Putting decomposition of energy use and pollution on a firm footing - clarifications on the residual, zero and negative values and strategies to assess the performance of decomposition methods

I show how the problems with zero and negative values in decomposition can in principle be resolved by avoiding ill-defined mathematical operations used to derive the decomposition formulae (division by zero and taking logarithms of zero and negative values). Referring to integral approximation, which is the basis of any decomposition analysis, I also discuss the residual in decomposition and show that the presence of a non-zero residual is natural and that requiring a zero residual as a strategy to identify optimal decomposition methods is without basis. To nevertheless advise on optimal decomposition methods, I suggest to investigate for which types of functions different decomposition methods are exact or good approximations and how they perform in simulations, where the exact integrals are known. Regarding these criteria the LMDI seems to perform best.<p>