Maximum entropy econometrics is well suited to estimate models with very few observations or to deal with multicollinearity. These are common problems in the estimation of a regional production function. In this paper, maximum entropy is used to analyze two issues that, so far, have not been fully addressed in the literature: the temporal stability of output elasticity of infrastructure and the change on its values across regions. We estimate the elasticity for each region to calculate the productivity and the social returns of infrastructure. The results show a decrease over time and the existence of important regional differences in both productivity and social returns of infrastructure. Hence, the effects of infrastructures on production can be very different across regions.