The Relevance of the Cobb–Douglas Function Nowadays: Insights from the Global Agricultural Sector

The world context has changed rapidly over the last few centuries. This is interesting because it has brought important innovations that have allowed us to improve human quality of life, but has also created new challenges for humanity due to the increased anthropological footprint. The question that the scientific community may pose sometimes is whether the old theories are still relevant in today’s frameworks. For example, is the Cobb–Douglas production function developed in the twenties of the last century still relevant for analyzing the current agricultural economic realities? This is a pertinent question, considering the changes in economic dynamics, the modernization of farms, and the innovations available for agricultural practices. From this perspective, this research aims to estimate the Cobb–Douglas model, considering panel data and cross-sectional methodologies for international countries’ agriculture, including spatial autocorrelation approaches, with statistical information from the FAOSTAT database for 162 countries for the period 2000–2023. This model was extended with variables selected through machine learning algorithms. The original linear Cobb–Douglas function model yields elasticities of 0.561 and 0.361 for the logarithm of net capital stocks and the logarithm of employment in agriculture, respectively. When the model is extended to take account of the results from machine learning approaches, the elasticities for the logarithm of agricultural land, the logarithm of net capital stocks, the logarithm of employment in agriculture, and the logarithm of export value are, respectively, 0.216, 0.43, 0.244, and 0.099. With the inclusion of dummy variables in the extended model for the years under consideration, the elasticity results obtained are not very different from those obtained using this model without these dummies. Taking country dummies into account, the elasticity results are 0.436, 0.231, 0.118, and 0.072, respectively, for the logarithms of agricultural land, net capital stocks, employment in agriculture, and export value. When spatial autocorrelation effects and panel data are taken into account, the results are not very different from those obtained for the model with country dummies (with the exception of the elasticity for the logarithm of net capital stocks, which is slightly lower). For the model incorporating spatial autocorrelation effects and cross-sectional data, the elasticities of the logarithms of agricultural land, net capital stocks, employment in agriculture, and export value are, respectively, 0.142, 0.336, 0.293, and 0.256. These findings suggest that the estimation of the Cobb–Douglas production function for the global agricultural sector, using data from different countries, should take into account heterogeneity between countries and spatial dependence in order to obtain relatively more stable elasticities. The results suggest that taking into account country-specific effects and spatial autocorrelation may be more important for the robustness of the estimates than simply extending the model with additional explanatory variables.