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The paper examines the various approaches to nonlinear estimation. In particular the Gauss-Newton method is applied to the Box-Cox transformation. This transformation is used to determine the relationship of explanatory variables (relative prices, incomes and lagged non-traded output) to the assumed dependent variable, output of non-traded goods in the Barbadian economy. It is demonstrated that on the assumption of the ideal properties for the disturbances, the proper choice of functional form for the explanatory variables in their logarithms. The linear pseudo-model is then applied to the model in an attempt to illustrate the direction that future research could take when the covariance structure of the disturbance is under question. (The papers are still in draft and are subject to revision. Not to be quoted or reproduced without the expressed permission of the authors)