Constant Elasticity of Substitution production function allows us, compared with a Cobb-Douglas function, to model different efficiency trends of labour and capital. In this article, we explore the efficiency trends of labour and capital in supply systems for the private and public sectors in Slovakia independently. If a single exponential trend for technical progress is used, the Cobb-Douglas production function can be used for the private sector and Leontieff production function for the public sector. We, however find a CES function with separate trends based on Box-Cox transformations outperforms capturing technological progress by models with a single exponential trend. Labour and capital efficiency gains in our preferred model are converging downwards to a positive constant for labour and increasing over time for capital in the private sector, whereas they are gradually decreasing for both factors in the public sector. The elasticity of substitution between labour and capital is significantly greater than zero, but also lower than 0.5 in preferred models for both sectors.