The treatment of non-essential inputs in a Cobb-Douglas technology

One problem when estimating a Cobb-Douglas production function with micro data is how to deal with the observations that show positive output but do not use some of the inputs. As the log of zero is not defined one standard procedure is to arbitrarily replace those zero values with "sufficinetly small" numbers. But can we do better than that? An alternative approach is presented and applied to Mexican farm-level data.