This paper uses a three-step Bayesian cross-entropy estimation approach in an environment of noisy and scarce data to estimate behavioral parameters for a computable general equilibrium model. The estimation also measures how labor-augmenting productivity and other structural parameters in the model may have shifted over time to contribute to the generation of historically observed changes in the economic arrangement. In this approach, the parameters in a computable general equilibrium model are treated as fixed but unobserved, represented as prior mean values with prior error mass functions. Estimation of the parameters involves using an information-theoretic Bayesian approach to exploit additional information in the form of new data from a series of social accounting matrices, which are assumed were measured with error. The estimation procedure is "efficient" in the sense that it uses all available information and makes no assumptions about unavailable information. As illustration, the methodology is applied to estimate the parameters of a computable general equilibrium model using alternative data sets for the Republic of Korea and Sub-Saharan Africa.