is smaller for Anglo-Saxon countries; and both of these groups of countries spend more than Mediterranean countries, where private and public insurance expenditures are low. In this paper we interpret these facts in a model with government redistribution as well as insurance market imperfections. As pointed out by Eaton and Rosen (1980) and Varian (1980), redistribution can be bene…cial ex ante in the presence of labour income risk; Low and Maldoom (2004) have recently extended that perspective to a setting with endogenous leisure choice and precautionary e¤ects on labour supply. Similar insights are relevant to recent studies that calibrate models with incomplete markets and linear tax-transfer schemes.1 In dynamic equilibrium models with …nancial market imperfections, redistribution can signi…cantly increase welfare (Floden and Linde, 2001), particularly when borrowing is constrained (Hansen and Imhoroglu, 1992). We revisit these …ndings in a stylized framework, focusing on informational issues in order to analyze the rationale for public policies along the lines of, for example, Agell (2002) and Bertola (2004). In general, the implementation of public policies, motivated by insurance concerns, entails e¢ ciency costs. Here, we highlight three determinants of public and private insurance provision. Firstly, public and private insurance entail transaction costs, which play a role similar to that of administration costs in the tax design research surveyed by Slemrod (1999). Secondly, all insurance is limited by moral hazard, where the extent of this problem depends on the public or private provision of insurance. Thirdly, we consider interactions with the loans market imperfections that previous research has shown to be relevant to the desirability of redistribution (Hansen and Imhoroglu, 1992; Bertola and Koeniger, 2007). We …nd that borrowing constraints make redistribution more bene…cial in our model, under plausible parametric assumptions. As a result, the Another strand of literature has investigated the optimal design of redistribution in dynamic settings with incomplete markets. See the survey by Kocherlakota (2005), and Shimer and Werning (2005)’s recent study about the optimal design of unemployment insurance if consumers have access to a savings technology.