Date of Award


Degree Type


Degree Name

Doctor of Philosophy


In this thesis we compare the translog and differential approaches to estimating a system of equations in the context of estimating trade elasticities. We treat all traded goods as distinct products and make use of production theory to obtain systems of domestic output supply, export supply, import demand and domestic factor usage equations. Both the translog and differential approaches provide equations which are approximations to the true but unknown equations and so there is no guarantee that the elasticity estimates will be the same. In the translog case the equations are derived by differentiating a translog approximation to a profit or cost function. In the differential case the equations are approximated directly by expressing them in their differential forms. They are then converted to proportional change form to facilitate imposition of the theoretical restrictions. We develop the theory for the differential model for the case of outputs, variable inputs and more than one fixed factor and find that all the restrictions of the theory cannot be incorporated in a convenient manner. There is no such difficulty in the translog framework.;In Chapter Four we specify and estimate a system of domestic output supply, export supply, import demand and fixed factor (labour and capital) shadow price equations for the aggregate U.S. economy for the period 1948-79. We test the restrictions of the theory for both approaches and calculate the elasticities. The restrictions which can be imposed are generally more easily accepted or less strongly rejected in the differential system. In the case of the variable quantity own price elasticities there is considerable agreement between both approaches. There is less agreement about cross price elasticities and about the elasticities where the restrictions could not be imposed in the differential model. We also find evidence of a structural break in the coefficients in both models.;Another major issue which we address in this thesis is that of simultaneous equation bias. In Chapter Five we estimate systems of output supply, export supply and import demand equations for Canada and the U.S. simultaneously for the period 1961-1980. In the translog case we find that taking account of simultaneous equation bias in conjunction with estimating equations as part of a system has some important effects for the trade elasticities. The results for the Canadian equations in the differential model are poor.



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