General remarks

Computing the StoNED estimator requires solving a convex nonparametric least-squares (CNLS) problem, which is not trivially simple. The CNLS problem can be solved by standard quadratic programming (QP) or nonlinear programming (NLP) algorithms and solvers. Such solvers are available in such mathematical programming packages as GAMS, AIMMS, Matlab, and Lindo, among others.

In our experience, the standard solvers work well in the usual range of sample sizes reported in the literature (the usual sample size in empirical applications is less than 300 observations). Problems with the sample size n ≤ 100 are usually solved in just a few seconds in GAMS. Problems with 100 ≤ n ≤ 300 usually take from a few minutes to half an hour to solve. However, the computational burden increases at a quadratic rate as the sample size increases. Problems with more than 300 observations may take several days, provided that a sufficient amount of physical memory is available. The recent study by Lee et al. (2011) develops more efficient algorithms that are applicable to larger scale problems (e.g., n = 600).


As an example, the GAMS code used in the application of StoNED to the Finnish electricity distribution networks is available below: 


The GAMS code imports the data of total cost, outputs, and the z-variable from the following Excel files: 




Note: Save the Excel files to a folder where GAMS can read them, and revise the xlimpot command in the GAMS code to refer to the correct folder.

As the website development proceeds, we plan to add further examples (other model specifications; MC simulations) to this site. Further examples are available by request from Timo Kuosmanen.



When the StoNED frontier has been estimated, it is easy to assess efficiency of a given point (observed firm, or an unobserved virtual unit) relative to the estimated frontier. This is sufficient for practitioners in many applications. In the application to the Finnish electricity distribution networks, we developed a simple Excel file that both energy companies and the regulator can use for their subsequent analyses and computations. For example, when the output increases, the new cost target can be computed using the Excel-spreadheet application without a need to estimate the StoNED frontier again.

The consulting firm Sigma-Hat Economics Oy has experience of StoNED estimation and development of suitable Excel-spreadsheet applications for the client's needs. 

JSN Epic template designed by