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Environmental Modelling & Software 62 (2014) 22e32

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Environmental Modelling & Software

journal homepage: www.elsevier .com/locate/envsoft

Drivers of environmental impact: A proposal for nonlinear scenariodesigning

Ely Jos�e de Mattos a, *, Eduardo Ernesto Filippi b

a Department of Economics, Pontifical Catholic University of Rio Grande do Sul, Brazilb Department of Economics and International Relations, Federal University of Rio Grande do Sul, Brazil

a r t i c l e i n f o

Article history:Received 1 October 2013Received in revised form29 June 2014Accepted 15 August 2014Available online

Keywords:IPATSTIRPATOrdered logistic modelEnvironmental impactEnvironment and development

* Corresponding author. Av. Ipiranga, 6681, Pr�edio 590619-900, Brazil.

E-mail addresses: ely.mattos@pucrs.br, elymattosedu_292000@yahoo.com.br (E.E. Filippi).

1 Chertow (2001) presents a historical perspective2 It is also replicated with some adjustments, f

Ausubel (2002), Schulze (2002).

http://dx.doi.org/10.1016/j.envsoft.2014.08.0131364-8152/© 2014 Elsevier Ltd. All rights reserved.

a b s t r a c t

Drivers of environmental impact are commonly studied in the related literature through the IPAT andSTIPAT models. The first is an accounting model and the second is a stochastic approach that enablesboth statistical tests of significance of the drivers and the consideration of a larger set of drivers. Thesemethodologies, however, are unable to take account of the level of all drivers in a nonlinear structure, i.e.,different impacts according to the level of the variable. This paper presents a global Ordered LogisticModel that estimates the probability of four ordinal categories of environmental impact (four definedcategories of Ecological Footprint). The results further the analysis of environmental impact offering anadditional understanding of what to expect in terms of environmental pressure when the current level ofthe drivers are changing. The study demonstrates the proposed methodology by offering some examplesof scenario analysis based on the estimated model.

© 2014 Elsevier Ltd. All rights reserved.

1. Introduction and background

The complex relationship between economic growth and theenvironment has been dealt with in specialized literature based onthe Environmental Kuznets Curve (EKC) since the 1990s (Grossmanand Krueger, 1995; Dinda, 2004). Nevertheless, significant efforts tounderstand the impacts of human activities on the environmentdate back to the 1970's (Ehrlich and Holdren, 1971; Commoner,1972). A classic model of analysis, credited to Paul Ehrlich andJohn Holdren, is known in the literature as “IPAT”. This modelproposes that environmental impact results from themultiplicativerelation between population, affluence and technologyðImpactðIÞ ¼ PopulationðPÞ$AfluenceðAÞ$TechnologyðTÞÞ.1

Although the model is seminal and widely replicated,2 the IPATpresents some significant limitations. One of them e which hadalready been pointed out by Ehrlich and Holdren during debateswith Commonere is discussed in thewell-knownpaper by ThomasDietz and Eugene Rosa “Rethinking the environmental impacts of

0, Sala 1105, Porto Alegre, RS

@gmail.com (E.J. de Mattos),

of IPAT.or instance: Waggoner and

population, affluence and technology” (Dietz and Rosa, 1994). Ac-cording to the authors, typical applications of the IPAT models aregrounded on data for population and affluence. Technology, how-ever, is indirectly obtained from the other variables: T ¼ I/(P,A). So,since one has the three variables available (impact, population andaffluence), the fourth one is automatically determined.

From an empirical point of view, this characteristic of the modelcan eventually underestimate the impacts of population andaffluencee because technology is defined endogenously andmightbe incorporating factors other than just the technological aspect.Dietz and Rosa (1994) call attention to the observations of Ehrlichand Holdren on this matter indicating that “… calculations un-derestimate the effect of population on the environment byattributing to the T term changes that could more properly beallocated to P or A” (p. 10). So, on one hand, IPAT is useful as a modelwith an accounting characteristic, which can generate conclusionson the intensity of the environmental impact from population sizeand from the environmental efficiency of production. On the otherhand, the model does not prove to be suitable for relative analysiswhere the motivation is to test the hypothesis of the significance ofthe human drivers of environmental impact, for instance.

It is exactly this limitation that forms the basis of the work ofDietz and Rosa (1994). The authors suggest that the IPAT should bereconsidered to establish a wider debate about the role played bypopulation, economic growth and technology in terms of theenvironment. Two points are especially important. The first is that

E.J. de Mattos, E.E. Filippi / Environmental Modelling & Software 62 (2014) 22e32 23

the model should be stochastic instead of an accounting exercise, tomake it possible to test the hypothesis on the significance of thedrivers. The second point is the explicit need to incorporate a largernumber of variables to be tested and studied.

In this context, an important step forward in the formulation ofmodels of environmental impact is the proposition of a modelnamed STIRPAT (Stochastic Impacts by Regression on Population,Affluence, and Technology) (Dietz and Rosa, 1994, 1997). The modelis formulated as follows:

Ii ¼ aPbi Aci T

di ei (1)

It can firstly be observed that in this formula, the index “i” ap-pears by the variables. These indexes indicate that the quantitiesvary across the observations.3 The coefficients (a, b, c, e, d) are theterms that have to be estimated from the set of observationsconsidered (countries, for example). For the sake of recognizingthat this model theoretically derives from IPAT it has to be clear thatthe IPAT classic is obtained from this very formulation when wehave the special case where a ¼ b ¼ c ¼ d ¼ 1.

The STIRPAT's theoretical equation should be estimated in nat-ural logarithms. In this case the model is presented as follows:

lnðIÞ ¼ aþ b½lnðPÞ� þ c½lnðAÞ� þXn

i¼1

bi½lnðXiÞ� þ e (2)

where a and e are logarithms of those same terms as in the mul-tiplicative formulation of the model. The technology component (T)is incorporated into the error term in the same way it is executedwhen dealing with the traditional IPAT model. Considering thelogarithm formulation the results are basically presented and dis-cussed as elasticity.

As previously mentioned, an important characteristic of thismodel is the possibility of expansion of the drivers in the formu-lation. The technology term is not frequently considered because ofthe absence of an adequate variable that can work properly asproxy.4 However, variables that represent other dimensions such asinstitutions, culture, and geography, for instance, can be added tothe model since they are conceptually consistent with the originalmultiplicative formulation. This is done through the Xi in the for-mula above. They represent all variables that the researcher wouldlike to evaluate as a significant driver of environmental impact.

Studies carried out by researchers such as Szutukowski (2010),Shi (2003), York et al. (2003), Knight and Rosa (2012), Wei et al.(2011), York and Rosa (2012), Liddle (2012) and others, haveapplied the STIRPAT model in different contexts and with differentpropositions. Szutukowski (2010), for example, analyzes the impactof population, income per capita and climate oscillation on theemissions of CO2 in several sectors for municipalities in USA. Knightand Rosa (2012), for their part, applied the STIRPAT model toinvestigate the impact of household dynamics on the consumptionof fuelwood.

These applications, however, are especially dedicated to theidentification of main drivers of environmental impact and relativeimportance when compared with each other. There are few refer-ences in these studies about projections or scenarios though.5Whatwould happen if the population grew by 10%? What would happenif the population grew by 10% when the population is small? Whatabout a very large population? The answers to this sort of questions

3 For the classic IPAT there is no need for the index because the accounting issupposed just for one observation or point in the time series.

4 The paper of Wei (2011) presents a discussion on this matter.5 A study which presents some projections is York (2007).

are not statistically explored in these studies because they are notusually meant to design scenarios.

Returning to the STIRPAT formulation, it is worth noting that the esti-matedcoefficientsb,canddareobviouslyconstants, i.e., theyrepresentfixedeffects. This means that regardless of the level or frontiers of the driver, theproportional impact caused by them is constant through the entire range ofthe variable. However, there is plenty of evidence in the literature empha-sizing that the effects of the drivers of environmental impact are level-dependente for example, the recent “Planetary boundaries: exploring thesafe operating space for humanity” by Rockstr€om et al. (2009) empiricallydemonstrates some irreversible turning points of sustainability.

On one hand, Dietz and Rosa (1997) argue that the stochasticmodel would handle the nonproportional effects if the coefficientswere replaced by more complex functions ewe have not identifiedany application of this methodology in the current literature. Somestudies, on the other hand, make use of quadratic terms of thedrivers for that same purpose: Shi (2003), York (2007), York et al.(2003), York and Rosa (2012), and Jorgenson and Clark (2013).However, those studies have explored just a couple of drivers inquadratic terms (generally GDP and urbanization); and not all ofthem. The reasons for that are probably the lack of justification forall the drivers and also the difficulties in estimating well-adjustedmodels containing a number of (significant) quadratic variables.

Regarding this matter, it is worth quoting the recent work ofLiddle (2013) which also points out some critical aspects concern-ing the traditional STIRPAT modeling. According to the author it isimportant to check if the environmental impact does vary acrossthe different levels of development. The methodology appliedconsists in estimating panels counting on poor, middle, and richcountries. The results e based on time-series techniques e indicatesignificant distinctions in the estimated coefficients (elasticity)according to the level of development.

Therefore, there is clearly a caveat in the current STIRPATmodelsfor the purpose of scenario designing. It is mandatory to take intoconsideration that the impact caused by every drivermight stronglydepend on its level (Stern, 2004; Dinda, 2004; Cavlovic et al., 2000;Cole et al., 1997). It is important to mention, however, that theSTIRPAT models have not been proposed to explore scenarios in theway just described e although some projections that are notdependent on the driver's levels can be identified in outstandingworks in the literature: York (2007), Liddle (2011a,b).

To be able to perform a scenario investigation it is necessary todraw on amodel that is able to take into account levels of all driversin a nonlinear fashion. A potential alternative for this is a nonlinearprobability model. This sort of model can measure the impact ofindependent variables on the probability of a specific outcome,whether it is binary, categorical or ordered. Although these modelsdo not estimate the environmental impact itself as IPAT and STIR-PAT do, they are able to present interesting scenario analyses interms of probabilities.

In this context, the main contribution of this paper is to proposea nonlinear probability model that can design scenarios based onthe theoretical scope of IPAT and STIRPAT models. Secondly, it aimsto present some specific scenarios based on the model proposed inorder to demonstrate the feasibility and characteristics of themethodology. To accomplish these objectives the paper iscomposed of two sections besides the introduction and conclusion.Section 2 presents the methodology, and Section 3 demonstratesthe results and some illustrative scenarios.

2. A nonlinear model for scenario designing: methodology,variables and the sample

For scenario designing of environmental impact we areassuming that three characteristics must be present: i) adequate

6 Wooldridge (2002) presents a Probit model based on a normal distributionfunction. The logistic model, however, works in the same way.

E.J. de Mattos, E.E. Filippi / Environmental Modelling & Software 62 (2014) 22e3224

theoretical background; ii) identification of a set of statisticallysignificant drivers of environmental impact; and, iii) analysis ofpotential environmental impacts that consider the level of the alldrivers in nonlinear fashion. The first element is met by the IPAT/STIRPAT literature and also the studies that deal with the differentdeterminants of pressure on nature. The second and third elementsare fully attended to by the application of a nonlinear probabilitymodel named Ordered Logit Model (OLM). The following sectionswill present the statistical model, the variables of environmentalimpact, the potential drivers, and the sample.

2.1. The ordered logistic model: a brief statistical presentation

An important aspect to be emphasized from the beginning ofthis methodology section is that the proposed model is not sup-posed to estimate directly the environmental impact as do bothIPAT and STIRPAT. The model will estimate probabilities of impact etaking into consideration that we are proposing it to study sce-narios, the estimated probabilities will meet this requirement.

The OLM is a model generally used to estimate probability ofoutcomes that have more than two categories (where the classiclogistic model could be enough). To be specific, the OLM is appliedto situations where the ordinal rather the cardinal aspect matters.For example, a Likert scale in five categories applied to the evalu-ation of agreement on a subject: (1) strongly disagree, (2) disagree,(3) neutral, (4) agree, and (5) strongly agree. In this example, it isthe order that reallymatters and the numbers themselves do not. Inthis case, the OLM would be able to estimate the probability ofresponse for each category based on the explanatory variablesconsidered. Most importantly: it does so using a logistic function(nonlinear).

This model is based on the same scope of the classic logisticregression. The logistic function presents the characteristic that isimportant for the scenario analysis proposed in this paper: mar-ginal effects of drivers are less representative on both extremes ofthe distribution and more representative on intermediary portions.For instance, consider the hypothetical impact of population on theprobability of a collapse on the food supply. It would be reasonableto consider that the marginal impact of population growth on thisprobability is minor when there is a small population or an alreadyestablished large population, than when compared to an interme-diary population. This is the reasoning of the logistic model andalso to some extent, an underlying assumption of it.

The same applies to the OLM, although there are ordinal cate-gories rather than a dichotomous outcome variable. The model hasthe same coefficients of impact for the explanatory variables but itpresents different constants, which are cut points (or thresholdparameters) to differentiate the categories. So the odds are pro-portional throughout the categories although at different levels.According to Wooldridge (2002) the OLM can be derived from alatent variable model. Assuming a latent variable is determined asfollows:

y* ¼ xbþ e (3)

where b is a vector of coefficients of the explanatory variables x.There is no constant in this specification because there are differentcut points which will play this role e the number of cut points is(J � 1), J being the number of categories. Define the still unknowncut points (ai) as follows:

y ¼ 0 if y* � a1y ¼ 1 if a1 < y* � a2«y ¼ J if y*>aJ

(4)

Under the standard normal assumption for e,6 the conditionaldistributions of y given x can be computed for each response:

Pðy¼0jxÞ¼ Pðy*�a1jxÞ¼ Pðxbþe�a1jxÞ¼4ða1�xbÞPðy¼1jxÞ¼ Pða1<y*�a2jxÞ¼4ða2�xbÞ�4ða1�xbÞ«Pðy¼ J�1jxÞ¼ P

�aJ�1<y*�aJ

��x�¼4

�aJ �xb

��4�aJ�1�xb

�

Pðy¼ JjxÞ¼ P�y*>aJ

��x�¼1�4

�aJ �xb

�

(5)

It is possible to identify that these probabilities sum to 1.0 andalso that when there exists just one category (J ¼ 1) it turns out tobe the regular binary model. The parameters a and b are estimatedby MLE. The main specification test to be performed must guar-antee the parallel regression assumption, i.e., the assumption thatthe angular coefficients are statistically the same for all categoriesethis test is proposed by Brant (1990). In summary, the OLM willestimate the probabilities of different categories of impact ac-cording to the drivers defined. Obviously the environmental impacthas to be expressed as categories of impact rather than a contin-uous scale. The next section discusses this dependent variable aswell as the use of it for the modeling process.

2.2. Ecological footprint as a variable of environmental impact

Several studies focusing on environmental impact are based onthe measurement of the inputs of human activity into theecosystem: basically pollution of water and air. As already indicatedin this paper, the majority of the studies analyzing drivers ofenvironmental impact are concentrated on gas emissions. Thesemeasures however, do not effectively capture the transformation ofnature caused by the human incursion (York et al., 2003). Accordingto the authors, to accomplish a wider understanding of environ-mental impact it is advisable to count on more comprehensive oraggregate indicators.

A fair candidate to such an index is the Ecological Footprint (EF)by Wackernagel and Rees (1996). This measure relies on theconcept of carrying capacity. According to the “Calculation Meth-odology for the National Footprint Accounts” (Ewing et al., 2010),this measure aims to quantify the demand and supply of ecosystemgoods and services in a static scope. The demand is the EF itself asthe supply is measured by the productive biocapacity of theecosystem. The balance between the two tells if the society isexploiting the natural resources more than it is able to offer or not.

The EF is in short, a measure of the pressure of human activityand resulting demands on the environment. It can be easily un-derstood as the measure of the biologically productive area that isneeded to sustain a certain society. The Global Hectare (Gha) is thestandard unit measure considering different lands and its yield andequivalent factors: cropland, grazing, fishing, forest, built-in land,and forest for carbon sequester. Although the calculation is com-plex and data demanding, the final result is quite intuitive and alsoinformative: the higher the EF, the greater the pressure of societyon the environment.

As York et al. (2003), Wei et al. (2011) and other studies havedeveloped STIRPAT models using the EF as the variable of environ-mental impact, we too propose to base our methodology on thesame measure. However, we apply the EF per capita instead of thetotal EF generally used in STIRPAT models. Considering that themethodology estimates the probability of a certain level of impacteand not the impact itself e the per capita unit is able to better

Table 1Descriptive statistics of the explanatory variables.

Mean Standarddeviation

Minimum Maximum CV

pop_total 49,191,426 155,263,741 1,133,007 1,320,000,000 316%pop_urb_per 55.0 21.3 12.6 97.3 39%pop_15_64 62.8 6.4 48.8 72.3 10%pop_denskm 109.3 143.5 1.7 1105.9 131%gdp_pc 10543.9 16119.1 164.2 82294.2 153%gdp_noserv 46.6 13.9 22.8 80.8 30%land_agr 44.3 20.6 2.3 85.6 47%

Fonte: Elaborated by the authors. Data from World Bank repository.

E.J. de Mattos, E.E. Filippi / Environmental Modelling & Software 62 (2014) 22e32 25

translate a condition of a country in terms of pattern of environ-mental pressure taking into account its very structural characteris-tics and not specifically its size in terms of populations andproduction.

Furthermore, as pointed out by Liddle (2013), if the environ-mental impact of population are based on an elasticity equal to 1.0,then the impact variable could be used in per capita terms and thetotal population should be removed as an explanatory variable aswell. The models estimated by York et al. (2003), e.g., have foundpopulation's elasticity close to unity. In preliminary tests using ourdatabase we have found similar results as York et al. (2003): totalpopulation's elasticity of 0.96 (confidence interval of 0.91e1.00using 5% of significance). Considering these arguments, the use ofEF per capita seems to be suitable.

The EF is a continuous variable (Gha) and the OLM is a modelapplied to ordered outcomes, as previously stated. In such a case itis mandatory to convert the EF into an ordered categorical variable.This process shall be executed considering that the ordered variableobtained has to present a clear and objective ordinal aspect. Thismeans that the categories of EF could not be delimited by equi-distant cuts on the scale e if processed this way, one obtains just acategorical variable with a sense of cardinality, which is notappropriate to the model proposed here.

To handle this question we adopted a categorization based onthe quartiles of the distribution of the EF per capita of the countriescomposing the database.7 In doing this we obtained a variablecomposed of four categories with different amplitudes of EF percapita, so the order is the element that defines the new variablerather than just the size of the EF determined a priori, for example.8

The categories received an intuitive nomenclature according totheir characteristics in terms of environmental impact: Low_EF (EFper capita � 1.42), Medium-low_EF (1.42 < EF per capita �2.27),Medium-high_EF (2.27 < EF per capita� 4.39), and High_EF (EF percapita >4.39) e Appendix A contains the list of countries in eachcategory. Through these categories it was possible to assign fourordered levels of environmental impact based on the EF per capita,which will be the dependent variable for the model. The data is bythe Global Footprint Network and is for 2007 covering 128counties.9

2.3. The potential drivers of environmental impact

The EF portrays the level of pressure of societies on the envi-ronment, and this pressure comes basically from the consumptionpattern. As can be seen in Appendix A, the countries with a higherlevel of development (in the sense of the material/incomeapproach) are in general also responsible for higher levels of EF. Wealso know that the consumption is strongly associated with a seriesof characteristics of the society. These characteristics can beconsidered the drivers of environmental impact and they comefrom different dimensions present in the theoretical scope.

As already discussed in this text, the IPAT/STIRPAT models aretheoretical references for the study of the drivers of environmentalimpact. Considering that our study is particularly focused on themethodology of scenario designing, we opted for following the

7 Different methods of categorization may be applied, even considering othervariables e see, for instance, the work of McKinney (2012) which uses the differ-ence between the EF and Biocapacity to study entropic disorder.

8 The test for parallel regression can asseverate that the variable is adequate. Aswe will show later in this paper it is well constructed.

9 This was the latest data available at the time of the estimations. We have notmade use of imputation data techniques e only countries where all data wasavailable were considered. This explains why we refer to 128 countries instead ofthe roughly 200 available at Global Footprint Network.

indications of the potential drivers that have already been identi-fied in works such as York et al. (2003) and Dietz et al. (2007). Wesuggest the drivers are divided into two different categories: pop-ulation and economics. For the population set of drivers, we pro-posed the initial following variables: total population10 (pop_total);percentage of total population that lives in urban areas (pop_urb);percentage of nondependent population, i.e., population between15 and 64 years old (pop_15_64); and, demographic density interms of people per Km (pop_denskm). These variables aim to takeaccount of the population pressure on the ecosystem based on size,interaction with the environment and geographical distribution.

For the economic drivers the initial variables were selected: GDPper capita US$ (gdp_pc); percentage of GPD which does not comefrom services (gdp_noserv); and percentage of agricultural area(land_agr). As opposed to the economic pressure translated directlyby the GDP per capita, the GDP of industry and agriculture (notservices) and the agricultural area attempt to incorporate differentaspects of the economic activity as drivers of environmentalimpact.

All the explanatory variables selected are theoretically suitablefor the model, as mentioned by York et al. (2003). Technology inturn, is not present as it is not generally a component of the STIRPATmodels. However, it is interesting to observe that the EF, in somesense, does incorporate technology itself: the changes in produc-tivity of lands, for example, are sources of improvements of themeasure of footprints e remembering that yield factors are used tocompute the EF. In such a case, the population and economicdrivers are in a certain way linked to technology.

All the variables for the 128 countries of the database come fromthe World Bank repository of statistics and refer to the year 2007.Table 1 shows the descriptive statistics of each driver. Except for theindependent population (pop_15_64), the other variables present aconsiderable dispersion with higher coefficients of variation(CV ¼ standard-deviation/mean).

The correlation between the drivers is also an importantelement for investigation before using them in a regression exer-cise. Table 2 shows the correlation matrix between all variables.There are just two correlations higher than 0.50. None of the esti-mated correlations invalidate or offer preliminary statistical evi-dence about multicolinearity at this point. The next sectionpresents the estimated model, the required statistical tests, andalso examples of scenario designing.

3. Results: the model and the scenarios

The model has been estimated using adequate computationalmethods which follow all the statistical assumptions indicated in

10 This variable is suggested in the model just for sake of the validation of EF in percapita unit. It is supposed that this variable is not going to be significant as wedemonstrate later.

Table 2Correlation matrix between explanatory variables.a

(1) (2) (3) (4) (5) (6) (7)

pop_total (1) 1.0000pop_urb_per (2) �0.0803 1.0000pop_15_64 (3) 0.1189 0.5083 1.0000pop_denskm (4) 0.1766 �0.0932 0.1598 1.0000gdp_pc (5) �0.0407 0.5251 0.4095 0.0838 1.0000gdp_noserv (6) 0.0352 �0.4240 �0.4330 �0.2399 �0.5066 1.0000land_agr (7) 0.0655 �0.0744 �0.0666 0.1842 �0.1477 �0.1171 1.0000

Source: elaborated by the authors.a Pearson correlation.

Table 3Estimated Ordered Logistic Model Dependent variable: ordinal EF per capita (4 categories).

Model I Model II

Coefficients SE p-Value Coefficients SE p-Value

pop_total �0.0000 0.0000 0.384 e e e

pop_urb_per 0.2302 0.0127 0.071 0.0255 0.0124 0.041pop_15_64 0.9997 0.0439 0.023 0.0906 0.0420 0.031pop_denskm �0.0044 0.0021 0.037 �0.0043 0.0020 0.037gdp_pc 0.0003 0.0000 0.000 0.0003 0.0000 0.000gdp_noserv �0.0121 0.0171 0.477 e e e

land_agr 0.0240 0.0104 0.021 0.0244 0.0103 0.018

Cut1 7.0926 2.8628 7.4262 2.4511Cut2 9.3804 2.9710 9.6761 2.5743Cut3 12.8019 3.0514 13.0938 2.6730

N 128 128LR (Chi-sqr) 167.72 (p ¼ 0.000) 163.22 (p ¼ 0.000)Pseudo-R2 0.4642 0.4600Mean VIF/

Highest VIFa1.44/1.77 1.38/1.71

Source: estimated by the authors.a Simulating linear regression.

E.J. de Mattos, E.E. Filippi / Environmental Modelling & Software 62 (2014) 22e3226

the previous sections. We have not applied any stepwise methodbecause it is important to evaluate the significance of each driver,case by case. The next section explore the validity of the model andperformance tests.

3.1. The model and its evaluation

Having the EF per capita categorized in four levels of environ-mental impact as the dependent variable, the first estimated Or-dered Logistic Model has counted on all the seven driverspreviously selected for this exercise (Model I in Table 3). It isimportant to remember that the “cut points” in Table 3 refer to theintercept parameters for calculating the probabilities.

Two variables had coefficients not statistically significant: totalpopulation (pop_total) and percentage of GDP not from services

Table 4Brant test (Model II).

Chi2 p > Chi2a Degrees of freedom

All 6.03 0.81 10pop_urb_per 1.13 0.50 2pop_15_64 2.10 0.35 2pop_denskm 0.99 0.61 2gdp_pc 2.29 0.32 2land_agr 0.19 0.91 2

Source: results estimated by the authors.a The absence of significance guarantees the parallel regression assumption.

(gdp_noserv). The former can be fully justified by the fact that thedependent variable is per capita which means that total populationis no longer effective as an explanatory variable itself. The studieswhich present this variable as highly significant have aggregatedependent variables instead of per capita ones e we have kept thetotal population in this first specification in order to demonstratethat. Regarding the GDP not from services, however, the lack ofsignificance is probably due to iteration with the other economicvariablese York et al. (2003) found the same lack of significance forthis variable.

The model without those two drivers remained well adjusted.Model II in Table 3 shows all the dependent variables significantat p < 0.05. The estimated cut points are displayed as “Cut1”,“Cut2”, and “Cut3”. The table also shows that the Likelihood Ratiotest is highly significant and there is no evident reason forconcern over multicolinearity (VIF measures are well withinacceptable limits).

Regarding the assessment of the model's specification it is vitalto check the parallel regression assumption through the Brant test(Brant, 1990). The results of this test are presented in Table 4. As canbe seen the test asseverates that the estimated OLM does notviolate this important assumption. This is the most importantspecification test for OLM.

The measurement of performance is totally dependent on boththe specific characteristics and the objectives of the model (Bennettet al., 2013; Jakeman et al., 2006). Considering that we have amodelwhich is already tested for specification, a coupling real vs. modeled

Fig. 1. Estimated probabilities for each country separated by category.

E.J. de Mattos, E.E. Filippi / Environmental Modelling & Software 62 (2014) 22e32 27

values sounds like the better approach for visual and quantitativeinspection of performance.11

Fig.1 displays the estimated probabilities for each country in ourdatabase separated by groups. Supposing a perfect model, onewould find that the highest probabilities calculated for eachcountry should be the one representing the category in which thecountry is originally classified. For example, for the countries per-taining to the Low_EF category in our database (first block in thegraph), the probability of Low_EF would be the highest for everysingle country e so we would see the blue bars higher all over thegroup.

For our estimated model, the graph in Fig. 1 plots results that arefairly reasonable. Considering the Low_EF and High_EF groups,more than 75% of the countries present the highest estimatedprobability of being assigned to the right category. For the inter-mediate categories, thismark is 55% for Medium-Low_EF group and72% for Medium-High_EF group. These results are comfortableconsidering that we have a relatively small sample with highvariability for some drivers.

3.2. Preliminary comments on the results

The model presented in Table 3, therefore, is well adjusted andholds the statistical characteristics and properties required by theOLM. These results fulfill the second requirement we identified forscenario designing: the identification of statistically significantdrivers of environmental impact. Starting from this point we areable to explore the results with the design of scenarios inmind. As afirst step it is interesting to focus on the estimated coefficients for abrief comparison with the findings of other studies e though thereare just a few works in the relevant literature about drivers ofenvironmental impact that use the EF as the dependent variable.

The positive coefficients for urbanization (pop_urb_per) andnondependent population (pop_15_64) are corroborated by studieslike York et al. (2003) andWei (2011).12 It is worth pointing out that

11 Besides the regular statistics routine we based this performance test on theadvices of Bennett et al. (2013).12 A study by Liddle and Lung (2010) presents a model for emissions of carbondioxide and also energy consumption. The authors suggest that different age groupsoffer different directions of impact, and that older age groups exert negativeimpacts.

the impact of nondependent population on the environment isbigger than the urbanization per se e as was also found by Yorket al. (2003). York and Rosa (2012), on the other hand, found theurbanization and dependency ratio to be not significant when thedependent variables are pollutants like SO2 and CO. The recentwork of Wei (2011) suggests that differences in the estimations'results are due mainly to the differences in the specification ofSTIRPAT models.

The demographic density (pop_denskm) presented a negativeimpact e meaning the higher the population concentration, thesmaller the potential impact. York et al. (2003) found the same signfor this variable.13 This is rather a controversial result in terms ofthe literature. Ehrlich and Holdren (1971) pointed out that it is ausual mistake “… to assume that population density (people persquare mile) is the critical measure of overpopulation or under-population” (p. 1214). An important aspect that should be consid-ered is the distribution of that population in relation to naturalresources. Griffith (1981), for instance, gives us an idea as to howcomplicated this sort of variable is for planning cities e andconsequently for the environment.

Finally, GDP per capita and the percentage of the area for agri-culture are both consistently significant. GDP is without the doubtthe variable that is almost universally important as a driver ofenvironmental impact. The majority of the literature on Environ-mental Kuznets Curve as well as the studies of IPAT and STIRPATmodels recognizes that the production/income per capita is directlyconnected to environmental pressures. Given that EF is a measurethat strongly incorporates agriculture production, it is quitereasonable to understand that correlated variables (such as agri-cultural area) represent a specific pressure of human activity on theenvironment e for example, Cooper and Griffiths (1994) delineatesome analysis on the deforestation resulting from populationgrowth and its consequent increment in demand.

Since we have identified that the model is valid and that thebasic resultse significance and sign of the driverse are in line withcurrent literature it is possible to move toward the innovativeaspect of this paper, that of scenario designing based on the OLM.The next section will construct some scenarios to demonstrate themethodology proposed and explore its potential.

13 Using the inverse of density the authors have found a positive sign.

Fig. 2. Scenario of probability of environmental impact Target driver: nondependent population (all other drivers hold constant on their global means).

E.J. de Mattos, E.E. Filippi / Environmental Modelling & Software 62 (2014) 22e3228

3.3. Nonlinear scenarios of environmental impact

Through the coefficients displayed in Table 3 it is possible toestimate the probability of occurrence of each category of envi-ronmental impact given the values of the drivers (see Eq. (5)). Inother words, we are able to estimate probability for any of the fourcategories of environmental impact given the levels of drivers.Holding all other drivers constant on their global means it isfeasible to analyze the trajectory of the probability of environ-mental impact when only one of them varies. This is the core of thescenario analysis proposed in this study: assuming a ceteris paribuscondition we can vary the drivers of interest and check the

Fig. 3. Scenario of probability of environmental impact Target driver: GDP per capita (all o

probability of the environmental impact throughout the range ofthe variable. To demonstrate this procedurewe present in detail theanalysis for nondependent population (pop_15_64) and GDP percapita (gdp_pc).

In Fig. 2 four curves can be identified, each of them representingthe probability of occurrence of a specific level of environmentalimpact (category of EF) e it is important to bear in mind that at anypoint of the graph the four curves sum up to unit (100% of proba-bility). So, we can see that a probability of low environmentalimpact (Low_EF) is higher than the other categories up to a level ofapproximately 20.0% of nondependent population. On the otherextreme, the probability of high environmental impact (High_EF)

ther drivers hold constant on their global means). Source: elaborated by the authors.

Fig. 4. Scenario of probability of environmental impact Target drivers: GDP per capita and percentage of population in urban areas (all other drivers hold constant on their globalmeans).

E.J. de Mattos, E.E. Filippi / Environmental Modelling & Software 62 (2014) 22e32 29

detaches from the other categories when the nondependent pop-ulation reaches a level around 80.0%.

We can observe that at the global mean level of nondependentpopulation (62.8%), the probability of environmental impact isturning: the probability of a medium impact starts to decrease andthe probability of high impact starts to grow faster. This cantherefore be considered in some sense, a critical point for thisvariable. Ceteris paribus, if we foresee new increments in thisvariable this may result in more environmental pressure in thefuture.

Works as Liddle (2013), Jorgenson and Clark (2013), York et al.(2003), and others have already clearly demonstrated the impor-tance of demographic structure on the environmental impact.Nevertheless, a novelty that our approach brings to light is that theimpact of the pace of demographic changewill be dependent on thecurrent level of that variable in the country. Consider that virtuallyall the countries in our database are beyond 50.0% of nondependentpopulation (and more than half have are over 60.0%). Given thissituation, we are led to conclude that it would be difficult to achievean effective relief in terms of environmental pressure through thisvariable alone in the short or middle-run e even considering thataccording to the estimations of the United Nations Department of

Fig. 5. Scenario of probability of environmental impact Target drivers: GDP per capita and pmeans). Source: elaborated by the authors.

Economic and Social Affairs, the population of this age group issupposed to stabilize (or at least to grow more slowly) by 2050.

If on one hand the prognostics regarding the demographicstructure are not exactly encouraging, on the other hand it has to beconsidered that there is not much optimism about the future ofconsumption (and consequently production) levels either (see forinstance the alerts contained in the Living Planet Report (WWF,2010)). The specific impact of economic growth can be visualizedthrough the same exercise performed above. Fig. 3 depicts theestimated probabilities for the GDP per capita holding all the otherdrivers constant on their global means.

The highest category of environmental impact (High_EF) isestimated to be dominant when the GDP per capita breaks the levelof US$14.500,00 e our sample of 128 countries counts 26 that haveexceeded this limit. The results inform that a constant growth ofGDP per capita implies a direct increase on environmental pressure.Based on this result it is possible to check that the argument for theEnvironmental Kuznets Curve is not confirmed e as in the work ofYork et al. (2003). It would be necessary to eventually verify aninversion in the estimated probability of high environmental im-pacts to confirm this hypothesis. The lack of evidence of an Envi-ronmental Kuznets Curvemay be associatedwith the essence of the

ercentage of nondependent population (all other drivers hold constant on their global

Countries by category of Ecological Footprint per capita.

Low_EF (PE � 1.42) Medium-low_EF(1.42 < PE � 2.27)

Medium-high_EF(2.27 < PE � 4.39)

High_EF(PE > 4.39)

Afghanistan Albania Argentina AustraliaAngola Algeria Belarus AustriaBangladesh Armenia Bolivia BelgiumCambodia Azerbaijan Bosnia and

HerzegovinaCanada

Cameroon Chad Botswana Czech RepublicCentral African Rep. China Brazil DenmarkCongo Colombia Bulgaria EstoniaCongo, Dem. Rep. Dominican Rep. Chile FinlandCote d'Ivoire Ecuador Costa Rica FranceEritrea Egypt Croatia GermanyEthiopia El Salvador Gambia IrelandGabon Georgia Hungary ItalyIndia Ghana Iran, Islamic

Republic ofJapan

Indonesia Guatemala Lebanon KazakhstanKenya Guinea Libyan Arab

JamahiriyaKorea, Rep. of

Kyrgyzstan Honduras Mauritania LatviaLao People's

Dem. Rep.Jamaica Mauritius Lithuania

Lesotho Jordan Mexico Macedonia TFYRLiberia Madagascar Nepal MalaysiaMalawi Mali Panama MongoliaMoldova Namibia Paraguay NetherlandsMorocco Nicaragua Poland NorwayMozambique Nigeria Romania PortugalPakistan Papua New

GuineaSerbia Russian

FederationPhilippines Peru Slovakia Saudi ArabiaRwanda Sudan South Africa SloveniaSenegal Swaziland Thailand SpainSierra Leone Syrian Arab

RepublicTrinidad andTobago

Sweden

Sri Lanka Tunisia Turkey SwitzerlandTajikistan Uganda Turkmenistan United KingdomTanzania,

United Rep.Uzbekistan Ukraine USA

Viet Nam Venezuela,Boliv. Rep.

Uruguay

Zambia

Source: elaborated by the authors based on data of the Ecological Footprint.

E.J. de Mattos, E.E. Filippi / Environmental Modelling & Software 62 (2014) 22e3230

environmental variable that is absolutely different from emissionsof greenhouse gases, for instance.

It is also important to consider that higher levels of GDP percapita are present in countries that are, for the most part, devel-oped e Sweden, Japan, Italy, USA, Germany, France, among others.All these nations register a high ecological footprint on earthbasically because of their consumption pattern. In such cases it isfeasible to comprehend that since other countries struggle forhigher levels of economic performance the impact on the ecosys-tems could be worsened e in our model this conclusion is illus-trated by the increasing probability of high EF.

Because of lack of space in this paper for a detailed analysis ofthe three other drivers, we have placed the graphs for these sce-narios in Appendix B e all of them preserve the same logic appliedto the previous one. An interesting additional resource that mightemerge from the methodology developed in this study is the pos-sibility of dealing with a scenario where two drivers can be visu-alized at the same time. Fig. 4 displays a graph that illustrates ascenario where the percentage of population in urban areas(pop_urb_per) and the GDP per capita (gdp_pc) are varying at thesame time e all other drivers hold constant on their global meansas usual.

As we are plotting a 3D graph it would not be appropriate tohave one surface for each category. So we only plotted a surface forthe probability of the highest level of environmental impact(High_EF). Since both drivers are positive, what can be seen is asurface that demonstrates an increasing probability of high envi-ronmental impact as both variables increase. The interesting part ofthis scenario, however, is an observation of the shape of the surfacethat illustrates the combined impact of the drivers on the proba-bility of High_EF: if urbanization is maintained at a low level(around 10.0%), even considering a higher GDP per capita theprobability does not exceed 60.0%. But when urbanization is pairedwith economic growth, the probability of the highest category ofenvironmental impact crosses the 90.0% mark.

In Fig. 5 it is possible to analyze a different scenario, nowcombining the GDP per capita and the nondependent populationshare. As we have already stated, this share of population is likely tostop growing at the same pace we observe nowadays. So, whatwould be the impact if the increments in GDP per capita keepgrowing despite the stabilization of the working age populationshare?

According to the estimations presented in Fig. 5, the answer tothat question indicates that we still have a considerably rapidgrowing process in the probability of High_EF. Nevertheless, if weallow for higher levels of nondependent population, the incrementin the estimated probability is even faster.

Therefore, the analytical scheme offered by this nonlinearprobability model widens the understanding of environmentalimpact. If one put the graphic aside, it is possible to design sce-narios with all the drivers varying at the same time. That versatilitycould be considered the central contribution of the methodologypresented in this paper.

4. Conclusions

The main focus of our methodology is a nonlinear probabilitymodel that tackles the limitation of static elasticity measures byconsidering the level of all the explanatory variables at once. TheOrdered Logistic Model estimates the probability of categories ofenvironmental impact. Although the results represent the proba-bility of impact rather than impacts themselves, they do providesome insight into what to expect in terms of pressure on nature if

the driver is increasing or decreasing.An important aspect of the proposed methodology is that it

makes possible to analyze the shapes of the probabilities for eachdriver individually. This is interesting, for instance, to identify thefeasibility of a faster growth of GDP per capita and still remainwitha low probability of high environmental impact e which could bethe case of some countries at initial stage of development and witha favorable combination of the other drivers.

If the regular STIRPAT models generally present a constantelasticity for each driver, the most significant aspect of the meth-odology presented in our study is that it offers nonlinear analysis ofall drivers together. We have illustrated this feature presentingsome scenarios for a couple of variables. The analysis performed bythe OLM is wider in the sense that it enables the comprehension ofa new dimension for environmental impact: prognostics in a fullynonlinear structure. However, the absence of an estimation of thedirect impact may require the combination of this methodologywith the previous one (IPAT/STIRPAT).

Appendix A

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Appendix B

Fig. 7. Scenario of probability of environmental impact. Population density (pop_denskm) (all other drivers hold constant on their global means). Source: elaborated by the authors.

Fig. 6. Scenario of probability of environmental impact. Percentage of population in urban areas (pop_urb_per) (all other drivers hold constant on their global means). Source:elaborated by the authors.

Fig. 8. Scenario of probability of environmental impact. Population density (pop_denskm) (all other drivers hold constant on their global means). Source: elaborated by the authors.

E.J. de Mattos, E.E. Filippi / Environmental Modelling & Software 62 (2014) 22e3232

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