Retirement Incomes: Private Savings versus Social Transfers

Abstract

It has long been known, from the work of Samuelson and Aaron, that if (approximately) the sum of the population and real earnings growth rates exceeds the real interest rate, all individuals can be made better off by using a pay‐as‐you‐go pension scheme. The basic overlapping generations model that is typically used to examine such intergenerational transfers makes no allowance for labour supply responses to taxes and transfers, and so cannot be used to examine optimal tax and pension levels. The present paper allows for labour supply effects, whereby a tax imposed to finance current pensions introduces distortions to labour supply and a reduction in the tax base. The optimal proportional tax rate, and therefore the optimal combination of private savings and social transfers, is derived in terms of the time preference rate, the taste for leisure, real interest and productivity and population growth rates. It is found that the condition under which the optimal tax is positive is the same as the Samuelson–Aaron condition. A crucial ingredient in obtaining this result is an assumption that pension levels are adjusted in line with the growth of wage rates rather than, for example, being held constant in real terms. This in turn is found to imply that earnings grow at the same rate as the wage, so long as preferences are such that leisure can be expressed as a proportion of full income.