The relative roles of energy and water intensity in the economic growth of the United States, 1950 – 2015

Water and energy are indispensable inputs to the modern economy and are of primary concern for the sustainability of the global economy. Continually growing use of water and energy cannot be sustained in the pursuit of greater wealth and prosperity, given planetary boundaries and other limitations on these resources. Water is a main input to the production of energy, and vice versa, and to some extent the two are substitutes. An economy ’ s energy intensity and water intensity measure the ef ﬁ ciency with which energy and water, respectively, are used in the generation of wealth. How far has an advanced economy like that of the US gone in decoupling energy and water use from economic growth? To answer this question, we decompose the growth of GDP per capita into improvement in energy and water intensity and the change in the per capita use of these two crucial inputs, using data for the US from 1950 to 2015. We ﬁ nd that water and energy use ef ﬁ ciency improvements are responsible for much more growth in per capita GDP than increases in water and energy inputs, and that water use can be decoupled more signi ﬁ cantly from increasing wealth than the use of energy. The results have important implications for the future of energy and material consumption by the global economy.


Introduction
The use of water and energy by human societies has been and remains essential for well being.Reliable, secure and affordable access to water and energy are among the Sustainable Development Goals (SDGs).The 'waterenergy nexus' is a concept that recognizes the inextricable link between water and energy resources in sustaining well-being and generating development (Schneider et al 20192019, Fayiah et al 2020).Water is used in the generation of electricity and in the extraction and use of fossil fuels while energy is needed in every stage of the water cycle from producing, moving, treating and heating water to collecting and treating wastewater (Gleick 1994, EEA 2012, Spang et al 2014, IEA 2016, Scanlon et al 2017).
Considerations about the role of water use in a transition to a sustainable economy tend to focus on the challenges of ensuring that the world's population, including the urban poor, has access to potable water and on the provision of water for irrigated agriculture (Rodell et al 2018).Climate change heightens concerns about water accessibility (OECD 2016, Boretti and Rosa 2019, UN 2020, WEF 2020).Water is indeed essential for human survival and biological well-being, but also indispensable as an input to human material culture.For most of human history water was as necessary as energy for the production of material output and the preparation of food (Kelly 2013, Lee andDaly 2000).The Neolithic Revolution and urbanization were made possible by the manipulation of water supply (Simmons 2007, Mithen 2012).Advances in the collection, distribution and storage of water were major drivers of technological change and economic growth in premodern civilization (Solomon 2010, Sedlak 2014).The manufacturing processes underpinning the Industrial revolution depended on water as much as on coal and oil (Hahn 2020).Water continues to be a vital factor of production in contemporary economies (UN 2021) and is used in greater mass quantities than any other commodity by modern cities.
The role of energy in achieving economic growth has long been recognized (Kümmel 2013, Morris 2015, Smil 2016, Wrigley 2016).The relationship between economic growth on one hand and energy and water use on the other is shaped by many drivers including technological development, households' and individuals' lifestyles, dietary choices and food production, ease of water availability, and demography (Distefano 2021).It is understood that economic growth induces improvements in the efficiency with which energy is used as the mix of fuels and energy technologies changes (Adams andMiovic 1968, Burke andCsereklyei 2016).Unlike energy needs, which can be met using a variety of fuels (IEA 2021), water is irreplaceable as an economic input in many processes.Unlike energy, water can be recycled, both by the natural water cycle and in urban or industrial settings reused using energy-intensive treatment technologies (Kumar et al 2021).Water is a type of material factor input, but it is an exotic and singular material in the sense that it is voluminous, heavy, naturally produced and transported, easily recyclable, and required in exceptionally large quantities and at exceptionally low unit cost for most economic activities.Additionally, water is without substitutes for many economic processes, like energy, but unlike other materials.Water and energy are therefore uniquely important as a subject of study for economic growth and sustainability.
Sustainable and net-zero development both require significant improvements in the efficiency with which water and energy are used in the continued creation of economic wealth (Davis et al 2018, Boretti 2023).Because both energy and water inputs are indispensable for the modern economy, and because they are major inputs to the production of each other per the energy-water nexus, they jointly constrain and enable sustainable economic growth (Baksi and Green 2007).The nature of this constraint could profoundly implicate the sustainability of economic growth in the 21st century.Indispensable, however, is not synonymous with copious.Is it possible to decouple energy and water consumption from economic activity?Improvements in water efficiency use in urban areas indicate that decoupling is feasible (Richter et al 2020, Gong et al 2021).Improvements in energy efficiency have been the norm for the past four decades (Nadel et al 2015).
A concept and metric that is useful in this regard is energy intensity: the total energy used by an economy per unit of output, e.g.gross domestic product.Energy efficiency (or productivity), the inverse of energy intensity, is defined as output per unit energy and reflects energy use improvements in automobile fuel economy, power plant heat rates, building operations, industrial processes, electricity generation plants, etc (Laitner and Hanon 2006).Economic productivity, measured as Gross Domestic Product per capita, results from the interaction of energy efficiency and the amount of energy used.From the standpoint of sustainable development, it is preferable for an economy to use less energy, and other inputs like water, to generate a given amount of economic output (Baksi and Green 2007).
To quantify the relative roles of energy and water use in economic growth, and the relative contribution of increasing use versus increasing efficiency of use, made we report the results of a 'growth accounting' exercise in which the growth of GDP per capita in the United States between 1950 and 2015 is decomposed into the improvement in efficiency and the increase of inputs per capita, for both energy and water inputs.The novelty of the results presented here lies in the use of a growth accounting framework (common in energy economics) to compare two measures for the efficiency with which an economy uses energy and water (energy intensity and water intensity).We avail ourselves of data on energy use and water withdrawal, as a measurement to capture water utilization, for the world's largest economy.We also present regression results allowing for a comparison of the role of energy use and water use as inputs into GDP per capita.
We find that water and energy use efficiency improvements are responsible for much more growth in per capita GDP than increases in water and energy inputs.We find that energy inputs cannot be as easily decoupled from per capita GDP growth as water.The results have important implications for the future of energy and material consumption by the global economy.
The paper is organized as follows.The second section below describes the data on energy use and water withdrawal available for the United States, and the methods used to elucidate the role of energy and water consumption and the efficiency of their use in the growth of economic productivity.Results are presented in section 3 and discussed in section 4; section 5 summarizes conclusions.

Data
Water use in the United States is captured by water withdrawal data which measures the volume of water that a category of water users removes from the 'immediate environment' comprising surface and ground water sources such as rivers, lakes, reservoirs, and aquifers.Common categories of water withdrawal use data include thermoelectric power, irrigation, public supply (delivered by water utilities to users for domestic, commercial, and industrial purposes and for public services, such as public pools, parks, firefighting, water and wastewater treatment, and municipal buildings), self-supply by industrial users, mining, and livestock operations (USGS 2018).Water Withdrawal data does not include water used in hydropower plants since this is all returned to the environment.The US Geological Survey's Water Use Science program publishes an authoritative water use census at the county level every five years since 1950, with the most recent 2015 census published in 2018.
Data on energy use in the United States are reported by the Department of Energy's Energy Information Administration (EIA).Yearly values for total energy consumption per capita measured in millions of British Thermal Units (Btus), and energy intensity per dollar of GDP measured as thousands of Btus per chained 2012 dollars, are reported since 1949 (EIA 2022).
Water consumption is measured as the amount of water that is withdrawn minus the water that is returned to the environment (Debaere and Kurzendoerfer 2017, USGS 2018, Ruddell 2018).That is, net water consumption is different from withdrawal of water from the environment because water can be recycled.By contrast, energy consumption and energy withdrawal are more mutually equivalent because energy can only be dissipated, not recycled, per the second law of Thermodynamics.In this study it is most appropriate to consider water withdrawal as the measurement of water use because it is the withdrawn water that is used as a material input to economic processes (analogous to other material inputs), not the water consumed net of recycling or return flows.
Figure 1 shows the time series for energy consumption per capita (measured as millions of BTUs per capita) and water withdrawal per capita (measured as thousands of gallons per capita) between 1950 and 2015).The water withdrawal variable was constructed using the reported variable of water withdrawal in billions of gallons per day to construct a total yearly total by multiplying it by 365.Both water and energy use per capita increased during the mid-20th century and have been decreasing since 1985, whereas energy use per capita has been decreasing, less rapidly, only since 2005.Energy use per capita remains at a significantly higher level in the early part of the 21st century than in the middle of the 20th century.Water withdrawal per capita has not only been steadily decreasing since 1975, in the 21st century it was lower than in 1950.Figure 2 shows the time-series for energy and water intensity from 1950 to 2015.Energy intensity is measured as thousands of BTUs per dollar of GDP while water intensity is measured as gallons of water per dollar of GDP.(GDP is measured using 2012 Chained dollars).Both intensity measures show a steady and pronounced decrease over a 65-year period, reflecting increased water and energy productivity in the economy.Figure 3 shows the energy intensity of water withdrawal from 1950 to 2015, measured as BTUs per gallon.The energy intensity of water has increased over time, due to the use of more electrically intensive water conveyance and treatment methods that move water   longer distances and produce it at a higher quality.In all three figures an inflection point is discernable circa 1980 when a number of environmental regulations were passed in the US including the Clean Water Act.

Methods
The variable GDP per capita (Y/P) serves as both a measure of economic productivity and material prosperity.A decomposition of GDP per capita proves useful in order to specify the relative importance of the input of energy and the efficiency of its exploitation in the creation of economic wealth (Malanima 2014).The decomposition is represented as the interaction of energy consumption per capita (E/P) times energy efficiency (Y/E): Since the variables in equation (1) as time-variables and taking the natural logarithm of equation (1) we can use the 'log difference method' to calculate per annun growth rates (Stock and Watson 2007).The rate of growth of GDP per capita (g y ) is the summation of the growth rate of energy use per capita (g epc ) and the growth rate of energy efficiency (g ee ): Treating water as a vital input into the process of wealth creation, GDP per capita can be similarly decomposed into water withdrawal per capita (WW/P) and water efficiency (Y/WW): The growth of GDP per capita thus equals the growth rate of water withdrawal per capita plus the growth rate of water efficiency: = + g g g .4 y wwc we

( )
An increase in the productivity (or inverse efficiency) of water or energy is a consequence of discoveries of new fuels, the development of new technologies for economic production, and improvements in the utilization of existing fuels or technologies for existing economic processes.By contrast, increases in the water or energy use per capita are a consequence of more water-or-energy-intensive lifestyle choices along with higher incomes, consumption, and GDP per capita.The relative roles of improving efficiency and overall growth per capita in energy and water use are presented below in the results.
The consumption of energy and the withdrawla of water are highly correlated with a correlation coefficient of 0.86.The use of both water use and energy use as independent variables in a regression equation with GDP per capita as the depedent variable is thus precluded due to multicollinearity (making the estimated regression coefficients and their signs biased and unstable).It is still revealing to compare the coefficients for the following time-series regression: with y = GDP per capita and X denoting either total energy use or total water withdrawal.

Results
The relative importance of change in energy use per capita and change in energy efficiency in the growth of GDP per capita can be ascertained for the period 1950 to 2015 per equation (2) as: The annual rate of growth of per capita GDP was 1.99% while energy per capita (E/P) and energy efficiency (Y/E) grew respectively at the rates of 0.45% and 1.54% per annum.While both energy efficiency and per capita energy inputs contributed positively to growth in GDP per capita, the increase in the efficiency of energy use contributed significantly more (over 3x more) to economic growth per capita than increasing consumption of energy.

( )
The per capita inputs of water actually decreased slightly, by −0.28% per annum, while the efficiency of water use increased by 2.28% per annum (roughly eight times).
The 1950 to 2015 period represents the modern history of the U.S economy.Calculating the growth accounting equations (2) and (4) for the periods 1950 to 1979, 1970 to 1990 and 1990 to 2015 reveals that the improvements in energy intensity and water intensity occurred from 1970 onwards (see table 1).The values presented in table 1 are annual percentage growth rates: negative values indicate declines in the value of a variable while positive values indicate increases in values.In the 1990 to 2015 period, the growth rate of energy use per capita was negative signifying a decrease in the amount of energy use per capita and concomitantly, a lessened role for energy use per capita as a driver of economic growth.
In the case of water withdrawal per capita, significant diminutions have occurred since 1970.The heyday of U.S. industrialization, the two decades between 1950 and 1970, were characterized by per capita increases in both energy and water use.
Equation (5) was estimated using the Prais-Winsten estimation method due to the presence of serial correlation in the errors of a Generalized Least Squares procedure (since the values of the independent variables exhibit temporal correlation).For each variable the data covered the period 1950 to 2015 in 5 year increments.The values of the estimated regression coefficients for total energy use and total water withdrawal are, respectively, with the r-square values for each regression as indicated.The coefficients can be interpreted as elasticities so that a 1% increase in the amount of energy or water used induces a β% increase in GDP per capita.The effects of increasing the use of energy on GDP per capita are almost twice that of increasing water use, and furthermore, much more of the variability in economic productivity is explained by the magnitude of energy use.

Discussion
Improvements in energy and water use efficiency have both contributed positively to US economic growth per capita since 1950 and have both contributed much more to growth than increasing inputs of water and energy.
Our results are consistent with those reported in Beca and Santos (2014) and Mahjabin, et al (2018) for the US regarding the time trend for improving water and energy intensity.This is a very positive finding for the sustainability of economic growth in the sense that the US has now demonstrated a long track record of supporting most of its growth through improved efficiency more than through increased consumption of two of the most indispensable and non-substitutable economic inputs: energy and water.Improvements in energy and water efficiency do not equate to the decoupling of economic growth from resource use (Ward et al 2016) but gains in efficiency are responsible for the majority of decoupling that has occurred in the US.
The findings highlight a difference between energy use and water use trends.The US has grown its per-capita wealth without increasing its per capita withdrawals of water, and indeed has slightly decreased per capita withdrawals as it has grown.Water withdrawal increases in support of GDP increases are 89% lower (2.27/2.55)than they would have been without improvements in water use efficiency.But in contrast to water use, energy use per capita has grown significantly despite large gains in energy efficiency.Energy plays a distinct and different role than water as an input to the modern economy.The US economy has required significant increases in energy inputs per capita to support economic growth, even as improved energy efficiency has reduced the need for increased energy inputs by 77% (1.54/1.99) to achieve today's wealth per capita.The time-series of the ratio of energy used by the economy to total water withdrawal reflects the different ways in which the economy has needed to utilize energy and consume water in order to grow (figure 3).BTUs per gallon withdrawn have almost doubled over the period of study from 527 in 1950 to 829 in 2015.
There could be 'Kuznet Curve' dynamics at play with respect to water use: as overall economic welfare improves individuals are better able to act on choices resulting in reduced water use (Carson 2010, Katz 2015, Sarkodie and Strezov 2019).However, diminishing returns from investment in efficiency could threaten continued efficiency gains.If energy efficiency gains were to taper off over time owing to the law of diminishing returns, the economy would require higher growth of energy and water input per capita to make up for lower efficiency gains.For water and other materials, the trend of year-over-year reductions in per capita inputs of material could be reinforced as energy-intensive recycling technologies like Direct Potable Reuse and 'circular economy' production processes continue to reduce the need for withdrawal of resources from the Earth's environment.Increased recycling of water and other materials in the economy will also require higher energy inputs.Under those conditions, this analysis implies that energy inputs per capita will grow over time in their relative importance for generating wealth, whereas material inputs like water will decrease in relative importance.The cost and efficiency of energy use should therefore continue to grow in relative importance compared with material inputs like water and should be an emphasis of policy and investment.
The results presented here are derived per capita to separate the role of population growth from the technological efficiency and behavioral choices of the population.It is clear that energy use and material uses like water will increase when population grows.Therefore, global demographics and population trends remain of primary importance for planning the sustainability of energy and water use, independent of changes in efficiency or behavior.
These results have important implications for the future of energy and material consumption by the global economy.If trends since 1950 continue in the US and in other countries following a similar economic growth trajectory to the US, we can expect global energy demand to continue growing but water demand to 'plateau' as it decouples from growth.We can also conclude that modern gains in water and energy efficiency-or conservation-have been very successful at enabling economic growth and improving the sustainability of the economy's water and energy consumption.Efficiency has improved due to a combination of policy, technology, and the relative cost advantages of conservation over consumption.Without these efficiency improvements in efficiency since 1950, the human economy would be much closer to (or further beyond) planetary energy and water carrying capacities than it is in 2024, and economic growth may have been lower due to higher water and energy costs.But, if efficiency gains suffer from diminishing returns in the 21st century, this means more of the economic growth of the future would need to be supported by increasing water and energy inputs, exacerbating water and energy sustainability problems worldwide.Continued emphasis on improved efficiency will be important in the future to forestall diminishing returns and the resulting sustainability threats.

Conclusions
Using a decomposition method for economic production, water withdrawal, and energy consumption in the US since 1950, this paper finds that water and energy use efficiency improvements are responsible for much more growth in per capita GDP than increases in water and energy inputs.We find that energy inputs have not been as easily decoupled from per capita GDP growth as water inputs.Energy efficiency and energy cost are therefore relatively important for continued per capita GDP growth.The 'Jevons Paradox' (when technological progress increases the efficiency with which a resource without inducing a decrease in the amount of the resource used) would seem to be at play in the case of energy (Polimeni et al 2015).Further work is needed to elucidate how the shift in the fuels used to provide energy to the economy will affect the demand of water resources.

Figure 1 .
Figure 1.Annual timescale of Energy Consumption per capita (millions BTUs per person) and Water Withdrawal per capita (gallons per person) US 1950-2015.

Figure 2 .
Figure 2. Annual timescale of Energy Intensity (thousands of BTUs per dollar of GDP) and Water Intensity (gallons of water per dollar of GDP).Efficiency, which is the inverse of intensity, has been increasing steadily over time; intensity has been increasing over time.

Figure 3 .
Figure 3. Energy Intensity of Water Withdrawal, the ratio of total energy consumed to total water withdrawn in the US economy as a whole, 1950-2015 (measured as BTUs per gallon), has been increasing over time.

Table 1 .
Results of decomposing the annual compound growth rate of GDPper capita into the growth rates of two energy or water-based determinants.Numbers represent percentages.