Residential water and energy use are linked in multiple ways. Various household activities and appliances involve both resources. Particularly in developing countries, households commonly apply energy-intensive coping strategies to deal with unreliable water supply. To understand the water-energy nexus at the private household level, here we introduce the concept of water-energy services (WES). We analyze household water and energy demand with a conceptual economic framework based on a household production model, and illustrate examples of the demand-side linkages with an empirical case study in India using an existing household-level dataset ( $n = 42, 152$ $n = 42, 152$ ). We conclude that household demand for one nexus resource depends not only on its own specific price, but also on the price for the other nexus resource as well as the opportunity cost of time, household income and income structure, other household characteristics, and production conditions for WES. Therefore, water and energy management should not be considered in isolation at the policy-making level. The economic framework developed here can serve as a conceptual basis and motivation for the empirical studies for developing sustainable water and energy management strategies.

Keywords:

1. Introduction

Household water use is often linked with energy use. The characteristics of the linkages between household water and energy use vary in different contexts. In many developed countries, roughly one-third of household energy use is directly linked to water-related purposes, while many other household activities, such as the use of wet appliances, involve the simultaneous use of water and energy (Kenway et al. 2011b, 2016). In developing countries, rooftop storage tanks accompanied by electric pumps are often observed as a coping strategy to address water quantity and pressure issues (Majuru et al. 2016). When water supply is unreliable, households often employ energy-intensive coping strategies to handle water issues. For example, energy may be employed to boil contaminated drinking water or to transport water from remote sources by vehicle (Eichelberger 2010; Rosenberg and Lund 2009; Laughland et al. 1993). For an urban context, Anand (2001) found that energy prices and access to energy can affect household water use in a case study of Chennai, India, with the cost of water quality improvement measures, e.g., boiling, being one of the hidden costs within household expenditure on water. Similarly, Pattanayak et al. (2005) revealed that the coping costs associated with handling the intermittent, insufficient, and poor-quality water supply in Kathmandu, Nepal, can be almost twice as high as the water bills paid to the utility. The evident interconnections demonstrated in the literature underscore the intricate economic linkages between water and energy use at the private household level, which remain understudied and warrant further research attention.

A water-energy nexus (WEN) perspective that considers the use of water and energy jointly and explores the economic linkages between the two resources could improve our understanding of household water and energy demand patterns. This can contribute to the development of efficient demand management strategies and policy mixes, e.g., the formulation of pricing instruments that encourage resource savings. Accounting for WEN linkages can also provide additional insights into challenges for equitable and affordable access to water.

However, few studies have explicitly discussed the linkages between household water and energy demand from an economic perspective. To the best of our knowledge, only two studies, conducted by Hansen (1996) and Maas et al. (2020), discussed conceptual economic models with WEN considerations, and both studies were developed in the context of developed regions. Hansen (1996) and Maas et al. (2020) also estimated the cross-price elasticity between household water and energy demand, with case studies of Copenhagen, Denmark, and Colorado, USA, respectively. They both found significant negative cross-price elasticities. An additional empirical analysis by Suárez-Varela (2020) identified positive cross-price elasticities between water and energy when estimating Spanish household water demand. The differences in the signs of the cross-price elasticities imply an ambiguity in the economic relationship between household water and energy demand, which is not explained by the existing conceptual frameworks (i.e., Hansen’s (1996) and Maas et al.’s (2020)).

This paper seeks to address the current research gap by developing a conceptual economic framework for systematically analyzing the demand-side WEN at the private household level. Our main research questions are: (1) How can we explain residential water and energy consumption decisions in the presence of household activities using both resources? (2) Why have positive and negative substitution elasticities between water and energy been observed in different case studies? (3) Which impacts will improvements to the technology employed by a household to process or use water and energy have on the consumption of both resources? Based on these questions, our research objective is to establish a conceptual framework for demand-side WEN that (1) is applicable for households in all types of contexts, particularly but not exclusively in developing countries, (2) explains the empirical differences in the sign of the cross-price elasticities between water and energy, and (3) explores how further opportunities in water and energy saving practices can be systematically analyzed for policy insights on demand-side resource management.

The paper is structured as follows. In Section 2, we present a literature review on conceptual and empirical econometric analyses of demand-side WEN at the household level and summarize household activities that reflect this nexus. Subsequently, in Section 3, we propose a conceptual economic framework based on a household production model. Building upon this conceptual framework, in Section 4, we conduct an economic analysis of demand-side WEN at the household level and analyze the impacts of changing prices, incomes, and household production conditions on household demand for water and energy. In Section 5, we illustrate exemplary aspects of demand-side WEN and the policy relevance with an empirical case study in India using a household-level dataset ( $n = 42, 152$ ) from the India Human Development Survey-II (IHDS-II) by analyzing the impact of household water use and supply conditions on electricity expenditure. In Section 6, we further discuss the implications of the framework with existing studies from the perspective of price impacts and improvements in household production conditions. Finally, in Section 7, we summarize our understanding of demand-side WEN at the household level and highlight key research and policy implications with a brief outlook on the need for future empirical studies.

2. Literature Review

2.1. Current conceptual and empirical econometric studies

As briefly discussed in the previous section, only two studies, by Hansen (1996) and Maas et al. (2020), discussed demand-side WEN at the household level with conceptual economic models. Both studies were designed based on the household production framework. Established in the mid-1960s, the household production theory introduces the concept that households act like small firms, they combine goods and services purchased on the market with their time to produce the commodities which they can consume to increase their utility (Becker 1965; Lancaster 1966; Muth 1966). Based on a household production model, Hansen (1996) derived a water demand function and included the energy price in the water demand analysis. He defined two aggregate final consumption goods according to their water dependency: water-dependent goods and water-independent goods. Hansen then estimated household water demand with pooled time-series data for Copenhagen, Denmark over the period from 1981–1990, and found a significant negative energy cross-price elasticity of −0.2. Maas et al. (2020), on the other hand, designed a conceptual framework based on the household production model assuming that households consume market goods that require neither electricity nor water, and various household services produced by the households themselves which require only water, only electricity, water and electricity as substitutes, or water and electricity as complements. The authors also estimated household water and electricity demands on the basis of billing data from 2006–2014 provided by a utility in Colorado, USA. Similar to Hansen’s findings, Maas et al. found an average cross-price elasticity between water and electricity of approximately −0.1, suggesting a complementary economic relationship between household water and energy use. In both Hansen’s and Maas et al.’s studies, the authors discussed the conceptual models broadly. The conceptual analysis was included either as a methodology (in Hansen’s paper) or as part of the introduction (in Maas et al.’s paper), to initiate empirical analyses with case studies in developed countries. However, a comprehensive conceptual framework that is applicable to the context of developing countries remain largely unexplored in the existing literature.

Besides the work of Hansen (1996) and Maas et al. (2020), to our knowledge, only one study, conducted by Suárez-Varela (2020), provides empirical estimates of the cross-price elasticity of demand between water and energy using econometric methods. In contrast to the other two empirical analyses, Suárez-Varela (2020) obtained positive cross-price elasticities between water and energy in the estimation of Spanish household water demand for the period 2006–2012, indicating a substitutional relationship between the two resources. The author briefly discussed that this might be related to the dataset, where hot water expenditures (including costs for both water and energy) were included under the energy category instead of the water category. However, a conceptual framework that reconciles the empirical observations on the different signs of the cross-price elasticities from an economic perspective is still lacking.

2.2. Household activities reflecting WEN

The broad concept of the WEN dates back to the 1970s when the water consumption requirements for energy production were addressed by Harte and El-Gasseir (1978) for the first time. At the outset, only water consumption for energy was considered in the nexus discussion. In 1994, Gleick further discussed the interactions between water and energy in both directions and brought energy requirements for water supply into view (Gleick 1994). Since then, more and more studies have been conducted on the linkages between water and energy use, and the term “WEN” has become widely used in scientific publications (Olsson 2015). Most of the existing studies on the WEN focus on the production/supply-side at the level of the overall economy (Grubert and Sanders 2018; Parkinson et al. 2018). Among the relatively fewer studies from the demand side at the household scale, analyses are often based on household activities in water or energy end-uses (Abdallah and Rosenberg 2014; Hussien et al. 2017).

Various studies in the literature have discussed water and energy use within different household activities, highlighting the demand-side WEN at the private household level.¹ Table A.1 in Appendix A shows a summary of existing studies on water- and energy-related household activities as well as the major connections between water and energy use revealed by each study. The interactions between household water and energy use can be observed in two types of household activities based on their purposes. These are: (1) activities for accessing water, for example, fetching water with vehicles (Eichelberger 2010) and pumping rainwater from harvesting tanks (Talebpour et al. 2014; Umapathi et al. 2013; Vieira and Ghisi 2016), and (2) activities in which water and energy are used for general domestic purposes (e.g., shower and bath, use of washing machines). Despite discussions on water- and energy-related activities at the household level, the existing literature so far fails to fully explain the economic linkages between household water and energy demand, which hinders the development of integrated water and energy demand management strategies.

3. Conceptual Framework

To address our research question of explaining residential water and energy consumption decisions in the presence of household activities using both resources, we develop a conceptual framework based on the household production concept proposed by Becker in 1965. In Becker’s theory on the allocation of time, “households will be assumed to combine time and market goods to produce more basic commodities that directly enter their utility functions,” which is the process of household production (Becker 1965, p. 495). Accordingly, a household does not benefit directly from the water and energy that they have purchased from the market or collected at the source. Their utility gains come from the final goods and services that the household members produce through various uses of these resources. For instance, in the case of washing clothes by hand, the increase in the utility of a household that motivates the consumption does not originate from water and washing powders, but from the cleaned clothes, which are the outputs produced by the household members by doing the laundry. The service of cleaned clothes can also be produced by using a washing machine with less labor, or be purchased from the market if the household chooses to go to the laundromat.

Based on the household production theory, the use of water and energy is a production process, which is managed and implemented by the household. The inputs to production include water, energy, potentially the other requisite goods or services purchased from the market, and labor (i.e., time) from the household members, while the outputs from the production are the services that enter directly into a household utility function. The household-level WEN is formed through this time-consuming household production process with water and energy as inputs. Here, the nexus indicates that the two inputs (i.e., water and energy) are combined and used for the particular purpose of household production. We define the outputs of this production process as “water-energy services.” More specifically, a water-energy service (WES) refers to any service produced and consumed by the household when water and/or energy is used for producing the service (see Figure 1).²

Figure 1. Household Production of WESs, Consisting of Processing and Production Stages: A Household Spends Money to Purchase Water, Energy, and Other Inputs from the Market, and Spends its Time Producing WESs with these Market Inputs. The Consumption of WESs Ultimately Increases the Household Utility

The production of household WES starts with the purchase of all necessary inputs and ends with the completion of the WES. The process consists of two stages, processing and production, which correspond to the two types of household activities reflecting WEN observed in the literature, respectively, (see Section 2.2). Their differences with regards to the relationship between water and energy use are explained in the following paragraphs.

The first stage refers to water processing, where energy can be used to improve water accessibility. Household access hurdles to water include pecuniary hurdle and non-pecuniary hurdles, i.e., spatial, temporal, and qualitative hurdles (Gawel and Bretschneider 2016, 2017). Figure 2 illustrates water at different accessibility stages and the role of water processing. The action of purchasing water trades a higher pecuniary hurdle for lower non-pecuniary hurdles by obtaining the water services provided by the utility or the suppliers. If the technical water service provided by the utility/suppliers fails to fully satisfy households’ need for water access, the action of purchasing results in an intermediate good — the partially accessible water. In this case, households have to take further actions to overcome the non-pecuniary hurdles to fully access water. This is also the starting point for the household production of WESs. For example, under intermittent water supplies, households can accordingly choose to use rooftop water tanks to store water in advance so that piped water is available for them at any time. The temporal hurdle is removed with the help of water storage. In other cases where the total quantity of municipal water cannot satisfy households’ demand or where the municipal water becomes unaffordable, households might turn to alternative water sources, such as well water. In the case of well water use, there is no supply schedule,³ but households have to pump the water before using it. They might sometimes have to disinfect the well water to make it potable. All these actions to overcome the temporal, spatial, and qualitative hurdles to access water can be called “water processing.” In this paper, we define “water processing” as the activities that are carried out by households to convert the partially accessible water from the market into fully accessible water which can then be directly used for domestic purposes. The water processing stage is an optional step after the acquisition of water from suppliers or sources. For instance, in areas with well-established municipal water supply, households often bypass the processing stage and only undertake activities for the second stage.

Figure 2. Water at Four Accessible Stages, Adapted from Gawel and Bretschneider (2016, p. 75): (a) Raw Water: Water at Sources which has not been Treated or Processed by the Utilities/Suppliers, and is not Directly Accessible for Households as One or More Access Hurdles Exists; (b) Social-economically Accessible Water: Water that is Treated, Stored, Distributed, and Transported by the Utilities/Suppliers, and the Cost of these Technical Services is Compensated by the Society so that Water can be Purchased by Households, from this Stage, Water is Accessible for Households, but One or More Access Hurdles Still Exist; (c) Partially Accessible Water: Water that is Supplied at the Technical Service Level, where the Non-pecuniary Hurdles are lowered by Utilities/Suppliers to Certain Extent, and has been Purchased by Households, i.e., the Pecuniary Hurdle is Overcome, but One or More Non-pecuniary Access Hurdles Still Exist; (d) Fully Accessible Water: Water that can be Directly Used by Households for Domestic Purposes, i.e., all the Pecuniary and Non-pecuniary Hurdles are Fully Overcome

The second stage includes all the domestic activities that require water and/or energy as necessary inputs. At this stage, households engage in production activities that (a) require both water and energy, either individually or in combination (e.g., cooking, dishwashing), or (b) require exclusively one resource (e.g., lighting, flushing a squatting pot). Activities in category (a) correspond to the second type of household activities that reflect the demand-side WEN revealed in the literature, as outlined in Section 2.2. These activities can be further divided into two groups: (1) water heating, e.g., for showering and bathing (excluding boiling water for quality reasons, which falls under water processing), where energy is used to modify the temperature of water, and (2) activities that use energy and/or water, often associated with the option of using electrical devices (e.g., vacuum cleaner, dishwasher, washing machine, etc.). Within the latter group, advancements in household appliance technology have enabled the integration of energy into the production of certain WESs (i.e., traditionally non-electrical services). For instance, WESs, such as cleaned tableware and a cleaned floor, can be produced without any input of energy in the traditional water-labor-intensive way (i.e., washing by hand and mopping the floor), whereas with the invention of dishwashers and vacuum cleaners, energy can possibly be involved as an input for producing these WESs.

Although household water and energy use patterns vary in different settings, the framework is able to capture the household-level WEN comprehensively across diverse contexts. In an urban and developed setting with reliable supply systems, household WES production typically revolves around the production stage alone. However, the adoption of technologies to expand water sources and encourage water savings, such as decentralized greywater recycling systems and rainwater harvesting installations, can extend the scope to include the water processing stage. In areas with unreliable supply systems, where households use energy-intensive coping strategies or alternative energy-intensive water sources to deal with water intermittency or pressure issues, the water processing stage may be prominent. This is similar to situations in rural settings where households may use multiple water sources, such as well water combined with piped water. However, agricultural water use in rural areas is excluded from this analysis as it does not contribute to household production of a WES as defined earlier. The conceptual framework proposed here provides a basis for further analysis of the economic relationship between water and energy, and the impact that improvements in the efficiency of household WES production have on the consumption of both resources.

4. Theoretical Economic Analysis

4.1. Maximizing household utility as a function of WES consumption

Based on the conceptual framework presented in Section 3, we conduct a formal analysis of the relationship between household water and energy use to further investigate our second and third research questions. A household can consume and obtain utility from two types of commodities, namely the WESs and non-WESs (i.e., a complementary set of services consumed by the household with regards to WESs).⁴ Assuming that an individual household i demands a fixed quantity of non-WESs during a given consumption period, household utility $U_{i}$ can be described as a strictly concave function of the quantities $Z_{i}$ of all WESs consumed by household i, and will shift with changes in the preference of the household depending on its specific characteristics $γ_{i}$ :

U i = U (Z i; γ i) . <math display="block" altimg="eq-00006.gif"><msub><mrow><mi>U</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>=</mo><mi>U</mi><mo stretchy="false">(</mo><msub><mrow><mi>Z</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>;</mo><msub><mrow><mi>γ</mi></mrow><mrow><mi>i</mi></mrow></msub><mo stretchy="false">)</mo><mo>.</mo></math> (1)

The WESs are produced by the household with water, energy, the other goods and services purchased from the market and the labor of household members (i.e., time input). The capital goods, i.e., the appliance or equipment used in the production, are included in the market goods and services fraction by referring to the services yielded by those goods (Becker 1965). Here, as our focus is to reveal the nexus between household water and energy use, we assume that the household stocks a fixed level of the other market goods and services (including capital goods) in the short term, which impacts the production conditions for WESs but will not impact the budget allocation. Assuming that household production is also a strictly concave function, it can be written as a function $Z_{i}$ of changing production conditions :

Z i = Z (x w i, x e i, t z i; φ p i, φ z i) . <math display="block" altimg="eq-00008.gif"><msub><mrow><mi>Z</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>=</mo><mi>Z</mi><mo stretchy="false">(</mo><msub><mrow><mi>x</mi></mrow><mrow><msub><mrow><mi>w</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></msub><mo>,</mo><msub><mrow><mi>x</mi></mrow><mrow><msub><mrow><mi>e</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></msub><mo>,</mo><msub><mrow><mi>t</mi></mrow><mrow><msub><mrow><mi>z</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></msub><mo>;</mo><msub><mrow><mi>φ</mi></mrow><mrow><msub><mrow><mi>p</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></msub><mo>,</mo><msub><mrow><mi>φ</mi></mrow><mrow><msub><mrow><mi>z</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></msub><mo stretchy="false">)</mo><mo>.</mo></math> (2)

In Eq. (2), $x_{w_{i}}$ and $x_{e_{i}}$ represent the total quantities of water and energy demanded by the household for WES production. The variable $t_{z_{i}}$ denotes the time allocated by household members to this production process. The production conditions are defined by the coefficients of technology and production efficiency, $φ_{p_{i}}$ and $φ_{z_{i}}$ . The two coefficients correspond to the two separate stages of WES production, the processing ( $φ_{p_{i}}$ ) and the production ( $φ_{z_{i}}$ ) stages, respectively. Figure 3 illustrates the interactions of different inputs for $Z_{i}$ along the water and energy flows within a household during WES production. The flows of water and energy are not symmetrical since energy can be used for changing certain characteristics of water (e.g., the status of accessibility by the households and temperature, as explained in Section 3), but not vice versa.

Figure 3. Interactions of Different Inputs during Household WES Production and the Flows of Water and Energy

The household allocates its income to purchase all the necessary market inputs for household production of WESs and non-WESs. Maximization of the household utility, i.e., Eq. (1), is therefore constrained by the total disposable income for WES production, consisting of a wage income share $W_{i}$ and other cash income share $V_{i}$ . Here, the necessary market inputs refer to water and energy from the market. Let $p_{w}$ and $p_{e}$ be the market prices for water and energy. Both prices are positive ( $p_{w} > 0$ , $p_{e} > 0$ ).⁵ The income constraint can be written as :

W i + V i = p w \cdot x w i + p e \cdot x e i . <math display="block" altimg="eq-00023.gif"><msub><mrow><mi>W</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>+</mo><msub><mrow><mi>V</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>=</mo><msub><mrow><mi>p</mi></mrow><mrow><mi>w</mi></mrow></msub><mo>\cdot</mo><msub><mrow><mi>x</mi></mrow><mrow><msub><mrow><mi>w</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></msub><mo>+</mo><msub><mrow><mi>p</mi></mrow><mrow><mi>e</mi></mrow></msub><mo>\cdot</mo><msub><mrow><mi>x</mi></mrow><mrow><msub><mrow><mi>e</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></msub><mo>.</mo></math> (3)

The total available time of a household, including flexible production time and market labor time, is restricted during a given period. The period of 24h per day is fixed. A household will allocate all its available time at work for wages ( $h_{i}$ ), and at home for household production of WESs ( $t_{z_{i}}$ ) and non-WESs ( $t_{y_{i}}$ ). The household production of both WESs and non-WESs does not necessarily have to take place on the household’s premises. For example, if the household needs to spend time fetching water from a public water stand for any part of WES production, the time spent fetching water is still part of the time input for household production of WESs ( $t_{z_{i}}$ ). The allocation of the time of all household members $T_{i}$ between $t_{z_{i}}$ , $t_{y_{i}}$ , and $h_{i}$ forms a physical time constraint :

T i = t z i + t y i + h i . <math display="block" altimg="eq-00033.gif"><msub><mrow><mi>T</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>=</mo><msub><mrow><mi>t</mi></mrow><mrow><msub><mrow><mi>z</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></msub><mo>+</mo><msub><mrow><mi>t</mi></mrow><mrow><msub><mrow><mi>y</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></msub><mo>+</mo><msub><mrow><mi>h</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>.</mo></math> (4)

Assuming that the household members work in the market at a wage rate $w_{i}$ , the wage share of income $W_{i}$ in Eq. (3) can thus be linked to the paid working hours. Since we consider a fixed consumption of non-WESs during the given period, we also assume that the expenditure of time for the non-WES production is a fixed value. We use $D_{i}$ to represent the total disposable time for WES production. Equations (3) and (4) can thereby be combined into a full income-time constraint :

w i \cdot D i + V i = p w \cdot x w i + p e \cdot x e i + w i \cdot t z i . <math display="block" altimg="eq-00037.gif"><msub><mrow><mi>w</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>\cdot</mo><msub><mrow><mi>D</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>+</mo><msub><mrow><mi>V</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>=</mo><msub><mrow><mi>p</mi></mrow><mrow><mi>w</mi></mrow></msub><mo>\cdot</mo><msub><mrow><mi>x</mi></mrow><mrow><msub><mrow><mi>w</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></msub><mo>+</mo><msub><mrow><mi>p</mi></mrow><mrow><mi>e</mi></mrow></msub><mo>\cdot</mo><msub><mrow><mi>x</mi></mrow><mrow><msub><mrow><mi>e</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></msub><mo>+</mo><msub><mrow><mi>w</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>\cdot</mo><msub><mrow><mi>t</mi></mrow><mrow><msub><mrow><mi>z</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></msub><mo>.</mo></math> (5)

The left-hand side of Eq. (5) indicates the full budget of a household in terms of time availability and funds over the given consumption period for WES production, while the right side represents the allocation of this budget. It should be noted that all elements in Eq. (5) are non-negative, as neither time, prices nor the demanded quantities of water and energy can take on a negative value.

Substituting Eq. (2) into the utility function Eq. (1) allows us to maximize household utility subject to the full income-time constraint Eq. (5). The Lagrangian can be defined as follows, where $λ$ is the Lagrange multiplier and represents the marginal utility of the full income :

L = U (Z (x w i, x e i, t z i; φ p i, φ z i); γ i) + λ (w i \cdot (D i - t z i) + V i - p w \cdot x w i - p e \cdot x e i) . <math display="block" altimg="eq-00039.gif"><mi>L</mi><mo>=</mo><mi>U</mi><mo stretchy="false">(</mo><mi>Z</mi><mo stretchy="false">(</mo><msub><mrow><mi>x</mi></mrow><mrow><msub><mrow><mi>w</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></msub><mo>,</mo><msub><mrow><mi>x</mi></mrow><mrow><msub><mrow><mi>e</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></msub><mo>,</mo><msub><mrow><mi>t</mi></mrow><mrow><msub><mrow><mi>z</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></msub><mo>;</mo><msub><mrow><mi>φ</mi></mrow><mrow><msub><mrow><mi>p</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></msub><mo>,</mo><msub><mrow><mi>φ</mi></mrow><mrow><msub><mrow><mi>z</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></msub><mo stretchy="false">)</mo><mo>;</mo><msub><mrow><mi>γ</mi></mrow><mrow><mi>i</mi></mrow></msub><mo stretchy="false">)</mo><mo>+</mo><mi>λ</mi><mo stretchy="false">(</mo><msub><mrow><mi>w</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>\cdot</mo><mo stretchy="false">(</mo><msub><mrow><mi>D</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>-</mo><msub><mrow><mi>t</mi></mrow><mrow><msub><mrow><mi>z</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></msub><mo stretchy="false">)</mo><mo>+</mo><msub><mrow><mi>V</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>-</mo><msub><mrow><mi>p</mi></mrow><mrow><mi>w</mi></mrow></msub><mo>\cdot</mo><msub><mrow><mi>x</mi></mrow><mrow><msub><mrow><mi>w</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></msub><mo>-</mo><msub><mrow><mi>p</mi></mrow><mrow><mi>e</mi></mrow></msub><mo>\cdot</mo><msub><mrow><mi>x</mi></mrow><mrow><msub><mrow><mi>e</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></msub><mo stretchy="false">)</mo><mo>.</mo></math> (6)

Based on Eq. (6), the first-order conditions for an optimum are :

x w i : U' (Z i) \cdot Z' (x w i) - λ \cdot p w = 0, <math display="block" altimg="eq-00040.gif"><msub><mrow><mi>x</mi></mrow><mrow><msub><mrow><mi>w</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></msub><mo>:</mo><msup><mrow><mi>U</mi></mrow><mrow><mi>'</mi></mrow></msup><mo stretchy="false">(</mo><msub><mrow><mi>Z</mi></mrow><mrow><mi>i</mi></mrow></msub><mo stretchy="false">)</mo><mo>\cdot</mo><msup><mrow><mi>Z</mi></mrow><mrow><mi>'</mi></mrow></msup><mo stretchy="false">(</mo><msub><mrow><mi>x</mi></mrow><mrow><msub><mrow><mi>w</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></msub><mo stretchy="false">)</mo><mo>-</mo><mi>λ</mi><mo>\cdot</mo><msub><mrow><mi>p</mi></mrow><mrow><mi>w</mi></mrow></msub><mo>=</mo><mn>0</mn><mo>,</mo></math> (7)

x e i : U' (Z i) \cdot Z' (x e i) - λ \cdot p e = 0, <math display="block" altimg="eq-00041.gif"><msub><mrow><mi>x</mi></mrow><mrow><msub><mrow><mi>e</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></msub><mo>:</mo><msup><mrow><mi>U</mi></mrow><mrow><mi>'</mi></mrow></msup><mo stretchy="false">(</mo><msub><mrow><mi>Z</mi></mrow><mrow><mi>i</mi></mrow></msub><mo stretchy="false">)</mo><mo>\cdot</mo><msup><mrow><mi>Z</mi></mrow><mrow><mi>'</mi></mrow></msup><mo stretchy="false">(</mo><msub><mrow><mi>x</mi></mrow><mrow><msub><mrow><mi>e</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></msub><mo stretchy="false">)</mo><mo>-</mo><mi>λ</mi><mo>\cdot</mo><msub><mrow><mi>p</mi></mrow><mrow><mi>e</mi></mrow></msub><mo>=</mo><mn>0</mn><mo>,</mo></math> (8)

t z i : U' (Z i) \cdot Z' (t z i) - λ \cdot w i = 0, <math display="block" altimg="eq-00042.gif"><msub><mrow><mi>t</mi></mrow><mrow><msub><mrow><mi>z</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></msub><mo>:</mo><msup><mrow><mi>U</mi></mrow><mrow><mi>'</mi></mrow></msup><mo stretchy="false">(</mo><msub><mrow><mi>Z</mi></mrow><mrow><mi>i</mi></mrow></msub><mo stretchy="false">)</mo><mo>\cdot</mo><msup><mrow><mi>Z</mi></mrow><mrow><mi>'</mi></mrow></msup><mo stretchy="false">(</mo><msub><mrow><mi>t</mi></mrow><mrow><msub><mrow><mi>z</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></msub><mo stretchy="false">)</mo><mo>-</mo><mi>λ</mi><mo>\cdot</mo><msub><mrow><mi>w</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>=</mo><mn>0</mn><mo>,</mo></math> (9)

λ : w i \cdot (D i - t z i) + V i - p w \cdot x w i - p e \cdot x e i = 0 . <math display="block" altimg="eq-00043.gif"><mi>λ</mi><mo>:</mo><msub><mrow><mi>w</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>\cdot</mo><mo stretchy="false">(</mo><msub><mrow><mi>D</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>-</mo><msub><mrow><mi>t</mi></mrow><mrow><msub><mrow><mi>z</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></msub><mo stretchy="false">)</mo><mo>+</mo><msub><mrow><mi>V</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>-</mo><msub><mrow><mi>p</mi></mrow><mrow><mi>w</mi></mrow></msub><mo>\cdot</mo><msub><mrow><mi>x</mi></mrow><mrow><msub><mrow><mi>w</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></msub><mo>-</mo><msub><mrow><mi>p</mi></mrow><mrow><mi>e</mi></mrow></msub><mo>\cdot</mo><msub><mrow><mi>x</mi></mrow><mrow><msub><mrow><mi>e</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></msub><mo>=</mo><mn>0</mn><mo>.</mo></math> (10)

In Eqs. (7)–(10), $U^{'} (Z_{i})$ represents the marginal household utility of WESs, which is always positive since we are solving a utility maximization problem subject to constraints. $Z^{'} (x_{w_{i}})$ , $Z^{'} (x_{e_{i}})$ and $Z^{'} (t_{z_{i}})$ are the non-negative marginal products of the respective inputs (i.e., water, energy, and time) for producing WESs.

4.2. The economic relationship between water and energy

Based on the conditions for the utility maximization, we are able to analyze the economic relationship between household water and energy demand, addressing our second research question. Knowing that the prices for water and energy, the opportunity cost of time, and the marginal utility of WESs are positive, combining Eqs. (7)–(9) gives us the following equilibrium :

Z' (x w i) ∕ p w = Z' (x e i) ∕ p e = Z' (t z i) ∕ w i . <math display="block" altimg="eq-00048.gif"><msup><mrow><mi>Z</mi></mrow><mrow><mi>'</mi></mrow></msup><mo stretchy="false">(</mo><msub><mrow><mi>x</mi></mrow><mrow><msub><mrow><mi>w</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></msub><mo stretchy="false">)</mo><mo stretchy="false">∕</mo><msub><mrow><mi>p</mi></mrow><mrow><mi>w</mi></mrow></msub><mo>=</mo><msup><mrow><mi>Z</mi></mrow><mrow><mi>'</mi></mrow></msup><mo stretchy="false">(</mo><msub><mrow><mi>x</mi></mrow><mrow><msub><mrow><mi>e</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></msub><mo stretchy="false">)</mo><mo stretchy="false">∕</mo><msub><mrow><mi>p</mi></mrow><mrow><mi>e</mi></mrow></msub><mo>=</mo><msup><mrow><mi>Z</mi></mrow><mrow><mi>'</mi></mrow></msup><mo stretchy="false">(</mo><msub><mrow><mi>t</mi></mrow><mrow><msub><mrow><mi>z</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></msub><mo stretchy="false">)</mo><mo stretchy="false">∕</mo><msub><mrow><mi>w</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>.</mo></math> (11)

Focusing on the demand for water and energy, for given inflection points, Eq. (11) can be rearranged as in Eq. (12), which leads to the equilibrium in Eq. (13) :

Δ Z i ∕ Δ x w i \cdot 1 ∕ p w = Δ Z i ∕ Δ x e i \cdot 1 ∕ p e, <math display="block" altimg="eq-00049.gif"><mi mathvariant="normal">Δ</mi><msub><mrow><mi>Z</mi></mrow><mrow><mi>i</mi></mrow></msub><mo stretchy="false">∕</mo><mi mathvariant="normal">Δ</mi><msub><mrow><mi>x</mi></mrow><mrow><msub><mrow><mi>w</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></msub><mo>\cdot</mo><mn>1</mn><mo stretchy="false">∕</mo><msub><mrow><mi>p</mi></mrow><mrow><mi>w</mi></mrow></msub><mo>=</mo><mi mathvariant="normal">Δ</mi><msub><mrow><mi>Z</mi></mrow><mrow><mi>i</mi></mrow></msub><mo stretchy="false">∕</mo><mi mathvariant="normal">Δ</mi><msub><mrow><mi>x</mi></mrow><mrow><msub><mrow><mi>e</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></msub><mo>\cdot</mo><mn>1</mn><mo stretchy="false">∕</mo><msub><mrow><mi>p</mi></mrow><mrow><mi>e</mi></mrow></msub><mo>,</mo></math> (12)

p e ∕ Δ x w i = p w ∕ Δ x e i . <math display="block" altimg="eq-00050.gif"><msub><mrow><mi>p</mi></mrow><mrow><mi>e</mi></mrow></msub><mo stretchy="false">∕</mo><mi mathvariant="normal">Δ</mi><msub><mrow><mi>x</mi></mrow><mrow><msub><mrow><mi>w</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></msub><mo>=</mo><msub><mrow><mi>p</mi></mrow><mrow><mi>w</mi></mrow></msub><mo stretchy="false">∕</mo><mi mathvariant="normal">Δ</mi><msub><mrow><mi>x</mi></mrow><mrow><msub><mrow><mi>e</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></msub><mo>.</mo></math> (13)

According to the law of demand, when the energy price increases (

$Δ p_{e} > 0$ ), the demand for energy decreases (

$Δ x_{e_{i}} < 0$ ). Based on the equilibrium condition in Eq. (13), when

$Δ x_{e_{i}}$ is negative, as both

$p_{e}$ and

$p_{w}$ are by definition positive,

$Δ x_{w_{i}}$ should be negative. Therefore, the sign of the cross-price elasticity of the demands between water and energy

$E = (Δ x_{w} ∕ x_{w}) ∕ (Δ p_{e} ∕ p_{e})$ should be negative, suggesting a complementary relationship between household water and energy demand in the short term with given production conditions (assumptions defined in Section 4.1).

Referring to the interactions of different inputs for household WES production illustrated in Figure 3, for both water processing and water heating, energy is required for changing one or several characteristics of water, e.g., temporal availability, quality, and temperature, so that water with adjusted characteristics can enter the next step of production to satisfy household needs. Water and energy are complements in these two types of activities.

However, as discussed in Section 3, in addition to water processing and water heating, the demand-side WEN is also reflected in the production stage activities that use energy and/or water associated with the option of using electrical devices to produce certain traditionally non-electrical services. Using electrical devices allows for the integration of energy for the production of certain WESs that previously involve only water inputs. When faced with changes, e.g., increases in energy costs, household retain the autonomy to choose whether to use the previously acquired appliances and select the operational mode with different water and energy settings. Water and energy can be substitutes in this type of production activities.⁶ However, for a given level of capital stock, e.g., determined ownership status of dishwashers and washing machines, there exists a limit to the extent to which energy can substitute water use. The substitutional potential between the two resources is more constrained in the short term compared to the long term, where adjustments to capital stock become feasible.⁷ As the capital stock of electrical devices determines household production conditions for WESs, the economic relationship between household water and energy demands can exhibit different features with changing production conditions. It is important to recognize that substitutions between water and energy often occurs as technology advances to provide new time-saving features. For example, using a robot vacuum for room cleaning saves time and water but consumes more electricity than traditional mopping methods. The effect of technological progress related to the production condition changes will be discussed in Section 4.4.

In other circumstances, when multiple water sources⁸ are accessible, the substitution relationships between water from different sources will affect the economic relationship between water and energy in general. The impact of multiple water sources is principally related to potential energy use for water processing. The use of water and energy for processing water from the same source is complementary, while the use of water energy for processing water from a different source is substitutional.⁹

Therefore, with a single water source, water and energy are strictly complementary during production steps of water processing and water heating. However, when multiple water sources are employed by households, the relationship between energy demand for water processing and the total water demand is contingent upon the proportion of water from different sources and the energy intensity of accessing each water source. Regarding the production step of using electrical devices for services traditionally not reliant on electricity, a distinction can be made between non-water-related devices (e.g., vacuum cleaners) and water-related devices (e.g., dishwashers and washing machines). If the use of electrical devices does not incorporate water as an input, water and energy become substitutional. The deployment of water-related electrical devices can introduce substitutional relationships between inputs (i.e., water and energy) after initially establishing complements in the electrified services (see footnotes 6 and 7). The overall relationship between household water and energy use remains subject to case specific circumstances. Depending on a household’s capital stock and preferences (e.g., whether or not a household has relatively fixed behavior patterns in water saving or energy saving), water and energy can exhibit either a complementary or a substitutional relationship overall.

4.3. Income and price effects on household WES consumption

To further understand the economic linkages underlying household WES consumption and its implications, we analyze the impact of income and price fluctuations on WES consumption. The impact of a household income change on the optimal utility level from WES consumption depends on which part of the income changes (i.e., whether it is wage-related). An increase in household wage income may also impact the opportunity cost of time for the household (Zozmann et al. 2022). With a rise in wage income, the household may allocate less time to household production due to the increased opportunity cost, while the increase in cash income enhances the household’s purchasing power for water and energy.¹⁰ This suggests that the optimal level of utility obtained from WESs may decrease, but the increased monetary budget may counteracts this effect. For example, under intermittent water supply, household members may need to wait at the tap during supply hours to fill their water storage as part of the first stage of WES production. The increased time cost may restrict their availability for this waiting period, leading to a decrease in piped water available for the subsequent production stage. In response, the household may use its increased monetary budget to purchase water from a more expensive but less time-consuming source (e.g., bottled water) to satisfy its needs, or reduce overall water use and consume less WES. In the latter situation, the final utility level from WESs decreases.

The final utility level from WESs after an income change can be higher or lower than the original level, depending on the extent of change in time costs compared to the enhanced purchasing power in the water-energy market. If the purchase of water and energy was constrained by the monetary fraction of the full budget prior to the change, an increase in wage income could ultimately raise the optimal utility obtained from WESs. This is similar to the impact of an increase in household non-wage income: With an increase in non-wage income, the household may afford more water and energy while its opportunity cost of time and the total available time for household production remain unaffected. In both cases, an income increase, either in the wage or non-wage fraction, can result in more water and energy consumption.

As shown in Eq. (5), the full income-time budget for the WESs in a household is allocated to three types of inputs, namely water and energy from the market and the time of the household members. If the market prices for both water and energy increase, for a given budget constraint, the household can no longer afford the same quantity of water and energy from the market as it could previously. The slope of the full budget constraint will change as illustrated in Figure 4(a) and the household’s optimal utility from WESs moves to a lower level with less purchased water and energy from the market but more time input from the household members. The extent of substitution among water, energy, and time depends on the household’s capacity to produce WESs, which is determined by the production conditions (e.g., ownership of relevant devices).

Figure 4. Changes in utility level from WESs and full budget allocation for the household production (a) when market prices for water and energy increase, and (b) when only the market price for water increases

When there is a price change in only one of the resources, similar substitutions occur as in the case with price changes for both resources. Figure 4(b) illustrates an example where the water price increases while the energy price remains constant. The price increase leads to a shift in the slope of the full budget constraint, indicating the substitution effect between water and energy-time. Consequently, the household adapts its consumption behavior by reducing water purchases and compensating for this reduction by increasing expenditures on energy and time to optimize utility. To achieve this, the household may employ time-intensive and/or energy-intensive methods for certain WES production, e.g., opting for a vacuum cleaner over a mop for floor cleaning. In another example, if the price for piped water increases to a level unaffordable for low-income households, they may choose to reduce their piped water use and instead allocate more time in collecting free water from rivers or public water stands. If electricity remains within their financial reach, they might consider using an electric water pump to extract groundwater. This reveals two major implications for water tariff restructuring: Firstly, an increase in water tariffs could expose hidden issues such as inequality and health concerns, as households may have to adopt certain time-intensive strategies that lead to an unequal distribution of labor within the household, e.g., female members often bearing the burden of transporting water over long distances in some regions (Crider and Ray 2022; Tomberge et al. 2021). Secondly, in areas with reliable energy access and lax groundwater regulation, an increase in water tariffs may raise electricity consumption and exacerbate over-exploitation of groundwater, particularly relevant in rural settings.

4.4. Effect of technological progress on household WES production

To address the third research question of understanding the impact of improvements to the technology employed by a household for WES production, we need to take into account the production cost for WESs. In making household production decisions, households not only strive to maximize their utility, but also to minimize their production cost. In the case of WES production, for a given capital stock, the full cost of producing one unit of WES includes the monetary cost of purchasing water and energy from the market as well as the labor cost of household members for production (i.e., the opportunity cost of time). Therefore, under the same assumptions described in Section 4.1, the full production cost of WESs $C_{i}$ for the optimal consumption quantity of WESs is :

Similar conditions as in the household utility maximization function can be derived from solving the cost minimization problem in Eq. (14). As indicated in the production function in Eq. (2), the household production of WESs is associated with production conditions defined by $φ_{p_{i}}$ and $φ_{z_{i}}$ . Therefore, the marginal cost of producing WESs ${MC}_{i}$ depends on the prices of water and energy, the opportunity cost of time and the production conditions for the two stages of household WES production :

MC i = MC (p w, p e, w i, φ p i φ z i) . <math display="block" altimg="eq-00063.gif"><msub><mrow><mstyle><mtext mathvariant="normal">MC</mtext></mstyle></mrow><mrow><mi>i</mi></mrow></msub><mo>=</mo><mstyle><mtext mathvariant="normal">MC</mtext></mstyle><mo stretchy="false">(</mo><msub><mrow><mi>p</mi></mrow><mrow><mi>w</mi></mrow></msub><mo>,</mo><msub><mrow><mi>p</mi></mrow><mrow><mi>e</mi></mrow></msub><mo>,</mo><msub><mrow><mi>w</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>,</mo><msub><mrow><mi>φ</mi></mrow><mrow><msub><mrow><mi>p</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></msub><msub><mrow><mi>φ</mi></mrow><mrow><msub><mrow><mi>z</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></msub><mo stretchy="false">)</mo><mo>.</mo></math> (15)

If the prices for the inputs to household WES production (i.e., water, energy, and time) increase, the marginal cost for WES production increases accordingly. For a given level of WESs produced, the household suffers from a higher cost with the original bundle of different inputs. As for the price effects on WES consumption discussed in Section 4.3, substitution among the production inputs (i.e., water, energy, and time) is possible under the constrains of market resource availability and production. For example, if there is an increase in the price for water from a certain source, a household can choose another water source with a lower market price which might be more energy and time-intensive to access. The household can also choose to change its habitual process in producing the WESs towards a water-saving process, which could require a greater energy or time input. Production cost is minimized when the marginal product of each input divided by its price reaches the same level, as confirmed in Eq. (11).

From a long-term perspective, households have the option of investing capital to change the production conditions for WESs. The changes in $φ_{p_{i}}$ and $φ_{z_{i}}$ adjust the shape of the marginal cost curve for WES production. Assuming constant market prices for inputs, if the existing level of WES production already satisfies household needs, an improvement in production conditions in terms of technology and efficiency can lower the overall production cost for WESs. For example, installing water-saving showerheads changes $φ_{z_{i}}$ and improves water efficiency in producing the hygiene WES through showering. If this change does not affect household showering behavior, the production cost for this specific WES decreases due to reduced water use for the same service level.

However, if the improvements in $φ_{p_{i}}$ and/or $φ_{z_{i}}$ enable increased WES production beyond the previous constraints, the total production cost may rise or fall based on the difference between the cost of additional WESs and the reduced cost due to improved productivity, leading to a rebound effect. This is already well known regarding the case of a single resource: For instance, acquiring a robot vacuum could facilitate more thorough cleaning of hard-to-reach areas, potentially increasing WES output without raising overall production costs if the household values time highly compared to electricity costs for cleaning. Another example is the installation of a rooftop water storage system that enables the household to store more water during supply gaps. This can improve productivity in water processing but may lead to increased consumption of the previously-inaccessible water. Considering WEN linkages shows, however, that rebound effects can also cross over between improved productivity for water processing and energy use, or vice versa. For example, if the storage system relies on an electric pump, energy use for water processing will increase accordingly at the processing stage. An overall increase in water consumption could also potentially elevate energy and time use for water-related activities at the production stage.

Changes in the total production cost can trigger shifts in the overall income-time allocation among water, energy, and time, depending on the specific technology or efficiency feature altered. A decrease in the total production cost does not necessarily lead to reduced water and energy use levels; rebound effects on water and energy consumption may occur. For example, households with a high opportunity cost of time may prioritize technologies that save time over resource-efficient options to lower their overall WES production cost. Although the household time input could decrease significantly, the amount of water and energy required for WES production may eventually rise with the improved production conditions.

4.5. WEN at the private household level reflected in demand functions

Based on Eqs. (7)–(10) as well as the production conditions discussed above, we can also derive demand functions that can inform policy making. The household water and energy demands depend on the prices for all the WES production inputs, household income, production conditions for water processing and the production stage, as well as the preference of the household. Therefore, the implicit demand functions for water and energy can be derived as :

Water : x * w i = D w (p w, p e, w i, D i, V i, φ p i, φ n i, γ i), <math display="block" altimg="eq-00069.gif"><mstyle><mtext mathvariant="normal">Water</mtext></mstyle><mo>:</mo><mspace width=".17em" class="nbsp"></mspace><msubsup><mrow><mi>x</mi></mrow><mrow><msub><mrow><mi>w</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow><mrow><mo>*</mo></mrow></msubsup><mo>=</mo><msub><mrow><mi>D</mi></mrow><mrow><mi>w</mi></mrow></msub><mo stretchy="false">(</mo><msub><mrow><mi>p</mi></mrow><mrow><mi>w</mi></mrow></msub><mo>,</mo><msub><mrow><mi>p</mi></mrow><mrow><mi>e</mi></mrow></msub><mo>,</mo><msub><mrow><mi>w</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>,</mo><msub><mrow><mi>D</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>,</mo><msub><mrow><mi>V</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>,</mo><msub><mrow><mi>φ</mi></mrow><mrow><msub><mrow><mi>p</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></msub><mo>,</mo><msub><mrow><mi>φ</mi></mrow><mrow><msub><mrow><mi>n</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></msub><mo>,</mo><msub><mrow><mi>γ</mi></mrow><mrow><mi>i</mi></mrow></msub><mo stretchy="false">)</mo><mo>,</mo></math> (16)

Energy : x * e i = D e (p w, p e, w i, D i, V i, φ p i, φ n i, γ i), <math display="block" altimg="eq-00070.gif"><mstyle><mtext mathvariant="normal">Energy</mtext></mstyle><mo>:</mo><mspace width=".17em" class="nbsp"></mspace><msubsup><mrow><mi>x</mi></mrow><mrow><msub><mrow><mi>e</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow><mrow><mo>*</mo></mrow></msubsup><mo>=</mo><msub><mrow><mi>D</mi></mrow><mrow><mi>e</mi></mrow></msub><mo stretchy="false">(</mo><msub><mrow><mi>p</mi></mrow><mrow><mi>w</mi></mrow></msub><mo>,</mo><msub><mrow><mi>p</mi></mrow><mrow><mi>e</mi></mrow></msub><mo>,</mo><msub><mrow><mi>w</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>,</mo><msub><mrow><mi>D</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>,</mo><msub><mrow><mi>V</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>,</mo><msub><mrow><mi>φ</mi></mrow><mrow><msub><mrow><mi>p</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></msub><mo>,</mo><msub><mrow><mi>φ</mi></mrow><mrow><msub><mrow><mi>n</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></msub><mo>,</mo><msub><mrow><mi>γ</mi></mrow><mrow><mi>i</mi></mrow></msub><mo stretchy="false">)</mo><mo>,</mo></math> (17)

where

$x_{w_{i}}^{*}$ and

$x_{e_{i}}^{*}$ , respectively, are the demand for water and for energy of household i. The demand functions indicate that energy price (

$p_{e}$ ) can impact water demand and vice versa. In a household water or energy demand analysis, the full price effect should therefore also include the cross-price elasticity of demand between water and energy. In the short term, the WEN is only reflected to a limited extent in the income effect (

$V_{i}$ ) on water and energy demand at the private household level. However, from a long-term perspective, if income changes lead to capital investments for improving WES production conditions, additional interactions between household water and energy use may emerge. As discussed in Section 4.4, changes in production conditions for either water processing (

$φ_{p_{i}}$ ) or the production stage (

$φ_{n_{i}}$ ) can impact both household water and energy demand. Moreover, concerning production conditions for water processing, if the necessity to process water is lessened or eliminated from the supply side (e.g., by improving the continuity and stability of piped water supply), the associated energy use and time cost for water processing can be correspondingly reduced. The impact of other household-specific factors, such as household size, structure, and education level, is reflected by the parameter

$γ_{i}$ , as defined in Section 4.1, which represents the specific characteristics of the household.

5. Empirical Case Study

We aim to illustrate the applicability and relevance of the conceptual framework proposed in Section 3. To achieve this, we choose India as a case study due to its unique characteristics and challenges in water and energy management. India, being the most populous country in the world (United Nations 2022), presents a compelling case study for several reasons. Firstly, the prevalence of heterogeneity in the water supply infrastructure accentuates variations in household water consumption patterns and inequalities in access to water, e.g., intermittent public water supply leads to reliance on mixed use of multiple water sources (Srinivasan et al. 2010; Shaban and Sattar 2011). Secondly, these disparities not only expose the conflicts and complexities arising from such differences, but also underscore the challenges of efficient resource management. By examining the impact of household water use and supply conditions on electricity expenditure, we illustrate the application of our conceptual framework and its policy relevance in addressing these challenges.

5.1. Data and method

5.1.1. Data

We use a nationally representative dataset from the IHDS-II (Desai et al. 2011–2012) to test hypotheses on the demand-side WEN at the household level derived from the previously presented conceptual framework. The IHDS-II is a multifaceted survey covering 42,152 households across rural and urban areas of India. The dataset includes household-level information on water use and supply conditions, energy expenditure, socio-demographic characteristics, and socio-economic factors, as shown in Table 1.¹¹

**Table 1. Descriptive Statistics**
	Overall ( $n = 42, 152$ )
Urban and rural categories (URBAN4_2011)
(0) Metro urban 0	3,078 (7.3%)
(1) Other urban 1	11,518 (27.3%)
(2) More dev vill 2	12,896 (30.6%)
(3) Less dev vill 3	14,660 (34.8%)
Household size (NPERSONS)
Mean (SD)	4.85 (2.32)
Median [Min, Max]	5.00 [1.00, 33.0]
Annual household income in INR (INCOME)
Mean (SD)	128,000 (217,000)
Median [Min, Max]	73,500 [−1,040,000, 11,400,000]
Monthly electricity expenditure in INR (FU1C)
Mean (SD)	280 (428)
Median [Min, Max]	175 [0, 9000]
NAs	5,690 (13.5%)
Main water source (WA1A)
(01) Piped (public supply) 1	20,303 (48.2%)
(02) Tube well 2	4,660 (11.1%)
(03) Hand pump 3	11,144 (26.4%)
(04) Open well 4	3,522 (8.4%)
(05) Covered well 5	652 (1.5%)
(06) River, canal, stream 6	424 (1.0%)
(07) Pond 7	162 (0.4%)
(08) Tanker truck 8	513 (1.2%)
(09) Rainwater 9	26 (0.1%)
(10) Bottled 10	199 (0.5%)
(11) Others 11	390 (0.9%)
NAs	157 (0.4%)
Water source inside or outside house/compound (WA2A)
(1) Outside 1	19,779 (46.9%)
(2) Inside 2	22,186 (52.6%)
NAs	187 (0.4%)
Daily piped water supply hours (WA3A)
Mean (SD)	4.01 (5.57)
Median [Min, Max]	2.00 [0, 24.0]
NAs	22,313 (52.9%)

5.1.2. Hypotheses

According to the IHDS-II dataset, electricity is widely used as energy source in India. Among the surveyed households, the majority (73.9%) reported positive monthly electricity expenditure (i.e., $FU1C > 0$ ). Regarding water use, as shown in Table 1, there is a disparity in whether the main water source is located inside or outside the house or compound (WA2A). Multiple water sources with varying levels of energy intensity were used by the surveyed households as their main water source (WA1A). Among these water sources, public piped water is the most frequently used source, however, it is highly interrupted (as shown by WA3A). The average daily piped water supply is 4.01h/day with a median of 2.00h/day. Given these preliminary observations, we derive two hypotheses on the demand-side WEN regarding the relationship between household electricity expenditures and water use patterns for the case study.

Hypothesis 1. Households with indoor water connections have higher electricity expenditures. The dataset shows that almost half of the households surveyed did not have access to indoor water connections. Examining the impact of indoor or outdoor water connections has implications for water policy in terms of expanding water supply networks, which is one of the top priorities in India’s water agenda (OECD 2014; Government of India 2021). Compared to indoor water connections, outdoor water connections present a greater spatial hurdle. On the one hand, overcoming the spatial hurdle requires substantial labor input and sometimes fuel input if the household uses vehicles to fetch water. The high labor intensity at the water processing stage may lead to a lower allocation of time to the production stage for WESs. Households may choose to increase the input of electricity for the production of certain WESs in order to save inputs of water and labor by using certain appliances or relevant settings, as explained in footnote 6. On the other hand, indoor water connections facilitate relatively easier access to water compared to outdoor sources, as the spatial hurdle is overcome. This can lead to two potential situations: (1) When there are no other non-pecuniary hurdles to water access, households with indoor connections may have access to water that is constrained for those with outdoor connections. As discussed in Section 4.4, the improved accessibility can lead to increased water availability, which has a rebound effect and may result in further increased production of WESs. This, in turn, can increase household electricity consumption through activities such as water heating. (2) When there are still other non-pecuniary hurdles, such as temporal and qualitative hurdles, indoor connections may offer opportunities to facilitate improved water processing efficiency compared to outdoor sources. For example, households could install a rooftop water storage system with an electric pump. As discussed in Section 4.2, since water and energy are complementary at the water processing stage, this may lead to increased electricity consumption for water processing. With the improved temporal and qualitative availability, as well as the potentially increased quantity of water accessible to households, the overall water consumption may also increase. This could potentially trigger a corresponding rise in WES production and the associated electricity input. Therefore, in any case, we expect households with indoor water connections to spend more on electricity.

Hypothesis 2. Households that mainly use water sources of higher energy intensity spend more on electricity. The dataset reveals that households use different water sources. The diverse water sources are likely to provide varying levels of supply service quality, which may result in divergent energy intensities of water sources. According to the dataset, the three most common water sources used by the surveyed households are public piped water supply, hand pump, and tube well. The public piped water supply is highly intermittent, indicating a considerable temporal hurdle for most households to access piped water. This temporal hurdle may prompt households to adopt coping strategies at the water processing stage of the WES production, such as using water storage to store water during supply hours for use during supply interruptions, which may involve the use of an electric pump (Majuru et al. 2016; Shin et al. 2023). As for hand pumps and tube wells, both require water processing, however, the former requires only labor inputs while the latter necessitates the use of pumps. Therefore, access to these three most frequently used water sources can be categorized as medium energy intensity (public piped water supply), low energy intensity (hand pump), and high energy intensity (tube well). Based on the discussions in Section 4.2 on the complementarity of water and energy for water from the same source during the water processing stage, we expect to observe that compared to households that mainly use public piped water supply, households mainly using tube wells have higher electricity expenditure, while those mainly using hand pumps have lower electricity expenditure. Furthermore, for households that mainly use public piped water supply, we expect that households with access to continuous piped water supply ( $24 \times 7$ ) would have lower monthly electricity expenditure than those with intermittent supply, considering the temporal hurdle that households have to overcome in the latter case.

5.1.3. Functional form and estimation method

To test the derived hypotheses, we estimate the relationship between monthly household electricity expenditure and explanatory variables related to water use and supply conditions, as well as household characteristics and socio-economic conditions such as household type, size, and income from the IHDS-II dataset. We employ a log-linear functional form and conduct multiple linear regressions with two ordinary least squares (OLS) models. The first model (OLS-1) is estimated for the full sample (Eq. (18)), while the second model (OLS-2) is estimated for a subsample of households using public piped water supply (Eq. (19)):

ln (FU1C) = β 0 + β 1 WA1A + β 2 WA2A + β 3 ln (INCOME p M) + β 4 NPERSONS + β 5 URBAN 42011 + u, <math display="block" altimg="eq-00083.gif"><mtable displaystyle="true"><mtr><mtd columnalign="right"><mo>ln</mo><mo stretchy="false">(</mo><mstyle><mtext mathvariant="normal">FU1C</mtext></mstyle><mo stretchy="false">)</mo></mtd><mtd columnalign="center"><mo>=</mo></mtd><mtd columnalign="left"><msub><mrow><mi>β</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>+</mo><msub><mrow><mstyle mathvariant="bold-italic"><mi>β</mi></mstyle></mrow><mrow><mstyle mathvariant="bold"><mn>1</mn></mstyle></mrow></msub><mstyle><mtext mathvariant="normal">WA1A</mtext></mstyle><mo>+</mo><msub><mrow><mi>β</mi></mrow><mrow><mn>2</mn></mrow></msub><mstyle><mtext mathvariant="normal">WA2A</mtext></mstyle><mo>+</mo><msub><mrow><mi>β</mi></mrow><mrow><mn>3</mn></mrow></msub><mo>ln</mo><mo stretchy="false">(</mo><mstyle><mtext mathvariant="normal">INCOME</mtext></mstyle><mi>p</mi><mi>M</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd></mtd><mtd></mtd><mtd columnalign="left"><mo>+</mo><mspace width=".17em" class="thinspace"></mspace><mspace width=".17em" class="thinspace"></mspace><msub><mrow><mi>β</mi></mrow><mrow><mn>4</mn></mrow></msub><mstyle><mtext mathvariant="normal">NPERSONS</mtext></mstyle><mo>+</mo><msub><mrow><mstyle mathvariant="bold-italic"><mi>β</mi></mstyle></mrow><mrow><mstyle mathvariant="bold"><mn>5</mn></mstyle></mrow></msub><mstyle><mtext mathvariant="normal">URBAN</mtext></mstyle><msub><mrow><mn>4</mn></mrow><mrow><mn>2</mn><mn>0</mn><mn>1</mn><mn>1</mn></mrow></msub><mo>+</mo><mi>u</mi><mo>,</mo></mtd></mtr></mtable></math> (18)

ln (FU1C) = β 0 + β 1 Continuous + β 2 WA2A + β 3 ln (INCOME p M) + β 4 NPERSONS + β 5 URBAN 42011 + u . <math display="block" altimg="eq-00084.gif"><mtable displaystyle="true"><mtr><mtd columnalign="right"><mo>ln</mo><mo stretchy="false">(</mo><mstyle><mtext mathvariant="normal">FU1C</mtext></mstyle><mo stretchy="false">)</mo></mtd><mtd columnalign="center"><mo>=</mo></mtd><mtd columnalign="left"><msub><mrow><mi>β</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>+</mo><msub><mrow><mi>β</mi></mrow><mrow><mn>1</mn></mrow></msub><mstyle><mtext mathvariant="normal">Continuous</mtext></mstyle><mo>+</mo><msub><mrow><mi>β</mi></mrow><mrow><mn>2</mn></mrow></msub><mstyle><mtext mathvariant="normal">WA2A</mtext></mstyle><mo>+</mo><msub><mrow><mi>β</mi></mrow><mrow><mn>3</mn></mrow></msub><mo>ln</mo><mo stretchy="false">(</mo><mstyle><mtext mathvariant="normal">INCOME</mtext></mstyle><mi>p</mi><mi>M</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd></mtd><mtd></mtd><mtd columnalign="left"><mo>+</mo><mspace width=".17em" class="thinspace"></mspace><msub><mrow><mi>β</mi></mrow><mrow><mn>4</mn></mrow></msub><mstyle><mtext mathvariant="normal">NPERSONS</mtext></mstyle><mo>+</mo><msub><mrow><mstyle mathvariant="bold-italic"><mi>β</mi></mstyle></mrow><mrow><mstyle mathvariant="bold"><mn>5</mn></mstyle></mrow></msub><mstyle><mtext mathvariant="normal">URBAN</mtext></mstyle><msub><mrow><mn>4</mn></mrow><mrow><mn>2</mn><mn>0</mn><mn>1</mn><mn>1</mn></mrow></msub><mo>+</mo><mi>u</mi><mo>.</mo></mtd></mtr></mtable></math> (19)

The dependent variable in both models is the natural logarithm of the monthly household electricity expenditure (FU1C). Regarding the explanatory variables, we take the natural logarithm of the monthly household income (INCOMEpM), which is calculated as the total annual household income (INCOME) divided by 12. By taking the natural logarithm of these two variables, we presumably exclude the observations with non-positive monthly electricity expenditure and income. For the OLS-1 model, we recategorize the main water source that the household normally uses (WA1A) into four categories, respectively, the three most frequently used water sources as originally defined in the IHDS-II dataset, and the other sources. For the OLS-2 model, we create a new dummy variable for continuous piped water supply (Continuous) based on the daily hours of public piped water supply that households receive (WA3A). The variable Continuous equals 1, if the daily public piped water supply hours that households receive is 24; otherwise, it equals 0. The other explanatory variables are the original variables as defined in the IHDS-II dataset (Desai et al. 2011–2012). Further explanations on these variables can be found in the footnote 11. For both models, $β_{i}$ and $β_{i}$ denote coefficients for the variables, and u represents the error term.

5.2. Estimation results and implications

Table 2 summarizes the estimation results for the two OLS models. All the coefficient estimates are statistically significant, and the impacts of the variables on household characteristics and socioeconomic conditions are of similar magnitude in the two models. In particular, the explanatory variables related to water use and supply conditions have a highly significant impact on household electricity expenditure, and the signs of the coefficients for these variables confirm the hypotheses derived in Section 5.1.2.

**Table 2. Estimates of the Natural Logarithm of Monthly Household Electricity Expenditure in India**
	Dependent variable
	Log_FU1C
	OLS-1	OLS-2
WA1A (02) Tube well 2	0.123***
	(0.015)
WA1A (03) Hand pump 3	−0.099***
	(0.013)
WA1A Others	−0.109***
	(0.013)
Continuous		−0.062**
		(0.026)
WA2A(2) inside 2	0.317***	0.454***
	(0.010)	(0.013)
Log_INCOMEpM	0.191***	0.197***
	(0.005)	(0.006)
NPERSONS	0.048***	0.058***
	(0.002)	(0.003)
URBAN4_2011(1) other urban 1	−0.410***	−0.355***
	(0.016)	(0.018)
URBAN4_2011(2) more dev vill 2	−0.765***	−0.781***
	(0.017)	(0.020)
URBAN4_2011(3) less dev vill 3	−0.864***	−0.864***
	(0.018)	(0.022)
Constant	3.853***	3.642***
	(0.045)	(0.059)
Observations	30,683	17,271
$R^{2}$	0.281	0.319
Residual Std. Error	0.768 (df $=$ 30673)	0.756 (df $=$ 17263)
F-statistic	1,330.388*** (df $=$ 9; 30673)	1,156.789*** (df $=$ 7; 17263)

Note: * $p < 0.1$ ; ** $p < 0.05$ ; *** $p < 0.01$ .

The highly significantly positive sign of the coefficient for the variable WA2A in both model estimates validates the Hypothesis 1 that households with indoor water connections have higher electricity expenditures compared to those with outdoor connections. The estimate for the coefficient of 0.317 from the OLS-1 model indicates that, given the water supply conditions in India during the IHDS-II survey period and all else being equal, households with indoor water connections could have an electricity expenditure around 1.37 times that of households with outdoor connections. The OLS-2 model deals with a subsample of households that use public piped water supply. Here, the log-linear model coefficient value for the variable WA2A of 0.454 indicates that for these households, the availability of indoor water access can lead to a 57% increase in electricity expenditure. This result suggests that while indoor connections may appear to facilitate household access to water, water access depends on multiple dimensions beyond spatial access (see Section 3). In India, for example, given the prevalence of highly intermittent piped water supply systems, ignoring the use of electricity for water processing may pose problems in underestimating the affordability burden of resource use for households.

With regards to the quality of supply services, the coefficients for the variable WA1A in the OLS-1 model indicate that, compared to households using mainly public piped water supply, those who use tube wells as their main water source spend significantly more on electricity, while households using mainly hand pumps spend significantly less on electricity. The negative sign of the coefficient for the variable Continuous in the OLS-2 model suggests that households with access to 24-h daily piped water supply tend to have significantly lower monthly electricity expenditures than those with intermittent supply. Both estimates validate the Hypothesis 2 that the energy intensity of the main water source used by households can significantly affect their electricity expenditure, and households that rely on energy-intensive water sources spend more on electricity. For example, all else being equal, compared to households that mainly use public piped water supply, households that mainly use tube wells could spend around 13% more, while households that mainly use hand pumps could spend around 9% less on electricity. Among households using public piped water, in an all else equal situation, those with 24-h daily piped water supply tend to have a significantly lower total electricity expenditure (−6%) than those receiving intermittent supply. Given India’s large population and diverse water supply infrastructure, there is high potential for water and energy policy interactions. Expanding continuous public piped water supply and improving the reliability and quality of existing water supply infrastructure, for example, may lead to substantial electricity savings.

Regarding the estimates for the other explanatory variables, they all exhibit a statistically significant impact on household electricity expenditure. Households with higher income have higher electricity expenditure. The income elasticity of electricity expenditure is around 0.19, indicating that electricity is inelastic to changes in income. The coefficients for the variable NPERSONS from both models suggest that larger households have higher electricity expenditure than small ones, probably due to higher overall energy consumption in larger households. Specifically, a one-unit increase in the household size is associated with a 5–6% increase in electricity expenditure, holding all other factors constant. Households in less developed areas spend less on electricity than households in urban and metropolitan areas. These findings provide valuable insights into the socio-economic and demographic factors that influence household electricity expenditure, complementing the prior confirmation of our main hypotheses about the influence of the water use and supply conditions on energy consumption.

In general, the empirical findings highlight the significant potential for integrated water and energy management. On the one hand, improving water supply infrastructure can be beneficial for the energy sector and for reducing household vulnerability to both water and energy use. Faulty public water infrastructure frequently leads to the use of energy-intensive water sources or coping strategies, such as the use of tube wells or electric water pumps to cover piped water intermittencies or deal with pressure issues. Establishing a continuous piped water supply system, for example, would significantly reduce the energy intensity of public piped water supply to households. Apart from providing households with secured access to piped water, it can help ease the burden of household energy expenditure and contribute to the reduction of unnecessary emissions. On the other hand, as energy expenditure is related to the energy intensity of water sources, energy pricing can be relevant for regulating certain types of water use, particularly groundwater extraction. For example, in addition to licenses or restrictions on groundwater extraction, policies such as special prices for electricity use for tube wells may be set up to regulate water use. It should also be noted that while the expansion of water supply networks is important, it alone is not sufficient to ensure secured access to water for all. An integrated nexus perspective is needed, addressing not only the connections (e.g., indoor water connections), but also the stability of the water supply system, such as constant pressure and continuity of piped water supply, to improve the conditions of access to resources, especially for those living in vulnerable conditions.

6. Discussion

6.1. Comparison with existing frameworks and implications for empirical design

In the conceptual framework developed in this paper, to address our first research question, we interpret household water and energy use as a time-consuming production process for WESs. This framework covers the demand-side WEN more comprehensively than the framework used in previous empirical studies by Hansen (1996) and Maas et al.’s (2020). In contrast to Hansen’s water-focused model (1996), we make the WEN more explicit by treating water and energy as joint inputs for the household production of WESs. Hansen (1996) had a clear and distinct interest in residential water demand and defined goods in the household consumption function as water-dependent and water-independent, where energy can be involved in either type of goods. We extend this assumption to WESs and non-WESs consumed by households. Non-WESs do not involve either water or energy, while WESs, according to our definition in Section 3, are produced by households with inputs of at least one of the nexus resources.

Our framework also differs from Maas et al.’s (2020) conceptual framework of household water and energy use by avoiding an a priori categorization of WES into either substitutional or complementary. The definition of WESs used here covers all household services related to water and/or energy use defined in Maas et al. (2020) (i.e., the household services involving only water, only electricity, water and electricity as substitutes, and water and electricity as complements). The distinction defined by Maas et al.’s (2020) between household activities requiring water and energy as substitutes and complements can be ambiguous. Technological advancements in various devices for household production may also increase the substitution potentials between water and energy. For example, the use of dishwashers and washing machines in the provision of cleaning services may require both water and energy inputs, however, washing appliances nowadays often offer various functions in terms of resource substitution. Therefore, aggregating all the household services that involve water and energy can improve the general applicability of the conceptual framework over time with consistent insights.

Our systematic analyses of the WEN at the household level support the assessment of Maas et al. (2020) that the theoretical relationship between water and energy is ambiguous and that empirical approaches are necessary for clarifying the economic relationship between water and energy. In addition, we add theoretical clarification by discussing water and energy use at different steps of production activities. As discussed in Section 4.2, the overall economic relationship between water and energy is ambiguous, because complementary and substitutional uses of water and energy exist at different stages of production. The balance between complementary and substitutional effects may vary from case to case. This clarification of the case-specific relationship between water and energy can be used to structure context information (as shown in Section 5.1.2 when deriving hypotheses for the empirical case study of India) and interpret empirical findings. From an empirical case study design perspective, it is important to know the supply conditions for both energy and water in order to analyze household energy demand, especially in developing regions. For example, as illustrated in Section 5, under conditions of intermittent water supply, contextual information such as how households cope with water intermittency and what kind of coping strategies they use can be essential for data collection and variables to consider in estimating the demand for electricity. In interpreting empirical results, if electricity-intensive coping strategies are commonly applied, a major interruption in water supply could be the cause of a sudden increase in electricity consumption. This is also relevant to impact analyses of utility infrastructures, e.g., the impact of an intermittent water supply on households is not only through access to water, but also energy consumption.

In line with Hansen’s and Maas et al.’s findings, our analyses indicate that household demands for water and energy are interlinked. In particular, empirical demand analyses should account for the effect of cross-price elasticity of demand between water and energy. Price, income, and other variables such as household characteristics and exogenous climate conditions are commonly applied to explain household water or energy demand (Arbués et al. 2003; Löschel and Managi 2019; Nauges and Whittington 2010; Zhou and Teng 2013). In developing countries, coping costs of time for water access are often included in the analysis of household water use (Amit and Sasidharan 2019; Cook et al. 2016; Gurung et al. 2017; Pattanayak et al. 2005). According to the implicit demand functions for water and energy derived in Section 4.5 (see Eqs. (16) and (17)), in addition to these factors, household demand for one nexus resource also depends on the price for the other nexus resource (i.e., $p_{e}$ impacts $x_{w_{i}}$ and $p_{w}$ impacts $x_{e_{i}}$ ), and the production conditions for WESs (defined by $φ_{p_{i}}$ and $φ_{n_{i}}$ ). Although these factors have so far not all been analyzed together in a single empirical case, the impacts of cross-price elasticity, and production conditions can often be observed in water and energy-related studies. The conceptual framework developed in our study not only supports the conception of empirical case studies in the future, but also provides further clarification of existing observations as we will exemplify in Sections 6.2 and 6.3.

6.2. Cross-price elasticity of demand between water and energy

The existing literature on demand-side WEN at the household level presents mixed empirical findings regarding the cross-price elasticity of demand. As presented in Sections 1 and 2.1, two studies (Hansen 1996; Maas et al. 2020) reported a negative sign for the cross-price elasticity, suggesting a complementary economic relationship between water and energy. In contrast, the study by Suárez-Varela (2020) obtained positive cross-price elasticities, indicating a substitution relationship. Addressing our second research question, this empirical disagreement can be explained by our systematization of WEN at the household level.

Hansen (1996) applied pooled time-series data over the period from 1981–1990 to estimate residential water consumption in Copenhagen, Denmark. In his model, energy price was included in the form of water-heating cost (i.e., price for each unit of heated water). As pointed out by Hansen (1996), water heating accounted for the largest share of the energy use of Danish households at that time, while the other energy-related activities accounted for smaller shares. Our analysis in Section 4.2 suggests a complementary relationship between water and energy in energy use for water heating, which is consistent Hansen’s finding of a negative cross-price elasticity. Similarly, Maas et al. (2020) found negative cross-price elasticities between water and electricity in estimating household water and electricity demands in Colorado, USA over the period from 2006–2014. Maas et al. (2020) directly included electricity and water prices along with meteorological variables in the demand estimates. In Colorado homes, the dominant use of energy is for space heating (54%), which has limited interactions with water use. Although 26% of household energy use is for appliances, electronics, and lighting, water heating alone accounts for 19% of household energy use (EIA 2009), which takes up a relatively dominant position in water-related energy use in this case study. Based on our analysis in Section 4.2, a complementary relationship again prevails here, accordingly.

In contrast, Suárez-Varela (2020) obtained positive cross-price elasticities between water and energy in estimating household water demand with pooled data from the Spanish Consumer Expenditure Survey over the period from 2006–2012. Within a demand system, a significant cross-price elasticity of water demand influenced by energy price of 0.344 was observed, while the impact of water price on energy demand was smaller in magnitude (0.044) and was insignificant. According to the author, in the applied dataset, the cost of hot water including costs for both water and energy was categorized under the energy section. Based on our conceptual framework, since the need for water processing was limited in the area under this case study, the major water and energy linkage considered here is that of activities that use energy and/or water associated with the option of using electrical devices for traditionally non-electrical services. The dominant substitutional relationship between water and energy is therefore foreseeable, as discussed in Section 4.2. Additional substitution between normal temperature water and heated water also influenced the value of cross-price elasticities. As the total price for hot water depended principally on the energy cost in this case study, the impact of energy price on the normal-heated water substitution was substantially greater than that of water price. Accordingly, the cross-price elasticity of water demand influenced by energy price was largely impacted by the substitution between water of different temperatures, while the cross-price elasticity of energy demand influenced by water price in this estimation could more closely reflect the substitution relationship between water and energy use in the activities with electrical devices for traditionally non-electrical services.

The discussion of the three empirical WEN analyzes above highlights the value of a systematic economic analysis of the WEN at the private household level. The empirical studies validate, from different perspectives, the economic relation between water and energy at the household scale which is systematically subjected to case distinctions as discussed in the previous sections. However, none of the existing studies analyzes cases in developing countries, where the water infrastructure is commonly under development and the heterogeneous features of water processing could be taken into consideration. The conceptual insights on household water and energy use in developing countries developed here can help us gain a comprehensive understanding of the WEN at the private household level. Future research could aim to empirically confirm these findings, although challenges such as the lack of data and the complexity of the context remain.

6.3. Improvements in production conditions for WESs

With regards to our third research question, the conceptual framework developed in this paper can also clarify some empirical observations regarding the impact of capital investment on household water use. For example, Umapathi et al. (2013) monitored the water use of 20 households with plumbed rainwater tanks for 12 months in the Southeast Queensland region of Australia and identified a significant piped water cost saving through the use of rainwater. The installation of a rainwater harvesting system, i.e., an improvement in the production conditions for water processing according to our conceptual framework, enabled household use of an alternative water source without a market price. In this case, promoting the use of rainwater was rather one of the water resource management strategies towards a reduction in dependency on piped water supply than a solution to a water shortage. It did not cause any substantial change in the quantity of WESs produced and consumed by the household. Our analysis in Section 4.4 suggests that an improvement in production conditions can reduce the cost for producing a given level of WESs, which is in accordance with the findings of Umapathi et al. In addition, the processing of rainwater to make it fully accessible by the households generated energy costs, because, as discussed in Section 4.2, energy and water use are complementary in water processing. The authors pointed out that the energy use for the rainwater harvesting system differed according to the specific features of the systems such as the size of rainwater pumps and the switching mechanism between the piped connection and rainwater tank, and suggested that improvements in the system designs might further reduce piped water consumption by increasing rainwater availability. The following insight from our conceptual framework provides a potential explanation: The change in production conditions for water processing can initiate a reallocation of the full income-time budget, and accordingly holds potential to save water and/or energy.

In another example of a case study in Kathmandu Valley, Nepal, where the piped water supply is unreliable and of poor quality, Gurung et al. (2017) compared household water supply coping costs between 2001 and 2014. The coping costs taken into account in this study included the opportunity cost of time, energy costs, and other capital costs, which are as a whole the cost for water processing defined in our framework. As incomes increased, the households’ water processing capacity was improved from 2001 to 2014 through various capital investments such as the installation of storage tanks and the drilling of private wells. An overall increase was observed in the coping costs, while the time households spent on water processing decreased. This can be interpreted with our conceptual framework: The result in Section 4.4 suggests that the improvements in production conditions for WES production do not necessarily lead to a reduction in monetary production cost, because the overall income-time budget will be reallocated among all the inputs, including time. As rising incomes sometimes indicate increases in the opportunity cost of time, Gurung et al.’s (2017) study also confirmed our argument in Section 4.4 that households with a higher opportunity cost of time might tend to adopt technologies and equipment with good performance in time-saving with less consideration for their efficiency in water and energy use.

Similarly, Devoto et al. (2012) found that households in Tangiers, Morocco, were willing to pay for improved water services such as a private water connection because it increased leisure time availability (i.e., one of the non-WESs consumed by the households as defined in our framework) and reduced water conflicts. According to our conceptual framework, supply-side measures that facilitate households’ access to water (e.g., improving the technical service level of the piped water services delivered by the water utilities) can lead to reduced demand for water processing. It allows us to derive additional implications from Devoto et al.’s study that improved water supply conditions have the potential to reduce the total WES production costs faced by households and thereby increase household welfare levels.

Our analysis has shown that the improvements in household production conditions for WESs have the potential to save water and energy. This resource-saving potential, however, depends on the specific technical features and the household WES consumption condition before the change. The insight from this highlights the importance of context analysis within the water- and/or energy-related campaigns or policy formulations, and provides guidance on the aspects to be taken into account for conceptualizing such campaigns or policies.

7. Conclusions

We review the literature on household activities reflecting WEN, which has not been included in any of the previous conceptual analyses, and propose a conceptual framework based on the household production theory to systematically interpret the demand-side WEN at the private household level. The framework is applicable to urban and rural households in both developing and developed countries. The residential water and energy consumption decisions in the presence of household activities using both resources (i.e., our research question 1) can be explained by the time-consuming household production process for WESs, using water and energy as inputs, particularly but not exclusively under conditions of intermittent water supply.

Based on the conceptual framework, we conduct an economic analysis of household water and energy demand to address our research questions 2 and 3. The utility derived from household water and energy use stems directly from the consumption of WESs produced by the household, using inputs of water, energy, and time from household members. Consequently, the household demand for one nexus resource depends not only on its own price, but also on the price of the other nexus resource, the opportunity cost of time, the household income and its structure, the production conditions for WESs, and the preference of the household depending on its specific characteristics. We analyze the economic relationship between water and energy according to different household production activities: (1) water processing, (2) water heating, and (3) activities that use energy and/or water, often associated with the option of using electrical devices for traditionally non-electrical services. Water and energy use are complementary in the first two types of activities, while in the third type energy may exhibit substitutional patterns with respect to water, with potential rebound effects. The balance between complementary and substitutional effects can vary among cases and households. Regarding the improvements in household production conditions for WESs, there exists a resource-saving potential, however, it depends on the specific technical characteristics and the consumption conditions of WESs in the household prior to the change. The insights developed here can be used to structure contextual information, e.g., the use of multiple water sources, household preferences in daily water and energy use, in empirical analyses of specific case studies. It can also provide valuable context for understanding the factors that influence household water and energy demand.

We further illustrate the demand-side WEN with an empirical case study in India. We identify significant impacts of household water use and supply conditions on their electricity expenditure. In particular, households that rely on energy-intensive water sources tend to spend more on electricity. For those using public piped water, households with 24-h daily piped water supply have a significantly lower total electricity expenditure by around 6%, compared to those with intermittent supply, holding other factors constant. The water affordability burden for households with poor water supply infrastructure may be underestimated if electricity input at the water processing stage is not taken into account.

Our analyses highlight three key research and policy implications. First, adjusting the tariff structure for one nexus resource can potentially help regulate or facilitate the use of the other nexus resource. Estimating the cross-price elasticity of demand between water and energy can provide additional insights for developing pricing instruments. Second, the nexus perspective provides a comprehensive dimension for analyzing household resource use security and affordability issues, especially under intermittent water supply systems. Without considering the demand-side WEN at the household level, resource access inequality and resource use vulnerability may be underestimated. Third, the promotion of water and energy-efficient technologies and behaviors has the potential to reduce household water and energy consumption. Contextual analyses from a household WES production perspective can improve efficiency in designing and implementing water and energy-related campaigns and policies.

The conceptual framework can be used to develop systematic empirical studies of household water and energy demand from a WEN perspective. This could involve including nexus-related variables from data collection to demand estimation. Such empirical case studies can help improve our understanding of the WEN at the private household level, which can potentially contribute to the development of water and energy management strategies (e.g., regulating water use with energy pricing instruments; establishing a stable municipal water supply system may also reduce household energy consumption). However, such studies are currently lacking, especially for developing regions. We hope that the linkages and relations between water and energy discussed in our study can motivate further thinking on the WEN at the private household level from the demand side as well as on the opportunities in resource management with WEN considerations.

Appendix A. Household Activities Reflecting WEN

**Table A.1. Summary of Studies Revealing Connections Between Household Water and Energy Use**
Author(s)	Region	Water-related activities	Energy-related activities	Major interactions between water and energy use revealed
Eichelberger 2010	Northwest Arctic Borough, Alaska	Shower, laundry, drinking, dishwashing, room cleaning	Use of the specific flush-haul system, hauling water with vehicles	Water and energy use for shower and laundry, energy use for physically accessing water
Kenway et al. 2011a 2013, 2016; Binks et al. 2016, 2017	Australia	Shower, bath, laundry, dishwashing, faucet, toilet, outdoor use, kettle, air conditioning	Shower, bath, laundry, dishwashing, faucet, toilet, outdoor use, kettle, air conditioning, others	Energy use for water heating, simultaneous water and energy use through various appliances
Beal et al. 2012	Queensland, Australia	Shower, laundry, dishwashing, faucet	Shower, laundry, dishwashing, faucet	Energy use for water heating
McKenzie et al. 2013	California, USA	Space cooling	Space cooling	Water and energy use for space cooling
Umapathi et al. 2013	Queensland, Australia	Laundry, faucet, toilet	Rainwater pumping	Energy use for rainwater pumping
Abdallah and Rosenberg 2014	USA	Shower, laundry, dishwashing, faucet, toilet	Shower, laundry, dishwashing, faucet, toilet	Energy use for water heating, water and energy use with wet appliances
Talebpour et al. 2014	Queensland, Australia	Laundry, toilet, irrigation	Rainwater pumping	Energy use for rainwater pumping
Escriva-Bou et al. 2015	California, USA	Shower, bath, laundry, dishwashing, faucet, toilet, outdoor use, others	Shower, bath, laundry, dishwashing, faucet	Energy use for shower and faucet end uses
Chini et al. 2016	USA	Laundry, faucet, toilet, irrigation	Household appliances and fixtures	Energy use for water heating
Jiang et al. 2016	Tianjin, China	Shower, bath, laundry, drinking, cooking, toilet, irrigation, cleaning	Water heating, laundry	Energy use for water heating, water and energy use for cooking and laundry
Vieira and Ghisi 2016	Florianópolis, Brazil	Shower, laundry, faucet, toilet	On-site pumping and UV disinfection	Energy use for grey water reclamation and rainwater harvesting systems
Wanjiru et al. 2016	Tshwane, South Africa	Water use in general	Water pumping	Energy use dealing with inadequate and unreliable portable water supply
Hussien et al. 2017, 2018	Duhok, Iraq	Shower, bath, laundry, cooking, dishwashing, faucet, toilet, room cleaning, outdoor use	Space heating, space cooling, water heating, lighting, wet appliances, various appliances	Energy use for water heating, water and energy use for cooking, dishwashing and laundry
Matos et al. 2017, 2018	Vila Real County, Portugal	Shower, bath, laundry, dishwashing, irrigation, car washing	Bath, laundry, dishwashing	Energy use for dishwashing, laundry and water heating for bathing
Spiegelberg et al. 2017	Philippines	Bath, laundry, drinking, cleaning, others	Water heating, cooling, food preparing, cooking, lighting, refrigeration, washing	Energy use for water heating and cooking
Cominola et al. 2018	Los Angeles, USA	Shower, bath, laundry, dishwashing, faucet, toilet, outdoor use, others	Water heating, dryer, laundry, dishwashing, pumping, lighting, air conditioning, others	Energy use for water heating, simultaneous water and energy use through various appliances
Mostafavi et al. 2018	Northern America	Hot water use, other indoor use	Water heating, laundry, dishwashing	Energy use for water heating
Porse et al. 2020	Los Angeles, USA	Water use in general	Water heating	Energy use for water heating
Zhuge et al. 2020	Beijing, China	Shower, foot bath, laundry, food preparing, cooking, dishwashing, room cleaning	Shower, foot bath, laundry, food preparing, cooking, dishwashing, room cleaning	Water and energy use for bathing, cooking and cleaning activities

Acknowledgments and Funding Sources

This work was conducted as part of the Belmont Forum Sustainable Urbanisation Global Initiative (SUGI)/Food-Water-Energy Nexus theme for which coordination was supported by the US National Science Foundation under grant ICER/EAR-1829999 to Stanford University. As a part of the Belmont Forum, the German Federal Ministry of Education and Research provided funding to the Helmholtz Centre for Environmental Research (UFZ) (033WU002). Any opinions, findings, and conclusions or recommendations expressed in this material do not necessarily reflect the views of the funding organizations.

Publisher’s Note

Acknowledgments and Funding Sources section has been inserted in this latest version of the paper.

ORCID

Yuanzao Zhu https://orcid.org/0000-0002-9801-5520

Christian Klassert https://orcid.org/0000-0003-0676-2455

Bernd Klauer https://orcid.org/0000-0003-3484-2903

Erik Gawel https://orcid.org/0000-0003-3634-9717

Notes

¹ The demand-side nexus between water and energy use at the household scale comes in two varieties: water-related energy use and energy-related water use. The term “related-use” refers to a causal relationship where changes in the use of one of the resources may result in changes in the other. This is reflected in various household activities both directly, i.e., by the changes in water and energy consumption within a household, and indirectly, i.e., by the corresponding impacts on water and energy use beyond the household during the life cycle of the production and provision of water and energy. For example, the direct linkages can be observed in those activities for which both water and energy are required as indispensable inputs (e.g., bathing, hot beverage drinking). They can also be observed in the activities which can involve either or both resources, and the amounts of water and energy needed will vary depending on the use of appliances (e.g., room cleaning with a mop/vacuum cleaner, dishwashing by hand/with a dishwasher). On the other hand, the indirect linkages between water and energy use represent the broad WEN impacts that are often based outside of a household premises. For example, the impact of household water and energy demand changes with overall water use for energy production or energy use for water provision. In this paper, by referring to the WEN at the private household level, we focus on the direct demand-side nexus between water and energy at the household scale, and will discuss household water and energy use as the actual amount of water and energy consumed by an individual household.

² We do not restrict a WES to services that include both water and energy, because substitution between water and energy can occur among household production processes that require only one of the resources each (e.g., using a vacuum cleaner or a mop for cleaning floor). This potential substitution accompanied with technological advances forms a non-negligible part of the household-level WEN.

³ Exceptionally, seasonal drought can lead to seasonal dry wells. This is a similar case of temporal water unavailability to that of an intermittent piped water supply schedule. Here, we discuss the general situation where households choose to use well water when water is available in the wells.

⁴ Activities such as sleeping and leisure are included in the household production of non-WESs. For example, household members consume time to sleep to recover physically and mentally and can improve the quality of sleep (i.e., production efficiency) by investing in capital goods (e.g., comfortable mattresses, pillows, bed linens) or by using non-capital inputs (e.g., pillow spray, aromatherapy oil).

⁵ The market prices can be 0, when water or energy from a certain source/supplier is provided at no monetary cost (e.g., water from a free public water stand or wood collected in a forest). However, price signal is one of the most important economic aspects for our analysis of the household-level WEN. Positive prices are necessary for the price elasticity analysis in the following part.

⁶ For example, mopping is one of the traditional methods for room cleaning. As a result of technological progress, households can choose vacuum cleaners to achieve the same level of cleanness as when using a mop. During this production process, less water but more electricity is consumed. Before dishwashers were popularized as domestic appliances, using water directly from faucets was common for cleaning dishes at home. However, compared to washing dishes in the traditional way, using dishwashers requires lower quantities of water by introducing electricity into the dishwashing process (Abdallah and Rosenberg 2014). Similarly, in the case of laundry, the households can choose between washing by hand and using washing machines. They can even decide to let the washing machines run longer and use less water to achieve the expected quality of cleaned clothes. Regarding the use of different types of air conditioners for space cooling, an evaporative air conditioner that depends on water as a necessary input uses only part of the energy required by a non-evaporative air conditioning system (Kenway et al. 2011a; McKenzie et al. 2013). Explicitly, activities with wet appliances such as dishwashers and washing machines require a simultaneous provision of water and energy inputs. However, from the perspective of households’ decisions on how to run the appliances, the use of water and energy can be substitutional in consideration of the various water and energy setting options based on the specific characteristics of the appliances.

⁷ Although the substitution potential between water and energy is higher in the long term, introducing water-related electrical devices into household WES production can lead to rebound effects, e.g., an increase in water use when using a dishwasher. This is because the use of electrical devices changes the production conditions for producing the corresponding WESs. By integrating energy with water in the household production process for a WES that previously did not require energy input, a higher-value WES may be generated, potentially altering household demand for that specific WES. For example, the adoption of dishwashers and washing machines can substantially reduce labor input from the household members for producing cleaned tableware and cleaned clothes. After purchasing these devices, as the capacity to produce WESs within a given timeframe expands, households may opt to engage in production activities more frequently (i.e., dishwashing and laundry). The introduction of energy into household production for these WESs can consequently lead to an increase in water consumption.

⁸ Households in developing regions frequently rely on multiple sources of water (Zozmann et al. 2022; Daly et al. 2021). For example, tanker water is commonly used as a supplement to piped water as a coping mechanism for insufficiencies and intermittencies in the piped water supply (Klassert et al. 2023).

⁹ For example, water storage tanks with electric pumps can be used as a daily coping strategy in the case of intermittent piped water supply with occasional water shortages (Majuru et al. 2016; Shin et al. 2023). The use of piped water and electricity to store/pump piped water to/from water tanks to cover the intermittency are complementary. However, if the household also uses an electric pump for well water in case of a piped water shortage, the use of piped water and the use of electricity for pumping well water are substitutes.

¹⁰ The increase in cash income can also enable households to decide on capital investments to improve long-term production conditions. The impact of changes in production conditions will be discussed in Section 4.4.

¹¹ URBAN4_2011: Four urban and rural categories based on Census of India 2011 and IHDS-II villages; NPERSONS: Number of persons in the household (i.e., all persons living under the same roof and sharing the same kitchen for more than six months during the year preceding the survey); INCOME: Total annual income of the household in Indian rupees; FU1C: Monthly electricity expenditure of the household in Indian rupees; WA1A: Main water source that the household normally uses; WA2A: Dummy variable for whether the water source is inside or outside the house or compound; WA3A: Daily hours of public piped water supply. All the variable names and corresponding question codes can be found in the codebook and the original survey questionnaire developed by Desai et al. (2011–2012).

References

Abdallah, AM and DE Rosenberg (2014). Heterogeneous residential water and energy linkages and implications for conservation and management. Journal of Water Resources Planning and Management, 140(3), 288–297. https://doi.org/10.1061/(ASCE)WR.1943-5452.0000340 Crossref, Google Scholar
Anand, PB (2001). Water scarcity in Chennai, India: Institutions, entitlements and aspects of inequality in access (WIDER Discussion Paper 2001/140). Helsinki: The United Nations University World Institute for Development Economics Research (UNU-WIDER). https://www.econstor.eu/handle/10419/53004. Google Scholar
Amit, RK and S Sasidharan (2019). Measuring affordability of access to clean water: A coping cost approach. Resources, Conservation and Recycling, 141, 410–417. https://doi.org/10.1016/j.resconrec.2018.11.003 Crossref, Google Scholar
Arbués, F, MA Garcıa-Valiñas and R Martínez-Espiñeira (2003). Estimation of residential water demand: A state-of-the-art review. The Journal of Socio-Economics, 32(1), 81–102. https://doi.org/10.1016/S1053-5357(03)00005-2 Crossref, Google Scholar
Beal, CD, E Bertone and RA Stewart (2012). Evaluating the energy and carbon reductions resulting from resource-efficient household stock. Energy and Buildings, 55, 422–432. https://doi.org/10.1016/j.enbuild.2012.08.004 Crossref, Google Scholar
Becker, GS (1965). A theory of the allocation of time. The Economic Journal, 75(299), 493. https://doi.org/10.2307/2228949 Crossref, Google Scholar
Binks, AN, SJ Kenway and PA Lant (2017). The effect of water demand management in showers on household energy use. Journal of Cleaner Production, 157, 177–189. https://doi.org/10.1016/j.jclepro.2017.04.128 Crossref, Google Scholar
Binks, AN, SJ Kenway, PA Lant and BW Head (2016). Understanding Australian household water-related energy use and identifying physical and human characteristics of major end uses. Journal of Cleaner Production, 135, 892–906. https://doi.org/10.1016/j.jclepro.2016.06.091 Crossref, Google Scholar
Chini, CM, KL Schreiber, ZA Barker and AS Stillwell (2016). Quantifying energy and water savings in the U.S. residential sector. Environmental Science and Technology, 50(17), 9003–9012. https://doi.org/10.1021/acs.est.6b01559 Crossref, Google Scholar
Crider, YS and I Ray (2022). Water and development: A gender perspective. In Oxford Research Encyclopedia of Environmental Science. Oxford University Press, https://doi.org/10.1093/acrefore/9780199389414.013.685. Crossref, Google Scholar
Cominola, A, ES Spang, MM Giuliani, A Castelletti, JR Lund and FJ Loge (2018). Segmentation analysis of residential water-electricity demand for customized demand-side management programs. Journal of Cleaner Production, 172, 1607–1619. https://doi.org/10.1016/j.jclepro.2017.10.203 Crossref, Google Scholar
Cook, J, P Kimuyu and D Whittington (2016). The costs of coping with poor water supply in rural Kenya. Water Resources Research, 52(2), 841–859. https://doi.org/10.1002/2015WR017468 Crossref, Google Scholar
Daly, SW, J Lowe, GM Hornsby and AR Harris (2021). Multiple water source use in low-and middle-income countries: A systematic review. Journal of Water and Health, 19(3), 370–392. Crossref, Google Scholar
Desai, S, V Reeve and National Council of Applied Economic Research. India Human Development Survey-II (IHDS-II) (2011–2012). Inter-university Consortium for Political and Social Research [distributor], 2018-08-08, https://doi.org/10.3886/ICPSR36151.v6. Google Scholar
Devoto, F, E Duflo, P Dupas, W Parienté and V Pons (2012). Happiness on tap: Piped water adoption in Urban Morocco. American Economic Journal: Economic Policy, 4(4), 68–99. https://doi.org/10.1257/pol.4.4.68 Crossref, Google Scholar
EIA (2009). Household Energy Use in Colorado: A Closer Look at Residential Energy Consumption. The U.S. Energy Information Administration, State fact sheets on household energy use. https://www.eia.gov/consumption/residential/reports/2009/state_briefs/pdf/co.pdf. Google Scholar
Eichelberger, LP (2010). Living in utility scarcity: Energy and water insecurity in Northwest Alaska. American Journal of Public Health, 100(6). https://doi.org/10.2105/AJPH.2009.160846 Crossref, Google Scholar
Escriva-Bou, A, JR Lund, and M Pulido-Velazquez (2015). Modeling residential water and related energy, carbon footprint and costs in California. Environmental Science and Policy, 50, 270–281. https://doi.org/10.1016/j.envsci.2015.03.005 Crossref, Google Scholar
Gawel, E and W Bretschneider (2016). Content and Implementation of a Right to Water: An Institutional Economics Approach. Ökologie und Wirtschaftsforschung, Volume 101. Marburg: Metropolis-Verlag. Google Scholar
Gawel, E and W Bretschneider (2017). Specification of a human right to water: A sustainability assessment of access hurdles. Water International, 42(5), 505–526. https://doi.org/10.1080/02508060.2017.1342062 Crossref, Google Scholar
Gleick, PH (1994). Water and energy. Annual Review of Energy and the Environment, 19(1), 267–299. https://doi.org/10.1146/annurev.eg.19.110194.001411 Crossref, Google Scholar
Government of India (2021). Guidelines for Planning, Design and Implementation of $24 \times 7$ Water Supply Systems. Ministry of Housing and Urban Affairs, Government of India. https://mohua.gov.in/pdf/62023520928a0advisory-on-water%20supply-final-new.pdf. Google Scholar
Grubert, E and KT Sanders (2018). Water use in the United States energy system: A national assessment and unit process inventory of water consumption and withdrawals. Environmental Science and Technology, 52(11), 6695–6703. https://doi.org/10.1021/acs.est.8b00139 Crossref, Google Scholar
Gurung, Y, J Zhao, KCB Kumar, X Wu, B Suwal and D Whittington (2017). The costs of delay in infrastructure investments: A comparison of 2001 and 2014 household water supply coping costs in the Kathmandu Valley, Nepal. Water Resources Research, 53(8), 7078–7102. https://doi.org/10.1002/2016WR019529 Crossref, Google Scholar
Hansen, LG (1996). Water and energy price impacts on residential water demand in Copenhagen. Land Economics, 72(1), 66–79. https://doi.org/10.2307/3147158 Crossref, Google Scholar
Harte, J and M El-Gasseir (1978). Energy and water. Science (New York, N.Y.), 199(4329), 623–634. https://doi.org/10.1126/science.199.4329.623 Crossref, Google Scholar
Hussien, WeA, FA Memon and DA Savic (2017). An integrated model to evaluate water-energy-food nexus at a household scale. Environmental Modelling and Software, 93, 366–380. https://doi.org/10.1016/j.envsoft.2017.03.034 Crossref, Google Scholar
Hussien, WeA, FA Memon and DA Savic (2018). A risk-based assessment of the household water-energy-food nexus under the impact of seasonal variability. Journal of Cleaner Production, 171, 1275–1289. https://doi.org/10.1016/j.jclepro.2017.10.094 Crossref, Google Scholar
Jiang, S, J Wang, Y Zhao, S Lu, H Shi and F He (2016). Residential water and energy nexus for conservation and management: A case study of Tianjin. International Journal of Hydrogen Energy, 41(35), 15919–15929. https://doi.org/10.1016/j.ijhydene.2016.04.181 Crossref, Google Scholar
Kenway, SJ, P Lant and T Priestley (2011a). Quantifying water–energy links and related carbon emissions in cities. Journal of Water and Climate Change, 2(4), 247–259. https://doi.org/10.2166/wcc.2011.005 Crossref, Google Scholar
Kenway, SJ, PA Lant, A Priestley and P Daniels (2011b). The connection between water and energy in cities: A review. Water Science and Technology: A Journal of the International Association on Water Pollution Research, 63(9), 1983–1990. https://doi.org/10.2166/wst.2011.070 Crossref, Google Scholar
Kenway, SJ, A Binks, R Scheidegger, H-P Bader, F Pamminger, P Lant and T Taimre (2016). Household analysis identifies water-related energy efficiency opportunities. Energy and Buildings, 131, 21–34. https://doi.org/10.1016/j.enbuild.2016.09.008 Crossref, Google Scholar
Kenway, SJ, R Scheidegger, TA Larsen, P Lant and H-P Bader (2013). Water-related energy in households: A model designed to understand the current state and simulate possible measures. Energy and Buildings, 58, 378–389. https://doi.org/10.1016/j.enbuild.2012.08.035 Crossref, Google Scholar
Klassert, C, J Yoon, K Sigel, B Klauer, S Talozi, T Lachaut, P Selby, S Knox, N Avisse, A Tilmant, JJ Harou, D Mustafa, J Medellín-Azuara, B Bataineh, H Zhang, E Gawel and SM Gorelick (2023). Unexpected growth of an illegal water market. Nature Sustainability, 6, 1406–1417, https://doi.org/10.1038/s41893-023-01177-7. Google Scholar
Lancaster, KJ (1966). A new approach to consumer theory. Journal of Political Economy, 74(2), 132–157. https://doi.org/10.1086/259131 Crossref, Google Scholar
Laughland, AS, LM Musser, WN Musser and JS Shortle (1993). The opportunity cost of time and averting expenditures for safe drinking water. Journal of the American Water Resources Association, 29(2), 291–299. https://doi.org/10.1111/j.1752-1688.1993.tb03209.x Crossref, Google Scholar
Löschel, A and S Managi (2019). Recent advances in energy demand analysis — insights for industry and households. Resource and Energy Economics, 56, 1–5. https://doi.org/10.1016/j.reseneeco.2019.04.001 Crossref, Google Scholar
Maas, A, C Goemans, DT Manning, J Burkhardt and M Arabi (2020). Complements of the house: Estimating demand-side linkages between residential water and electricity. Water Resources and Economics, 29, 100140. https://doi.org/10.1016/j.wre.2019.02.001 Crossref, Google Scholar
Majuru, B, M Suhrcke and PR Hunter (2016). How do households respond to unreliable water supplies? A systematic review. International Journal of Environmental Research and Public Health, 13(12), 1222, https://doi.org/10.3390/ijerph13121222. Crossref, Google Scholar
Matos, C, I Bentes, S Pereira, AM Gonçalves, D Faria and A Briga-Sá (2018). Which are the factors that may explain the differences in water and energy consumptions in urban and rural environments? The Science of the Total Environment, 642, 421–435. https://doi.org/10.1016/j.scitotenv.2018.06.062 Crossref, Google Scholar
Matos, C, A Briga-Sá, I Bentes, D Faria and S Pereira (2017). In situ evaluation of water and energy consumptions at the end use level: The influence of flow reducers and temperature in baths. Science of the Total Environment, 586, 536–541. https://doi.org/10.1016/j.scitotenv.2017.02.008 Crossref, Google Scholar
McKenzie, ER, TE Pistochini, FJ Loge and MP Modera (2013). An investigation of coupling evaporative cooling and decentralized graywater treatment in the residential sector. Building and Environment, 68, 215–224. https://doi.org/10.1016/j.buildenv.2013.07.007 Crossref, Google Scholar
Mostafavi, N, F Gándara and S Hoque (2018). Predicting water consumption from energy data: Modeling the residential energy and water nexus in the integrated urban metabolism analysis tool (IUMAT). Energy and Buildings, 158, 1683–1693. https://doi.org/10.1016/j.enbuild.2017.12.005 Crossref, Google Scholar
Muth, RF (1966). Household production and consumer demand functions. Econometrica, 34(3), 699. https://doi.org/10.2307/1909778 Crossref, Google Scholar
Nauges, C and D Whittington (2010). Estimation of water demand in developing countries: An overview. The World Bank Research Observer, 25(2), 263–294. https://doi.org/10.1093/wbro/lkp016 Crossref, Google Scholar
OECD (2014). India Policy Brief: Improving Water Security in India. OECD Publishing, Paris. https://www.oecd.org/policy-briefs/India-Improving-Water-Security.pdf. Google Scholar
Olsson, G (2015). Water and Energy: Threats and Opportunities. London: IWA Publishing. Available at: http://gbv.eblib.com/patron/FullRecord.aspx?p=3425858. Crossref, Google Scholar
Parkinson, SC, M Makowski, V Krey, K Sedraoui, AH Almasoud and N Djilali (2018). A multi-criteria model analysis framework for assessing integrated water-energy system transformation pathways. Applied Energy, 210, 477–486. https://doi.org/10.1016/j.apenergy.2016.12.142 Crossref, Google Scholar
Pattanayak, SK, J-C Yang, D Whittington and KC Bal Kumar (2005). Coping with unreliable public water supplies: Averting expenditures by households in Kathmandu, Nepal. Water Resources Research, 41, W02012. https://doi.org/10.1029/2003WR002443 Crossref, Google Scholar
Porse, E, KB Mika, A Escriva-Bou, ED Fournier, KT Sanders, E Spang and S Pincetl (2020). Energy use for urban water management by utilities and households in Los Angeles. Environmental Research Communications, 2(1), 15003. https://doi.org/10.1088/2515-7620/ab5e20 Crossref, Google Scholar
Rosenberg, DE and JR Lund (2009). Modeling integrated decisions for a municipal water system with recourse and uncertainties: Amman, Jordan. Water Resources Management, 23, 85–115. Crossref, Google Scholar
Shaban, A and S Sattar (2011). Water security and sustainability in urban India. International Journal of Global Environmental Issues, 11(3–4), 231–254. https://doi.org/10.1504/IJGENVI.2011.044552 Crossref, Google Scholar
Shin, HC, P Yousefi, S Park, DJ Yu, MA Janssen, S Vallury and E Araral (2023). Coping with unreliable water supply: An experimental study of exit and voice. Water Resources Research, 59(6), e2022WR032468. https://doi.org/10.1029/2022WR032468 Crossref, Google Scholar
Spiegelberg, M., DE Baltazar, MPE Sarigumba, PM Orencio, S Hoshino, S Hashimoto and A Endo (2017). Unfolding livelihood aspects of the water–energy–food nexus in the Dampalit watershed, Philippines. Journal of Hydrology: Regional Studies, 11, 53–68. https://doi.org/10.1016/j.ejrh.2015.10.009 Crossref, Google Scholar
Srinivasan, V, SM Gorelick and L Goulder (2010). A hydrologic-economic modeling approach for analysis of urban water supply dynamics in Chennai, India. Water Resources Research, 46, W07540. https://doi.org/10.1029/2009WR008693 Crossref, Google Scholar
Suárez-Varela, M (2020). Modeling residential water demand: An approach based on household demand systems. Journal of Environmental Management, 261, 109921. https://doi.org/10.1016/j.jenvman.2019.109921 Crossref, Google Scholar
Talebpour, MR, O Sahin, R Siems and RA Stewart (2014). Water and energy nexus of residential rainwater tanks at an end use level: Case of Australia. Energy and Buildings, 80, 195–207. https://doi.org/10.1016/j.enbuild.2014.05.018 Crossref, Google Scholar
Tomberge, VMJ, JS Bischof, R Meierhofer, A Shrestha and J Inauen (2021). The physical burden of water carrying and women’s psychosocial well-being: Evidence from rural Nepal. International Journal of Environmental Research and Public Health, 18(15), 7908. Crossref, Google Scholar
Umapathi, S, MN Chong and AK Sharma (2013). Evaluation of plumbed rainwater tanks in households for sustainable water resource management: A real-time monitoring study. Journal of Cleaner Production, 42, 204–214. https://doi.org/10.1016/j.jclepro.2012.11.006 Crossref, Google Scholar
United Nations, Department of Economic and Social Affairs, Population Division (2022). World Population Prospects 2022: Summary of Results. UN DESA/POP/2022/TR/NO. 3. Google Scholar
Vieira, AS and E Ghisi (2016). Water-energy nexus in low-income houses in Brazil: The influence of integrated on-site water and sewage management strategies on the energy consumption of water and sewerage services. Journal of Cleaner Production, 133, 145–162. https://doi.org/10.1016/j.jclepro.2016.05.104 Crossref, Google Scholar
Wanjiru, EM, L Zhang and X Xia (2016). Model predictive control strategy of energy-water management in urban households. Applied Energy, 179, 821–831. https://doi.org/10.1016/j.apenergy.2016.07.050 Crossref, Google Scholar
Zhou, S and F Teng (2013). Estimation of urban residential electricity demand in China using household survey data. Energy Policy, 61, 394–402. https://doi.org/10.1016/j.enpol.2013.06.092 Crossref, Google Scholar
Zhuge, C, M Yu, C Wang, Y Cui and Y Liu (2020). An agent-based spatiotemporal integrated approach to simulating in-home water and related energy use behaviour: A test case of Beijing, China. Science of the Total Environment, 708, 135086. https://doi.org/10.1016/j.scitotenv.2019.135086 Crossref, Google Scholar
Zozmann, H, C Klassert, B Klauer and E Gawel (2022). Heterogeneity, household co-production, and risks of water services — water demand of private households with multiple water sources. Water Economics and Policy, 8(01), 2250006. Link, Google Scholar