Three Essays on Energy Economics 
 
by 
  
Jing Gao 
 
 
 
 
A dissertation submitted to the Graduate Faculty of  
Auburn University 
in partial fulfillment of the  
requirements for the Degree of 
Doctor of Philosophy 
 
Auburn, Alabama 
August 4, 2012 
 
 
 
 
Keywords:  Substitution, Technological Change, Generalized impulse, Variance decompositions, 
Threshold, Exponential Smooth Transition Vector Error Correction 
 
 
Copyright 2012 by Jing Gao 
 
Approved by 
 
Robert G. Nelson, Chair, Professor of Agricultural Economics and Rural Sociology 
Henry Thompson, Professor of Economics 
C. Robert Taylor, Professor of Agricultural Economics and Rural Sociology 
Hyeongwoo Kim, Associate Professor of Economics 
 
 
 
 
 
 
 
ii 
 
 
 
 
Abstract 
 
 
This dissertation consists of three essays in applied energy economics focusing on 
interfuel substitution in the electric power industry, the linkages among energy consumption, 
emissions and economic growth, and the price linkages among biofuel, energy and food. 
The first chapter estimates substitution under static and dynamic scenarios, 
examining changes in technology and total factor productivity from 2001 to 2008.  Two-stage 
estimation reveals regional characteristics and underlying elements in fuel and factor choice 
processes.  Substitution varies widely depending on the region, coal technology, capital 
investment, and R&D activities.  
The second chapter explores the causal relationship between CO2 emissions, hydrocarbon 
energy consumption, non-hydrocarbons energy consumption, and economic growth in the US for 
1960-2009 with vector error correction modeling techniques, generalized impulse response, and 
variance decomposition in a multivariate context. The results show strong evidence for uni-
directional causal relationship running from hydrocarbon consumption to investment, and weak 
evidence for bi-directional causality between non-hydrocarbon consumption and investment; 
uni-directional causality running from CO2, hydrocarbon energy consumption, and population to 
non-hydrocarbon energy consumption, from hydrocarbon and non-hydrocarbon energy 
consumption to GDP.   
The third chapter studies the price transmission system in the U.S. food-ethanol-energy 
links by capturing the price nonlinearities to examine the price relationships between corn, 
soybean, wheat, ethanol, oil and gasoline in the latest U.S. ethanol markets by using Exponential 
Smooth Transition VECM. The results show impacts of the ethanol industry on food prices and 
energy prices and provide insights for policy makers and economic agents.  
 
 
iii 
 
 
 
 
Acknowledgments 
 
 
I would like to express my deepest gratitude to my advisor Dr. Robert Nelson for offering 
invaluable guidance and continuous support throughout my PhD study. I owe sincere gratitude to 
Dr. Henry Thompson and Dr. Robert Taylor for the advice, guidance, and unending patience 
with me in developing the theory behind this dissertation. I am thankful to Dr. Hyeongwoo Kim 
as the outside reader of this dissertation. As always, I am also deeply indebted to my family and 
friends for their unvarying love and support. 
 
 
 
 
 
 
 
 
 
 
 
 
 
iv 
 
 
 
Table of Contents 
 
Abstract ........................................................................................................................................................ ii 
Acknowledgments ........................................................................................................................................ iii 
Chapter 1: Substitution in the Electric Power Industry:                                                                                 
An Interregional Comparison in the Eastern US ........................................................................................... 1 
1. Introduction ................................................................................................................................................ 1 
2. Literature Review ....................................................................................................................................... 2 
3. Model ........................................................................................................................................................ 6 
3.1. The static model ..................................................................................................................................... 6 
3.2. The dynamic translog adjustment model .............................................................................................. 10 
4. Data and data sources .............................................................................................................................. 11 
5. Results ..................................................................................................................................................... 13 
5.1. Fuel cost share equation estimation and interfuel substitution ............................................................. 13 
5.2. Factor cost share equation estimation and interfactor substitution....................................................... 15 
5.3. Technological Change and Total Factor Productivity (TFP) ............................................................... 17 
6. Conclusion and policy implication .......................................................................................................... 19 
Chapter 2: CO2 Emissions, Non-Hydro Energy Consumption and Economic Growth:  A US Study Based 
on Cointegration and Error-correction ........................................................................................................ 36 
1. Introduction ............................................................................................................................................. 36 
2. Literature Review .................................................................................................................................... 37 
3. Model and methodology .......................................................................................................................... 40 
3.1 Model .................................................................................................................................................... 40 
3.2 Unit root, cointegration and long-run causality ..................................................................................... 40 
3.3 Vector error-correction modeling (VECM) and short-run causality ..................................................... 41 
4. Data ......................................................................................................................................................... 42 
5. Empirical Results .................................................................................................................................... 44 
5.1 Tests of unit root hypothesis ................................................................................................................. 44 
5.2 Tests for multivariate cointegration ...................................................................................................... 44 
v 
 
5.3 Error-correction model and short-run causality .................................................................................... 44 
5.4 Generalized impulse response and variance decompositions ................................................................ 47 
6. Conclusion and Policy Implications ........................................................................................................ 48 
Chapter 3: Price Discovery in the Food-Ethanol-Fuel System in Ethanol Markets: An Exponential Smooth 
Transition VECM Perspective..................................................................................................................... 59 
1. Introduction .............................................................................................................................................. 59 
2. Literature Review ..................................................................................................................................... 61 
3. Methodology ............................................................................................................................................ 62 
3.1Cointegration and Linear Vector Error Correction Model (VECM) ...................................................... 62 
3.2Exponential Smooth Transition Vector Error Correction Model (ESTVECM) ..................................... 63 
4. Data .......................................................................................................................................................... 65 
5. Empirical Results ..................................................................................................................................... 66 
5.1Unit root and cointegration..................................................................................................................... 66 
5.2VECM estimation ................................................................................................................................... 67 
5.3STVECM estimation .............................................................................................................................. 69 
6. Conclusion ............................................................................................................................................... 70 
List of References ........................................................................................................................................ 80 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
vi 
 
 
 
 
 
List of Tables 
 
Chapter 1 
Table 1. Selected studies on fuel substitution in the electric power industry .............................................. 22 
Table 2. Selected studies on factor and fuel substitution using the two-stage translog function outside 
electric power industry ................................................................................................................................ 23 
Table 3. t-values from panel unit root test results ....................................................................................... 23 
Table 4. Parameter estimates of static and dynamic translog fuel cost share equations ............................. 24 
Table 5. Mean fuel and factor cost share for each region ........................................................................... 25 
Table 6. Static Hicksian conditional price elasticity and Allen elasticities of substitution for fuel inputs . 25 
Table 7. Static Marshallian unconditional price elasticities for fuel inputs ................................................ 26 
Table 8. Dynamic Hicksian conditional price elasticity and Allen elasticities of substitution for fuel inputs
 26 
Table 9. Dynamic Marshallian fuel price unconditional elasticity .............................................................. 27 
Table 10. Static and dynamic parameter estimates for factor share equations ............................................ 27 
Table 11. Static Hicksian price elasticities and Allen elasticities of substitution for factor inputs ............. 29 
Table 12. Dynamic Hicksian price elasticity and Allen elasticities of substitution for factor inputs .......... 30 
Table 13. Technological change in fuel and factor demand ........................................................................ 31 
Table 14. Total factor productivity growth rates for factor-input model .................................................... 31 
Chapter 2 
Table 1 Unit root test results ....................................................................................................................... 51 
Table 2 Johansen cointegration tests ........................................................................................................... 52 
Table 3 Short-run causality from error-correction models .......................................................................... 53 
Table 4 Granger causality test results .......................................................................................................... 54 
Table 5 Generalized forecast error variance decomposition ....................................................................... 55 
Table 6 Causality test results comparisons with related studies .................................................................. 55 
Chapter 3 
Table 1 Unit root test results ....................................................................................................................... 73 
vii 
 
Table 2 Johansen cointegration tests ........................................................................................................... 74 
Table 3 Error-correction models ................................................................................................................. 75 
Table 4 Granger causality test results .......................................................................................................... 76 
Table 5 ESTVECM parameter estimates ?????????????????????????77 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
viii 
 
 
 
 
List of Figures 
 
Chapter 1 
Figure 1. Indices of average factor prices for the electric power industry in the eastern US ...................... 33 
Figure  2. Indices of average fuel prices for the electric power industry in the eastern US ........................ 33 
Figure 3.  The electric regions in US ........................................................................................................... 33 
Figure 4. Total factor productivity growth rates by regions for factor-input model ................................... 34 
Figure 5.  Energy production efficiency by region...................................................................................... 35 
Figure 6. Labor production efficiency by region......................................................................................... 35 
Chapter 2 
Figure 1 Trends of the variables (before taking logarithms) ....................................................................... 57 
Chapter 3 
Figure 1. Price series on ethanol and fuels .................................................................................................. 78 
Figure 2. Price series on ethanol and agricultural commodities .................................................................. 78 
Figure 3 Threshold variable series (ECT) ................................................................................................... 79 
Figure 4 Transition function (G) series ....................................................................................................... 79 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1 
 
Chapter 1: Substitution in the Electric Power Industry: An Interregional 
Comparison in the Eastern US 
1. Introduction 
Energy plays a crucial role in the global economy and will become the major economic issue 
of the coming century. Most recently, many policies have been initiated to promote various 
energy efficiency improvements and encourage development of specific energy sources. For 
instance, the Energy Policy Act of 2005 seeks to increase coal as an energy source while also 
reducing air pollution by clean coal initiatives. According to the Annual Energy Review of the 
Energy Information Administration (EIA), in 2008 the electric power sector accounted for 91 
percent of all coal consumption and 29 percent of all natural gas consumption, while fossil fuels 
(coal, petroleum, and natural gas) accounted for 71 percent of all electricity net generation in the 
US. Fuel choices and factor alternatives in electricity generation are important issues in energy 
policy. Based on the fact that the electricity generation industry is restructuring and regulation is 
moving from states to regional and national levels, accurate estimates of fuel and factor use in 
interregional electricity generation are essential for policy makers and planners.  
Several studies using various estimation models and samples have been devoted to the 
analyses of energy production and fuel/factor substitution in energy generation. Attention has 
been mostly given to national studies or international comparisons of interfuel substitution in the 
electric power.  However, aggregate national estimates may mask regional characteristics of the 
electricity market and result in inappropriate policies. No previous research has estimated the 
regional fuel or factor substitution in electricity generation specifically for the eastern regions of 
the US. In addition, this is the first study to apply a two-stage model to account for both energy 
and non-energy inputs in electric power generation under both static and dynamic scenarios. 
2 
 
The focus of this study is to compare regional results from the two-stage estimation 
method and to reveal regional characteristics and underlying elements in fuel and factor choice 
processes.  The results show widely-varing elasticities of substitution depending on the 
regions for estimation. As a by-product of this analysis, technology changes and total factor 
productivity are also examined to compare production efficiencies and provide policy 
implications for different regions so that decision makers can efficiently allocate energy 
resources.  
The organization of the paper is as follows. Section II gives a summary of previous studies 
on interfuel and interfactor substitution analyses. Section III and Section IV include discussions 
of the theoretical model and data sources. Section V presents the empirical results.  
2. Literature Review 
The majority of previous studies of interfuel and interfactor substitution in the electric power 
industry rely on greatly aggregated data at the industry or national level. For example, Hudson 
and Jorgenson (1974), Atkinson and Halvorsen (1976b), Griffin (1977), Uri (1978), Mountain 
(1982), S?derholm (1999), S?derholm (2000) and Lee (2007) all used aggregate national data. 
Only two studies have used US regional data and no previous regional study has focused on the 
eastern part of US. Uri (1977) analyzed fuel substitution for nine US census regions. Bopp and 
Costello (1990) compared elasticities for five US geographic regions with national elasticities. 
However, the data employed in those two regional analyses were based on geographic census 
divisions which do not consider the regional characteristics and regulation structure of the 
electricity market. 
3 
 
Among the attempts to model the energy sector, Hudson and Jorgenson (1974) were the first 
to conduct an econometric study of hydrocarbon demand. They applied a translog cost model 
with US annual data and included the fuel prices of coal, oil, natural gas and electricity for 1947-
1971. According to their results, oil demand was price elastic while coal and gas demand was 
inelastic. The cross elasticities suggested that the three fuels were substitutes, though coal and oil 
were strong substitutes (1.09) while oil and gas (0.39), and coal and gas (0.09) were weak 
substitutes. 
Griffin (1977) incorporated a polynomial distributed lag into the translog model and applied 
a translog cost function to the data of 20 OECD countries for 1955, 1960, 1965, and 1969 with 
two separate models to estimate interfuel substitution elasticities in the European electric power 
industry. His results showed larger price elasticities with cross sectional data than with time 
series data, probably because that the time series results reflect only a partial adjustment to a new 
equilibrium. 
Uri (1977) applied pooled time series analysis to nine US regions from 1952 to 1974. In a 
subsequent paper Uri (1978) did a similar study with aggregate monthly data covering 1974 to 
1976. The resulting smaller elasticities led him to conclude that short run elasticities were lower 
than long run estimates.  
Mountain (1982) included imported electricity in the translog cost function as an input. He 
used pooled time series data from 1964 to 1975 for two districts in Canada. The empirical results 
showed strong substitution between domestic and imported electricity, and strong short run 
substitution between coal and oil. 
Bopp and Costello (1990) conducted a monthly time series analysis from 1977 to 1987 with 
two translog cost function models: one for five US regions, the other for the entire US. The 
4 
 
empirical results showed that oil was own-price elastic while gas was inelastic. The latter result 
was expected as it is known that gas is typically a peak fuel for generators designed to run during 
busy times. The results also demonstrated that the price elasticities were lower in the regional 
model than in the aggregate.   
S?derholm (1999) conducted a pooled annual aggregate national analysis for seven 
European countries using a translog cost function for the years 1978-1995. The results showed 
strong substitution between gas and oil. S?derholm (2000) employed a regulatory intensity 
variable as an exogenous variable and estimated a generalized Leontief cost function with the 
same dataset. The results showed significant interfuel substitution in European electricity 
production and the estimation from the perspective of regulation intensities showed that it was 
hard to separate the individual effects of the SO2 regulations. 
In addition to aggregate level analysis, in order to characterize the fuel choice in individual 
electricity generating plants or firms some research has also been devoted to firm-level or plant-
level analysis. Atkinson and Halvorsen (1976a), Haimor (1981), Ko and Dahl (2001), Lee (2002), 
Considine and Larson (2007) and Tuthill (2008) used micro data from the US, while Tauchmann 
(2006) analyzed firm-level data from Germany.  
Atkinson and Halvorsen (1976a) employed a translog profit function to examine the demand 
for hydrocarbons by US electric plants, using data on capital quantities, labor quantities, coal 
price, oil price, and natural gas price. They used cross sectional data for 1972. Their results 
showed that oil and coal were own-price elastic and cross-price elastic. By applying the same 
translog profit function, Atkinson and Halvorsen (1976b) compared the three hydrocarbons using 
a short run substitution analysis with monthly time series for the years 1972?1974. Contrary to 
5 
 
their earlier results, the own price elasticity of natural gas was highly elastic and significant. All 
cross elasticities were significant and indicated substitutability. 
Haimor (1981) applied a translog model to plant-level data,  including capital stock and 
labor price as variables influencing the fuel choices of 45 plants that used all three fuels (coal, oil 
and gas) during the years 1970-1975. His findings showed strong substitution between coal and 
oil and large changes in response to unstable markets, making forecasting difficult. 
Ko and Dahl (2001) employed a translog cost function to estimate interfuel substitution with 
monthly panel data for 185 US utilities for the year 1993. They divided the utilities into four fuel 
choice capability sets of coal and oil, coal and gas, gas and oil, and coal and oil and gas. Their 
results showed that coal was own-price elastic while oil and gas were inelastic, and that 
substitution was strong between coal and oil, but weak between gas and the other two fuels. 
Table 1 compares the data, models and elasticities from the selected studies. A limitation of 
the estimation method in most of these studies arises when interfuel substitutions are estimated 
assuming exogenous energy aggregates.  Because fuel price changes almost certainly stimulate 
substitution among both fuels and factors of production, ignoring this feedback effect may result 
in unreliable conclusions. 
While the current study is the first application in the electricity sector of a two-stage translog 
model that incorporates feedback effects between interfactor and interfuel substitutions, this is a 
well-established method for determining fuel substitution elasticities in the manufacturing sector. 
Pindyck (1979), Andrikopoulos, Brox and Paraskevopoulos (1989), Cho (2004) and Ma, Oxley, 
Gibson and Kim (2008) all use this method to examine industrial interfuel substitution. A 
comparison of their data and main results is given by Table 2. All of those studies employing 
6 
 
two-stage translog functions and panel data show inconclusive substitution results for different 
countries. 
In the electric power industry, however, only two firm-level studies employed two-stage 
decisions. Mountain?s (1982) incorporated imported electricity as an input and applied the 
translog cost function to firm-level data from New Brunswick and Nova Scotia in Canada.  In the 
first stage, the optimal quantities of imported and domestic electricity were estimated, and in the 
second the fuel choice in domestic electricity given the exogenous quantity of domestic 
electricity was determined. Tauchmann (2006) applied a linear non-structural function to firm-
level data from German electricity generating firms for the years 1968-1998. The author 
estimated optimal capacities in the first stage, and examined fuel substitution given exogenous 
capacities in the second.  
The two-stage estimation method in the current paper differs from Tauchmann in several 
details: it employs instrumental variables for aggregate energy prices, it estimates interfuel and 
interfactor substitution with regional-level data from the eastern US, and it estimates Marshallian 
unconditional elasticities to capture feedback effects. 
 
3. Model 
3.1. The static model 
For many years, the electricity generation industry vertically-integrated in the US has been 
operating as regulated monopolists. As economies of scale always exist at generation stage, the 
average cost of producing a unit of power is at lowest when the entire demand is supplied by 
monopoly rather than by many competitive producers. By selecting the low cost option at each 
point in time, Kaserman and Mayo (1991) found that the total costs from the input stage are 
minimized, and the vertical structure of the utilities is determined by this cost minimization 
7 
 
process. To simplify the estimation process of the two-stage cost share system, cost-
minimization is considered in two-stages. In the first stage, total costs are minimized in the 
consumption of capital, labor and aggregated energy.  In the second, aggregate energy costs are 
also minimized in the consumption of coal, oil and natural gas. Following the approach 
suggested by Pindyck (1979), the two-stage cost function is specified as:  
(1)                     C=f [G13Gb4fG1e1G13Gb50G1e1G13Gb49G123aG13Gb47G1e1G13Gb53G1e1G13Gb4bG1e1G96G123bG1e1G1cG1e1G96] , 
where C denotes total cost; G13Gb4fG3G83G90G86G3G13Gb50G3denote factor prices of capital and labor; G13Gb49G3denotes a 
conditional function of the prices of three fuel inputsG3G13Gb47G1e1G13Gb53G3G83G90G86G3G13Gb4bG3G1e2Y denotes output generation; 
t denotes time which can also capture the trend of technical change;. Equation (1) is assumed to 
be weakly separable.  
The translog cost model introduced by Christensen, Jorgenson and Lau (1971) has been 
widely used to estimate energy demand elasticities as it has the advantage of reducing 
multicollinearity and reducing the number of parameters estimated. Under the assumption that 
the production function is weakly separable in factor inputs of capital, labor and energy, and that 
these three factors are homothetic, the first stage translog cost function is written as the 
logarithmic second-order Taylor expansion: 
(2)            lnC = G7d9Gb34 + G3c3 G7d9GbdcG3Gbe1GbdcGb40Gb35 lnG732GbdcGbe7 +G7d9GbdcGbe7G3G750Gd45G7d9GbdcGbecG8eG90G73bGbe7 Gd45Gb35Gb36G3G3c3 G3c3 G7d9GbdcGbddG3Gbe1GbddGb40Gb35 G8eG90G732GbdcGbe7Gbe1GbdcGb40Gb35 G3G8eG90G732GbddGbe7 +Gb35Gb36G7d9Gbe7Gbe7G750Gb36G3+ 
Gb35
Gb36G7d9GbecGbecG123aG748G74aG73bGbe7G123b
Gb36 Gd45G3c3 G7d9GbdcGbecG3Gbe1GbdcGb40Gb35 G748G74aG73bGbe7G8eG90G732GbdcGbe7G1e1Gd45G3c3 G7d9GbdcGbe7G3Gbe1GbdcGb40Gb35 G750lnG732GbdcGbe7 Gd45G7d9GbecGbe7G3G750lnG73bGbe7 , 
where C denotes total cost; G8bG3G83G90G86G3G8cGd4cGeG1e1GfG1e1G8G1e2G3G732GbdcGbe7 denotes the price of factor i at time t; G73bGbe7 denotes 
the generation output at time t; t denotes time or technical change; and G7d9 denotes  parameters to 
be estimated.  
8 
 
Taking the partial derivative of (2) with respect to lnG732GbdcGbe7 and applying Shephard?s Lemma 
yields the first stage cost share equation (G734Gbdc): 
(3)             G734GbdcGbe7=G7d9Gbdc Gd45G3c3 G7d9GbdcGbddG8eG90G732GbddGbe7Gbe1GbddGb40Gb35 +G7d9GbdcGbecG748G74aG73bGbe7+G7d9GbdcGbe7G750 .                                                 
Assuming that the parameters are linear functions of regional dummy variables G726Gbe0 and that 
all the coefficients are allowed to vary across regions except for the interaction forms of factor 
prices, then the factor cost share equation is given by: 
(4)            G734GbdcGbe7=G123aG7d9GbdcGbe2 Gd45G3c3 G7d9GbdcGbe0G726Gbe0G123bGbdeGbdcGb40Gb35 Gd45G3c3 G7d9GbdcGbddG8eG90G732GbdcGbe7Gbe1GbdcGb40Gb35 +G123aG7d9GbdcGbecGb34Gb3eG3c3 G7d9GbdcGbecGbe0G726Gbe0G123bGbdeGbdcGb40Gb35 G748G74aG73bGbe7            
                         +G123aG7d9GbdcGbe7Gb34Gb3eG3c3 G7d9GbdcGbe7Gbe0G726Gbe0G123bGbdeGbdcGb40Gb35 G750.  
The imposed symmetry and homogeneity restrictions can be written as: 
(5)            G7d9GbdcGbdd=G7d9GbddGbdc, for all i and j ,                                                      
(6)           G3c3 G123aG7d9GbdcGbe2 Gd45G3c3 G7d9GbdcGbe0G726Gbe0G123bGbdeGbdcGb40Gb35Gbe1GbdcGb40Gb35 =1,                          
(7)           G3c3 G7d9GbdcGbddGbe1GbdcGb40Gb35 =G3c3 G123aG7d9GbdcGbecGb34Gb3eG3c3 G7d9GbdcGbecGbe0G726Gbe0G123bGbdeGbdcGb40Gb35Gbe1GbdcGb40Gb35 =G3c3 G123aG7d9GbdcGbe7Gb34Gb3eG3c3 G7d9GbdcGbe7Gbe0G726Gbe0G123bGbdeGbdcGb40Gb35Gbe1GbdcGb40Gb35 =0. 
 Hicksian cross-price elasticities, own-price elasticity for input i with respect to changes in 
prices of input j, and Allen partial elasticities of substitution between factor-inputs are computed 
as: 
(8)          G8Gb67Gb68G5dbG3=G3Gc08Gcd4Gcd5Gbcb
Gcd4
+G734GbddG1e1  G5caiGd4dj and G8Gb67Gb67G5dbG3G3=Gd46G373Gd45Gc08Gcd4Gcd5Gbcb
Gcd4
+G734GbddG1e1                              
(9)           G250Gb67Gb68G3 =Gb49Gc5fGc60
G5dbG3
GbcbGcd5,G3G5caiGd4dj,  and  G250Gb67Gb67
G3 =Gb49Gc5fGc5fG5dbG3
GbcbGcd4G1e4                                                                        
In the second stage, the homothetic aggregate energy price function is given by: 
9 
 
(10)         ln G732Gbbe = G7daGb34 + G3c3 G7daGbdcG3Gbe1GbdcGb40Gb35 lnG732GbdcGbe7 +G3Gb35Gb36G3G3c3 G3c3 G7daGbdcGbddG3Gbe1GbddGb40Gb35 G8eG90G732GbdcGbe7Gbe1GbdcGb40Gb35 G3G8eG90G732GbddGbe7 + G3c3 G7daGbdcGbe7G3Gbe1GbdcGb40Gb35 G750lnG732GbdcGbe7 ,                 
where G732Gbbe is the aggregate energy price;  G732GbdcGbe7 is the fuel price at time t;  and G7da is an estimated 
parameter. 
Taking the partial derivative of Equation (9) with respect to lnG732GbdcGbe7 and imposing the same 
assumptions about regional dummy variables as in the factor cost share equation gives the 
second stage cost share equation (G735Gbdc): 
(11)                 G735GbdcGbe7=G123aG7daGbdcGbe2 Gd45G3c3 G7daGbdcGbe0G726Gbe0G123bGbdeGbdcGb40Gb35 Gd45G3c3 G7daGbdcGbddG8eG90G732GbdcGbe7Gbe1GbdcGb40Gb35 +G123aG7daGbdcGbe7Gb34Gb3eG3c3 G7daGbdcGbe7Gbe0G726Gbe0G123bGbdeGbdcGb40Gb35 G750G1e4                 
The symmetry and homogeneity restrictions are: 
(12)                G7daGbdcGbdd=G7daGbddGbdc, for all i and j,                               
(13)  G3c3 G123aG7daGbdcGbe2 Gd45G3c3 G7daGbdcGbe0G726Gbe0G123bGbdeGbdcGb40Gb35Gbe1GbdcGb40Gb35 Gd4c1,          
(14)  G3c3 G7daGbdcGbddGbe1GbdcGb40Gb35 =G3c3 G123aG7daGbdcGbe7Gb34Gb3eG3c3 G7daGbdcGbe7Gbe0G726Gbe0G123bGbdeGbdcGb40Gb35Gbe1GbdcGb40Gb35 =0.                  
Conditional Hicksian cross-price elasticities, own-price elasticity for input i with respect to 
changes in prices of input j, and conditional Allen partial elasticities of substitution between 
factor inputs are computed as: 
(15)                 G87Gb67Gb68G5dbG3=G3Gc09Gcd4Gcd5Gbcc
Gcd4
+G735Gbdd  G5caiGd4dj and  G87Gb67Gb67G5dbG3G3=Gd46G373Gd45Gc09Gcd4Gcd5Gbcc
Gcd4
+G735GbddG1e1                        
(16)                 G250Gb67Gb68G3 =Gb63Gc5fGc60
G5dbG3
GbccGcd5 G3G5caiGd4dj  and  G250Gb67Gb67
G3 =Gb63Gc5fGc5fG5dbG3
GbccGcd4.                                                              
10 
 
To examine the feedback effect between interfuel and interfactor elements, conditional 
Hicksian price elasticities are transformed to unconditional Marshallian price elasticities by the 
following equation: 
(17)   G8Gb67Gb68=G87Gb67Gb68+G87Gb67Gb76 (1+G244Gb6e)G3G735Gbdd=G87Gb67Gb68G5db+G87Gb67Gb76G244Gb6eG735Gbdd.                                                         
where G8Gb67Gb68  denotes unconditional Marshallian price elasticities; G87Gb67Gb76  denotes the expenditure 
elasticity from the conditional cost function; G244Gb6e denotes the income elasticity from the total cost 
function. Given G87Gb67Gb76 Gd4c1 by homotheticity and G244Gb6e Gd4cG8Gb49Gb49G5db , the unconditional Marshallian price 
elasticities are calculated from the following equation: 
(18)                G8Gb67Gb68=G87Gb67Gb68G5db+G8Gb49Gb49G5db G735Gbdd .                                           
3.2. The dynamic translog adjustment model 
In the basic static analysis, it was assumed that fuel and factor demands remain constant in 
the short term. However, as shown in Figures 1 and 2, the aggregate energy price and oil price 
increased sharply while the average payroll, coal price and gas price increased more slowly 
during the sample period. Since the substitution effect may not be able to adjust instantaneously, 
in this section an adjustment process is considered. This Partial Adjustment Model (PAM), 
presuming an underlying stationary procedure in the data, assumes that the observed cost share 
in period t is somewhere between the equilibrium cost share and the observed cost share in t-1. 
The adjustment process is described as follows: 
(19)   G734Gbe7-G734Gbe7Gb3fGb35=? (G734Gbe7G5db-G734Gbe7Gb3fGb35), 0<??1,                             
11 
 
where G734Gbe7G5db denotes the equilibrium level of cost share at time t; G734Gbe7 denotes the observed cost share 
at time t; G734Gbe7Gb3fGb35 denotes the observed cost share at time t-1; ? denotes the adjustment coefficient,  
such that for instantaneous adjustment ?=1. 
As shown by Taheri (1994), the dynamic factor cost share equation and fuel cost share 
equations are given by: 
(20) G734GbdcGbe7=G123aG7d9GbdcGbe2 Gd45G3c3 G7d9GbdcGbe0G726Gbe0G123bGbdeGbdcGb40Gb35 Gd45G3c3 G7d9GbdcGbddG8eG90G732GbdcGbe7Gbe1GbdcGb40Gb35  
+G123aG7d9GbdcGbecGb34Gb3eG3c3 G7d9GbdcGbecGbe0G726Gbe0G123bGbdeGbdcGb40Gb35 G748G74aG73bGbe7+G123aG7d9GbdcGbe7Gb34Gb3eG3c3 G7d9GbdcGbe7Gbe0G726Gbe0G123bGbdeGbdcGb40Gb35 G750+  G123aG7d9GbdcGbe5Gb34Gb3eG3c3 G7d9GbdcGbe5Gbe0G726Gbe0G123bGbdeGbdcGb40Gb35 G734Gbe7Gb3fGb35 
(21) G735GbdcGbe7=G123aG7daGbdcGbe2 Gd45G3c3 G7daGbdcGbe0G726Gbe0G123bGbdeGbdcGb40Gb35 G3c3 G7daGbdcGbddG8eG90G732GbdcGbe7Gbe1GbdcGb40Gb35 +G123aG7daGbdcGbe7Gb34Gb3eG3c3 G7daGbdcGbe7Gbe0G726Gbe0G123bGbdeGbdcGb40Gb35 G750+G123aG7daGbdcGbe6Gb34Gb3eG3c3 G7daGbdcGbe6Gbe0G726Gbe0G123bGbdeGbdcGb40Gb35 G735Gbe7Gb3fGb35  
4. Data and data sources 
From the perspective of US electricity market development and political factors, states are 
usually divided into ten major areas 1 as shown in Figure 3, according to Federal Energy 
Regulatory Commission (FERC). Since there is transmission within the FERC regions but very 
little between, interregional trade will not be discussed in this paper. Considering the location 
and level of electricity market growth, seven regions 2covering 30 states 3were chosen for this 
study. 
                                                           
1 The ten regions include California, Midwest, New England, New York, Northwest, PJM 
Interconnection (PJM), Southeast, Southwest, Southwest Power Pool (SPP) and Texas. 
2 The regional division was as follows: (1) Alabama; (2) Southeast (Florida, Arkansas, Louisiana, 
Mississippi, Georgia, Tennessee, North Carolina, South Carolina); (3) PJM (Delaware, District 
of Columbia, Maryland, New Jersey, Ohio, Pennsylvania, Virginia, West Virginia); (4) New 
12 
 
 The dataset is a panel consisting of annual region-level observations from 2001 to 2008.  
Annual state-level labor data are from the Quarterly Census of Employment and Wages (QCEW) 
of the Bureau of Labor Statistics (BLS) and include all employee numbers and total wage 
payments by federal, local and private owners. The average wage of labor is obtained by 
dividing the total payroll by its corresponding number of employees. The price of capital is 
obtained by estimating the production function VA=f (rK, L, E), where VA is value-added. The 
price of capital is a shadow price and the nameplate capacity4 is used as a proxy for capital.  
Fuel prices (coal, oil and gas), generation data and capacity data for the 30 states come from 
EIA- 28, FERC-423, EIA-906 and EIA-860. The price of aggregate energy is obtained from the 
equation: ln G732Gbbe = G7daGb34 + G3c3 G7daGbdcG3Gbe1GbdcGb40Gb35 lnG732GbdcGbe7 +G3Gb35Gb36G3G3c3 G3c3 G7daGbdcGbddG3Gbe1GbddGb40Gb35 G8eG90G732GbdcGbe7Gbe1GbdcGb40Gb35 G3G8eG90G732GbddGbe7 + G3c3 G7daGbdcGbe7G3Gbe1GbdcGb40Gb35 G750lnG732GbdcGbe7, where G732Gbbe is 
the aggregate energy price;  G732GbdcGbe7 is the fuel price at time t;  G7da are parameters that can be estimated 
from Equation (11), except for G7daGb34 which is calculated following Pindyck (1979), so that G732GbbeG3 Gd4cG373 
in 2001. 
                                                                                                                                                                                           
York; (5) Midwest (North Dakota, South Dakota, Nebraska, Minnesota, Iowa, Wisconsin, 
Illinois, Indiana, Michigan); (6) SPP (Kansas, Oklahoma); (7)Texas. 
3 Each region covers several full states and several parts of states according to FERC.  Since the 
data for parts of states are inaccessible, full-state and majority-states coverage are aggregated to 
approximate the regions. 
4 Nameplate capacity refers to the full-load sustained output of a generator registered with 
authorities for classifying the power output. 
13 
 
5. Results 
The empirical analysis starts with pretests of stationarity properties of the variables. The 
panel unit root test developed by Levin, Lin and Chu (2002) is employed to allow for individual 
effects, time effects and possibly a time trend. Lags of the dependent variable are introduced to 
allow for serial correlation in the errors. The test with the null hypothesis of nonstationarity, 
could be regarded as an Augmented Dickey-Fuller (ADF) test when lags are included. Panel unit 
root test results shown in Table 3 indicate that each variable has no unit root and is stationary. 
To estimate the static translog model, the fuel cost share system in (11) is first estimated by 
employing Seemingly Unrelated Regression (SUR), imposing the symmetry and homogeneity 
restrictions from (12), (13) and (14) and dropping the gas cost share equation. Using the 
estimated parameters, the aggregate energy prices, treated as an instrumental variable in factor 
share equations, are computed by (10). The same SUR technique is used to estimate the factor 
cost share system given by Equation (4), dropping the capital cost share equation and imposing 
the symmetry and homogeneity restrictions given by Equations (5), (6) and (7). 
5.1. Fuel cost share equation estimation and interfuel substitution 
Table 4 present the parameter estimates for the static and dynamic translog fuel cost share 
equations. Both the models have good explanatory power. The G734Gb36 is 0.99 for the coal share 
equation and 0.89 for the oil equation in the static model and the G734Gb36 is 0.99 for the coal equation 
and 0.90 for the oil equation in the dynamic model. More than half of the parameters are 
statistically significant. Durbin-Watson (DW) values are 2.467 and 1.501 for coal and oil in the 
static model, implying that first order serial correlation is inconclusive. In the dynamic models, 
the DW value is 2.437 for coal, suggesting inconclusive serial correlation and 2.223 for oil with 
no serial correlation. 
14 
 
Using the parameters estimated above and the sample means of each fuel cost share for each 
region from Table 5, the static Hicksian conditional price elasticities of fuel demand and the 
Allen elasticities of substitution are calculated and reported in Table 6. The static Marshallian 
unconditional price elasticities are presented in Table 7. 
As shown in Table 6, the results are generally larger than results from previous studies 
shown in Table 1. All of the own price elasticities for coal are negative except for New York and 
Texas. In general, the smaller the cost share the larger the own price elasticity will be. The 
elasticities range between -0.04 in the Midwest, where coal has the larger cost share in electricity 
generation, and -0.18 in SPP with a smaller coal cost share.  The negative signs for New York 
and Texas are contrary to theory but they are plausible since coal consumption and coal cost 
shares are extremely low (less than 19% of shares) in these two regions. Alabama and Texas 
have the largest own price elasticities for oil at -8.75 and -7.79 respectively, and New York has 
the smallest at -1.04, which is  reasonable since the first two states both have very low oil shares 
in their electric power sectors. Own price elasticities for natural gas vary from -0.19 in Texas to -
0.75 in the Midwest. 
Coal and oil appear to be substitutes only in the Southeast and PJM regions, whereas in the 
other five regions they are complements.  The complementarity in those five regions is probably 
due to their much lower oil consumption and relatively low oil cost shares in the sample period. 
In contrast, coal and gas are all substitutes except for New York. Coal and gas are the most 
substitutable (G250Gd4c0.45 and G250=0.42) in Alabama and SPP and the least substitutable (G250Gd4c0.11 and 
G250Gd4c0.08) in the Southeast and Texas.  It is not surprising that coal and gas have substantial 
substitution possibilities in New York because coal consumption there is very low and hence 
15 
 
their coal cost share is only about 6% while their gas share is about 66%. Oil and gas are all 
substitutes in the seven regions and the elasticities of substitution are between 1.67 in New York 
and 22.58 in Alabama. The Marshallian unconditional price elasticities are shown in Table 7. 
These incorporate the feedback effect between interfuel and interfactor and are more consistent 
with economic theory except for the own price elasticity of coal in New York. 
The dynamic Hicksian conditional price elasticities, Allen elasticities of substitution, and 
dynamic Marshallian unconditional price elasticities are shown in Tables 8 and 9. These are 
slightly smaller than the static models, but with only slightly larger variance and in similar 
direction, which indicates the models are consistent with each other and with factor demand 
theory. 
5.2. Factor cost share equation estimation and interfactor substitution 
Table 10 show the parameter estimates for the static and dynamic translog factor cost share 
equations. Both the static and dynamic models have good explanatory power with G734Gb36=0.99 for 
the capital and the labor share equation. More than half of the parameters are statistically 
significant. In the static model, Durbin-Watson values are 1.743 with no serial correlation for 
energy-input, and 1.836 for labor-input suggesting inconclusive serial correlation. In the dynamic 
model, DW values are 2.053 and 2.027 for labor and energy inputs showing no serial correlation 
problem.   
Based on the parameter estimates and the means of each factor cost share for each region 
from Table 5, the static Hicksian price elasticities of factor demand and Allen elasticities of 
substitution are reported in Table 11.  
16 
 
The results show that all the own price elasticities have negative signs, consistent with 
economic theory. Own price elasticities for capital are relatively small, between -0.26 in PJM 
and -0.56 in SPP.  Own price elasticities for labor vary from -0.75 in SPP to -1.29 in PJM. The 
Southeast and PJM have the largest own price elasticities for aggregate energy of -3.22 and -2.36 
respectively. New York has the smallest at -1.57. 
Capital and labor are substitutes with values for partial elasticities of substitution around 
unity in all seven regions. Capital and aggregate energy appear to be the substitutes with the 
largest magnitude of elasticities. They are most substitutable in the Southeast (G250Gd4c1.63) and least 
substitutable in New York and the Midwest (G250=1.20 and G250=1.22). Labor and aggregate energy 
are substitutes in all seven regions, with a range of elasticities between 2.89 in SPP and 8.17 in 
Southeast.  
In sharp contrast, the dynamic Hicksian conditional price elasticities and dynamic Allen 
elasticities of substitution presented in Table 12 show different results in signs and magnitudes 
from the static results. Surprisingly, the own price elasticities of capital are positive.  Capital and 
energy are substitutes under the static model, but are complements under the dynamic model 
based on lagged shares. The elasticities of substitution vary from 1.20 in New York to 1.63 in 
Southeast.  Labor and energy also appear to be complementary in the dynamic model with 
elasticities between 2.89 in SPP and 8.17 in the Southeast.  This result reflects the impact of the 
sharp increase in energy price during the periods of 2001 to 2005 and 2006 to 2008. When the 
energy price is fairly low, capital and labor could be substitutable with aggregate energy. But 
later, the sharply increasing energy price makes capital price and labor wage relatively cheaper 
than before and the substitutable relationships between capital and energy or labor and energy 
are no longer stable and efficient. 
17 
 
5.3. Technological Change and Total Factor Productivity (TFP) 
To address the issue of technological change, following the methods of Binswanger (1974) 
and Debertin (1990), the technical changes of each fuel/factor during the sample period are 
captured through the following equations: 
(22)          G737GbdcGbd9Gbe8Gbd8Gbdf=G1240Gc21GbccGcd4Gc21Gbe7G1241G123aGb35Gbcc
Gcd4
G123bGd4c Gc09Gcd4GcdfGc2cGc36G3c3 Gc09Gcd4GcdfGcd8GbbdGcd8
Gcd6
Gcd4Gc38Gc2d
GbccGcd4 ,                                                                       
(23)          G737GbdcGbd9Gbd4Gbd6Gbe7Gbe2Gbe5=G1240Gc21GbcbGcd4Gc21Gbe7G1241G123aGb35Gbcb
Gcd4
G123bGd4c Gc08Gcd4GcdfGc2cGc36G3c3 Gc08Gcd4GcdfGcd8GbbdGcd8
Gcd6
Gcd4Gc38Gc2d
GbcbGcd4 ,                                                                    
where G7d9G1e1G7da are the parameter estimates from the static translog models, and G734Gbdc and G735Gbdc denote the 
factor share and fuel share of the ith inputs. Given that the factor/fuel shares are always positive, 
the technical change is progressive if G737Gbdc is positive, and regressive if negative. If G737Gbdc is close to 
zero, the technological change is considered neutral.  
As shown in Table 13 the impact of technological change in oil is larger than in coal and gas. 
Technological change bias appears to be coal regressive, but oil and gas progressive in most of 
the regions.  Table 13 also presents technological change bias in factor demand, which tends to 
be capital regressive, but labor and energy progressive in most of the regions. 
In addition to technological change bias, total factor productivity (TFP) is an important 
index accounting for changes in total output not caused by the amount of inputs used in 
production. Increases in TFP usually result from technological improvement or innovation, 
efficiency and specialization. Following Avila and Evenson (1995), the least restrictive 
derivation is from the accounting relationship where TFP is the residual between output growth 
rate and inputs? growth rates. The derivation is as follows. 
18 
 
First consider that the total value of production is equal to total value of inputs:  
(24)            G732Gbd2GcdfG73bGbe7=G3c3 G732GbdcGbe7G3Gbe1GbdcGb40Gb35 G733GbdcGbe7,                                     
where G732Gbd2Gcdf denotes the price of output i at time t; G733GbdcGbe7 denotes the quantity of input i at time t.  The 
rate of change, taking variable G732Gbd2Gcdf as an example, is defined as: 
(25)          G732Gbd2GcdfGde2=Gc21Gbc9GccaGcdfGbc9
GccaGcdfGc21Gbe7
G740G750.                                          
Equation (24) is expressed in change rate form by (26). Then divide both sides of Equation (26) 
by G732Gbd2GcdfG73bGbe7 and substitute G734Gbdc, the factor share of input i, for Gbc9Gcd4GcdfGbcaGcd4GcdfG3c3 Gbc9
Gcd4GcdfG3Gcd9Gcd4Gc38Gc2d GbcaGcd4GcdfG3G3G3
.  The total factor productivity 
growth rate is expressed by Equation (27). 
(26)          G73bGbe7 Gc21Gbc9GccaGcdfGc21Gbe7 G740G750Gd45G732Gbd2Gcdf Gc21Gbd2GcdfGc21Gbe7 G740G750=G3c3 G732GbdcGbe7G3Gbe1GbdcGb40Gb35 Gc21GbcaGcd4GcdfGc21Gbe7 G740G750Gd45G3c3 G733GbdcGbe7 Gc21Gbc9Gcd4GcdfG3Gc21Gbe7 G740G750Gbe1GbdcGb40Gb35 .                
(27)         G736G728G732Gbe7 Gd4cGde3 G73bGbe7Gde1 Gd46G3c3 G3Gbe1GbdcGb40Gb35 G733Gc2aGbe7Gde2                                    
The indexes of TFP estimates from the factor-input model are shown in Table 14 and Figure 
4 for each region. Labor and energy production efficiency (output per unit input) are shown in 
Figures 5 and 6. 
Table 14 expresses the TFP growth rates for factor inputs from 2001 to 2008 by region, as 
well as the average TFP for each region and each year. Alabama and SPP perform worst with 
most of the low TFP in each year, which is mainly due to the low labor production efficiency in 
Alabama and the low energy and labor production efficiency in SPP as shown in Figures 5 and 6. 
However, New York and Texas, with low energy production efficiency and medium labor 
production efficiency, perform rather better than the other regions.  
19 
 
From the perspective of time period, average regional TFP shows the best performance in 
2005 and 2008, which is probably due to the implementation of the Energy Policy Act of 2005, 
the Energy Independence and Security Act of 2007, and the Emergency Economic Stabilization 
Act of 2008. In the worst-performing regions, most experienced negative TFP growth rate in 
2002 and 2007. Large negative TFP developments in Alabama and SPP pulled the average down 
below zero. The negative indices suggest deteriorating effects from elements other than factor 
inputs in the electricity industry. Those elements are likely to involve insufficient innovation or 
R&D, the reduction or delay in ?clean? capacity investment because of the uncertainty of 
environmental policy, the potential cost for pollution control or tradable emissions, or the 
reduction of investment in hydrocarbons under policies that encourage generation from 
renewable sources or ?green? sources. It is likely that regions with low or negative TFP realize 
less technological improvement and bear higher underlying cost from environmental regulations. 
6. Conclusion and policy implication 
This paper examines static and dynamic regional interfuel and interfactor substitution and 
measures technological change, production efficiency and total factor productivity in the eastern 
US electric power industry. In this study, electricity generation considers three fuel inputs (coal, 
oil and gas) and two factor inputs (capital and labor). A two-stage translog model is used to 
analyze annual data from seven regions in the eastern US. 
For interfuel elasticities, the empirical results show that all the own price elasticities in the 
static and dynamic models are negative. Oil has the largest magnitude of own price elasticities 
while coal has the smallest. While complementarity exists between coal and oil, substitutability 
is shown between coal and gas, and between oil and gas in both the static and dynamic models, 
with the exceptions of New York and Texas, which have opposite signs for cross price 
20 
 
elasticities compared to other regions. However, it also has to be taken into consideration that 
coal is used in baseload generators that never shut down, gas used as a peak fuel is not designed 
to run continuously, and switching fuels is costly or impossible except between coal and oil. 
The results imply that regulations on the price of oil would be the most effective, and the 
least effective on the price of coal. Policy makers? use of a full array of taxes and subsidies 
should take into account the varying elasticities of substitution in different regions. For instance, 
New York and Texas might suffer from a taxation/subsidy policy that was desirable for Alabama.  
For interfactor elasticities, the static and dynamic models tell different stories. In the static 
model, for all seven regions, the elasticities are of the same sign without exception: own price 
elasticities are negative, cross elasticities are positive and statistically significant. Aggregate 
energy has the largest magnitude of own price elasticities while capital has the smallest. The 
static model shows unit substitutability between capital and labor, weak substitutability between 
capital and energy, and strong substitutability between labor and energy.  
In sharp contrast, the dynamic model shows positive own price elasticities for capital in all 
regions and negative cross price elasticities, with the exceptions of Alabama and the Southeast.  
Capital and labor appear to be complementary in five regions. Complementarities are 
detected between capital and aggregate energy, and between labor and aggregate energy under 
the dynamic models.  The results suggest that energy price has the largest response to price 
regulations and capital has the smallest. However, unlike the risk of making inconsistent policies 
for fuel inputs, government planners could be more confident in making consistent policies 
related to capital, labor and aggregate energy.  
21 
 
The technological change estimates show regional variation, but the general trend suggests 
movement to energy-intensive technology with higher efficiency in coal input and capital 
investment. The results of the total factor productivity analysis also suggest the need for more 
technological or R&D investments in the electricity industry, especially for regions with low or 
negative TFP such as Alabama and SPP. Energy policy authorities should consider incentivizing 
corresponding regulations for those regions with negative TFP.   
In summary, these elasticity estimates are relatively high compared to other national or 
international studies, which is sensible considering that regional differences are lost in 
aggregation. These results also reveal different magnitudes and signs in regional elasticities of 
substitution, suggesting that energy price policy and energy tax/subsidy policy should pay more 
attention to regional characteristics so as to more efficiently allocate resources. 
 
 
 
 
 
 
 
 
 
 
 
 
 
22 
 
Appendix: 
Table 1. Selected studies on fuel substitution in the electric power industry 
Author Country  Dataset Estimation Techniques Estimated Substitution Elasticities 
Hudson and 
Jorgenson 
(1974) 
US 
state-level, 
1947-1971, 
annual 
translog cost 
model 
G87Gb47Gb53G5db =1.09 
G87Gb47Gb4bG5db =0.09 
G87Gb53Gb4bG5db =0.39 
Atkinson and 
Halvorsen 
(1976a) 
US firm-level cross section,1972 
translog 
normalized 
restricted 
profit 
function 
G87Gb47Gb47G5db =-0.01; G87Gb47Gb53G5db =0.3 to 5.52 
G87Gb53Gb53G5db =0.01; G3G87Gb47Gb4bG5db =-0.79 to 0.2 
G87Gb4bGb4bG5db =-2.55;G3G87Gb4bGb53G5db =0.25 to 8.22 
Atkinson and 
Halvorsen 
(1976b) 
US 
aggregate, 
monthly time 
series, 1972?
1974,shortrun 
translog 
profit 
function 
G87Gb47Gb47G5db =-0.39 to -3.9 
G87Gb53Gb53G5db =-0.56 to -4.12 
G87Gb4bGb4bG5db =-0.34 to -10.5 
G87Gb47Gb53G5db =0.3 to 5.52 
G87Gb47Gb4bG5db =-0.79 to 0.21 
G87Gb4bGb53G5db =0.25 to 8.22 
Griffin (1977) 20 OECD countries 
pooled data; 
1955, 1960, 
1965 and 1969; 
annual 
translog cost 
function 
G87Gb47Gb47G5db =-0.66; G87Gb53Gb53G5db =-3.46 
G87Gb4bGb4bG5db =-0.9;   G87Gb47Gb53G5db =0.5 
G87Gb47Gb4bG5db =0.16;   G87Gb4bGb53G5db =0.58 
Uri (1977) 9 US regions 
pooled data, 
1952?
1974,annual 
translog cost 
function 
G87Gb47Gb47G5db =-0.38 to -4.01 
G87Gb53Gb53G5db =-0.34 to -3.04 
G87Gb4bGb4bG5db =-0.55 to -2.95 
G250Gb47Gb53G3 =1.90 to 121.93 
G250Gb47Gb4bG3 =1.72 to 3.54 
G250Gb53Gb4bG3 =1.94 to 4.06 
Bopp and 
Costello (1990)  
(1)5 US 
regions 
(2)US 
short 
run ,monthly 
time 
series,1977?
1987 
two translog 
cost function 
models 
G87Gb47Gb47G5db =-0.52 to 0.38  
G87Gb53Gb53G5db =-0.39 to -1.29  
G87Gb4bGb4bG5db =-0.25 to -0.4 
G87Gb47Gb53G5db =0.73; G87Gb53Gb47G5db =0.57   
G87Gb47Gb4bG5db =1.14;G3G87Gb53Gb4bG5db not reported 
G87Gb4bGb47G5db =0.29 to 0.82 
G87Gb4bGb53G5db =1.15 to 1.42 
S?derholm 
(2000) 
7 Western 
European 
countries 
pooled annual 
aggregate 
national data 
1978-
1995,shortrun 
generalized 
Leontief cost 
function 
G87Gb47Gb47G5db =-0.08 to -0.49 
G87Gb53Gb53G5db =-0.23 to -2.98  
G87Gb4bGb4bG5db =-0.22 to ?8.81 
G87Gb47Gb53G5db =0.07 to 2.34 
G87Gb53Gb47G5db =0.07 to 1.04 
G87Gb47Gb4bG5db =0.01 to 0.56 
G87Gb4bGb47G5db =0.02 to 0.93 
G87Gb4bGb53G5db =0.22 to 7.88 
G87Gb53Gb4bG5db =0.52 to 1.94 
23 
 
Ko and Dahl 
(2001) US 
monthly panel 
data for 185 US 
utilities in 1993 
translog cost 
function 
G87Gb47Gb47G5db =-0.57;  G87Gb53Gb53G5db =-3.05 
G87Gb4bGb4bG5db =-1.46; G87Gb47Gb53G5db =0.29 
G87Gb53Gb47G5db =3.21;   G87Gb47Gb4bG5db =0.28 
G87Gb4bGb47G5db =1.54;   G87Gb53Gb4bG5db =-0.15 
G87Gb4bGb53G5db =-0.08 
Table definitions: C=coal; O=oil; G=gas. 
Table 2. Selected studies on factor and fuel substitution using the two-stage translog 
function outside electric power industry 
Author Dataset Inputs Country 
and 
industry 
Estimation 
techniques 
Main Results 
Pindyck(1
979) 
Pooled 
data, 1963-
1973;annua
l 
K,L,E(C,
O, G, EL) 
Ten 
Countries; 
 
Two-stage 
translog cost 
function 
(K:L), (E:L)=substitutes 
(C:O),(C:E),(C:G),(E:O)=
substitutes 
(G:O),(G:E)=complement
s 
Cho(2004) Pooled 
data; 1981-
1997; 
quarterly 
data 
K,L,E(C,
O EL) 
Korea Two-stage 
dynamic 
translog cost 
function 
(K:L), (K,E)=substitutes 
(E:L)=complements 
(C:O)= substitutes 
(E:O),(C:E)=complement
s 
Ma, 
Oxley, 
Gibson 
and 
Kim(2008) 
 
Pooled 
data; 1995-
2004; 
annual 
K,L,E(C,
O, G, EL) 
Ten 
regions of 
China; 
Industry 
Two-stage 
translog cost 
function 
(K:L),(K:E),(E:L)=substit
utes 
(C:E),(G:O),(E:O)=substi
tutes 
(C:O)=complements 
Andrikopo
ulos, Brox 
and 
Paraskevo
poulos 
(1989) 
Pooled; 
1962-
1982;annua
l 
K,L,E(C,
O,G,EL) 
Ontario; 
seven 
manufactu
ring 
industries 
Two-stage 
translog 
production 
function; FIML 
(K:L),(E:L)=substitutes 
(C:G),(G:O),(E:O)=substi
tutes 
(C:O)=complements 
Taheri 
(1994) 
Pooled 
data; 1974-
1981 
 US; 
eleven 2-
digit 
manufactu
ring 
Dynamic two-
stage translog 
cost function 
(C:O),(E:O)=substitutes 
(G:O)=complements 
Table definitions: K=capital; L=labor; E=energy; C=coal; O=oil; G=gas; EL=electricity; 
NEL=non-electricity energy; 
Table 3. t-values from panel unit root test results 
Fuel Factor 
lnP1 -9.58*** lnY -0.01*** 
lnP2 -12.27*** lnw -50.22*** 
24 
 
lnP3 -2.53*** lnr -4.81*** 
S1 -6.00***a lne -4.00*** 
S2 -8.04*** R1 -7.17*** 
S3 -3.47*** R2 -1.1e+04***a 
  R3 -1.5e+04***a 
Notes: The adjusted t values are obtained from Levin-Lin-Chu panel unit root tests including 
time trend with one lag. LR variance: Bartlett kernel, 6 lags average (chosen by LLC). Ho= 
Panels contain unit roots. Ha= Panels are stationary. (*), (**) and (***) denote rejection of the 
null hypothesis at the 10%, 5% and 1% level. a denotes time trend not included. 
 
Table 4. Parameter estimates of static and dynamic translog fuel cost share equations 
Static  Dynamic  
Variable Coal Oil Gas Variable Coal Oil Gas 
Intercept 
 
0.351*** 
(0.030) 
0.222*** 
(0.066) 
0.427*** 
(0.072) 
Intercept 
 
0.21* 
(0.12) 
0.22*** 
(0.08) 
0.57* 
(0.14) 
lnp1 
 
0.167*** 
(0.018) 
-0.033* 
(0.025) 
-0.133* 
(0.031) 
lnp1 
 
0.18*** 
(0.02) 
-0.03* 
(0.03) 
-0.14* 
(0.04) 
lnp2 
 
-0.033 
(0.025) 
-0.094* 
(0.053) 
0.127 
(0.059) 
lnp2 
 
-0.03* 
(0.03) 
-0.10* 
(0.06) 
0.13* 
(0.07) 
lnp3 
 
-0.133*** 
(0.020) 
0.127*** 
(0.045) 
0.006*** 
(0.049) 
lnp3 
 
-0.14*** 
(0.03) 
0.13** 
(0.05) 
0.01** 
(0.06) 
t 
 
-0.001 
(0.003) 
0.003 
(0.007) 
-0.001 
(0.008) 
t 
 
0.00 
(0.01) 
0.00 
(0.01) 
0.00 
(0.01) 
d2 
 
-0.218*** 
(0.018) 
0.176*** 
(0.035) 
0.042*** 
(0.039) 
d2 
 
-0.13 
(0.15) 
0.07 
(0.18) 
0.06 
(0.23) 
d3 
 
0.096*** 
(0.018) 
0.082** 
(0.035) 
-0.178** 
(0.040) 
d3 
 
0.39** 
(0.17) 
0.09* 
(0.09) 
-0.48* 
(0.19) 
d4 
 
-0.451*** 
(0.018) 
0.345*** 
(0.036) 
0.106*** 
(0.040) 
d4 
 
-0.42*** 
(0.08 
0.25*** 
(0.09) 
0.17*** 
(0.12) 
d5 
 
0.239*** 
(0.018) 
-0.014* 
(0.035) 
-0.225* 
(0.039) 
d5 
 
0.52* 
(0.26) 
0.00 
(0.12) 
-0.52 
(0.29) 
d6 
 
-0.052*** 
(0.019) 
-0.005* 
(0.037) 
0.057* 
(0.041) 
d6 
 
0.03 
(0.16) 
0.00 
(0.08) 
-0.03 
(0.17) 
d7 
 
-0.344*** 
(0.018) 
-0.018 
(0.035) 
0.361 
(0.040) 
d7 
 
-0.26* 
(0.13) 
-0.04 
(0.11) 
0.30 
(0.17) 
d2t 
 
-0.002 
(0.003) 
-0.006 
(0.006) 
0.008 
(0.007) 
d2t 
 
0.00 
(0.01) 
0.00 
(0.01) 
0.00 
(0.01) 
d3t 
 
-0.003 
(0.003) 
0.002 
(0.006) 
0.001 
(0.007) 
d3t 
 
-0.01* 
(0.01) 
0.00 
(0.01) 
0.01* 
(0.01) 
d4t 
 
0.008** 
(0.003) 
-0.018*** 
(0.006) 
0.010** 
(0.007) 
d4t 
 
0.01* 
(0.01) 
-0.02** 
(0.01) 
0.01* 
(0.01) 
d5t 
 
0.003 
(0.003) 
0.007 
(0.006) 
-0.010 
(0.007) 
d5t 
 
0.00 
(0.01) 
0.01* 
(0.01) 
-0.01 
(0.01) 
25 
 
d6t -0.013*** (0.003) 0.006 (0.006) 0.007 (0.007) d6t  -0.01* (0.01) 0.01* (0.01) 0.01* (0.01) 
d7t 0.009*** (0.003) 0.006* (0.006) -0.014 (0.007) d7t  0.01* (0.01) 0.01* (0.01) -0.01* (0.01) 
    s  0.23* (0.21) 0.44 (2.06) -0.67 (2.07) 
    d2s  -0.15 (0.38) 0.02 (2.12) 0.13 (2.15) 
    d3s  -0.51* (0.29) -0.27 (2.08) 0.78 (2.10) 
    d4s  1.03* (0.81) -0.05 (2.06) -0.98 (2.21) 
    d5s  -0.43* (0.36) -0.85 (3.67) 1.28 (3.69) 
    d6s  -0.13 (0.30) -0.70 (2.58) 0.84 (2.59) 
    d7s -0.04 (0.46) 1.42 (7.76) -1.38 (7.77) 
Notes: Numbers in parentheses are the standard errors. Parameter estimates and standard errors 
for gas are calculated based on homogeneity restrictions and error propagation. (*), (**) and (***) 
denote statistically significance at the 10%, 5% and 1% level. 
 
Table 5. Mean fuel and factor cost share for each region 
  Fuel  Factor 
  G735Gbbc G735Gbc8 G735Gbc0  G734Gbc4 G734Gbc5 G734Gbbe AL  0.50 0.01 0.49  0.58 0.32 0.10 
SE  0.26 0.17 0.57  0.70 0.25 0.04 
PJM  0.57 0.12 0.32  0.77 0.17 0.07 
NY  0.06 0.28 0.67  0.69 0.18 0.13 
MW  0.74 0.03 0.23  0.69 0.19 0.12 
SPP  0.40 0.02 0.58  0.48 0.43 0.09 
TX  0.18 0.01 0.81  0.50 0.41 0.09 
Table 6. Static Hicksian conditional price elasticity and Allen elasticities of substitution for 
fuel inputs 
   AL  SE  PJM  NY  MW SPP      TX G87
Gb47Gb47G5db G3 
 
-0.17 
(0.07) 
-0.05 
(0.11) 
0.22 
(0.12) 
-0.10 
(0.06) 
0.04 
(0.09) 
0.06 
(0.10) 
-0.14 
(0.06) 
0.06 
(0.09) 
0.08 
(0.10) 
1.76 
(0.06) 
-0.25 
(0.09) 
-1.49 
(0.10) 
-0.04 
(0.06) 
-0.01 
(0.09) 
0.05 
(0.10) 
-0.18 
(0.06) 
-0.06 
(0.10) 
0.25 
(0.10) 
0.10 
(0.07) 
-0.17 
(0.12) 
0.07 
(0.13) 
G87Gb47Gb53G5db G3 
 
G87Gb47Gb4bG5db G3 
 
26 
 
G87Gb53Gb47G5db G3 
 
-2.26 
(0.12) 
-8.75 
(0.15) 
11.01 
(0.16) 
0.23 
(0.13) 
0.27 
(0.16) 
-0.50 
(0.17) 
-4.52 
(0.12) 
0.45 
(0.13) 
22.58 
(0.19) 
 
0.06 
(0.10) 
-1.40 
(0.12) 
1.34 
(0.13) 
0.03 
(0.11) 
0.39 
(0.13) 
-0.42 
(0.14) 
0.23 
(0.10) 
0.11 
(0.11) 
2.34 
(0.16) 
 
0.28 
(0.10) 
-1.70 
(0.12) 
1.42 
(0.13) 
0.15 
(0.11) 
0.52 
(0.13) 
-0.66 
(0.14) 
0.49 
(0.10) 
0.26 
(0.11) 
4.47 
(0.16) 
 
-0.06 
(0.10) 
-1.04 
(0.12) 
1.12 
(0.13) 
-0.41 
(0.11) 
0.47 
(0.13) 
-0.32 
(0.14) 
-0.89 
(0.10) 
-2.22 
(0.11) 
1.67 
(0.16) 
 
-0.22     
(0.10) 
-3.66 
(0.12) 
3.88 
(0.13) 
0.15 
(0.11) 
0.59 
(0.13) 
-0.75 
(0.14) 
-0.30 
(0.10) 
0.20 
(0.11) 
17.09 
(0.16) 
 
-1.30 
(0.10) 
-5.74 
(0.13) 
7.04 
(0.13) 
0.17 
(0.11) 
0.24 
(0.13) 
-0.41 
(0.14) 
-3.27 
(0.10) 
0.42 
(0.11) 
12.04 
(0.16) 
 
-2.24 
(0.13) 
-7.79 
(0.16) 
10.03 
(0.17) 
0.02 
(0.14) 
0.17 
(0.17) 
-0.19 
(0.18) 
-12.39 
(0.13) 
0.08 
(0.14) 
12.45 
(0.20) 
 
G87Gb53Gb53G5db G3 
 
G87Gb53Gb4bG5db G3 
 
G87Gb4bGb47G5db G3 
 
G87Gb4bGb53G5db G3 
 
G87Gb4bGb4bG5db G3 
 G250
Gb47Gb53G3  
 
G250Gb47Gb4bG3  
 G250
Gb53Gb4bG3  
 Notes: Numbers in parentheses are the standard errors. Elasticities are calculated with the means 
of each fuel cost shares for each region as shown in Table 5. 
 
Table 7. Static Marshallian unconditional price elasticities for fuel inputs 
 AL SE PJM NY MW SPP TX G8
Gb47Gb47 -1.08 -0.95 -1.48 1.66 -1.24 -0.94 -0.25 
G8Gb47Gb53 -0.08 -0.49 -0.22 -0.70 -0.07 -0.10 -0.20 
G8Gb47Gb4b -0.67 -1.78 -0.66 -2.54 -0.33 -0.87 -1.51 
G8Gb53Gb47 -3.17 -0.78 -1.06 -0.15 -1.43 -2.05 -2.59 
G8Gb53Gb53 -8.77 -1.94 -1.97 -1.49 -3.72 -5.78 -7.82 
G8Gb53Gb4b 10.12 -0.50 0.67 0.06 3.51 5.92 8.45 
G8Gb4bGb47 -0.69 -0.82 -1.19 -0.50 -1.06 -0.59 -0.34 
G8Gb4bGb53 0.25 -0.15 0.24 0.03 0.54 0.20 0.14 
G8Gb4bGb4b -1.39 -2.26 -1.41 -1.37 -1.12 -1.52 -1.76 
Table 8. Dynamic Hicksian conditional price elasticity and Allen elasticities of substitution 
for fuel inputs 
  AL   SE   PJM   NY   MW   SPP   TX   
G87Gb47Gb47G5db G3 
 
-0.15 
(0.11) 
-0.05 
(0.19) 
0.20 
(0.19) 
-0.07 
(0.21) 
0.04 
(0.31) 
0.02 
(0.32) 
-0.12 
(0.20) 
0.06 
(0.30) 
0.06 
(0.31) 
1.91 
(0.27) 
-0.23 
(0.360 
-1.66 
(0.36) 
-0.02 
(0.23) 
-0.01 
(0.35) 
0.03 
(0.36) 
-0.16 
(0.20) 
-0.06 
(0.31) 
0.22 
(0.32) 
0.15 
(0.22) 
-0.16 
(0.42) 
0.01 
(0.42) 
G87Gb47Gb53G5db G3 
 
G87Gb47Gb4bG5db G3 
 
27 
 
G87Gb53Gb47G5db G3 
 
-2.15 
(0.38) 
-8.02 
(0.43) 
11.16 
(0.43) 
0.21 
(0.38) 
0.28 
(0.44) 
-0.48 
(0.44) 
-4.29 
(0.20) 
0.41 
(0.20) 
22.90 
(0.46) 
0.07 
(0.68) 
-1.42 
(0.75) 
1.35 
(0.76) 
0.01 
(0.70) 
0.39 
(0.77) 
-0.40 
(0.77) 
0.26 
(0.33) 
0.04 
(0.33) 
2.36 
(0.79) 
0.29 
(0.67) 
-1.72 
(0.74) 
1.43 
(0.74) 
0.11 
(0.68) 
0.52 
(0.75) 
-0.64 
(0.76) 
0.51 
(0.31) 
0.20 
(0.32) 
4.52 
(0.77) 
-0.05 
(0.67) 
-1.06 
(0.73) 
1.12 
(0.74) 
-0.44 
(0.70) 
0.48 
(0.76) 
-0.31 
(0.76) 
-0.82 
(0.37) 
-2.48 
(0.38) 
1.68 
(0.77) 
-0.18 
(0.86) 
-3.75 
(0.95) 
3.93 
(0.95) 
0.10 
(0.89) 
0.60 
(0.97) 
-0.71 
(0.98) 
-0.25 
(0.37) 
0.14 
(0.37) 
17.32 
(0.98) 
-1.23 
(0.72) 
-5.90 
(0.80) 
7.13 
(0.80) 
0.15 
(0.74) 
0.24 
(0.82) 
-0.39 
(0.82) 
-3.10 
(0.32) 
0.38 
(0.33) 
12.20 
(0.83) 
-2.14 
(1.34) 
-8.02 
(1.46) 
10.16 
(1.46) 
0.00 
(1.35) 
0.17 
(1.47) 
-0.18 
(1.47) 
-11.84 
(0.43) 
0.01 
(0.43) 
12.62 
(1.49) 
G87Gb53Gb53G5db G3 
 
G87Gb53Gb4bG5db G3 
 
G87Gb4bGb47G5db G3 
 
G87Gb4bGb53G5db G3 
 
G87Gb4bGb4bG5db G3 
 G250
Gb47Gb53G3  
G250Gb47Gb4bG3  
 
G250Gb53Gb4bG3  
Notes: Numbers in parentheses are the standard errors. Elasticities are calculated with the means 
of each fuel cost shares for each region as shown in Table 5. 
 
 
Table 9. Dynamic Marshallian fuel price unconditional elasticity  
        
AL SE PJM NY MW SPP TX 
G8Gb47Gb47 -0.93 -0.74 -1.23 1.82 -1.07 -0.8 -0.14 
G8Gb47Gb53 -0.07 -0.38 -0.17 -0.62 -0.06 -0.09 -0.19 
G8Gb47Gb4b -0.56 -1.45 -0.55 -2.57 -0.29 -0.73 -1.33 
G8Gb53Gb47 -2.93 -0.61 -0.82 -0.14 -1.23 -1.87 -2.44 
G8Gb53Gb53 -8.03 -1.85 -1.95 -1.45 -3.8 -5.93 -8.04 
G8Gb53Gb4b 10.4 -0.12 0.82 0.21 3.61 6.18 8.83 
G8Gb4bGb47 -0.58 -0.66 -0.99 -0.53 -0.94 -0.49 -0.3 
G8Gb4bGb53 0.26 -0.04 0.3 0.09 0.55 0.21 0.15 
G8Gb4bGb4b -1.25 -1.88 -1.26 -1.23 -1.03 -1.34 -1.51 
Table 10. Static and dynamic parameter estimates for factor share equations 
Static    Dynamic    
Variable Capital Labor Energy Variable Capital Labor Energy 
Intercept 
 
-6.034** 
(2.799) 
3.640* 
(3.243) 
3.393* 
(4.284) 
Intercept 
 
5.51* 
(3.80) 
-7.33* 
(5.06) 
2.82* 
(6.32) 
lnp1 
 
0.253*** 
(0.019) 
-0.183*** 
(0.022) 
-0.070*** 
(0.029) 
lnp1 
 
0.30*** 
(0.03) 
-0.22*** 
(0.04) 
-0.08*** 
(0.04) 
28 
 
lnp2 
 
-0.183*** 
(0.022) 
0.071** 
(0.029) 
0.112** 
(0.037) 
lnp2 
 
-0.22*** 
(0.04) 
0.09* 
(0.05) 
0.13* 
(0.06) 
lnp3 
 
-0.070*** 
(0.007) 
0.112*** 
(0.012) 
-0.042*** 
(0.014) 
lnp3 
 
-0.08*** 
(0.01) 
0.13*** 
(0.02) 
-0.05*** 
(0.02) 
lny 
 
0.338** 
(0.150) 
-0.153 
(0.175) 
-0.185 
(0.230) 
lny 
 
-0.30* 
(0.20) 
0.43* 
(0.27) 
-0.13* 
(0.34) 
t 
 
-0.011*** 
(0.003) 
0.010*** 
(0.003) 
0.001*** 
(0.004) 
t 
 
0.00 
(0.00) 
0.00 
(0.01) 
0.00 
(0.01) 
d2 
 
-1.492 
(0.055) 
0.204 
(0.061) 
1.288 
(0.082) 
d2 
 
-8.59 
(0.07) 
5.89 
(0.09) 
2.70 
(0.11) 
d3 
 
-4.650* 
(0.053) 
1.138 
(0.059) 
3.512 
(0.079) 
d3 
 
-1.85 
(0.07) 
0.84 
(0.09) 
1.02 
(0.12) 
d4 
 
18.281*** 
(0.042) 
-15.326*** 
(0.049) 
-2.955*** 
(0.064) 
d4 
 
2.71 
(0.05) 
-2.16 
(0.07) 
-0.56 
(0.08) 
d5 
 
8.594* 
(0.073) 
-6.917 
(0.081) 
-1.676 
(0.109) 
d5 
 
28.17** 
(0.11) 
-29.02** 
(0.14) 
0.85** 
(0.18) 
d6 
 
-8.503* 
(0.045) 
5.561* 
(0.050) 
2.942* 
(0.068) 
d6 
 
-9.09* 
(0.05) 
7.75 
(0.07) 
1.33 
(0.08) 
d7 
 
-8.492* 
(0.080) 
13.906* 
(0.088) 
-5.414* 
(0.118) 
d7 
 
-15.42* 
(0.09) 
22.72* 
(0.12) 
-7.30* 
(0.16) 
d2y 
 
0.039 
(0.027) 
0.007 
(0.030) 
-0.046 
(0.040) 
d2y 
 
0.45 
(0.03) 
-0.32 
(0.04) 
-0.13 
(0.06) 
d3y 
 
0.203 
(0.027) 
-0.046 
(0.029) 
-0.157 
(0.040) 
d3y 
 
0.11 
(0.04) 
-0.07 
(0.05) 
-0.03 
(0.06) 
d4y 
 
-0.988*** 
(0.023) 
0.823*** 
(0.026) 
0.165*** 
(0.034) 
d4y 
 
-0.15 
(0.03) 
0.13 
(0.04) 
0.03 
(0.05) 
d5y 
 
-0.453* 
(0.036) 
0.352 
(0.040) 
0.101 
(0.054) 
d5y 
 
-1.39*** 
(0.05) 
1.40** 
(0.07) 
0.00 
(0.09) 
d6y 
 
0.461* 
(0.025) 
-0.299 
(0.027) 
-0.162 
(0.037) 
d6y 
 
0.49* 
(0.03) 
-0.40 
(0.04) 
-0.09 
(0.05) 
d7y 
 
0.400* 
(0.040) 
-0.684* 
(0.045) 
0.284* 
(0.060) 
d7y 
 
0.80* 
(0.05) 
-1.16* 
(0.06) 
0.36 
(0.08) 
d2t 
 
0.000 
(0.004) 
0.000 
(0.004) 
-0.001 
(0.006) 
d2t 
 
-0.01 
(0.01) 
0.01 
(0.01) 
0.00 
(0.01) 
d3t 
 
0.002 
(0.004) 
-0.003 
(0.004) 
0.001 
(0.006) 
d3t 
 
-0.01 
(0.00) 
0.00 
(0.01) 
0.00 
(0.01) 
d4t 
 
0.013*** 
(0.003) 
-0.011*** 
(0.003) 
-0.002*** 
(0.004) 
d4t 
 
0.00 
(0.00) 
0.00 
(0.01) 
0.00 
(0.01) 
d5t 
 
0.013*** 
(0.005) 
-0.011** 
(0.005) 
-0.001** 
(0.007) 
d5t 
 
0.02*** 
(0.01) 
-0.02** 
(0.01) 
0.00 
(0.01) 
29 
 
d6t 
 
-0.022*** 
(0.007) 
0.017** 
(0.008) 
0.005** 
(0.010) 
d6t 
 
-0.01 
(0.01) 
0.01 
(0.01) 
0.00 
(0.01) 
d7t 
 
0.005 
(0.005) 
-0.001 
(0.006) 
-0.003 
(0.008) 
d7t 
 
-0.01* 
(0.01) 
0.01* 
(0.01) 
0.00 
(0.01) 
    S  0.47*** (0.08) 0.46*** (0.12) -0.93*** (0.14) 
    d2s  -0.30 (0.20) -0.26 (0.23) 0.56 (0.30) 
    d3s  0.10 (0.21) 0.08 (0.27) -0.18 (0.34) 
    d4s  -0.21 (0.19) -0.17 (0.21) 0.38 (0.29) 
    d5s  0.57* (0.31) 0.54 (0.42) -1.11 (0.52) 
    d6s -0.34*** (0.12) -0.37** (0.16) 0.71** (0.20) 
    d7s -0.29** (0.13) -0.27* (0.17) 0.56* (0.21) 
Notes: Numbers in parentheses are the standard errors. Parameter estimates and standard errors 
for capital are calculated based on homogeneity restrictions and error propagation. (*), (**) and 
(***) denote statistically significance at the 10%, 5% and 1% level. 
Table 11. Static Hicksian price elasticities and Allen elasticities of substitution for factor 
inputs 
 AL SE PJM  NY MW SPP TX G8
Gb4fGb4fG5db G3 
 
-0.45 
(0.24) 
0.32 
(0.26) 
0.13 
(0.31) 
0.58 
(0.27) 
-0.92 
(0.29) 
0.34 
(0.33) 
0.76 
(0.34) 
1.07 
(0.35) 
-1.83 
(0.39) 
-0.32 
(0.26) 
0.25 
(0.28) 
0.07 
(0.33) 
0.71 
(0.29) 
-1.05 
(0.31) 
0.34 
(0.36) 
1.15 
(0.37) 
2.08 
(0.38) 
-3.22 
(0.42) 
-0.26 
(0.26) 
0.17 
(0.28) 
0.09 
(0.33) 
0.77 
(0.29) 
-1.29 
(0.31) 
0.52 
(0.35) 
1.04 
(0.36) 
1.31 
(0.38 
-2.36 
(0.42) 
-0.34 
(0.25) 
0.18 
(0.27) 
0.16 
(0.32) 
0.69 
(0.28) 
-1.26 
(0.30) 
0.57 
(0.35) 
0.80 
(0.36) 
0.74 
(0.37) 
-1.57 
(0.41) 
-0.34 
(0.28) 
0.19 
(0.30) 
0.15 
(0.35) 
0.69 
(0.31) 
-1.22 
(0.32) 
0.53 
(0.37) 
0.84 
(0.39) 
0.80 
(0.40) 
-1.64 
(0.45) 
-0.56 
(0.26) 
0.43 
(0.27) 
0.13 
(0.32) 
0.48 
(0.28) 
-0.75 
(0.30) 
0.27 
(0.35) 
0.68 
(0.36) 
1.23 
(0.37) 
-1.91 
(0.41) 
-0.54 
(0.28) 
0.41 
(0.30) 
0.13 
(0.36) 
0.50 
(0.31) 
-0.78 
(0.33) 
0.28 
(0.38) 
0.70 
(0.40) 
1.25 
(0.41) 
-1.95 
(0.46) 
G8Gb4fGb50G5db G3 
 
G8Gb4fGb49G5db G3 
 
G8Gb50Gb4fG5db G3 
 
G8Gb50Gb50G5db G3 
 
G8Gb50Gb49G5db G3 
 
G8Gb49Gb4fG5db G3 
 
G8Gb49Gb50G5db G3 
 
G8Gb49Gb49G5db G3 
 
30 
 
G250Gb4fGb4fG3  -0.78 
(0.29) 
1.00 
(0.30) 
1.31 
(0.34) 
-2.88 
(0.34) 
3.34 
(0.37) 
-17.97 
(0.45) 
-0.46 
(0.31) 
1.00 
(0.33) 
1.63 
(0.37) 
-4.11 
(0.36) 
8.17 
(0.40) 
-77.32 
(0.49) 
-0.34 
(0.31) 
1.00 
(0.32) 
1.36 
(0.37) 
-7.75 
(0.36) 
7.87 
(0.40) 
-35.43 
(0.49) 
-0.49 
(0.30) 
1.00 
(0.32) 
1.20 
(0.36) 
-7.21 
(0.35) 
4.24 
(0.39) 
-11.72 
(0.48) 
-0.49 
(0.33) 
1.00 
(0.34) 
1.22 
(0.39) 
-6.48 
(0.38) 
4.26 
(0.42) 
-13.19 
(0.52) 
-1.17 
(0.30) 
1.00 
(0.32) 
1.41 
(0.36) 
-1.77 
(0.36) 
2.89 
(0.40) 
-20.26 
(0.48) 
-1.08 
(0.33) 
1.00 
(0.35) 
1.41 
(0.40) 
-1.89 
(0.39) 
3.05 
(0.43) 
-21.62 
(0.53) 
 
G250Gb4fGb50G3  
 G250
Gb4fGb49G3  
 
G250Gb50Gb50G3  
 
G250Gb50Gb49G3  
 
G250Gb49Gb49G3  
 Notes: Numbers in parentheses are the standard errors. Elasticities are calculated with the means 
of each factor-input cost shares for each region as shown in Table 5. 
Table 12. Dynamic Hicksian price elasticity and Allen elasticities of substitution for factor 
inputs 
 AL SE PJM NY MW SPP TX 
G8Gb4fGb4fG5db  
 
0.03 
(0.37) 
0.08 
(0.43) 
-0.11 
(0.49) 
0.15 
(0.47) 
-0.84 
(0.52) 
0.7 
(0.58) 
-0.62 
(0.58) 
2.18 
(0.63) 
-1.56 
(0.68) 
0.03 
(0.43) 
0.08 
(0.48) 
-0.11 
(0.54) 
0.15 
(0.61) 
-0.84 
0.07 
(0.86) 
0.06 
(0.95) 
-0.13 
(1.08) 
0.16 
(1.09) 
-0.95 
(1.17) 
0.79 
(1.29) 
-2.22 
(1.43) 
4.8 
(1.50) 
-2.58 
(1.60) 
0.07 
(0.97) 
0.06 
(1.06) 
-0.13 
(1.18) 
0.16 
(1.31) 
-0.95 
0.11 
(0.02) 
-0.01 
(0.03) 
-0.09 
(0.03) 
-0.06 
(0.03) 
-1.15 
(0.03) 
1.2 
(0.04) 
-1.07 
(0.03) 
3.02 
(0.03) 
-1.95 
(0.03) 
0.11 
(0.02) 
-0.01 
(0.03) 
-0.09 
(0.03) 
-0.06 
(0.04) 
-1.15 
0.07 
(0.73) 
-0.02 
(0.82) 
-0.04 
(0.93) 
-0.09 
(0.92) 
-1.12 
(1.00) 
1.22 
(1.11) 
-0.01 
(1.20) 
1.59 
(1.26) 
-1.37 
(1.36) 
0.07 
(0.83) 
-0.02 
(0.91) 
-0.04 
(1.02) 
-0.09 
(1.13) 
-1.12 
0.06 
(1.34) 
-0.01 
(1.51) 
-0.05 
(1.69) 
-0.04 
(1.85) 
-1.09 
(2.00) 
1.13 
(2.16) 
-0.3 
(2.46) 
1.72 
(2.58) 
-1.42 
(2.73) 
0.06 
(1.49) 
-0.01 
(1.65) 
-0.05 
(1.81) 
-0.04 
(2.18) 
-1.09 
0.02 
(0.69) 
0.14 
(0.77) 
-0.16 
(0.88) 
0.16 
(0.88) 
-0.7 
(0.95) 
0.54 
(1.05) 
-0.82 
(1.13) 
2.44 
(1.20) 
-1.62 
(1.28) 
0.02 
(0.79) 
0.14 
(0.86) 
-0.16 
(0.96) 
0.16 
(1.08) 
-0.7 
0.02 
(1.05) 
0.14 
(1.19) 
-0.15 
(1.34) 
0.16 
(1.41) 
-0.72 
(1.53) 
0.55 
(1.67) 
-0.85 
(1.85) 
2.51 
(1.95) 
-1.66 
(2.07) 
0.02 
(1.18) 
0.14 
(1.30) 
-0.15 
(1.44) 
0.16 
(1.69) 
-0.72 
G8Gb4fGb50G5db  
 
G8Gb4fGb49G5db  
 
G8Gb50Gb4fG5db  
 
G8Gb50Gb50G5db  
 
G8Gb50Gb49G5db  
 
G8Gb49Gb4fG5db  
 
G8Gb49Gb50G5db  
 
G8Gb49Gb49G5db  
 
G250Gb4fGb4fG3  
 
G250Gb4fGb50G3  
 
G250Gb4fGb49G3  
 
G250Gb50Gb50G3  
 
G250Gb50Gb49G3  
31 
 
 
G250Gb49Gb49G3  
(0.66) 
0.7 
(0.78) 
(1.42) 
0.79 
(1.77) 
(0.04) 
1.2 
(0.04) 
(1.22) 
1.22 
(1.51) 
(2.33) 
1.13 
(2.94) 
(1.16) 
0.54 
(1.43) 
(1.82) 
0.55 
(2.26)  
Notes: Numbers in parentheses are the standard errors. Elasticities are calculated with the means 
of each factor-input cost shares for each region as shown in Table 5. 
Table 13. Technological change in fuel and factor demand 
 Fuel  Factor 
   Coal Oil Gas  Capital Labor Energy 
AL  0.00 0.22 0.00  -0.02 0.03 0.01 
SE  -0.01 -0.02 0.01  -0.02 0.04 0.02 
PJM  -0.01 0.04 0.00  -0.01 0.04 0.04 
NY  0.10 -0.05 0.01  0.00 -0.01 -0.01 
MW  0.00 0.29 -0.05  0.00 -0.01 0.00 
SPP  -0.04 0.44 0.01  -0.07 0.06 0.07 
TX  0.04 0.61 -0.02  -0.01 0.02 -0.02 
 
Table 14. Total factor productivity growth rates for factor-input model 
  2002 2003 2004 2005 2006 2007 2008 Average 
AL -0.23 0.00 -0.44 0.07 -0.18 -0.12 0.05 -0.12 
SE -0.18 0.00 0.00 0.30 -0.05 -0.04 0.05 0.01 
PJM 0.06 -0.15 0.03 0.10 0.08 -0.09 0.00 0.00 
NY 0.03 0.04 0.02 -0.13 0.11 -0.06 0.20 0.03 
MW -0.07 0.13 0.06 -0.07 0.06 -0.05 -0.01 0.01 
SPP 0.01 -0.12 -0.06 -0.10 -0.06 0.00 -0.01 -0.05 
TX -0.08 0.07 0.15 0.06 0.08 0.00 0.01 0.04 
Average -0.07 0.00 -0.04 0.03 0.01 -0.05 0.04 -0.01 
32 
 
 
-4
-2
0
2
4
6
8
10
2001 2002 2003 2004 2005 2006 2007 2008
lnPk lnPl lnPe
Inde
x 
33 
 
Figure 1. Indices of average factor prices for the electric power industry in the eastern US 
 
Figure  2. Indices of average fuel prices for the electric power industry in the eastern US 
 
    Figure 3.  The electric regions in US 
 
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
2001 2002 2003 2004 2005 2006 2007 2008
lnPc lnPo lnPg
Inde
x 
34 
 
 
Figure 4. Total factor productivity growth rates by regions for factor-input model 
 
 
-0.50
-0.40
-0.30
-0.20
-0.10
0.00
0.10
0.20
0.30
0.40
2002 2003 2004 2005 2006 2007 2008
0
200
400
600
800
1000
1200
1400
1600
1800
2000
2001 2002 2003 2004 2005 2006 2007 2008
Out
put
 pe
r uni
t in
put
 
 TF
P I
nde
x 
TX 
SPP 
MW 
NY 
PJM 
SE 
AL 
TX 
SPP 
MW NY 
PJM 
SE 
AL 
35 
 
Figure 5.  Energy production efficiency by region 
 
Figure 6. Labor production efficiency by region 
 
 
 
 
 
 
 
 
 
 
 
 
 
0
10000
20000
30000
40000
50000
60000
70000
80000
2001 2002 2003 2004 2005 2006 2007 2008
Ou
tpu
t p
er 
un
it i
np
ut 
TX 
SPP 
MW 
NY 
PJM 
SE 
AL 
36 
 
Chapter 2: CO2 Emissions, Non-Hydro Energy Consumption and Economic 
Growth:  A US Study Based on Cointegration and Error-correction  
1. Introduction 
The objective of this paper is to examine the causal relationships between CO2 emissions, 
hydrocarbon energy consumption, non-hydrocarbon energy consumption, and real GDP growth 
in the US from 1960 to 2009. 
The most critical environmental problem of the time is global warming, which is 
exacerbated by continuously increasing greenhouse gas emissions. Carbon dioxide emissions 
accounted for more than 98% of greenhouse gas emissions in the last two decades according to 
World Bank World Development Indicators. Considering that the majority of emissions are 
caused by combustion of hydrocarbons, environmental policies mainly focus on improving 
energy efficiency, reducing energy consumption and switching fuel choices, all of which affect 
economic development.  
Efficient and timely measures to jointly improve the condition of the environment and 
economic development are important for the US because it is one of the largest energy 
consumers and energy-related CO2 emitters.  The portion of hydrocarbon energy consumption in 
the US has decreased from 96% in 1960 to 83% in 2009, as non-hydrocarbon consumption has 
increased. The nexus of energy-environment-economics is an important issue that takes into 
account the dependence of the US on fuel consumption and the potential economic sacrifices to 
reduce CO2 emissions. 
The prime issue objective of this paper is to test whether hydrocarbon energy consumption, 
GDP growth, investment and population growth affect CO2 emissions; in addition, whether the 
latter affects the former. The organization of this paper is as follows: Section 2 gives reviews of 
37 
 
recent literature. Theoretic models and methodologies are illustrated in section 3. Section 4 
describes the data and data sources. The empirical results are discussed in section 5. Section 6 
concludes with policy implications.   
  2. Literature Review 
There are three branches of recent studies exploring causal relationships between pollutant 
emissions, energy consumption, and economic development. The first branch focuses on the link 
between energy consumption and economic growth. More energy consumption is required as the 
economy develops, therefore as energy consumption grows, the economy develops 
correspondingly. Earlier studies employing Granger causality and cointegration techniques in 
bivariate models following Kraft and Kraft (1978) failed to reach a unanimous conclusion, 
probably due to the omitted variables bias and the substitution effects between energy and other 
inputs. Stern (1993) concluded that energy consumption Granger-causes GDP by applying a 
multivariate model with energy, consumption, GDP, capital, and labor force in the US. Various 
multivariate studies have examined the causality between energy and economic growth but still 
produce conflicting results, such as Masih and Masih (1998), Stern (2000), Asafu-Adjaye (2000), 
Glasure (2002), Soytas and Sari (2003), Oh and Lee (2004), Altinay and Laragol (2004), Wolde-
Rufael (2004), Ghali and Elsakka (2004), and Lee (2006). 
The second branch studies the relationship between emissions and economic growth, which 
initially relies on the environmental Kuznets curve (EKC) hypothesis indicating an inverted U-
shaped connection between environmental degradation and economic development. The 
empirical results of Unruh and Moomaw (1998), Heil and Selden (1999), Taskin and Zaim 
(2000), Friedl and Getzner (2003), Coondoo and Dinda (2008), and Managi and Jena (2008) are 
controversial and are criticized for lack of feedback from emissions to GDP (see Hill and 
38 
 
Magnani 2002, Stern 2004). Chontanawat et al. (2008), Aslanidis and Iranzo (2009), Payne 
(2010) and Ozturk (2010) implemented extended research on the environmental Kuznets curve, 
the results of which are inconclusive as well. 
The third, and newest, branch associates the first two branches and explores the nexus in 
environmental pollution, energy consumption, and economic development within a multivariate 
system. A series of econometric techniques has been applied and the results have been varied 
based on the variables involved, sample length and different countries. Their data, methods, and 
results of causal relationship are compared with the present study in Table 6. 
Soytas et al. (2007) using the TY procedure 5and a Vector autoregression (VAR) model, 
found energy consumption Granger-causes carbon emissions but found no causal relationship 
between GDP and emissions, or between energy consumption and GDP after controlling for the 
capital stock and labor from 1960 to 2004 for the US.  
Ang (2008) applied multivariate cointegration as well as an error-correction model (ECM), 
and showed that GDP Granger-causes energy consumption and CO2 emissions weakly Granger-
cause GDP in Malaysia during the period 1971-1999. 
Soytas and Sari (2009) investigated the Granger causality link between economic growth, 
CO2 emissions and energy consumption controlling for the capital stock and labor in Turkey for 
the period 1960-2000 again using the TY procedure and VAR models. They found no link 
between GDP and emissions, and CO2 emissions uni-directionally Granger cause energy 
consumption. 
                                                           
5 TY procedure is an augmented VAR approach proposed by Toda and Yamamoto (1995) and 
can be applied for any arbitrary level of integration. 
39 
 
Beside emissions, energy consumption and GDP, Halicioglu (2009) added the variable of 
foreign trade and investigated the causal relationship between the four covariates in Turkey for 
the period 1960-2005 with cointegration and ECM. The findings show a bi-directional Granger 
causality between emissions and GDP. 
Zhang and Cheng (2009) employed the TY procedure and VAR model of economic growth, 
energy use, CO2 emissions, capital and urban population in China from 1960 to 2009. Results 
suggest a uni-directional Granger causality running from GDP to energy consumption and from 
energy consumption to CO2 emissions.  
Menyah and Wolde (2010) examined the causal relationship between nuclear energy 
consumption, renewable energy consumption, and CO2 emissions in the US for the period 1960-
2007 by applying the TY procedure and found uni-directional causality from nuclear energy 
consumption to CO2 emissions, and no causality between renewable energy consumption and 
CO2. 
Pereira and Pereira (2010) extended the literature to estimate the impact of shocks to the 
demand for specific types of energy by employing cointegration. The results show strong 
evidence for Portugal from 1977 to 2003 that energy consumption has a significant impact on 
economic performance. 
To my knowledge, this paper is the first to estimate causal relationship between CO2 
emission, hydrocarbon energy consumption, non-hydrocarbon energy consumption, and 
economic development after controlling for investment and total population. Hydrocarbon 
energy and non-hydrocarbon energy are separated because emissions are mainly caused by the 
combustion of hydrocarbons energy sources. Beside the policy implications from causal 
40 
 
relationships between emissions, energy consumption and economics, contributions to fuel-
choice and fuel-switching policy are expected. 
3. Model and methodology 
3.1 Model 
To explore the long-run nexus between carbon dioxide emissions, energy consumption and 
economic development, the general model can be specified as follows: 
G725Gbe7 =G3G742G3G123aG728Gbe7G1e1 G730Gbe7G1e1 G73bGbe7G1e1 G72dGbe7G1e1 G732Gbe7G123b,                                                                                         (1) 
where G725Gbe7 denotes carbon dioxide emission, G728Gbe7 denotes hydrocarbon energy consumption, G730Gbe7 
denotes non-hydrocarbon energy consumption, G73bGbe7 denotes real GDP, G72dGbe7 denotes investment, andG3
G732Gbe7G3denotes total population.  
According to previous studies, the choice of linear or quadratic models depends on the 
dataset and the relationship between C and Y.  To estimate the relationship between CO2 
emission, energy consumption, and economic growth, in the studies of Halicioglu (2009) for 
Turkey, and Apergis and Payne (2009) for the Commonwealth of Independent States, quadratic 
form models are applied.  However, linear models are generally employed in most of the studies, 
such as Glasure and Lee (1997) for South Korea and Singapore, Soytas, Sari and Ewing (2007), 
and Ang (2008) for Malaysia, Soytas and Sari (2009) for the US, Zhang and Cheng (2009) for 
China, Menyah and Rufael (2010), and Pereira and Pereira (2010)  for Portugal.  
3.2 Unit root, cointegration and long-run causality 
Cointegration refers to a linear combination of nonstationary variables. To apply this 
methodology, unit root hypothesis tests and integration analysis are necessary before proceeding 
to cointegration and error correction. Augmented Dickey-Fuller (ADF) t-tests (Dickey and Fuller, 
1979) and Phillips-Perron (PP) tests (Perron, 1988) are conducted to test the null hypothesis of a 
41 
 
unit root in the different variables including 1974 and 1978 dummies. The optimal lag form is 
selected using the BIC6.  
Two or more variables are cointegrated if they are integrated of the same order and their 
linear combination is stationary (Engle and Granger 1987). Cointegrated variables show a long 
term equilibrium relationship and share common stochastic trends, thus there must exist at least 
one unidirectional or bidirectional causality in the Granger sense. Moreover, if the variables are 
detected to be cointegrated, spurious problems would be ruled out.   
The multivariate cointegration method is well developed by Johansen and Juselius (1990). 
The multivariate system constitutes a first-order vector autoregression (VAR) and all the 
variables are supposed to be endogenous as follows: 
G755Gbe7=  + G3c3 G2c6GbddGbe0Gb35 G755Gbe7Gb3fGbdd+G752Gbe7      ,                       (2) 
where G755Gbe7 denotes vector of endogenous I(1) variables, that is G725Gbe7G1e1G728Gbe7G1e1 G730Gbe7G1e1 G73bGbe7G1e1 G72dGbe7 and G732Gb72; G749 
denotes lag length which is determined by a mixed criterion of AIC, BIC and likelihood ratio; G2c6Gbdd 
denotes the coefficient matrix;  denotes a vector of constant terms; and G752Gbe7 denotes the residual 
matrix. The number of cointegrating vectors, i.e. the cointegrating rank, can be detected by 
maximal eigenvalue and trace tests. 
3.3 Vector error-correction modeling (VECM) and short-run causality  
According to Engle and Granger (1987), cointegrated variables must have an error 
correction representation. Short-run dynamics of cointegrated variables, influenced by the 
deviation from the long-run relationship, can be examined by the Vector Error Correction Model 
(VECM), which implies that changes in the endogenous variables are functions of changes in 
                                                           
6 BIC: Bayesian information criterion 
42 
 
exogenous variables and the level of disequilibrium captured by error correction terms in the 
cointegrating relationship. This technique allows for a causal linkage between variables and 
reintroduces the information lost in the differencing process. 
Since the nexus between CO2 emission, non-hydrocarbon energy consumption and 
economic growth are of primary concern, a trivariate VECM can be specified as follows 
assuming one cointegrated relationship. 
?lnG725Gbe7 = G7d9Gb35+ G3c3 G7e6GbdfGbdcGb40Gb35 Gb35GbdcG727G725G736Gbe7Gb3fGb35 + G3c3 G7dbGb35GbdcG21fG748G74aG725Gbe7Gb3fGb67GbdfGbdcGb40Gb35 + G3c3 G7dcGb35GbdcGbdfGbdcGb40Gb35 G21fG748G74aG728Gbe7Gb3fGb67 + G3c3 G7e0Gb35GbdcGbdfGbdcGb40Gb35 G21fG748G74aG730Gbe7Gb3fGb67 + 
G3c3 G7eaGb35GbdcGbdfGbdcGb40Gb35 G21fG748G74aG73bGbe7Gb3fGb67 Gd45G3c3 G7ecGb35GbdcGbdfGbdcGb40Gb35 G21fG748G74aG72dGbe7Gb3fGb67+G3c3 G7eeGb35GbdcGbdfGbdcGb40Gb35 G21fG748G74aG732Gbe7Gb3fGb67+G7ddGb35Gbe7          ,                   (3) 
?lnG11Gbe7 =G7d9Gb36+ G3c3 G7e6GbdfGbdcGb40Gb35 Gb36GbdcG727G725G736Gbe7Gb3fGb35 + G3c3 G7dbGb36GbdcG21fG748G74aG725Gbe7Gb3fGb67GbdfGbdcGb40Gb35 + G3c3 G7dcGb36GbdcGbdfGbdcGb40Gb35 G21fG748G74aG728Gbe7Gb3fGb67 + G3c3 G7e0Gb36GbdcGbdfGbdcGb40Gb35 G21fG748G74aG730Gbe7Gb3fGb67 + 
G3c3 G7eaGb36GbdcGbdfGbdcGb40Gb35 G21fG748G74aG73bGbe7Gb3fGb67 Gd45G3c3 G7ecGb36GbdcGbdfGbdcGb40Gb35 G21fG748G72dGbe7Gb3fGb67+G3c3 G7eeGb36GbdcGbdfGbdcGb40Gb35 G21fG748G74aG732Gbe7Gb3fGb67+G7ddGb36Gbe7  ,           (4) 
?lnG1cGbe7 = G7d9Gb35+ G3c3 G7e6GbdfGbdcGb40Gb35 Gb37GbdcG727G725G736Gbe7Gb3fGb35 + G3c3 G7dbGb37GbdcG21fG748G74aG725Gbe7Gb3fGb67GbdfGbdcGb40Gb35 + G3c3 G7dcGb37GbdcGbdfGbdcGb40Gb35 G21fG748G74aG728Gbe7Gb3fGb67 + G3c3 G7e0Gb37GbdcGbdfGbdcGb40Gb35 G21fG748G74aG730Gbe7Gb3fGb67 +      
G3c3 G7eaGb37GbdcGbdfGbdcGb40Gb35 G21fG748G74aG73bGbe7Gb3fGb67 Gd45G3c3 G7ecGb37GbdcGbdfGbdcGb40Gb35 G21fG748G74aG72dGbe7Gb3fGb67+G3c3 G7eeGb37GbdcGbdfGbdcGb40Gb35 G21fG748G74aG732Gbe7Gb3fGb67+G7ddGb37Gbe7  ,       (5) 
where ? denotes the first-difference operator; l denotes the lag length set at one based on the 
SIC 7criterion;  G8G6G17Gb72Gb3fGb35 denotes the error-correction term and is the residual in period t-1 
obtained from the long-run cointegrating relationship; G24c denotes the speed of adjustment 
parameter; and G242Gb72 denotes a serially uncorrelated error term with mean zero. 
4. Data 
The dataset consists of annual national level observations in the US from 1960 to 2009. Data 
on carbon dioxide emissions (C) (in kt), real GDP (Y) (in constant 2000 US$),  gross fixed 
capital formation (K) (in constant 2000 US$) and total population (P) are from World Bank 
                                                           
7 SIC: Schwarz information criterion 
43 
 
World Development Indicators. Hydrocarbon energy consumption (F) and non-hydrocarbon 
energy consumption (N) (both in kt of oil equivalent) are from the US Energy Information 
Administration (EIA). According to the Annual Energy Review (AER) of the EIA, hydrocarbon 
energy includes coal, net import of coal coke, natural gas only (excludes supplemental gaseous 
fuels) and petroleum. Non hydrocarbon energy includes nuclear electric power and renewable 
energy8. As Friedl and Getzner (2003) pointed out, since the Kyoto Protocol advocates reducing 
the proportion of emissions, total data rather than per capita data should be employed. Follo,ing 
Lee (2005), and Soytas and Sari (2009).  gross fixed capital formation9 is considered a 
dependable proxy for investment since shifts of investment always approach shifts of capital 
stock with constant depreciation rate.  
All data are annual and their trends before taking natural logarithms are shown in Figure 1, 
in which 1960 is taken as the base year so as to deliver the data series in the same scale. Figure 1 
implies that C, F, Y, K and P generally stay together. It is also obvious that C and F move very 
closely suggesting a likely interaction between them for the following tests and discussion. G 
and P increase steadily over the period while K appears to grow faster from 1991. Hydrocarbon 
consumption (F) as well as CO2 emissions (C) both experienced a slight decrease in 1974 due to 
the energy crisis and a sharp decrease in 1978due to the Public Utilities Regulatory Policies Act 
which was approved by Congress in 1978 to encourage electricity generation from renewable 
sources. However, non hydrocarbon consumption seems to increase throughout the sample with 
                                                           
8 Renewable energy includes: hydro electric power, geothermal, solar/PV, wind, and biomass 
(EIA 2009) 
9?Gross fixed capital formation, a flow value, measures the value of net additions to fixed assets 
and excludes financial assets, stocks of inventories, other operating costs and land sales and 
purchases. It is called ?gross? because the measure does not make any adjustments to exclude the 
depreciation of fixed assets. ?(from UNSNA and IMF Balance of Payments system) 
44 
 
a sharp growth rate from 1970 to 1977. Figure 1 also shows an approximately linear relationship 
between C and Y, which suggests a linear model rather than a quadratic model. 
***Figure 1*** 
 5. Empirical Results 
5.1 Tests of unit root hypothesis  
All the variables are examined with ADF and PP unit root tests. The  ADF tests with 
intercept and trend give better results showing that all the variables appear to have a unit root in 
levels but are stationary in first differences, implying that they are all integrated at order one, that 
is I(1). The tests results are reported in Table 1. 
***Table 1*** 
5.2 Tests for multivariate cointegration  
Table 2 presents results of Johansen cointegration tests based on the trace statistic and 
maximum eigenvalue statistic. This paper focuses on the single cointegrating equation at 0.05 
indicated by the eigenvalue test rather than the three equations indicated by the trace test, for the 
reason that the optimal rank of one is constant in the eigenvalue test but inconstant in the trace 
test if different maximum lags are allowed to be included in the underlying VAR model. Results 
of Lagrange-multiplier tests (LM) are also reported in Table 2 indicating no evidence of serial 
correlation in the residual at lag one. The two dummy variables applied to explain 
macroeconomic shocks are found to be statistically insignificant and thus are not included in the 
following analyses.  
***Table 2*** 
5.3 Error-correction model and short-run causality 
The optimal lag is determined to be one by the SIC criteria in the ECM. The expected 
directions of the error correction coefficients are positive for dlnF and dlnP, and negative for 
45 
 
dlnC, dlnN, dlnY and dlnK. That is to say, when the carbon dioxide emission level exceeds the 
long-run equilibrium level, hydrocarbon energy consumption and population should rise, non-
hydrocarbons consumption, real GDP and capital stock should fall, and if permitting of CO2 
emissions or environment policy is stabilizing, carbon dioxide emissions should fall.  
The error-correction models and short-run causality are reported in Table 3, in which the 
expected signs are found, with two exceptions. The sign is as expected for the statistically 
significant coefficients (capital stock). 
The error correction term, estimating the speed of adjustment back to the long-run 
equilibrium, is statistically significant with expected sign, and large in magnitude for the capital 
stock equation, which suggests an error correction system. When the capital stock is above or 
below the equilibrium, it adjusts extremely quickly (by 109% in the first year), or it takes about 
11 months to converge to the long-run balance in the case of any shock to the capital equation. 
Table 3 also implies that only lnN is econometrically exogenous, which cannot be explained 
by other variables over the lagged changes. Furthermore, strong clues are provided that there 
exists a two-way short-run linkage between carbon dioxide emissions and hydrocarbon energy 
consumption, between real GDP and population, and between capital stock and population.  
Additionally, there also exists uni-directional causality from changes of hydrocarbon energy 
consumption to changes of capital stock. 
***Table 3*** 
Based on the proven existence of causality in the cointegrating relationships and some 
ambiguous insignificant coefficients, it is necessary to carry out the Granger causality tests to 
46 
 
specify the directions of causal links. Results presented in Table 4 show that more than one-third 
of parameters are significant.  
***Table 4*** 
Table 4 indicates that hydrocarbon consumption Granger-causes carbon dioxide emissions, 
which is expected because the leading source of carbon dioxide emissions is the combustion of 
hydrocarbons. Considering the contemporaneous effects caused by a lag, the causality is 
manifested one year later.  
CO2 emissions, hydrocarbons energy consumption and population uni-directionally Granger 
cause non-hydrocarbon energy consumption. That is, under the control of environmental or 
energy regulations, non-hydrocarbon consumption is probably stimulated by the high level of 
CO2 emission or by the substitution effect from decreased consumption of hydrocarbon energy. 
To mitigate the conflict between limited resources and unlimited demand as the population 
grows, the consumption of renewable energy and green energy are critical for sustainable 
economic growth.  
Hydrocarbon and non-hydrocarbon energy consumption uni-directionally Granger cause real 
GDP, which is consistent with the previous studies, but the reverse does not hold. Hydrocarbon 
energy consumption and real GDP uni-directionally Granger cause capital stock. 
Table 4 also reveals three bi-directional causal relationships between non-hydrocarbon 
energy consumption and capital stock, real GDP and population, and capital stock and 
population.   
47 
 
5.4 Generalized impulse response and variance decompositions 
The Granger causality tests show several causal relationships within the sample period other 
than the trend in the future. To supplement the causality tests beyond the sample periods and 
examine how variables in general respond to innovations in other variables, the generalized 
impulse response method is employed following Pesaran and Shinv (1998) and the forecast error 
variances of all variables are decomposed into their percentage attributed to shocks in all 
variables in the system. 
Figure 2 demonstrates the generalized impulse response results which give some support for 
Granger causality test results. CO2 emissions do not respond to Y, F, N, K and P initially, 
respond negatively to Y during the first eight periods, and respond positively to F, N, K and P 
thereafter. Shocks to C have positive and significantly larger initial impacts on itself, which lasts 
longer. Hydrocarbons energy consumption appears to have a positive initial response only to C 
and itself. Non-hydrocarbon energy consumption has a slight positive response to F but 
significant response to itself, verifying the exogeneity observed in the error correction model. 
Moreover, C, F and N have positive and significant initial impacts on real GDP. Initially, capital 
positively responds to all variables except P, while population only slightly responds to K and 
itself. 
***Figure 2*** 
The generalized variance decomposition reported in Table 5 is generally consistent with the 
error-correction process. The results indicate that the forecast error variance of hydrocarbon 
energy consumption explains around 11.8% of the error variance of carbon dioxide emissions 
while the latter explains more than 64% of the former. Likewise, the error variance of population 
accounts for more than 20% of the error variance of capital stock and the latter explains around 
48 
 
27% of the former, both of which imply bi-directional causality. Moreover, around 30% of the 
forecast error variance of real GDP is explained by the variance of carbon dioxide emissions and 
another 30% by hydrocarbon energy consumption, plus about 15% by population. Hydrocarbons 
consumption accounts for more than 30% of the variance in capital stock. 
***Table 5*** 
6. Conclusion and Policy Implications 
This paper explores the causal relationships between CO2 emission, hydrocarbon energy 
consumption, non-hydrocarbon energy consumption, and economic growth for the US in the 
period 1960-2009 by employing the cointegration procedure, generalized impulse response, and 
variance decomposition in a multivariate model including the capital stock and total population. 
Taking into account all the results above, the synthetic conclusion seems to be reasonable 
and as expected. Table 6 compares the causal relationship in the study with related previous 
studies in different contexts.  
***Table 6*** 
Most importantly, strong evidence shows that hydrocarbon consumption uni-directionally 
causes investment. In other words, an increase of hydrocarbons consumption results in an 
increase of CO2 emissions, which is followed by subsidies.   
Furthermore, according to the results hydrocarbon consumption also positively affects GDP 
growth, as the substitution effects between hydrocarbons and non-hydrocarbons are relatively 
lower in GDP growth than in CO2 emissions. That is to say, the benefit of lower CO2 emissions 
surpasses the sacrifices of a lower GDP. An appropriate and efficient way to balance the increase 
of GDP and the decrease of carbon emissions in the US is to substitute hydrocarbon with non-
49 
 
hydrocarbon energy consumption. This result is consistent with results showing that total energy 
consumption affects CO2 emissions from Soytas, et.al.(2007) for the US, and from Zhang and 
Cheng (2009) for China, given that hydrocarbon accounts for the overwhelming majority of 
energy consumption.  
As there is no causal effect on CO2 emissions detected from non-hydrocarbons energy 
consumption in the empirical results, the policy to reduce hydrocarbon energy consumption or 
switch to non-hydrocarbon energy is more appropriate than the one raised by previous studies 
which suggested reducing total energy consumption, and which would adversely affect economic 
growth.  
Weak evidence indicates a uni-directional causal relationship running from CO2 emissions, 
hydrocarbon consumption, and population to non-hydrocarbon consumption.  Fuel-switching 
from hydrocarbons to non-hydrocarbons could be expensive but effective for the co-ordination of 
emissions, hydrocarbons, and non hydrocarbon energy if induced by mandates and subsidies, 
since the cost differences are very high. 
Hydrocarbon and non-hydrocarbon energy consumption causes economic growth, but not 
vice versa, which is in line with results for Portugal in Pereira and Pereira (2010) but opposite to 
the results in Zhang and Cheng (2010) for China, and Ang (2008) for Malaysia. This result 
implies that inappropriate energy policies may impede economic growth and that authorities 
should be cautious to balance the energy regulations and economic development. 
In addition, the results imply a bi-directional causal link between non-hydrocarbon energy 
consumption and investment.  The gap between increasing energy demand and decreasing 
emission calls for a huge sum of investments to produce non-hydrocarbon energy.  For instance, 
50 
 
the investment to build a nuclear electricity generator or a high-power hydroelectric power 
facility is substantial but advisable. 
 
 
 
 
 
 
  
51 
 
 
Table 1 Unit root test results 
 ADF tests  PP tests 
 levels First 
differences 
 levels First 
differences 
Intercept 
C -3.27**(0) -4.05***(0)  -3.02** -3.99*** 
F -3.35**(1) -3.35**(0)  -3.49** -3.35** 
N -2.26(0) -3.78***(0)  -1.62 -3.66*** 
Y -2.19(0) -4.38***(0)  -2.44 -4.04*** 
K -1.35(2) -4.33***(2)  -1.45 -2.99*** 
P -0.69(2) -3.13**(2)  -1.67 -3.13** 
Intercept and Trend 
C -1.77(0) -4.69***(0)  -1.87 -4.74*** 
F -2.46(1) -4.14**(0)  -1.88 -4.14** 
N 0.16(0) -4.25***(0)  -0.50 -4.25*** 
Y -2.97(1) -4.77***(0)  -1.40 -4.36*** 
K -3.14(1) -4.40***(1)  -1.86 -3.14 
P -2.28(2) -3.14 (1)  -3.09 -2.95 
Notes: All variables are in natural logs. Max lag length is set to 10. Optimal lag lengths are 
determined by SIC and are in parentheses. The bandwidth is selected using the Newey-West 
method.  Barlett-Kernel is chosen as the spectral estimation method. H0=the series has a unit root. 
(*), (**) and (***) denote rejection of the null hypothesis at the 10%, 5% and 1% level. 
 
 
 
 
 
 
 
 
 
 
 
52 
 
 
 
Table 2 Johansen cointegration tests 
Hypothesized 
Cointegration 
Rank 
Trace statistic Maximum eigenvalue statistic LM test statistic
a 
G7e3Gbe7Gbe5Gbd4Gbd6Gbd8 0.05 critical value G7e3Gbe0Gbd4Gbeb 0.05 critical value  
r = 0 132.03*** 95.75 48.40*** 40.08 --- 
r ? 1 83.62*** 69.82 30.47 33.88 32.97 
r ? 2 53.15** 47.86 27.41* 27.584 --- 
r ? 3 25.74 29.80 13.36 21.13 37.75 
a H0: no autocorrelation at lag order. Johansen normalization restrictions are imposed. 
Optimal lag length=1 by SIC.  (*), (**) and (***) denote rejection of the null hypothesis at the 
10%, 5% and 1% level. 
 
 
 
 
 
 
 
 
 
 
 
 
 
  
53
 
 Ta
ble
 3 
Sh
or
t-r
un
 ca
us
ali
ty
 fr
om
 er
ro
r-c
or
re
cti
on
 m
od
els
 
 
Co
eff
ici
en
ts 
of 
Eq
ua
tio
ns 
EC
-1 
D C
 
D F
 
D N
 
D Y
 
    
  D
K 
D P
 
C 
D c
 
  D F
 
  D N
 
  D Y
 
  D K
 
  D P
 
0.0
9 
(0.
53
) 
 0.1
0 
(0.
58
) 
 0.1
6 
(0.
64
) 
 -0.
18
 
(-1
.39
) 
 -1.
09
**
* 
(-3
.50
) 
 0.0
1 
(1.
48
) 
-0.
85
**
 
(-2
.39
) 
 -0.
64
**
 
(-1
.82
) 
 -0.
21
 
(-0
.41
) 
 -0.
20
 
(-0
.75
) 
 -0.
52
 
(-0
.79
) 
 -0.
00
4 
(-0
.36
) 
1.4
3*
**
 
(3.
59
) 
 1.1
6*
**
 
(2.
94
) 
 0.3
5 
(0.
59
) 
 0.4
7 
(1.
57
) 
 1.4
7*
* 
(1.
98
) 
 0.0
1 
(0.
95
) 
0.0
5 
(0.
51
) 
 0.1
0 
(1.
11
) 
 0.4
9*
**
 
(3.
53
) 
 0.0
5 
(0.
68
) 
 0.0
7 
(0.
42
) 
 0.0
01
 
(0.
37
) 
-0.
64
 
(-0
.98
) 
 -0.
44
 
(-0
.68
) 
 -0.
33
 
(-0
.34
) 
 -0.
09
 
(-0
.19
) 
 0.2
9 
(0.
24
) 
 -0.
05
**
 
(-2
.43
) 
0.1
1 
(0.
56
) 
 0.0
4 
(0.
17
) 
 -0.
02
 
(-0
.06
) 
 0.0
6 
(0.
38
) 
 0.0
3 
(0.
07
) 
 0.0
1*
 
(1.
94
) 
2.5
5 
(0.
99
) 
 4.3
7*
 
(1.
72
) 
 -3.
80
 
(-1
.00
) 
 3.4
7*
* 
(1.
81
) 
 14
.25
**
* 
(2.
98
) 
 0.7
3*
**
 
(9.
51
) 
-0.
01
 
(-0
.24
) 
 -0.
03
 
(-0
.96
) 
 0.0
7 
(1.
37
) 
 -0.
01
 
(-0
.45
) 
 -0.
15
 
(-2
.23
) 
 0.0
03
**
* 
(3.
38
) 
 
Not
es:
 EC
-1 i
s e
rror
 cor
rec
tion t
erm
. D
 de
not
es t
he
 fir
st di
ffe
renc
e o
pe
rat
or.
 The
 chi
-squa
red s
tat
ist
ics
 ar
e i
n p
are
nthe
ses
. O
pti
ma
l 
lag
 le
ng
th=
1 b
y S
IC
.  (
*),
 (**)
 and (
***
) de
not
e r
eje
cti
on of
 the
 nul
l h
yp
oth
esi
s a
t the
 10%
, 5%
 and 
1%
 le
ve
l. 
54 
 
Table 4 Granger causality test results 
Dependent 
Variable 
C F N Y K P 
C --- 17.32*** 2.97 3.65 3.12 0.27 
F 3.85 --- 0.95 1.66 0.61 0.63 
N 6.35** 5.20* --- 0.65 5.12* 9.94*** 
Y 1.04 6.55** 5.49* --- 1.99 12.76*** 
K 3.93 13.18*** 5.09* 11.52*** --- 21.28*** 
P 0.44 1.83 0.25 19.67*** 10.04*** --- 
Notes: The statistics are chi-square statistics given by Granger causality Wald tests. 
(*), (**) and (***) denote significance at the 10%, 5% and 1% level indicating that the 
column variable Granger causes the row variable. The optimal lag length is 1 and is based 
on SIC. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
55 
 
Table 5 Generalized forecast error variance decomposition 
Dep
endent 
variable 
Hori
zon DC DF DN DY DK DP 
DC 1      100.00 0.00 0.00 0.00 0.00 0.00 
5 82.40 11.80 1.35 1.02 1.32 2.11 
10 78.72 11.87 2.01 0.35 2.91 4.16 
15 76.11 11.84 2.10 0.18 4.03 5.74 
        
DF 1 79.95 20.05 0.00 0.00 0.00 0.00 
5 64.56 28.16 2.67 0.67 1.19 2.76 
10 64.82 24.00 3.30 0.23 2.80 4.87 
15 64.11 22.03 3.25 0.17 3.95 6.49 
        
DN 1 0.01 1.05 98.94 0.00 0.00 0.00 
5 0.36 0.78 95.81 0.36 0.55 2.15 
10 2.08 1.25 89.18 1.68 1.21 4.59 
15 2.97 1.53 86.42 2.25 1.43 5.41 
        
DY 1 40.41 21.14 2.99 35.46 0.00 0.00 
5 34.19 40.09 7.01 9.20 2.16 7.35 
10 31.75 37.25 8.73 4.73 4.56 12.98 
15 31.97 34.91 8.62 3.29 5.84 15.38 
        
DK 1 32.26 25.60 3.45 25.63 13.05 0.00 
5 15.98 43.96 4.58 5.82 14.89 14.77 
10 9.29 36.53 5.47 5.61 19.59 23.51 
15 7.78 33.57 5.43 5.24 21.26 26.72 
        
DP 1 0.18 0.19 1.24 0.63 11.76 86.00 
5 0.29 0.09 1.05 4.32 24.39 69.86 
10 2.49 0.21 0.67 3.41 26.60 66.62 
15 4.96 0.53 0.44 2.61 27.17 64.28 
Notes: D denotes the first difference operator. 
 
 
Table 6 Causality test results comparisons with related studies 
Author Period country Method Variables Results 
Soytas, et.al.(2007) 1960-2004 US TY, VAR Y,K, E,C,P1 E?C 
Ang(2008) 1971-1999 Malaysia CI, ECM Y*,E*,C* G?E, 
C?G# 
56 
 
Zhang and 
Cheng(2009) 
1960-2007 China10 TY, VAR Y,K,E,C,P2 G?E 
E?C 
Soytas and Sari(2009) 1960-2000 Turkey TY. VAR Y,K,E,C,P1 C?E 
Halicioglu (2009) 1960-2005 Turkey CI,  ECM Y,E,C,T G?C 
Menyah and 
Rufael(2010) 
1960-2007 US TY, VAR Y,E(Nu,R) E(Nu) ?C 
Pereira, Pereira(2010) 1977-2003 Portugal CI, VAR Y,K4,E,C,P1         E?G 
Gao 1960-2009 US CI, ECM Y,K,E(F,N),C,P3 E(F) ?C 
C?E(N)# 
E(F,N) ?G 
#E(F) ?E(N)# 
Notes: Y, K, E (Nu, R, F and N), C, T and P denote real GDP, capital stock, total 
energy consumption (nuclear energy consumption, renewable energy consumption, 
hydrocarbons consumption and non-hydrocarbons energy consumption), CO2 emissions, 
foreign trade and population.1 total labor force, 2urban population, 3total population, 4 
private investment, *per capita. # denotes weak causality. ? denotes uni-directional causality 
running from the left variable to the right one. ? denotes bi-directional causality. 
 
 
 
 
 
 
 
 
                                                           
10 China (excluding Hong Kong, Macao, Taiwan) 
57 
 
 
Figure 1 Trends of the variables (before taking logarithms) 
 
 
 
 
 
 
 
 
 
 
 
0
50
100
150
200
250
19
61
19
63
19
65
19
67
19
69
19
71
19
73
19
75
19
77
19
79
19
81
19
83
19
85
19
87
19
89
19
91
19
93
19
95
19
97
19
99
20
01
20
03
20
05
20
07
C F N Y K P
58 
 
Figure 2 Generalized impulse responses 
-.02
.00
.02
.04
.06
.08
2 4 6 8 10 12 14
LNC LNF LNN
LNY LNK LNP
Response of LNC to Cholesky
One S.D. Innovations
-.02
.00
.02
.04
.06
.08
2 4 6 8 10 12 14
LNC LNF LNN
LNY LNK LNP
Response of LNF to Cholesky
One S.D. Innovations
-.04
-.02
.00
.02
.04
.06
.08
2 4 6 8 10 12 14
LNC LNF LNN
LNY LNK LNP
Response of LNN to Cholesky
One S.D. Innovations
.000
.004
.008
.012
.016
.020
2 4 6 8 10 12 14
LNC LNF LNN
LNY LNK LNP
Response of LNY to Cholesky
One S.D. Innovations
-.02
.00
.02
.04
.06
2 4 6 8 10 12 14
LNC LNF LNN
LNY LNK LNP
Response of LNK to Cholesky
One S.D. Innovations
-.001
.000
.001
.002
.003
.004
2 4 6 8 10 12 14
LNC LNF LNN
LNY LNK LNP
Response of LNP to Cholesky
One S.D. Innovations
59 
 
Chapter 3: Price Discovery in the Food-Ethanol-Fuel System in Ethanol 
Markets: An Exponential Smooth Transition VECM Perspective 
 
1. Introduction 
In the United States, the most important and widely used type of biofuel as fuel 
additives currently is ethanol, which is mainly produced from corn. As a renewable and 
domestically available resource, the use of ethanol helps to reduce harmful greenhouse 
gas and pollution. The production of ethanol in the United States was near 14 billion 
gallons in 2011 with a rapid increase compared to 10.75 billion gallons in 2009. Global 
Ethanol Production reached 88.7 billion litres in 2011.  
The rapidly expanding production and demand for ethanol bears directly and 
indirectly upon the related markets. The spreading use of ethanol decreases the world?s 
reliance on crude oil. There have been debates about the effectiveness of ethanol in 
replacing gasoline. Considering the large acres of land required for crops, the production 
and the use of ethanol tend to increase food prices. There is a dispute concerning whether 
corn based ethanol produces more greenhouse gases and less usable energy than soybean 
based biodiesel. There is an increasing acceptance of wheat ethanol in Europe but it is 
still a very small proportion in the U.S. 
The price of corn, the main input in ethanol production, as well as the prices of 
soybean and wheat, doubled during the last three decades and are closely associated with 
the price of ethanol in recent years. Based on the high production cost of US corn-ethanol, 
corn subsidies are always required to implement ethanol policies. Increased domestic 
production of corn is a likely consequence of policies. Using corn for ethanol decreases 
60 
 
the amounts of corn available for other uses such as food industry uses and animal feed. 
The corn used for ethanol purchased within a limited area and not sold for exports 
commands a higher price. The net effect of increased ethanol production increases the 
price of animal feed.G3
Ethanol and biofuel policies have had considerable effects on ethanol and corn 
production, as well as the price links among the related markets. The Energy Policy Act 
of 1992, one of the first Federal programs for the implementation of bioenergy was 
followed by another major legislative initiative, the Energy Policy Act of 2005, which 
assigned more power to Congress in regulating this industry. In 2006, the ban on the use 
of MTBE11, which was found to contaminate groundwater, promoted further expansion 
of the ethanol market. Nowadays, various new laws and regulations, including the 
Energy Independence and Security Act of 2007 (EISA), have created mandates for 
increased use of, and subsidies for, ethanol. The EISA mandates an increase in biofuels 
from the 2007 level of 4.7 billion gallons to a total of 36 billion gallons by 2022. The 
EISA also specifies that at least one billion gallons of the new fuels come from biodiesel, 
and 16 million from other non-cornstarch sources, such as sugar, cellulosic ethanol, or 
waste products.  In July of 2011, legislation to extend the tax credits and tariff was 
defeated in the United States Senate.   
The main purpose of this chapter is to identify the price relationships among fuel, 
ethanol and agricultural commodities and to test the nonlinearity characteristics of price 
adjustment and the instability of regimes in ethanol markets. The organization of the 
paper is as follows: Section 2 reviews recent studies and Section 3 illustrates the 
                                                           
11 MTBE: Methyl tert-butyl ether is a gasoline additive and can be used as an oxygenate.  
61 
 
theoretical models and methodologies applied. Section 4 describes data and data sources. 
Section 5 discusses the empirical results, and Section 6 concludes. 
 
2. Literature Review 
Considerable research has assessed the price nexus among fuel, ethanol and food 
by linear methodologies. The most popular methodologies have been structural vector 
autoregression (SVAR), vector error correction models (VECM), cointegration, and 
multivariate generalized autoregressive conditional heteroskedascity models (MGARCH), 
etc. Zhang et al. (2007) employed a SVAR model to test the hypothesis that limit pricing 
on MTBE refiners explained the lack of ethanol entry, and to estimate the price 
relationships in ethanol, corn and gasoline. Their research found that ethanol prices were 
subject to various shocks and have been driven by supply changes. Zhang et al. (2009) 
assessed the price nexus among ethanol, corn and soybean by using cointegration, vector 
error correction and MGARCH models. They found no long-run price links between 
agricultural commodities and fuel energy. 
Nonlinearities of price adjustments in the ethanol market have been explored only 
recently. The well accepted methodology is Threshold Vector Error Correction Model 
(TVECM), which can be accessed by Logistic Smooth Transition VECM or Exponential 
Smooth Transition VECM. Rapsomanikis (2006) employed a TVECM to test for the 
nonlinearity in the price adjustment of ethanol, sugar and oil in Brazil. The results 
suggested strong threshold nonlinearity in the ethanol price system but no  causal 
relationship between oil and ethanol. The results also indicated that sugar and ethanol can 
be linearly cointegrated. Balcombe (2008) estimated the price equilibrium relationships 
62 
 
among ethanol, oil and suger in Brazil by using several bivariate error correction models 
including Bayesian MCMC12 algorithms and model selection methods. The author found 
that there exists a long-run price relationship between sugar and oil in Brazil. The study 
also revealed nonlinearities in the price transition of sugar, ethanol and oil but linearity 
between ethanol and sugar. Serra et al. (2011) applied a smooth transition vector error 
correction model to examine price links among corn, oil, gasoline and ethanol prices. In 
contrast to Zhang et al. (2009), they found strong long-run price relationships between 
corn and fuel. In addition, their results revealed that an increase in corn price can 
generate an increase in the price of ethanol and therefore an increase in gasoline prices. 
This paper is the first to assess the price relationships among gasoline, oil, ethanol, 
corn, soybean and wheat in the United States and only the second to employ the 
Exponential Smooth Transition VECM method in the ethanol market.  
3.  Methodology 
3.1 Cointegration and Linear Vector Error Correction Model (VECM) 
Unit root hypothesis tests and integration analysis are necessary before 
proceeding to cointegration and error correction. Augmented Dickey-Fuller (ADF) t-tests 
(see Dickey and Fuller, 1979) are conducted to test the null hypothesis of a unit root in 
the different variables. The optimal lag form is selected using the AIC13 and SIC14.  
Cointegration refers to a linear combination of nonstationary variables. Two or 
more variables are cointegrated if they are integrated of the same order and their linear 
combination is stationary (Engle and Granger, 1987). Cointegrated variables show a long 
                                                           
12 MCMC: Monte Carlo Markov Chain 
13 AIC: Akaike information criterion 
14 SIC: Schwarz information criterion 
63 
 
term equilibrium relationship and share common stochastic trends, thus there must exist 
at least one unidirectional or bidirectional causality in the Granger sense.  
Cointegrated variables must have an error correction representation, according to 
Engle and Granger (1987). Short-run dynamics of cointegrated variables, influenced by 
the deviation from the long-run relationship, can be examined by the Vector Error 
Correction Model (VECM), which implies that changes in the endogenous variables are 
functions of changes in exogenous variables and the level of disequilibrium captured by 
error correction terms in the cointegrating relationship. This technique allows for a causal 
linkage between variables and reintroduces the information lost in the differencing 
process. Assuming one cointegrated relationship, the trivariate VECM can be specified as 
follows. 
dlnG13Gb49Gb72 = G23dGb35+ G3c3 G24cGb6aGb67Gb40Gb35 Gb35Gb67G8G6G17Gb72Gb3fGb35 + G3c3 G240Gb35Gb67G86G8eG90G13Gb49G123aGb72Gb3fGb67G123bGb6aGb67Gb40Gb35 + G3c3 G241Gb35Gb67Gb6aGb67Gb40Gb35 G86G8eG90G13Gb4bG123aGb72Gb3fGb67G123b + 
G3c3 G245Gb35Gb67Gb6aGb67Gb40Gb35 G86G8eG90G13Gb53G123aGb72Gb3fGb67G123b + G3c3 G250Gb35Gb67Gb6aGb67Gb40Gb35 G86G8eG90G13Gb47G123aGb72Gb3fGb67G123b Gd45G3c3 G252Gb35Gb67Gb6aGb67Gb40Gb35 G86G8eG90G13Gb57G123aGb72Gb3fGb67G123b+G3c3 G254Gb35Gb67Gb6aGb67Gb40Gb35 G86G8eG90G13Gb75G123aGb72Gb3fGb67G123b+G242Gb49Gb72, (1) 
where G8G6G17Gb72Gb3fGb35 denotes the error-correction term and is the residual in period t-1 obtained 
from the long-run cointegrating relationship; G24c denotes the speed of adjustment parameter; 
G242Gb72 denotes a serially uncorrelated error term with mean zero; d denotes the first-difference 
operator; l denotes the lag length (set at 3 based on AIC and SIC criteria, and the LM 
autocorrelation test). 
3.2  Exponential Smooth Transition Vector Error Correction Model (ESTVECM) 
Most of the previous studies used linear estimation methods to estimate the price 
relationships in ethanol markets. However, based on the fact that the ethanol market in 
the U.S is policy-oriented, many factors can drive the price system in ethanol market to 
64 
 
nonlinear adjustment, which is defined as threshold-type nonlinear price behavior 
following Serra (2011) and Rapsomanikis and Hallam (2006).  These factors include 
mandates of subsidies and tax credits, adjustment costs, transaction costs, and any 
potential risk arising from the related industries. 
The threshold vector error correction model (TVECM) has been employed to 
examine the nonlinear characteristics between prices of different commodities 
(Rapsomanikis and Hallam, 2006). Based on the fact that the price transitions and 
adjustments are always continuous, a smooth transition procedure is introduced in this 
study to replace the discrete regime changes by the exponential smooth transition vector 
error correction model (ESTVECM) following Rothman et al. (2001). 
A six-dimensional STVECM is specified to estimate the price linkages among 
ethanol, gasoline, oil, corn, soybean and wheat as  
G86G8eG90G13Gb72 Gd4cG1240G23eGb35 Gd45G3G249G3Gb35G9cGb72Gb3fGb35 Gd45G3c3 G245G3Gb35G1e1Gb68G86G8eG90G13Gb72Gb3fGb68Gb6eGb3fGb35Gb68Gb40Gb35 G1241Gd6bG373Gd46GaG123aG95Gb72Gb3fGb62G1e2G240G1e1G85G3G123bGd6f+G1240G23eGb36 Gd45G3G249G3Gb36G9cGb72Gb3fGb35 Gd45
G3c3 G245Gb36G1e1Gb68G86G13Gb72Gb3fGb68Gb6eGb3fGb35Gb68Gb40Gb35 Gd6fGd6bGaG123aG95Gb72Gb3fGb62G1e2G240G1e1G85G3G123bGd6f+?                                                                                    (2) 
where G13Gb72 =(PEt, PGt, POt, PCt, PSt, PWt) denotes a (6*1) vector of prices at time t; G23eGb67 is a 6*1 
vector and G245G3Gb67G1e1Gb68 is a 6*6 matrix, both of which denote the short run dynamics, i=1,2 and 
j=1,?p-1; G3G3G249G3Gb67G3is a 4*r matrix capturing the long-run adjustment speed to disequilibrium 
under different regimes, i=1,2;  G9cGb72Gb3fGb35 is a r*1 vector of the error correction term and r is 
the rank of error correction model. GaG123aG95Gb72Gb3fGb62G1e2G240G1e1G85G3G123b is the smooth transition function 
characterized as a smooth regime switching procedure that allows two regimes to be 
associated continuously with extreme values, GaG123aG95Gb72Gb3fGb62G1e2G240G1e1G85G3G123b=0 and GaG123aG95Gb72Gb3fGb62G1e2G240G1e1G85G3G123b=1;  G95Gb72Gb3fGb62 
65 
 
is the lagged residual from the error correction term and is assumed to be the transition 
variable, which indicates the disequilibrium magnitude; d denotes a delay period; and 
parameters G240 and c are combined parameters that reveal the transition speed between two 
regimes and the threshold between regimes. G240 is set to be 0.2 as a starting value following 
Serra et al. (2011). 
The transition between regimes depends on G95Gb72Gb3fGb62 and the corresponding value of 
GaG123aG95Gb72Gb3fGb62G1e2G240G1e1G85G3G123bG1e4G3 To build the exponential smooth transition vector error correction model 
(ESTVECM), the exponential smooth transition function nested in the TVECM model is 
as follows. 
GaG123aG95Gb72Gb3fGb62G1e2G240G1e1G85G3G123bGd4cG373Gd46G741G754G74cG1244Gd46Gb93G123aGb71Gc6aGc37Gc5aGb3fGb61G123bGc19Gc2eG123aGb71
Gc6aGc37Gc5aG123b
G1245,   G240>0,                                                                (3) 
where G7eaGb36G123aG95Gb72Gb3fGb62G123b is the variance of the transition variable. 
The estimation procedure can be summarized in the following steps. After the 
stationary tests and multivariate cointegration tests, a linear VECM model is firstly 
estimated. With the optimal lags and ranks from linear VECM suggested by LM tests of 
residual autocorrelation and AIC and SIC , the ESTVECM model is estimated by using 
nonlinear least squares regression. 
4. Data 
This paper uses monthly national level prices on ethanol, gasoline, oil, corn, 
soybean and wheat from January 1982 to April 2012 in the U.S.  Nominal average prices 
on gasoline (in dollars per gallon) and oil (in dollars per gallon) were collected from the 
Bureau of Labor Statistics.  Ethanol average rack prices (in dollars per gallon) were 
collected from the government of Nebraska website.  
66 
 
Much research conducted to examine the role of futures markets in agricultural 
commodities has found that futures prices respond quickly to new information and 
provide unbiased forecasts of the subsequent cash price in well-designed contracts. 
Following Garcia and Leuthold (2004) and Carter (1999), in this paper the price proxy 
for corn, soybean, and wheat (all in dollars per bushel) are average monthly settlement 
prices for the nearby agricultural commodity futures contract and were obtained from the 
database of the USDA Economic Research Service.  
The trends of these price series (before taking natural logarithms) are shown in 
Figure 1 and Figure 2. The trends in fuel prices including ethanol, gasoline and oil are 
relatively flat compared to the trends in agricultural commodities prices. Figure 1 
indicates that the prices of ethanol, gasoline and oil generally move together. The trends 
were relatively flat before the 2001 recession but moved sharply upward after 2001 
probably due to the economic expansion. Ethanol experienced its peak price in May 2006 
while the peak prices for oil and gasoline were both in May 2008. From Figure 2 we can 
see that there were sizable price increases from July 2006 to June 2008 in all three 
agricultural commodities right after a sharp price increase in ethanol from November 
2004 to May 2006. 
5. Empirical Results 
5.1 Unit root and cointegration 
All the variables were subjected to ADF unit root tests. The results with intercept 
are similar to results with intercept and trend. The tests reveal that all the variables appear 
to have unit roots in levels but be stationary in the first differences, implying that they are 
all integrated at order one. Test results are reported in Table 1. 
67 
 
                                            ***Table 1*** 
Table 2 presents consistent results of Johansen cointegration tests based on trace 
statistics and maximum eigenvalue statistics. Results of Lagrange-multiplier tests (LM) 
are reported in the same table, suggesting that there is no residual autocorrelation at lag 
three. The results indicate one cointegrating equation illustrated in Table 4 at the 0.05 
significance level, which is in line with Serra (2011) in that there exist long-run relations 
between fuel and agricultural commodities.  
 
***Table 2*** 
5.2  VECM estimation 
The expected directions of error correction coefficients are negative for all the 
price variables. That is to say, when the price of ethanol exceeds the long-run equilibrium 
level, the price of ethanol itself, as well as the prices of fuel energies including oil and 
gasoline, and the prices of agricultural commodities should move downward. The error-
correction models and short-run causality are reported in Table 3, in which the expected 
signs are found with two exceptions. The optimal lag is determined to be three by AIC 
and SIC criteria and LM tests of residual autocorrelation in the ECM. 
The error correction term, estimating the speed of adjustment back to the long-run 
equilibrium, is statistically significant with expected sign, and large in magnitude for 
prices of ethanol, gasoline, corn and soybean. When the ethanol price is above or below 
the equilibrium, it adjusts 3.7% in the first year, while for the prices of gasoline, corn and 
soybean, these speeds of adjustment are 4%, 2.1% and 2.7% respectively. Table 3 also 
shows that all the variables are econometrically endogenous and can be explained by at 
68 
 
least one of the other variables over the lagged changes. Most of the signs for significant 
non-error-correction parameters are positive as expected, with only one exception. 
Furthermore, there is strong evidence that a two-way short-run linkage exists 
between gasoline price and wheat price. In addition, there also exists uni-directional 
causality running from gasoline price to ethanol price, gasoline price to corn price, oil 
price to corn price and corn price to soybean price. 
***Table 3*** 
Based on the proven existence of causality in cointegrating relationships and 
some ambiguous insignificant coefficients, it is necessary to carry out the Granger 
causality tests to specify the directions of causal links. Results presented in Table 4 show 
that more than two-thirds of parameters are statistically significant.  
***Table 4*** 
Table 4 indicates that there are bi-directional Granger price causalities between 
ethanol and wheat, gas and oil, gas and corn, gas and soybean, gas and wheat, and oil and 
wheat. Oil price uni-directionally Granger causes corn and soybean prices. The fuel 
energies appear to have causal relationships with agricultural commodities, which is 
consistent with previous studies. Fuel prices can inflate prices of agricultural 
commodities worldwide, including those crops that have no relation to biofuels, such as 
rice and fish (Quaiattini, 2008). Besides, there are also uni-directional Granger causalities 
running from corn price to soybean price, and from wheat price to corn price and soybean 
price, which can be explained as substitution effects between those agricultural 
commodities. 
69 
 
5.3 STVECM estimation 
In the estimation of STVECM, the optimal lags and ranks are selected based on 
the results from VECM estimation. The optimal lag is three according to AIC and SIC, 
and the results of the LM test of residual autocorrelation in VECM estimation. 
Table 5 shows the estimated parameters in ESTVECM, among which the most 
interesting parameters in the estimation areG3G249G3Gb67, G240 and c, which represent the adjustment 
speed to equilibrium, the transition speed to another regime and the threshold 
respectively. The statistically significant threshold parameter is -0.064 and it suggests 
that the system is within or around the first regime (G=0) in the neighborhood of -0.064. 
According to Serra (2011), the threshold variable can measure the disequilibrium 
magnitude if there is only one cointegration relation and error correction term. The 
estimation results for  G3G249G3Gb67 suggest that only ethanol price in both regimes is statistically 
significant. The speeds of ethanol price adjustment to the long-run equilibrium are 0.947 
in regime 1 and 0.908 in regime 2. Different from the findings in Serra (2011), the oil and 
gasoline markets, as well as the agricultural market, do not respond to the price 
disequilibrium in the ethanol market. The parameter of G240 is statistically significant and 
equal to 0.59, indicating a medium speed of transition between the two regimes. 
***Table 5*** 
There is strong evidence for short run adjustments in all the prices for the two 
regimes, and all of the short-run dynamics parameters (G23eGb67G123b are statistically significant in 
the two regimes. The parameters of short-run dynamics (G245G3Gb67G1e1Gb68) are statistically significant 
at lag three for the price of gasoline, oil, corn, soybean and wheat. The results of 
70 
 
autocorrelation tests shown in Table 5 indicate that none of the six equations have 
residual autocorrelation. 
Figure 3 shows the time trends for the threshold variableG123aG9cGb72Gb3fGb35), which varied 
from-0.37 to 0.56 and represented the degree of disequilibrium in the ethanol market 
from January 1982 to April 2012.  Figure 4 shows the time series of G values (between 0 
and 1) calculated from transition functions with estimated parameters. It is apparent that 
lower G values tend to be associated with lower deviations from the equilibrium. In that 
way, from both Fig.3 and Fig.4, we can find the instability of the regime caused by such 
factors as policy switching and growth in the economy in 1986 and in the period from 
Dec.2001 to Dec. 2007. In 1986, the Federal government reduced 2% of the discount rate. 
The US  also experienced declining interest rates and a sharp drop in oil prices. (Cacy, 
1987) From 2001 to 2007, the U.S economy experienced an expansion after the recession. 
Moreover, the Clean Air Act, the 2005 Energy Policy Act, and the 2006 ban on MTBE 
led to a massive expansion of the ethanol market and a large induced demand for corn. 
6. Conclusion  
This paper studies the price system in food-ethanol-energy links by using 
Exponential Smooth Transition VECM to examine the price relationships between 
ethanol, corn, soybean, wheat, oil and gasoline for the latest 364 months in the U.S. 
ethanol markets.  
The empirical results indicate one cointegration relationship among all the prices, 
which are all endogenous for long-run cointegration. The results also indicate strong 
short-run and long-run relationships between the prices of fuels and agricultural 
commodities. Specifically, there exist strong two-way causalities between the prices of 
71 
 
gasoline and wheat, ethanol and wheat, gasoline and corn, gasoline and soybean, and oil 
and wheat, as well as one-way causalities running from gasoline to ethanol, gasoline to 
soybeanG19e8oil to corn, oil to soybean, corn to soybean, wheat to corn, and wheat to 
soybean. Among the previous studies on the price relationships between food and fuel, 
few took into account the price of wheat. However, since 2008, the U.S started producing 
to considerable wheat based ethanol and therefore wheat price should be included. An 
increase in the price of fuel or agricultural commodities will probably cause an increase 
in another fuel or agricultural commodities. That is to say, the use of food crops for 
ethanol causes food prices to rise. In addition, an increase in gasoline price will also raise 
the price of corn and ethanol. Rising corn price was a leading factor causing the boom in 
ethanol prices in the last two decades, since corn-based ethanol dominated the biofuel 
supply.  
The results of the estimation from the smooth transition VECM model with a 
nested exponential function suggest that only in the long-run does ethanol price make 
significant adjustments towards equilibrium, while in the short-run dynamic analysis the 
other prices of gasoline, oil, corn, soybean and wheat make significant adjustments. The 
estimated threshold value shows a fairly low disequilibrium magnitude in ethanol market. 
The fuel market and the agricultural commodity market insignificantly respond to price 
disequilibrium in the ethanol market. The speed of transition between the two regimes is 
at a medium level. 
Future prospects for corn ethanol mainly depend on the fuel price, corn price and 
Federal ethanol and biofuels policies. The government should balance food price and fuel 
72 
 
price by fixing a market-policy-oriented ethanol price. One way to do this is to promote 
second generation biofuels which are made mostly from biomass, woody crops, 
agricultural residues or waste. Future research should also consider the cost of livestock 
feed and the environmental externalities, as well as changes in land use over time to get a 
comprehensive picture of the entire ethanol price system. 
 
 
 
 
 
 
 
 
 
 
 
 
 
73 
 
 
 
Table 1 Unit root test results 
 Intercept  Intercept and Trend  
ADF tests levels First 
differences 
 levels First differences 
          PEthanol -2.479(2) -14.303***(1)  -3.230*(2) -14.305***(1) 
PGas -0.559(2) -10.447***(4)  -2.853(2) -10.565***(4) 
POil -0.453(1) -13.440***(0)  -2.421(1) -13.520***(0) 
PCorn -1.998(1) -14.146***(0)  -2.664(1) -14.163***(0) 
PSoybean -1.885(1) -14.474***(0)  -2.595(1) -14.493***(0) 
PWheat -2.120(1) -14.535***(0)  -3.016(1) -14.534***(0) 
 
Notes: All variables are in natural logs. Maximum lag length is set to ten. Optimal 
lag lengths are determined by SIC and are in parentheses. The bandwidth is selected 
using the Newey-West method.  Barlett-Kernel is the spectral estimation method. H0=the 
series has a unit root. (*), (**) and (***) denote rejection of the null hypothesis at the 
10%, 5% and 1% level respectively. 
 
 
 
 
 
 
 
 
 
 
 
 
 
74 
 
 
 
Table 2 Johansen cointegration tests 
Hypothesized 
Cointegration 
Rank 
Trace statistic Maximum eigenvalue statistic Lagrange-multiplier  testa 
G7e3Gbe7Gbe5Gbd4Gbd6Gbd8 0.05 critical 
value 
G7e3Gbe0Gbd4Gbeb 0.05 critical 
value 
lag chi2 
r = 0 130.744*** 95.754 65.434*** 0.078 1 82.036*** 
r ? 1 65.310 69.819 23.283 33.877 2 74.966*** 
r ? 2 42.027 47.856 17.797 27.584 3 44.382 
r ? 3 
 
24.230 29.797 15.146 21.132 4 56.9491** 
Cointegration relationship (standard error in parentheses) 
PE  +2.905PG  -2.839PO -0.676PC  +0.869PS  -0.231PW -1.434 =0 
         (0.348)       (0.295)     (0.257)     (0.258)        (0.250) 
  
a H0: no autocorrelation at lag order. Johansen normalization restrictions are imposed. 
Optimal lag length=1 by SIC.  (*), (**) and (***) denote rejection of the null hypothesis 
at the 10%, 5% and 1% level respectively. 
 
 
 
 
 
 
 
 
 
 
 
75 
 
 
 
Table 3 Error-correction models 
Equations EC-1  PEthanol PGas POil PCorn PSoybean PWheat C 
PEthanol -0.037*** 0.248*** 0.203** -0.087 0.032 0.085 0.105 0.001 
  (-0.014) (0.057) (0.094) (0.093) (0.085) (0.085) (0.076) (0.004) 
PGas -0.04*** 0.046 0.432*** 0.055 0.041 0.025 0.075* 0.001 
  (0.008) (0.034) (0.057) (0.056) (0.051) (0.051) (0.046) (0.002) 
POil 0.026*** -0.016 -0.001 0.321*** 0.022 0.042 0.047 0.002 
  (0.008) (0.036) (0.059) (0.058) (0.053) (0.053) (0.048) (0.002) 
PCorn -0.021* 0.002 -0.216*** 0.178** 0.201*** 0.051 0.087 0.001 
  (0.012) (0.049) (0.081) (0.08) (0.073) (0.073) (0.066) (0.003) 
PSoybean -0.027** -0.063 0.064 0.017 0.12*** 0.161** -0.001 0.001 
  (0.011) (0.045) (0.074) (0.073) (0.066) (0.066) (0.06) (0.003) 
PWheat 0.011 0.033 -0.13* 0.077 -0.038 0.048 0.259*** 0.001 
  (0.011) (0.045) (0.075) (0.074) (0.067) (0.067) (0.061) (0.003) 
 
Notes: EC-1 is error correction term. D denotes the first difference operator. The chi-
squared statistics are in parentheses. Optimal lag length=1 by SIC.  (*), (**) and (***) 
denote rejection of the null hypothesis at the 10%, 5% and 1% level respectively. 
Standard errors are in parentheses. 
       
 
 
 
 
 
 
 
 
 
 
76 
 
 
 
Table 4 Granger causality test results 
Dependent 
Variable PEthanol PGas POil PCorn PSoybean PWheat 
PEthanol ---  10.89***  13.03*** 7.64*** 7.40*** 10.60*** 
PGas  1.314 ----  10.60*** 8.21*** 5.310*** 5.57*** 
POil  0.17  6.20*** ---- 0.69 1.35 3.03* 
PCorn  1.84  5.92***  4.83*** ---- 1.40 12.7*** 
PSoybean  1.66  2.39*  3.86*** 4.08** ---- 8.19*** 
PWheat  6.20***  3.9**  2.95* 0.64 0.19 ---- 
Notes: The statistics are chi-square statistics given by Granger causality Wald tests, (*), 
(**) and (***) denote significance at the 10%, 5% and 1% level respectively indicating 
that the column variable Granger causes the row variable. The optimal lag length is 1 and 
is based on SIC. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
77
 
 Ta
ble
 5 
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G23eGb67 
G=
1 (
i=2
) 
0.3
83
**
* 
0.0
14
 
0.4
10
**
* 
0.0
21
 
0.3
06
**
* 
0.0
28
 
1.0
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**
* 
0.0
16
 
1.8
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**
* 
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15
 
1.3
67
**
* 
0.0
16
 
G=
0 (
i=1
) 
0.3
65
**
* 
0.0
14
 
0.3
77
**
* 
0.0
22
 
0.2
53
**
* 
0.0
26
 
1.0
28
**
* 
0.0
19
 
1.9
08
**
* 
0.0
17
 
1.3
70
**
* 
0.0
18
 
G3G249G3
Gb67 
G=
1 (
i=2
) 
0.9
47
**
* 
0.0
99
 
-0.
07
0 
0.1
39
 
0.0
88
 
0.1
74
 
0.0
14
 
0.1
10
 
0.0
31
 
0.0
98
 
0.0
03
 
0.1
08
 
G=
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i=1
) 
0.9
08
**
* 
0.0
96
 
-0.
03
2 
0.1
21
 
0.0
17
 
0.1
40
 
0.0
10
 
0.1
12
 
0.0
25
 
0.0
99
 
-0.
00
2 
0.1
09
 
G245G3Gb67
G1e1Gb72Gb3f
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G=
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i=2
) 
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01
0 
0.3
09
 
0.0
26
 
0.8
78
 
0.0
90
 
1.0
18
 
-0.
18
9 
0.4
25
 
-0.
12
0 
0.4
13
 
-0.
18
7 
0.4
59
 
G=
0 (
i=1
) 
0.0
67
 
0.3
03
 
0.0
52
 
0.7
54
 
-0.
03
6 
0.8
30
 
-0.
15
0 
0.4
32
 
-0.
03
2 
0.4
15
 
-0.
11
8 
0.4
62
 
G245G3Gb67
G1e1Gb72Gb3f
Gb36 
G=
1 (
i=2
) 
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03
4 
0.3
08
 
-0.
42
8 
0.8
78
 
-1.
15
8 
1.2
49
 
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24
9 
0.4
25
 
-0.
13
1 
0.4
12
 
-0.
10
1 
0.4
60
 
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i=1
) 
-0.
13
5 
0.2
95
 
-0.
52
5 
0.7
75
 
-0.
47
8 
0.8
20
 
-0.
19
4 
0.4
34
 
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19
8 
0.4
14
 
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17
7 
0.4
60
 
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G=
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i=2
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0.1
73
 
0.1
92
 
1.0
91
**
 
0.4
77
 
1.7
47
**
 
0.7
30
 
0.8
99
**
* 
0.2
61
 
0.7
61
**
* 
0.2
56
 
0.7
07
**
 
0.2
85
 
G=
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i=1
) 
0.1
81
 
0.1
82
 
1.0
49
**
 
0.4
23
 
1.1
35
**
 
0.5
01
 
0.8
60
**
* 
0.2
66
 
0.7
99
**
* 
0.2
57
 
0.7
54
**
* 
0.2
85
 
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0.0
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2 
0.0
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4 
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0.7
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0.9
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Figure 1. Price series on ethanol and fuels 
 
 
Figure 2. Price series on ethanol and agricultural commodities 
 
 
 
0
2
4
6
8
10
12
14
16
Mo
nth
19
83
04
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0
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8
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16
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 US
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Soybean
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79 
  
 
Figure 3 Threshold variable series (ECT) 
 
 
 
Figure 4 Transition function (G) series 
 
 
 
-0.6
-0.4
-0.2
0
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0.6
0.8
Mo
nth
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82
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0
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1
Mo
nth
19
82
10
19
83
10
19
84
10
19
85
10
19
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10
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10
80 
  
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