Essays on Pensions and Information
Abstract: The first essay examines the outcome in a competitive private pension market characterised by adverse selection. In addition to using the private pension market, the consumers can save in a bequeathable asset. Assuming two types of agents and using the Coalition Proof Equilibrium with Private Information we show that the outcome in the private pension market may be separating or pooling. A separating equilibrium may be associated with profits. A pooling equilibrium is associated with supplementary savings in the bequeathable asset. It is argued that the option of saving in a second bequeathable asset generally does not benefit any consumer since its dominating effect is to aggravate the incentive compatibility problem. The second essay uses a simple two period model to examine the outcome of voting over a fully funded public pension system by a single cohort of consumers. Public pensions are interpreted as public provision of a private good. In addition to the public pension system the consumers have a supplementary private pension market available. The private market is characterised by adverse selection. The return in the private market is negatively related to size of the public system, which causes some consumers to have nonsingle-peaked preferences. Necessary conditions for public system to be a majority voting equilibrium are given. Numerical examples reveal that a political equilibrium is likely to be associated with supplementary savings in the private market by only a small fraction of the population. There typically also exists a local political equilibrium with a small public pension system and a large private market. This means that reaching the global political equilibrium often requires a vote over a discrete increase in the size of the public system. In the third essay 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-subsidise between the sectors, and it is demonstrated how the responsiveness of the labour force allocation limits the optimal extent of cross-subsidisation. The second-best policy is, however, time-inconsistent. The time-consistent equilibrium is explored and is argued to provide weak incentives to acquire risk reducing skills. The fourth essay continues to explore the design of optimal public disability insurance in a two-sector economy. Focusing on time-consistent outcomes the essay asks if there is a rationale for supplementing a public disability system with an intervention in the education market. The answer is affirmative; since the disability insurance system will subsidise the high-risk/low-skill sector, a worker who acquires skills does not capture the full social benefit of the investment. The education policy forestalls the time-consistency problem, and the conclusion is argued to carry over to a situation where the government can commit to a disability insurance system.
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