Kaya identity

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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. This identity states that total emission level can be expressed as the product of four inputs: human population, GDP per capita, energy intensity (per unit of GDP), and carbon intensity (emissions per unit of energy consumed).[1] This equation is both 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 a concrete form of the more general I = PAT equation. The latter seeks to describe environmental (I)mpact in terms of the factors (P)opulation, (A)ffluence and (T)echnology. In the Kaya identity, impact is carbon emissions, while technology is split into energy use per unit of GDP and carbon emissions per unit of energy consumed.[2]


The Kaya identity was developed by Japanese energy economist Yoichi Kaya.[3] 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).

Kaya identity is expressed in the form:

F = P \times \frac{G}{P} \times \frac{E}{G} \times \frac{F}{E}


F is global CO2 emissions from human sources

P is global population

G is world GDP

E is global energy consumption[4]

Use in IPCC reports[edit]

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.[2]

Use in other scientific analysis[edit]

The Kaya identity is reviewed in a 2002 paper.[5]

A 2007 article[6] 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.


  1. ^ Kaya, Yoichi; Yokoburi, Keiichi (1997). Environment, energy, and economy : strategies for sustainability. Tokyo [u.a.]: United Nations Univ. Press. ISBN 9280809113. 
  2. ^ a b Nakicenovic, Nebojsa; Swart, Rob, eds. (2000). "Chapter 3: Scenario Driving Forces, 3.1. Introduction". IPCC Special Report on Emissions Scenarios. 
  3. ^ Rehmeyer, Julie. "Yoichi Kaya's carbon fix formula". Wired. Retrieved 20 July 2012. 
  4. ^ "The "Kaya Identity"". PennState Department of Meteorology. Meteo 469, From Meteorology to Mitigation: Understanding Global Warming. Retrieved 27 November 2015. 
  5. ^ 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. 
  6. ^ 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. 

External links[edit]