Balancing matrices with both positive and negative entries: a generalized cross-entropy solution

This paper presents a matrix balancing technique based on Generalized Cross-Entropy (GCE) that can be suitable for matrices containing both positive and negative entries. One comparative advantage of the technique presented here is that it allows for the incorporation of inference into the estimates. An additional advantage is that this technique makes possible sign flips in the cells of the initial and the estimated matrices, which can be something desirable in situations where assuming sign-preservation for all the entries of the matrix could be too restrictive. A simple illustrative example shows how GCE works when adjusting a matrix characterized by having positive and negative entries within a Supply and Use Tables (SUT) framework, producing comparatively better indicators of error than other adjusting techniques.