China Economic Review 31 (2014) 130–144

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China Economic Review

Measuring plant level energy efficiency in China's energy sectorin the presence of allocative inefficiency

Baiding HU⁎,1

Department of Accounting, Economics and Finance, Lincoln University, Lincoln 7647, Canterbury, New Zealand

a r t i c l e i n f o

⁎ Corresponding author. Tel.: +64 3 423 0231.E-mail address: Baiding.Hu@lincoln.ac.nz.

1 I would like to thank the anonymous referee for hel

http://dx.doi.org/10.1016/j.chieco.2014.08.0111043-951X/© 2014 Elsevier Inc. All rights reserved.

a b s t r a c t

Article history:Received 3 March 2014Received in revised form 27 August 2014Accepted 27 August 2014Available online 3 September 2014

Most studies on measuring China's energy efficiency were conducted in the framework of theinput-oriented Data Envelopment Analysis. This approach generally calculates the technicalefficiency by shrinking all the input factors equally proportionally subject to the observed outputstill being producible. Thus, all the input factor efficiencies, including the energy efficiency, aremeasured as the technical efficiency. One drawback of this approach is the presumption of anidentical input factor frontier for all input factors and of unrestricted factor substitutability. Thepresent study employs a stochastic frontier analysis approach to measuring energy efficiencythat not only allows for non-identical input factor frontiers, but also controls for the effects onthe measure of energy efficiency of substitution away from energy or substitution of energy fornon-energy factors. This approach is applied to evaluating the efficiency performances of threetypes of energy amongst a sample of coal mines, petroleum refineries and power plants inChina's energy sectorwhich is specifically targeted by the Chinese government to improve energyefficiency.

© 2014 Elsevier Inc. All rights reserved.

JEL classification:D22D24Q41C51

Keywords:Energy efficiencyStochastic frontier analysisSubstitutionsTechnical efficiencyAllocative efficiency

1. Introduction

China's environmental challenges and increasing dependence on energy imports have prompted the Chinese government to strivefor improvement of energy efficiency and reduction of energy intensity. Therefore, assessment of China's energy efficiency hasattracted a lot of attention, for example, He, Zhang, Lei, Fu, and Xu (2013), Wu, Fan, Zhou, and Zhou (2012), Su, Zhou, Nakagami,Ren, and Mu (2012), Shi, Bi, and Wang (2010), Li and Hu (2012), Yang, Yang, and Chen (2011), and Wei, Ni, and Shen (2009), justto name a few. These studies show, amongst other things, that energy efficiency performances vary conspicuously between sectorsand regions. For example, the He et al. (2013) study that is concerned with energy efficiency in the iron and steel industry showsthat the average energy efficiency at the industry level was 61.1% on average over the period 2001–2008. This is in contrast to81.6% on average over the period 1997–2008 for the industrial sector (Wu et al., 2012). Such a big difference prompts further studieson energy efficiency performances in other sectors to provide amore comprehensive understanding of energy efficiency in China. Thepresent papermeasures energy efficiency performance at plant-level for China's energy sector. The energy sector is the largest energyuser both in terms of total energy consumption and the share of energy cost in the total cost (at a 2-digit industry classification level).Moreover, the Chinese government has recognised that oneway tomanage the country's environmental challenges and heavy depen-dence on imported energy is for the energy sector to achieve greater efficiency.

pful comments.

131B. Hu / China Economic Review 31 (2014) 130–144

Most studies on measuring China's energy efficiency were conducted in the framework of the input-oriented Data EnvelopmentAnalysis. This approach generally calculates the technical efficiency by shrinking all the input factors equally proportionally subjectto the observed output still being producible. Thus, all the input factor efficiencies, including the energy efficiency, are measured asthe technical efficiency. One drawback of this approach is the presumption of an identical input factor frontier for all input factors.The study of Shi et al. (2010) imposed a restriction to hold the non-energy input fixed while seeking the energy input frontier,which, although addressing the above-mentioned presumption somehow, essentially assumed that the energy and non-energyinputs are perfect substitutes. There has been a controversy regarding whether energy and capital are substitutes or complementsin the literature. For example, Hudson and Jorgenson (1974), Berndt and Wood (1975), and Fuss (1977) found the two factors ascomplements, while Griffin and Gregory (1976) and Pindyck (1979) found them as substitutes.

Substitutions between production factors are generally price induced but can also result from other actions on the part of theproducer. In the case of an energy input, a substitution away from it can show up as an improvement in energy efficiency in thesense that the output-energy ratio can increase. It is not impossible, albeit unlikely, that the ratio could rise amid a decline inthe technical efficiency of energy utilisation. This paper aims to measure energy efficiency in such a way that an improvement(worsening) in energy efficiency is necessarily the result of an improvement (worsening) in the technical efficiency of energyutilisation which is normally determined by technological and managerial factors, and hence is deemed the true cause of energyefficiency. Since factor substitutions and changes in technical efficiency can take place simultaneously, there is a need to control forthe substitution effect to evaluate energy efficiency.

Using the stochastic frontier analysis (SFA), the current study is able to address the above-mentioned methodological issues bymeasuring energy efficiency as the gap between the substitution-corrected actual andminimal feasible energy consumption. To con-trol for the substitution effects amounts to correcting the effects of energy-related allocative inefficiencies on the energy efficiencymeasure. Substitution–correction can be achieved by adopting a counter-factual approach which involves simultaneously evaluatingall factor use efficiencies against their respective would-be factor uses should there be an absence of allocative inefficiencies.

The data used in the study were collected from 150 plants from China's energy sector and cover the period 2000–2005 when thegrowth of total energy consumption had exceeded that of total output measured as the gross domestic product of the country. Thisperiod had also witnessed a significant growth of the dependence on imported oil and a big surge of oil prices. The efficiencies ofthree types of energy, namely, coal, electricity and other fuels (ofs), are estimated in conjunction with capital and labour efficiencies.The ofs mainly include natural gas and petroleum products. The analysis produces the estimates of plant and time specific energyefficiencies and a four-way decomposition analysis to evaluate the effects of returns to scale on the energy efficiencies.

The contributions of the paper to the literature are threefold. First, it provides amicro-level and industry specific energy efficiencyanalysis for China's energy sector which is a major energy consumer and is flagged by the government to improve energy efficiency.The literature shows that the level of energy efficiency varies significantly between industries and regions in China. Therefore, newindustry and/or region specific studies enrich the general understanding of the performance of energy efficiency in the country.Second, the micro-level data enables comparisons of efficiency performances between coal mines, petroleum refineries and powerplants in the country. Knowledge of the efficiency performances of the three types of energy producer is important for the designof China's industry specific energy policy. A surge in capital investment in the coal industry during the study period also lends itselfto inquiries about changes in productivity and efficiency as consequences of the large scale capital expansion. Third, the presentstudy addresses the effects on measuring energy efficiency of possible substitutions between energy and non-energy factors thatare generally unobservable.

The plan of the paper is as follows. The following section presents a brief review of energy efficiencymeasurement in the literature.Section 3 provides a commentary on themacroeconomic characteristics of the energy sector in terms of pricemovements and outputgrowths. Section 4 describes the analytical framework. Data description andmodel specification and estimation are given in Section 5.Section 6 presents discussions of empirical results with some concluding remarks contained in Section 7.

2. Previous studies on measurement of energy efficiency

In the literature, energy efficiency is commonly measured as the ratio of output to energy input, that is, output per unit of energy.The numerator and the denominator of the ratio are typically aggregates of outputs and energy inputs, respectively. Therefore, anincrease in the ratio is interpreted as an improvement in energy efficiency. Such a ratio cannot, however, differentiate betweensubstitution away from energy, which amounts to energy conservation, and an improvement in energy efficiency itself, since bothcan lead to an increase in the ratio. Substitution away from energy will take place when energy becomes more expensive relativeto other production factors, such as, capital; while a more efficient utilisation of energy will result when there is an improvementin technical efficiency and/or a technological progress in energy utilisation. Substitution can also take place between different typesof energy, which introduces energy quality issues intomeasurement of aggregate energy efficiency. Thus, there is a need to overcomethe deficiency of using the ratio to measure energy efficiency.

While Allan, Hanley, McGregor, Swales, and Turner (2007) measure energy efficiency in the thermodynamic sense, that is, an im-provement in energy efficiency is equivalent to an increase in the value of heat contents for the same amount of energy in naturalunits, most studies measure energy efficiency as the ratio of output of a process to energy input into the process (Patterson, 1996).For example, Farla, Cuelenaere, and Blok (1998) interpreted the inverse of energy intensity, measured as the ratio of physical energyconsumption to output, as energy efficiency in The Netherlands. Their study attributed changes in such a ratio to changes in energyefficiency and structure, where “energy efficiency” was the inverse of energy intensity at the sector level. Koopmans and te Velde(2001) measure energy efficiency as energy conservation due to substitution of new and energy-saving capital for energy with a

132 B. Hu / China Economic Review 31 (2014) 130–144

fixed output level, which, in essence, used the energy–output ratio as an indicator of energy efficiency. Similarly, the ratio was used asthe measure of energy efficiency in a number of other studies, such as, Fredriksson, Vollebergh, and Elbert (2004), Buck and Young(2007), Han, Fan, Jiao, Yan, and Wei (2007), and Shi (2007).

Conrad (2000) and Mukherjee (2008) took a modelling approach to themeasurement of energy efficiency. In Conrad (2000), theenergy efficiency was measured as a function of firms' R&D expenditure. The parameter of the function partially characterises theconditional distribution of the total cost of production and the R&D expenditure on minimising energy waste. The energy wastewas regarded as the only source of energy inefficiency. Since firms seek cost minimisation and energy waste increases the cost, theparameter of the function was estimated by maximising the profit function. A drawback of this approach is that cost minimisationmakes the firm seek allocative efficiency which will not necessarily result in a minimal use of all the inputs, that is, cheaper inputstend to get used more within the technical possibility of substitution.

Mukherjee (2008) measured energy efficiency as the gap between the observed energy consumption and the feasible minimalenergy consumption which was the energy consumption frontier. The energy consumption frontier was deterministic and thereforeany uncontrollable random shock to the production process would make the frontier shift and hence was interpreted as a change inenergy efficiency. This limitation can be addressed by the stochastic frontier approach which Boyd (2008) adopted to measure theenergy efficiency for the US cornmilling industry. Boyd treated the best industry practice as the frontier being represented by a singleplantwhose energy inefficiencywas the smallest amongst all the plants where the inefficiencywas estimated against a stochastic andplant specific energy use frontier. Also employing the SFA approach, Filippini and Hunt (2011) evaluated energy efficiency for 29OECD countries, controlling for a range of factors, such as, income, price, climate.

Recently assessment of China's energy efficiency has attracted a lot of attention, for example, He et al. (2013), Wu et al. (2012),Su et al. (2012), Shi et al. (2010), Li and Hu (2012), Yang et al. (2011), and Wei et al. (2009), just to name a few. Most of the studiesmeasure energy efficiency at the economy level or regional level and are in the framework of the input-oriented Data EnvelopmentAnalysis (DEA) whereby energy efficiency is measured as the technical efficiency. As in any DEA analysis, all factor use inefficienciesare equal to the technical inefficiency, which implicitly assume an identical functional relationship between the factor use frontier andthe technical inefficiency for all factors, a restriction that is absent in the SFA.

3. A commentary on China's energy sector

Compared to other sectors, the energy sector is both an energy producer and an energy consumer. As an energy producer, itsoutput determines the extent of the country's reliance on energy imports. China's continuing rapid economic growth has placed anenormous pressure on the country's energy sector. During the study period 2000–2005, the growth of energy consumption exceededthat of GDP for 2 years as shown in the top panel in Fig. 1. The total energy production has increased, on average, at the rate of 8.2% perannum over the period 2000–2009, whereas the total energy consumption for the same time period has increased, on average, at the

1

5

9

13

17

2001 2002 2003 2004 2005

Annual growth rate : GDP vs Energy

Energy GDP

1.2

1.6

2.0

2.4

2.8

3.2

2000 2001 2002 2003 2004 2005 2006 2007 2008 2009

Total energy produc�on and consump�on (billion tons of SCE)

Total Energy Produc�on Total Energy Consump�on

Fig. 1. Growth rates of GDP and energy consumption, and quantities of energy production and consumption. Note: All data are from various issues of China StatisticalYearbook compiled by National Bureau of Statistics of China. GDP is measured in real terms and Energy is measured in standard coal equivalent (SCE).

133B. Hu / China Economic Review 31 (2014) 130–144

rate of 8.6% per annum. The growth differential has resulted in an average annual energy import of about 0.2 billion tons of standardcoal equivalent (SCE). The bottom panel in Fig. 1 shows the differences between energy production and energy consumption overthe 10-year period, indicating that the shortage of domestic energy supply was generally increasing. To address environmentalchallenges, reduce energy imports, and boost energy efficiency, the government has realised the importance of reliance on domesticresources in energy conservation and exploration with the conservation taking precedence.

Energy pricemovements in China can be generally depicted by the country's industry producer price indices. Of the fourteen or soindustry producer indices compiled by the National Bureau of Statistics of China, three are concerned with energy prices, namely, theprices of electricity, coal and petroleum products. The top panel in Fig. 2 shows the year-on-year producer price indices for the threeenergy industries over the period 1980–2006. Two spikes in the prices of petroleum products were recorded in 1993 and 2000, re-spectively. The conspicuous price surge in 1993 marked the beginning of China's consumption of petroleum products exceedingthe domestic production, and the one in 2000 witnessed the largest ever increase in crude oil prices since the oil price shocks inthe 1970s. Although the year-on-year price growth slowed down post the year 2000, all the prices kept rising steadily on their1990 levels with those of petroleum products rising the fastest.

The bottom panel in Fig. 2 contrasts the average year-on-year price growth indices for the three types of energy for two differentperiods; period 1986–1991, which may be considered the beginning of the end of energy self-sufficiency for China, and period2001–2006, which witnessed the substantial influence of international energy markets on the country's energy demand. The fastergrowth rate in the prices of petroleum products can be attributed to China's increasing importation of crude oil from 1993 onwards.As expected, the average price growth rate of petroleum products during period 2001–2006 was the highest, largely due to the oilprice surges in international markets. Unlike crude oil, China has a large reserve of coal albeit the locations of the resource are gener-ally far from its consumption centres andmovements in domestic coal prices should bemainly driven by onshore supply and demand.That the coal price also went up faster during the 2001–2006 period simply reflects huge domestic coal demand, be it for electricitygeneration or heating. It should be pointed out that the electricity price in Chinawas particularly under government control and henceits price indices did not reflect market demand and supply situations.

Against the backdrop of the energy price growth depicted above, the average growth rates of fuel consumption for various fuels bythe energy sector and the economy are shown by the two panels in Fig. 3, whereby the SCE is the sum of all the other nine types ofenergy. The dichotomy of time period and energy user sheds some light on the nexus between the growth rate of energy pricesand those of energy consumption and on how the two energy users responded to the same energy price changes. The top (bottom)panel shows the consumption growth rates of the various types of energy for the two users when the energy prices were growingrelatively slowly (faster). During period 1986–1991, the total energy consumption grew faster for the energy sector than forthe economy as a whole thanks to the faster growth in the consumption of six of the nine fuels. In contrast, during period 2001–2006, the total energy consumption by the energy sector slowed down relative to that by the rest of the economy. For most of thefuels, the growth rate of fuel consumption for the energy sector lagged behind the rest of the economy. Therefore, it can beexpected that the rise of energy prices would have a bigger impact on the energy sector than on the rest of the economy.

Compared to its energy input growth, the energy sector's output grew faster, which resulted in a continuous rise in the ratios ofoutput to energy. Fig. 4 shows the ratio of the sector's real Gross Value of Output (GVC) to its SCE input. It is an output–energy

90110130150170190

Producer price indices: previous year = 100

Power Industry Coal Industry Petroleum Industry

100.0

105.0

110.0

115.0

Power Coal Petroleum

Average year-on-year growth rates of fuel prices

1985-1991 2000-2006

Fig. 2. Growth rates of fuel prices. Note: All data are from various issues of China Statistical Yearbook compiled by National Bureau of Statistics of China.

0.95

1.05

1.15

1.25

1.35

Average year-on-year growth rate of fuel consump�on1985-1991

Energy sector Economy

0.850.951.051.151.25

Average year-on-year growth rate of fuel consump�on2000-2006

Energy sector Economy

Fig. 3.Average year-on-year growth rates of fuel consumption.Note: All data are fromvarious issues of China Statistical Yearbook compiled byNational Bureau of Statistics ofChina. SCE: Standard Coal Equivalent.

134 B. Hu / China Economic Review 31 (2014) 130–144

ratio and therefore a measure of energy efficiency since a genuine improvement in the technical efficiency of energy utilisation canlead to an increase in the ratio. The figure clearly shows acceleration in the improvement in energy efficiency as measured by theratio starting from the end of the 1990s, and the ratio remained at the relatively high level for the post-1990s period. Suchsectoral-level performance of energy efficiency can be contrasted and compared with plant-level performances that resulted fromthe analysis from the sections below.

4. Analytical framework

As outlined in Section 1, the analytical framework of the present study dwells on an SFA approach to the estimation of a joint factoruse frontier to obtain the substitution-corrected actual use of energy and the energy use frontier. For the given output and prices, theenergy use frontier, hence energy efficiency, is only determined by technical efficiency and allocative efficiency under the costminimisation assumption on the part of the producer. In the case of a Cobb–Douglas production frontier, Schmidt and Lovell(1979) (SL) showed that both technical and allocative efficiencies affect factor use frontiers in a linear fashion, which allows explicitevaluation of the effects on the factor use frontier of both technical and allocative efficiencies. Since the Cobb–Douglas productionfunction imposes unitary elasticity of substitution, which is considered too restrictive, the present study adopts the flexible translogfunctional form for the stochastic production frontier model to characterise the firm production. Under the translog production

1000

2000

3000

4000

5000

6000

(RMB'000 per 10,000 tons of SCE)

Fig. 4. GVO-Energy ratio: energy sector. Note: All data are from various issues of China Statistical Yearbook compiled by National Bureau of Statistics of China. GVO: GrossValue of Output in real terms.

135B. Hu / China Economic Review 31 (2014) 130–144

technology, it is not feasible to conduct an explicit evaluation of the efficiency of factor use since the factor use frontier cannot bederived analytically. Therefore, the evaluation has to be done numerically as demonstrated by Kumbhakara and Wang (2006)(KW) that resorted to a numerical procedure to estimate production efficiencies for 72 US electric utilities.

The existence of allocative inefficiencies indicates that the factors were either over- or underused which would suggest thatthe overused factors have been substituted for the underused factors. For example, for a given output level, the amount of energyconserved has to be substituted for by other production factors to maintain the output level ceteris paribus. In the case of a genuineimprovement in energy efficiency, less energy is required to produce the same amount of output ceteris paribus, thus the energysaved need not be substituted for by other production factors. Such substitutions can be deliberate or inadvertent on the partof the producer. The Chinese government's energy conservation and emission reduction initiatives could make producers simplycut back energy input to comply with regulations. Clearly, for a fixed level of technical efficiency, if energy has been overused(underused), then the energy efficiencymeasured is likely to be underestimated (overestimated). The SFA approachmakes it possibleto control for the effect on the energy efficiency measure of substitutions away from energy (or the opposite) that incur allocativeinefficiency. More specifically, the actual factor uses are to be replaced by their would-be factor uses if there have not been allocativeinefficiencies.

Using the SFA approach to gauging energy efficiency was conducted in Boyd (2008) and Filippini and Hunt (2011). However, thefunctional forms of the energy use frontiers in those studies were specified irrespective of the underlying production technology,which amounts to assuming that different production technologies entail identical energy use frontiers, marginal products and factorsubstitutability. The present study is different to the two SFA studies mentioned above in two aspects. First, the energy use frontiersare derived from the underlying production technology to recognise the nexus between the production technology and the factor usefrontiers. Second, the energy use frontiers are jointly determined with the other factor use frontiers, which is necessary to control forthe above-mentioned substitution effects on the evaluation of factor use efficiency. Consider a production process that employs theproduction technology, g(⋅), and k production factors, denoted by x = (x1, x2, ⋯ xk), to produce a single output, y, with y ≤ g(x),where g(x) represents the maximum possible output, or, the output frontier.

The actual output may be subject to random disturbances and technical inefficiency that prevent the attainment of the outputfrontier. The model below is assumed to characterise the relationship between the actual output, y, actual inputs, xa, and technicalinefficiency,

ln y ¼ lng xa� �þ v‐u ð1Þ

where u is a nonnegative numbermeasuring technical inefficiencies and v is a random disturbance. The factor use frontiers, xf, are theminimal feasible factor uses, for the given g(⋅), to produce the output level, y, that is, xf ≤ xa. The factor use inefficiencies for all the kfactors are the differences between xa and xf, which measure the percentages of overuse, i.e., the percentages above the frontiers. SLdefines the factor use frontiers as the would-be factor uses were there no technical and allocative inefficiency, namely, the xf satisfiesthe following conditions (ignoring the random disturbance),

ln g x f� �

¼ ln g xa� �−u ¼ ln y ð2Þ

g fj

g f1

¼ gajga1

ζ j ¼wj

w1; j ¼ 2; ⋯k ð3Þ

where g fj ¼ ∂g xð Þ

∂x j

���x¼x f

, gaj ¼ ∂g xð Þ∂x j

���x¼xa

, ζj is a positive constant, and wj is the price of factor j.

The u in Eq. (2) represents the output loss due to technical inefficiency. In otherwords, the actual inputs, xa, should have generateda larger output than y in the absence of technical inefficiency. Eq. (3) states the first order conditions of cost minimisation, that is, nofactors are either over- or underused or there is the absence of allocative inefficiency. The system that comprised Eqs. (2) and (3)contains the same number of equations as the number of the unknown factor use frontiers. Hence, the energy use frontier is simulta-neously determined with the other factor use frontiers.

Since all points on the production possibility frontier represent the factor uses in the absence of technical inefficiency, the unique-ness of the factor use frontiers requires extra identifying conditions. The requirements for allocative efficiency specified in Eq. (3)serve as such identifying conditions. It is necessary to point out that while the presence of technical inefficiency will surely lead tofactor use inefficiencies, the presence of allocative inefficiencies can be ambiguous, depending on whether the factor is underusedor overused. An improvement in allocative efficiency necessitates an increase (a reduction) in the uses of underused factors (overusedfactors), that is, an increase (decrease) in factor-use inefficiency. Therefore, Eq. (3) provides a vehicle to control for the substitutioneffects that interfere with the evaluation of factor use efficiency.

An implication of Eqs. (2) and (3) is that if factor j is underused (ζj N 1), then, xjawill be necessarily smaller than xjf, a contradiction to

the definition of frontier. Thus, there arises the need to substitution-correct xja to measure the efficiency of factor j.When the g(⋅) takes the Cobb–Douglas functional form, the solutions to xf have closed form expressions (SL). For example, given

the return of scale, r, an amount of technical inefficiency, u, the energy inefficiency, in the absence of any allocative inefficiency, isgiven by 1

r u. With three production factors, namely, labour, capital and energy, and the allocative inefficiencies of capital and energy,

136 B. Hu / China Economic Review 31 (2014) 130–144

ξK and ξE, the energy inefficiency amounts to 1r βKξK−ξE þ 1

r u, where βK is the elasticity of output with respect to capital. Clearly, anoveruse (underuse) of energy, ξE N 0 (ξE b 0), increases (decreases) energy inefficiency while the direction of the effect of ξK dependson the sign of βK.

Since the Cobb–Douglas production function imposes the restriction of unity of elasticity of technical substitution between pro-duction factors, the present paper adopts the translog (Christensen, Jorgenson, & Lau, 1973) functional form which is flexible inrepresenting the underlying production technology, g(⋅). The price of pursuing the flexibility is the unavailability of closed form so-lutions to xf, therefore, numerical solutions have to be sought.

5. Data and model specification

5.1. Data

The data used for the present study consist of output and inputs for 150 plants, of which 51 are coalmines, 44 power plants and 55petroleum refineries, for the period 2000–2005 (National Bureau of Statistics of the People's Republic China). The output was mea-sured as the gross value of output in the year 2000 prices. The inputs include labour, capital and various types of fuel. The total em-ployee number was used as the labour input, with the price of labour being the average wage, i.e., total labour cost/totalemployees. Capital related measures include the year-end original value and annual average balance of the net value of fixed assetsin real terms. In light of Holz (2006), the capital stock data for the plants were imputed by applying the growth rates of structuresand equipment at the level of the energy sector to plants' original values of fixed assets. The price of capital at the plant level was un-available, so the price index of fixed asset investment at the national level was used as a proxy.

The fuel inputs comprise coal and electricity, diesel, gasoline, kerosene, crude oil, liquefied petroleum gas (LPG) and natural gas(NG). Table 1 provides a profile of the sample plants in terms of fuel consumption and output–energy ratios. Clearly, coal and electric-itywere themost commonly used fuels in the sense that almost every plant had reported consumption of themevery year. In contrast,diesel and gasolinewere the least commonly consumed fuels since only about a third of the plants consumed them,with about a fifthof the plants having not used the other four fuels. Therefore, those six fuels were aggregated based on their heat content values in gigajoules (GJ) to form the third type of energy, ofs, for the present analysis. There are two reasons for such an aggregation,first, apart fromtheir being not consumedby every plant, those that did consume themconsumed in small quantities and, in some cases, the quantitieswere so small that they were almost negligible. Secondly, to include them separately in the model increases the numbers of param-eters and fuel frontiers significantly.

The output–energy ratios in Table 1 were computed by dividing a plant's real gross output value by the plant's fuel consumption.These ratios are rawmeasures of energy efficiency and could be misleading if, as elaborated earlier in the paper, the rise of the ratiowasdue to substitution away from the fuel. Over thewhole sample period 2000–2005, the ratios suggest that the efficiency of coalwasdeclining while those of electricity and ofs were improving. These ratios should be the true indicators of energy efficiency providedneither substitution away from electricity and ofs nor substitution of coal for other factors took place.

The fuel prices at the plant level were computed by dividing the quantity of fuel consumption by the corresponding fuel expendi-ture. The shortcoming of this approach to obtaining the price information is that the computed pricewas the average price rather thanthe actual tariff that the plant had faced. Table 2 provides some descriptive statistics about the six variables in Eq. (4) and price indicesfor the three types of energy for the whole sample as well as for each type of plant. Of the three types of energy, the price of coal had

Table 1Profiles of energy consumption and energy-output ratios: sample plants.

Number of plants by type:51 coal mines44 power plants55 petroleum refineries150 plants in total

Energy consumption by number of plantsCoal Electricity Diesel Gasoline Kerosene Crude oil LPG NG

2000 150 150 42 33 129 123 135 1382001 150 150 44 34 129 123 136 1382002 150 150 41 33 129 123 135 1382003 149 150 36 31 129 123 136 1352004 149 150 31 33 127 127 134 1372005 149 150 34 33 133 126 136 134

Average growth rates of output-energy ratios (%)Output/coal Output/electricity Output/ofs

2000–2002 −9.6 −2.2 0.32001–2003 −4.9 5.5 9.52002–2004 −0.2 13.9 17.62003–2005 3.0 15.6 21.92000–2005 −2.9 8.4 12.4

Data source: National Bureau of Statistics of China.

137B. Hu / China Economic Review 31 (2014) 130–144

risen faster than any of the ofs overall. The same can be said for the coal mines and refineries although the price of ofs increased thefastest for the power plants.

5.2. Model specification and estimation

The data set for the present study contains 150 plants over a 6-year period. The assumption of a translog production technology foreach of the plants means that Eq. (1) is specified as follows,

2 O'Dthat ougsibility.the Jacothus, intivate anbut also

ln yit ¼ ln g xitð Þ þ vit‐uit

¼ α0 þ αcDci þ αpDpi þXk

αk ln xkit þ αt t þXk

0:5αkk ln xkitð Þ2 þ αttt2

þXk

Xk0≠k

αkk0 ln xkit ln xk0it þXk

αkt ln xkitt þ vit‐uit

ð4Þ

where k indexes the 5 explanatory variables, i indexes the 150 plants and t the 6 years. The variable definitions are as follows,

y gross output value in real terms (10,000 RMB),x1 total number of employees,x2 capital stock in real terms (1000 RMB),x3 tons of coal,x4 10,000 kWh electricity,x5 ofs (GJ),Dc dummy variable equal to 1 for coal mines and 0 otherwise,Dp dummy variable equal to 1 for power plant and 0 otherwise,

The production function given by Eq. (4) differentiates the three types of energy plant by the two plant-type dummy variables, Dc

and Dp, which is themost parsimonious way tomodel plant type differences in production frontier.2 The u in Eq. (4) represents time-varying individual differences for the panel data set, after controlling for the various production inputs and plant type. These differ-ences are assumed to result from plant- and time-specific technical inefficiencies, which are nonnegative random variables. The vare assumed independently and identically distributed random disturbances that render the output frontier stochastic and are uncor-related with the u.

Since the translog function is a second-order approximation to the true production function, namely, ln g(xit), the exact form forthe marginal products, gj, in Eq. (2) are unknown. However, the cost minimisation condition as indicated in Eq. (2) also implies thatthe ratio of the output elasticity with respect to input j to that with respect to input 1 is equal to the ratio of the cost shares of the twoinputs (KW), namely,

∂ ln y=∂ ln xj

∂ ln y=∂ ln x1¼ wjxj

w1x1ð5Þ

where

∂ ln y∂ ln xj

¼ α j þ αjj ln xj þXk≠ j

αjk ln xk þ αjtt ð6Þ

Unlike the technical inefficiency, u, which only appears in the production function, allocative inefficiency is the result of the failureto achieve costminimisation and therefore should only appear in Eq. (5). Using labour (x1) as thenumeraire, the allocative inefficiencyin the use of factor j, ξj, is such that Eq. (5) holds if the price of factor j is wjeξ j instead of wj, that is,

∂ ln y=∂ ln xj

∂ ln y=∂ ln x1¼ wje

ξ j x j

w1x1ð7Þ

onnell, Rao, and Battese (2008) introduced the concept of metafrontier to address issues that arise in comparisons between heterogeneous groups of producersht to have their own frontiers. The present study chooses not to adopt the stochastic metafrontier approach based on two reasons. One is about computing fea-The constraints for maximising the current likelihood function are already very complex and tedious (For example, they have to make sure the determinant ofbian matrix as well as that of the covariance matrix of the allocative inefficiencies to be positive). The constraints for the metafrontier are observation specific,this case, 900 more constraints to be satisfied. The other is about the imperativeness of a metafrontier. The practical examples that O'Donnell et al. use to mo-d demonstrate themetafrontier analysis are all of international comparisons. The 150 plants included in the present study are not only from the same countryfrom the same sector.

Table 2Descriptive statistics for the dependent and explanatory variables.

Variable Mean Standard deviation Minimum Maximum

y 12.13 2.50 6.39 18.65x1 7.26 2.03 2.30 11.64x2 12.00 2.72 4.35 17.98x3 7.68 3.11 −2.35 13.83x4 10.17 3.97 0.00 16.87x5 6.40 3.80 1.69 16.08

Average fuel price indicesCoal Electricity ofs

Whole sample 2000 100.00 100.00 100.002001 103.68 101.80 100.782002 101.88 108.86 103.022003 107.69 103.10 103.112004 108.59 112.83 108.382005 122.30 109.11 116.25

Coal mines 2000 100.00 100.00 100.002001 101.99 102.20 100.042002 98.72 101.05 106.712003 109.32 98.32 96.162004 107.36 107.72 99.862005 129.82 103.62 117.11

Power plants 2000 100.00 100.00 100.002001 110.88 96.87 100.202002 104.23 98.62 97.182003 108.48 95.97 104.032004 112.41 108.32 119.832005 116.14 120.77 121.13

Refineries 2000 100.00 100.00 100.002001 100.34 103.32 102.712002 103.44 118.20 101.962003 105.48 109.12 114.952004 107.16 118.15 112.782005 118.97 108.80 109.91

Note: y: gross output value in real terms (10,000 RMB), x1: total number of employees, x2: capital stock in real terms (1000 RMB), x3: tons of coal, x4: 10,000 kWhelectricity, x5: ofs (GJ). All data are from the National Bureau of Statistics of China.

138 B. Hu / China Economic Review 31 (2014) 130–144

A positive (negative) ξj indicates that input jwas underused (overused) compared to labour, since the input was used as if itsprice were wjeξ j which is higher (lower) than the actual price, wj. Given that the prices, wj, are exogenous to the producer, analternative interpretation would be that the plant could have achieved allocative efficiency/cost minimisation by using e−ξ j x j

amount of input j instead of xj. Thus, while Eq. (5) describes the situation whereby there is absence of allocative inefficiency(ξj = 0), Eq. (7) implies that the amount of input j should be varied by 100 eξ j−1

� �per cent in order to achieve allocative effi-

ciency. As demonstrated above, factor use inefficiencies are caused by either or both of technical and allocative inefficiencies.Like the u, the ξ s are also unobservable and have to be estimated. Substituting Eq. (6) for the partial derivatives in Eq. (7)yields,

ξ j ¼ ln α j þ αjj ln xj þXk≠ j

αjk ln xk þ αjt t

0@

1A− ln α1 þ α11 ln x1 þ

Xk≠1

α1k ln xk þ α1tt

!

– ln wjxj

� �þ ln w1x1ð Þ j ¼ 2; 3; 4; 5

ð8Þ

Therefore, the ξ s are estimated once the production function in Eq. (4) are estimated. Since the logarithms arefunctions of the production function coefficients, Eq. (8) actually imposes restrictions on the values of the productionfunction coefficients. Upon obtaining the estimates of the u and ξ s, the estimates of the five factor use inefficienciesbecome obtainable.

When the inputs are treated as exogenous variables, the technical inefficiencies, u, can be consistently estimated after estimatingEq. (4) using least squares. However, the inputs should be treated as endogenous variables for the present study since the plants wereassumed to select the level of input to minimise the production cost for a given level of y. Thus, Eq. (4) will have to be estimated by

139B. Hu / China Economic Review 31 (2014) 130–144

either an instrumental variable estimator, such as, the Generalised Method of Moments estimator (Hansen, 1982) which requiresorthogonality assumptions, or a maximum likelihood estimator (MLE) which requires distributional assumptions for both u and v.Since in the literature on efficiency studies researchers commonly make distributional assumptions about the inefficiency variableand the stochastic noise, the present study uses an MLE for estimation with the assumption that the u is a random draw from atruncated normal distribution at zero, N+(0, σu

2), and the v from the normal distribution, N(0, σv2). These distributional assumptions

are also necessary for using the conditional mean method of Battese and Coelli (1988) to estimate observation specific u. To use theinformation on cost minimisation implied by Eq. (8), it is assumed that the factor use inefficiencies follow a multivariate normaldistribution, namely,

Table 3MLE est

Varia

ConstCoalRefinx1x2x3x4x5tx12

x22

x32

x42

x52

t2

Note: Si(1000 R

ξ ¼ξ2ξ3ξ4ξ5

2664

3775 � N 0;Σð Þ ð9Þ

Therefore, the likelihood function for Eq. (4) for each observation is the joint probability density function of vit - uit and ξit, with theJacobian being thematrix of thefirst derivatives of vit - uit and ξitwith respect to xit. Since the elements inΣ in Eq. (9) can be estimatedby their sample counterparts, KW suggested that the likelihood function can be concentrated with respect to those elements so thatthe number of parameters to be estimated is reduced by 10.

Once Eq. (4) is estimated and hence Eq. (8), the plant and year specific factor use frontiers, xjitf , are the solutions to the followingsystem where θ denotes the MLE estimates of all the parameters in Eq. (4),

yit ¼ ln g x fit

� ����θ þ vit ¼ yit þ vit ¼¼ α0 þ αcDci þ αpDpi þ

Xk

αk ln xfkit þ αt t þ

Xk

0:5αkk ln xfkit

� �2 þ αttt2 þ

Xk

Xk0≠k

αkk0 ln xfkit ln xf

k0 it

þXk

αkt ln xfkitt þ vit

ð10Þ

0 ¼ ln

α j þ αjj ln xfjit þ

Xk≠ j

αjk ln xfkit þ αjtt

α1 þ α11 ln xf1it þ

Xk≠1

α1k ln xfkit þ α1tt

0BBB@

1CCCA− ln

wjitxfjit

w1itxf1it

!j ¼ 2; ⋯;5 ð11Þ

The above system is obtained from the estimated Eqs. (4) and (8) by setting the uit= ξjit=0 since factor use frontiers are definedas factor uses in the absence of both technical and allocative inefficiencies. The differences between the factor use frontiers and theactual factor uses, xjit − xjit

f , measure factor use inefficiencies.

6. Empirical results

Table 3 presents the MLE estimates of Eq. (4) and shows that most of the coefficients are significant at the conventionalsignificance levels. As illustrated above, the various measures of efficiency can be constructed based on the estimated coefficients.Below are the discussions of the estimated measures of efficiency.

imates of the production function parameters.

bles Coefficients Standard error Variables Coefficients Standard error

ant. 5.6798⁎⁎⁎ 0.1754 x1x2 −0.0135⁎ 0.0076−0.4336⁎⁎⁎ 0.0509 x1x3 −0.0020 0.0058

ery 0.7991⁎⁎⁎ 0.0224 x1x4 −0.0069⁎⁎ 0.00360.8179⁎⁎⁎ 0.0298 x1x5 −0.0019 0.0034

−0.3665⁎⁎ 0.0215 x2x3 0.0022 0.0040−0.0035 0.0210 x2x4 0.0079⁎⁎⁎ 0.0020−0.0189 0.0161 x2x5 0.0025 0.0033

0.1832⁎⁎⁎ 0.0292 x3x4 −0.0003 0.00080.0066 0.0100 x3x5 −0.0007 0.0012

−0.0293⁎⁎⁎ 0.0129 x4x5 0.0020⁎ 0.00110.0595⁎⁎⁎ 0.0036 tx1 −0.0187⁎⁎⁎ 0.00510.0012 0.0021 tx2 0.0222⁎⁎⁎ 0.00480.0020⁎⁎⁎ 0.0005 tx3 0.0001 0.00110.0062⁎⁎⁎ 0.0008 tx4 −0.0019 0.0014

−0.0002 0.0009 tx5 0.0031⁎⁎ 0.0010

gnificance: ***: 1% level; **: 5% level; *: 1% level. y: gross output value in real terms (10,000 RMB), x1: total number of employees, x2: capital stock in real termsMB), x3: tons of coal, x4: 10,000 kWh electricity, x5: ofs (GJ). All data are from China's National Bureau of Statistics.

Table 4Estimated technical and allocative inefficiencies (percentages) (sample means).

Year TI Capital Coal Electricity ofs

Over Under Over Under Over Under Over Under

All2000 6.50 87.72 100.89 65.72 62.52 68.92 61.19 73.50 82.422001 5.15 84.01 108.27 68.62 76.84 68.21 88.44 73.31 109.762002 4.20 85.45 97.26 63.58 75.85 67.26 83.03 79.78 83.912003 3.47 84.96 63.78 65.31 57.40 68.96 48.83 67.20 105.182004 3.01 86.55 34.93 71.51 43.09 76.14 55.15 75.16 114.852005 3.18 86.56 42.73 71.76 36.16 79.45 45.21 75.59 123.81

Coal mines2000 7.43 82.50 140.51 58.56 73.41 57.31 71.38 64.91 73.992001 5.95 78.42 124.39 61.93 118.95 54.44 125.81 58.71 98.582002 5.00 79.01 106.00 61.08 115.99 63.46 121.11 74.80 106.492003 4.33 83.38 72.87 57.95 81.94 61.27 54.68 58.51 97.862004 4.16 76.78 62.07 53.20 63.53 76.48 71.87 101.172005 5.37 79.08 59.01 50.92 68.09 77.45 74.20 90.08

Petroleum refineries2000 5.78 87.61 61.86 48.76 69.13 45.28 74.32 105.842001 4.25 86.49 102.72 66.40 50.26 72.77 63.84 77.50 108.162002 3.28 84.64 32.48 59.99 47.25 63.26 49.44 81.39 96.842003 2.58 80.29 23.05 60.23 45.03 66.46 48.93 72.96 109.932004 2.09 89.31 23.02 72.46 49.29 76.68 28.35 72.34 102.322005 1.81 89.55 74.63 39.78 78.17 27.02 76.61 106.77

Power plants2000 6.31 93.82 21.64 72.48 57.51 76.76 66.08 77.57 0.232001 5.34 87.29 51.60 74.15 31.34 74.65 50.41 80.40 0.182002 4.43 93.68 44.57 68.42 39.84 74.66 43.06 81.99 0.132003 3.56 92.67 90.86 74.86 29.37 77.75 32.59 68.03 0.312004 2.84 94.67 46.85 77.51 18.63 86.77 28.11 83.32 0.442005 2.33 91.61 42.73 80.49 12.75 91.88 21.24 75.44 5.51

Note: numbers in the table are sample estimates and ofs (other fuels).

140 B. Hu / China Economic Review 31 (2014) 130–144

6.1. Technical and allocative inefficiencies

Since under the analytical framework factor use inefficiencies are caused by technical and allocative inefficiencies, discussions onthe two types of inefficiency are conducted first. The observation specific technical inefficiency estimates indicate the percentage bywhich the production level by plant i in year twas below the frontier, that is, 100 e−uit per cent. To facilitate discussions, a summary ofthe estimates of both the types of inefficiency are presented in Table 4, whereby the figures were averaged for the whole sample aswell as for each of the three types of the plant. Column 2 shows that the technical inefficiency evaluated at the sample mean reducedfrom 6.5% in 2000 to 3.2% in 2005, an indication that overall the technical inefficiency was declining over the study period for all theplants. In other words, the average production level of the sample plants rose from 93.5% of the frontier to 96.8%. Of the three types ofplant, the petroleum refineries weremore technically efficient than the power plants that, in turn, outperformed the coal mines. Thatthe coalmines were the least technically efficient plants may be no surprise given that small and individually owned coalmines werecommon during the period. Due to the nature of the technology, petroleum refineries and power plants were seldom small in size andwere much more sophisticated in technology and management.

Columns 3–10 present the estimated allocative inefficiencies. In computing the allocative inefficiencies, labour was used as thenumeraire, that is, the x1 in Eq. (8). The numbers in the table are the sample averages of the percentages of over- and underuse ofthe input factors, which are observation specific allocative inefficiency estimates, namely, 100 eξkit−1

� �per cent. The averages

were computed separately for plants that experienced underuse (eξkit−1 N 0) and those that experienced overuse (eξkit−1 b 0), toavoid cancellation of positive and negative estimates if an overall mean were computed. The magnitude of overuse was around85% over the years, whereas that of underuse varied largely, from about 100% to 35%. The range of these percentages are not unusual,considering that KW found an overuse of capital of 221% for the 72US electric utilities and SL reported an overuse of capital of 93% and45%, respectively, compared to fuel and labour for 150 US steam-electric generating plants.

For coal and electricity, the percentage of overuse rose in 2005 while that of underuse declined, on their 2000 levels. The extenttowhich coalwas overusedwas found larger for the petroleum refineries andpower plants than for the coalmineswhichhad a higherpercentage of underuse of coal than the other plants. This is also the case for electricity. For ofswhichwas largely composed of petro-leumproducts, the petroleum refineries had the highest percentage of underuse, followedby the coalmines and electricity generatorsthat experienced negligible amount of underuse.

141B. Hu / China Economic Review 31 (2014) 130–144

The way allocative inefficiency is defined necessitates that the allocative inefficiency in one factor input should be correlated withthat in another. The covariances of the allocative inefficiencies were estimated separately for each type of plant. A positive covariancewould suggest that the two factors tend to be over- and underused jointly, while a negative onewould suggest that if one factor is over-(under-) used, then theother factor tends to be under- (over-) used. For the coalmines, the allocative inefficiency in capital is negativelycorrelatedwith that in ofs, which, in turn, is negatively correlatedwith that in coal. For the power plants, a negative correlation is foundbetween capital and ofs, and between electricity and ofs. All positive correlations are found for the petroleum refineries.

6.2. Energy use inefficiency

The technical and allocative inefficiencies experienced by the 150 plants necessarily indicate the existence of factor useinefficiencies.

To evaluate the energy use efficiency, the five factor use frontiers were solved from the system of Eqs. (10) and (11) whereby theuit and the ξjitwere set to zero tomimic the situation of absence of technical and allocative inefficiencies.3 Denote the solutions, name-ly, the factor use frontiers, by x|ξ = 0, u = 0, and the observed factor use, which was subject to both technical and allocative inefficien-cies, by xjξ¼ξ; u¼u , then, xjξ¼ξ; u¼u - x|ξ = 0, u = 0 ≥ 0 measures the inefficiencies of factor use, the larger the difference, the larger

the inefficiency. However, to control for the substitution effects, xjξ¼ξ; u¼u is replaced with xjξ¼0; u¼u , namely, the would-be factor

uses in the absence of allocative inefficiency, to compute the factor use inefficiencies that were purely due to technical inefficiency,η =xjξ¼0; u¼u - x|ξ = 0, u = 0, which are percentages above the frontiers because the variables are in logarithms.

Table 5 reports the sample averages of η, for all the five factors for the whole sample as well as by plant type. In general, the effi-ciencies of all the fuels for all the sample plantsmoved up and down during the 6-year period, with the efficiency in coal use being thelowest and that in ofs use the highest. The efficiencies of coal and electricity improved over the period,while that of ofs declined. Theseresults are in contrast with the output-energy ratios for the three fuels reported in Table 1 in that the output-coal ratio pointed to adeterioration in coal efficiency and an improvement in ofs efficiency over the period.

Of the three types of plant, the petroleum refineries recorded the lowest efficiency in the use of all the three fuels in almost everyyear. However, the refineries also experienced the largest improvement in coal efficiency as the coal use inefficiency reduced from185% above the frontier in 2000 to 132% in 2005, a reduction of more than 50 percentage points. The coal mines and power plantswere similar in the efficiencies of using the three fuels. In the case of electricity efficiency, although all the plants had experiencedthe ups and downs, the year of 2005 still witnessed an efficiency improvement on the 2000 levels for all except the refineries. Forofs, the coal mines and refineries managed to abate its inefficiency at the end of the study period compared to those at the beginningof the period. However, the levels of the inefficiency in ofs use experienced by the two types of plant were conspicuously higher thanthat found in the power plants for the early years of the period.

6.3. The effects of economies of scale on fuel efficiencies

Economies of scale influence factor use efficiencies via shifting the factor use frontiers. In the case of a Cobb–Douglas technology,the impact of the economies of scale on the factor use frontier can be explicitly evaluated (SL). Specifically, as illustrated in Section 4,themagnitude of technical inefficiency fully gets translated to factor use inefficiencies under constant returns to scale.When there areincreasing returns to scale, the factor use inefficiencies are only a fraction of the technical inefficiency. In the case of decreasing returnsto scale, the factor use inefficiencies exceed the technical inefficiency. Under the translog technology, the economies of scale varybetween observations and the effects of returns to scale on factor use efficiency cannot be expressed by a closed-form expression.This section evaluates how economies of scale play a role in factor use inefficiencies.

Since factor use inefficiencies under the Cobb–Douglas technology are a function of returns to scale, technical and allocativeinefficiencies, this section evaluates the effects of returns to scale on the factor use inefficiencies by controlling for technical andallocative inefficiencies. This amounts to, for each input, a four-way decomposition of the variation in the input inefficiency into apart attributable to returns to scale effects, a part attributable to technical inefficiency, a part attributable to allocative inefficiency,and a part attributable to statistical noise as follows

3 It iscriterion

ηjit ¼ γ0 þ γ1uit þ γ2ξit2 þ γ3ξit3 þ γ4ξit4 þ γ5ξit5 þ γ6rtsit þ εitj; j ¼ 1; ⋯5: ð12Þ

where the rtsit is equal to the sum of the marginal products of all the factors for plant i at time t, namely, the sum of Eq. (6) over all j.The study period had witnessed an increasing scale of input for the three types of energy and a decreasing scale for the other two

input factors. The changes in the average input scales of the plants for thefive factors over the studyperiod are presented in Fig. 5. Bothlabour and capital experienced a decrease in input scale while the other three energy factors saw their input scales rising for all thethree types of plant. While the average scale increases in coal input for the three types of plant were similar, that in electricity wasvaried from 60% for the coal mines to just over 30% for the petroleum refineries and to just under 10% for the power plants. Thevariations for ofs were also noticeable. This may suggest a substantial variation in the effects of economies of scale on factor useefficiency across the factors.

worthwhile to point out that the system of Eqs. (10) and (11) may not be solved exactly because of the nonlinearity in the variables. When the convergencecould not be achieved, the Parameter Perturbation Procedure due to Freudenstein and Roth (1963) was adopted to find the solutions.

Table 5Estimated factor use inefficiencies (sample means).

Year Labour Capital Coal Electricity ofs

All2000 152.28 160.97 161.96 51.37 30.692001 144.76 171.82 111.11 30.81 35.162002 180.88 172.89 103.56 30.64 21.002003 145.21 151.39 102.09 32.43 35.102004 147.37 175.27 142.15 36.04 20.242005 137.42 167.19 122.84 28.12 45.79

Coal mines2000 170.98 69.00 94.05 55.30 25.542001 198.91 96.29 91.09 43.27 29.402002 186.36 88.69 100.14 29.82 30.202003 188.09 71.50 93.47 24.97 35.902004 156.33 88.53 80.81 43.03 26.292005 177.13 80.84 62.21 35.14 15.69

Refineries2000 186.53 197.69 185.22 69.46 42.272001 152.06 197.34 161.24 50.91 40.892002 198.30 196.97 165.98 75.40 38.672003 171.78 197.73 135.04 67.35 42.052004 172.67 193.09 115.71 66.19 20.552005 115.53 178.89 132.10 71.06 38.95

Power plants2000 167.62 173.53 101.81 44.86 15.962001 145.76 138.21 86.37 41.39 14.762002 161.65 163.62 71.58 31.60 27.002003 126.30 138.02 95.25 43.15 20.292004 114.76 134.20 82.29 35.29 28.692005 125.73 148.17 80.05 43.72 35.69

Note: numbers in the table are sample estimates and ofs (other fuels).

142 B. Hu / China Economic Review 31 (2014) 130–144

The regression results indicate statistical significance of returns to scale in determining factor use efficiency for labour, capital andcoal. Specifically, a 1% increase in returns to scale could reduce labour inefficiency by 0.13 percentage points, capital inefficiency by0.08 percentage points and coal inefficiency by 0.02 percentage points. Compared to these three factors, electricity and ofs weremuch scarcer.

7. Concluding remarks

This paper has considered the estimation of energy efficiency in China's energy sectorwith the plant-level data in the framework ofa stochastic frontier analysis. Energy efficiencywas considered as only driven by technical efficiency, after controlling for technologicalprogress. If the underlying technical efficiency of energy utilisation remains unchanged, then, for a fixed level of output, changes inenergy input can only result from either substitution away from energy or substitution of energy for non-energy factors. To address

-20%

0%

20%

40%

60%

Coal mines Petroleum refineries Power plants

Labour Capital coal electricity other fuels

Fig. 5.Changes in input scales: 2000–2005 by plant type.Note: All input scaleswere computed based on the sample plants used in the present studywhichwere sourced fromthe National Bureau of Statistics of China.

143B. Hu / China Economic Review 31 (2014) 130–144

such substitution effects on the evaluation of energy use efficiency, the actual quantity of substitution is needed, which, however, aregenerally not observable. The research used the measure of allocative efficiency to control for the substitution and, as a result, theenergy efficiency was measured as the gap between the would-be energy in the absence of allocative inefficiencies and the energyuse frontiers.

The study period covers the Tenth Five-Year period when the surge of China's energy demand became the focus of the world,which prompted designing and implementing energy efficiency policies on the part of the Chinese government. These policiesmainly aimed at hardware advancement as the source of energy efficiency improvement. For example, some of the policies includedraising and strictly controlling energy-efficiency standards for new productive capacity and residential energy-using devices, energy-efficiency audits of new investment projects, minimum energy-efficiency standards for new equipment, and improving existingproductive capacity, retiring obsolete productive capacity, maximum energy consumption quotas for energy-intensive products,implement national energy-conservation projects. Retrospectively, the plant-level efficiency estimates in the study serve as anevaluation of the energy efficiency policies. More energy efficient hardware is generally the result of technological progress, andthis is vindicated to some extent by the estimated positive impact of the time variable in the production function, which, in turn,appears in energy demand frontier. As demonstrated in the analytical framework of the present study, energy efficiency at theplant level is driven by the plant's technical efficiency once the effects of better hardware are controlled for. The empirical resultsshowed that overall the technical efficiency was improving and therefore energy efficiency was improving, which would suggestthat the energy efficiency policies had increased the awareness of the urgency to save energy on the part of the management atplant level.

Of the efficiency performances of the three fuels, the efficiency of coalwas found the lowest, followed by those of electricity and ofs.On average, the efficiencies of coal and electricity improved over the study period. Of the three types of plant, the petroleum refineriesrecorded the lowest efficiency in the use of all the three fuels in almost every year. This could be explained by the following. Sincethere was a conspicuous shortage of supply of petroleum products in the country, especially after entering the new century, thereused to be an influx of capital into the petroleum refining industry lured by the potential to profiteer. Petroleum refining plantsestablished as this result were mostly characterised by lower levels of technology and management. The research also found thatreturns to scale were significant only in determining the coal efficiency with an increase in returns to scale leading to a reductionin coal inefficiency.

Some policy implications can be drawn out of these findings. First, government regulations are necessary on the entry to thepetroleum refining industry in order to control the distribution of refining capacity. Newly built plants needed to be closer towhere the demand was to squeeze the space for inefficient and profiteering oriented refining capacity to emerge. Second, sincecoal is consumed by all the three types of plant and larger scales result in better efficiency, this finding supports various governmentefforts to merge small plants and enterprises to form large firms.

The limitations of the study are that first the fuel prices were computed as the average fuel price rather than the actual tariffs,which may be unsuitable for estimating the first order conditions entailed by cost minimisation. Second the fuels in the category,ofs, are combined only based on statistical reasons to avoid dealing with zero consumption in the modelling exercises. Finally, theimputation method for capital stock at the plant level should ideally be plant specific.

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