Comparing three penalty functions - Cross-Entropy approach, Quadratic and Linear Loss – in SAM balancing and splitting applications

We review three candidates for balancing data which enable to consider bounds, different priorities and unknown row or column totals and thus are useful for SAM splitting and balancing: Cross-Entropy, a Highest Posterior Density Estimator resulting in a quadratic loss penalty function and minimizing absolute differences, i.e. linear loss. The approaches are assessed first by a systematic Monte-Carlo experiment with known distribution of the errors. Here we find quite limited numerical differences between the Cross-Entropy and quadratic loss. The Cross-Entropy approach was however considerably slower than the other candidates. Second, we tested the three approaches for differently sized larger SAM split problems with unknown errors, considering here also besides CONOPT4 the specialized LP/QP solvers CPLEDX and GUROBI. Again, the differences in results between the quadratic loss and the Cross-Entropy approach were quite small while the quadratic loss problem could be extremely fast solved with the specialized QP solvers. However, they did not achieve the same accuracy as CONOPT4, while under linear loss, the specialized solvers are faster by around factor ten at a similar accuracy. We conclude that using linear loss in combination with a specialized solver or a quadratic loss approach are the most suitable candidates for larger SAM splitting / balancing problems. JEL codes: C67 Input–Output Models, C63 Computational Techniques, C88 Other Computer Software Keywords: Data balancing, SAM balancing, Highest Posterior Density, Cross Entropy