### I=PAT.   An Introduction

This equation recognises that the impact of a human population on the environment can be thought of as the product of the population's size (P), its affluence (A), and the environmental damage inflicted by the technologies used to supply each unit of consumption (T). Sometimes, because of the difficulty in estimating A and T, per capita energy use is employed as a surrogate for their product (1) . Some equate T with impact per unit of economic activity (2), and for others T is a rather fuzzy category covering all sources of variation apart from population and affluence (3) . The equation was proposed and developed by Ehrlich, Holdren and Commoner in the early 1970s (4, 5, 6, 7).

The impact equation was introduced in a paper by Ehrlich and Holdren in 1971 in the form I = P. F, where F is a function that measures per capita impact. They were however concerned that some commentators were underestimating the significance of population growth in two ways:

First, it is easy to mistake changes in the composition of resource demand or environmental impact for absolute per capita increases, and in this way to underestimate the role of the population multiplier. They cite the demographer Coale who disparaged the role that population growth had played in causing environmental problems in the USA . Coale had argued that from 1940 to 1969 population had grown by 50 percent, but per capita use of electricity had multiplied several times (760 per cent increase). Now Ehrlich and Holdren point out that this massive increase in electricity consumption was in large part caused by changes between the components of the total energy budget. Electricity had only comprised 12 per cent of the US energy consumption in 1940 while it was 22 per cent by 1970. In terms of impact, what primarily matters most is not change in electricity consumption, but the change in the total energy use. This had increased much less dramatically than electricity use – by 140 per cent. Ehrlich and Holdren concluded that 38 per cent of the increase in energy use may be attributed to population growth.

Second, sometimes people have failed to realise that per capita consumption, and the associated per capita impact on the environment, are themselves functions of population size.

Impact can increase either faster or more slowly than linearly with population size. Impact can increase faster than population in situations where the law of diminishing returns operates. One of the examples given by the authors give concerns fisheries. The richest fishery stocks are depleted, so the yield per unit effort drops, and more and more energy per capita is required to maintain the supply. The authors explain that this same law is operating in agricultural production, mineral extraction and use of renewable water supplies.

On the other hand per capita consumption and per capita impact may decrease with population growth through what are known as economies of scale . In our companion essay “How many people can the earth support? Part 1” in section B, we note some examples of this phenomenon. Ehrlich and Holdren point out that as far as the USA is concerned, the population is already so large that it has largely achieved any possible economies of scale.

The upshot of these considerations is that in the course of their paper, Ehrlich and Holdren modify their impact equation to indicate that per capita consumption and associated per capita impact are functions of population size. So they then write the equation as I = P . F (P).

In assessing the relative importance of the three factors P, A and T in causing the big increase in pollution (200 – 2,000 percent) in the United States since the Second World War, Commoner (6) concluded that changes in technology, T, were primarily responsible. Change in pollution level, he says, cannot be accounted for simply by the growth of the human population, since the latter only increased by 42 per cent; so the ratio between the amount of pollution generated and the size of the population increased sharply since 1946.

Could increase in affluence be the chief culprit? Commoner argues no. Affluence as measured by GNP per capita increased by about 50 per cent, which is, alone, clearly insufficient to account for the observed increase in per capita pollution. Since GNP is only a crude over-all average of the goods and services produced in a country, it would be better to break it down into specific items such as food, clothing and shelter, etc. which he proceeded to do. With food, there was a slight decline in per capita calorific intake, a slight increase in protein consumption. With clothing, while styles changed, there was essentially no change in per capita production. As far as shelter was concerned, the number of housing units occupied per capita rose only slightly from 0.272 to 0.295.

The technological revolution, in contrast, had led to a big increase in pollution. New technologies had replaced old ones – e.g. soap powder replaced by synthetic detergents, natural fibres (cotton, wool) replaced by synthetic ones. Steel and lumber had been displaced by aluminium, plastics and concrete, railroad freight by car freight, returnable bottles by unreturnable ones. In farming, per capita production remained almost constant, but the harvested acreage decreased – in effect fertilisers had replaced land. Older methods of insect control were displaced by synthetic insecticides such as DDT, etc. etc. etc. In all these cases what had changed drastically was the technology of production, rather than the over–all output of economic goods.

These changes had led to others. To provide the raw materials needed for the new synthetic fibres, pesticides, detergents, plastics and artificial rubber, the production of synthetic organic chemicals also grew rapidly. The synthesis of these chemicals in turn used a great deal of chlorine. To make chlorine, an electric current is passed through a salt solution by way of a mercury electrode. So mercury consumption for this purpose vastly increased – by 3,930 per cent. Chemical products, along with cement for concrete, use rather large amounts of electric power, which had increased considerably, ...and so on.

In summing up the contributions of P, A and T to increased pollution, Commoner concluded as follows. Population accounted for 12-20 per cent of the increase. Affluence accounted for 1-5 percent except for the component of passenger travel, where the contribution rises to 40 per cent of the total. In contrast, technology accounted for about 95 per cent of the total pollution except in passenger travel where it only accounts for 40 per cent. So T, is far more significant than P or A.

Commoner goes on to comment on the frequently stated opinion that since affluence levels are far higher in developed countries than in developing countries, we should reduce the level of affluence in developed countries. He thinks however, that “affluence” as measured by things like GDP or power consumption, is itself illusory. To a considerable extent it reflects ecologically faulty, socially wasteful types of production rather than actual real welfare of human beings. So the needed production reforms can be carried out without seriously reducing the present level of useful goods available to the individual.

Holdren and Ehrlich (7) come to different conclusions as to the significance of the population factor both in pollution growth in the USA , and more generally. They state the impact equation as:

Environmental degradation = population × consumption per person × damage per unit of consumption.

They say:

“For problems described by multiplicative relations ... no factor can be considered unimportant. The consequences of the growth of each factor are amplified in proportion to the size and the rate of growth of each of the others”.

They then looked at the increase in pollution in the USA since the Second World War.

They took as an example, automobile emissions of lead. The appropriate measure of “consumption” is, they argue, vehicle–miles per person, which increased two–fold between 1946 and 1967. The impact per unit of consumption in this case is emissions of lead per vehicle-mile, which increased 83% or 1.83–fold in this period. Since the population increased 41%, or 1.41–fold, between 1946 and 1967, we have a relative increase in emissions of 1.41 × 2.0 × 1.83 = 5.16 or 416%. They point out that the dramatic increase in the total impact arose from the rather moderate but multiplicative contributing factors.

They go on to contrast this result with what they regard as the erroneous conclusion, arising from the assumption that the contributing factors are additive rather than multiplicative, that a 41% increase in population “explains” only 1/10 th of 416%.

Holdren and Ehrlich later discuss what they term “non-linear effects”. They say there are non–linear effects when a small increase in population generates a disproportionately large increase in environmental disruption. Altogether, they clearly regard population growth as a very significant factor in causing the increase of human impact world wide

Alternative formulations of the Impact equation

The equation in the form of I=PAT quickly became established as the norm and has been used and cited by many organisations and individual people ever since.

However, in more recent times, various alternative formulations of the equation have been proposed, of which I will just mention three. Dietz and Rosa (2) gave a stochastic reformulation of the impact equation which they claimed facilitates the application of social research statistical tools to studies on I=PAT. Their formulation is I = aP b A c T d e. They define A and T as per capita economic activity and the impact per unit of economic activity respectively; a, b, c, and d are parameters and e, a residual term.

Schulze and his colleagues (8) noticed that students they were teaching were puzzled because they know that behavioural choices affect environmental impacts, but the role of behavioural choices is not intuitively clear from the I=PAT equation: The equation “suggests that, aside from important choices about future birth rates, the only ways a rational individual can reduce her environmental impacts are by reducing her wealth or using more efficient technologies. But of course, per capita impacts also depend upon modifying behaviour (B)”. So Schulze proposes modifying the formula to I=PBAT, which calls attention “to the many behavioural choices that are immediately available to all individuals”. He points out that affluence and technology do not dictate behavioural decisions. He gives the example of a person who is wealthy and only uses the most efficient devices. But the environmental impact of that individual will still depend on whether or not the person is a profligate consumer.

David Willey of the Optimum Population Trust noted in 2000 that consumption is influenced by lifestyle and organisation - improved organisation in rich countries could lead to a reduced per capita consumption, but in poor countries better organisation might lead to a huge increase in consumption. So he proposed changing the impact equation to I = PLOT (population, lifestyle, organisation, technology) (9) .

Some recent studies

From the above considerations one may well imagine that the relationships between the elements of the impact equation might not be simple ones. And this leads us to some recent studies which illustrate both the complexities of the relationships and the difficulties in attempting to unravel them.

Fischer–Kowalski and Amann (3) studied the complexity in the A – I relationship, referring to studies on Material Flow Analysis (MFA). MFA is a set of methods for describing and analysing what has been termed socio-economic metabolism , the sum total of the material and energetic flows into, within, and out of the socio–economic system. This is in the context of human beings being collectively organised to maintain ways of life within a natural (and social) environment. At the centre of such studies was the belief that impact need not necessarily grow proportionately to affluence. Therefore, it should be possible to achieve some measure of delinking of material input and output (impact), and economic activity measured by GDP (a measure of affluence). Delinking came to be subdivided into two categories – relative delinking and absolute delinking. If there was a reduction in environmental impact per unit of GDP, it is termed relative delinking. If on the other hand economic growth continues but the absolute amount of materials used declined, it is termed absolute delinking.

The study was carried out for several industrialised countries, first on the input size, then on the output side, using a simple bivariate type of analysis - -plotting changes in GDP and either direct material input ( DMI) or material outflows (DPO), against time in years, between 1975 and 1995. They also plotted material intensity, that is DMI/GDP or DPO/GDP, against time. The countries investigated are amongst the richest in the world and between them have more than 50% of the world's income at their disposal.

On the input side, in general, GDP grew faster than DMI, indeed in the UK DMI had fluctuated slightly but hardly increased at all. The material intensity actually declined in all the countries. On the other hand, nowhere did absolute reductions of material input occur. So, conclude the authors, here is clear evidence for relative delinking, but not for absolute delinking. The graphs for two of the countries are shown in Fig.1.

Figure 1

On the output side – waste emissions and the disposal of materials (DPO or material outflows), they use data from the same countries, except, for no stated reason, and unfortunately for us in the UK , omitting the UK . The results were broadly similar.

The authors went on to pose the question - has this relative delinking been achieved as the result of deliberate government policies? At first examination the answer, say the authors, is no. For they find that relative delinking is just as pronounced in the UK and the USA as in the Netherlands and Germany, yet the latter pair of countries have placed more emphasis on policies of sustainability involving a slowdown of material growth, than the former pair of countries.

Now in a further investigation, the authors broke down output (DPO) into component parts. Here they found some evidence of absolute delinking. For example with solid wastes deposited in landfills, the authors results point to the conclusion that the more affluence increases, the lower is the level of waste production- there was an absolute decline of waste outflows i.e. absolute delinking, which they think suggests effectiveness of deliberate government policy. The think the main reason why overall DPO only shows relative delinking is that one component, namely CO2 emissions, does not show even relative delinking clearly.

However, the authors later also examined their data using Kuznet curves (see later) and here they found that changes in per capita environmental impact (measured by DMI and DP0) do not seem to be related to affluence in any consistent way.

Later in the paper they explore the relationship of their results to international trade between industrialised countries and developing countries over the period 1975 to 1995. They find a big difference between the two groups. In industrialised countries, imports greatly exceed exports, while in the developing countries the reverse situation holds. In industrialised countries both imports and exports rise in proportion to material input (DMI). In developing countries on the other hand exports rose steadily, while imports stagnate.

Now they also looked into the way that material flows and product value vary over the stages of production from the initial extraction of raw materials to the final disposal of worn out finished products. In the early stages a lot of material is extracted, of which only a small part is of value. Much unusable material is discarded. Economic value only accrues to the usable parts, is proportional to the efforts invested in extracting them, and is still fairly low. In the next step in the production process material intensity decreases i.e. there is less mass with higher value. In the final stage, consumption, the commodities produced have a relatively very small material weight while their value at the point of sale for consumption is at a maximum. So at point of sale material intensity reaches its minimum – a little material for a lot of money. We see here that at each stage of the production process value is added.

Now if we think of countries, those heavily involved in the early extraction processes will have a high material intensity while those further away from along the whole production sequence will be less materially intensive. But product value increases along the production sequence. One might therefore expect, as countries continue with their economic activities over a period of years, that in contrast to industrialised countries, in developing countries GDP would rise more slowly that material input.

And evidence was found that this is the case with two countries investigated - Venezuela over the period 1988 to 1996 and Brazil over the period 1975 to 1995. Fig.2 shows the graph for Brazil. So the industrialised nations reap the profit from the extraction of raw materials more so than the countries where the extraction takes place.

Figure 2

All this goes to show that the situation in industrialised countries reported earlier and shown in fig.1 is not so simple as it may at first have appeared. And in terms of the impact equation I=PAT, the interrelationship between environmental impact and affluence is much more complex than it might earlier have been thought to be. A full understanding of the impact equation must take into account the variety of socio-economic systems in different countries and the effects of globalisation. As the authors say:

“All socio-economic systems for which the I=PAT question may be posed are embedded not only in natural environments but also in networks of social systems with which they interact. The very nature of this interaction seems to be of crucial importance for their environmental (and of course also their economic) performance, and this is even more so in the face of globalization”.

In view of what has already been said about the interaction of the different variables, it should come as no surprise that investigators have found it very difficult to separate the impacts of population, affluence and technology,, and some have turned during and since the last decade of the Twentieth Century to a method which makes use of Environmental Kuznets curves, EKCs .

These curves are used to model the interrelation between affluence (measured in per capita GDP) and environmental impacts (in terms of physical amounts per capita) as 3rd order polynomial functions, while keeping population numbers constant. Technology understood as including all sources of variation apart from population and affluence, shows up as (random) deviation from the polynomial function.

There is what is called the environmental Kuznets curve (EKC) hypothesis. This hypothesis has it that the environment is initially exploited to a great extent in order to create economic growth. When an economy becomes developed enough, the environment becomes more valued, and technical progress makes it possible to create wealth with less environmental stress. Therefore as countries become more wealthy environmental stress will begin to decline at a certain income level. The corresponding curve is shown in Fig. 3. We should expect developing countries to be located on the left-hand side of the EKC, rich industrialised countries to lie on the right-hand side (and also in their history to show a turning point in the relationship with GDP), as explained by Seppälä and colleagues (10) . Not surprisingly, this hypothesis has provoked controversy. Some authors have even gone so far as to suggest that if the EKC hypothesis holds, economic growth is not at all a threat to global stability, and there are no environmental limits to growth. The corollary of this is that there would be no need for a nation to develop an environmental policy, economic growth will, in the long run, lead to a better environment. However, the authors just mentioned could not find evidence in support of the hypothesis when studying direct material flows of industrialised nations over the time period 1975 to 1995.

Figure 3

Implications of the impact equation for sustainable development.

We know that all three variables, P A and T affect the impact of human populations on the environment. Since it is clear that man's impact on the globe is already far too great (see our companion essay, “How many people can the earth support ?”), it would be logical to seek ways to reduce the magnitude of all three variables P, A and T in the impact equation, in every country across the globe..

Now we all know that affluence measured by consumption is highest in the industrialised countries lowest in the developing countries, and some information about this is given in the ecological footprint section of our companion essay to which I referred above. At the same time, we also all know that population growth is very small in the industrialised nations, but still very rapid in most developing countries. So we might come to the simple conclusion that apart from trying to improve technology everywhere, the industrialised nations should concentrate on reducing consumption, while the developing nations should focus on controlling and reducing population growth.

The very limited analysis given earlier shows however, that while these remain valid objectives, matters are much more complicated than they might appear to be at first sight. Trade between the industrialised nations and the developing nations introduces other considerations into the picture. National policies, and global policies (world Trade Organisations, United Nations etc) need to take into account the complexities of the whole situation which have only been lightly touched upon in this essay.

Finally, and to venture into the subject matter of what we hope to deal with in a later essay, if you look at policy statements by governments and environmental organisations, you will find, first, that they generally downplay the importance of P, and second and correspondingly, that they direct their efforts primarily at improving technology, T and to a lesser extent exhorting people in the richer countries to reduce consumption (which comes under A). Apart from vague general statements about the desirability of stabilising the human population, the increase of the human population, when not ignored completely, is treated as an independent variable to which all environmental policy must be adapted. In our view, this is a fundamental mistake, which, if not corrected, will make it impossible to achieve sustainable development.

Acknowledgements

We thank Marina Fischer-Kowalski for permission to reproduce the graphs of figures one and two.

References

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2. Dietz, T. and Rosa , E.A. (1994). Rethinking the environmental impacts of Population, Affluence and Technology. Human Ecology Review. Summer/Autumn, 1.

3. Fischer–Kowalski, M and Amann, C. (2001). Beyond IPAT and Kuznets curves: Globalisation as a vital factor in analysing the environmental impact of socio–economic metabolism. Population and Environment 23, 1: 7–47

4. Ehrlich, P.R. and Holdren, J. P. (1971). Impact of population growth . Science 171: 1212-1217.

5. Commoner, B. (1972a). The environmental cost of economic development. In Population resources and the Environment. Washington, DC: Government Printing Office.

6. Commoner, B. (1972b). The closing circle. Jonathan Cape , London .

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8. Schulze, P. C. (2002). I=PAT . Ecological Economics 40; 149-150.

9. Willey, D. (2000). Some hopes and thoughts for the future . Optimum population Trust, Manchester .

10. Seppälä, T. et al. (2001). The EKC hypothesis does not hold for Direct Material Flows: Environmental Kuznets Curve Hypothesis tests for Direct material Flows in five industrial countries. Population and Environment 23, 2: 217-237.