| Abstract: | Basically, we have attempted to show the following in the course of setting out the algebra of regression analysis of selected regional employment multiplier models: (1) When the basic features of the model are shaped by the assumption of an unlagged response of local employment to changes in export employment, the least squares estimates of the multipliers are highly sensitive to the export coefficients vector A, given the sample observation matrix X. In a completely disaggregated model such as Equation (21), the multipliers are solely determined by the export coefficients and thus are entirely independent of sample observations. However, this independence does not hold in the case of a partially disaggregated model. The identity relation is also destroyed when a lag relationship is introduced into a completely disaggregated model. (2) A simple lag model produces results bascially different from those obtained by an unlagged model if the overall differences between current and lagged observations are significant. (3) Given a matrix of sample observations on employment, it is possible to estimate the upper limits of a least-squares aggregate multiplier and its variance simply from knowledge of the export coefficients (4) The export coefficients vector has also an important bearing upon the correlation coefficient. The correlation is unity if and only if the export coefficients vector is proportional to the local employment coefficients vector, while it is zero if and only if the export coefficients vector is a vector all of whose elements are one. Also, the correlation coefficient is equal to one when a completely disaggregated model is used. There is finally the question of what these results mean in terms of the formulation of a multiplier model. First of all, in view of the crucial importance of the export coefficients and the difficulties of estimating them, most of the existing models do not seem to offer promising results. Furthermore, all the models examined here have made some simplifying assumption with respect to the constancy of the export coefficients. It remains highly uncertain whether these coefficients are reasonably stable over time. Of course, it would be theoretically more acceptable to relax the assumption of the invariance of export coefficients and to obtain such coefficients at different points of time for each industry. However, this would be accomplished only at the cost of increased difficulties of estimating larger numbers of export coefficients. In addition, there is some doubt as to the validity of the assumption that export employment is proportional to export sales. Since a lag relationship is important not only in terms of attempts to formulate multiplier models more realistically, but also in terms of its significant effect on the multiplier values obtained, the nature and the form of a lagged response and its estimation problems need to be investigated in depth. Finally, problems of least squares bias and efficiency, inference, and prediction which may arise in the context of various models presented here remain to be investigated. A detailed analysis of such problems must be the subject of further investigation. |
