( Minus 1 ) and Energy Costs Constants : Sectorial Implications

This paper provides empirical evidence and theoretical grounds to support the existence of energy cost constants, i.e., relatively stable energy costs to income ratios, not only country-wide, but also inmajor energy end-use sectors.These ratios are similar across different countries at different stages of economic development, but they also depend on the country-specific economy structure and legacy of previous long-standing energy pricing, taxes, and subsidies policies, which it takes time to shift from.The aggregated country-wide energy costs constant (range) is a linear combination of those for sectors weighted by the contributions of respective sectors’ income indicators to either gross output or GDP. Deviation of energy costs shares from the constrained range is possible but limited. The “rule of gravitation” goes: for the whole cycle real energy prices in each sector may grow only as much as energy intensity declines, and inversely promoting energy efficiency can be viewed as a policy, of which the environmental cobenefits will be undermined by rebound effects, unless it is accompanied by rising energy prices.


Introduction
The divergence in energy prices across different countries is often associated with a comparative advantage on the presumption that higher energy prices equate to countries bearing a higher cost burden of energy provision.Bashmakov [1] formulated three general laws of energy transitions with the first one saying that, in the long-term, energy costs to income ratios are relatively stable with just a very limited sustainable fluctuation range.He discovered that energy costs to income proportions are relatively stable over decades and very similar across regions and large countries.This means, as Grubb et al. [2] showed that the gap in average energy prices among countries is reversely reflected in energy needed to produce a unit wealth with implied energy intensity to price elasticity around-1 ("minus one phenomenon"), meaning that, given time, the higher energy prices are fully offset by reduced energy intensity.Bashmakov [3] presented this phenomenon slightly differently, showing that the average energy productivity is directly proportional to average real energy price with energy productivity to energy price elasticity equal to plus one.Thus keeping energy prices low allows for only some short-term competitive gains, while in the longer term such policy conserves technological backwardness leading to competitive losses and reductions in income.To improve the competitiveness, it is more important to generate additional income through the penetration of new products and technologies, rather than keeping energy prices low.
Efforts to explore the evolution of the energy costs to income ratios in individual sectors, i.e., what is called "energy cost share" (ECS) herein, are still scarce, mainly due to the shortage of country-or region-level energy cost data [1,[4][5][6][7][8].National statistics for ECSs are better developed for housing and personal transport energy costs.ECSs can be assessed also based on KLEMS and WIOD databases [4,[6][7][8][9][10].For the purpose of verifying the results obtained from national sources, as well as from KLEMS and WIOD databases, and so as to expand the field of analysis, another dataset of energy expenditures covering OECD countries since the early 1970s was developed [11].From all those sources we explore the hypothesis of long-term constancy in energy expenditures relative to income in individual sectors advanced by Bashmakov [1].We explore patterns over time and the critical thresholds and consider theoretical interpretations and practical implications, focusing on energy intensity price

Energy Costs Constants in Major Energy
Use Sectors In addition to national statistics three international datasets were used in this study, including EU KLEMS database [10] and the World Input-Output Database (WIOD) [9].The first one provides information on intermediate energy inputs at current purchasers' prices for many OECD countries.KLEMS allows it to estimate the energy costs share in gross output (ECS go ) and the ratio of energy costs to value added (ECS va ); however, it does not include all sectors or all energy costs, as it misses out household energy uses (in private housing and by personal transport).Energy costs for each industry or sector are assessed as the sum of energy costs for "mining and quarrying" plus "total manufacturing" less energy costs from "mining and quarrying of energy producing materials" and "coke, refined petroleum and nuclear fuel" so as to avoid double counting.Time series on intermediate energy inputs in the EU KLEMS database end in 2005.
WIOD database covers more recent years, includes 35 sectors, and standardizes input-output tables for 40 countries and the world for each year of the 1995-2011 period (WIOD1).Another set of WIOD data organized as a single IOT for 35 sectors and 40 countries covers 2000-2014 (WIOD2).WIOD database provides information to estimate not only the ECS gdp , but also the ECS go .Of the 35 sectors in this dataset, 3 reflect energy supply activities: mining and quarrying; coke, refined petroleum, and nuclear fuel production; and electricity, gas, and water supply.WIOD1 provides data (time series for "supply" and "use" tables) for coal, lignite and peat, crude petroleum and natural gas, and uranium and thorium ores, as well as electricity, gas, steam, and hot water supply as intermediate energy costs items for each sector.This allows for better accounting of energy costs, as some nonenergy related inputs are removed.But this additional disaggregation is only provided by IOT rows, not by columns, and does not allow it to separate between energy-related and other activities in "mining and quarrying" and in "electricity, gas, and water supply".It does not allow it to separate nonenergy use in "chemicals, chemical products, and man-made fibers" and in "rubber and plastic products" industries either.Energy export is deducted, while energy import is taken into account.Wholesale and retail mark-ups are added.Since WIOD1 presents data (time series for "use" tables) in purchaser basic prices, all taxes are accounted for.Details of assessing ECSs based on KLEMS and WIOD data are provided in Appendix.
To explore the issues more robustly and to eliminate the costs of fuel used for nonenergy purposes, an alternative dataset on energy-related expenditures for OECD countries for 1971-2012 was used.It was built principally using data from IEA Extended Energy Balances and Energy Prices and Taxes datasets, supplemented by estimates on energy prices from proxies and external sources.End-use energy product prices were provided by the Cambridge Econometrics, although for heat and jet fuel different sources specified in the methodological annex to the Grubb et al. [11] were used (these data are originally sourced from the IEA Energy Prices and Taxes database and consist of the final price paid by the end-user per unit of final energy product consumed, including taxes (but excluding any posttax subsidies).Data points that are missing in the IEA database are "gap filled" by Cambridge Econometrics, mainly using price growth rates contained in the E3ME model, and those of proxy countries).
At the energy end-use sector i level, four factors determine the evolution of the energy costs to income ratio (ECS (in EU [6], it is called real unit energy cost)): where E i is energy consumption; PE i is energy price; I i and IR i are income aggregates in current and constant prices for sector i; PY i is price deflator; EPR i is energy productivity (reverse ratio to energy intensity); EI i is sectors' energy intensity; PER i is real price of energy.
Identity (1) shows that these four factors may be reduced to major two: energy intensity (or energy productivity) and real (deflated) energy price.In the long run, ECS i can remain stable only if an increase (decrease) in the price of energy or energy intensity is coupled with a strictly proportional decrease (increase) in the other.As such, the relationship between average annual rates of growth for these two factors must be around -1 (+1 for energy productivity).These are very long-run elasticities of energy intensity or energy productivity to real energy price.and evolution of ECSs are key to the conclusions on the competitiveness.As to the level, it substantially depends on the composition of activities presented under the aggregate "industry".In IEA energy balances, "industry" includes mining and quarrying (except fuel), manufacturing (except fuel processing and fuel used as feedstock), and construction.Studies based on WIOD datasets account for industrial energy costs differently.Astrov et al. [7] show energy costs for manufacturing including feedstock.They report ECS go growing from 3.8 to 7.5% for EU-27 in 1995-2011, from 3.4 to 9% for Japan, from 4.8 to 11.3% for the US, and from 6.2 to 8.1% for China.Horne and Reinolds [8] provide national data for Australia's manufacturing sector (growth from 4.5 to 9.8%).In an effort to avoid double count (i.e., first accounting of crude oil costs as input to refineries and then of the costs of refined products as input to end-use sectors or accounting of fuel costs for power generation and then of power supply costs for end-use sectors) while assessing end-use energy costs, Astrov et al. [7] exclude "coke, refined petroleum products, and nuclear fuels" from costs account.This brings ECS go for 2011 down to 3% for the EU-27, to 5.4% for Japan, to 2.9% for the US, and to 5.9% for China.These estimates include feedstock.Bashmakov [4] and Grubb et al. [11] account for mining and manufacturing net of energy costs related to energy sector's own needs and net of feedstock.Using WIOD1 time series for 1995-2011 in the so-called "use tables" we approximate in the best possible way end-use energy costs in manufacturing, avoid double counting of energy costs embodied in locally consumed final energy products, and exclude feedstock costs (Figure 1).The difference between a variety of concepts in assessing ECS go for industry may be illustrated for the US: ECS go for mining, manufacturing, and construction in 2011 is 10.2%, for mining and manufacturing 10.9%, and for manufacturing excluding coke, refined petroleum products, and nuclear fuels as well as feedstock 2.1%.Corresponding values for China are 6.6%, 7.2%, and 4.4% and for UK 6.7%, 9%, and 3.1%.So judgments about competiveness very much depend on selected industrial sector boundaries and energy costs accounting method and are more relevant for individual industries and (even better) products comparisons (see [6]).Studies based on WIOD1 data are limited to a sample based on the period of stable or growing energy prices, 1995-2011.To expand the time sample to have a closer look at temporal patterns of the ECSs evolution we use data from EU KLEMS and WIOD2 databases, which are less consistent with the developed concept of end-use energy costs for manufacturing.Partial overlapping of samples from different datasets for each country allows it to illustrate the similarity of temporal patterns to make more robust conclusions (Figure 1).
There is statistical evidence that manufacturing ECS go-ind fluctuates driven by energy prices and energy intensity evolutions with the sustainable range limited to 2-5%.As the quality of energy costs data improves (moving from EU KLEMS and WIOD2 to WIOD1 data to allow for more accurate end-use energy costs account), the spread between countries shrinks and better reflects actual differences stemming from the industrial sector's product and technological compositions.All datasets are quite consistent in reproducing the temporal pattern of ECS go evolution (high values for South Korea from EU KLEMS reflect the high share of nonenergy use, which in 2014 was nearly as large as industrial energy consumption and close to that for China (from WIOD2), high share of costs for other than fuel mining and quarrying activities in the total "mining and quarrying" aggregate).
WIOD data fit well with panel data for different countries.Based on the German statistics for the "production sector" Welsch and Ochsen [35] concluded that (a) in the long-term the share of energy costs in the overall costs is stable, and all changes induced by production factors substitution are mutually neutralized in the end; (b) in 1976-1994, the ECS in gross output varied between 4.2 and 6.4%.If all industries and construction are considered, then WIOD1 provides the range 3.1-5.6%for 1995-2011.Based on the data for 3,425 manufacturing companies in Italy (19,000 observations over 2000-2005), Bardazzi et al. [36] report that the ECS in gross output was in the range 3.8-6.2%.Moreover, the ECS was nearly proportional to energy intensity.WIOD1 average values for those years for all industries and construction vary between 4.7 and 6.7%.Using panel data for 6,806 Indian firms (54,962 observations over 1992-2012) Sadath and Acharya [37] show that the ECS as a fraction of sales was ranging from 3.3 to 8.7%.WIOD1 data for Indian industrial sector show that the ECS go-ind fluctuated in the range of 6.3-8% in 1995-2011.So aggregated time-series data assessed based on WIOD1 and microeconomic panel data confirm that the sustainable lanes of industrial ECS go-ind evolution are quite narrow and similar across a variety of countries and are nearly proportional to energy intensity.
Based on data provided by Fouquet [15], after labor, which is considered a standalone production factor, is excluded from the energy balance and labor costs are excluded from energy costs, the ECS for industry, agriculture, construction, and services fluctuated in the range of 5-8% in 1550-1900 and 3-5% in 1900-2010 [4].Although the accuracy of such historical estimates is debatable, similarity of current and historical ECSs for industry deserves to be further explored.
The ECS go-ind has been cyclically evolving since 1970.After the upper ECS go-ind threshold is approached or exceeded, the ECS go-ind drops, and whenever the lower threshold is crossed, this indicator, on the contrary, grows.Like a pendulum, the ratio returns to the long-term mean, fluctuating within the zone of sustainable dynamics.ECS go-ind is driven by the evolution of energy prices, mitigated by energy intensity dynamics.There are several lines of adjustment to energy price shocks: (1) rationing and acceleration of energy intensity decline, (2) reduction in real energy prices when the first line fails to completely mitigate the price shock effect, and (3) shifting energy intensive production abroad.At a fixed time, the mitigation potential is limited by maximum annual energy intensity reduction, which for developed economies stays close to 2-3% per year.A structural change towards industries with lower ECS go is activated when ECS go-ind approaches high levels, thus adding to the energy intensity decline pace [7].Both in the short-and medium-term, energy intensity decline fails to fully offset energy price shocks [7,8].But if ECS go-ind stays stable for the whole quarter to third of the century-long cycle, it means (see identity (1)) that longterm or, better, very-long-term energy intensity to real energy price elasticity is equal to -1 (minus one phenomenon), and energy productivity to energy price elasticity is equal to +1.So with sufficient time given, either energy intensity decline fully offsets energy price shocks, or real energy price is forced to decline, and ultimately it may grow only as much as energy intensity declines.Thus long-term progress in energy efficiency sets the long-term limits to real energy price growth.
For 14 studies published in 1981-2010, Adeyemi and Hunt [38] found that average price elasticity equals to -0.37 for time-series studies and to -0.46 for panel data studies.They also presented their own estimates of long-term income elasticities for 15 OECD countries for 1962-2010 ranging between 0.34 and 0.96 with 0.63 average.This does not contradict the "minus one" phenomenon.Cross-section studies generate higher energy price elasticities, than time-series studies [36,[38][39][40].Panel studies show what is closer to very-long-term price elasticity.It is also known that elasticities at a lower level of aggregation are higher and for panel data they reflect the fact that firms have had enough time to adjust to longstanding production factors price proportions.For Italian firms, Bardazzi et al. [36] showed that energy price elasticity is -1.13, which is consistent with a similar finding by Haller and Hyland [40] for Irish firms (-1.46).So very-long-term price elasticity is close to -1 for industrial companies.
If energy demand is a log linear function of income and energy price ( =  ×    ×    ), its average annual growth rates (T e ) can be presented as   =  ×   +  ×   , where T y and T p -are average annual income and real energy price growth rates correspondingly.Energy intensity to energy price elasticity (c=T e /y /T p , or average annual growth (decline) rate of energy intensity/average annual growth rate of energy price) is a function of energy demand price elasticity (b, or average annual growth (decline) rate of energy demand/average annual growth rate of energy price) corrected for income elasticity (a) and for the ratio of average annual income growth rates to average annual real energy price growth rates:  [9], and World Bank, 2017 [12].
Depending on the ECS go-ind position relative to the upper and lower thresholds (see Figure 2(b)) neither a nor b is constant either; they are drifting.Based on the data for Danish industrial companies, Bjorner et al. [41] proved that the higher the ECS go-ind (and so the energy intensity), the higher the energy price elasticity.When energy prices grow faster than income, the ECS increase, and so b drifts up and vice versa (see [4] for more detail) (empirical literature on asymmetric price reactions explains the asymmetry effect through the uneven technological and behavioral change under different energy prices regimes; through different customer reactions to different components of energy prices [38]; through risk aversion of human nature [42]; and through purchasing power thresholds, which drive uneven technological and behavioral change and affect economic activity [1,43].All of these factors may be important, and there is no agreement about the causality of asymmetric price reactions).Therefore, evolution of a and b, along with the relationship between T y and T p for high ECS (  =   −   , see below) and instability of the T y /T p ratio, all give momentum to the elasticity of energy intensity to real energy price making its long-term (cycle-long) stability at "minus one" amazing.If the cycle-long time frame is taken, then empirically the T y /T p ratio is 1.5-2.5, and with b=-0.2. ..-0.66 c= -1 for the cycle duration if the income elasticity is 0.5-0.9, with most probable range of 0.7-0.8, which quite matches empirical estimates.So there is no contradiction between empirically estimated limited short-and medium-term energy demand price elasticities and cycle-long "-1" energy intensity to energy price elasticity.
ECS va-ind (which is not a share in purely economic terms, but rather the ratio of energy costs to value added) stays mostly in the range of 6-20%, as in different countries value added in the industry forms about 20-37% of industrial gross output depending on the structure of the industrial sector and relative costs of production factors.ECS va-ind reaches high values for India and Russia, 28 and 35%, respectively (for Russia it is due to high value of ECS go-ind (7.6-10.6% in 1995-2011) and for India due to both relatively high ECS go-ind (6.3-8% in 1995-2011) and low share of value added in industrial gross output (21.6-23.2%)).Assessed ECS va-ind are in line with 4-10% estimates made by authors based on the dataset developed by Grubb et al. [11] (estimated as energy costs for end-use in industry (as defined by IEA balances) divided by industrial value added as reported by WDI database.For such estimates correction up is needed as WDI industrial value added incorporates the mining component as well as coke, refined petroleum products and nuclear fuels and also electricity, gas and water supply components, thus the denominator of the ratio is overestimated).
The question is why does ECS go-ind gravitate?When ECS go-ind grows by 1 percent point, other things equal, the value added declines by 1%/VAS go-ind and vice versa.WIOD1 data allow to estimate VAS go-ind for manufacturing (within the boundaries for which ECS go-ind was estimated) in the range of 20-37%.For each ECS go-ind 's additional percent point VAS go -in declines by 2.7-5% (see Figure 2) (this is an obvious result of a simple calculation: when base ratio of value added to gross output is 20-37%, then adding 1 percent point to energy costs (and thus to the intermediate product) reduces the share of value added in gross output by 1 percent point, or to 1%/(20-37%) related to the base level of value added share) depressing demand for consumer goods and services (when the labor cost part of VAS go-ind declines) and investment demand (when the capital part of VAS go-ind declines).In order to compensate for VAS go-ind declines and to keep industrial value added at a constant level, it needs to grow on average at least by If VAS 0 =37%, k=2.7-5, and T=3, then T va =2.5-5.1%=(1.08. ..1.16) (1/3) -1=(37%/(37%-2.7. ..5%)) (1/3) -1).For VAS 0 = 20%, T va should fall in the range 5-10%.Such compensation may be unfeasible within a limited time frame (T).If so, value added (in real prices) may temporarily decline.In case ECS go-ind grows quite slowly, the steady VAS go-ind decline means that final demand (for consumer and investment goods) continuously lags behind gross output growth.Such situation may be only temporarily sustainable as long as demand for industrial goods is driven by external demand (export) followed by stagnation originated from loss in competiveness due to total factor productivity decline.So every additional percent point of ECS go-ind is equivalent to 2.7-5% loss in the share of value added and needs at least 2.5-10% annual growth to avoid a decline in industrial real value added.This is a much bolder, than limited to 2-5% the ECS go-ind , illustration of the real importance of ECS go-ind evolution for economic growth.When ECS go-ind goes too high and energy becomes less affordable, it depresses demand for goods and services and both industry and economy slow down, since nearly half of industrial intermediate product comes from agriculture, construction, transport, and services.This, in turn, negatively affects demand for industrial products and leads to capacity load reduction.When the limits to purchasing power are approached and the threshold is exceeded, all this (supplemented by accelerated energy efficiency technologies penetration and structural shifts towards less energy intensive industries) marks a situation where further 1% energy price growth leads to more than 1% reduction in energy demand.Energy costs stop growing; ECS go-ind peaks and then reverses to the center of "gravitation".Every additional 1% in energy price growth, if not fully compensated via energy intensity decline, is compensated by declining energy demand, as previous levels of energy use are no longer affordable for many customers, and so additional price increase generates no additional revenue to suppliers.This sets the limit to monopoly pricing [44].Average annual growth rates of energy sales (T esales ) can be presented as   =   +   and   =   +   −   , thus   =   −  .When maximum energy sales are reached, then   =   +   = 0, or   = −  .At this moment   is close to zero and so   ≈   ≈ 0. Therefore, local maximums for energy costs and those for ECS are reached at nearly the same time.After an ascending trajectory, ECS first stops and then starts to decline with both real energy price and energy intensity reductions contributing to the ECS downhill path.In other words, real energy sales demonstrate "stop, reverse, and go" dynamics.After the "stop and reverse" part of the real energy sales' trajectory pattern is over (it takes 5 to 6 years), energy sales then keep relatively stable at a new equilibrium level, which is below local maximum, while ECS keeps declining, as nearly fixed energy costs are divided by growing industrial output.
On the contrary, when ECS go-ind goes too low, demand for goods and services accelerates and gives momentum to economic growth.When ECS go -in declines by 1%, the VAS go -in grow by 2.7-5%, and even with moderate gross output growth (3%) it will escalate demand for labor and capital by 12-20%.Meeting this demand results in additional energy demand.When supply fails to meet growing demand from low energy cost resources, energy prices start growing and drive ECS go -in up from the approached bottom back to the center of "gravitation".
Figure 2(b) presents "wing" functions for industry for several countries.Obviously, the relationship between the ECS and industrial value added growth (T ind-va ) is complex (economic crises are driven not only by ECS growth) but generally appears as shown in a stylized "wing function" (dash lines in Figure 2(b)).For all countries trend lines show a negative slope between the ECS go -in and T ind-va (1 year lag).The existence of this relationship cannot be judged simply based on the whole sample R 2 .First, because there are many factors driving T ind-va , including total factors' productivity ("dark matter" of economic growth), which is very difficult to model due to the complexity of impacts, secondly, because the relationship is nonlinear by nature and needs different functional forms for separate ECS go -in intervals, and thirdly, because data quality on ECSs still needs much improvement.If a few dots are removed from the plot, those for negative T ind-va coupled with moderate ECS go-ind , where crisis was generated by other factors, as well as a few high points (some of them showing the rebound effect, growth from the low base after deep T ind-va decline), then the stylized "wing" function will be manifested even better.The whole point is the range for TFP contribution to the economic growth declines and shrinks, as very costly energy requires that some resources be reallocated from acquisition of other production factors, thus reducing their contribution to TFP.King [32] illustrated this for TFP based on data for 44 countries.Until the ECS reaches its upper critical threshold, it is all the other production factors that determine T ind-va , while energy is affordable and thus does not perform the "growth limiting" function, with just a minor slowing effect in place.As soon as ECS go-ind goes beyond this threshold, it becomes the dominant factor.A thick line in Figure 2(b) shows aggregated relationship between averages for both T indva-1 and ECSs across 11 countries with data sample clustered in four ranges by ECSs values: 1-2%, 2-3%, 3-4%, and 4-5%.When average ECS go-ind grows from 1.7% to 3.3%, T indva-1 declines from 3.4% to 0.6%.So k=-1.8, or per each additional ECS go-ind percent point the value added growth rate in the manufacturing sector declines by 1.8%.Beyond the upper threshold (when average for countries ECS go-ind exceeds 3.3%) the depressing effect of additional ECS 1 percent point scales up to k=-7.7.So empirical data show that economic growth in the industrial sector is quite sensitive to ECS go-ind 's escalation with very low chances of keeping it positive after ECS go-ind has exceeded 3.5-4%.The "wing" function range (between the dashed lines) is continuously shrinking, as the threshold is left further  and further behind, forcing energy demand to decline and completely blocking the impacts of all other factors that can promote economic growth.Thresholds are not the same for different countries depending on their economies' structure and its sensitivity to energy costs growth.

2.3.
Agriculture.WIOD database allows it to estimate energy costs shares in agriculture, hunting, forestry, and fishing (below called agriculture) in gross output (ECS go-agr ) and in value added (ECS va-agr ).In many countries, the share of agriculture in gross output and value added varies in the range of 2-3% (10% of value added and 5.7% of gross output in China).The bigger the part of agriculture, the lower the level of mechanization, and the lower both ECS go-agr and ECS va-agr (energy costs for agriculture, as specified in this paper, do not account for fodder.Agricultural labor is considered a standalone production factor).
As liquid fuel dominates in the energy mix in agriculture, the ECSs are very sensitive to the prices of petroleum products.For developed countries, ECS go-agr grew from 3-5% in 1995 to 5.5-7.5% in 2011, and for Mexico ECS go-agr grew from 2.3% in 1995 to 4% in 2011, while for China it was relatively stable in the range of 1.3-2.1%.ECS va-agr for developed countries grew up from 4-9% in 1995 to 9-18% in 2011, for Mexico from 4% in 1995 to 7% in 2011, and for China it was in the range of 2.4-3.7% for the whole period.
Countries for which WIOD and KLEMS provide consistent data show growing (UK, Italy), stable (US, Canada and France), or declining (Germany) trends for ECS go-agr in 1970-2011.Alternative data sources for ECSs estimation are limited.Available IEA data for energy use and energy price in the agricultural sector are not really consistent or reliable.Thus data quality improvement is needed before more robust conclusions on regularities of ECSs evolution in agriculture can be formulated.

Services.
Data sources that were used to estimate energy costs shares in gross output for services are the same as those used for industry.Energy cost share in services (ECS go-ser ) also shows a cyclical gravitation around relatively stable levels with the range shrinking to 1-3% as data quality improves (Figure 3).The differences between the countries are not so much affected by competition, as many services are only traded domestically.The fluctuation amplitude is smaller compared to industry, making the evolution of the economywide ECS go-ser more stable and the shift towards the service economy becomes a converging factor across countries for economy-wide ECS evolution.
The services sector has (a) a higher value added to gross output ratio (over 50%) compared to industry and (b) lower ECS go .Thus ECS va-ser for many countries stays in the range 2.5-5.5%, which is below that for industry (6-20%) (producing alternative estimates using Grubb et al. [11] dataset is difficult, as WDI data on value added in services include transport.If nevertheless these data are used as denominator, and IEA data on energy use in the commercial sector are used as nominator, then for most countries ECS va-ser can be assessed in the range 1-3%).In their detailed study on the determinants of energy intensity in the service sector (split by subsectors) in 1980-2005 Mulder et al. [45] provided a number of important findings: (a) the shift towards a service economy has contributed to lower overall energy intensity in the OECD (IEA [46] reports that the creation of one unit of value added in the manufacturing sector requires 4 to 22 times as much final energy input, as in the service sector), but this contribution would have been considerably larger, if the service sector had realized the same degree of energy efficiency improvements as the manufacturing sector; (b) in most OECD countries energy intensity levels in the service sector tend to decrease relatively slowly after 1995 (it was true for most OECD countries in (c) deployment of information and communication technologies contributed to energy intensity growth in the service sector, while energy prices played a limited role in driving variations in energy productivity.The (b) and (c) are related: the energy distribution costs component in the energy prices for the services sector is much higher compared to industry, and so driven by fuel prices average energy price growth rate is lower.Therefore, the energy intensity improvement effect, inspired by price change, is lower too.With a switch from energy intensity to ECS go-ser based on WIOD1 data, this list of stylized facts for the service sector can be supplemented with the following: (a) ECS go-ser for every services subsector differ much across countries reflecting gaps in both energy intensities and energy prices; (b) if averages by subsectors (across countries plotted in Figure 4) are taken, than retail trade have the highest ECS go-ser (3%), followed by hotels and restaurants (2.8%), wholesale trade and public administration, defense and compulsory social security (2.4% each), sale, maintenance and repair of motor vehicles and motorcycles, and retail sale of fuel as well as post and telecommunications (2.3% each); financial intermediation (0.9%) and real estate activities (0.6%) have the lowest ECS go-ser ; (c) the contribution of subsector-specific ECS go-ser change, on the one hand, and structural change within the service sector, on the other, to overall ECS go-ser evolution in 1995-2011 was quite different across countries with subsectorspecific ECS go-ser fully dominated in determining aggregated services sector's ECS go (contribution over 80%) in France, India, US, Japan, and Canada; ranging from 50 to 66% in Italy, Korea, and Germany, but lost to structural effect for the UK and China; (d) in the very long-term, there is "minus one" phenomenon (energy intensity decline rates are equal to, and so put the limits to, real energy price growth in the service sector. When ECS go-ser grows by 1 percent point, the value added share in services gross output (VAS go-ser ) declines by 2.5-7%, thus depressing demand for consumer goods and services (services dominate in the intermediate product of the services sector).In contrast to industry, the whole cycle-long range of ECS go-ser evolution (from bottom to top) is limited to 1 percent point.To avoid a decline in the services value added (with additional 1 percent point of ECS go-ser ), the services value added has to grow by 3-16% (50. ..70%/(50. ..70%-2.5. ..7%)), with a median close to 5%.As it takes more than a decade for ECS go-ser to grow by additional 1 percent point from bottom to top of the cyclical trajectory, average rates of services value added growth have to be at least over 0,5% per year, if the service sector's value added is to keep growing.Therefore, a depressing effect of ECS go-ser on the economic growth does exist.It is smaller compared to industry, but, coupled with the latter, becomes stronger across the whole economy.

Transport.
Transport energy costs are split by two aggregates for commercial (freight and public) transport and personal transport.To estimate ECSs for the first one (ECS go -com-tr ), both WIOD and KLEMS datasets provide energy costs, gross output, and value added.Data on ECS per-tr are available from national and international statistics on personal expenditures ( [14,19], among many).Grubb et al. [11] provide energy cost data for the whole transport sector, which may be used only to estimate transport ECSs in total gross output or GDP.
In terms of commercial transport, all countries can be split into two groups: (1) with ECS go -com-tr fluctuating in the range 4-10% and (2) the one for which ECS go ranges between 10 and 24% (Figure 5).Energy products and manufactured  energy intense goods form a large part of the freight cargo making the freight turnover per unit of GDP or gross output much higher for countries with a heavier economy structure.ECS go -com-tr follows liquid fuel prices, and the second group is much more vulnerable to energy prices shocks.These two groups have different "centers of gravitation".Based on presented data (which could benefit from quality improvement), it seems that both "centers of gravitation" are relatively stable in time.
Empirically, for each ECS go -com-tr additional percent point, the value added share in gross output (VAS go-comtr ) declines by 0.2-4.6%(Figure 6).VAS go -com-tr ranges between 37 and 63%.Through the whole cycle, the ECS go -com-tr may vary as much as 1-13% (for many countries it is limited to 3-4%).Therefore, to avoid an absolute decline in commercial transport value added driven by ECS go -com-tr increment by 1 percent point in 3 years, gross output has to grow by about 0.1-4.5% per year, whereas in order to compensate 4 percent points ECS go -com-tr increment, it has to escalate annually by 0.7-25.8%.If fuel prices skyrocket, there could be not enough time left for such compensation, and commercial transport value added may decline.Parallel reduction of demand for transport work from industry and services depress the commercial transport value added even further.
The share of personal transport energy costs in personal incomes (Figure 7) has also been cyclically moving for more than half a century in many countries, where personal automobile transport penetrated early (over 85 years in the U.S.), mostly staying in the narrow range between 2 and 3% of personal income before tax.For the UK, the ECS per-tr is shown related to consumer expenditure, which is about 75-80% of private income.If for the UK the ECS per-tr is shown  related to income, it will shift down by approximately 0.6-0.8% and move to the 2-3% range.For countries with initially low personal cars saturation rate, the ECS per-tr keeps growing to the 2-3% range and only then stabilizes.For the US, the average ECS per-tr has been 2.4% for nearly 90 years (1929-2017) and serves as the "center of gravitation".This means that very long-term energy intensity to price elasticity is -1, while Brons et al. [39] found mean short-term price elasticity of -0.34 and long-term elasticity of -0.84 in their meta-analysis Figure 7: Personal transport energy costs shares for different countries.Sources: updated from Bashmakov [4] and Bashmakov and Grubb [5] using the Economic Report of the President 1982-2015; data from Timmer et al. [9]; Fouquet [13]; and national statistics.for gasoline demand, which can be taken as representative for the automobile transport.Globally, IEA [47] assessed the ECS per-tr at 2.1% of disposable income in 2015 and expects it to vary in a narrow range of 1.7-2.1% by 2040.As the global level of personal automobile transport saturation is, and until 2040 will be, lower than that in the US, both the global level of ECS per-tr and its stability are quite consistent with historical data for the US and other countries as plotted in Figure 7.
Mechanism of ECS per-tr "gravitation" and its impact on the economic growth is different compared to the business activities discussed above.Reallocation of consumer expenditures towards fuel for personal vehicles reduces demand for other (mostly durable) goods and services.It can be illustrated based on the 1959-2017 US data on new motor vehicles purchase.Deviations from the trend for ECS per-tr and for the share of income spent on new motor vehicles are evolving in reversed phases (Figure 8(a)).There is a "wing" function showing that when deviations of ECS per-tr from the trend exceed 0.5%, the share of income spent on new motor vehicles goes below the trend-line.Whenever ECS per-tr stays more than 0.5% below the trend, the share of income spent on new motor vehicles never stays much below the trend (not more than 0.2%).So when the upper threshold (2.4% plus 0.5%) for the ECS per-tr is exceeded, the dynamics for new automobiles demand lags behind income.When income stagnates, demand for new automobiles declines absolutely, slowing down metallurgy, rubber and plastics production, and trade, and the slowdown effects spread throughout the economy.When ECS per-tr is below the lower threshold (2.4% minus 0.5%), demand for new cars grows about as much as income, or even faster, providing additional impulse for economic growth.When ECS per-tr stays between the two thresholds, the relationship is much less certain, and other factors determine the rate of new motor vehicles purchase.
2.6.Residential.Stability of the residential energy cost to GDP, or to personal income before tax, ratio deserves a special attention.In contrast to other end-use sectors for which historical data are available only for decades, time sample for residential sector is much longer.Fouquet [15] shows that in 1500-2000 the residential energy cost to GDP ratio in the UK (for heating, cooking, and lighting) was fluctuating around 2-3%.If personal income is assumed at about two-thirds of GDP, it translates into 3-5% of personal income before tax.The first part represents estimates available from some studies for 1500-1870, the second one represents statistical data since 1929 onwards.Index inc reflects the ECS for residential sector in income before tax, while index exp reflects the ECS in personal consumption expenditures.Sources: Fouquet [15]; Fouquet [13]; Timmer et al. [9] and Timmer et al. [10]; Government of India [16,17]; Statistics Bureau of Japan [18]; ONS UK [19]; INSEE [20]; NrCAN [21]; OECD [22]; Rosstat [23]; NBS China [24]; Economic Report of the President, 1982-2015 [25].
Citing historic studies, Fouquet [13] shows that (a) in the UK in the 1790s consumers spent about 5% of their budget on fuel; (b) E. Engel estimated that Belgian workmen in the 1850s spent 5% of the total budget on fuel and light irrespective of their income levels (this study did not include upper-income classes); (c) C. Wright [48] found that in 1870 Massachusetts households spent a virtually constant share of incomes on fuel and light (6%) and proposed Engel's Third Law: "The percentage of outlay. ..for fuel and light is invariably the same, whatever the income" (see [49]).For country totals, this share should be closer to Fouquet's (3-5%) estimate, as rural and richer population spends smaller shares of their incomes on energy for housing.More recent cross-country comparisons of the share of housing costs in personal incomes before tax (ECS hous-inc ) show that (a) it is relatively stable not only over the recent decades, but over centuries as well, and (b) it is quite similar across different countries at very different stages of their economic development [1,4].The ECS hous-inc in Japan fluctuated around 3.2% for 68 years; in the U.S. around 2.5% for 89 years (with a slow declining trend); in India around 3.4% for 52 years; in China around 4.3% in 1995-2015 (in 1990, the share of housing and communal services (H&CS) (excl.rent) in urban families' income was 4%.Assuming that energy costs amount to half of H&CS costs results in about 2% share of energy costs) (for urban households only, which is higher than for rural households; and including water supply and sewage costs, which enlarges this share by about 0.5-1%); in the UK around 4% for about five centuries (since 1929, the share in personal expenditures is shown, which would be about 0.6-1% lower when compared to income before tax); in Russia at around 2.2% in 1960-2016, but 3.1% in 1995-2016 after transition to the market economy; in France at around 3.1% for over 63 years (Figure 9).Relative stability of ECS hous over decades and centuries is a clear confirmation that the upper and lower thresholds exist.For all countries, irrespective of the stage, model, or pattern of economic development (which had been changing a lot over decades and differs widely across countries), the sustainable fluctuation range of ECS hous-inc is very narrow.When corrected for comparable indicators (only the share of energy costs in income before tax) for the above countries the average ECS hous-inc stays in a quite narrow range of 2.5-3.5% (this range is correlated with, and causally related to, the living space to income ratio in individual countries).Calculations based on IEA datasets on energy use and energy prices in the housing sector [11] and data on private consumption (from WDI database) allow for very similar estimates with ECS hous-exp staying mostly in the 2-3.5% range.Globally, IEA's [47] assessment is 2.3% of disposable income in 2015 to stay in the range 2.1-2.4% till 2040 (for some countries (Japan, Mexico), the ECS hous-exp assessed using IEA datasets provides lower ECSs compared to the ones assessed based on national or OECDstat data.That is the reason for slightly lower IEA global ECS hous estimate for 2015).
On centuries-long and decadal scales, small declining slopes are visible for some countries.Presently, sustainable lanes for ECS hous-inc are in the 2.5-3.5% ranges.Back in 1790-1870, they used to be about 3-6% declining on average by about 0.25-1.3%per 100 years or by 0.003-0.013%per year.However, this declining trend does not manifest in all countries: in Australia, France, China, and Russia the trend is either flat or growing.In many former planned economies and China, which had been blocking market mechanisms for decades using command and control instruments (see the low share of energy costs in Russia in the 1960-1980s and in China in 1990), the established income/living space balance (see below) was destroyed during the transition periods.This forced households to spend a relatively large share of their income (compared to mature market economies) to pay their energy bills in inefficient buildings purchasing resources at much higher prices, than during the communist era.Until a new balance is established, the low income part of the society has to do with a large share of energy costs and to sacrifice either the payment discipline or indoor comfort.Therefore, for these countries the ECS hous-inc first goes up, peaks, and only then starts declining.In Russia and China, the peaks are already approached.
Going beyond the upper threshold, or staying much below the lower one, is possible, but only for a short period of time.The existence of these thresholds and the market inertia generate consumer reactions overshooting in either direction and finally determine the cyclic nature of the ECS hous-inc dynamics.The rate of households' savings in most developed countries is limited to 10% of personal incomes (with the average close to 5%), and in many countries it is negative (https://data.oecd.org/hha/household-savings.htm#indicatorchart). Fluctuation of ECS hous-inc in the range of ±0.5% means an opposite evolution of savings' rate by about 10% of its base value (0.5%/5%).Stepping over the upper threshold of the ECS hous-inc brings down the demand for furnishings and durable household equipment (Figure 10).The "wing" function for the US shows: the further the ECS hous-inc deviates up from the linear trend in excess of 0.4%, the lower the share of income spent on furnishings and durable household equipment comes down below the trend.This relationship is even stronger for UK.So demand for consumer goods is adversely affected, and this impulse spreads throughout the whole economy via production chains and time lags.
Distributions presented in Figure 11 challenge Engel's Third Law.The declining ECS hous-inc trend observed for some countries is partly determined by the sliding down of ECS hous-inc as the income grows (Figure 11).It is important to consider the share of energy costs in income, not in consumer expenditures, because all housing welfare programs are based on the ECS hous-inc either before tax or disposable.The "energy costs cross" is an intersection of per capita housing energy costs and the ECS hous-inc .While this "cross" looks quite similar across the four countries shown in Figure 11, there are important specific features for each country reflecting income and energy costs distribution curves by income deciles.Elasticity of the ECS hous-inc to income is negative.For the richest group, this ratio is as low as 2-3%, while for the poorest group it may approach, or even exceed, 10%.The ratio of low income households' ECS hous-inc to the average ECS hous-inc in the four countries is close to 2:1 varying from 1.5:1 to 3:1.In UK (if calculated as a share of expenditures) it was stable for over two centuries: 7.8% for the first decile versus 4.4% average in 2011 [26] and 8% versus 4%, respectively, back in 1790.
The "cross" is shaped by the interaction of income and living space distribution curves.The latter is a function of income, but with a positive intersection meaning that people with very low incomes are provided with minimum social housing:   =  min + Δ  +   , where LS y is average per capita living space for those with income level Y; LS min is minimal per capita social housing space standard; ΔLS cp is living space that was provided in former centrally planned economies irrespective of income in excess to minimal standards; Y is per capita income.Cross-country and incountry dynamic regressions show that living space elasticity of income is below unity and stays close to 0.5-0.7.Therefore, as income grows, per capita living space to income ratio declines.The larger LS min +ΔLS cp , the slower it declines, same as ECS hous-inc driven thereby.In former centrally planned economies income had little or no observable effect on the distribution of housing space (see [50] study for Russia).So the function of living space distribution by income had been flat for decades and never showed any change until after transition to the market economy was launched; yet it still reflects the legacy of centrally planned housing policy (in 2013, in Russia income disparity exacerbated compared to the Soviet era: the income of the eighth decile income group was about 5 times higher, than that of the first one, but the gap in per capita living space was still small: just 1.5.In other words, in the former centrally planned economies the balance between income and the living space in possession was destroyed, and after the transition started, energy costs to income ratios skyrocketed making many poor unable to pay their energy bills.As the economy develops, the balance between incomes and acquired living space is being slowly reestablished.Yet there is still a long way to go.Until this balance is reestablished, the average share of energy costs in income will stay relatively high for transition economies).
Affordability means spending money on certain goods and services without sacrificing other needs, i.e., at no impact on the well-being.Affordability is a function of utility and quantity of goods and services needed, price, income, and consumption pattern.There are basic, life-sustaining goods and services.A household has to have some minimal level of housing and communal services, which it cannot refuse.However, as the income is limited, only a part of it can be allocated for paying housing and communal bills.Therefore, there is always an upper energy cost limit, beyond which a household cannot afford housing services for the high utility of other basic needs.Evaluations of energy affordability need to take account of many factors, such as living and heated space (a low income family may heat only one room and to a temperature below the comfort level); amount of energy needed to provide a required minimum comfort level (energy efficiency of housing); limits to possible substitution of various energy carriers; energy prices; income levels and income distribution; consumption patterns and consumers' behavior; welfare programs.This list may be further developed to include population age and employment structure, composition of households, dwelling ownership structure,   [14] and ONS UK [19].combination of rural and urban population, availability of network energy (electricity, pipeline gas, district heating).
There are two direct affordability thresholds for housing energy costs that account for income disparity [51,52]: (i) The first threshold is a 3-5% ECS hous-inc or 4-7% energy costs share in consumer expenditures.If this threshold is exceeded, the payment discipline, or adequate energy consumption, declines, and the further it goes beyond 3-4%, the lower the payment discipline, or the comfort level of services drops to, or below, the survival level.(ii) The second threshold is the marginal ECS hous-inc for the poorest group of households.When it exceeds 7-10% (9-13% of consumer expenditures with no account of support provided for the "energy poor"), no measures, no matter how severe, can raise the energy payment collection rate, or energy services may be only provided at, or below, the survival level.This second threshold is a key for designing welfare programs for the energy poor (until recently, in the UK households were considered to be in "fuel poverty" if they had to spend more than 10% of their disposable household income (before deducting taxes but including housing benefit and income support for mortgage interest in income) on fuel to keep their home in a "satisfactory" condition (for heating, this means 21 ∘ C in the main living area and 18 European Commission [53] came to very similar conclusions: (a) the share of households that face a significant burden by settling their energy bills might be better approximated based on the average national spending ratio, than as a universal threshold at the EU level; (b) a twice higher, than the national average, ECS hous-inc is a better energy poverty indicator.They Figure 11: Distribution of energy expenditures and energy costs share ("energy costs share and income cross") by income deciles in four countries.Note: data for Japan, Russia, and China show the shares of energy costs in incomes that make eligible for support for the energy poor.2005 data for UK show the energy cost share for households that do not receive support.For the first two deciles the share of energy costs in income is approximately 2% higher than for those who get support.This pattern for the UK is expected to keep stable until 2020.Sources: Palmer and Cooper, 2013 [26]; Druckman and Jackson, 2008 [27]; Statistics Bureau of Japan, 2015 [28]; China Statistical Yearbook 2013 [29]; Rosstat [23]; Belfield et al., 2014 [30].
found that approximately 65 million people, or 13% of all EU-27 households, spend at least a twice larger share of their income on energy, than the national average.Two indirect energy affordability (or energy poverty) indicators can be used [51,52]: (a) payment discipline, particularly (but not exclusively) in locations where network suppliers cannot stop supply to those who do not pay; and (b) underconsumption when households cannot afford paying as much as is required to ensure sanitary and comfort conditions in their homes (one housing affordability indicator is the housing cost overburden rate, showing the share of population living in households that spend 40% or more of the household disposable income on housing.At the EU-28 level, the housing cost overburden rate was about 11% in 2012.However, in addition to energy costs this indicator includes other large components, such as real and imputed rents, housing operation and maintenance costs, as well as water supply costs (Eurostat [54])).The latter indicator is more difficult to document and aggregate and is mostly evaluated based on consumer satisfaction surveys, while the first one is statistically reported.However, while dealing with the first indicator, it is important to distinguish between low income and other debtors.The European Commission [53] supported the idea of using the share of households that experience utility payment difficulties (share of population that has been in arrears with energy bills payments in the last 12 months) as an energy poverty indicator and assessed that 8% (nearly the whole decile) of the EU-27 population in 2008 belonged to this category.The same indicators are used by the Buildings Performance Institute Europe [55].
When the ECS hous-inc reaches or exceeds 3-5%, the collection rate or indoor comfort drops, and if this ratio stays above this threshold for a long time, the collection rate/indoor comfort will not improve again.The first threshold is the upper limit of sustainable evolution of the ECS hous-inc in time, while the second threshold limits the upper deviation of the ECS hous-inc cycling trajectory from the trend.
Bashmakov [1,51] described the ability to keep homes adequately warm, or percentage of the population living in households in arrears, as a "wing" function of the share of energy costs in income.For lower ECS hous-inc , both these indicators are determined by other factors, such as housing energy efficiency, strictness of payments collection, etc.But as the share approaches the first threshold, the range of impacts provided by other factors shrinks and the share of those with adequately warm homes and in no arrears on energy bills declines.As the average ECS hous-inc reaches the second threshold, the gap between the upper and the lower boundaries of the "wing" shrinks to a very narrow zone, and comfort and the payment discipline decline faster.When the second threshold is approached, energy demand or payment discipline elasticity to the ECS hous-inc exceeds -1 in absolute values.Further price growth by 1% does not generate any additional revenues for energy supplier (beyond the absolute upper limit of purchasing power).Either demand or collection rate declines by 1% at best (or even more, if there are substitution options), and further tariff growth only induces indebtedness or revenue losses.If the affordability thresholds are exceeded, even welfare programs fail to completely address the low collection rate problem.Demand for housing energy peaks, while demand for other goods and services shrinks, as a larger part of income is spent for energy.So approaching the upper thresholds contributes to economic stagnation.
Why is the first threshold relatively stable over centuries?The answer is rooted in the relationship between the income, living space and energy use per living space.Average annual rate of the ECS hous-inc change is the sum of average rates of real energy prices evolution, specific energy use per unit of living space and the living space per income ratio.The first component grows by about 1-1.5% per year in the long-term [11,26].The second one is negative, as specific energy consumption steadily declines by about 1% per year.If the income elasticity of living space is about 0.5, and average per capita income growth is 0.5-1% per year, then the third component declines by 0.25-0.5% per year.Thus the balance varies from a small decline to a small increase, keeping the ECS hous-inc relatively stable in the long run.As income grows, the ECS hous-inc drifts down (Figure 11), while energy cost distribution drifts upwards (following improving living conditions and resulting energy costs growth) preventing the average ECS hous-inc from decline.As a result, "center of gravitation", the intersection of the "energy costs cross", stays relatively stable.In countries with a changing balance between living space and income (former centrally planned economies or countries with new aggressive social housing programs) a steady shift to a new center of ECS hous-inc fluctuations may be observed driven by a change in the relative impacts provided by the above three components.
Why is the second threshold stable and about twice larger than the first one?The answer is rooted in the analysis of income distributions.The ECS hous-inc for the low income group to the average value is where PE is the price of energy; e is specific energy consumption per unit of living space; LS min is living space for the low income group; Y is personal income; n is the income/living space elasticity coefficient; m is constant in living space to income function; s is the ratio of average income to low income; l and av are indices of low income/average group parameters.
With purely income-based floor space distribution (with no social housing) (LS min =0), the ECSR is s (1-n) multiplied by prices and energy intensities adjustment ratios.With flat housing space distribution function (m=0, or n=0), ECSR equals s adjusted for prices and energy intensities.There is an income inequality metric, P50/P10 ratio (P50/P10 is the ratio of the median deciles' disposable income to the upper bound value of disposable income of those in the lowest decile.OECD [22], Income inequality (indicator).doi: 10.1787/459aa7f1-en).This ratio is quite stable in time, and the at-risk-of-poverty rate related to it.For most countries, it stays at 1.8-3 (OECD database).For such income distributions s=Yav/Y10≥P50/P10 with the former close to 4 (3)(4)(5).No country has a perfectly flat living space by income distribution, and many countries have some minimum social housing.With n=0.5-0.7,s (1-n) is close to 2 (1.7-2.3) for no social housing (as a rule, the higher the Yav/Y10 ratio, the higher the living space to income elasticity).For equal living space distribution, income gap (s) should be smaller for all income levels.If it is twice as low as for developed market economies, then s is close to 2. Therefore, ECSR stays close to 2 corrected by relative prices and energy intensities.Cleaner, easier-to-handle, and so more expensive energy carriers are rather used by richer households.Average energy prices tend to be higher for them, than for their low income counterparts, but this difference is offset by lower energy use per unit of living space.Low income households can afford only relatively low-quality cheap energy, but they are not so energy efficient, as their higher-income counterparts.Vringer et al. [56] showed that, while households with high energy consumption require 50% more (high income) and 100% more (low income) energy, than households with low energy consumption with similar incomes, average energy costs difference within the income groups is limited to 4%.This is exactly what the "minus one" phenomenon should deliver.So energy prices and energy intensities adjustment multiplier stays close to unity.The result is that both average ECS hous-inc and its upper variation thresholds are nearly stable on the decadal and century scale.Therefore, given sufficient time, real energy prices evolution is nearly fully offset by the evolution of energy intensity via "minus one" phenomenon.Like Newton's third law goes, for every action (real price growth) there is an equal and opposite reaction (energy intensity decline).And this action/reaction balance keeps the ECS hous-inc nearly constant with a possible weak dominance of energy intensity decline in the long-term.Energy efficiency improvements allow it to mitigate demand for more expensive, better quality energy services, and to keep energy costs within the affordability limits.For the poor, energy efficiency allows for a better indoor comfort (rising from the survival to a normal level) at the same cost.
Bashmakov [57] shows that for the residential sector studies provide average long-term energy demand to income elasticity of 0.5 (ranging from 0.17 to 1.11), which is very consistent with living space to income elasticity and longterm price elasticity at -0.22 (ranging from -0.11 to -0.5).With long-term T y /T p ratio close to 1.5-2.5 according to (2) this fits the conditions under which very long-term energy intensity to real energy price elasticity equals -1.

The Whole Economy.
The above line of thinking described for the housing sector is applicable to other sectors as well.The energy efficiency distribution curves for similar facilities are shaped close for individual dwellings, multifamily buildings, power stations, boilers, cement or steel works [58][59][60].They consist of three parts: the first one showing facilities with the best energy efficiency parameters; the middle part, where energy intensity of facilities is steadily rising; and the third part that includes least efficient energy units.The right-hand tail of the distribution (energy intense facilities) is most vulnerable to energy price shocks.ECS distributions are nearly proportional to the energy intensity ones.In different sectors, ECSs vary in narrow ranges, similar across different countries.Each ECS go-ind additional percent point reduces VAS go -in by 2.7-5%.Thus ECSs growth may result in a complete loss of profits and push energy intense facilities out of business.This limits the upper thresholds levels and keeps the ECSs in separate sectors on the orbit around the "center of gravitation".
Data quality for the ECS estimates for individual sectors in different countries needs much improvement.Nevertheless, the analysis above allows it to state that energy affordability thresholds manifest in all major final energy use sectors (see also [1,4,5]).Therefore, the aggregated energy costs constant (range) is a linear combination of those for sectors weighted by contributions of respective sectors' income indicators to either gross output or GDP (Table 1).The aggregated range is consistent with those economywide presented for different countries [4,5].With extreme values excluded from both ends of the range, the sustainable range of the share of energy costs in gross output is 4-6%, and of the energy costs to GDP ratio is 8±2%.These ranges of sustainable evolution may shift slightly up or down depending on the country's specific economy structures and legacy of previous long-standing energy pricing, tax and subsidies policies, which it takes time to shift from.This paper, based on sectorial decomposition, provides additional explanation of the "minus one" phenomenon.
Negative impacts of ECSs increments on economic growth identified in this paper for major sectors and for the whole economy (the latter supported with findings described in the literature) are summarized in Table 2 in two dimensions: direct impact on activity growth (manufacturing value added and GDP) and indirect impact (declining shares of value added in sectors' gross output, which need to be compensated via output growth).Where possible, the impacts are split by ECSs ranges below and exceeding the threshold.
One percentage point increase in ECS for industry cuts potential manufacturing value added growth (with a oneyear lag) by 1.8% when ECS stays below the threshold and by 7.7% after the threshold is exceeded.Other things are equal; it translates into GDP slowdown by 0.4-1.1% and by 1.5-4.6%,respectively, depending on the industry's contribution to GDP.In [1,4] the "wing" function for the whole economy was presented to show that after ECS gdp has exceeded the upper threshold, every additional 1% of ECS gdp cuts GDP growth rate by nearly 1-2%.Similar findings for the whole economy are supported by other studies [32,61,62].Fizaine and Court [31] found that the slowdown effect for the US equals some 0.5% for the whole ECS range.King [32] found it close to 0.4% on average for 44 countries.However, these samples were not split by low and high ECS ranges.So assuming the relationship is not linear, the impact for ECS growth in the high range should be higher.Fizaine and Court [31]  intended to statistically test Bashmakov's thresholds effects, i.e., the negative correlation between ECS gdp and the rates of U.S. GDP growth after the threshold values of energy costs share are exceeded, but found the sample too small for robust statistical results and made a point that using cross-country panel data may help in such analysis.They concluded that "statistically speaking, the U.S. economy cannot afford to allocate more than 11% of its GDP to energy expenditures in order to have a positive growth rate".In the short term, this corresponds to the maximum affordable average energy price of twice the current level.In manufacturing, services, and commercial transport sectors, every additional 1 percent point of ECS drives the share of value added in gross output down.Whenever output does not demonstrate fast enough growth in one of these sectors, value added growth is hampered first in these sectors, and then recession spreads over time across other sectors too.The last column (6) in Table 2 illustrates the ranges of ECS variations observed in 1995-2011.Data in this column show how much the growth rates should scale up in order to prevent value added from decline (column 5).The larger ECS's increase on a limited time frame, the higher output growth is needed to keep value added growing, and so the lower the chance of avoiding recession, but associated substantial decline in value added shares and loss of profits by the most energy intense facilities pushes them out of business undermining the possibility for output growth.Additional 1% of ECS for private transport leads to a drop in the share of income spent on new motor vehicles, while additional 1% of ECS for residential sector reduces the share of income spent on furnishings and durable household equipment.In either case, personal savings rate declines drastically.A slowdown in the income growth leads to an absolute decline in cars and durable consumer goods outputs pushing GDP further to recession.Many of these effects are interconnected and manifest stronger, when ECSs exceed sector-specific and economy-wide thresholds.It is the need for maintaining dynamic economic growth that serves a gravitation force setting the limits to ECSs deviations beyond the constrained range where energy is both available and affordable.
Important support to the "-1" comes from Lowe's [63] paper, in which he comes up with a conclusion that energy price elasticity for a system with multiple energy transformation stages ("subsystems") asymptotically tends to unity as the number of subsystems increases, even if all partial elasticities for subsystems are below unity.If the whole economy is viewed as a distributed in time multistage energy conversion system, which embodies some energy at each stage, then Lowe's conclusion works for the whole economy or for a particular sector.The "minus one" effect stems from the empirically verified assumption that at least in some subsystems energy efficiencies depend on energy price impulses (see discussion above on energy price elasticities).Negative price elasticity partly mitigates the impact of growing energy price by lowering the amount of embodied energy at a given stage and subsequent stages.It takes time (from half a year to three years or more, including fuel transportation and storage time; time to embody more expensive energy in new products and services) for the initial price shock to spread all over the economy.But then for many years to come more expensive energy embodied in fixed capital, labor, and materials stocks smoothly impacts energy use efficiency.The higher energy price elasticity of energy efficiency within a given process, the smaller price impact is provided to subsequent time periods (stages).However, the smaller energy price elasticity of energy efficiency at each stage, the longer (or the more stages) it takes to completely mitigate initial price impulse with energy efficiency gains.When embodied energy analysis is applied, it means that changes in material efficiency improvements and structural shifts also contribute to the process.If there is overshooting, and at some stage energy efficiency to price elasticity temporally exceeds unity, then  Note.Data before mid-20th century are limited to England/Wales and Sweden.Fizaine and Court [31] show that in 1850-1950 total ECS gdp for the US was mostly in the range 7-15%.Sources: Csereklyei et al. [34]; Fouquet [15]; Kander [33]; Bashmakov and Grubb [5]; Bashmakov [4].
overall system elasticity exceeds unity at the same stage, but later system-wide elasticity starts declining asymptotically from that above unity level back to unity.After overshooting in the reverse direction it goes below unity, but then starts rising towards unity.This abstractly explains how an ECS cycle works in a pendulum regime.Only in a completely price inelastic system energy intensity will not mitigate energy price shock via energy costs decline.On the contrary, in a perfectly price elastic system at some stage energy costs scale down to the initial level.If income is added as a constant to this analysis, then ECS comes down to its initial level in the multiyear process.When energy price elasticities at each stage are close to -0.2, it takes about 25 years to get integrated price elasticity to unity [63].This result does not depend on initial energy efficiencies at each conversion stage (or energy efficiency in a given year), but only on energy intensity to price elasticities.This explains why the timing of complete energy cost adjustment to the initial level after price shocks should be relatively similar across systems and countries at different stages of development, providing partial price elasticities are similar.So the long cycle duration is a function of relatively low energy price elasticity and does not depend much on the achieved energy efficiency level.If so, the "minus one" phenomenon becomes relevant for economies across long time horizons and depends on the role of market forces in the economy (economic aspect), as well as on technical opportunities (technical aspect) allowing for faster adjustment to price shocks.
Based on available historical studies, Bashmakov [4] tested how stable ECSs are not only on decadal, but also on centuries scale.Despite a wide range of ECSs fluctuations in individual sectors for five centuries (1500-2014) (with an effort made to ensure energy costs accounting comparability and exclude manpower from the energy balance), the estimates are very close to the recently observed values.In 1550-2010 (corrected by the authors), total ECS gdp varied between 7% and 15% (Table 3).
All the above analysis requires a minor reformulation of the first law of energy transitions [1]: First law of energy transitions: in the long-term, energy costs to income ratios are relatively stable with just a very limited sustainable fluctuation range (with a very small upward or downward trend in this range reflecting centuries-long shifts in the structure of the economy).

An alternative formulation may go:
in the long-term, real energy prices can grow only about by as much as energy intensity declines.

Conclusions: Energy Costs Constants Policy Implications
Climate and energy policies would benefit from understanding how price instruments drive energy efficiency improvements.Environmental pricing and taxation timing need to be flexible, account for market-driven energy price fluctuations, and be consistent with limits to energy affordability and energy efficiency improvement rates.Sectorial ECS constants offer a new angle to energy taxation and environmental pricing as they suggest making a focus on ECSs, not on prices.The historical evidence is systems can adjust to price shocks, but slowly over 2 or 3 decades.The analysis points towards crucial issues of affordability thresholds, timing, and the relationship between different policy instruments.In major sectors price mechanisms can be designed so as not to force businesses or people to ultimately pay a share of their incomes for energy beyond the threshold levels in order to avoid economic recession, loss of welfare, and competitiveness.The "minus one" phenomenon means that, with limited annual energy intensity decline rates, it takes time for the economy to mitigate energy price shocks.Failure to account for such inertia reverses the energy price trajectory to finally limit real energy price growth to energy intensity decline levels.The traditional conception is that prices should drive improvements in efficiency and innovation mostly through market mechanisms.Our logic throws serious doubt upon this: energy efficiency progress limits real energy price growth.Instruments other than market mechanisms are important to improve the limits to energy productivity change and to make pricing tools more effective not only at a given moment, but in the future as well (strategic policies).ECSs above the thresholds we have identified for separate sectors appear to involve increasingly high economic and welfare costs and certainly political obstacles.Policy conclusions go beyond suggesting a different narrative behind energy pricing (including carbon pricing) policies and a need to involve multiple policy instruments.Affordable energy price (including carbon price) can grow only at a rate equal to average energy intensity decline plus GHG emission per unit of energy reduction rate.Otherwise, the trade-off between maximizing economic growth and minimizing GHG emissions is inevitable [32].In carbon pricing, governments need to directly mimic the adjustment processes that lead to improved energy and carbon intensities [11].To keep the motivation spring charged, energy and carbon pricing policies should keep ECSs close to, yet below, the upper thresholds for individual sectors, and thus carbon pricing and energy tax policy should be flexible to be effective (Sweden developed carbon tax policy in a way that kept ECS below 10% after 1990 and below 8% after 1997 even when the tax reached 131 US$/tCO2 in 2016).This naturally happens when energy price shocks limit economic dynamics, and carbon price declines (as illustrated by the EU ETS experience).
Energy costs are eclipsed by other cost categories when investigating competitiveness [8] and impacts on economic growth [64].The real importance of ECS evolution to economic growth originates from the fact that its every additional percent point (often not much visible below the GDP waterline) squeezes the value added share in gross output by 2.7-5%, which, if not compensated by 2.5-10% annual output growth, generates recession.Possibility for such compensation is undermined by the loss of profits and businesses by most of energy intense facilities.The ECSs constancy is to be taken into account in studies focusing on energy use, energy efficiency, energy prices, and economic development interactions, in energy-economic modeling and energy and climate policy-making.IEA [47] estimated that up to 2040 worldwide households' ECS for housing and private transport will stay close to 2015 values.Bashmakov [3] used the energy cost constants approach in his global GHG emission model (MOG 3 EM).So some projections already account for the "minus one" effect.
Grubb et al. [2] call ECSs constancy the most important relationship in energy economics.There is a group of physical constants (including the gravitational constant) playing a fundamental role in the basic theories of physics.They are subject to experimental verification, and the question regarding their time dependence is still open, as well as the question of why they have specific values.Given the available data, the energy costs constants cannot be verified with the precision achieved in physics.Much effort to improve energy costs accounting techniques is needed to improve the accuracy of ECSs measurements.The nature of energy costs constants may be different from the ones in physics with a better spatial (for different countries and conditions) and time dependence.But the "rule of gravitation" is identified (for the whole cycle, real energy prices in each sector may grow by only as much as energy intensity declines), as well as the first approximation of the "centers of gravitation", orbits, and orbiting time parameters for individual sectors and for the whole economy.

Figure 3 :
Figure 3: Energy costs shares in services gross output.Sources: authors based on data from Timmer et al. [10] and Timmer et al. [9].

Figure 5 :
Figure 5: Energy costs shares in commercial transport gross output.Sources: authors based on data from KLEMS, Timmer et al. [9, 10], and WDI database.

Figure 6 :
Figure 6: Value added share in commercial transport gross output as a function of ECS.Sources: authors based on data from Timmer et al. [9] and WDI database.

Figure 8 :
Figure 8: Relationship between personal transport energy costs shares and share of income spent on new motor vehicles in the US (1959-2017).Source: calculated based on BEA [14].

Figure 10 :
Figure 10: Relationship between housing energy cost shares and the share of income spent on furnishings and durable household equipment in the US and UK.Source: calculated based on BEA[14] and ONS UK[19].
UK, average weekly energy expenditures per household (2011) and the share thereof in income (2005) Japan, average weekly energy expenditures per household and the share thereof in income, 2013 share of housing energy costs in income before tax share of housing energy costs in expenditures (c) Russia, average monthly energy expenditures per household and the share thereof in income, 2013 China, average annual energy expenditures per household and the share thereof in income, 2012.Not all deciles are covered by the information source

Table 1 :
Composition of aggregated energy costs to income ratios.

Table 2 :
Impacts of economy-wide and sector-specific energy costs shares' evolution on economic growth parameters.Ranges in column 5 could also be interpreted as annual average value added share or profit margin ratio loss for the most energy intense facilities associated with additional 1 percent point of ECS.
* Excluding manpower and with corrections to values for transport based on British macroeconomic statistics.* * Bashmakov [4].* * * Only personal transport.