Knowledge that Transforms

On the basic assumption that individual consumption of a good is a stochastic phenomenon, the first part of this article shows that under general conditions market quantity demanded is asymptotically (as n, the number of individuals in the market, increases) distributed as normal with and variance a function of own price given all other prices and individual incomes. Next, by the use of integral transforms, it is shown that the unknown market demand function can be approximated by a specific functional form. The estimation problems involved with such a model are discussed in the last part of the paper. Two BASIC, but fundamental, problems facing any econometrician attempting to estimate market demand curves are the choice of functional form and the justification of the normal form for the distribution of the disturbance terms. This paper goes some little way toward meeting both problems. The first step is to regard quantity demanded as a random variable. It is assumed that the axioms of choice of modern demand theory refer to the mean quantities demand curves one can derive the normal distribution as a limiting form for it is assumed that the consumer in determining his preferences determines the parameters of the distribution function of quantity demanded. Market stochastic demand curves are obtained from individual stochastic demand curves by taking the sum of the quantities demanded over all individuals in the market. It is shown that under certain weak assumptions about the characteristics of individual demand curves one can derive the normal distribution as a limiting form for stochastic market demand curves. The limits are taken as n, the number of individuals in the market, approaches infinity. It is shown that under the assumptions of the problem both the and variance of the market stochastic demand function are decreasing functions of own price. The second step in the argument is to obtain approximations for the functional relationships between the and own price and between the variance and own price for the market curve. This is achieved by stating those conditions under which upper and lower bound functions can be defined. The approximations to the actual, but unknown, functions are obtained by considering the convex combination of both bound functions. The last section of the paper discusses the problems involved in estimating the parameters of the limiting form of the market stochastic demand function.

[It is now popular to construct economic models in differential equation form. Perhaps the most serious econometric problem faced when dealing with a differential equation system is the practical difficulty of finding consistent estimates of the important structural parameters. In this paper a simple three-equation Phillips model is considered and consistent estimates of the structural parameters are provided by the minimum-distance procedure. The small-sample distributions of these estimates are investigated by the Monte Carlo method; and the results are then compared with those of the three-stage least-squares estimates found by making a discrete approximation to the system of differential equations.]

The technique of partial aggregation is explored as a means of preserving the confidentiality of data while enabling research scholars to utilize the information for analytic purposes. For this purpose, two criteria are developed for evaluating the analytic consequences of partial aggregation: One measure indicates the degree of divergence or non-conformity between estimates produced by unaggregated data and partially aggregated data; and the other measure pertains to efficiency loss and expresses the fraction of the useful information in the unaggregated data which remains after the data have been grouped or partially aggregated. These measures are then applied in an experimental test using data from the Call Reports and the Income and Dividend Statements of nearly 5400 member banks of the Federal Reserve System. This experiment consists of evaluating the effect on twenty different regression models of three different levels of aggregation and seven different rules for arraying the data prior to aggregation.