Cobb–Douglas production function: on the causal effects of factors and predictions

Generalized Cobb–Douglas production function formulation is widely used in different many economic fields, not limited to the industrial area, and is undoubtedly one of the most widely used concepts in economics. In this note, we analyze two aspects of its use, related to the causal effects of some of its factors and the use of its output (prediction) in a broader causal model. In the first case, some sufficient conditions allowing for a causal interpretation of the coefficients linked to each production factor are shown. We will show that the coefficients can also have a causal meaning, in addition to the classical direct elasticity. Furthermore, these conditions can also support the analyst in the choice of the factors to be included in his/her model. In the second case, we consider the output of a Cobb–Douglas function as a nonlinear component of a wider causal model and we compute a counterfactual effect conditioning (also) on the function factors. In both cases, it is required to evaluate the Cobb–Douglas function for some duly defined fixed values of its factors. An example, with a synthetic generated dataset, is shown at the end of the paper.