Forecasting province-level CO2 emissions in China

Transcription

1 College of Charleston From the SelectedWorks of Wesley Burnett 2013 Forecasting province-level CO2 emissions in China Xueting Zhao, West Virginia University J. Wesley Burnett, West Virginia University Available at:

2 Lett Spat Resour Sci DOI /s ORIGINAL PAPER Forecasting province-level CO 2 emissions in China Xueting Zhao J. Wesley Burnett Received: 15 March 2013 / Accepted: 18 October 2013 Springer-Verlag Berlin Heidelberg 2013 Abstract Due to criticisms of potential identification issues within spatial panel data models, this study contributes to the literature by comparing forecasts of provincelevel carbon dioxide emissions against empirical reality using dynamic, spatial panel data models with and without fixed effects. From a policy standpoint, understanding how to predict emissions is important for designing climate change mitigation policies. From a statistical standpoint, it is important to test spatial econometrics models to see if they are a valid strategy to describe the underlying data. We find that the best model is the spatio-temporal panel data model which controls for fixed effects. Our findings demonstrate the importance of considering not only spatial and temporal dependence but also the individual or heterogeneous characteristics within each province. Keywords Spatial dynamic panel data Forecasting Carbon dioxide emissions China JEL Classification C33 C53 Q50 1 Introduction Understanding the spatial and temporal distribution of carbon dioxide (CO 2 ) emissions can aid policy by helping to develop proper regulatory frameworks to mitigate harmful X. Zhao Division of Resource Management, West Virginia University, 2051B Agricultural Sciences Building, PO Box 6108, Morgantown, WV , USA xueting.zhao@mail.wvu.edu J. W. Burnett (B) Division of Resource Management, West Virginia University, 2044 Agricultural Sciences Building, PO Box 6108, Morgantown, WV , USA wesley.burnett@mail.wvu.edu

3 X. Zhao, J.W. Burnett anthropogenic greenhouse gas (GHG) emissions, which are the cause of global climate change. While the geographic distribution of CO 2 emissions does not affect the global climatic impact, the distribution of the sources of the emissions will be important for policy formulation at the international, national, and ultimately at the local level. Assuming that China, adopts an international multi-lateral agreement to mitigate emissions, such as the Kyoto Protocol, then it must begin to look inward to determine the major sources of emissions and how to reduce these emissions. As no viable technologies yet exist to mitigate CO 2 (i.e., in significant quantities at economical costs), the alternative is increase the price (through taxation or some market-oriented policy) of such sources to account for the externalities or social costs associated with climate change. Most sources of CO 2 come from energy-related activities, principally through coal-fired electricity generation and transportation (U.S. Energy Information Administration 2012). In developing countries, such as China, energy consumption is an important component of economic growth, so increasing the cost of energy arguably comes at the expense of future potential economic growth. Such measures may be politically unpalatable, as they are in the United States. Therefore, understanding the subnational-level sources of emissions and spatial interactions of these sources across regions will be important for formulating national-level policies to mitigate GHG emissions. Spatial panel data models are a promising means to examine the spatial and temporal distribution of CO 2 emissions. There has been tremendous growth in the spatial econometric literature over the past two to three decades. Spatial econometrics is an applied field of econometrics that deals with sample data that is collected with reference to location measured as points in space. What distinguishes spatial econometrics from traditional econometrics is that the locational data may be characterized by spatial dependence or spatial heterogeneity (LeSage and Pace 2009). The idea of spatial dependence, or technically spatial autocorrelation, is similar to the concept of temporal autocorrelation found within the times series literature. As in time series, if this autocorrelation is present and unaccounted for then it could lead to biased or worse inconsistent regression estimates. Traditional econometrics had largely ignored spatial autocorrelation until the development of spatial econometrics. Recent advances in spatial econometrics have led to the development of longitudinal or panel data models that control for spatial autocorrelation. Longitudinal data are simply cross-section observations collected over time. These models offer the dual benefit of potentially controlling for province-level unobserved or heterogeneous fixed effects and spatial dependence. Despite the advances in this literature, spatial econometric models have come under criticism recently for problems associated with identification and for a lack of appeal to theoretical foundations (Partridge et al. 2012). The problem of identification is similar to Manski (1993) reflection problem, where group average characteristics (neighboring province carbon dioxide emissions and structural characteristics) affect individual outcomes (local carbon dioxide emissions) but the parameters in the model are not identifiable. We concede these criticisms carry weight, and rather than appealing to causality based upon correct model specification and/or the correct interpretation of parameter estimates, we instead appeal to an alternative validation strategy that is less dependent on prior theory. That is, we take these models as a black box and test

4 Forecasting province-level CO 2 emissions in China them against empirical reality (Freedman 1991). Against this background, we compare forecasts of province-level carbon dioxide emissions against empirical reality using dynamic panel data models with and without spatial effects. This study contributes to the literature by offering an assessment of how the spatial panel data models perform in forecasting against non-spatial panel data models in a root mean square error context. We compare the performance of several predictors for province-level CO 2 emissions for one through five-year-ahead forecasts. Based on forecast performance, we find, a spatio-temporal panel data model (that controls for fixed effects) outperforms the other models analyzed. This finding suggests the importance of considering not only spatial and temporal dependence but also the individual or heterogeneous characteristics within each province. 2 Background In general terms, there are two kinds of spatial panel data models. One is a nondynamic, spatial panel data model, which has received considerable attention, in the context of forecasting, over the past decade (Baltagi and Li 2006; Baltagi et al. 2012; Elhorst 2010; Kelejian and Prucha 2007; Kelejian and Robinson 2000). Unlike Baltagi and Li (2006) and Baltagi et al. (2012), which focus primarily on spatial error component models, this study examines a variety of spatial panel data models including spatial autoregressive, spatial error, and dynamic, spatial panel data models. The nondynamic, spatial panel data model controls for both the unobservable province-level fixed effects and potential spatial dependence (autocorrelation) inherent in the underlying data, but these models do not necessarily control for temporal autocorrelation. Given the recent interests in using spatial panel data models for forecasting purposes, dynamic, spatial panel models make for a nice alternative to the non-dynamic counterparts as the former controls for both spatial and temporal autocorrelation hence, these types of models are often called spatio-temporal panel data models. Giacomini and Granger (2004) arguably offered the seminal paper in this literature. In recent years, more and more papers have moved toward forecasting with dynamic, spatial econometric models (Kholodilin et al. 2008; Angulo and Trívez 2010; Schanne et al. 2010; Kholodilin and Mense 2012; Ohtsuka and Kakamu Similar to our study, a few papers have used this methodology to examine the sub-national forecasts of carbon dioxide emissions (Auffhammer and Carson 2008; Auffhammer and Steinhauser 2007, 2012). Unlike the studies mentioned above, Angulo and Trívez (2010) analyzed the forecasting ability of a dynamic, spatial panel data model without including explanatory variables so that the authors could predict employment in fifty Spanish provinces. Fingleton (2009) evaluated the difference between ex ante predictions (in which case the independent variables are forecasted) and ex post predictions (in which case the independent variables are known). He concluded that ex ante prediction is more problematic and should be analyzed with some caution. To avoid any potential problems with ex ante predictions, we follow a similar method as Angulo and Trívez (2010), which does not include any explanatory variables other than the temporal and spatial

5 X. Zhao, J.W. Burnett lag of the dependent variable. Therefore, we abstract away from using any explanatory variables in our analysis and instead focus on pure dynamic panel data models, both with and without heterogeneous fixed effects. 1 3 Data and methodology 3.1 Data Our data consists of a panel of China s thirty provinces and municipalities from the China Statistical Yearbooks and the provincial Statistical Yearbooks for the period (CSY 2012). Hong Kong, Macao, Taiwan and Tibet are excluded due to a lack of data. Our dependent variable, CO 2 emissions, were calculated following the IPCC Guidelines (Intergovernmental Panel on Climate Change 2006). Carbon dioxide emissions are based on estimates of province-level energy consumption. Therefore, these estimates represent energy-related emissions. The calculation of CO 2 emissions is based on final energy consumption, which is consistent with estimates used by the World Bank s Development Indicators and the Carbon Dioxide Information Analysis Center within the U.S. Department of Energy. Specifically, CO 2 emissions are measured as a linear function of different fossil fuel types, which includes three types of energy sources: coal, petroleum and natural gas (CESY 2012). For further information about how the energy-related emissions are estimated we refer the reader to Burnett et al.(2013). Energy-related emissions are often used because it is too costly to monitor such a large variety of mobile and stationary sources of carbon dioxide emissions (Auffhammer and Steinhauser 2007). The distinction between actual versus estimated emissions is important however, because we do are not making any claims that there are spillovers in CO 2 emissions themselves, but rather there are province-level spillovers in energy consumption which in turn create CO 2 emissions. That is, we argue that there is spatial dependence among the drivers of energy-related emissions and other economic forces which cross province lines. The latter is consistent with the concept of economic distance, which suggests that the closer two regions are to one another in geographic distance, the more likely their economy s will have an effect on one another (Conley and Ligon 2002). 3.2 Regression model In this particular study, we apply three different spatial econometric models with individual intercept for each province (fixed effects models) and common intercept for all of them (pooled models). In brief, we analyzed the following models: spatial autoregressive (SAR), spatial error model (SEM), spatio-temporal panel data models (STPD), and non-spatial, ordinary least squares (OLS). 1 The fixed effects are sometimes referred to as spatial fixed effects, so we use the terms interchangeably throughout the rest of this manuscript.

6 Forecasting province-level CO 2 emissions in China Dynamic, pooled panel data models The dynamic, pooled panel data model imposes the homogeneity restriction on both the intercept and slope coefficients across all provinces. It assumes equal average growth rates in all provinces and allows us to take advantage of the panel dimension. The dynamic, pooled panel data model is given as follows N N y it = α + ρ W ij y jt + βy i,t 1 + λ W ij y j,t 1 + φ it j=1 j=1 N φ it = δ W ij φ jt + ε it, j=1 (1) where y it denotes CO 2 emissions for the cross-sectional unit i at time t. The parameter α is the common intercept for all the provinces; β is a scalar parameter on the temporally lagged dependent variable; ρ denotes the scalar spatial autoregressive parameter on the dependent variable; λ is the spatial autocorrelation coefficient on the temporally lagged dependent variable; and δ is the spatial autocorrelation coefficient on the error term. 2 It should be noted that this model follows closely to that of Angulo and Trívez (2010), who explicitly identify that the estimators are biased but consistent with T, the total number of observations. The bias stems from including the temporally lagged dependent variables (or dynamic terms) on the right hand side of the equation. Nickell (1981) demonstrated that using the standard within-group estimator (more on this below) for dynamic models, with fixed individual effects, generates biased or worse inconsistent estimates as the number of cross-sectional observations tends toward infinity and the number of time series observations remains fixed. This is sometimes referred to as dynamic panel data bias. Using Monte Carlo analysis, Judson and Owen (1999) found that dynamic panel data bias is sizeable, even for models in which T = 20; however, this biasedness is reduced by having a sufficiently large number of time series observations within the panel, and the degree of bias is affected by the strength of temporal autocorrelation within the data. Our approach somewhat circumvents this problem of dynamic panel data bias. Because we are appealing to the validation strategy of forecast performance evaluation to assess the models, so we are less concerned about proper model specification, estimation, and fit of the within-sample data, which is an alternative validation strategy. In other words, if the bias is substantial then one would expect that it would be revealed through the forecast error performance of the particular model. Thus, in an indirect manner, forecast performance evaluation is an alternative approach to assess estimation bias. That is, forecast performance evaluation can be an alternative to Monte Carlo analysis which directly seeks to estimate the degree of bias. 2 The method for estimating the model with spatial autoregressive coefficient, ρ, alone is by maximum likelihood. The algorithm for this method is provided by LeSage and Pace (2009). The method for estimating the model with contemporaneous, ρ, and lagged spatial autoregressive coefficient, λ, is by quasi-maximum likelihood (Yu et al. 2012).

7 X. Zhao, J.W. Burnett The term W in Eq. (1) denotes the spatial weighting matrix, which is a compact reflection of the geographic relationship among different provinces. In this paper, the spatial weighting matrix is specified as the binary contiguity matrix which is determined by observing whether the regions share a common border. That is, the matrix elements w ij = 1 if two regions i and j share a common border and w ij = 0 otherwise. Generally, the spatial weighting matrix is normalized according to row standardization this allows for an interpretation of the spatial autocorrelation coefficient as representing an average weighted spatial value from neighboring regions. In other words, the sum of the elements W ij in each row equals one after normalization (LeSage and Pace 2009). More specifically, the term N j=1 W ij y jt denotes the weighted average value of the neighboring provinces on the dependent variable; Nj=1 W ij y j,t 1 denotes the weighted average value of the neighboring provinces on the temporal dependent variable; and N j=1 W ij φ jt denotes the weighted average value of the neighboring provinces on the error terms. The restriction of the parameters within Eq. (1) defines the specific type of spatial panel data model used. The spatial autoregressive model (SAR) is obtained by restricting both λ = 0 and δ = 0 this model exhibits spatial dependence within only the dependent variable. The spatial error model (SEM) is obtained by restricting both ρ = 0 and λ = 0 this model exhibits spatial dependence within only the error terms. The spatio-temporal panel data models (STPD) is obtained by restricting δ = 0 this model allows for spatial dependence within both the dependent variable and the temporal dependent variable. Finally, if all the parameters with the exception of β are restricted, then the model reduces to the traditional pooled OLS model Dynamic panel data models with fixed/random effects The dynamic panel data models could be treated with fixed effects or with random effects. The model is given as follows N N y it = α i + ρ W ij y jt + βy i,t 1 + λ W ij y j,t 1 + φ it N φ it = δ W ij φ jt + ε it. j=1 j=1 j=1 (2) The only difference between the fixed effects panel data model and the random effects panel data model is the intercept. In the fixed effects model, α i is introduced as a dummy variable for each spatial unit, while in the random effects model, α i is treated as a random variable that is independently and identically distributed with zero mean and variance σ 2 α Dynamic fixed effect panel data models The dynamic fixed effect panel data model allows for province-specific intercepts, in order to account for the heterogeneity

8 Forecasting province-level CO 2 emissions in China among spatial units. We can also define the same three types of spatial models as above by restricting the parameters. Performing out-of-sample forecasting is straightforward when assessing pooled panel data models, but it more challenging when fixed effects are included. Schmalensee et al. (1998) and Auffhammer and Steinhauser (2012) forecasted the out-of-sample by examining a variety of specifications. Elhorst (2012) circumvented direct estimation of the fixed effect terms by demeaning the variables to eliminate the fixed effects from the regression equation this provides an easier method to forecast the models. The least squares dummy variable (LSDV) estimator can be obtained by transforming the data as deviations from mean as follows (Elhorst 2010) y it = y it 1 T T y it. (3) t=1 This transformation eliminates the individual fixed effects. This type of estimator is sometimes referred to simply as the fixed effects estimator or within estimator instead of LSDV depending on which literature one reads Dynamic random effects panel data models The dynamic random effect panel data model assumes that the random variables α i and ε it are independent of each other. We could define three types of spatial models with random effects as well. For the within-sample data (first 15 years), we find that the fixed effects model is more appropriate than the random effects model by using the Hausman s specification test (results not provided). The explanation of the Hausman test could be reviewed in the book of Baltagi (2005). However, whether the random effects model is an appropriate specification for the out-sample data remains uncertain. So we would like to estimate the random effects panel data models as well. Similar as the fixed effects panel data models, Elhorst (2009) provided the direct estimation of the random effect terms by demeaning the variables. The variable estimators could be obtained by the following equation y it = y it (1 θ) 1 T T y it. (4) t=1 where θ denotes the weight attached to the cross-sectional component of the data, with 0 θ 2 = σ 2 /(T σ 2 α + σ 2 ) 1. If θ = 0, this transformation simplifies to the demeaning procedure of Eq. 3 and hence the random effects model to the fixed effects model. 4 Forecast performance of the different models The purpose of this section is to obtain and evaluate the CO 2 emission forecast performance for the thirty provinces in China. Before forecasting, we first regress the models using the within-sample observations or the first fifteen years of data. We then use the

9 X. Zhao, J.W. Burnett parameter estimates from these regressions to forecast out against the out-of-sample observations or the last 5 years of data. We assume the spatial autocorrelation (ρ,λ,δ) is consistent with the within-sample data when we do the out-of-sample forecasting. In other words, we compare the forecasts against empirical reality (in a forecasting error context) to determine which model provides the most accurate predictions. Based upon the regressions and post-diagnostic testing, the results of the within-sample regressions imply that the SAR model is the most appropriate specification of the dynamic pooled panel data models; the SEM model is the most appropriate specification of the dynamic random effects panel data model; and the spatio-temporal model is the most appropriate specification of the dynamic fixed effects panel data model. The results of these tests are provided in the Appendix A. We compute the prediction (forecasts) for the ith individual province at a future period T + τ for τ = 1, 2,...,5. The forecasts are conducted by regressing the model on the entire initial within-sample (15 years) designation, and then forecasting over the entire out-of-sample period (n years) using the empirical observations of the independent variables within the out-of-sample period. This method provides a metric for evaluating the short- or medium-run predictive ability of the model. Prediction is evaluated by means of root mean square error (RMSE), which is defined as { } 1/2, 1 T N RMSE = [F(t) A(t)] 2 (5) N t=1 i=1 where T is the total periods and N is the total number of provinces. The term F(t) denotes the forecast value and A(t) denotes the actual empirical observation. Since the errors in a RMSE test are squared before they are averaged, the RMSE gives a relatively higher weight to large errors so the RMSE arguably offers a more severe penalty for inaccurate forecasting errors. Note that the smaller the RMSE value, the smaller the forecast error, so lower values imply more accurate forecasts. The results of the forecast error performance, in the context of RMSE, of the dynamic pooled panel data model and dynamic fixed effect panel data model are presented in Table 1. From this table, we can highlight four important results. First, in terms of the dynamic pooled panel data model, the SAR model outperforms the other spatial models (SEM and STPD) and the non-spatial model (OLS) in all years of forecasting. Second, in terms of the dynamic fixed effect panel data model, the STPD model outperforms the other spatial models (SAR and SEM) and the non-spatial model (OLS) in all years of forecasting. These out-of-sample forecasting results are consistent with the withinsample estimations. Third, in terms of dynamic random effect panel data model, the non-spatial model (OLS) outperforms the other spatial models (SAR, SEM and STPD), these out-of-sample forecasts are not consistent with the within-sample estimation. Finally, it is also very clear that the fixed effect models outperform their pooled model and random effect model counterparts, and the spatio-temporal panel data model with fixed effects outperforms all other models. As a check for robustness we also tested the forecasting error performance of the models with one-year-ahead iterated forecasts. That is, we regressed the models over the first fifteen years of time series

10 Forecasting province-level CO 2 emissions in China Table 1 Forecast error performance of the different dynamic panel data models Numbers highlighted in bold indicate the smallest forecast errors in each group of estimators. Numbers highlighted in bold and italics indicate the smallest forecast errors among all the estimators 1 year 2 years 3 years 4 years 5 years Average Pooled models OLS SAR SEM STPD Fixed effects models FE SAR SEM STPD Random effects models RE SAR SEM STPD observations and then forecasted out by one year. In the next iteration we regressed the model over 16 years of time series observations and then forecasted out by one year. The results (not provided) did not change and the forecast error performance still implied that the spatio-temporal panel data model with fixed effects provided the best predictions. 5 Conclusion The interest in spatial econometrics models has grown markedly in the past three decades, and we are beginning to see more and more of these models in empirical applications. Criticisms surrounding identification issues and a lack of appeal to theory have cast some doubt on these models. To further test the validity of spatial panel data models, we compared the forecasting performance of these models against empirical reality using root mean square error tests. Our findings suggest that a dynamic, spatiotemporal panel data model with fixed effects outperforms all the other models analyzed. These findings imply that spatial panel data models performed better in forecasting ability than the non-spatial models, and the models that control for fixed effects perform better than models that do not control for such effects. The findings within this study are important for two reasons. From a policy standpoint, it is important to predict the trending behavior of carbon dioxide emissions. Understanding the changing trends will help better equip policy makers to design effective climate change mitigation policies in China. From a statistical standpoint, it is important to continue to test spatial econometric models to see how they perform against non-spatial models. With advances in spatial panel data econometrics, this methodology can now be tested in terms of the model s forecasting ability. Our results suggest that controlling for both time and space improves prediction.

11 X. Zhao, J.W. Burnett Future studies should consider the forecasting ability of spatial panel data models by incorporating explanatory variables in the models. Moreover, the evaluation of the long-run predictions will help better serve policy making in the context of climate change mitigation. As the spatial panel data literature continues to expand, spatial econometric models should be further tested against empirical reality to help prove their validity. The inference from these findings may be limited only to the framework within this particular study. That is, it is possible that the superior predictive ability of the spatio-temporal panel data models over the non-spatial models is limited to China s province-level carbon dioxide emission intensities during this particular timeframe. Appendix A A.1 Empirical results of dynamic pooled panel data model The estimation results of the dynamic pooled panel data models of the within-sample (the first fifteen years) is presented in Table 2. From the results, we found that the spatial autocorrelation parameter of ρ in the SAR model is shown as statistically significant, but the spatial autocorrelation parameter of δ in the SEM model and the parameters of ρ and λ in the STPD model are shown as non-significant. The SAR model is suggested as a more appropriate specification than the non-spatial model as well as the other spatial models (SEM and STPD) for the within-sample pooled regression analysis. We also perform the Lagrange Multiple (LM) tests to test the hypotheses whether the SAR model and SEM is prefer than the non-spatial model. The LM test results show the SAR model is statistically significant, but the SEM model is not (the results can be provided as required). Table 2 Estimation results of the dynamic pooled panel data models The symbols ***, ** and * denote a 1, 5 and 10 % significance level, respectively. Numbers in the parentheses represent t-test Determinants OLS SAR SEM STPD Constant *** (7.8092) *** (7.4237) *** (7.0589) *** (6.3437) C i,t *** ( ) *** ( ) *** ( ) *** ( ) W*C i,t 1 NA NA NA ( ) W*C it NA ** (1.9011) NA (1.3454) δ NA NA NA (1.4380) σ R Sample Log like

12 Forecasting province-level CO 2 emissions in China Table 3 Estimation results of the dynamic fixed effect panel data models The symbols ***, ** and * denote a 1, 5 and 10 % significance level, respectively. Numbers in the parentheses represent t-test Determinants OLS SAR SEM STPD C i,t *** ( ) *** ( ) *** ( ) *** ( ) W*C i,t 1 NA NA NA ** (2.5189) W*C it NA *** (7.3357) NA *** (2.6382) δ NA NA *** NA (3.8433) σ R Sample Log like A.2 Empirical results of dynamic fixed effect panel data model The estimation results of the dynamic fixed effect panel data models of the withinsample (the first fifteen years) is presented in Table 3. From the results, we found that the spatial autocorrelation parameter of ρ in the SAR model, the parameter of δ in the SEM model, and the parameters of ρ and λ in the STPD model are shown as statistically significant, the spatial models are suggested as a more appropriate specification than the non-spatial models for the within-sample fixed effect regression analysis. As an additional step, we perform Likelihood Ratio (LR) tests to test the hypotheses whether the STPD model can be simplified to the SAR or SEM model. According to the LR test result (7.221, 2 df, p < 0.01), the null hypothesis of the STPD model could be simplified to SAR model is rejected at a one percent significant level; the null hypothesis of the STPD model could be simplified to SEM model is also rejected at a one percent significant level based on the LR test result (48.985, 2 df, p < 0.01). These results imply that the SAR and SEM models are rejected in favor of STPD model. A.3 Empirical results of dynamic random effect panel data model The estimation results of the dynamic random effect panel data models of the withinsample (the first fifteen years) is presented in Table 4. From the results, we found that the spatial autocorrelation parameter of ρ in the SAR model, the parameter of δ in the SEM model, and the parameters of ρ in the STPD model are shown as statistically significant, the spatial models are suggested as a more appropriate specification than the non-spatial models for the within-sample random effect regression analysis.

13 X. Zhao, J.W. Burnett Table 4 Estimation results of the dynamic pooled panel data models The symbols ***, ** and * denote a one, five and ten percent significance level, respectively. Numbers in the parentheses represent t-test values Determinants OLS SAR SEM STPD C i,t *** ( ) *** ( ) *** ( ) *** ( ) W*C i,t 1 NA NA NA ( ) W*C it NA *** (3.8628) NA ** (2.5473) δ NA NA ** NA (2.3437) σ R Sample Theta NA *** ** *** We also perform the Lagrange Multiple (LM) tests to test the hypotheses whether the SAR model and SEM is preferred over the non-spatial model. The LM test results show the SEM model is statistically significant, but the SAR model is not (the results can be provided as required). References Angulo, A.M., Trívez, F.J.: The impact of spatial elements on the forecasting of Spanish labour series. J. Geogr. Syst. 12, (2010) Auffhammer, M., Carson, C.: Forecasting the path of China s CO 2 emissions using province-level information. J. Environ. Econ. Manage. 55, (2008) Auffhammer, M., Steinhauser, R.: The future trajectory of U.S. CO 2 emissions: the role of state vs. aggregate information. J. Reg. Sci. 47(1), (2007) Auffhammer, M., Steinhauser, R.: Forecasting the path of U.S. CO 2 emissions using state-level information. Rev. Econ. Stat. 94(1), (2012) Schmalensee, R., Stoker, T.M., Judson, R.A.: World carbon dioxide emissions: Review 80, (1998) Baltagi, B.H.: Econometric Analysis of Panel Data, 3rd edn. Wiley, New York (2005) Baltagi, B.H., Li, D.: Prediction in the panel data model with spatial correlation: the case of liquor. Spatial Econ. Anal. 1(2), (2006) Baltagi, B.H., Bresson, G., Pirotte, A.: Forecasting with spatial panel data. Comput. Stat. Data Anal. 56, (2012) Burnett, J.W., Bergstrom, J.C., Dorfman, J.H.: A spatial panel data approach to estimating U.S. state-level energy emissions. Energy Econ. (2013, forthcoming) CESY (2012) China energy statistical yearbook, Technical report, National Bureau of Statistics of China. Conley, T.G., Ligon, E.: Economic distance and cross-country spillovers. J. Econ. Growth 7(2), (2002) CSY (2012) China statistical yearbook, Technical report, National Bureau of Statistics of China. Elhorst, J.P.: Spatial panel data models. In: Fischer, M.M., Getis, A. (eds.) Handbook of Applied Spatial Analysis, pp Springer, Berlin. Elhorst, J.P.: Dynamic panels with endogenous interaction effects when T is small. Reg. Sci. Urban Econ. 40, (2010) Elhorst, J.P.: Matlab software for spatial panels. Int. Reg. Sci. Rev. 35(3), 1 17 (2012) Fingleton, B.: Prediction using panel data regression with spatial random effects. Int. Reg. Sci. Rev. 32(2), (2009) Freedman, D.A.: Statistical models and shoe leather. Soc. Methodol. 21, (1991)

14 Forecasting province-level CO 2 emissions in China Giacomini, R., Granger, C.W.J.: Aggregation of space-time processes. J. Econ. (2004) Intergovernmental Panel on Climate Change (2006) 2006 IPCC guidelines for national greenhouse gas inventories: workbook volume 2. Technical report, United Nations Judson, R.A., Owen, A.L.: Estimating dynamic panel data models: a guide for macroeconomists. Econ. Lett. 65, 9 15 (1999) Kelejian, H.H., Prucha, I.R.: The relative efficiencies of various predictors in spatial econometric models containing spatial lags. Reg. Sci. Urban Econ. 37, (2007) Kelejian, H.H., Robinson, D.: Returns to investment in navigation infrastructure: an equilibrium approach. Annu. Reg. Sci. 34, (2000) Kholodilin, K.A., Siliverstovs, B., Kooths, S.: A Dynamic panel data approach to the forecasting of the GDP of German Länder. Spatial Econ. Anal. 3(2), (2008) Kholodilin, K.A., Mense, A.: Forecasting the prices and rents for flats in large German cities. Working Paper (2012) LeSage, J., Pace, R.K.: Introduction to Spatial Econometrics. CRC Press, Boca Raton (2009) Manski, C.F.: Identification of endogenous social effects: the reflection problem. Rev. Econ. Stud. 60, (1993) Nickell, S.J.: Biases in dynamic models with fixed effects. Econometrica 49, (1981) Ohtsuka, Y., Kakamu, K.: Space-time model versus VAR model: forecasting electricity demand in Japan. J. Forecast. 32, (2013) Partridge, M.D., Boarnet, M., Brakman, S., Ottaviano, G.: Introduction: whither spatial econometrics. J. Reg. Sci. 52(2), (2012) Schanne, N., Wapler, R., Weyh, A.: Regional unemployment forecasts with spatial interdependencies. Int. J. Forecast. 26, (2010) U.S. Energy Information Administration (2012) Monthly energy review, tables (2012). Yu, J., de Jong, R.: Estimation for spatial dynamic panel data with fixed effects: the case of spatial cointegration. J. Econ. 167, (2012)