INTRODUCTIONPrevious studies of the demand for gasoline typically fall into either of two categories. The first category is the flow adjustment model which expresses gasoline consumption as a function of the real price of gasoline, disposable income, and gasoline consumption in the previous period.' The second category is the stock adjustment model.' The basic principle of this type of model is that consumers adjust their purchases of a good based on some desired level or holding of the stock. Various methods of cross-section, time series, and pooled crosssection time series estimation have been employed in the estimation of these models. In particular, Houthakker and Verleger [9], Kraft and Rodekohr [lo], and Mehta, Narasimham, and Swamy [14] have estimated pooled models using state data. Kraft and Rodekohr have estimated stock and flow models and derived an explicit relationship between these models and determined the superiority of the stock adjustment model over the flow adjustment procedure" In particular, the flow model does not explicitly capture changes in the average efficiency of the stock of automobiles. RIoreover, these models use state crosssections pooled into an aggregate national equation and therefore provide no regional implications.Our analysis compares price and income elasticities from stock adjustment models for each of the nine census regions. The models are estimated using annual temporal cross-section data at the state level of aggregation for gasoline consumption, gasoline price, income and the stock of automobiles. A random coefficient specification of each demand model is estimated for each of the nine
In an earlier paper Kraft and Rodekohr [5] presented an empirical study of the regional demand for gasoline in the United States. The analysis compared stock adjustment models for each of the nine United States census regions. The models were estimated using annual temporal cross-section data at the state level of aggregation for gasoline consumption, gasoline price, income, and the stock of automobiles. In accordance with Swamy's [9] procedure, a random coefficient specification of each demand model was estimated for each of the nine census regions assuming heteroscedastic disturbances over time, and variable intercept and slope coefficients across states within each of the regions. The individual states were pooled into census regions, therefore yielding nine regional gasoline demand models. Each census region was a time series of cross-sections of states.Assuming that the coefficients in a regression equation were random across units in a temporal cross-sectional analysis, we presented an efficient method of estimating the mean and the variance-covariance matrix of a distribution which the coefficient vector follows. In concluding, our earlier paper stated that, ". . . the elasticities vary considerably from region to region and are different from those of earlier studies. In particular, the price elasticities have a wide variance from those of earlier studies. The regional differences are also quite apparent in comparing the influence of automobile stocks on demand in the different regions. The stock variables may in fact reflect various omitted factors which are not captured in the remaining variables." Comments by Johnson [4] and Greene [l] which appear in this issue suggest improvements or refinements in our earlier paper. In particular, we found the comments by Johnson to be very helpful and are incorporating his suggestions in our current work in estimating regional energy demand functions.As pointed out by Johnson, we correctly tested for interregional homogeneity of the coefficient vector using an F test for each of the nine census regions.However, as correctly pointed out by Johnson, we failed to test for spatial autocorrelation when using geographically distributed data. As shown by Schulze 181, the problem of spatial autocorrelation is different from that of temporal autocorrelation because the variable of a time series is only influenced by past values while in a spatial connection, dependence can exist in all directions.
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