The economic impact of a deep decarbonisation pathway for China: a hybrid model analysis through bottom-up and top-down linking

Abstract

The development of mid-century low-emission development strategies is critical to guiding national actions on long-term mitigation. One of the key concerns in developing mitigation strategies is the cost of the low-carbon transition. In this study, we estimate the macroeconomic cost of a deep decarbonisation pathway for China, by integrating an energy-systems optimisation model with an economic model through hard linking. Our results indicate that deep decarbonisation increases the energy expenses of Chinese households in the mid-run due to the higher cost of electricity. However, firms will benefit from moderate decarbonisation as a result of a reduction in coal and oil consumption. As a result, energy-efficiency improvements lead to a reduction in firms’ total energy costs, partially compensating the crowding-out effect of low-carbon investments on general productive capital. Our mitigation scenario has therefore a small macroeconomic cost compared to business as usual, equal to a lag in the growth of less than one year in 2050.

Appendices

Appendix 1

1.1 The bottom-up model China-MAPLE

The China-multi-pollutant abatement planning and long-term benefit evaluation model, China-MAPLE, is an energy-system optimisation model based on The Integrated MARKAL-EFOM System (TIMES) model generator (Loulou et al. 2016). TIMES has been developed and is maintained under the International Energy Agency’s Energy Technology Systems Analysis Programme (IEA-ETSAP). In China-MAPLE, the model generator translates the customised energy system into a linear optimisation problem to minimise the overall system cost within a set of technical and economic constraints. The objective of the model is to identify the least-cost way to meet energy-service demands through the minimisation of the total discounted system cost over the entire modelling time horizon. The system cost consists of investment, operation and maintenance, and energy input costs of all the technologies invested in and operated up to the end horizon. Therefore, the model assumes perfect foresight and perfect competition.

China-MAPLE (Wang et al. 2017; Yang and Teng 2017, 2018; Yang et al. 2017, 2018) portrays the entire energy system of China with a detailed description of thousands of technologies in energy supply, process, conversion, and end-use sectors (Fig. 7).

Fig. 7

The structure of the energy-system model China-MAPLE “IOT” stands for Input–output table, “E” for Energy. Totals may not add up due to rounding

Energy supply describes resource exploration and extraction in different regions of China through supply curves for primary energy, including coal, oil, gas, and nuclear, as well as renewables. Imported energy is also modelled through different supply curves to represent cost variants among different producing countries. The energy process and conversion module cover activities in coal washing, coking, oil refining, and electricity and heat generation. These technologies are represented in China-MAPLE by the parameters of resource endowment, efficiency, investment cost, fixed and variable operating costs. The energy end-use module captures the activities of end-use sectors, such as industry, transportation, and the building sector (i.e. the physical output of industrial products, the passenger-kilometres travelled and ton freight-kilometres transported, the lighting, cooking, heating, water heating, air-conditioning, and use of electrical equipment by households). Those activities are projected according to socio-economic assumptions and the plans of the government. When the model is used alone, the socio-economic assumptions are exogenous; when coupled to KLEM-CHN, they are obtained from KLEM-CHN. Carbon dioxide emissions and important air-pollutant emissions associated with fossil-fuel consumption are also modelled. For more information about China-MAPLE, please refer to (Yang and Teng 2017, 2018; Yang et al. 2017, 2018).

Appendix 2

2.1 Top-Down model KLEM-CHN

The macroeconomic core of KLEM is a dynamic, recursive model deriving from a Solow-Swan growth model. KLEM-CHN pictures economic growth in 5-year time steps as driven by exogenous assumptions on the supply and productivity of labour. The vector of domestic energy and non-energy outputs at year $t$, is a function of the stock of capital, labour force and intermediate consumption of energy, and non-energy goods. The function varies with year $t$ via exogenous labour productivity gains (the Harrod-neutral assumption on technical progress). Capital stock dynamics follow the standard accumulation rule at a constant depreciation rate with explicit accounting of year-to-year variations between 5-year time steps (see Appendix 4). Considering the 5-year interval and 2050 horizon of KLEM-CHN, both its labour and capital markets are clear by adjustments of the wage $w$ and the rental price of capital ${p}_{K}$. Its trade balance is exogenous (Eq. 13 of Appendix 2) following neoclassical practise but its macroeconomic closure is on domestic savings rather than on investment, following Johansen (1960), to reflect the degree of governmental control on the Chinese economy. This implies a growth trajectory more robust to scenario variants at the cost of final consumption variations—which we will duly report when analysing scenarios. The investment effort is set as a share of GDP (Eq. 9 of Appendix 2) that evolves to warrant that the capital stock grows apace with efficient labour when potential growth, defined by efficient labour increases, concretises (see Appendix 4).

KLEM models non-energy production as a nested structure of Constant Elasticity of Substitution (CES) trade-offs between inputs (Eqs. 2345 and 6 of Appendix 2), and non-energy trade as elastic to prices (Eqs. 10 and 11 of Appendix 2). However, linkage to China-MAPLE translates into full exogeneity of the energy system. The growth trajectories traced by KLEM-CHN thus build around exogenous energy consumptions and trade as well as around exogenous assumptions on the cost structure of energy supply beyond its own energy intensity and on the specific margins (differences of consumer prices to average supply costs) on each energy sale. For lack of easily exploitable information in China-MAPLE, the costs of potential energy savings in the non-energy sector proceed from the nested CES specification as incremental value-added costs, under the assumption that “business-as-usual” China-MAPLE energy consumptions and non-energy output increasing at the pace of efficient labour supply define cost-free energy-productivity gains (“autonomous energy efficiency improvements”, AEEI).⁵

These constraints on energy volumes, costs and prices weigh on economic growth and non-energy consumption by reserving part of value-added to exogenous energy expenses and endogenous, attached energy-efficiency costs and part of primary factor endowments to the supply of some exogenous volume of energy.

For reference purposes, we list all variables and parameters below (Table 2), with the exception of a series of constant parameters calibrated on 2010 values, which we introduce with equations when necessary. The model counts 43 variables and 43 equations: Eqs. 1, 14, 15, 20, 27, 29, and 32 cover both sectors and thus count twice; Eq. 28 defines the prices of the IO matrix and thus counts 4 times. All equations prevail at each time period of the model, from 2010 (calibration year) to 2050 in 5-year steps. However, we drop time index t except when necessary. We index good-specific notations with subscript $E$ for the aggregate energy good and subscript $Q$ for the aggregate non-energy good.

Table 2 KLEM-CHN notations

Production

Trade-offs in the production of the energy good are exogenous assumptions flowing from the China-MAPLE model (see Appendix 5). The only required equation is the breakdown of primary energy inputs into energy transformation—the equation holds for the non-energy sector too:

$${E}_{i}={\alpha }_{Ei} {Y}_{i}$$

(1)

Non-energy production follows a “production tree” of nested CES functions (Fig. 8).⁶

Fig. 8

Production structure of the non-energy good

At the foot of the tree, capital, and labour trade-off with a constant ${\sigma }_{KL}$ elasticity of substitution to form a $KL$ aggregate. The mobilised quantity of labour ${L}_{Q}$ is augmented by a productivity factor $\phi$: $KL={\left({\alpha }_{KL }{{K}_{Q}}^{{\rho }_{KL}}+{\beta }_{KL }{(\phi {L}_{Q}) }^{{\rho }_{KL}}\right)}^{\frac{1}{{\rho }_{KL}}}$, with here and elsewhere, for convenience, ${\rho }_{i}= \frac{{\sigma }_{i}-1}{{\sigma }_{i}}$. Facing prices ${p}_{K}$ and ${p}_{L}$, cost minimisation induces

$${L}_{Q}= \frac{1}{\phi } {\left(\frac{ \phi {\beta }_{KL}}{{p}_{L}}\right)}^{{\sigma }_{KL}}{\left({\alpha }_{KL}^{{\sigma }_{KL}}{{p}_{K}}^{1-{\sigma }_{KL}}+ {\beta }_{KL}^{{\sigma }_{KL}}{\left(\frac{{p}_{L}}{ \phi }\right)}^{{1-\sigma }_{KL}}\right)}^{-\frac{1}{{\rho }_{KL}}}KL$$

(2)

$${K}_{Q}= {\left(\frac{ {\alpha }_{KL}}{{p}_{K}}\right)}^{{\sigma }_{KL}}{\left({\alpha }_{KL}^{{\sigma }_{KL}}{{p}_{K}}^{{1-\sigma }_{KL}}+ {\beta }_{KL}^{{\sigma }_{KL}}{\left(\frac{{p}_{L}}{ \phi }\right)}^{{1-\sigma }_{KL}}\right)}^{-\frac{1}{{\rho }_{KL}}}KL$$

(3)

Higher up the tree, aggregate factor $KL$ (value-added) and energy ${E}_{Q}$ again trade off with a constant ${\sigma }_{KLE}$ elasticity of substitution to form a $KLE$ aggregate. However, ${E}_{Q}$ is forced following China-MAPLE results (see Sect. 3.3 and Appendix 5) at levels much lower than potential growth (the growth of efficient labour $\phi L$), even in business-as-usual scenarios. Accommodating such intensity drops under standard values of ${\sigma }_{KLE}$ would result in implausible increases of the required $KL$ intensity. To redress this bias, we introduce autonomous efficiency gains to ${E}_{Q}$ (i.e. autonomous energy efficiency improvements AEEI) in the form of productivity gains ${\phi }_{E}$. The corresponding $KLE={\left({{\alpha }_{KLE }KL}^{{\rho }_{KLE}}+{\beta }_{KLE }{\left({\phi }_{E} {E}_{Q}\right)}^{{\rho }_{KLE}}\right)}^{\frac{1}{{\rho }_{KLE}}}$ yields

$$KL={\left(\frac{{KLE}^{{\rho }_{KLE}}}{{\alpha }_{\mathrm{KLE}}}- \frac{{\beta }_{\mathrm{KLE}}}{{\alpha }_{\mathrm{KLE}}}{\left({\phi }_{E} {E}_{Q}\right)}^{{\rho }_{KLE}} \right) }^{\frac{1}{{\rho }_{KLE}}}$$

(4)

We calibrate ${\phi }_{E}$ in such a way that ${\phi }_{E} {E}_{Q}$ (“efficient ${E}_{Q}$” or the actual energy service rendered by ${E}_{Q}$) grows apace with natural growth in business-as-usual (BAU) conditions, i.e. we make the assumption that the energy efficiency gains of the non-energy sector in BAU conditions do not require increased value-added expenses. This will define the value-added costs of the increased energy-consumption cuts of any scenario more ambitious than BAU.

On the tier immediately above, the $KLE$ aggregate and non-energy input ${\alpha }_{QQ} {Y}_{Q}$ trade-off with a constant ${\sigma }_{Y}$ elasticity of substitution to form domestic output ${Y}_{Q}$. Facing prices ${p}_{KLE}$ and ${p}_{QQ}$, cost minimisation induces

$$KLE={\left(\frac{{\alpha }_{\mathrm{Y}}}{{p}_{KLE}}\right)}^{{\sigma }_{\mathrm{Y}}}{\left( {\alpha }_{\mathrm{Y}}^{{\sigma }_{\mathrm{Y}} }{p}_{KLE}^{{1-\sigma }_{\mathrm{Y}}}+ {\beta }_{\mathrm{Y }}^{{\sigma }_{\mathrm{Y}}}{p}_{QQ}^{{1-\sigma }_{\mathrm{Y}}}\right)}^{-\frac{1}{{\rho }_{\mathrm{Y}}}} {Y}_{Q}$$

(5)

$${\alpha }_{QQ}{Y}_{Q}={\left(\frac{{\beta }_{\mathrm{Y}}}{{p}_{QQ}}\right)}^{{\sigma }_{\mathrm{Y}}}{\left({\alpha }_{\mathrm{Y}}^{{\sigma }_{\mathrm{Y}} }{p}_{KLE}^{{1-\sigma }_{\mathrm{Y}}}+ {\beta }_{\mathrm{Y }}^{{\sigma }_{\mathrm{Y}}}{p}_{QQ}^{{1-\sigma }_{\mathrm{Y}}}\right)}^{-\frac{1}{{\rho }_{\mathrm{Y}}}} {Y}_{Q}$$

(6)

Final consumption and investment

Household consumption of energy ${C}_{E}$ is exogenous (see Appendix 5) whilst household consumption of the non-energy good ${C}_{Q}$ adjusts to close the model considering the domestic savings demand resulting from the investment and trade balance assumptions (“Johansen” closure, see Appendix 2).

Public spending ${p}_{{G}_{Q}}{G}_{Q}$ is a constant share ${s}_{G}$ of GDP (public spending in energy goods is zero by national accounting convention):

$${p}_{{G}_{Q}}{G}_{Q}= {s}_{G}GDP$$

(7)

with $GDP$ defined on the expenditure side as

$$GDP={\textstyle\sum_{i=E,Q}}p_{C_i}C_i+p_{G_Q}G_Q+p_{I_Q}I_Q+{\textstyle\sum_{i=E,Q}}p_{X_i}X_i-{\textstyle\sum_{i=E,Q}}p_{M_i}M_i$$

(8)

Investment expenses ${p}_{{I}_{Q}} {I}_{Q}$ are an exogenous ratio ${s}_{I}$ of $GDP$ (investment in energy goods is nil)

$${p}_{{I}_{Q}}{I}_{Q}= {s}_{I} GDP$$

(9)

See Appendix 4 for the calibration of the investment path.

International trade

Energy imports and exports ${M}_{E}$ and ${X}_{E}$ are exogenous, dictated by China-MAPLE results. For the non-energy good, the share of imports ${M}_{Q}$ in total supply ${S}_{Q}$ has a ${\sigma }_{Mp}$ elasticity to terms of trade:

$$\frac{{M}_{Q}}{{S}_{Q}}={A}_{M}{\left(\frac{{p}_{{Y}_{Q}}}{{p}_{{M}_{Q}}}\right)}^{{\sigma }_{{M}_{p}}}$$

(10)

with ${A}_{M}$ one constant calibrated on 2010 data. Similarly, the exported share of total supply follows:

$$\frac{{X}_{Q}}{{S}_{Q}}={A}_{X}{\left(\frac{{p}_{{X}_{Q}}}{{p}_{{M}_{Q}}}\right)}^{{\sigma }_{{X}_{p}}}$$

(11)

with ${A}_{X}$ one constant calibrated on 2010 data. The trade balance $B$ is

$$B={\textstyle\sum_{i=E,Q}}p_{X_i}X_i-p_{M_i}M_i$$

(12)

It is exogenous in the sense that its share to GDP maintains at a constant ${A}_{B}$ ratio (calibrated on 2010 data) via endogenous adjustments of the real effective exchange rate (the ratio of the CPI to the foreign price index, which is not computed):

$$\frac{B}{GDP}={A}_{B}$$

(13)

Market clearings

Market balance for each good $i$ stems from the definitions of total domestic supply ${S}_{i}$ seen from the use and resource sides:

$$S_i={\textstyle{\scriptstyle\sum}_{j=E,Q}}\alpha_{ij}Y_j+C_i+G_i+I_i+X_i$$

(14)

$${S}_{i}={Y}_{i}+{M}_{i}$$

(15)

On the labour market, the unemployment rate is forced at its calibration-year level ${A}_{u}$:

$$u={A}_{u}$$

(16)

Market balance is.

$$\left(1-u\right) L={L}_{Q}+{L}_{E}$$

(17)

The wage $w$ adjusts to meet this constraint. This amounts to perfect market specification.⁷

In the non-energy sector, labour consumption, and output are conventionally related via labour intensity:

$${L}_{Q}={\lambda }_{Q} {Y}_{Q}$$

(18)

Labour mobilised in the energy sector ${L}_{E}$, whose intensity ${\lambda }_{E}$ derives from China-MAPLE (see Appendix 5) benefits the same productivity gains as non-energy labour ${L}_{Q}$. Thus,

$$\phi {L}_{E}={\lambda }_{E} {Y}_{E}$$

(19)

On the capital market, demands of the two productions balance out capital endowment $K$:

$${\sum }_{i=E,Q}{K}_{i}= K$$

(20)

With for the non-energy sector, similarly to labour:

$${K}_{Q}={\kappa }_{Q} {Y}_{Q}$$

(21)

Capital mobilised in the production of the energy good ${K}_{E}$ is constrained not to contract faster than the depreciation rate $\delta$:

$${K}_{E,t}=max\left(\left(1-\delta \right) {K}_{E,t-1};{\kappa }_{E} {Y}_{E}\right)$$

(22)

This constraint was devised for the exploration of the Saudi economy’s massive energy sector at annual time steps. It is inoperative in the fast-growing context of the Chinese economy modelled at 5-year intervals.

Producer and consumer prices

Primary factor payments $w$ the wage and ${p}_{K}$ the price of capital rental are common to both sectors. They adjust according to their market balances.

The price of the $KL$ aggregate ${p}_{KL}$ is the canonical function ($KL$ being a CES product of $K$ and $L$) of prices ${p}_{K}$ and ${p}_{L}$ and of the elasticity of substitution of the two inputs ${\sigma }_{KL}$:

$${p}_{KL}={ \left({\alpha }_{KL}^{{\sigma }_{KL}}{\left(\frac{{p}_{K}}{{\Omega }_{K}}\right)}^{1-{\sigma }_{KL}}{+ \beta }_{KL}^{{\sigma }_{KL}}{\left( \frac{w}{ {\Omega }_{L} \phi }\right)}^{{1-\sigma }_{KL}}\right)}^{\frac{1}{1-{\sigma }_{KL}}}$$

(23)

Contrary to ${p}_{KL}$, ${p}_{KLE}$ the price of the $KLE$ aggregate specific to non-energy production cannot be defined as a function of prices ${p}_{KL}$ and ${p}_{EQ}$ and of the elasticity of substitution of the two inputs ${\sigma }_{KLE}$, because exogenously setting ${E}_{Q}$ in the $KLE$ aggregate truncates the underlying cost-minimisation programme. Consequently, ${p}_{KLE}$ is rather inferred from the simple accounting equation:

$${p}_{KLE} KLE= {p}_{KL} KL+{p}_{EQ} {E}_{Q}$$

(24)

The producer price of the non-energy good ${p}_{YQ}$ is again the canonical CES price of the $KLE$ aggregate and the non-energy input to production ${\alpha }_{QQ} {Y}_{Q}$, to which a constant ad valorem output tax ${\tau }_{{Y}_{Q}}$ as well as a constant rent mark-up ${\tau }_{{R}_{Q}}$, are added:

$${p}_{{Y}_{Q}}\left(1-{\tau }_{{Y}_{Q}}-{\tau }_{{R}_{Q}}\right)= {\left({\alpha }_{Y}^{{\sigma }_{Y}} {p}_{KLE}^{1-{\sigma }_{Y}}+{\beta }_{Y}^{{\sigma }_{Y}} {p}_{QQ}^{1- {\sigma }_{Y}}\right)}^{\frac{{\rho }_{Y}-1}{{\rho }_{Y}}}$$

(25)

For the energy good, the producer price is simply the sum of production costs:

$${p}_{YE}={p}_{QE}{ \alpha }_{QE}+{p}_{EE} {\alpha }_{EE}+w {\lambda }_{E}+{p}_{K} {\kappa }_{E}+{\tau }_{{R}_{E}} {p}_{YE}+{\tau }_{{Y}_{E}} {p}_{YE}$$

(26)

The import prices of both goods are exogenous: ${p}_{MQ}$ is constant because the imported non-energy good is the chosen numéraire of the model; and ${p}_{ME}$ follows an exogenous trajectory inferred from China-MAPLE (Appendix 5).

The average supply price of good $i$, ${p}_{Si}$, flows from

$${p}_{{S}_{i}} {S}_{i}= {p}_{{Y}_{i}} {Y}_{i}+ {p}_{{M}_{i}} {M}_{i}$$

(27)

Turning to purchasers’ prices, the price of good $i$ for the production of good $j$, ${p}_{ij}$, is equal to the supply price of good $i$ augmented from agent-specific margins ${\tau }_{{MS}_{ij}}$ and ad valorem sales taxes ${\tau }_{{ST}_{i}}$:

$${p}_{ij}={p}_{{S}_{i}} \left(1+{\tau }_{{MS}_{ij}}\right)\left(1+{\tau }_{{ST}_{i}}\right)$$

(28)

The consumer prices of households, public administrations, the investment goods, and exports are constructed similarly but drop the unnecessary specific margins when energy is not concerned (public consumption, investment), as well as sales taxes as regards exports:

$${p}_{{C}_{i}}={p}_{{S}_{i}}\left(1+{\tau }_{{MSC}_{i}}\right)\left(1+{\tau }_{{ST}_{i}}\right)$$

(29)

$${p}_{{G}_{Q}}={p}_{{S}_{Q}}\left(1+{\tau }_{{ST}_{i}}\right)$$

(30)

$${p}_{{I}_{Q}}={p}_{{S}_{Q}}\left(1+{\tau }_{{ST}_{i}}\right)$$

(31)

$${p}_{{X}_{i}}={p}_{{S}_{i}}\left(1+{\tau }_{{MSX}_{i}}\right)$$

(32)

In the case of the energy good, the specific margin ${\tau }_{{MSX}_{E}}$ endogenously adapts to accommodate the exogenous ${p}_{{X}_{E}}$ prescription (see Appendix 5). The consumer and import price indexes $CPI$ and $MPI$ are computed as chained indexes, i.e. from one period to the next, according to Fisher’s formula:

$${CPI}_{t}={CPI}_{t-1} \sqrt{\frac{\sum {p}_{Ci,t} {C}_{i,t-1}}{\sum {p}_{Ci,t-1} {C}_{i,t-1}}\frac{\sum {p}_{Ci,t} {C}_{i,t}}{\sum {p}_{Ci,t-1} {C}_{i,t}}}$$

(33)

$${MPI}_{t}={MPI}_{t-1} \sqrt{\frac{\sum {p}_{Mi,t} {M}_{i,t-1}}{\sum {p}_{Mi,t-1} {M}_{i,t-1}}\frac{\sum {p}_{Mi,t} {M}_{i,t}}{\sum {p}_{Mi,t-1} {M}_{i,t}}}$$

(34)

Appendix 3 A hybrid energy/economy CHN dataset

Bringing consistent energy and national accounting data into a hybrid energy/economy dataset can have a significant bearing on energy/economy modelling results (Combet et al. 2014). For that reason, it should be a prerequisite to proper bottom-up/top-down coupling experiments lest BU-derived variations apply to flawed cost, budget or trade balance shares. This Appendix summarises our procedure of building a hybrid energy/economy dataset for China and provides the resulting data in the 2-sector format of KLEM. Because this format is shared with that of KLEM-KSA, its exposition is repeated from Soummane et al. (2019), Appendix C.⁸

Our hybridising procedure consists in crossing national accounting input–output data on energy expenses, energy balance data on energy flows and energy market price data. In case of discrepancy beyond some tolerance level, we prioritise the flow and price data from energy statistics and substitute the resulting expense estimate to the corresponding national accounting data. We adjust all non-energy elements of the cost structures of energy suppliers to rebalance the uses and resources of energy goods. We aggregate all corrections of uses and resources in a separate sector, which therefore blends actual non-energy activities of energy firms (unaccounted for in supply tables) and mere statistical errors. In the compact format of KLEM, we have no choice but to aggregate this correction sector to the non-energy sector.

In the case of China, we performed the procedure on the 42-sector input–output (IO) matrix of 2010 (National Statistics Bureau, 2011) with information from the more disaggregated 135-sector IO matrix of 2012 (National Statistics Bureau, 2015), the energy balance of 2010 and sets of energy prices from various sources including the China Price Statistics Yearbook 2011, the China Cement Yearbook 2011, the World Economic Operation Report 2011–2012, the China Yearbook 2011, the China Customs Statistical Yearbook 2011, the Handbook of Brief Energy Data 2016, the International Energy Agency, and the ENERDATA Company.

The first step of our data treatment procedure was to disaggregate the 42-sector input–output table (IOT) of the year 2010 into 135 sectors, by replicating the sub-sectoral shares of the available 135-sector table of the year 2012. We then aggregated the resulting table into 44 sectors (15 of which unchanged from the initial 42-sector matrix) maximising compatibility with the energy-flow disaggregation of the energy balance. Additionally, for lack of direct Chinese sources, we turned to the GTAP database to separate oil and gas extraction into its two components. We also used the energy consumptions of the two GTAP sectors to disaggregate the energy consumptions of ‘oil and gas extraction’ in the energy balance. We aggregated gas extraction to gas distribution to form one single natural gas supplying activity.

The second step of our data treatment was to cross-market price statistics with energy flows to obtain adjusted energy expenses. When lacking price statistics, we constructed price estimates as deviations from the average market price of the relevant energy carrier, taking account of the reported IOT expenses and energy flows. More precisely, if ${p}_{\mathrm{iot}}$ the price resulting from the division of the IOT expense by the energy balance flow is above ${p}_{\mathrm{av},\mathrm{iot}}$ the average ${p}_{\mathrm{iot}}$ across end-users of the same energy carrier, we defined the estimated price ${p}_{\mathrm{est}}$ as

$${p}_{\mathrm{est}}={p}_{\mathrm{av},\mathrm{ stat}}+\frac{{p}_{\mathrm{iot}}-{p}_{\mathrm{av},\mathrm{iot}}}{{p}_{\mathrm{max},\mathrm{iot}}-{p}_{\mathrm{av},\mathrm{iot}}} 0.25 {p}_{\mathrm{av},\mathrm{ stat}}$$

with ${p}_{\mathrm{av},\mathrm{ stat}}$ the average of available market price statistics for the same energy carrier and ${p}_{\mathrm{max},\mathrm{iot}}$ the maximum ${p}_{\mathrm{iot}}$ across end-users of the same energy carrier. Conversely, if ${p}_{\mathrm{iot}}$ is below ${p}_{\mathrm{av},\mathrm{iot}}$ we defined ${p}_{\mathrm{est}}$ as

$${p}_{\mathrm{est}}={p}_{\mathrm{av},\mathrm{ stat}}+\frac{{p}_{\mathrm{av},\mathrm{iot}}-{p}_{\mathrm{iot}}}{{p}_{\mathrm{av},\mathrm{iot}}-{p}_{\mathrm{min},\mathrm{iot}}} 0.25 {p}_{\mathrm{av},\mathrm{ stat}}$$

with ${p}_{\mathrm{min},\mathrm{iot}}$ the minimum ${p}_{\mathrm{iot}}$ across end-users of the same energy carrier.

The third step of our procedure was to substitute the adjusted energy expenses i.e. the products of the price statistics or estimated prices and the energy flows, to the original energy expenses of our 44-sector IOT. We then adjusted non-energy inputs into energy sectors by replicating the ratio of non-energy inputs to energy inputs in the original IOT, taking account of the revised energy-input total. We also homothetically adjusted non-energy inputs into non-energy sectors to maintain the totals of intermediate inputs into all sectors.

The main difficulty in the procedure was the reconciliation of the perimeters and nomenclatures of national accounts and the energy balance. National accounts record commercial flows between economic residents and trade with foreign residents. The energy balance records physical energy flows, their trade, their transformations from primary form to secondary vectors and their final consumption by end-uses. Computing commercial flows from energy balance data, therefore, required treatment of power and heat autoproductions (which only appear through primary energy consumptions in national accounts) and of international bunkers (a geographic notion orthogonal to the administrative definition of the perimeter of national accounts). It also required disaggregating the road transport end-use between households’ direct consumptions of vehicle fuels and those of firms, among which transport service suppliers.⁹

The resulting IOT in billion renminbi (RMB) and satellite account of energy flows in million tons of coal-equivalent (Mtce) is organised as follows (Fig.9). In the column, resources of the non-energy good Q and the energy good E build-up from intermediate consumptions (Q or E uses), labour costs L, capital costs K, output taxes “Y taxes”, the rent on natural resources R, imports M, specific margins SM and net-of-subsidies “Sales taxes”. Specific margins on energy uses are calibrated as the difference between sales at prices inferred from the energy-flow account and sales at the average resource price ${p}_{{S}_{E}}$ (an average of output and import prices, see Appendix 2) augmented by net sales taxes. They allow modelling agent-specific prices (see Eqs. 28293031 and 32 of Appendix 2), i.e. overcoming undesirable consequences of the uniform pricing standard, as Combet et al. (2014) demonstrated. All specific margins on Q uses are nil in the absence of any satellite account of physical flows that would point at agent-specific pricing.

Fig. 9

Hybrid dataset of 2010 China in KLEM-CHN 2-sector format

In line, Q and E are used as inputs into productions, as consumption goods for households (C) and public administrations (G), as investment goods (I) or as exports (X). In the energy-flow account, the energy consumption of the non-energy sector (“E uses” in ‘Prod Q’) aggregates the total final energy consumption net of households’ consumption C, which proceeds from residential energy consumptions and a share of refined products consumptions for transportation purposes. The energy consumption of the energy sector (“E uses” in “Prod E”) aggregates commercial flows between energy firms.

By national accounting convention, the consumption of energy goods by public administrations is nil.¹⁰ Investment of energy goods is nil as well, once stock variations have been cancelled out by adjusting output. Exports (X) and imports (M) are close matches to their energy balance counterparts. The price of each energy use is specific thanks to specific margins SM (see above).

According to our hybrid dataset (Fig. C.11), in 2010 the Chinese energy sector represents 19.1% of total imports and 7.5% of value added, 5.5% of the output cost of non-energy supply, and 5.2% of households’ consumption budget. Before hybridisation, the corresponding indicators were 1.8% of total imports, 8.3% of value added, 5.7% of the output cost of non-energy supply, and 3.6% of households’ consumption budget.

Appendix 4 Calibration of KLEM-CHN capital dynamics

Capital accumulation of KLEM-CHN follows standard perpetual inventory specifications but with explicit accounting of year-to-year variations between the 5-year time steps of the model.

Calibration of the base-year capital stock

Our original hybrid energy/economy calibration data (see Appendix 3) lacks some estimate of the initial capital stock. Turning to statistics on such matter risks raising consistency issues with 2010 investment and the accumulation rule, leading to capital stock trajectories with trends diverging from efficient labour supply and thus to artificial relative abundance or scarcity of the capital stock—with ultimate impacts on the costs of more capital-intensive trajectories. Following Soummane et al. (2019), we rather define ${K}_{0}$ the base-year capital stock of KLEM-CHN as.

$${K}_{0} ={I}_{Q,0}\frac{1}{\delta +{g}_{1}}$$

(35)

with $\delta$ the depreciation rate dividing the 2010 investment volume ${I}_{Q,0}$ to account for the amount of capital ($\delta K$) that will be retired at the end of 2010 and must therefore be replaced by ${I}_{Q,0}$; and ${g}_{1}$ the potential growth rate between 2010 and 2011, resulting from the combined growth of labour supply and labour productivity i.e. the growth of efficient labour. Dividing ${I}_{Q,0}$ by ${g}_{1}$ warrants that the 2011 capital stock resulting from 2010 investment grows apace with efficient labour.

Full-horizon calibration of investment rate dynamics

Starting from ${K}_{0}$ and ${I}_{Q,0}$, the standard accumulation rule defines the trajectory of the capital stock as

$${K}_{y+1}=\left(1-\updelta \right) {K}_{y}+{I}_{Q,y}$$

(36)

with time subscripts $y$ conveying that we keep track of this trajectory in yearly time steps in-between each of the 5-year intervals of KLEM-CHN. Our choice of a Johansen closure means to reflect the strongly planned nature of the Chinese economy. Similar to the savings rate dynamics under neoclassical closure, it requires some assumptions on the investment rate dynamics. We calibrate these dynamics in such a manner that the capital stock grows at the same pace as efficient labour when (real) GDP also does. Notwithstanding the small discrepancies between the investment price index and the GDP price index, the year-$y$ investment effort (share of GDP invested) ${s}_{I,y}$ should thus follow:

$${s}_{I,y}= {s}_{I,0}\left(\frac{1+{g}_{y+1}}{1+{g}_{y}}-\left(1-\delta \right)\right)\frac{{K}_{0}}{{I}_{\mathrm{Q},0}}$$

(37)

With ${g}_{y}$ the potential growth rate between year 0 and year $y$ is defined as the growth rate of efficient labour $\frac{\phi {L}_{y}}{{L}_{0}}$ in KLEM notations. This equation holds at each 5-year interval as well to define the investment effort effectively enforced in KLEM-CHN.

Five-year dynamics of the capital stock

KLEM-CHN computes capital stocks in 5-year time steps $t$ as

$${K}_{t+1}={\left(1-\updelta \right)}^{5} {K}_{t}+{A}_{t} {I}_{t}$$

(38)

where ${A}_{t}$ is a multiplier of ${I}_{t}$ that means to approximate the effect of investment growth between $t$ and $t+1$ on ${K}_{t+1}$, duly accounting for depreciation. We compute ${A}_{t}$ in the case when potential growth realises, where it is analytically tractable as a function of the depreciation rate $\delta$ and of potential growth rates $g$:

$$A_t=\sum\nolimits_{i=0}^4\left(1-\delta\right)^{4-i}\frac{g_{y+i+1}+\delta}{g_{y+1}+\delta}$$

(39)

where year $y$ is time period $t$ and years $y+1$ to $y+3$ are the 3 years between period $t$ and period $t+1$.

Appendix 5 KLEM-CHN parameter trajectories inferred from China-MAPLE

KLEM-CHN parameter trajectories inferred from China-MAPLE cover 5 energy volumes, 2 prices of energy trade, 3 margins on energy sales and one deviation from base year values identically affecting the calibrated non-energy, labour and capital intensities of energy supply (${\alpha }_{QE}$, ${\lambda }_{E}$, and ${\kappa }_{E}$ in KLEM-CHN notations).

The 5 energy volumes are the 4 non-nil uses of energy of KLEM-CHN’s satellite account of energy flows (see Appendix 3)—inputs to transformation by energy firms ${E}_{E}$, final consumptions of non-energy firms ${E}_{Q}$, final consumptions of households ${C}_{E}$ and exports ${X}_{E}$—as well as energy imports ${M}_{E}$. Together, these five flows define energy “output” ${Y}_{E}$ in the input–output sense of KLEM-CHN, as the difference between the sum of uses and imports ${E}_{E}+{E}_{Q}+{C}_{E}+{X}_{E}-{M}_{E}$. For a given scenario, we compute the 5 flows at every five-year interval in China-MAPLE following a procedure of nomenclature and perimeter harmonisation very similar to that producing KLEM-CHN’s hybrid calibration data. One significant difference is that China-MAPLE only tracks net imports of energy goods, which we must disaggregate between gross imports and exports. We do so by assuming that, for each energy good, the two trade flows evolve inversely from their base-year (2010) levels, which we know from the Chinese energy balance.

We also easily compute at every five-year interval ${p}_{XE}$ and ${p}_{ME}$ the prices of aggregate energy exports and imports as the weighted averages of the prices of all exported and imported energy commodities in China-MAPLE.

The margins on domestic energy sales ${\tau }_{{MS}_{EE}}$, ${\tau }_{{MS}_{EQ}}$ and ${\tau }_{{MSC}_{E}}$ and ${\delta }_{E}$ the scalar to base-year values of the 3 non-energy intensities of energy supply (not an explicit KLEM-CHN parameter) flow from the complex procedure described at the end of Sect. 3.4. Let us illustrate this procedure. Keeping on using KLEM-CHN notations (see Appendix 2) and indexing calibration (2010) values with 0 subscripts, at each time $t$ of China-MAPLE trajectory, our first step is to compute a “KLEM-BU” energy output price building on constant non-energy costs and taxes, as

$${p}_{YE,t}^{BU}=\frac{{p}_{QE,0}{ \alpha }_{QE,0}+{p}_{EE,t} {\alpha }_{EE,t}+{w}_{0} {\lambda }_{E,0}+{p}_{K,0} {\kappa }_{E,0}}{1-{\tau }_{{R}_{E},0} {p}_{YE,t}^{BU}-{\tau }_{{Y}_{E},0} {p}_{YE,t}^{BU}}$$

(40)

which is simply the sum of unit input costs into energy production, Eq. 26 of KLEM. The only elements of this cost structure evolving through time are the energy intensity of energy supply (transformation) ${\alpha }_{EE}$ and its market price ${p}_{EE}$—for the sake of readability we drop time indexes henceforth. Both are derived from China-MAPLE at each time step, ${\alpha }_{EE}$ as the ratio of the total energy input into energy supply ${E}_{E}$ and of energy ‘output’ in the input–output sense of KLEM-CHN ${Y}_{E}$; ${p}_{EE}$ as the weighted average of the prices of the energy flows aggregating in ${E}_{E}$.

Our second step is to average ${p}_{YE}^{BU}$ and ${p}_{ME}$ the China-MAPLE-derived price of energy imports at same time $t$, into the ‘KLEM-BU’ supply price ${p}_{SE}^{BU}$. We do this taking account of what China-MAPLE indicates on the aggregate balance of imports and domestic output into supply at time $t$, following Eq. (15) of KLEM-CHN:

$${p}_{SE}^{BU}=\frac{{Y}_{E}}{{Y}_{E}+{M}_{E}} {p}_{YE}^{BU}+\frac{{M}_{E}}{{Y}_{E}+{M}_{E}}{p}_{ME}$$

(41)

Still following KLEM-CHN equations, we then build “KLEM-BU” domestic energy market prices as:

$$\forall j\in \left\{Q,E\right\} {p}_{Ej}^{BU}={p}_{SE}^{BU} \left(1+{\tau }_{{MS}_{Ej},0}\right)\left(1+{\tau }_{{ST}_{E},0}\right)$$

(42)

$${p}_{{C}_{E}}^{BU}={p}_{SE}^{BU}\left(1+{\tau }_{{MSC}_{E},0}\right)\left(1+{\tau }_{{ST}_{E},0}\right)$$

(43)

as well as the “KLEM-BU” energy export price:

$${p}_{{X}_{E}}^{BU}={p}_{SE}^{BU}\left(1+{\tau }_{{MSX}_{E},0}\right)$$

(44)

Our third step is to identify which of these four “KLEM-BU” prices is the closest from the corresponding China-MAPLE prices including the very ${p}_{EE}$ governing their trajectories and to compute the value of ${\delta }_{E}$ bridging the gap between this KLEM-BU price and its China-MAPLE counterpart. We renew the comparison at every time period. Let us assume that at some time period $t$ the gap is smallest between ${p}_{EQ}^{BU}$ and the average price of final energy consumption by firms inferred from China-MAPLE ${p}_{EQ}^{MAPLE}$, then ${\delta }_{E}$ at time $t$ is the solution to

$$\begin{array}{c}\frac{{Y}_{E}}{{Y}_{E}+{M}_{E}}\frac{\left(1+{\delta }_{E}\right)\left({p}_{QE,0}{ \alpha }_{QE,0}+{w}_{0} {\lambda }_{E,0}+{p}_{K,0} {\kappa }_{E,0}\right)+{p}_{EE} {\alpha }_{EE}}{1-{\tau }_{{R}_{E},0} -{\tau }_{{Y}_{E},0}} \left(1+{\tau }_{{MS}_{EQ},0}\right) \left(1+{\tau }_{{ST}_{E},0}\right)\\ +\frac{{M}_{E}}{{Y}_{E}+{M}_{E}}{p}_{ME}\left(1+{\tau }_{{MS}_{EQ},0}\right) \left(1+{\tau }_{{ST}_{E},0}\right)={p}_{EQ}^{\mathrm{MAPLE}}\end{array}$$

(45)

where the values without 0 subscript ${Y}_{E}$, ${M}_{E}$, ${p}_{EE}$, and ${\alpha }_{EE}$ are all inferred from time $t$ China-MAPLE results similar to ${p}_{EQ}^{\mathrm{MAPLE}}$.

The last stage of our procedure is to factor in the resulting ${\delta }_{E}$ in updated “KLEM-BU” prices and to compute what adjustment of the specific margins allows aligning these updated “KLEM-BU” prices on their China-MAPLE counterparts.

Appendix 6 Scenario assumptions

See Table 3

Table 3 Scenario constraints