Putting decomposition of energy use andpollution on a firm footing - clarifications onthe residual, zero and negative values andstrategies to assess the performance ofdecomposition methods

摘要

I show how the problems with zero and negative values in decompositioncan in principle be resolved by avoiding ill-defined mathematicaloperations used to derive the decomposition formulae (division by zero andtaking logarithms of zero and negative values). Referring to integral approximation,which is the basis of any decomposition analysis, I also discuss theresidual in decomposition and show that the presence of a non-zero residualis natural and that requiring a zero residual as a strategy to identify optimaldecomposition methods is without basis. To nevertheless advise on optimaldecomposition methods, I suggest to investigate for which types of functionsdifferent decomposition methods are exact or good approximations and howthey perform in simulations, where the exact integrals are known. Regardingthese criteria the LMDI seems to perform best.