**Nguyen Ngoc Thach**

Institute for Research Science and Banking Technology, Banking University HCMC, Ho Chi Minh City 70000, Vietnam; thachnn@buh.edu.vn

Received: 16 December 2019; Accepted: 21 January 2020; Published: 1 February 2020

**Abstract:** Most studies in Vietnam use the Cobb-Douglas production function and its modifications for economic analysis. Extremely rigid presumptions are a main weak point of this functional form, particularly if the elasticity of factor substitution (ES) is equal to one, which hides the role of the ES for economic growth. The CES (constant elasticity of substitution) production function with more flexible presumptions, concretely its ES, is not unitary, and has been used more and more widely in economic investigations. So, this study is conducted to estimate the average ES through the specification of an aggregate CES function for the Vietnamese nonfinancial enterprises. By performing Bayesian nonlinear mixed-e ffects regression via Random-walk Metropolis Hastings (MH) algorithm, based on the data set of the listed nonfinancial enterprises of Vietnam, the author found that the CES function estimated for the researched enterprises has an ES lower than one, i.e., capital and labor are complimentary. This finding shows that Vietnamese nonfinancial enterprises can confront a downward trend of output growth.

**Keywords:** ES; CES function; Bayesian nonlinear mixed-e ffects regression
