Implications of different income distributions for future residential energy demand in the U.S.

For this study, we use the GCAM with greater spatial detail in the U.S. region, referred to as GCAM-USA [45, 46]. This version of the model disaggregates the U.S into 51 subregions (50 states and District of Columbia) and works within the global GCAM modeling framework. The model explores human and Earth-system interconnections and is designed to explore how these evolve over time under the influence of critical socio-economic and bio-physical driving forces that can be modified according to different 'what-if' types of scenarios. The recursive-dynamic projections of GCAM are simulated in a way that consistently resolves interactions between the energy, economy, land, water, and climate systems within a fully integrated computational system. GCAM-USA is an open-source model and can be downloaded from an online repository. In this work, we use version 5.2 of GCAM-USA, which we further modified in ways that are explained below.

As a relevant feature for this study, we focus on the energy system, and in particular, the residential sector [47–49], while still maintaining the close integration with the other human and physical systems mentioned above. The building sector in GCAM-USA is disaggregated into 'residential' and 'commercial' sub-sectors. The floorspace demand is driven by population and income, so more (and/or richer) people will demand more floorspace until a satiation level is achieved. Below this satiation point the marginal utility of floorspace is positive. Above that point, the marginal utility is negative. The floorspace demand function in GCAM-USA is based on the formulation by Isaac and Van Vuuren [50], which has been extensively applied within integrated assessment modeling frameworks. It is summarized in the following equation

$$\begin{equation}{f_{r,t,i}} = {s_r} \times \left[ {1 - \exp \left( { - \frac{{{\text{ln}}2}}{{{\mu _{r,i}}}}{I_{r,t,i}}} \right)} \right].\end{equation} \tag{ 1 }$$

So, the per capita floorspace ( f) in region r, period t, and quintile i is determined by the exogenously defined satiation level (s), per capita income (I), and a time-invariant calibration-shape parameter ($\mu$; 'satiation impedance') that represents the 'unobservable' effects driven by the variables that are not covered by the model. The details on these parameters can be found in the Supplementary information (SI, section 3.1.1), which also includes the link to the open-access GitHub repository with detailed model documentation. Total floorspace (${F_{r,t,i}}$) will be calculated as per capita floorspace (${\,f_{r,t,i}}$; see equation (1)) multiplied by population.

GCAM-USA models 14 residential services, namely cooling, heating, cooking, lighting, water heating, clothes dryer, clothes washer, computers, dishwashers, freezers, furnace fans, refrigerators, televisions, and other energy services. Cooling and heating are classified as thermal services while the other services are considered non-thermal. Demand for building services (per unit of floorspace area) depends on heating and cooling degree days, building shell conductivity, income, and satiation levels. The model also assumes satiation levels for service demands. This is summarized in the following equation (the sub-index for each service has been omitted for overview purposes):

$$\begin{align}{d_{r,t,i}} &= {k_{r,i}} \times ({\text{D}}{{\text{D}}_{r,t}} \times { }{\eta _{r,t,i}} \times {R_{r,t}} - { }{\lambda _r}{\text{ I}}{{\text{G}}_{r,t,i}}){ }\nonumber\\&\quad\times\left[1 - \exp \left( {\frac{{ - {\text{ln}}2}}{{{\mu _{r,i}}}}{ }\frac{{{I_{r,t,i}}}}{{{P_{r,t}}}}} \right)\right]{ }\end{align} \tag{ 2 }$$

where d is the service demand per unit of floorspace area in region r, period t and quintile i, k is a calibration parameter, DD is degree days, η is the exogenous average building shell conductance (see SI, section 3.1.2), R is the exogenous average floor-to-surface ratio of buildings (fixed to 5.5), IG is the internal gain heat from other building services, λ is an exogenous scale parameter that acts upon internal gains, $\mu$ is a calibration-shape parameter ('satiation impedance'), I is the per capita income and P the price of the service. Note that for non-thermal services, $({\text{D}}{{\text{D}}_{r,t}} \times { }{\eta _{r,t,i}} \times {R_t} - { }{\lambda _r}{\text{ I}}{{\text{G}}_{r,t,i}})$ = 1. Total service demand for each region, period, and quintile (${D_{r,t,i}}$) will be calculated as service per unit of floorspace (${d_{r,t,i}}$) multiplied by total floorspace (${F_{r,t,i}}$).

The energy competition between fuels and technologies follows a logit choice model [51, 52] that prevents a winner-take-all response. So, parameters such as the fuel (endogenous) and non-fuel costs, share-weights, and the logit-exponents will have direct implications in the fuel-technology choice. The model has high-resolution details for energy services, incorporating different energy sources and/or technological options for producing each service. Additionally, the model assumes different pathways for the energy efficiency of each fuel-technology combination. Within each fuel, we explicitly model 'regular' and 'hi-efficiency' ('hi-eff') technologies where applicable. All the sector-fuel-technologies covered by the model are summarized in table S2. In terms of emissions, GCAM-USA estimates the emissions of CO₂ at state, sector, and technology level for each period.

The main methodological innovation of this study is the incorporation of income quintiles to the residential sector. Each income quintile (${Q_i})$ represents 20% of the population (fixed for all the scenarios and periods) and they are ordered from poorer (Q1) to richer (Q5). These quintiles are treated as distinct consumers in the residential energy sector and evolve over time as GCAM-USA is simulated forward and respond to income and price changes in ways defined by the demand functions discussed above. The SI (section 3.2) includes a detailed description on how these quintiles have been constructed and incorporated into the model. Finally, the calibration year of the version of the model used in this study has been updated to 2015 instead of 2010, which is the final calibration year in the default GCAM-USA version (v5.2). This upgrade enables us to more accurately calibrate our floorspace and service demand functions to recent history. Figure 1 summarizes the model structure and highlights the methodological innovations developed for this study.

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We note that GCAM-USA does not include details on the household market, so the price effect is not captured by the model. GCAM-USA is not designed to include the full representation of households, so there are some variables, such as the household members or occupancy profiles that are not captured and would have some effect on our results [53]. Likewise, our floorspace function currently does not include vintage dynamics of the building sector (e.g. age structure of buildings, and capital stock turnover). In addition, floorspace is not linked with land-use in the model, so it does not capture the potential effects on land use change emissions of shifting industrial or agricultural into residential land. Nevertheless, the effects and preferences that are not covered by the variables in the model, are captured by the calibration parameter ($\mu$), which corrects the difference between the observed and the estimated values in the final calibration year. To represent these fixed unobservable effects, this calibration parameter is kept invariant during the whole time-horizon. We note that, recent work has compared our building energy projections against a more sophisticated and detailed buildings model and found that future residential energy projections would be consistent across the models [54].

We introduce three illustrative scenarios for the U.S. that vary across assumptions about future income distributions. Our reference scenario is the 'Constant Income Distribution' scenario (hereinafter Constant), where income distributions remain constant at 2015 proportions throughout the century. We then construct the 'More Egalitarian Income Distribution' scenario (Egalitarian) in which all the states transition to the current income distribution of the most equal country in the world (Slovenia) in 2100. We note that the country with the narrowest gap across income quintiles is the one that we refer to as the most 'equal'. In this scenario, lower income quintiles become relatively wealthier while upper quintiles see a modest decrease in income share compared to the Constant scenario. Our third scenario, namely, 'More Skewed Income Distribution' (Skewed) assumes that all states transition to the current income distribution of the most unequal country in the world (South Africa) in 2100. In this scenario, only the income share of the wealthiest quintile increases relative to the Constant case, while the income shares for the four lower quintiles decrease compared to the Constant scenario. These scenarios are summarized in table 2, and more information can be found in SI (section 3.3, figure S5).

We note that the above scenarios are purely illustrative, so the transition to the egalitarian and skewed distributions is not symmetric. While actual distributions might evolve differently into the future, these scenarios are designed to be simple 'what-ifs' based on observed outcomes. In addition, we acknowledge that the income distributions in 2100 may not be bounded to today's extremes. However, given the large uncertainty in how income distributions might evolve over a century-scale timeframe, the scenarios have been designed to lie at the boundaries of what is observable.

We also note that population and average income of each state increase over time following central estimates in existing literature [37, 55, 56]. These trajectories are equal for the three analyzed scenarios. This helps us ensure that the effects across scenarios are exclusively due to changes in the income distribution. For example, we assume that population in California grows from 39 M in 2015 to 57 M in 2100. Similarly, average per capita income grows from 40 to 118 thousand dollars per person (Thous$/pers). Then, differences across scenarios are exclusively driven by share of the income allocated to each quintile during the analyzed time horizon. While the central scenarios follow the 'business-as-usual' conditions and central estimates for the socioeconomic narrative, additional scenarios which include alternative socioeconomic pathways, modeling assumptions, and the transition to a low carbon economy have been explored in a sensitivity analysis (section 3.3).

Finally, the focus of our analysis is on a century-scale timeframe. While this long-term perspective is important in the context of CO₂ emissions and power-sector investments [57], we present results for the 2050 timeframe in the SI (figures S14–S16).

Demands for per capita floorspace and residential energy services (e.g. cooling, heating, water heating, lighting, etc) increase over time in the Constant scenario in response to increasing per capita income. Considering that average income and population increase over time in all scenarios, floorspace in 2100 accounts for 38 billion square meters (billion m²) in the Constant scenario- an increase of 107% relative to 2015 (figure S7). Similarly, residential energy demand increases by 86% in the same periods, achieving around 20 EJ in 2100 (figure S8).

Changes in the income levels of different consumers (classified as income quintiles) driven by the transition to alternative income distributions entail variations in both floorspace and residential energy demands. In the Egalitarian scenario, floorspace and residential energy demands in 2100 are 11% and 10% higher compared to the Constant scenario (figure 2). This is because, as income shifts from upper to lower quintiles, the rise in demand for floorspace and energy by the lower (less satiated) quintiles is greater than the decline in demand for floorspace and energy by the upper (and more satiated) income groups. In contrast, floorspace and residential energy demands in 2100 are 15% and 19% lower in the Skewed scenario than in the Constant scenario. In the Skewed scenario, lower quintiles are relatively poorer and upper quintiles are relatively richer (compared to the Constant scenario). In fact, only the wealthiest quintile (Q5) is relatively richer in the Skewed scenario compared to the Constant scenario (figure S5). Hence, lower quintiles have lower floorspace and energy demands. Since the wealthiest quintile is already closer to satiation, the higher income in this scenario results in modest increases in floorspace and energy demands (+0.6% and +5%). Aggregated floorspace and residential energy demands in the Skewed scenario are lower than in the Constant scenario. Most of the changes in residential energy demand due to the transitions to alternative income distributions translate into changes in electricity and gas use (SI, figures S10 and S11). However, the transitions do not significantly affect the fuel composition of the residential sector—that is, the relative shares of the fuels remain almost unchanged (SI, section 4.2). These changes in floorspace and residential energy demands have little impact on aggregated system-wide CO₂ emissions.

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Substantial differences in energy demands by service exist across quintiles and scenarios. In the Constant scenario, all quintiles increase their total residential energy consumption by 2100 due to the over-time increase in population and floorspace demand (figure 3, top row). In the Egalitarian scenario, the lower quintiles increase their energy demand for all services (including thermal and non-thermal) as they become relatively richer, compared to Constant (figure 3, central row). In the Skewed scenario, consumers in the wealthiest quintile (Q5) have achieved the satiation level for thermal services (heating and cooling; figure 3, bottom row). Hence, with relatively higher income in this scenario, the demands of the wealthiest quintile for these services hardly increase (+2.3% and +1.5% respectively). However, the demand for non-thermal services (e.g. appliances, water heating, lighting, cooking, or electronic devices) increases more substantially (+8%).

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The evolution of per capita floorspace, total floorspace, and the residential energy demand have significant divergences across the U.S. states. Northern states, such as Minnesota or Vermont, have the highest per capita floorspace values in 2100 in the Constant scenario, as they have less urbanized areas and highest initial values (figure 4 top row). However, the most populated states, namely California, Texas, Florida, and New York show the highest values for absolute floorspace and residential energy demand, in base years, and in 2100.

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The impacts of alternative income distributions are heterogeneous across the U.S. In the Egalitarian scenario, per capita floorspace, floorspace, and residential energy increase throughout the U.S, compared to the Constant scenario (figure 4 central row). Most of these increases occur in Southwestern states (e.g. Nevada, New Mexico, and Arizona). These states are relatively more unequal in the base year (figure S3). Hence, the transition to a more egalitarian distribution results in higher increases in income for the lower income quintiles in these states compared to other states. In addition, the lower income quintiles in these states also have lower per capita floorspace and residential energy per unit floorspace in the base year, which implies more room for demand growth as income increases in this scenario. In the Skewed scenario, per capita floorspace, total floorspace, and residential energy decreases in all states in 2100, but the reductions are greater in the Northern states (e.g. Montana or Wyoming) which become relatively more unequal compared to the Constant scenario (figure 4 bottom row).

These changes in residential energy have some moderate impacts on total CO₂ emissions (see figure 2(C)), mostly attributable to the residential sector (associated with the consumption of primary fuels), and the power sector (as a result of changes in residential electricity demand), with additional minor effects in other sectors due to indirect equilibrium effects. At U.S. level, the increase in energy consumption associated with the transition to the Egalitarian scenario, only increases economywide CO₂ emissions by 1.8% in 2100, with different patterns across states (figure 5). Focusing on the residential sector (SI figure S12), the largest increases in residential CO₂ emissions occur in California (+10%) and Southern and Eastern states such as Florida (+12%), Delaware (+11%), and New York (+10%), in which residential energy increases are the highest. In the Skewed scenario, 2100 residential CO₂ emissions decrease relative to the Constant scenario due to lower residential energy demands. The largest reductions in the residential CO₂ occur in Northern states such as Minnesota (−27%), Wyoming (−27%), Idaho (−26%), and Colorado (−24%) where decreases in residential energy demands are the highest.

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Changes in residential energy have implications for other GHG and air pollutant emissions as well but are also concentrated in the residential sector with little impact on system-wide emissions. For example, the increase in biomass and gas use in the residential sector associated with heating or non-thermal services (e.g. water heating) in the Egalitarian scenario results in an increase in carbon monoxide (CO), nitrogen oxides (NO_x ), and non-methane volatile organic compounds emissions by 6%–7% in 2100 in the residential sector, while in the Skewed scenario, they are reduced between 15%–16% due to the reduction in residential energy (figure S13). Although the reductions are small, these changes in air pollutant emissions could have adverse implications for human health [58, 59]. Including income distribution effects in other sectors could potentially have more significant consequences (which we further elaborate upon in section 4—Discussion—later in the paper).

Furthermore, the higher electricity and energy demands result in a subsequent increase in power sector investments. In cumulative values (2020–2100), the investment needs associated with the power sector account for $3.26 trillion in the Constant scenario. The higher energy consumption in the Egalitarian scenario results in a national increase in investment needs of $0.2 trillion (+6%), over the base case. In absolute terms the highest investment increases are located in the largest states (Texas, California or Florida). However, in relative terms, the tradeoff is especially relevant in Southern states such as Florida, where investments increase around 10% compared to the Constant scenario. Conversely, the decrease in energy demand in the Skewed scenario reduces the cumulative power sector investments by around $0.5 trillion (−14%). Although the higher reductions occur in the most populated states, the largest relative reductions in power sector investments occur in Florida (−16% compared to Constant), followed by Alaska (−12%), Idaho (−12%), and New York (−11%).

To explore the robustness of our findings, we conduct a sensitivity analysis on the following key factors: future population; future Gross Domestic Product (GDP) growth; the level of satiation in floor space demand; the assumed period for the transition of income distributions from the base levels to the scenario-specific target values; system-wide deployment of non-emitting technologies; and the deployment of energy efficiency measures in the residential sector (figure 6). Specifically, we run the following sensitivity scenarios (a) higher population; (b) higher GDP growth; (c) a scenario where population and GDP are fixed at 2015 levels ('Fixed GDPpc'); (d) lower and (e) higher floor space satiation levels compared to the central assumptions; (f) a transition to the egalitarian and skewed distributions by 2050 (as opposed to 2100 which is our central assumption); (g) a transition to a low-carbon economy; and (h) alternative building shell efficiency assumptions that combine a more ambitious efficiency improvement over time with an explicit differentiation by quintile. More details on the description of these sensitivity scenarios can be found in the SI (section 3.4).

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In all of the above sensitivity cases, residential energy demand increases in the Egalitarian case and decreases in the Skewed scenario (relative to the Constant scenario)—suggesting that the qualitative insights of our analysis are robust across different assumptions even if there are some quantitative differences. For example, the lower floor space satiation level assumption [50, 60] (60 m²/person as opposed to 100 m²/person in our central assumptions)—which is indicative of a transition toward a more urban lifestyle and compares with low energy demand scenarios reported in the literature [61]—results in lower residential energy demands in all scenarios, compared to the scenarios with central assumptions (100 m²/person). Under this assumption, all quintiles are closer to their satiation levels in the base year. Hence, changes in energy demands in the Egalitarian and Skewed scenarios compared with the Constant scenario are substantially moderated. With the lower satiation level, residential energy in 2100 increases by around 2.5% and decreases by around 9% under the Egalitarian and Skewed scenarios respectively compared to the Constant scenario.