What STIRPAT tells about effects of population and affluence on environmental impact?

What STIRPAT tells about effects of population and affluence on environmental impact? Taoyuan Wei 1 July 21, 2010 Abstract In the literature of STIRPAT application to environmental impacts of population and affluence, controversial results are obtained from different studies. One example is the effects of population size, which is concluded to be unity in some studies (e.g., York et al. 2003) while far from unity in some others (e.g., Shi 2003). Another problem that may arise in the STIRPAT application is multicollinearity, which is encountered in several studies (e.g., Fan et al. 2006; Lin et al. 2009). To solve the multicollinearity problem, various strategies are adopted, e.g., excluding correlated variables, ridge regression, and PLS regression. How can we interpret these results? I offer a consistent framework facilitating to understand these results in the present paper. This is done by deriving a latent model equivalent to STIRPAT, which explicitly specifies the different role of technology (T) in the STIRPAT formulation from that in IPAT accounting model. By the latent model, I conclude that the different specification of STIRPAT formulation can be used to explain the controversial results on environmental impacts of population and affluence. Moreover, methods like ridge regression and PLS regression are plausible only if the common components of high correlated variables have the same explanatory power on the dependent variable in the model. Keywords: IPAT, STIRPAT, Carbon emissions, Energy consumption, GDP, Population, Ridge regression, PLS regression, ecological elasticity 1 Author address: Center for International Climate and Environmental Research - Oslo (CICERO), University of Oslo, P.O. Box 1129 Blindern, 0318 Oslo, Norway (e-mail: taoyuan.wei@cicero.uio.no). Electronic copy available at: http://ssrn.com/abstract=1645803

1. Introduction As originated by Dietz and Rosa (1994; 1997), the STIRPAT model was developed from the widely applied IPAT accounting model analyzing environmental Impacts of Population size, Affluence, and Technology (Ehrlich and Holden 1971; 1972). Noticing that the relationship of variables in IPAT is definitional, Dietz and Rosa (1994; 1997) modify the IPAT to the innovative stochastic model of STIRPAT (Stochastic Impacts by Regression on Population, Affluence and Technology), which allows statistically testing hypotheses about anthropogenic driving forces of environmental impacts. STIRPAT was already applied to analyze ecological footprint, carbon emissions, and energy footprint in several studies (e.g., Dietz and Rosa 1997; York et al. 2003; Jia et al. 2009). As a stochastic model, STIRPAT can be used for at least two purposes: predicting environmental impacts based on key driving forces and estimating coefficients of the driving forces appearing in the STIRPAT model. A coefficient of a driving force in logarithmic form of STIRPAT represents the elastic relationship between the driving force and its environmental impacts, i.e., the percentage change of environmental impacts if the driving force changes by one percent. The coefficients are called ecological elasticity (EE) after York et al. (2003). York et al. (2003, Section 3.2) also argue that the technology (T) can be directly disaggregated by including additional factors in the STIRPAT model that are theorized to influence impact per unit of production. However, York et al. (2003) do not explicitly mention that the disaggregation may alter the estimates of ecological elasticity (EE) of driving forces that already exist in the model. For example, the EE of population size is estimated to be significantly different among three studies: Dietz and Rosa (1997), Shi (2003), and York et al. (2003). None of these studies mentions that the potential effects on the EEs of alternative disaggregation of the technology (T) in STIRPAT. The ignorance of the effects may lead to misinterpretation of the EEs 2. Another potential problem related to the disaggregation of the technology (T) is multicollinearity, which has been encountered in several studies (e.g., Xu and Chen 2005; Fan et al. 2006; Lin et al. 2009). An example is the high correlations between GDP per capital and urbanization level represented by percentage of population residing in urban areas 2 Shi (2003, Footnote 5) notes that the difference may be, at least in part, dependent on the sample size. I would guess the sample size plays trivial role in this context even though it is important in some other cases. 2 Electronic copy available at: http://ssrn.com/abstract=1645803

(Xu and Chen 2005; Lin et al. 2009). Moreover, multicollinearity may even emerge between population size (P) and affluence (A) in the STIRPAT when time series data of only one single region are adopted. A typical example is the case of China, where the correlations between P and A (represented by GDP per capita) are as high as 0.992 during 1978-2006 (Lin et al. 2009, Table 3). In order to solve the multicollinearity problem, alternative methods are applied, e.g., excluding variables (e.g., Xu and Chen 2005), ridge regression (e.g., Wang and He 2006; Lin et al. 2009; Peng and Zhu 2010), and partial linear squares (PLS) regression (e.g., Fan et al. 2006; Jia et al. 2009). Excluding variables provides unbiased estimates while ridge and PLS regressions provide biased estimates even though better predictions can be obtained for dependent variables, i.e., environmental impacts in the STIRPAT. Unfortunately, the researchers who apply ridge and PLS regressions tend to over-interpret their estimates of the ecological elasticity (EE) and offer misleading information of environmental impacts resulting from related driving forces. For example, if it happens that affluence (A) has almost linear relationship with population size (P) in a single region, none of the two regressions can really distinguish the impacts of P from A just by the time series data of the single region. Besides excluding variables, which we do not prefer to in this case, a way-out may be applying multi-regional data by dividing a single region to be many sub-regions, e.g., dividing China to be provinces (Xu and Chen 2005). If the data on sub-regions are not available, it would be better to adopt results from other related studies than adopting ridge and PLS regressions. Definitely if we just want to better predict the environmental impacts, ridge and PLS regressions are suitable choices. The remaining of the paper is organized as follows. The next section will provide a latent model that is implicitly assumed by the STIRPAT specification. The latent model can be applied to explain the potential effects on the ecological elasticity (EE) of disaggregation of technology (T) and the multicollinearity problem, where the latter is described in Section 3. Section 4 applies the latent model to the case described by Lin et al. (2009), where the data they applied are sufficiently transparent. Section 5 offers brief comments on some other related studies. The last section summarizes the findings. 2. Technology from IPAT to STIRPAT The IPAT accounting model describes environmental impacts (I) as a multiplicative function of population size (P), affluence (A) represented by per capital consumption or production, 3

and the environmental impacts level caused by technology per unit of consumption or production (T). Since first used by Ehrlich and Holden (1971; 1972), the IPAT accounting model and its variations have been applied extensively (Dietz and Rosa 1994). For example, the model has been reformulated as Kaya equation, which is the basis for calculations, projections, and scenarios of greenhouse gases (GHGs) implemented by the Intergovernmental Panel on Climate Change (Nakićenović 2004). The basic IPAT model can be formulated by ( 1 ), where the subscript i denotes the observational units and t the time. This is an identity equation, where generally T is unknown and can be calculated on the basis of the other three variables. This feature is viewed as a weakness of the IPAT by Dietz and Rosa (1994) since part of the effects of population and/or affluence on the environment may improperly be attributed to the technology term. To overcome the weakness, Dietz and Rosa (1994; 1997) reformulate the IPAT to be a stochastic model that can be used to empirically test hypotheses, namely STIRPAT (Rosa and Dietz 1998), ( 2 ) where a, b, c, and d are parameters to be estimated and e is an error term. Here unlike in the IPAT, the technology is denoted by. For simplicity, I assume that I, P, and A have the same meaning in the STIRPAT as in the IPAT even though P and A can be disaggregated in the STIRPAT model as claimed by Rosa and Dietz (1998). In the literature following Rosa and Dietz (1998), the technology in the STIRPAT is represented by the same letter T as in the IPAT. This gives an impression that the technology has the same meaning in both models. This may sometimes lead researchers to misinterpret results from the STIRPAT. To avoid such kinds of misinterpretation, I explicitly describe this secret of treating the technology in different ways from IPAT to STIRPAT in the present paper. Just by comparing Eq. ( 1 ) with Eq. ( 2 ), we yield the relations between the technology terms of IPAT and STIRPAT, ( 3 ), which in fact is the latent model equivalent to the STIRPAT. In the latent model, it becomes transparent that the estimates of parameters a, b, c, d and the error term e depend on the choice of to a large extent. An extreme and trivial case is to set, which leaves no 4

room for hypothetic tests and we go back to IPAT, where the proportionality assumption holds, i.e., a=b=c=d=e=1. Except this extreme case, we can obtain several versions of STIRPAT from Eq. ( 3 ) by adding more assumptions on the STIRPAT model. Case 1. By assuming in Eq. ( 3 ), a special version of the STIRPAT can be obtained, ( 4 ), which corresponds to the specification adopted by Dietz and Rosa (1997) and Xu and Chen (2005). This specification is interpreted as that is included in the error term,..., making it consistent with the IPAT model, where T is solved for to balance I, P and A (York et al. 2003, p. 354). However, even in this version, the error term cannot be interpreted similar as in the IPAT since the technology (T) is disaggregated to be four terms: constant (a), effects of P and A, and the error term (e). The proper interpretation of this specification can be stated as follows. The technology (T) in IPAT is first explained by P and A. The remaining unexplained part of T is divided into two parts: its expectation (a) and deviation (e). In doing so, it is possible to wrongly allocate more environmental impacts to P and/or A if there is some independent components of that happens to be high correlated to P and/or A. This has to be checked before the error term (e) is interpreted as technology multiplier for environmental impacts proposed by Dietz and Rosa (1997). A remaining question is that if only one period (panel) data is used, the interpretation of technology multiplier is just the antilog of the error term. If multi-period (time series) data is used, how could we tell? Case 2. If is represented by, the quadratic of affluence (A), this case becomes the STIRPAT considering environmental Kuznets curves (e.g., models 1 and 4 in York et al. 2003). Case 3.. This in fact assumes that the technology (T) in IPAT is independent on population size (P). With this assumption, Eq. ( 3 ) can be simplified as ( 5 ), which implies that T in IPAT can be explained by A and and the remaining of T is 5

represented by a and e. This case can be applied if T in IPAT is believed to be independent on P. Case 4. If, Eq. ( 3 ) becomes ( 6 ), which implies that the STIRPAT is in fact searching a instrumental variable or representative of the technology (T) in IPAT. A STIRPAT has to avoid such kinds of choice for the technology ( ). Otherwise, the estimated EEs for P and A makes no sense. A typical example of this case is to adopt energy intensity as with carbon emissions from energy consumption as the dependent variable in a STIRPAT for a single region (e.g., Lin et al. 2009). If carbon emissions are calculated with fixed emissions coefficients, i.e., emissions per unit of energy use, energy intensity could be a perfect instrumental variable for carbon intensity in IPAT with rather stable energy use structure in the region. I will comment more on this by taking Lin et al. (2009) as an example below. 3. Multicollinearity Certain part of T in IPAT may in fact be determined by P and/or A. This is why STIRPAT is necessary. By Eq. ( 3 ), an ideal choice of should be independent on P and A. However, in some cases, we would like to know a driving force that is highly correlated to P and/or A. If such driving forces are included in STIRPAT, we are likely to have the multicollinearity problem. This can happen if a choice of that ( 7 ), where g, h, k, and m are constant parameters, u is an error term, and other than P and A. denotes driving forces If time series of a single region are applied in a STIRPAT, multicollinearity can appear even between P and A. This should not imply that P is the major driver of A. The common components of A and P play different role in environmental impacts even though they are perfectly correlated. The regression methods like ridge and PLS regressions are not suitable to solve the multicollinearity problem since they tread the common components of A and P in the same way. This kind of multicollinearity can be expressed by 6

( 8 ), where g and h are constant parameters and u is an error term. To solve the multicollinearity problem, we have to consider more about the meanings behind the data relations. For example, is P really a major driver of A if P and A are highly correlated for a single region? Is A is a major driver of if they are highly correlated? If yes, the method of excluding variables is suitable strategy to solve the multicollinearity. Methods like ridge and PLS regression can be adopted if the purpose is just for prediction since they provide biased estimates of parameters. If not, we have no way to separate the environmental impacts of these highly correlated variables just by the data with multicollinearity. Hence, a solution could be adopting other data without the multicollinearity problem or results from other studies if other data are not available. 4. The case in Lin et al. (2009) In this section, I will illustrate the effects on EEs of disaggregation of the technology (T) and the multicollinearity problem by taking Lin et al. (2009) as an example since the data they applied are sufficiently transparent. They use the national data of China during 1978-2006 for their analysis. In the spirits of York et al. (2003), who indicate that sociological or other factors can be added into Eq. ( 2 ), as long as these additional factors are conceptually consistent with the multiplicative specification of the model, Lin et al. (2009) revises Eq. ( 2 ) by adding urbanization level (UL) and industrialization level (IL) to the set of factors, resulting in Eq. ( 9) below 3. ( 9 ), where are parameters to estimate. P is population size, A is represented by GDP per capita, and is energy intensity, i.e., energy consumption per unit GDP, which is denoted by T in Lin et al. (2009). The dependent variable is the environmental influences of pollutants that are emitted by primary energy consumption. Pollutants include Carbon (C), SOx, NOx, particulate and volatile organic compounds (VOC). Primary energy is classified to be four groups: coal, oil, gas, and primary power (hydro-, nuclear and wind power). By 3 The logarithetic form of STIRPAT that is directly obtained by taking logarithms on both sides of equations ( 2 ) is adopted in Lin et al. Lin, S., D. Zhao and D. Marinova (2009). "Analysis of the environmental impact of China based on STIRPAT model." Environmental Impact Assessment Review 29(6): 341-347. 7

setting constant respective weights for the influences of pollutants and normalizing the influence of pollutants emitted by unit coal consumption to be 1, i.e., the influence coefficient of coal is 1, Lin et al. (2009) calculate the influence coefficients of other primary energy. The calculated influence coefficients vector is denoted by B. 4 If the energy consumption structure of a year is denoted by a vector, we can calculate the impact coefficient of total energy consumption as the inner product of B and, i.e., ( 10 ), which can be taken as a representitive of the energy consumption structure of that year noticing that the influence coefficients vector B is constant for each year. Following the calculation process, we can write down a variant of IPAT model that is consistent with the data applied in Lin et al. (2009), ( 11 ), where the technology (T) in IPAT is disaggregated to be two terms: energy intensity ( ) and energy consumption structure 5 ( ). By comparing Eq. ( 11 ) with ( 9 ), the STIRPAT model represented by Eq. ( 9 ) is equivalent to that ( 12 ), which implies that all variables on the right hand side are used to explain a representative of the energy consumption structure ( ). To justify the results in Lin et al. (2009), the authors have to clarify why Eq. ( 12 ) is plausible. For example, it is estimated that (Lin et al. 2009, Table 5), which, by Eq. ( 12 ), implies that one percent change in population (P) could contribute to half percent change in the representative of energy consumption structure ( ). Arguments are necessary to tell why it could be. I would argue that this result is mainly caused by the high correlations between P and A for China during 1978-2006. If the data by provinces are used instead of the national data, It can be expected to break the high correlations between P and A to obtain a plausible result. Xu and Chen (2005) have used the provincial data to analyze the impacts of P and A on ecological footprint (EF) and found that proportional environmental impacts of population size (P). 4 It is denoted by in Lin et al. (2009). 5 It is denoted by B in Lin et al. (2009) even though it is changing over time. 8

Multilcollinearity As noticed by the authors, there exists the multicollinearity problem between all variables other than. Before any methods of regressions are adopted in the analysis, a necessary step should be checking whether the correlated parts of independent variables can explain the dependent variable at the same degree. For example, I concern the correlations between P and A, which happen to be very close to 1 (Lin et al. 2009, Table 3). The high correlations do not hold in general (e.g., York et al. 2003; Xu and Chen 2005). However, there is no effective regression method that can distinguish the impacts of P from that of the part of A correlated to P. The ridge regression applied by the authors at least gives an improper estimates for the impacts of P. I also concern the high correlations between A, UL, and in the sense of whether the estimates of parameters are plausible. If part of A can be explained by UL and/or, including all of them in the regression implies wrong estimates of parameters since the impacts of UL or are shared by itself and the part of A explained by it. Just imagine the extreme case to include the same variable twice in a regression, where the parameter values would be half of the right one if they are correctly estimated. This is why methods like ridge and PLS regressions are not plausible to estimate parameters in a STIRPAT model. 5. Brief comments on other related studies Impact of population pressure on CO 2 emissions I focus on three studies on the impact of population pressure on CO 2 emissions by STIRPAT models. The estimated results show that a 1 percent increase in population is associated with an increase in emissions of 1.15, 1.424, and around 1 percent by Dietz and Rosa (1997), Shi (2003, Model 1), and York et al. (2003) respectively. Shi (2003, Footnote 5) mentions that sample sizes may be one cause of these differences. As mentioned above, I would argue the specifications of the STIRPAT models should be the major cause of these differences. The model used by Dietz and Rosa (1997) does not include any specific technology variables (Case 1 in Section 2). Shi (2003) includes one autocorrelation term that can be taken as an variable added for technology ( ) in that STIRPAT model. On the contrary, York et al. (2003) added at least one term of the quadratic of A in their models (Case 2 in Section 2). Just like the values of parameters changing dramatically from IPAT to any STIRPAT, the differences 9

of specifications on the technology in these models should have considerable effects on the estimated results of parameters. Multicollinearity The multicollinearity problem has been appeared in several studies. Besides Lin et al. (2009), several STIRPAT studies have reported the multicollinearity in the data they applied, e.g., Xu and Chen (2005), Fan et al. (2006), Wang and He (2006; 2008), Chen et al. (2009), Jia et al. (2009), Peng and Zhu (2010), and Zhu et al. (2010). Xu and Chen (2005) and Fan et al. (2006) apply data of more than one region and the other studies just apply data of one region. The latter studies can be analyzed following the same way described in Section 4 on Lin et al. (2009). Next I will focus on the cases of Xu and Chen (2005) and Fan et al. (2006). Xu and Chen (2005) apply the provincial panel data of China and find multicollinearity only when introducing an additional variable of urbanization level, which is high correlated to the affluence (A) term represented by GDP per capita. This is also reported by Lin et al. (2009) for China as a whole region. This implies that application of multi-regional data can help to eliminate certain multicollinearity problem, e.g., the high correlations between population (P) and affluence (A) for China as a whole region are eliminated by using sub-regional data in Xu and Chen (2005). However, the high correlations between GDP per capital and urbanization level still exist. Unlike Lin et al. (2009), Xu and Chen (2005) adopt the method of excluding correlated variables to eliminate the multicollinearity. Their method is plausible to provide unbiased estimates of parameters. It is unclear to me whether Fan et al. (2006) apply multi-regional data or not to analyze impact factors of CO 2 emissions. It seems that they aggregate the data of all the countries in the world to several groups and then analyze the time series of each group respectively. If so, they essentially apply the data of one single region and the multicollinearity can be expected as the case in Lin et al. (2009). The version of the STIRPAT model in Fan et al. (2006) specifies the technology ( ) as three variables: energy intensity, urbanization, and percentage of population aged 15 64 6. The 6 Fan et al. (2006, p.381) mentions that Population is decomposed to two variables: the percentage of population aged 15 64 and the proportion of the population living urban areas. I would argue this is a wrong description. Population in the context means population size (P). If P is decomposed to two variables, P should disappear from the STIRPAT model. If the technology follows the definition in IPAT, these two variables should be components of the technology. 10

correlations between any one of the latter two variables and any one of the other variables are not reported. According to tables in Appendix B of Fan et al. (2006), there are always high correlations between population size and energy intensity. The adopted method of PLS regression would always take the correlated parts of these two variables in the same way. This treatment may lead to misleading estimates of parameters if population size and energy intensity are independent variables. 6. Conclusions I have offered a latent model equivalent to STIRPAT, which explicitly specifies the different role of technology (T) in the STIRPAT formulation from that in IPAT accounting model. By the latent model, I argue that specifications of STIRPAT formulation can be used to explain different estimates of environmental impacts of population size (P) and affluence (A). Moreover, it is helpful to determine how to eliminate the multicollinearity problem that may appear in a STIRPAT model. The change in meanings of the technology is the key issue from IPAT to STIRPAT. Technology (T) is deterministic in IPAT while technology ( ) in STIRPAT is implicitly assumed depending on A, P and other drivers. In essential, STIRPAT implicitly assumes that the remaining part of T in IPAT other than specified factors in the model is mainly captured by P and A. Hence, the environmental impacts (I ) of P and/or A depend on the specifications of STIRPAT formulations and may lead to controversial results. This may be the major cause of different results of estimated ecological elasticity (EE) in the literature of STIRPAT applications. When the technology is disaggregated in a STIRPAT model, a potential problem is the multicollinearity since the added variables may be highly correlated with other variables in the STIRPAT like population size (P) and affluence (A). If data of a single region, such as China, are applied in a STIRPAT model, the high correlations may arise even between population size (P) and affluence (A). To eliminate the multicollinearity problem, the method of excluding correlated variables is plausible for both prediction of environmental impacts and estimates of parameters (EEs). However, methods like ridge and PLS regressions are suitable to obtain better prediction of environmental impacts but not correct estimates of parameters. The parameters estimated by these two methods are not suitable to be interpreted as the ecological elasticities. 11

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