Social Insurance with Risk-Reducing Investments

Abstract

A two-sector model with sector-dependent disability risks is presented. Working in the low- risk sector requires skills that can be obtained by investments in education. Moral hazard precludes full insurance. The labour force allocation is responsive to the incentives created by a social insurance system. The rationale for intervention lies in the government's power to cross-subsidize between the sectors, and it is demonstrated how the responsiveness of the labour force allocation limits cross-subsidization. The second-best policy is time-inconsistent. The consistent equilibrium is explored and is argued to provide weak incentives to reduce risks. ties to live off their own work. Recently, social insurance has come under scrutiny owing to increased pressures to reduce government expenditures. One critical view that has been put forward is that a public system that pools work- ers with different occupations may cause a significant loss of welfare. Since different occupations are associated with different levels of risk, it is argued that pooled systems, while adhering to a general notion of fairness, cause an inefficient allocation of the labour force. Put in simple terms, pooled systems implicitly subsidize risky activities and thereby promote excessive undertaking of such activities. The purpose of this study is to investigate the problem of social insurance design in a setting where workers can influence the disability risks they are exposed to by choosing a low-risk occupation. The model presented has two sectors, a high-risk sector and a low-risk sector. Working in the low-risk sector requires some kind of costly investment which we represent as a choice of 'education', although it is clear that any investment undertaken by the work- ers-e.g. migration investments-leads to precisely the same trade-offs. The workers choose which sector to enter in response to the incentives created by the social insurance system. This allows an analysis of the trade-off between the efficiency of the labour force allocation and distributive concerns, as well as a characterization of optimal social insurance under various assumptions about the government's ability to cross-subsidize and to affect occupational choices. Following the seminal work by Diamond and Mirrlees (1978), a moral-hazard problem precludes full insurance and creates a second-best environment. Our framework is similar in some respects to that of Whinston (1983). In a pure moral hazard framework Whinston shows that optimal contracts cross- subsidize in favour of more accident-prone workers to an extent that makes them better off than less accident-prone workers; on this point we extend Whinston's result by identifying the exact redistributive rule and by providing an interpretation of the result as an instance of 'tagging'. Whinston further