Problems of estimating demand parameters in a complete system of equations: An analysis of the demand for food items in the U.K

Summary This is the first attempt to estimate the income and price coefficients of 27 food items from the quarterly data as collected by the U.K. National Food Surveys. The model used in an adaptation of the Rotterdam differential model, where, as against traditional single-equation models, the per capita consumption of each item is shown explicitly as a function of per capita income, own price and the prices of all other commodities. Besides the estimation of actual parameters, the paper focuses on the methodological problem of analysing the food budget at a finely disaggregated level, in a complete system of demand equations. The problem is of particular interest in the context of a food budget, since the prices of disaggregated food items show a definite tendency towards multi-collinearity. A multi-stage budgeting procedure would be of enormous convenience in such a situation; however, this procedure would be justifiable only if the broad groups of food items are proven to be ‘group-wise independent’. The analysis here indicates that there are no grounds for assuming group-wise independence among broad categories of food items in the U.K The merits as well as the limitations of a complete system of demand equations, as against the single equation approach, assume special significance in this context.