By Roger Burbach

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2, the theory behind the estimators is discussed; in particular, various types of maximum likelihood estimation are discussed, as well as that specification which leads to ordinary least squares. First, however, some notation must be introduced. lt is total expenditure, Ot is time, et is the vector of errors and b 0 , b 1 and care then-vectors of parameters. e. e. lt- p;c. g. 0 = 0 in a base year, say 1963. Clearly, if n is at all large the estimation problem is of considerable difficulty. Since I wish to be able to handle up to 40 commodities, 120 parameters must be dealt with (or 118 if we take the constraints into account) and if we are to estimate the variance-covariance matrix of the disturbances et, we add another 780.

37) below, the solution of which leads to the estimators required. Much of the original work on maximum likelihood estimation of models of this type was done by Barten (1969), and the unified treatment given here owes much to his presentation. Specifically for the linear expenditure system, and independently of Barten, estimators were formulated by Solari (1971), and by Parks (1971). As far as the full information estimators are concerned, the formulae presented here are identical to theirs. 3), the treatment is quite general and may be applied to any system of equations.

It would only be with respect to these that assumption and model selection would predominate over exogenous information in the final determination of the estimates. Otherwise, 20 DEMAND IN POST-WAR BRITAIN the model would only act as a vehicle for the transmission of undistorted messages from the data. In later chapters we shall see that reality is not quite so cooperative. The choice of alternative models leads to major differences in the interpretation of the evidence, even in cases where the models differ little in principle.

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