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The Kaya identity is an equation relating factors that determine the level of human impact on climate, in the form of emissions of the greenhouse gas carbon dioxide. It states that total emission level can be expressed as the product of four inputs: population, GDP per capita, energy use per unit of GDP, carbon emissions per unit of energy consumed. This equation is very simple and tricky, as it can be reduced to only two terms, but it is developed so that the carbon emission calculation becomes easy, as per the available data, or generally in which format the data is available.
The Kaya identity is somewhat related to the I = PAT equation. The main difference is that the Kaya identity is only valid for CO2-emissions, while the I = PAT equation describes a more general impact.
The Kaya identity was developed by Japanese energy economist Yoichi Kaya. It is the subject of his book Environment, Energy, and Economy: strategies for sustainability co-authored with Keiichi Yokobori as the output of the Conference on Global Environment, Energy, and Economic Development (1993 : Tokyo, Japan).
The identity is expressed in the form:
One limitation of this equation as stated is that it does not account for a) the direct release of carbon dioxide by deforestation through burning b) the loss of the carbon sink due to that deforestation. Work needs to be done on the historical geography of deforestation. Trend lines are often shown showing the rise in CO2 output since the start of the industrial revolution, but the rise in consumption of fossil fuels was paralleled by massive temperate deforestation across Europe, North America and Australasia during the same period - which obviously also saw massive Global Population and Gross World Product Growth.
 Use in IPCC reports
The Kaya identity plays a core role in the development of future emissions scenarios in the IPCC Special Report on Emissions Scenarios. The scenarios set out a range of assumed conditions for future development of each of the four inputs. Population growth projections are available independently from demographic research; GDP per capita trends are available from economic statistics and econometrics; similarly for energy intensity and emission levels. The projected carbon emissions can drive carbon cycle and climate models to predict future CO2 concentration and climate change.
 Use in other scientific analysis
The Kaya identity is reviewed in a 2002 paper.
A 2007 article uses the Kaya Identity in its analysis of recent trends in carbon emissions, and finds:
... cessation or reversal of earlier declining trends in the energy intensity of gross domestic product (GDP) (energy/GDP) and the carbon intensity of energy (emissions/energy), coupled with continuing increases in population and per-capita GDP. Nearly constant or slightly increasing trends in the carbon intensity of energy have been recently observed in both developed and developing regions. No region is decarbonizing its energy supply.
- Rehmeyer, Julie. "Yoichi Kaya's carbon fix formula". Wired. Retrieved 20 July 2012.
- Waggoner, P. E.; J. H. Ausubel (2002). "A framework for sustainability science: A renovated IPAT identity" (PDF). PNAS 99 (12): 7860–5. Bibcode:2002PNAS...99.7860W. doi:10.1073/pnas.122235999. PMC 122985. PMID 12060732.
- Raupach, M.R.; et al. (May 22, 2007). "Global and regional drivers of accelerating CO2 emissions" (PDF). PNAS 104 (24): 10288–10293. Bibcode:2007PNAS..10410288R. doi:10.1073/pnas.0700609104. PMC 1876160. PMID 17519334.