Consumption Patterns Over Pay Periods

This paper establishes a theoretical framework to characterise the optimal behaviour of individuals who receive income periodically but make consumption decisions on a more frequent basis. The model incorporates price uncertainty and imperfect credit markets. The simulated numerical solution to this model shows that weekly consumption functions are ordered such that the functions within the payment period are highest in the first and the last week of the payment cycle for all wealth levels. Using weekly expenditure data from the FES, we estimate the coefficient of relative risk aversion (point estimates are between 1.2 and 7) and the extent of measurement error in the data (which accounts for approximately 60% of the variance in the data). The purpose of life-cycle models of consumption is to explain how individuals allocate consumption optimally to different periods of their lifetime given available information about lifetime resources, future uncertainty and the nature of financial markets (see Zeldes (1989a), Deaton (1991), Attanasio et al. (1999), Gourinchas and Parker (2002)). The evidence shows that attitude to risk, the rate of time preference, demographic factors and labour supply are all important determinants of long-run consumption behaviour (see Banks et al. (2001) and Gourinchas and Parker (2002)). The focus of the existing literature is long run consumption behaviour over the life cycle and it is accepted that the frequency of income receipt should be irrelevant for the pattern of expenditure within a payment period (Browning and Collado, 2001). This paper challenges that assertion and argues further that examining such short-run behaviour can help us to understand behaviour in the long-run. Specifically, in this paper we consider individuals who receive a regular income (known) on a monthly basis while their consumption decisions take place more frequently, say weekly. In the short run income is certain, and uncertainty is assumed to arise from short run variation in prices between weeks. Of course short run randomness in prices faced by individuals may reflect different phenomena, like changes in the local availability of some or all goods, or variation in the opportunity cost of some goods etc. In this paper we assume that uncertainty is gradually " resolved " during a monthly payment period (each week) and we are interested in the optimal consumption decision as that uncertainty is revealed 2. We expect that the optimal consumption level will not only depend on the level of disposable wealth but also on the …