Scale Economies and Input Contributions: Evidence from Log-Linear and Translog Production Functions

Abstract

This study analyzes the determinants of gross output (GO) using the Cobb–Douglas and Translog production functions for the years 2005 to 2025. The relationship between labor (L) and capital (K) inputs and production performance is examined using a time-series econometric approach. Secondary data were collected from various reports of the MoSPI, RBI, and NITI Aayog. The Cobb–Douglas production function was used to estimate output elasticities and returns to scale, and the Translog production function was used to account for non-linearities and substitution effects between inputs. The findings reveal that capital has a greater contribution to gross output than labor ,which reflects the capital intensity of the industry. The estimated returns to scale suggest increasing returns to scale in the production. The marginal productivity of the production factors exhibited a decreasing trend in the Translog model, while there were positive interaction effects between labor and capital, reinforcing complementarities between production factors. Even though there were temporary disruptions during the COVID-19 period, there are indications of increased productivity over time from the trends in technical and allocative efficiency. Overall, the study indicates that technological progress, resource allocation efficiency, and capital accumulation are important factors for improving production efficiency and productivity growth. Comparative specification (Cobb-Douglas vs. Translog) provides a wider picture of the structure of production and economies of scale in the industry. Panel data by region or industry could also be incorporated in future studies to provide a better understanding of the spatial variation in production behaviors. Other factors, such as technology adoption, infrastructure, and human capital, can further reinforce the analysis. Further insights may be gained through advanced econometric methods, such as structural equation modelling, ARDL models, and stochastic frontier analysis, as well as an analysis of long-run productivity dynamics and structural changes after the pandemic.