## Wednesday 23 October 2013

### Does I = PAT?

The equation I = PAT was invented by Barry Commoner in 1972 and is widely used by the pressure group Population Matters in arguing for population control. It asserts that humanity's environmental impact (I) depends on population (P), affluence (A) and technology (T). The last factor is best understood as a measure of the resource inefficiency of our various industrial, agricultural and other processes.

The terms P and A are easy to understand and relatively easy to measure. GDP per head is a workable measure of A. I and T are much harder since there are many kinds of environmental impact, eg greenhouse gas emissions, deforestation, mineral resource depletion and loss of biodiversity, which are not always strongly correlated. (see, eg, Cole and Neumayer, 2004).  That is, we need a set of IPAT equations, one for each kind of environmental impact. Each will need its own T value which will be defined as I/PA rather than calculated independently.

IPAT, therefore, is not so much a proposed law of nature as a suggestion for relevant factors when considering environmental change. Initially IPAT was useful but it can now be seen to be rather misleading.

The variations between groups
The equation suggests (at least when applied globally) that the affluence of the world's population can be expressed by a single number. Though technically correct it's very misleading. The reality, obviously, is of vast variations in affluence and lifestyle both between countries (contrast Somalia and Switzerland for instance) and within countries (contrast bankers and farm workers).

Single numbers are sensible where everyone is the same or where a characteristic shows a normal distribution (as for human height for instance). Affluence shows a Pareto or, colloquially, 80:20 distribution (20% of the people own 80% of the wealth) and is thus not well represented by a single number.

The interdependence of P and A
The equation suggests that population and affluence are independent variables which in general they are not. During the 19th century the UK's population and prosperity rose together as the agricultural, industrial and scientific revolutions (plus the spread of empire) produced ever more food, manufactured goods and services. In this period the true independent variable was probably 'progress'. This pattern has been repeated many times as other countries have industrialised and in most cases the main growth phase has been followed by a marked reduction in population growth.

Today growth in affluence is greatest where population growth is modest.

The parity of P and A
The equation suggests that population and affluence are of comparable importance in creating environmental impact. In fact that's not true. In recent decades our impact has risen much faster than population and is largely driven by increasing affluence. Some of this is due to the increasing wealth of the mega-rich 1% (or 0.1% globally I suppose) but much is due to the increasing numbers of Koreans, Brazillians, Indians and Chinese who can afford cars, meat and broadband Internet.

The meaningless differential
The equation suggests that its first differential would be
dI/dP =AT.

That is, that a small (say 1%) increase in population will produce the same proportional increase in environmental impact. That, of course, is unreal. The world's population comprises many subpopulations with very different lifestyles and levels of affluence. One extra Briton will consume much more than one extra Bengali and will have correspondingly more impact.

So this first differential will be accurate only if every subpopulation increases by the same small amount. But that isn't happening. Some countries are still experiencing rapid population growth whilst growth elsewhere is static or even negative.

The first differential also requires an associated growth in the local economy to provide the extra people with goods and services. It is, at least, unclear whether local economies can respond in this way without accelerating impacts on the environment. Two examples may illustrate this:
• As people migrate to London suburbs they will need roads, houses and schools. If they find work and pay taxes they can afford them. But since there can be no more land we may expect more air pollution, less green space, higher house prices and higher population densities.
• As population increases in many East African villages the women must walk further for firewood. That gives them less time for farming and childcare whilst reducing the ground cover.
The complexity of things
The IPAT equation suggests a simplicity that simply does not exist. The complexity of things is not in doubt and its time to stop using this simplistic equation.

Refs
Cole, M. A. and Neumayer, E. "Examining the impact of demographic factors on air pollution," Population Environment 26.1 (2004): 5-21.

Commoner, Barry. 1972:  “The Environmental Cost of Economic Growth.” in Population, Resources and the Environment. Washington, DC: Government Printing Office Pp. 339-63, 1972.