Life-cycle Consumption Model Research Articles

Univariate detrending methods with stochastic trends

This paper discusses detrending economic time series, when the trend is modelled as a stochastic process. It considers unobserved components models in which the observed series is decomposed into a trend (a random walk with drift) and a residual stationary component. Optimal detrending methods are discussed, as well as problems associated with using these detrended data in regression models. The methods are applied to three time series: GNP, disposable income, and consumption expenditures. The detrended data are used to test a version of the Life Cycle consumption model.

The Cost of Annuities: Implications for Saving Behavior and Bequests

The fact that most elderly U. S. individuals maintain a flat age-wealth profile, rather than buy individual life annuities, contradicts the standard life-cycle consumption model. Average expected yields on individual life annuities in the United States during 1968–1983 were lower by 4.21–6.13 percent, or 2.43–4.35 percent after allowing for adverse selection, than yields on plausible alternative investments. Simulations of a model of saving and portfolio allocation show that during the early retirement years such yield differentials can account for the absence of annuity purchases even without a bequest motive. At older ages the combination of such yield differentials and a bequest motive can do so. It is common experience that as we grow older and nearer to eternity we become more, not less, anxious about money [Derek Brewer, Chaucer and His World, p. 213].

Consumption Constraints, Uncertain Income Streams and the Life Cycle Model

There has been a strong resurgence of interest in the life cycle model of consumption with a stochastic income stream. In particular, with various degrees of restrictiveness, it is argued that this theory implies that consumption should follow a Markov process. At one extreme with additive quadratic preferences, perfect capital markets and a known constant interest rate, this holds exactly. More generally with additive preferences, expected discounted marginal utilities obey the martingale condition. The purpose of the present note is to point out that such results depend on the existence of interior solutions and that such an assumption is much more restrictive in this framework than it is generally in economics.With income risk and expected utility maximisation, the utility of each state is weighted by its probability. Suppose that there are some high and low income possibilities and income has a positive mean. The utility function may possess one of two properties: either the marginal utility of consumption in a state remains finite or becomes unbounded as consumption becomes low.

Econometric Modelling of the Sterling Effective Exchange Rate

The exchange rate is recognised as a particularly tricky subject for modelling and prediction. The problems of unobservables such as expectations, of simultaneity, and of policy changes (both overt and covert) in the sample period to which models must be fitted may account for the disappointing results of recent attempts to test theories of exchange rate determination. This paper develops an appropriate empirical model to deal with these problems; it allows consideration of the proper interpretation of theoretical assumptions and determination of how far modelling for ex ante prediction can succeed. The exchange rate is recognised as a particularly tricky subject for modelling and prediction. The problems of unobservables such as expectations, of simultaneity, and of policy changes (both overt and covert) in the sample period to which models must be fitted may account for the disappointing results of recent attempts to test theories of exchange rate determination-see for example the pessimistic conclusions of Hacche and Townend (1981). The aim of this paper is to develop an appropriate empirical model for these purposes, to consider in particular the proper interpretation of theoretical assumptions, and to determine how far, in this case, modelling for ex ante prediction can succeed. The core of the model is the view of the exchange rate as a price determined in an efficient market with low transactions costs and well-informed transactors. In this view the observed rate represents a market equilibrium apart from random deviations, and where equilibrium is contingent upon an expected future state of the world, the expectations are assumed rational in the sense of being unbiased relative to a given information set. The implications of strong and weak forms of rationality, in which the information set is either relatively wide or narrow, must however be carefully distinguished. Under the most extreme rationality hypothesis it will not be possible to improve on a simple modified random walk model for ex ante prediction, and so the role of additional lagged variables is an important empirical issue. (Compare for example the life-cycle model of consumption as in Hall (1978) and see also Davidson and Hendry (1981).) Although there has been a good deal of investigation of exchange market rationality-e.g. Frenkel (1981), Levich (1978), Hacche and Townend (1981), Baillie, Lippens and MacMahon (1983)-the evidence remains inconclusive. Another important issue which the paper seeks to understand, separate from although related to the rationality question, is the volatility of the exchange rate relative to the variables which might be expected to explain it. Explanation in terms of a linear short-run equilibrium model-e.g. the overshooting hypothesis-does not account convincingly for the very large shifts periodically observed in response to apparently minor stimuli. A theoretical justification for a nonlinear econometric framework is developed and this model is found to dominate the linear alternative on goodness-of-fit criteria.

Survival versus Consumption

We develop an indirect method to estimate utility and willingness to pay (WTP) for reductions in the risk of death at various ages. Using a life-cycle model of consumption, we assume that an individual sets his consumption level each year so as to maximize his expected lifetime utility. Alternative assumptions about opportunities for borrowing and annuities characterize two polar types of societies. In our Robinson Crusoe case, an individual must be entirely self-sufficient, and annuities are not available. In our perfect markets case, an individual can borrow against future earnings and purchase actuarially fair annuities; we show that under these assumptions WTP is the sum of livelihood (discounted expected future earnings) and consumer surplus. To illustrate our methods, we derive WTP for an average financially independent American man under plausible assumptions. The model is calibrated to 1978 earnings (e.g., $18,000 per year for men aged 45–54 with at least some income). In the Robinson Crusoe case, WTP increases from $500,000 at age 20 to a peak of $1,250,000 at age 40, and declines to $630,000 at age 60. In the perfect markets case, age variations are less pronounced; WTP is $1,050,000 at age 20, peaks at $1,070,000 at age 25, and declines to $600,000 at age 60. These results suggest that individuals value risks to their lives at several times the pro-rata share of their future earnings.

Imperfect Capital Markets and Life-Cycle Saving

The life-cycle theory of consumption, which has long taken an important place among consumption theories, provides us with a micro basis for the consumption choice over time. The standard results of this theory are that the level of consumption at any point in time depends on the present value of the entire lifetime earnings and the rate of change of consumption at each point in time depends on the difference between the subjective and objective discount rates.t Although this model is capable of explainiing consumption choice over time, it is incapable of explaining any but monotonic consumption profiles. The optimal consumption path predicted by this model is either always increasing over time or always decreasing over time.2 This is a direct result of the fact that both the subjective and objective discount rates are exogenous, so that their difference is always constant.' Many authors have found that the time shape of consumption is not monotonic (Watts, 1958; Tobin, 1967; Thurow, 1969; Nagatani, 1972). There is evidence of the existence of a 'hump' in an individual's consumption profile, the hump occurring in the middle of his lifetime. Given this empirical evidence, it seems that the standard model fails to explain observed behaviour. Nagatani (1972) provided a life-cycle consumption model capable of explaining cyclical consumption profiles. He considers an individual facing uncertainty concerning his future wage income. The individual's subjective evaluation of the future changes with time and experience, and according to these changes he revises his plans: The continuous revision of plans, in light of changing future outlook, is capable of explaining non-monotonic consumption profiles.

Distribution Effects and the Aggregate Consumption Function

This paper investigates whether and how the of affects the fraction of disposable which is consumed. It is shown that a slight generalization of the permanent or life-cycle model of consumption makes each individual's lifetime marginal propensity to consume a fraction of his lifetime disposable resources unless two taste parameters are equal. In considering what this implies for the aggregate consumption function, the tenuous connection between theoretical constructs and observed facts is stressed. Previous empirical work on the subject is criticized for failing to define properly either income distribution or consumption, and a new test, based on the theory, is outlined. Because of data limitations, a number of compromises with this ideal test must be made, and several alternative models are estimated. On the whole, they suggest that equalizing the of would either leave aggregate consumption unchanged or diminish it slightly.