- Email: [email protected]
Spatial interaction models for biomass consumption in the United States
Energy 36 (2011) 6555e6558
Contents lists available at SciVerse ScienceDirect
Energy journal homepage: www.elsevier.com/locate/energy
Spatial interaction models for biomass consumption in the United States Sicong Wanga, Shifeng Wangb, * a b
Department of Economics, Swansea University, Swansea SA2 8PP, UK Institute of Biological and Environmental Sciences, School of Biological Sciences, University of Aberdeen, Aberdeen AB24 3UU, Scotland, UK
a r t i c l e i n f o
a b s t r a c t
Article history: Received 24 February 2011 Received in revised form 13 July 2011 Accepted 6 September 2011 Available online 29 September 2011
Five alternative spatial interaction patterns of biomass consumption in the United States in 2005 are compared using the spatial autoregressive model. The influences of geographical locations, biomass price and income on biomass consumption are translated into the spatial weight matrices of spatial autoregressive model. The results indicate that not only the geographical locations but also both the biomass price and the income significantly affect spatial interaction among biomass consumption in the United States. The results also show that spatial interaction among biomass consumption in the United States becomes weaker with the farther neighbor states. Spatial interaction among biomass consumption incurred by the income becomes stronger than that incurred by the biomass price. When the influences of both the biomass price and the income are combined together into the hybrid spatial autoregressive model, spatial interaction among biomass consumption is the strongest. Ó 2011 Elsevier Ltd. All rights reserved.
Keywords: Renewable energy Biomass consumption Spatial interaction Geographical influence
1. Introduction Renewable energy, in recent years, has been advocated by many researches [1e9], and is expected to an effective way of eliminating environmental pollution resulted from energy consumption [10]. Biomass is one kind of renewable energy, and has been identified as the single largest source of renewable energy in the United States, accounting for half of all renewable energy consumption by 2009, and contributes about 4.1% of the total U.S. energy consumption of about 95 quadrillion Btu [11]. Many studies involving biomass consumption have been recently carried out (e.g. [12e16]). Some of them revealed that biomass consumption can be impacted by economic factors (e.g. [12,13,16]). For example, Naki cenovi c et al. [12] and D’Apote [13], using the time series data, explored the variation of biomass consumption against GDP through distinguishing the developing countries and the developed countries. However, few studies can be found about how the economic factors influence biomass consumption across locations. Since the proximity of geographical locations will form the clustering of the interesting attribute, ignoring this will make results invalid [17]. Therefore, it is of interest to examine the geographical influences of economic factors on biomass consumption. In other words, we should investigate spatial interaction among biomass consumption
* Corresponding author. Tel.: þ44 1224 273810. E-mail address: [email protected] (S. Wang). 0360-5442/$ e see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.energy.2011.09.009
incurred by the economic factors. The paper explored the geographical influences of both the biomass price and the income level on biomass consumption in the United States, because both factors are two of the most crucial factors influencing the acceptance of biomass. Spatial autoregressive models are one of the most widely referenced spatial econometric models for spatial interaction (spatial autocorrelation) which is often found among observations across regions, and is similar to time series dependence but has multi-directions in geographical space. The model was first suggested by Cliff and Ord [18,19], and was a variant of the model considered by Whittle [20]. In this model, the spatial interaction is captured by a spatial weight matrix which reflects the neighbors’ influences on each location. Therefore, the spatial autoregressive model can capture the hidden influence reflected by the sample data, and draw some useful inference such that the model can provide some useful implications for the issue questioned. The spatial autoregressive model is widely applied particularly in the study of house price, county policy expenditures, local wages, per capita state and local government expenditures, employment growth, agricultural and environmental economics, and ecology etc. [21e26]. In this paper, it was used to investigate the geographical influences of both the biomass price and the income level on biomass consumption in the United States. The rest of the paper is structured as follows. The data sources and the methods are set forth in section 2. Section 3 mainly reports and discusses results. Finally, the conclusions will be formulated.
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S. Wang, S. Wang / Energy 36 (2011) 6555e6558
2. Materials and methods 2.1. Data sources The study is confined to the United States. The spatial resolution is the state level, and the total number of states under consideration is 49.1 The data sets acquired include biomass consumption, biomass price and the total disposable personal income, pertained to 2005. Among these data sets, both the biomass consumption data and the biomass price data are acquired from U.S. Energy Information Administration [27]. In here, biomass refers to wood and waste, and consumption refers to the total consumption by the residential, commercial, industrial, and transportation sectors of the economy of the considered states. The biomass price refers to the price of biomass itself not the biomass productions’ price. In economics, there are many indexes to measure the income level, such as minimum wage, average wage and disposable personal income etc. We take the total disposable personal income to be the measure of the income level, which is the sum of the disposable personal income of all the residents of state, in order to better reflect the purchasing power of the consumers of state. We do this, because the disposable personal income considers the personal current taxes paid to federal, state, and local governments, and represents the income that is available to persons for spending or saving [28]. This data are acquired from Regional Economic Information System, Bureau of Economic Analysis, U.S. Department of Commerce [29]. Biomass consumption is in trillion Btu, the biomass price is in nominal dollars per million Btu, and the total disposable personal income is in billions of dollars. We do not uniformly standardize the units for these data because we only take into account the order of magnitudes of these three variables, which will be discussed below.
2.2. Spatial autoregressive model The geographical influence is generally described in spatial econometrics terms to spatial interaction process which is often modeled with spatial autoregressive model. Formally, the simplest spatial autoregressive (SAR) model can be expressed as
Y ¼ rWY þ m
(1)
where Y is the N 1 vector of dependent variables. r is the spatial autoregressive coefficient, and the N N matrix W is the spatial weight matrix. m is the error term, assumed as the normal distribution with zero mean and variances of s2IN. On the basis of equation (1), we can choose different spatial weight matrix W to reflect different potential interactions, such that we have a variety of alternative model specifications. The SAR model can be typically estimated by the maximum likelihood (ML) method because the ordinary least square method will give rise to biasness [30]. The logarithm likelihood function of SAR model is
ðN=2Þ:lnð2pÞ ðN=2Þlns2 þ jIN rWj 1 Y 0 ðIN rWÞ0 ðIN rWÞY 2s2
(2)
In order to obtain the ML estimators of SAR model, the following typical assumption is needed: ASSUMPTION: all leading diagonal elements of W are zero and jrj < 1 so that the matrix IrW is non singular.
1 The data from Alaska and Hawaii are excluded, and the federal district is referred here as state for better description.
Under this assumption, Anselin [30] proved that the ML estimator was consistency, efficiency and asymptotic normality. Kelejian and Prucha [31] found using Monte Carlo that the ML estimator of SAR model was effective for the finite sample, including the small sample. The goodness of fit for the SAR model is unmeasured by the normal R2 because of the inconsideration of the intercept term in the SAR model [32]. Therefore, the modified measure, called uncentered R2, is adopted (see [32] for more technical details). 2.3. Alternative models As discussed above, the spatial autoregressive models will rely mainly upon the spatial weight matrices which reflect some types of hypothetical interaction among the underlying attribute. Therefore it is of interest to construct the spatial weight matrices. Five alternative spatial weight matrices are used in this study. Model 1 and Model 2 are based on the geographical proximity of states in the United States. Models 3 and model 4 are closely related with the biomass price and the total disposable personal income, respectively. Model 5 is the hybrid of Model 3 and Model 4. The reason why these three models are considered is that the biomass price and the total disposable personal income are the crucial components of influencing biomass consumption. More specially, Model 1 assumes that biomass consumption will be only influenced by the directly connected neighborhood states. Thereby if the state i directly connects with the state j with the common geographic boundaries, then the (i,j)th element of spatial weight matrix W is 1, otherwise zero. Hence the resulting spatial weight matrix is symmetry. Model 2 assumes that the biomass consumption will be influenced by the second order neighbors’ states. So if the shortest path from state i to state j on the graph connecting adjacent sites have two edges, then the (i,j)th element of spatial weight matrix W is 1, otherwise zero. Model 3 assumes that the biomass consumption will be influenced by the biomass price, and the influence path is down from the lowest price to the highest price. Hence the spatial weight is defined by the hierarchy of the biomass price. So if the state i directly connects the state j in the biomass price chain, then the (i,j)th element of spatial weight matrix W is 1, otherwise zero. Model 4 is rather similar with Model 3 except that the biomass price chain is replaced by the total disposable personal income chain, and the hierarchy is reversed. Model 5 is a little complication. If the state i directly connects the state j with respect to either the biomass price chain or the disposable personal income chain or both, then the (i,j)th element of spatial weight matrix W is 1, otherwise zero. Finally, all spatial weight matrices are row-standardized. 3. Results and discussion The overall results are reported in Table 1, which include the parameter values, the t-statistic values in the parenthesis for the parameter as well as the uncentered R2 values for Models. The estimation method for all models is the maximum likelihood estimation method. Table 1 shows that the spatial autoregressive coefficient r for all the models are significant, indicating that the spatial interaction among biomass consumption in the United States relates closely with the geographical locations, the biomass price and the total disposable personal income. That is, the biomass consumption in one state will be influenced not only by biomass price and the total disposable personal income of the same state, which is consistent with [12,13,16], but also by biomass price and the total disposable personal income of its neighbor states. With respect to Table 1, the value of uncentered R2 of Model 5 is evidently the biggest, whereas
S. Wang, S. Wang / Energy 36 (2011) 6555e6558
6557
Table 1 Comparison of five models.
r
R2
a
Model 1
Model 2
Model 3
Model 4
Model 5
0.742996a (5.490004) 0.6107
0.762998a (4.349242) 0.4694
0.594996a (4.048456) 0.5256
0.596989a (4.072945) 0.5297
0.819968a (5.818518) 0.6491
Any significance levels.
Model 2 has the smallest uncentered R2. The uncentered R2 are decaying gradually with the sequence of Models 5, 1, 4, 3 and 2, reflecting that spatial interaction among biomass consumptions in the United States become weaker with the farther neighbors, and become stronger with the two additional economical factors (i.e. the biomass price and the total disposable personal income). Model 1 and Model 2 are based on the proximity of geographical location. Results show that the proximity of geographical location shapes spatial interaction among biomass consumption in the United States. Wang [33], mapping the biomass consumption for U.S. states, found that the biomass consumption in the U.S. was clustered. Most of large biomass consumption was around the border states of the U.S., especially around the south-west border states of the U.S. This, to some extent, supports our results. The values of uncentered R2, however, indicate that biomass consumption is rather more influenced by the direct neighbors than by the farther neighbors. The t-statistics for spatial autoregressive coefficients r of Models 3 and 4 evidently show that the biomass price and the total disposable personal income are the key factors incurring spatial interaction among biomass consumption. When the biomass price (income) decreases (increases), the biomass consumption will increase, and vice versa. This is in accordance with our experience. Moreover, it can be seen from Table 1 that Models 3 and 4 have the similar pattern, indicating that the biomass price and the total disposal personal income have the almost equivalent spatial influences on biomass consumption in the United States. However, the higher R2 of Model 4 than Model 3 indicates that spatial interaction among biomass consumption is influenced more strongly by the total disposable personal income than by the price of biomass itself. This suggests that biomass consumption in the United States is more sensitive to income than to the price of biomass itself, partly because when income increases, people have more flexible financial budget which will incentive them to consider the environmental benefit of biomass relative to conventional energy. Model 5 assumes that spatial interaction among biomass consumption is bridged by both the biomass price and the total disposable personal income. Results of Model 5 evidently show that the combination of both the biomass price and the total disposable personal income will greatly significantly improve the uncentered R2 relative to Models 3 and 4. It suggests that spatial interaction among biomass consumption in the United States spread not only through the biomass price but also through the income, providing a potential policy that in order to increase more biomass consumption, increasing income and decreasing biomass price simultaneously are more reasonable.2 4. Conclusions As an effective way of eliminating environmental pollution, biomass should receive more attention. This paper presents five spatial autoregressive models to testing spatial interaction among biomass consumption in the United States. The results indicate that
2 For biomass products, the transportation cost should be also considered in the potential policy.
spatial interaction among biomass consumption in the United States does have something to do with the biomass price and the income level. Spatial interaction among biomass consumption in the United States spread not only through the biomass price but also through the income level. In addition, the proximity of geographical locations also has a great effect on spatial interaction among biomass consumption in the United States. The results also show that spatial interaction among biomass consumptions in the United States becomes weaker with the farther neighbors. Spatial interaction among biomass consumption incurred by the income becomes stronger than that incurred by the biomass price. When both the biomass price and the income are combined into the hybrid spatial autoregressive model, spatial interaction among biomass consumption is the strongest, and the goodness of fit has greatly significant improvement. Therefore when making reasonable spending policy for biomass, we should take into account these two factors. Acknowledgments We gratefully acknowledge the helpful comments from the anonymous referees. References [1] Shen YC, Chou CJ, Lin GTR. The portfolio of renewable energy sources for achieving the three E policy Goals. Energy 2011;36:2589e98. [2] Sheinbaum C, Ruiz BJ, Ozawa L. Energy consumption and related CO2 Emissions in five Latin American countries: changes from 1990 to 2006 and Perspectives. Energy 2011;36:3629e38. [3] Renó MLG, Lora EES, Palacio JCE, Venturini OJ, Buchgeister J, Almazan O. A LCA (Life Cycle Assessment) of the methanol production from sugarcane Bagasse. Energy 2011;36:3716e26. [4] Wang SF, Koch B. Determining profits for solar energy with remote sensing data. Energy 2010;35:2934e8. [5] Seiler JM, Hohwiller C, Imbach J, Luciani JF. Technical and economical evaluation Of enhanced biomass to liquid fuel processes. Energy 2010;35:3587e92. [6] Torchio MF, Santarelli MG. Energy, environmental and economic comparison of different powertrain/fuel options using well-to-wheels assessment, energy and external costs e European market analysis. Energy 2010;35:4156e71. [7] Wang SF, Leduc S, Wang SC, Obersteiner M, Schill C, Koch B. A new thinking for renewable energy model: remote sensing-based renewable energy model. International Journal of Energy Research 2009;33:778e86. [8] Andersen RS, Towers W, Smith P. Assessing the potential for biomass energy to contribute to Scotland’s renewable energy needs. Biomass and Bioenergy 2005;29:73e82. [9] Tuck G, Glendining MJ, Smith P, House JI, Wattenbach M. The potential distribution of Bioenergy Crop in Europe under present and Future Climate. Biomass and Bioenergy 2006;30:183e97. [10] Cascade Mints. http://www.e3mlab.ntua.gr/cascade.html, (accessed on Feb. 2008). [11] Energy Information Administration. Monthly Energy Review, http://www.eia. doe.gov/emeu/mer/contents.html; September 2010 (accessed on 28.06.11.). [12] Naki cenovi c N, Grübler A, Mcdonald A. Global energy perspectives. Cambridge: Cambridge University Press; 1998. Laxenburg, Austria: IIASA (International Institute for Applied Systems Analysis). [13] D’Apote SL. IEA biomass energy analysis and Projection. In: IEA, editor. Biomass energy: data, Analysis and Trends, http://www.iea.org/pubs/proc/ files/bioend/; 1998 (accessed on Sep. 2008). [14] IEA. World energy outlook 2002: energy and poverty. http://www. worldenergyoutlook.org/weo/pubs/weo2002/energypoverty.pdf. (accessed at Sep. 2008). [15] World Bank. World development indicators; 2002. CD-ROM. [16] Victor NM, Victor DG. Macro patterns in the use of traditional biomass fuels. Working paper of the program on energy and sustainable development. Stanford University; 2002.
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[17] Anselin L, Griffth D. Do spatial effects really matter in regression analysis? Papers of the Regional Science Association 1988;65:11e34. [18] Cliff AD, Ord JK. Spatial processes: models and applications. London: Pion; 1983. [19] Cliff AD, Ord JK. Spatial autocorrelation. London: Pion; 1973. [20] Whittle P. On Stationary Processes in the Plane. Biometrica 1954;41:434e49. [21] Can A. The Measurement of neighborhood dynamics in urban house prices. Economic Geography 1990;66:254e72. [22] Can A. Specification and estimation of Hedonic housing price models. Regional Science and Urban Economics 1992;22:453e74. [23] Case A, Hines Jr J, Rosen H. Budget spillovers and fiscal policy independence: evidence from the states. Journal of Public Economics 1993;52:285e307. [24] Buettner T. The effect of unemployment, aggregate wage, and spatial contiguity on local wages: an investigation with German district level data. Paper in Regional Science 1999;78:47e67. [25] Nelson GC, Hellerstein D. Do roads cause deforestation? Using satellite images in econometric analysis of land use. American Journal of Agricultural Economics 1997;79:80e8.
[26] Kissling WD, Carl G. Spatial autocorrelation and the selection of simultaneous autoregressive models. Global Ecology and Biogeography 2008;17:59e71. [27] U.S. Energy Information Administration. Annual Energy Review, http://www. eia.doe.gov/totalenergy/data/annual/index.cfm; 2005 (accessed at May 2008). [28] Regional Economic Information System, Bureau of economic analysis, U.S. Department of Commerce. State personal income and employment methodology. http://www.bea.gov/regional/docs/spi2009/. (accessed on 30.06.11.). [29] Regional Economic Information System, Bureau of economic analysis, U.S. Department of Commerce. http://www.bea.gov/national/index.htm, (accessed at May 2008). [30] Anselin L. Spatial econometrics: methods and models. Dordrecht: Kluwer; 1998. [31] Kelejian HH, Prucha IR. A Generalized Moments estimator for the autoregressive parameter in a spatial model. International Economic Review 1999; 40:509e33. [32] Greene WH. Econometric analysis. 5th ed. Pearson Education, Inc; 2003. [33] Wang S.F. Spatial Modelling of renewable energy Integrating Remote sensing data. PhD thesis. University of Freiburg, Germany; 2010.
Contents lists available at SciVerse ScienceDirect
Energy journal homepage: www.elsevier.com/locate/energy
Spatial interaction models for biomass consumption in the United States Sicong Wanga, Shifeng Wangb, * a b
Department of Economics, Swansea University, Swansea SA2 8PP, UK Institute of Biological and Environmental Sciences, School of Biological Sciences, University of Aberdeen, Aberdeen AB24 3UU, Scotland, UK
a r t i c l e i n f o
a b s t r a c t
Article history: Received 24 February 2011 Received in revised form 13 July 2011 Accepted 6 September 2011 Available online 29 September 2011
Five alternative spatial interaction patterns of biomass consumption in the United States in 2005 are compared using the spatial autoregressive model. The influences of geographical locations, biomass price and income on biomass consumption are translated into the spatial weight matrices of spatial autoregressive model. The results indicate that not only the geographical locations but also both the biomass price and the income significantly affect spatial interaction among biomass consumption in the United States. The results also show that spatial interaction among biomass consumption in the United States becomes weaker with the farther neighbor states. Spatial interaction among biomass consumption incurred by the income becomes stronger than that incurred by the biomass price. When the influences of both the biomass price and the income are combined together into the hybrid spatial autoregressive model, spatial interaction among biomass consumption is the strongest. Ó 2011 Elsevier Ltd. All rights reserved.
Keywords: Renewable energy Biomass consumption Spatial interaction Geographical influence
1. Introduction Renewable energy, in recent years, has been advocated by many researches [1e9], and is expected to an effective way of eliminating environmental pollution resulted from energy consumption [10]. Biomass is one kind of renewable energy, and has been identified as the single largest source of renewable energy in the United States, accounting for half of all renewable energy consumption by 2009, and contributes about 4.1% of the total U.S. energy consumption of about 95 quadrillion Btu [11]. Many studies involving biomass consumption have been recently carried out (e.g. [12e16]). Some of them revealed that biomass consumption can be impacted by economic factors (e.g. [12,13,16]). For example, Naki cenovi c et al. [12] and D’Apote [13], using the time series data, explored the variation of biomass consumption against GDP through distinguishing the developing countries and the developed countries. However, few studies can be found about how the economic factors influence biomass consumption across locations. Since the proximity of geographical locations will form the clustering of the interesting attribute, ignoring this will make results invalid [17]. Therefore, it is of interest to examine the geographical influences of economic factors on biomass consumption. In other words, we should investigate spatial interaction among biomass consumption
* Corresponding author. Tel.: þ44 1224 273810. E-mail address: [email protected] (S. Wang). 0360-5442/$ e see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.energy.2011.09.009
incurred by the economic factors. The paper explored the geographical influences of both the biomass price and the income level on biomass consumption in the United States, because both factors are two of the most crucial factors influencing the acceptance of biomass. Spatial autoregressive models are one of the most widely referenced spatial econometric models for spatial interaction (spatial autocorrelation) which is often found among observations across regions, and is similar to time series dependence but has multi-directions in geographical space. The model was first suggested by Cliff and Ord [18,19], and was a variant of the model considered by Whittle [20]. In this model, the spatial interaction is captured by a spatial weight matrix which reflects the neighbors’ influences on each location. Therefore, the spatial autoregressive model can capture the hidden influence reflected by the sample data, and draw some useful inference such that the model can provide some useful implications for the issue questioned. The spatial autoregressive model is widely applied particularly in the study of house price, county policy expenditures, local wages, per capita state and local government expenditures, employment growth, agricultural and environmental economics, and ecology etc. [21e26]. In this paper, it was used to investigate the geographical influences of both the biomass price and the income level on biomass consumption in the United States. The rest of the paper is structured as follows. The data sources and the methods are set forth in section 2. Section 3 mainly reports and discusses results. Finally, the conclusions will be formulated.
6556
S. Wang, S. Wang / Energy 36 (2011) 6555e6558
2. Materials and methods 2.1. Data sources The study is confined to the United States. The spatial resolution is the state level, and the total number of states under consideration is 49.1 The data sets acquired include biomass consumption, biomass price and the total disposable personal income, pertained to 2005. Among these data sets, both the biomass consumption data and the biomass price data are acquired from U.S. Energy Information Administration [27]. In here, biomass refers to wood and waste, and consumption refers to the total consumption by the residential, commercial, industrial, and transportation sectors of the economy of the considered states. The biomass price refers to the price of biomass itself not the biomass productions’ price. In economics, there are many indexes to measure the income level, such as minimum wage, average wage and disposable personal income etc. We take the total disposable personal income to be the measure of the income level, which is the sum of the disposable personal income of all the residents of state, in order to better reflect the purchasing power of the consumers of state. We do this, because the disposable personal income considers the personal current taxes paid to federal, state, and local governments, and represents the income that is available to persons for spending or saving [28]. This data are acquired from Regional Economic Information System, Bureau of Economic Analysis, U.S. Department of Commerce [29]. Biomass consumption is in trillion Btu, the biomass price is in nominal dollars per million Btu, and the total disposable personal income is in billions of dollars. We do not uniformly standardize the units for these data because we only take into account the order of magnitudes of these three variables, which will be discussed below.
2.2. Spatial autoregressive model The geographical influence is generally described in spatial econometrics terms to spatial interaction process which is often modeled with spatial autoregressive model. Formally, the simplest spatial autoregressive (SAR) model can be expressed as
Y ¼ rWY þ m
(1)
where Y is the N 1 vector of dependent variables. r is the spatial autoregressive coefficient, and the N N matrix W is the spatial weight matrix. m is the error term, assumed as the normal distribution with zero mean and variances of s2IN. On the basis of equation (1), we can choose different spatial weight matrix W to reflect different potential interactions, such that we have a variety of alternative model specifications. The SAR model can be typically estimated by the maximum likelihood (ML) method because the ordinary least square method will give rise to biasness [30]. The logarithm likelihood function of SAR model is
ðN=2Þ:lnð2pÞ ðN=2Þlns2 þ jIN rWj 1 Y 0 ðIN rWÞ0 ðIN rWÞY 2s2
(2)
In order to obtain the ML estimators of SAR model, the following typical assumption is needed: ASSUMPTION: all leading diagonal elements of W are zero and jrj < 1 so that the matrix IrW is non singular.
1 The data from Alaska and Hawaii are excluded, and the federal district is referred here as state for better description.
Under this assumption, Anselin [30] proved that the ML estimator was consistency, efficiency and asymptotic normality. Kelejian and Prucha [31] found using Monte Carlo that the ML estimator of SAR model was effective for the finite sample, including the small sample. The goodness of fit for the SAR model is unmeasured by the normal R2 because of the inconsideration of the intercept term in the SAR model [32]. Therefore, the modified measure, called uncentered R2, is adopted (see [32] for more technical details). 2.3. Alternative models As discussed above, the spatial autoregressive models will rely mainly upon the spatial weight matrices which reflect some types of hypothetical interaction among the underlying attribute. Therefore it is of interest to construct the spatial weight matrices. Five alternative spatial weight matrices are used in this study. Model 1 and Model 2 are based on the geographical proximity of states in the United States. Models 3 and model 4 are closely related with the biomass price and the total disposable personal income, respectively. Model 5 is the hybrid of Model 3 and Model 4. The reason why these three models are considered is that the biomass price and the total disposable personal income are the crucial components of influencing biomass consumption. More specially, Model 1 assumes that biomass consumption will be only influenced by the directly connected neighborhood states. Thereby if the state i directly connects with the state j with the common geographic boundaries, then the (i,j)th element of spatial weight matrix W is 1, otherwise zero. Hence the resulting spatial weight matrix is symmetry. Model 2 assumes that the biomass consumption will be influenced by the second order neighbors’ states. So if the shortest path from state i to state j on the graph connecting adjacent sites have two edges, then the (i,j)th element of spatial weight matrix W is 1, otherwise zero. Model 3 assumes that the biomass consumption will be influenced by the biomass price, and the influence path is down from the lowest price to the highest price. Hence the spatial weight is defined by the hierarchy of the biomass price. So if the state i directly connects the state j in the biomass price chain, then the (i,j)th element of spatial weight matrix W is 1, otherwise zero. Model 4 is rather similar with Model 3 except that the biomass price chain is replaced by the total disposable personal income chain, and the hierarchy is reversed. Model 5 is a little complication. If the state i directly connects the state j with respect to either the biomass price chain or the disposable personal income chain or both, then the (i,j)th element of spatial weight matrix W is 1, otherwise zero. Finally, all spatial weight matrices are row-standardized. 3. Results and discussion The overall results are reported in Table 1, which include the parameter values, the t-statistic values in the parenthesis for the parameter as well as the uncentered R2 values for Models. The estimation method for all models is the maximum likelihood estimation method. Table 1 shows that the spatial autoregressive coefficient r for all the models are significant, indicating that the spatial interaction among biomass consumption in the United States relates closely with the geographical locations, the biomass price and the total disposable personal income. That is, the biomass consumption in one state will be influenced not only by biomass price and the total disposable personal income of the same state, which is consistent with [12,13,16], but also by biomass price and the total disposable personal income of its neighbor states. With respect to Table 1, the value of uncentered R2 of Model 5 is evidently the biggest, whereas
S. Wang, S. Wang / Energy 36 (2011) 6555e6558
6557
Table 1 Comparison of five models.
r
R2
a
Model 1
Model 2
Model 3
Model 4
Model 5
0.742996a (5.490004) 0.6107
0.762998a (4.349242) 0.4694
0.594996a (4.048456) 0.5256
0.596989a (4.072945) 0.5297
0.819968a (5.818518) 0.6491
Any significance levels.
Model 2 has the smallest uncentered R2. The uncentered R2 are decaying gradually with the sequence of Models 5, 1, 4, 3 and 2, reflecting that spatial interaction among biomass consumptions in the United States become weaker with the farther neighbors, and become stronger with the two additional economical factors (i.e. the biomass price and the total disposable personal income). Model 1 and Model 2 are based on the proximity of geographical location. Results show that the proximity of geographical location shapes spatial interaction among biomass consumption in the United States. Wang [33], mapping the biomass consumption for U.S. states, found that the biomass consumption in the U.S. was clustered. Most of large biomass consumption was around the border states of the U.S., especially around the south-west border states of the U.S. This, to some extent, supports our results. The values of uncentered R2, however, indicate that biomass consumption is rather more influenced by the direct neighbors than by the farther neighbors. The t-statistics for spatial autoregressive coefficients r of Models 3 and 4 evidently show that the biomass price and the total disposable personal income are the key factors incurring spatial interaction among biomass consumption. When the biomass price (income) decreases (increases), the biomass consumption will increase, and vice versa. This is in accordance with our experience. Moreover, it can be seen from Table 1 that Models 3 and 4 have the similar pattern, indicating that the biomass price and the total disposal personal income have the almost equivalent spatial influences on biomass consumption in the United States. However, the higher R2 of Model 4 than Model 3 indicates that spatial interaction among biomass consumption is influenced more strongly by the total disposable personal income than by the price of biomass itself. This suggests that biomass consumption in the United States is more sensitive to income than to the price of biomass itself, partly because when income increases, people have more flexible financial budget which will incentive them to consider the environmental benefit of biomass relative to conventional energy. Model 5 assumes that spatial interaction among biomass consumption is bridged by both the biomass price and the total disposable personal income. Results of Model 5 evidently show that the combination of both the biomass price and the total disposable personal income will greatly significantly improve the uncentered R2 relative to Models 3 and 4. It suggests that spatial interaction among biomass consumption in the United States spread not only through the biomass price but also through the income, providing a potential policy that in order to increase more biomass consumption, increasing income and decreasing biomass price simultaneously are more reasonable.2 4. Conclusions As an effective way of eliminating environmental pollution, biomass should receive more attention. This paper presents five spatial autoregressive models to testing spatial interaction among biomass consumption in the United States. The results indicate that
2 For biomass products, the transportation cost should be also considered in the potential policy.
spatial interaction among biomass consumption in the United States does have something to do with the biomass price and the income level. Spatial interaction among biomass consumption in the United States spread not only through the biomass price but also through the income level. In addition, the proximity of geographical locations also has a great effect on spatial interaction among biomass consumption in the United States. The results also show that spatial interaction among biomass consumptions in the United States becomes weaker with the farther neighbors. Spatial interaction among biomass consumption incurred by the income becomes stronger than that incurred by the biomass price. When both the biomass price and the income are combined into the hybrid spatial autoregressive model, spatial interaction among biomass consumption is the strongest, and the goodness of fit has greatly significant improvement. Therefore when making reasonable spending policy for biomass, we should take into account these two factors. Acknowledgments We gratefully acknowledge the helpful comments from the anonymous referees. References [1] Shen YC, Chou CJ, Lin GTR. The portfolio of renewable energy sources for achieving the three E policy Goals. Energy 2011;36:2589e98. [2] Sheinbaum C, Ruiz BJ, Ozawa L. Energy consumption and related CO2 Emissions in five Latin American countries: changes from 1990 to 2006 and Perspectives. Energy 2011;36:3629e38. [3] Renó MLG, Lora EES, Palacio JCE, Venturini OJ, Buchgeister J, Almazan O. A LCA (Life Cycle Assessment) of the methanol production from sugarcane Bagasse. Energy 2011;36:3716e26. [4] Wang SF, Koch B. Determining profits for solar energy with remote sensing data. Energy 2010;35:2934e8. [5] Seiler JM, Hohwiller C, Imbach J, Luciani JF. Technical and economical evaluation Of enhanced biomass to liquid fuel processes. Energy 2010;35:3587e92. [6] Torchio MF, Santarelli MG. Energy, environmental and economic comparison of different powertrain/fuel options using well-to-wheels assessment, energy and external costs e European market analysis. Energy 2010;35:4156e71. [7] Wang SF, Leduc S, Wang SC, Obersteiner M, Schill C, Koch B. A new thinking for renewable energy model: remote sensing-based renewable energy model. International Journal of Energy Research 2009;33:778e86. [8] Andersen RS, Towers W, Smith P. Assessing the potential for biomass energy to contribute to Scotland’s renewable energy needs. Biomass and Bioenergy 2005;29:73e82. [9] Tuck G, Glendining MJ, Smith P, House JI, Wattenbach M. The potential distribution of Bioenergy Crop in Europe under present and Future Climate. Biomass and Bioenergy 2006;30:183e97. [10] Cascade Mints. http://www.e3mlab.ntua.gr/cascade.html, (accessed on Feb. 2008). [11] Energy Information Administration. Monthly Energy Review, http://www.eia. doe.gov/emeu/mer/contents.html; September 2010 (accessed on 28.06.11.). [12] Naki cenovi c N, Grübler A, Mcdonald A. Global energy perspectives. Cambridge: Cambridge University Press; 1998. Laxenburg, Austria: IIASA (International Institute for Applied Systems Analysis). [13] D’Apote SL. IEA biomass energy analysis and Projection. In: IEA, editor. Biomass energy: data, Analysis and Trends, http://www.iea.org/pubs/proc/ files/bioend/; 1998 (accessed on Sep. 2008). [14] IEA. World energy outlook 2002: energy and poverty. http://www. worldenergyoutlook.org/weo/pubs/weo2002/energypoverty.pdf. (accessed at Sep. 2008). [15] World Bank. World development indicators; 2002. CD-ROM. [16] Victor NM, Victor DG. Macro patterns in the use of traditional biomass fuels. Working paper of the program on energy and sustainable development. Stanford University; 2002.
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