Modelling the Joint Determination of Household Labour Supplies and Commodity Demands

Abstract

In addition to choosing the allocation of total expenditure between commodities, households may also be able to make decisions over the allocation of their time between market work and leisure. In both theoretical and empirical work it has often been the case that these decisions have been analysed separately. In this paper we stress the theoretical attractions of considering the joint determination of the allocation of time between work and leisure and the allocation of total expenditure between commodities in a utility maximising framework. Using a sample of individual households we attempt to evaluate the empirical importance of the joint determination model over the separate determination of labour supplies and commodity demands. Our approach follows that of Abbott and Ashenfelter (I976), Phlips (I978), Barnett (I979), Deaton and Muellbauer (I980), and Atkinson and Stern (I980). Here we pay particular attention to the following four important aspects of household decision-making over commodity demand and labour supply. The first concerns the commonly assumed restriction on the household's preferences of (weak) separability between goods and leisure. This assumption allows the estimation of commodity demand systems and Engel curves that exclude wage-rate variables. In cross-section household budget data with large variation in wage rates across the sample the invalidity of this assumption would involve a serious mis-specification. Any correlation between the excluded wage variable and the included price, income and demographic variables would lead to biased parameter estimates and hence biased estimated elasticities. Similarly, this assumption allows the estimation of labour supply curves that exclude relative price variables and its invalidity could produce biased labour supply elasticities. A second aspect of household decision-making which we wish to highlight arises from the suspicion, commonly alluded to in labour economics texts, that primary male workers may not be free to choose their hours of work. Thus we estimate a matched pair of rationed and unrationed systems following the work of Neary and Roberts (i 980) and Deaton and Muellbauer (I 979). The separability restriction is not unrelated to this point, since without it we will see that the rationed hours of work enter demand systems in a complex fashion. In effect,