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Pooling Cross Section and Time Series Data in the Estimation of a Dynamic Model: The Demand for Natural Gas

Pietro Balestra
Marc Nerlove

Abstract

In this paper, we consider two basic aspects of demand analysis, with application to the demand for natural gas in the residential and commercial market. The more fundamental one consists in the formulation of a demand function for commodities--such as natural gas--whose consumption is technologically related to the stock of appliances. We believe that in such markets, the behavior of the consumer can be described best in terms of a dynamic mechanism. Related to this is the more specific problem of estimating the parameters of the demand function, when the demand model is cast in dynamic terms and when observations are drawn from a time series of cross sections. Accordingly, this paper is centered around these two major themes, although, as the title suggests, the emphasis is placed on the second one. In Section 1, we present the theoretical formulation of the dynamic model for gas. In Section 2, the results of the estimation of the gas model by ordinary least squares methods are presented. These results, together with more fundamental theoretical considerations, suggest a different approach. The essence of this approach, which is not restricted to the gas model, is discussed in Section 3, while two alternative procedures for estimating the coefficients of the dynamic model in the light of this new approach are proposed in Section 4. It is subsequently shown that the application of these procedures to the gas data produces results that are reasonable on the basis of a priori theoretical considerations.