Scaling relations, such as the IPAT equation and the Kaya identity, are useful for quickly gauging the scale of economic, technological, and demographic changes required to reduce environmental impacts and pressures; in the case of the Kaya identity, the environmental pressure is greenhouse gas emissions.

However, when considering large-scale economic transformation, as with a shift to a low-carbon economy, the IPAT and Kaya identities and their cousins fail to capture the legacy of existing capital, on the one hand, and the need for new investment, on the other. While detailed models can capture these factors, they do not allow for rapid exploration of widely different alternatives, which is the appeal of the IPAT and Kaya identities.

This paper presents an extended Kaya identity that includes investment and capital stocks. The identity it proposes is a sum of terms, rather than a simple scaling relation. Nevertheless, it allows for quick analysis and rapid exploration of a variety of different possible paths toward a low-carbon economy.

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