Population ageing and intertemporal consumption: Representative agent versus social planner

Abstract

This paper examines the optimal path of consumption over time in the context of population ageing. Older age groups are considered to have relatively greater ‘needs’, resulting for example from additional health costs. These differences give rise to the concept of the ‘equivalent number of persons’, as distinct from the population size. Emphasis is given to the difference between a framework involving a representative agent and one in which plans are made by a social planner. The precise conditions under which consumption growth paths are the same under the representative agent and the social planner are established. This equivalence is found to hold only in the case where the social planner's value judgements are such that individuals are considered to be the appropriate unit of analysis. An alternative assumption, in which equivalent persons are regarded as the appropriate units, is found to give rise to a different optimal consumption path. Numerical examples demonstrate the relative orders of magnitude for a range of parameter values. The differences are found to be potentially important. The choice of appropriate consumption units – individuals or equivalent persons – is far from arbitrary since it involves possibly conflicting value judgements. This choice has implications for policies designed to influence the optimal saving rate, such as superannuation policy and the fiscal balance.

Introduction

The aim of this paper is to examine the optimal path of aggregate consumption in the context of population ageing, where older age groups are considered to have relatively greater ‘needs’, resulting for example from additional health costs. These differences give rise to the concept of the ‘equivalent number of persons’, as distinct from the population size. Many models in this context employ the concept of a hypothetical representative agent who is assumed to be infinitely lived and who has the characteristics (that is, the ‘needs’) of an average person in the population in each year. The present paper compares the representative agent approach with an alternative in which the optimal aggregate consumption stream is determined by a social planner who is considered to maximise a social welfare, or evaluation, function defined over the same time horizon. The value judgements of the social planner are made explicit in the form of the welfare function.

Using an individualistic and additive welfare function, total consumption per equivalent person contributes to social welfare in each period. In this preliminary investigation, individuals are considered to differ only by age and hence the planner is not concerned with inequality. One important issue relates to the choice of consumption unit in weighting the consumption per equivalent person in each period. Two cases are examined here — the use of individuals and of equivalent persons. Each of these cases has sensible, but possibly inconsistent, welfare rationales.

The analysis is motivated by the extensive debate regarding the implications of population ageing, and the potential for tax smoothing to achieve an optimal time path of aggregate consumption. The idea that governments should smooth the tax burden over time was first advanced by Barro (1979), who showed that, in a deterministic setting, a flat path of the tax rate over time would minimize the distortions to behaviour arising from taxation. A key insight is that the tax rate must not distort intertemporal consumption choices and must therefore tax consumption at the same rate through time in the long run (Chamley, 1986).¹ Therefore the path of the ratio of optimal income tax to GDP depends on the optimal path of consumption. Consumption smoothing implies a varying ratio of consumption to income and therefore a varying path of the optimal income tax to GDP ratio. In addition, because the optimal consumption path implies an optimal saving path, the analysis in the present paper has implications for policies designed to affect optimal saving such as superannuation policy and the fiscal balance. It is shown that these policy implications depend on value judgements in the evaluation of social welfare.²

The dominant framework for macroeconomic modelling is based on the behaviour of representative agents because the outcomes can be traced to microeconomic foundations. These agents can have either infinite lives, single period lives leading over time to a dynasty of individuals, or finite multi-period lives which imply a number of overlapping generations at a point in time. The origin of this framework was provided by Ramsey (1928) who assumed an infinitely lived individual. It is widely used in modelling economic growth and macroeconomic aggregates. Seminal expositions of a range of these models include, for example, Barro and Sala-I-Martin (1995) and Obstfeld and Rogoff (1996). All large scale multi-sector, multi-region models (computable general equilibrium models) used to model national and world economies are based on the behaviour of representative agents. Examples include the OECD's MINILINK model, the IMF's MULTIMOD model and the European Commission's QUEST model.³ A common feature of these models is that the agents optimise intertemporally and this feature is the focus of attention below.

However, the representative agent framework has been subject to a number of strong criticisms; see, for example, Kirman (1992). Also, it has limitations in social welfare analysis of public policies such as fiscal policy where it is useful to know the socially optimal outcome. This is because the representative agent model generates Pareto optimal aggregate outcomes only under strict assumptions; see, for example, Lewbel (1989). For this reason it is sometimes assumed that the economy is run by a benevolent social planner or decision maker.

This paper contributes to the literature by identifying a source of difference between the representative agent and social planner paradigms in the particular context of population ageing. The difference turns out to depend on whether the social planner is concerned with individuals or equivalent persons in evaluating social welfare.

The basic framework of analysis, involving a difference between the number of people and the equivalent population size, is described in section 2. The optimal consumption path of a representative agent is examined in section 3. Section 4 turns to the optimal path determined by a social planner, where particular attention is given to the choice of the unit of analysis. Some comparisons are made in section 5, followed by numerical examples in section 6. Brief conclusions are in section 7.