Consumption Functions
Past and future conditional

The life-cycle hypothesis takes as its starting point the assumption that in each period the individual or household chooses its labour supply and commodity demands so as to maximize its lifetime utility, subject to its stock of assets and the time available to the household for work and leisure. Partly because of its importance for policy analysis, the life-cycle model has served as a continuing focus for applied research since it was first introduced by Modigliani and Brumberg in 1955. If substitution between time periods is an important aspect of household behaviour, static models or models with 'ad-hoc' dynamics will provide inaccurate predictions of household behaviour and of welfare changes.

The estimation of life-cycle models raises a variety of questions. Do we possess appropriate data with which to estimate 'life-cycle-consistent' models? Which model specification provides the least restrictive method of recovering from a particular set of microdata the parameters of the individual preferences which underlie the life-cycle model? In Discussion Paper No. 150, Research Fellow Richard Blundell surveys alternative approaches to the estimation of the life-cycle model. He also discusses the advantages of particular types of microdata in estimating the parameters of the life-cycle model and the econometric approach best suited to particular types of data.

Under certain circumstances, the household's multiperiod decision can be analysed in two stages. First, the household chooses its total expenditure and hours worked in each time period so as to equalize the marginal utility of wealth across all time periods; second, the household decides how to allocate each period's total expenditure on particular commodities. Blundell notes that when 'two-stage' budgeting occurs, a single summary or 'conditioning' variable can capture the effects of all the unobservable 'life- cycle' variables, which reflect past decisions and future anticipations. Labour supply or commodity demands, for example, can be expressed in terms of current-period observable variables, such as wages and relative prices, and an unobservable variable which summarizes the effects of other variables, such as expected future income. Although this summary variable is unobservable, it is constant across time, if perfect foresight is assumed. The introduction of replanning and uncertainty simply adds an 'innovation' representing new information, so that the summary variable follows a random walk.

Blundell characterizes alternative econometric approaches to the estimation of life-cycle models by their choices for the summary variable. Provided sufficiently strong assumptions are made, different empirical specifications can be derived which are all consistent with the same underlying life-cycle model. The summary variable can be chosen so that many of the microdata sets traditionally used for estimating static models can also be used for the estimation of models consistent with the life-cycle hypothesis. The relationships between these alternative representations of behaviour may then be exploited to retrieve many important parameters of household preferences under relatively unrestrictive assumptions.

The assumptions necessary to permit two-stage budgeting and the use of summary variables rule out habit formation and the presence of adjustment costs in household behaviour. Blundell considers tractable empirical specifications which allow for such factors. If the prime concern is to predict short-run behaviour from individual data in a theoretically consistent fashion, then it may be unnecessary to model habits and adjustment costs explicitly. It may be sufficient instead to include in the model summary variables which incorporate the effects of previous decisions. The detailed structure of family composition may, for example, capture the important determinants of previous female labour market behaviour. Inclusion of such observable variables may eliminate the need for a model in which the dynamic effects of the past enter explicitly.


Econometric Approaches to the Specification
of Life-Cycle Labour Supply and Commodity Demand Behaviour
Richard Blundell

Discussion Paper No. 150, January 1987 (ATE)