Attribution of changes in an intensity index

Several methods have been proposed to quantify the individual attribution to the changes in aggregate intensity, but rarely identified that one's attribution to either the intensity "A/B" form or "B/A" form that both represent one kind of efficiency indexes (cost/benefit or benefit/cost) should be equal, which is defined as the reciprocal attribution rate test. We review some existing decomposition analysis methods and propose a new method for attribution of changes in an aggregate intensity index that satisfies factorreversal test, time-reversal test, and reciprocal attribution rate test by transforming intensity into a multiplicative formula that does not depend on the denominator weight. A numeric illustration, sensitivity analysis, and actual case studies for China are further provided to verify and compare the scopes of application and economic meanings of different methods for attributing intensity indicators. This proposed new method is a suitable tool for scientists and policy-oriented institutions to well monitor and analyze intensity transition in particular. (C) 2020 Elsevier Ltd. All rights reserved.