Capital–Energy Substitutability and Labour–Energy Complementarity in Nigeria’s Manufacturing Sector: Evidence from a Translog Cost Function

Abstract

Understanding the scope for substitution between energy and non-energy inputs is central to the design of energy taxes, subsidies, and environmental regulation. Using annual data for 1981–2023, this study estimates Allen (AES) and Morishima (MES) elasticities among capital, labour, and energy in Nigeria’s manufacturing sector within a translog cost framework that explicitly includes manufacturing output (to capture scale effects) and a time trend (to capture disembodied technological change). The system is estimated by iterated Seemingly Unrelated Regression (iSUR), imposing linear homogeneity and symmetry restrictions. The results indicate that capital and energy are Morishima substitutes, with MES-KE rising from 1.95 in 1981 to 4.50 in 2023 (a 131% increase), consistent with technology-driven growth in substitutability. Energy and labour are also substitutes (mean MES-EL = 2.32), although the degree of substitution declines over time. By contrast, capital and labour are Morishima complements (mean MES-KL = −1.94), implying that higher capital prices reduce demand for both capital and labour. Relative to AES, MES better captures directionality and time variation; AES estimates remain close to 1–2 with limited movement. Policy implications follow: higher energy prices are likely to induce substitution toward capital, whereas higher capital costs may depress employment. Accordingly, policy interventions should target energy directly rather than capital.