Current macro-econometric models mostly incorporate just two factors of production, labour and capital (with a time-dependent multiplier representing technological change or total factor productivity). These models assume that energy is an intermediate product of some combination of human labour and capital. These models also assume that the supply of energy is driven by economic demand. We assume the contrary, i.e. that useful energy is a primary input, derived (mostly) from natural capital. This failure to capture the impact of primary resources (as useful energy) on economic growth leads to inappropriate formulation of economic growth theories. To understand that impact better we need explicit evidence of marginal products of capital, labour and useful energy or useful work. As applied to the explanation of the past half century of economic growth of the EU-15 countries, the new results demonstrate the use of non-parametric relationships between capital, labour and useful energy to explain economic growth. They also indicate that marginal products of capital, labour and useful energy are variable - the marginal product depends on the levels of capital stock, labour input and useful energy flows. The proposed semi-parametric production function suggests country-specific policy implications for the EU (and other countries). (C) 2015 Elsevier Ltd. All rights reserved.