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Computable General Equilibrium (CGE) models have been widely used for quantitative analysis of global economic issues. However, CGE models are frequently criticized for resting on weak empirical foundations. This paper builds on recent work in macro-econometric estimation, developing an approach to parameter estimation for a widely employed global CGE model, the Global Trade Analysis Project (GTAP) model. An approximate likelihood function is developed and the set of optimum elasticity values is obtained by maximizing this approximate likelihood function in the context of a back casting exercise. In addition, two statistical tests are performed. The first of these tests compares the standard GTAP elasticity vector with the estimated trade elasticity vector. It rejects the null hypothesis of equality between the two sets of trade elasticities. The second test examines the widely maintained hypothesis known as the "rule of two", by which the elasticity of substitution across imports by sources is set equal to twice the elasticity of substitution between domestic goods and imports. We fail to reject this common rule of thumb. We conclude that there is much to be gained by nesting CGE models within an estimation framework as this opens the way for formal evaluation of model performance and parameterization.