Perfect Price Aggregation and Empirical Demand Analysis - Anderson, Ronald W. (Econometrica, 1979)
THIS PAPER CONSIDERS how certain theoretical results on consistent commodity aggregation can be applied to the problem of the estimation of a complete system of demand equations. The method proposed here builds upon the classic results of Gorman [16], particularly the case he calls perfect price aggregation. These results are well known in the literature on two-stage budgeting but have not been widely applied to problems of empirical demand analysis. This relative neglect of perfect price aggregation is regrettable because several of their features recommend their use in econometric applications. In the perfect price aggregate approach to demand analysis, demand equations are characterized as a two-level system consisting of a system of group expenditure functions and a number of systems of conditional demand functions. This two-level system provides a manageable way of introducing greater detail into a complete system of demand equations. Information about particular commodities may be introduced in the specification of conditional demand functions. As will be discussed below, the two-level system can be estimated by an iterative estimation method in which the maximum number of demand equations which can be estimated is greatly increased over the number found in past estimates of complete systems of demand equations. Even when one is principally interested in estimating group expenditures the perfect price aggregate approach is attractive because the intragroup substitutions due to detailed price changes can affect total group expenditures and this effect is taken into consideration through the computation of the perfect price indices. Thus it may be possible that a perfect price aggregate model will yield better estimates of group expenditures than would an approach which did not explicitly treat aggregation problems. Another pleasing feature of the perfect price aggregate approach to demand analysis is that it avoids the misspecification which results when the commodity