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.]

[This paper contains the derivation of the exact finite sample distribution function of the LIML identifiability test statistic associated with an overidentified nondynamic structural equation which contains two endogenous variables. Some of the properties of the moments of this statistic are also investigated.]

Wallace and Hussain (1969) considered the use of an error components regression model in the analysis of time series of cross-sections and developed an estimator of the coefficient vector based on an estimated variance-covariance matrix of error terms. In this paper, we have shown that under the set of assumptions adopted by Wallace and Hussain there are an infinite number of estimators which have the same asymptotic variancecovariance matrix as the Wallace-Hussain estimator and also that it is not possible to choose an estimator on the basis of asymptotic efficiency. We have developed an alternative estimator of the variance-covariance matrix of error terms and have used this estimator in developing a feasible Aitken type estimator for the coefficient vector. We have derived some small sample properties of this estimator and have compared them with those of other estimators of the coefficient vector.

IN THEIR ARTICLE [5], Liu and Breen propose a new estimator of the large-sample asymptotic covariance matrix for the limited information maximum likelihood estimator in simultaneous equations, and express surprise that their estimator is different from the estimator proposed by Chernoff and Divinsky [1]. Additionally, they question the interpretation of a statistic used in the past to test over-identifying restrictions.

In Italian: Lo Spazio nei Piani Economici, Franco Angeli Editore, Milan, 1972, 391 p. In Spanish: El Factor Espacio en la Planificación del Desarollo, Series ‘Fondo de Cultura Económica’, Fondo de Cultura Económica, Mexico, 1980, 405 p.