Impact of Industry 4.0 technologies on the production function of an enterprise: econometric assessment and scenarios analysis

In the context of the Fourth Industrial Revolution (Industry 4.0), the quantitative assessment of digital technologies' impact on enterprise economic performance becomes critically important. Traditional production functions, limited to accounting only for labor and capital, cannot fully capture the effects of the introduction of cyber-physical systems, robotics, and artificial intelligence. This study aims to fill this gap by developing and econometrically estimating an extended Cobb-Douglas production function that incorporates a composite Industry 4.0 index. The theoretical framework draws on the works of classical economists and contemporary digital transformation researchers, including concepts of the technological multiplier and the productivity paradox. The methodology is based on constructing a regression model in which the exogenous variables are capital stock, labor input, and a composite Industry 4.0 index. The latter aggregates indicators of robot density, the level of adoption of the Internet of Things, and artificial intelligence technologies. Due to the limited availability of micro-level data on Russian enterprises, the empirical estimation was conducted on a simulated dataset of 150 observations. The data generation parameters — variable distributions and their correlations — were calibrated to match actual statistical data from Rosstat, the OECD, and the International Federation of Robotics for the period 2018−2023. Model parameters were estimated using the least squares method with numerical optimization. The results demonstrate that incorporating the digitalization factor dramatically improves model fit compared to the classical specification that does not account for technology. The estimated output elasticities with respect to capital and labor are statistically significant and consistent with theoretical expectations for a manufacturing production function. The digitalization coefficient reveals that a higher Industry 4.0 technology adoption level leads to a substantial increase in output, holding capital and labor constant. Based on scenario analysis of four digital transformation strategies, the most effective approaches in terms of risk-adjusted trade-off are identified. The findings have practical implications for industrial enterprise management when justifying investment budgets for digital technologies, as well as for public authorities in designing industrial policies aimed at stimulating robotization and increasing labor productivity. Limitations of the study include the aggregated nature of the Industry 4.0 index, which does not account for differentiated effects of individual technologies, and the use of simulated data, which requires further model validation on real panel data.