The central characteristic of the standard model of consumption choice over the life cycle is that the income generation process is effectively exogenous to the household. This follows from the assumed separability of leisure and consumption. The main preoccupation of the literature over the last couple of decades has been the "excess sensitivity puzzle", created by the fact that the data show household consumption tracking income over the life cycle in a way that is hard to reconcile with the premise that the capital market allows the household to decouple its consumption and income paths. The controversy continues over how to resolve this puzzle within a model that takes the only household decision variables to be its dated consumptions, with its income stream treated effectively as exogenous.
The leading contenders for resolution of this puzzle seem to be: precautionary or buffer&stock saving; liquidity constraints in the extreme form of the complete absence of borrowing possibilities; and demographic effects, especially the presence of children.
The first of these argues that, to avoid the consequences of adverse shocks to income in the future, households in the earlier phase of the life cycle build up buffer stocks of assets, and then, in their mid&forties to fifties, begin accumulating savings for retirement and possibly for bequests. In its purest form, this approach seems to be capable of fully explaining the data on house hold expenditure and saving, in particular the tendency for consumption to track income in the early phase, while leaving virtually no explanatory role for liquidity constraints on the one hand, and demographic factors on the other. Indeed, it implies that liquidity constraints, even if they exist, are non&binding. The household does not want to borrow, completely deterred by the risk that its future income will fall to zero and it will be left unable to meet its debt obligations. However, if there is a positive lower bound on income (social security, support from other family members), the theory allows that consumers might indeed want to borrow, though never more than the present value of this lower bound on the income stream. In this case there may be room for other explanations of consumption behaviour.
Under absolute no&borrowing constraints, an impatient householdns current consumption will be constrained by its income, and so will track it over time. As opposed to the buffer stock model, households do not borrow because they cannot.
Finally, the demographics approach suggests that if consumption is deflated for family size, it shows the relatively flat time profile consistent with the permanent income hypothesis, under which a household uses the perfect capital market to decouple its consumption and income streams in such a way as to maintain constancy of its discounted marginal utility of income over time. Browning and Ejrnaes (2002) argue that in this way the data can be fully explained without introducing a precautionary motive.
In his recent survey, Carroll remarks that the development of the precautionary savings approach brings the life cycle model back to its roots in the work of Milton Friedman in the 1950ns. Friedmanns analysis was called into question by the results of the models of the 1970ns and 80ns, based on explicit intertemporal optimization under uncertainty. Carroll argues convincingly that in fact Friedmanns intuitions were more closely consistent with the data, and that the recent precautionary savings models provide a superior theoretical underpinning for these intuitions.
However, we should take notice of the fact that one of the single most important socio&economic developments in the forty&five years or so since Friedmanns work has been the large expansion in female labor force participation, with its far&reaching implications for the householdns labor supply and income generation process.
The point which motivates the present paper is that it no longer makes any sense, if it ever did, to take the householdns labour income as effectively exogenous, essentially because a significant component of the householdns income is or could be generated by secondary earner labour supply, and the decisions on the time allocation of the secondary earner make this endogenous.
As long as models of consumption choices are estimated solely on the type of income and expenditure data available in family expenditure surveys, it does not seem possible to reject the claims made by any of the parties in contention just discussed. However, when we expand the data set to include the householdns time allocation and labour supply decisions, as this paper does, we see that, precisely because of the importance of female labor supply in the modern household, the assumption of an exogenous process of household income determination is no longer sustainable. In other words, possible exogenous uncertainty in the income of the primary household earner may be small beer compared to the variations in household income generated by endogenous choices of secondary earner labour supply. This leads to an approach which integrates life cycle choices of time allocation, labour supply and consumption.
In following up this approach, we do incorporate elements of both demographics and capital market imperfections. Decisions on female labour supply are closely related to the presence of children and the choice of sources of supply of child care. Moreover, it seems possible to explain the data only by assuming some kind of capital market imperfection, though our data set, which gives detailed information for each household on purpose, source, amount and cost of borrowing, does not support the extreme assumption of no borrowing. Also, we certainly would not rule out the possibility that some saving could be precautionary in nature, but do not believe, from our inspection of the data, that this can be anything like a complete explanation of household consumption behaviour over the life cycle.
An important feature of our modelling approach is the characterisation of the life cycle not in terms of calendar years, but rather in terms of the phases through which a typical family goes over its lifetime. By organising the data in this way we are trying to bring out more clearly than in the existing literature the effects of children on the time allocation and labour supply decisions of the household, and, through that, on its income stream and saving decisions. Thus we argue that the time paths of saving and consumption of market goods reflect the movements in household income that are determined by changes in female labour supply over time, which in turn are determined by the process of substitution between market and household work associated with bringing up children.
We then go on to argue that the data strongly suggest that some form of imperfect capital market assumption is indispensable to explaining what happens to household consumption, saving, labor supply and leisure in the early stages of the life cycle. There may appear to be some evidence of oprecautionarypsaving, in the form of a high level of household saving before the advent of children, but, at least in the context of the present model, this would be better characterized as oanticipatorypsaving.13 In anticipation of the major impact that the arrival of children will have on family resources,
and faced with a capital market that does not offer unsecured loans at a reasonable interest rate, young households save at a higher rate than at any other time in their lives.
Furthermore, the data indicate that households exhibit very considerable heterogeneity in their consumption, labour supply and saving decisions, within and across phases of the life cycle. In particular, saving behaviour depends very closely on female labour supply. For example, households with no significant female labour supply do virtually no saving once they have children, other than that involved in house purchase and superannuation schemes. Controlling for primary earner income, there is a high propensity to save out of secondary earner income.
The paper is set out as follows. In the next section we present empirical life cycle profiles of consumption, saving, labour supply and domestic work, obtained by combining information on income, household expenditure and time use. The results suggest a pattern of full consumption14 over the life cycle that is very different from that obtained by studies of expenditure on market goods alone. We then go on to formulate a theoretical model of a familyns life cycle choices, calibrate a simplified version of it and then show that this generates a time profile that replicates the data very closely. Section 6 concludes.
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