Returns to scale with a Cobb-Douglas production function for four small Northern Italian firms

With this piece of evidence, I try to shed light upon the effects of fixed and variable costs on revenues for four firms operating in the sectors of lathing and milling, packaging machine construction, mechanical component production and shoe parts building, all four in the vicinity of Bologna, Italy, through the estimation of a linear bivariate simultaneous equation model where variable and fixed costs explain revenues; with a sample of eleven/twelve years of annual data for each firm, and find that a marginal increase in variable costs lead to more than proportional increases in revenues; similarly for fixed costs; I consider both contemporaneous regressions and distributed lags ones. I further estimate a Cobb-Douglas production function, in order to find out whether the returns to scale are increasing, constant or decreasing comparing various estimation methods: OLS, instrumental variable method, dynamic panel methods, as well as the Levinsohn and Petrin 2003 method, first separately for each single firm and then pooling the individual firms' samples in a panel; I find support for the hypothesis of slightly increasing returns to scale with the baseline Cobb-Douglas transformed in logarithms with capital, labour and materials as inputs.