IPAT and its Variants

IPAT, I=PAT, or Impact = Population × Affluence × Technology, is a simple framework that allows us to understand how much various factors contribute to an overall impact. Here we consider the development of IPAT and variations.

Origins of IPAT

An early and especially simple formulation of an IPAT-like identity was introduced by Ehrlich and Holdren (1971). The identity is I=PF, or Impact = Population × Per Capita Impact. The identity is tautologically true, in that F is defined as the quotient I÷P. Two specific applications of I=PF are given as follows.

The equation I=PF may be misleading as stated in that it implies that the two variables, population and per capita impacts, are independent variables, when in fact there are interrelationships between them. Ehrlich and Holdren (1971) introduce a variant I = P × F(P) to indicate that per capita impact may depend on overall population size. The paper considers two mechanisms by which F may depend on P: economies of scale, which are manners in which F may decrease with P, and diminishing returns, which are manners in which F may increase with P. While the paper does not offer specific numbers to make the case, it argues that diminishing returns are a more significant factor than economies of scale, and thus we should expect F to increase with P. In other words, total impact increases superlinearly with population.

Raskin (1995) also applies a simple two-factor model to estimate the relative contributions of population and per-capita emissions–labeled as intensity–to world carbon dioxide emissions from 1950 to 1990. He also estimates the relative contributions to projected changes in emissions from 1990 to 2050. In the first scenario, he divides the world into two regions, what at the time were considered “more developed” and “less developed” countries. He finds that from 1950 to 1990, population growth explains 38% and 22% of the growth in emissions in the more developed and less developed regions, respectively. Paradoxically, he also finds that when the world is considered as a whole, then population growth explains 60% of the growth in emissions. Similarly, using projections on the development of population and economic growth, and with some assumptions on switching to fuels with lower emissions, Raskin (1995) finds that population growth will explain 34% of the growth in CO₂ emissions from 1990 to 2050 in more developed countries, 53% of emissions growth in less developed countries, and 75% of emissions growth worldwide.

Raskin’s explanation for the observed paradox–that population seems to have a greater effect when considering the world as a whole than it does in any constituent regions–is that because population growth is higher, and emissions intensity is lower, in less developed countries than in more developed countries, aggregating the two groups depresses observed intensity compared to what one would observe when considering each of the two groups separately. The pattern is a form of Simpson’s paradox (Simpson (1951)), the phenomenon by which a trend that appears in each of several individual groups disappears or is reversed when considering the aggregation of the groups. Raskin (1995) cautions against applying a variant of IPAT analysis on too aggregated a region, and he suggests that lower contribution from population growth observed from considering more and less developed countries separately is more revealing than the lager contribution observed from considering the Earth as a whole. Raskin further warns that this issue is especially hazardous, given the deep polarization in ecology between those who argue that the population growth is the more important factor in understanding environmental impacts and those who argue that affluence is the most important factor.

The IPAT Equation

As Chertow (2000) recounts, IPAT developed in the course of a debate between Barry Commoner, who argued that ecologically poor technology should be understood as the primary driver of negative environmental impacts, and Paul Ehrlich and John Holdren, who argued that population and affluence should be understood as the primary drivers of environmental impacts. The debate was conducted, among other venues, in the Population, Resources, and the Environment, the final report of the Nixon administration’s Commission on Population Growth and the American Future–Ehrlich and Holdren (1972a) and Commoner (1972a)–and in a 1972 issue of the Bulletin of the Atomic Scientists–Ehrlich and Holdren (1972b) and Commoner (1972b).

As York, Rosa, and Dietz (2003) explain, the IPAT equation Impact = Population × Affluence × Technology expresses environmental impacts as the product of three factors. Population is straightforward and the same as above. Affluence is typically expressed as gross domestic product (GDP) per capita, so that GDP = PA. Technology T is taken to be a residual; T = I÷(PA). Dietz and Rosa (1994) criticize IPAT on the grounds that since the technology term T is a residual, it captures all factors that are not population and affluence, potentially having little to do with technology as common understood. The challenge is analogous to characterizing the residual term in the Solow-Swan economic growth model (Solow (1956) and Swan (1956)). Instead, Dietz and Rosa (1994) propose that T be a well-defined, independent measure.

References

Chertow, M. R. “The IPAT Equation and Its Variants”. Journal of Industrial Ecology 4(4), pp. 13-29. October 2000.

Ehrlich, P. R., Holdren, J. R. “Impact of Population Growth”. Science 171(3977), pp. 1212-1217. March 1971.

Raskin, P. D. “Methods for estimating the population contribution to environmental change”. Ecological Economics 15(3), pp. 225-233. December 1995.

Simpson, E. H. “The Interpretation of Interaction in Contingency Tables”. Journal of the Royal Statistical Society: Series B (Methodological) 13(2), pp. 238-241. July 1951.

Commoner, B. The environmental cost of economic growth. In Population, Resources and the Environment. Edited by R. G. Ridker. Washington DC: U.S. Government Printing Office, pp. 339–363. 1972a.

Ehrlich, P., Holdren, J. Impact of population growth. In Population, Resources, and the Environment. Edited by R.G. Riker. Washington DC: U.S. Government Printing Office. pp. 365–377. 1972a.

Commoner, B. A bulletin dialogue on “The Closing Circle”: Response. Bulletin of the Atomic Scientists 28(5), pp. 42-56. 1972b.

Ehrlich, P., Holdren, J. A bulletin dialogue on the ‘Closing Circle’: Critique: One dimensional ecology. Bulletin of the Atomic Scientists 28(5), pp. 16–27. 1972b.

York, R, Rosa, E.A., Dietz, T. “STIRPAT, IPAT and ImPACT: analytic tools for unpacking the driving forces of environmental impacts”. Ecological economics 46(3), pp. 351-365. October 2003.

Dietz, T., Rosa, E.A. “Rethinking the environmental impacts of population, affluence and technology”. Human Ecology Review 1(2), pp. 277-300. Summer/Autumn 1994.

Solow, R.M. “A contribution to the theory of economic growth”. The Quarterly Journal of Economics 70(1), pp. 65-94. February 1956.

Swan, T.W. “Economic Growth and Capital Accumulation”. Economic Record 32(2), pp. 334-361. November 1956.