There are three main problems in analyzing the origins of economic growth: First, the choice of irrelevant production functions, second, the failed ignorance of such indispensable variables as human capital in a research model, and third, the use of unreliable econometric methods. Using the Bayesian non-linear regression via the Metropolis-Hasting algorithm, this work estimates a human capital-extended variable elasticity of substitution (VES) function in a Solow-Swan one-sector growth model for Vietnam, an emerging economy. The study reports the following findings: (1) A variable elasticity of substitution between capital and labor (ES) of higher than one implies that the possibility of unbounded endogenous growth has been generated in the economy of Vietnam; (2) Despite a continuous increase in physical investment over the transition period, the labor share rises relative to the capital share in Vietnam due to including embodied human capital in the model; (3) Scale economies do not take place in Vietnam, i.e., the economy approaches a status of perfect competition market; and (4) The human capital-extended VES production model is found to be appropriate for evaluating endogenous growth.