DI refers to the ratio of (i) change in the rate of a given pollutant emission (e.g., SO2) and (ii) change in the rate of economic growth (GDP) within a certain time period (typically 1 year). For example, if we define ∆Pt = Pt/Pt − 1 (pollution emission) and ∆Yt = Yt/Yt−1(economic growth), then the DI in year t: DI = ∆Pt/∆Yt. When DI ≥ 1, it means that the increasing rate of pollutant emissions keeps pace with or is higher than economic growth; when DI = 1, it is the turning point between absolute coupling and relative decoupling; when 0 < DI < 1, it means that the rate of growth in pollutant emissions falls short of that of economic growth; when DI = 0, it means the economy is growing, while pollutant emission remains constant; when pollutant emissions decrease while the economy keeps growing, then DI < 0.

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