Environmental Reviews. Cause-effect analysis for sustainable development policy

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1 Envronmental Revews Cause-effect analyss for sustanable development polcy Journal: Envronmental Revews Manuscrpt ID er r2 Manuscrpt Type: Revew Date Submtted by the Author: 24-Feb-2017 Complete Lst of Authors: Cucurach, Stefano; Unversty of Calforna, Santa Barbara, Bren School of Envronmental Scence & Management Suh, Sangwon; Unversty of Calforna, Santa Barbara, Bren School of Envronmental Scence & Management Keyword: Sustanable Development Goals, Causalty, Cause-effect mechansms, Quanttatve Sustanablty Assessment, Sustanablty polcy

2 Page 1 of 82 Envronmental Revews Cause-effect analyss for sustanable development polcy Stefano Cucurach a, Sangwon Suh a,* a Bren School of Envronmental Scence and Management, Unversty of Calforna, Santa Barbara, Calforna 93106, Unted States * correspondng author: e-mal: phone: (805) , fax: (805) Word count:

3 Envronmental Revews Page 2 of Abstract The sustanable development goals (SDGs) launched by the Unted Natons (UN) set a new drecton for development coverng the envronmental, economc and socal pllars. Gven the complex and nterdependent nature of the soco-economc and envronmental systems, however, understandng the cause-effect relatonshps between polcy actons and ther outcomes on SDGs remans as a challenge. We provde a systematc revew of cause-effect analyss lterature n the context of quanttatve sustanablty assessment. The cause-effect analyss lterature n both socal and natural scences has sgnfcantly ganed ts breadth and depth, and some of the poneerng applcatons have begun to address sustanablty challenges. We focus on randomzed experment studes, natural experments, observatonal studes, and tme-seres methods, and the applcablty of these approaches to quanttatve sustanablty assessment 17 wth respect to the plausblty of the assumptons, lmtatons and the data requrements. Despte the promsng developments, however, we fnd that quantfyng the sustanablty consequences of a polcy acton, and provdng unequvocal polcy recommendatons s stll a challenge. We recognze some of the key data requrements and assumptons necessary to desgn formal experments as the bottleneck for conductng scentfcally defensble cause-effect analyss n the context of quanttatve sustanablty assessment. Our study calls for the need of mult-dscplnary effort to develop an operatonal framework for quantfyng the sustanablty consequences of polcy actons. In the meantme, contnued efforts need to be made to advance other modelng platforms such as mechanstc models and smulaton tools. We hghlghted the mportance of understandng and properly communcatng the uncertantes assocated wth such models, regular montorng and feedback on the consequences of polcy actons to the modelers and decson-makers, and the use of what-f scenaros n the absence of well-formulated cause-effect analyss. 2

4 Page 3 of 82 Envronmental Revews Keywords Sustanable development goals; causalty; cause-effect mechansms; quanttatve sustanablty assessment; sustanablty polcy 3

5 Envronmental Revews Page 4 of Introducton The Sustanable Development Goals (SDGs, hereafter) launched on January 1, 2016 nclude 17 goals, 169 targets and 303 ndcators (Unted Natons 2014, Malk et al. 2015), whch wll help frame the agendas and polces of the Unted Natons member states through 2030 (Hák et al. 2016). These goals are not only comprehensve, coverng the economc, socal and envronmental dmensons of sustanablty, but also hghly nterconnected (Internatonal Councl for Scence 2015), makng t essental to understand synerges, trade-offs and conflcts between them n order to support decsons (Schndler and Hlborn 2015). Wthout such understandng, a polcy to mprove on one goal could conflct wth another goal. For example, polces targetng at mprovng energy provson could conflct wth another goal on clmatechange mtgaton, or those amng at the protecton of marne ecosystem could clash wth the provson 42 of sustanable food for all (Laurent and Snha 2015) Varous tools and metrcs have supported sustanable development decsons, whch we collectvely refer to quanttatve sustanablty assessments (QSAs) n ths revew. Examples of QSAs nclude, but not lmted to, lfe cycle assessment (LCA) (Gunée 2002, ISO 2006, Hellweg and Mla Canals 2014), varous footprntng approaches (Wedmann and Mnx 2007, Peters 2010, Hoekstra and Mekonnen 2012, Mancn et al. 2015, Mchalsky and Hooda 2015), assessment of planetary boundares (Rockström et al. 2009, Hughes et al. 2013, Whteman et al. 2013, Steffen and Rchardson 2015), envronmental nputoutput models (Huppes et al. 2006, Tukker et al. 2006, Suh 2009, Hertwch 2010, Lenzen et al. 2012, Hertwch et al. 2014), ecosystem valuaton approaches (Groot et al. 2010, Costanza et al. 2014), and materal flow analyss (MFA) (Matthews et al. 2000, Brunner and Rechberger 2004, Haberl et al. 2007, Fscher-Kowalsk and Swllng 2011), among others [see e.g. (Ness et al. 2007)]. In partcular, so called, consequental LCA (CLCA) ams at quantfyng the consequences that a certan acton or a polcy decson has on the envronment and natural resources (Brander et al. 2008, Creutzg et al. 2012, Zamagn et al. 2012, Plevn and Delucch 2014, Suh and Yang 2014). 4

6 Page 5 of 82 Envronmental Revews The complexty and the nterconnected nature of the soco-economc and envronmental systems, however, poses a challenge to QSA practtoners n modelng the consequences of a polcy acton n the context of sustanable development (Cucurach and Suh 2015). Furthermore, recent developments n economcs, ecosystem scence, and systems bology on causalty research have yet to be embraced by QSA approaches. 1 Over the past decades, the causalty lterature has evolved to address varous conceptual and techncal ssues such as endogenety (Antonaks et al. 2014, Kreuzer 2016) and reverse causalty [see e.g. (Me-chu 1987, Chong and Calderon 2000, Barsky and Klan 2004, Chaumont et al. 2012)] n parsng out causal relatonshps from complex phenomena. For example, Angrst and Krueger (1992) test the effect of chldren s age when startng school on ther eventual years of schoolng completed and on educatonal attanment. Usng nstrumental varables, the authors conclude that the effect of the startng age on educatonal attanment s modest. Instrumental varables have also been used to test the effects of educaton on health (Cutler et al. 2008, Grossman 2008, Cont et al. 2010, Cutler and Lleras-Muney 2010, Heckman et al. 2014), educaton on well-beng (Oreopoulos and Salvanes 2011, Oreopoulos and Petronjevc 2013), and socal connectons on well-beng (Kahneman and Krueger 2006, Fowler et al. 2008). However, few of such technques have been appled to QSAs. Ths revew ams at surveyng the technques of cause-effect analyss n the context of QSAs. For each method to nfer causalty (cause-effect analyss technque n the remander of the text), we present and revew relevant applcatons n the feld of sustanablty that show how cause-effect analyss technques can allow QSAs to ncrease the value of nformaton they provde to decson makers. Our survey of 1 For example, Wenzettel et al. (2013) use mult-lnear regresson and concluded that affluence drves the global dsplacement of land use, thus beng the man cause of bodversty loss globally. The study does provde a strong correlaton between affluence and bodversty loss but does not unvocally allow nterpretaton of the results as a causal relatonshp. Lkewse, Suwes et al. (2013, 2015) use a stochastc logstc model to assess whether the populaton growth of a naton s drven (.e. caused) by ether local avalablty of water resources used or by mport of water resources from neghborng countres. As acknowledged by the authors, both studes do not consder a number of other envronmental, cultural, and health-related factors, thus lmtng the nterpretablty of the result as a causal relatonshp. Some of these problems have been wdely dscussed and well understood n the causalty lterature (Aldrch, 1995; Rmer, 1998; Smon and Iwasak, 1988). 5

7 Envronmental Revews Page 6 of causalty lterature was drawn from peer-revewed artcles on theory and methods, causalty handbooks, and case studes applyng the technques. Based on the lterature surveyed, we classfy the analytcal approaches to cause-effect analyss technques. Each class of technques was, n turn, searched on the ISI Web of Scence and on Google Scholar n combnaton wth the keywords sustan*, envron*, emssons, pollut*, econ*, CO2, and GDP. The remander of the revew s organzed as follows: the next secton presents a short chronology of causalty theory; n secton 3, we start from the deal approach to causalty provded by Rubn s causal model, and then we analyze the technques that are based on observatonal (.e. non-expermental) data; n secton 4 we dscuss the applcablty of cause-effect analyss technques to QSA; fnally secton 5 dscusses outlook to close ths revew A bref chronology Causalty has nterested phlosophers and scentsts snce the tme of Arstotle (see Physcs II 3 and Metaphyscs V 2). For mllenna, however, causal problems have often rested n the realm of phlosophcal delght rather than nsprng scentfc research. Pearl (2000a) notes that the questons on causalty dd not enter nto formal scentfc dscourses for a good part of the 19 th century. In the dawn of the 20 th century, Hume (1902 sec. VII) formally defned a cause as an object followed by another, and where all the objects, smlar to the frst, are followed by objects smlar to the second. Or, specfcally, where, f the frst object had not been, the second never had exsted. A smlar dea of cause was also at the bass of the expermental work of Mll (1856). However, Russel (1912) stated that causal relatonshps and physcal equatons are ncompatble, descrbng causalty as a word relc and excludng the exstence of causalty from mathematcs and physcs. In 1911, Pearson stll descrbed causalty as another fetsh amdst the nscrutable arcana of even modern scence (Pearson 1911). Interestngly, a mechanstc vew of causalty also exsted n the early 20 th century phlosophy. For example, Laplace thought that cause and effect can be understood perfectly gven enough knowledge and data: We may regard the present state of the unverse as the effect of the past and 6

8 Page 7 of 82 Envronmental Revews the cause of the future. An ntellect whch at any gven moment knew all of the forces that anmate nature and the mutual postons of the bengs that compose t, f ths ntellect were vast enough to submt the data to analyss, could condense nto a sngle formula the movement of the greatest bodes of the unverse and that of the lghtest atom; for such an ntellect nothng could be uncertan and the future just lke the past would be present before ts eyes (Laplace 1902). In the 1950s, further formalzatons of probablstc causalty appeared n the phlosophcal lterature (Salmon 1980). Good (1963) and Suppes (1970) attempted to dentfy the tendency of an event to cause another by (1) constructng causal relatons on the bass of probablstc relatons between events, (2) employng the statstcal relevance as the basc concept, and (3) assumng temporal precedence of causes [see Russo and Wllamson (2007) for a detaled account of probablstc causalty and of assumptons and 110 axoms]. Probablstc causalty places emphass upon the mechansms of causalty, prmarly uses concepts of process and nteracton, and appeals to laws of nature (Russo 2009). In the 70s causalty stll remaned as one of the most mportant, most subtle, and most neglected of all the problems of Statstc (Dawd 1979). It s only wth the poneerng work of Rubn on a formal potental outcome/counterfactual analyss (Rubn 1974) that the statstcal lterature reconnects wth causalty and establshes a statstcal defnton of causalty. The work of Rubn gave momentum to the development and applcaton of statstcal models, or cause-effect analyss technques, whch n the last decades have expanded nto varous applcatons ncludng the foundatonal statstcal prncples set n the early work of Wrght (1921) n the feld of genetcs. 3 Approaches to causalty research 3.1 Correlaton studes and ther lmtatons Cause-effect analyss technques presented n ths revew enable answerng three types of causal questons: (1) dentfyng causes (.e. why a sngular event occurs), (2) assessng effects (.e. the what-f type of queston, referred to the change n effect of some change n the cause), and (3) descrbng 7

9 Envronmental Revews Page 8 of mechansms [.e. how some effects follow from a certan cause (Holland 2003)]. Before we begn the revew of the manstream approaches to causalty research, here we provde a bref dscusson on correlaton studes. As ponted out by many n the lterature (Pearl 2000b), correlaton and causaton should not be confused. Postve correlaton may be defned probablstcally for two varables, X and Y, as follows: (1) P( Y X) P( Y) P( X) > 0, meanng that the probablty that X andy occur jontly s larger than the product of probabltes for each occurrng ndependently. Smlarly, negatve correlaton, can be defned as: (2) P( Y X) P( Y) P( X) < 0, 133 and the two varables, X andy are uncorrelated f: 134 (3) P( Y X) = P( Y) P( X) Correlaton typcally ndcates that whenever X occurs, there s a hgher chance of observngy. A well- known example s that homelessness and crme rate are correlated, however, mere correlatons do not provde a scentfc evdence of whether homelessness causes crme, or that crme causes homelessness (Sughara et al. 2012). The underlyng cause could be another varable (e.g. unemployment) that may nfluence both. 3.2 Randomzed experment Statstcal dfferences n the outcomes of expermental studes Expermental randomzed studes, n contrast to correlaton studes, provde an deal means to nferrng causalty (Angrst and Pschke 2008). In randomzed experments, ndvduals (or unts) taken from a suffcently large populaton are dvded nto two subgroups: one n whch ndvduals receve a treatment (treatment group), and one n whch 8

10 Page 9 of 82 Envronmental Revews ndvduals do not receve a treatment (control group). Let us consder the case, n whch a large number of smlar ctes are randomly dvded nto two groups. One group enforces a road space ratonng and the other does not. We can defne { 0,1} T =, for all 1,..., = N, as a bnary random varable descrbng the treatment (e.g., enforcng a road space ratonng or not enforcng a road space ratonng). Let us defne Y as the varable to be explaned, or response varable, such as the urban ar qualty. 151 The observed outcome for an ndvdual, Y, can be wrtten as: 152 (4) Y1 f T = 1 Y = Y0 f T = 0 = Y + Y Y T. ( ) In order for equaton (4) to hold, Rubn (1978, 1980) defnes the so-called stable-unt-treatment-value assumpton (SUTVA). The assumpton mples that a causal effect of one treatment relatve to another for a partcular expermental unt s the dfference between the result f the unt had been exposed to the frst treatment and the result f, nstead, the unt had been exposed to the second treatment (Rubn 1978). SUTVA rests on the dea that the potental outcome of one partcpant s not affected by the treatment appled to another partcpant. For example, one cty nsttutonalzng a road space ratonng polcy does not affect another cty n the experment. Furthermore, t assumes that for each unt there s a sngle verson of each treatment level (.e. only one type of road space ratonng of equal effcacy s used by all ctes under study). The assumpton ntroduced by Rubn (1980) holds f the value of Y for any ndvdual exposed to a treatment T wll be the same no matter what mechansm s used for the assgnment of T to for all ndvdual partcpants and treatments (Rubn 1986) so that: (5) Y( T T T ) = Y( T),,...,. 1 2 n The assumpton s volated f multple versons of the treatments or nterferences (e.g. communcaton) between ndvdual partcpants exst (Rubn 1986). The plausblty of the assumpton has been subject 9

11 Envronmental Revews Page 10 of matter of a number of publcatons [we refer the reader to e.g. Sobel (2006) for more nformaton on the ssue]. It s, however, notable that ths assumpton s hardly plausble n a polcy context, where a polcy nstrument s often modfed or customzed to the local or regonal crcumstances and polcy outcomes are often benchmarked or publczed wdely, drectly or ndrectly affectng others n the experment. We wll come back on ths ssue later n ths revew In the notaton ntroduced n equaton (4), Y 0 s the potental outcome for an ndvdual (e.g., ar qualty ndex, AQI for cty ) had the ndvdual not been exposed to the treatment (e.g., road space ratonng), regardless of whether the ndvdual s actually exposed to the treatment or not; whereas Y 1 s the potental outcome had the ndvdual been exposed to the treatment. In general, Y1 Y0 represents the 176 causal effect of T ony at the ndvdual level. However, t s not possble to observe both potental outcomes smultaneously from any gven ndvdual (e.g., a partcular cty), snce an ndvdual s ether exposed to treatment or control, not to both at the same tme. Therefore, the aggregate causal effects and, n partcular, the average causal effect (.e. the average effect n the general populaton) s observed nstead n realty. The observed dfference n average outcome (e.g., AQI) between the treatment group (e.g., ctes enforcng road space ratonng) and control (e.g., those not) can be expressed as E Y T = 1 E Y T = 0. For example, f the average AQI of the ctes that exercse road space ratonng s 5 and that for those not s 2 usng a 1-to-10 qualty scale (least to most severe polluton), the observed dfference n average outcome becomes 3, whch can be nterpreted as a worsenng effect. However, road space ratonng s lkely to be ntroduced to the ctes wth heavy traffc and ar polluton n the frst place, and therefore the observed dfference n the AQI between the two groups cannot be drectly translated nto the causal effect of a road space ratonng. Ths problem, referred to as selecton bas, s elaborated further n the next secton. 10

12 Page 11 of 82 Envronmental Revews Rubn s causal model The expected outcome of a group of ndvduals who were not exposed to the treatment can be expressed as E Y0 T = 0. Usng the same example, ths term shows the AQI of the ctes that dd not use road space ratonng. The expected outcome for group of ndvduals that were exposed to the treatment, had the group not exposed to the treatment can be expressed as E Y0 T = 1. For example, ths term would show the average severty of ar polluton measured n AQI of those ctes that exercse road space ratonng, f they had not taken such a measure. Suppose that a group of ctes have been usng road space ratonng. Suppose, further, that one can reverse the tme and let the same group avod usng road space ratonng. If ths were possble, E Y0 T = 1 would be the current average AQI of these ctes after reversng the tme. However, ths term s obvously not measureable. If t were measurable and f the 200 treatment s ndependent of potental outcomes (.e. wth T randomly assgned), the causal effect of the 201 treatment, E Y1 T = 1 E Y0 T = 1, can be wrtten as: 202 E Y T = 1 E Y T = 1 = E Y T = 1 E Y T = 0 E Y T = 1 + E Y T = (6) average treatment effect on the treated observed dfference n response selecton bas The term, E Y1 T = 1 E Y0 T = 1 represents the average causal effect of treatment for those who were treated (e.g., the dfference n AQI as a result of usng road space ratonng). The term 205 E Y T = 1 + E Y T = represents the selecton bas (Angrst and Pschke 2008) that represents the fact that those who need treatment are more lkely to seek treatment. For example, suppose that the average AQI of the ctes that actually used road space ratonng f they had not ntroduced road space ratonng s 8, and that of those that dd not s 2. In ths case, the selecton bas becomes 8 2 = 6, and therefore the rght-hand-sde of the equaton becomes 3 6= 3, meanng that the average road space ratonng AQI mproved on average by 3. 11

13 Envronmental Revews Page 12 of However, as noted earler the term, E Y0 T = 1 cannot be drectly observed or calculated. Therefore, one would have to fnd a counterfactual for ths term n order to estmate the causal effect of the treatment n eq. (6) (Angrst and Pschke 2008). Ths can be obtaned by the random assgnment of. Under the Rubn s causal model, the problem of spurous correlatons dscussed n the prevous secton can only be elmnated by usng randomzaton of observatons to the categores of a hypotheszed causal factor (e.g., treatment vs. control) or by usng a method that somehow mmcs randomzaton process [(Morgan 2013); see secton 3.3.1]. Randomzaton reduces the chance of ntentonal or unntentonal bas, and t allows for effects and errors due to unaccounted-for varables to act randomly, rather than consstently, affectng the response across treatments (Shaffer and Johnson 2008) For example, random assgnment, or randomzng can be acheved by choosng the treatment and control groups wth statstcally equvalent level of AQIs. Random assgnment makes the treatment T 222 ndependent of potental outcomes. In partcular, T s ndependent ofy 0, thus allowng us to swap the 223 terms E Y0 T = 1 and E Y0 T = 0 n the followng expresson: E Y T = 1 E Y T = 0 (7) = E Y1 T = 1 E Y0 T = 0 = E Y T = 1 E Y T = Gven random assgnment, Eq. (7) can be further reduced to: 226 (8) E Y T = 1 E Y T = = E Y1 Y0 T = 1 [ Y ] = E Y The relatonshp dentfed n eq.(8) contans no selecton bas, thus sgnfyng, for example, that whether each ndvdual cty n the populaton under study has nsttuted a road space ratonng polcy or not, t 12

14 Page 13 of 82 Envronmental Revews does not affect the dentfcaton of the causal effect. The effect of a randomly-assgned road polcy on the cty that mplemented t s, n fact, the same as the effect of the road polcy on a randomly chosen cty. 3.3 Observatonal studes For a whle, much of the causalty lterature, n partcular n the epdemologcal, psychologcal and educatonal scences (Campbell and Erlebacher 1970), has mpled that only properly randomzed experments could lead to useful and trustable estmates of causal effects. However, as Rubn states (1974), such contenton would be untenable f taken as applcable to all felds of scence, gven that much of the scentfc development has been obtaned for a bg part of the past century wthout usng randomzed experments. The statement stll holds today, snce randomzed experments are only feasble under certan condtons, and would probably be counter-productve n those contexts n whch observatonal data s not mmedately avalable. 2 Conceptually, there are two major crtcsms to Rubn s model. Frst, as dscussed earler, t s mpossble 241 to detect the ndvdual causal effect, Y1 Y0, thus makng the true causal effect mpossble to detect (Russo et al. 2011). Puttng ths nto a practcal context, the same person (or cty) cannot smultaneously take and not take a pankller (or nsttute a polcy) to observe the effect. In some cases, experments can be done for the same unt over tme. Second, Rubn s model s confned to a Platonc heaven stuaton, n whch one can observe only average representatons, rather than drect causal effects (Dawd 2007, p. 510). At a more practcal level, Rubn (1974) also noted that randomzed studes cannot be wdely appled when: (a) the cost of performng the equvalent randomzed experment to test for all potental alternatves (or treatments) s prohbtve; (b) there s a presence of ethcal reasons accordng to whch the treatments 2 In ther satre, Smth and Pell (2003) pont out that the effectveness of parachutes has never been proven usng a randomzed control tral. 13

15 Envronmental Revews Page 14 of cannot randomly assgned; or (c) the estmates based on the results from experment ndcate that t would requre several years to be completed (Rubn, 1974). For these reasons, researchers rely on observatonal data,.e. data that were not generated usng an expermental desgn. Observatonal data are obtaned from surveys, longtudnal and panel data, censuses, and admnstratve records, and can vary both temporally and spatally (Chrstman 2008). Observatonal data are typcally nexpensve to collect and are n plentful supply (Iacus et al. 2012). Investgators usng observatonal data (.e. from observatonal studes) share the common objectve of devsng causal relatons and, thus, face smlar problems to expermenters (Cochran 2009). Complex nteractons are also present n observatonal studes and can greatly complcate the nterpretaton of effects, although they reflect the nherent complexty of natural systems (Shaffer and Johnson 2008) Matchng methods and quas-expermental desgns In the absence of a randomzed experment and when only observatonal data s avalable, cluster analyss technques such as matchng (Stuart 2010) allow for harnessng the benefts of Rubn s model by equatng (or balancng ) the dstrbuton of covarates n the treatment and control groups. Well-matched organzed samples of the treatment and control groups can acheve such goal. The methods am to replcate as closely as possble a randomzed experment, by prunng the observatonal dataset and makng sure that the emprcal dstrbutons of covarates are smlar (Ho et al. 2006, Stuart 2010). Treatment and control unts are pared based on a number of observable pre-treatment covarates (.e. observable characterstcs). The ndvduals n a group are pared solely for the purpose of obtanng the best possble estmate of the effect of a causal varable T on an observed outcomey. Usng matchng, dfferences n outcomes for unts wth dfferent treatment levels but the same values for pre-treatment varables can be nterpreted causally (Yang et al. 2015). For example, matchng could be based on the probablty of T for each 273 ndvdual n the populaton, calculated as a functon of Q k, wth k = 1,..., V, whch represent the set of 14

16 Page 15 of 82 Envronmental Revews background varables of nterest, that s assumed to predct botht and Y (Morgan and Hardng 2006). The matchng procedure wll select only matched sets of treatment and control cases that contan equvalent values for these predcted probabltes (Morgan and Hardng 2006). The matchng algorthm allows selectng from the jont dstrbuton of Qk andy only the nformaton that s related to the causal varable (or treatment varable) T, and the procedure s conducted untl the dstrbuton ofq k s equvalent for both the treatment and control cases, thus untl the data are balanced, or matched (Morgan and Hardng 2006). Matchng methods do not drectly allow for makng causal nferences, snce they are data-processng algorthms not statstcal estmators, thus they requre the use of some type of causal estmator to make 283 such nferences [e.g. testng the dfference n means between Y n the treatment and control groups; see (Iacus et al. 2012)]. As Stuart (2010) ponts out, after the analyst has created treatment and control groups wth adequate balance, and desgned the observatonal study, the analyss moves to the outcome nterpretaton stage. At ths stage, the analyss wll typcally be lmted to technques of regresson adjustment usng matched samples and use regresson-based technques n combnaton wth the matched samples. Matchng methods, n fact, are best used n combnaton wth regresson models (see secton 3.3.2), nstrumental varables models, or structural equaton models [SEM (Ho et al. 2006)]. Matchng technques have been wdely used n economcs (Abade and Imbens 2006), medcne (Chrstaks and Iwashyna 2003), and socology (Morgan and Hardng 2006), among other felds of scence [see also (Sekhon 2011)]. Commonly used matchng methods nclude dfference-n-dfferences matchng (Abade 2005), multvarate matchng based on the Mahalanobs dstance metrc (Cochran et al. 1973), nearest neghbor matchng (Rubn 1973), propensty score matchng (Calendo and Kopeng 2008), genetc matchng (Damond and Sekhon 2012), and coarsened exact matchng (Iacus et al. 2012) [see (Stuart and Rubn 2008) for a revew]. Quas-expermental desgns usng the treatment and control 15

17 Envronmental Revews Page 16 of dualty also nclude dfference n dfferences technques used wth longtudnal data, for whch we refer the reader to (Abade 2005, Athey and Imbens 2006, Donald and Lang 2007, Puhan 2012). Observatonal studes become relevant f performed on all causally-mportant varables and on several control groups that are each representatve of a potentally dfferent bas (Rubn 1974). Observatonal studes do requre the analyst to carefully study the process of data generaton and the treatment/assgnment mechansm (Iacus et al. 2012). In observatonal studes wthout randomzaton the analyst uses the desgn phase to help wth approxmatng hypothetcal randomzed experments. The socalled dentfcaton strategy descrbes the manner n whch a researcher uses observatonal data not generated by a randomzed tral to approxmate a real experment (Angrst and Pschke 2008). The use of an observatonal study allows estmatng the average effect on the treated (or ATT) and the average 307 treatment effect (or ATE), based on data avalablty (Stuart 2010) Regresson-based causalty SEM have become a core method for assessng causalty n the socal scences, especally for research questons that cannot be tackled by expermental testng (Pearl 2009). The varables of nterest for causal research are for ths reason also called latent varables, because of ther naccessblty through drect measurement wthout a substantal measurement error (Bollen 2002). In many cases, t s mpossble or too expensve to conduct controlled experments, but SEM allows for dscovery of lkely causal relatons from observatonal data (Shmzu et al. 2006). SEM can also be combned wth graphcal constructs that allow layng out the causal relatonshps under analyss pctorally. A partcular knd of graph used n causal analyss s the drected acyclc graph (DAG) or Bayesan network (Pearl 1995, Morgan 2013). DAGs are vsual representatons of qualtatve causal assumptons and can be related to probablty dstrbutons lnked to the data under study and to causal frameworks. 16

18 Page 17 of 82 Envronmental Revews Causal models are usually characterzed by the presence of a set of explanatory varables or covarates X (.e. the putatve causes) and a response varable Y (.e. the putatve effect) n the form, for nstance, of a smple structural equaton: 323 (9) Y = β X + ε, whereβ s the causal effect on Y for a one unt dfference n X, representng the coeffcent determnng the extent of the nfluence of X ony, and ε represents the errors, unmeasured factors, or all other nfluences on Y The nterpretaton ofε andβ s not trval. Error terms may be nterpreted determnstcally or epstemcally (Russo 2009). In the frst case, we may assume that errors represent the lack of knowledge 329 of the analyst. Thus f complete knowledge would be n hand, a precse relatonshp, between X andy, could be determned wthout error. The SEM reports determnstc causal relatons. In the epstemc acceptaton of the concept, the SEM represents causal relatons that are thought to be genunely ndetermnstc, thus errors are to be modelled probablstcally (Russo 2009). Ths second acceptaton s the one we hold n ths revew. The parameter β has n the context of SEM a causal nterpretaton, thus t should quantfy the extent of the causalty. Thus, we can defne (Russo 2009): X (10) β= r σ. σ Y 337 The correlaton coeffcent r can be calculated as the rato between the covaranceσ and the varances XY σ X andσ Y : σ σ σ XY (11) r=. X Y 17

19 Envronmental Revews Page 18 of Smlarly, we may proceed and calculate all β s and δ s n the SEM. 341 Let us now consder the example below representng a generc bvarate regresson equaton: 342 (12) Y = α + β X + ε where s the ntercept and s the error term. In a causal nterpretaton of Eq. (12)β represents the structural causal effect that apples to all members of the populaton of nterest. Thus, n addton to beng lnear, ths equaton says that the functonal relatonshp of nterest s the same for all members of the populaton. Logarthmc transformatons or other functonal transformatons of the varables of nterest n the model can be typcally consdered (Baocch 2012). The ordnary least squares estmator of the bvarate regresson coeffcentβ s then (Morgan and Wnshp 2007): 349 X (13) β =. OLS σ Y σ X The above s just an example of the applcaton of regresson technques for the estmaton of the regressors of nterest. Regresson technques provde a good estmaton of the causal parameters, f the error terms n SEM are uncorrelated wth the regressor (see assumptons n secton 4.1). The coeffcent of determnaton r 2 may be used to evaluate the goodness of ft of the model. Example of regresson technques nclude least squares and partal least squares technques (Wold 1982, Angrst and Imbens 1995, Tenenhaus et al. 2005, Esposto Vnz et al. 2010). In the next secton we focus on the causal nterpretaton of regresson technques and on the nstrumental varable approach. Further applcatons of regresson-based technques nclude regresson-dscontnuty desgns, for whch we refer the reader to (Hahn et al. 2001, Imbens and Lemeux 2008, Lee and Lemeux 2010) Causal nterpretaton of regressons We focus on ths secton on the causal nterpretaton of regressons as estmators of causalty. We refer the reader to (Berk 2004, Gelman and Hll 2006, Morgan and Wnshp 2007, Angrst and Pschke 2008, 18

20 Page 19 of 82 Envronmental Revews Freedman 2009, Hansen 2015) for a complete presentaton of regresson technques and for a complete analyss of the lmtatons of such approaches. Regressons do not necessarly hold a causal nterpretaton, and they can be smply nterpreted as a descrptve tool or as a technque to estmate a best-fttng lnear approxmaton to a condtonal expectaton functon that may be nonlnear n the populaton (Morgan and Wnshp 2007). However, regresson, f well specfed, can provde nformaton about the causal relaton between X andy. It s the more ambtous queston of when a regresson has causal nterpretaton that concerns us n ths revew, due to ts applcablty for complex systems under study for QSA. To arrve at a causal model from a regresson model, the analyst ams to study how one varable would respond, f one ntervened and manpulated other varables (Freedman 2009). Ths mples that the causal results from a regresson-based cause-effect analyss depend on the hypothess framework of the analyst. It s wthn ths framework that causalty can be determned. 374 Let us assume that X s a vector of covarates that are assocated n some way wth a response varable 375 Y. The condtonal expectaton functon (CEF) of Y s denoted as E Y X and denoted as E Y X = x for any realzaton x of X [see (Angrst and Pschke 2008) for a formal defnton and proof of theorems]. Least squares regresson allows the calculaton of a regresson surface that s a best- fttng lnear-n-the-parameters model of E Y X, thus of the assocaton betweeny and any realzaton x of X, mnmzng the average squared dfferences between the ftted values and the true 380 values of E Y X = x (Morgan and Wnshp 2007, Angrst and Pschke 2008) A regresson can be consdered causal when the CEF t approxmates s causal, or when the CEF descrbes dfferences n average potental outcomes for a fxed reference populaton (Angrst and Pschke 2008). As dscussed n secton 3.2.1, experments wth random assgnments ensure that the causal 19

21 Envronmental Revews Page 20 of varable of nterest s ndependent of potental outcomes, thus the groups under comparson are effectvely comparable. A core assumpton for the causal nterpretaton of regresson, s the condtonal ndependence assumpton [or CIA; see (Rosenbaum 1984, Lechner 2001, Angrst and Pschke 2008)], whch s at the bass of most emprcal work n economcs. The CIA s requred for a regresson to dentfy a treatment effect. The expermental desgn ntroduced n secton 3.2 ensures that the causal varable of nterest s ndependent of potental outcomes, whch guarantees that the groups beng compared are truly comparable (Angrst and Pschke 2008). Ths noton can be emboded regressons that are causally nterpreted. CIA, also called as selecton-on-observables, determnes that the covarates to be held fxed are assumed to be known and observed. As a consequence, accordng to ths assumpton the resdual n the causal model s uncorrelated wth the regressors. Regresson can be used as an emprcal strategy to 394 turn the CIA nto causal effects. Under CIA the covarates X are held fxed for the causal nference to be vald. These control varables (or covarates) are assumed to be known and observed (Angrst and Pschke 2008). Let us consder a generc causal model: (14) f ( B) = + B+, α ρ η where B s a varable that can take on more than two values. The equaton s lnear and assumes the functonal relatonshp under consderaton beng the same for all ndvduals n the populaton under study. Unlke the factor η that captures all unobserved factors determnng the outcome for each specfc ndvdual B s not ndexed per ndvdual. The causal model, therefore, tells us the extent of B for any value of B and not for a specfc realzaton B. We can further specfy the causal model for the ndvdual case, thus we consder that the causal relatonshp between putatve causes and response s lkely to be dfferent for each ndvdual, as n: (15) Y= α+ ρb+ η. 20

22 Page 21 of 82 Envronmental Revews A classc example s that B could be the number of years of schoolng for a certan ndvdual and could represent the current salary for that ndvdual (Angrst and Krueger 1992). Eq. (15) s smlar to a bvarate regresson model. However, t s Eq. (14) that explctly assocates n the model constructed by the analyst the coeffcents n Eq. (15)wth a causal relatonshp, thus establshng the causal assocaton. Y 411 The causal model determnes that B may be correlated wth ( ) f B and the resdual term η. 412 We can, then, consder the vector of covarates X.The random resdual part of Eq.(15) η can be decomposed under CIA nto a lnear functon of observable characterstcs X and an error term υ : (16) η = Xγ+ υ, 415 whereγ s a vector of populaton regresson coeffcents that satsfes the relatonshp E η X = X γ. 416 The vectorγ s defned by the regresson of η on X, thus the resdualυ and X are uncorrelated by constructon [see (Angrst and Pschke 2008) for further detals and proof of concept]. By vrtue of CIA, we can defne (Angrst and Pschke 2008): E f B X, B = E f B X = α+ ρb+ E η X = α+ ρb+ X γ. (17) ( ) ( ) We can re-wrte the causal model as: (18) Y= α+ ρb+ Xγ+ υ The resdual n the causal model s uncorrelated wth the regressors B and X, thusρ effectvely represents the causal effect of nterest, allowng for the attrbuton of causal meanng to the regresson. The selecton of the rght set of control varables s the subject of an extensve lterature. We refer the reader to Angrst and Krueger (2001) and Angrst and Pschke (2008) for a detaled analyss of the matter. 21

23 Envronmental Revews Page 22 of Instrumental varables and causalty We have just seen how regressons can be causally nterpreted wthn the boundares of a specfc model. A major complcaton s the possblty that regressors and errors [e.g., B, X, and υ n the example n Eq.(18)] are correlated, thus undermnng the statstcal valdty of the model. Under such condton, regresson estmates would lose ther causal nterpretaton. For the causal nterpretaton to hold, the regressors have to be asymptotcally uncorrelated wth the errors or resduals. The potental nconsstency 432 s determned by the fact that changes n B are not only assocated wth changes ny but also wth 433 changes nυ We consder that the potental outcomes can be wrtten as (Angrst and Pschke 2008): (19) Y= α+ ρb+ Aγ+ υ Here A s a vector of control varables, whch unlke X n the example n Eq. (18)s unobserved. Instrumental varable methods (Heckman and Vytlacl 2001, Newey and Powell 2003, Frebaugh 2008, Bollen 2012) allow the analyst to ntroduce an nstrumental varable, say Z, that s correlated wth the causal varable of nterest B, and uncorrelated wth both A and υ, such that [ ] 0 E Zυ =. Such a condton s a specal case of CIA ntroduced n the prevous secton. In ths case t s the nstrumental varable Z that s ndependent of potental outcomes, rather than the varable of nterest B. It follows then that the causal effectρ can be expressed as (Angrst and Pschke 2008 chap. 4): 443 Y Z Z (20) ρ=. σ σ σ B Z σ Z 444 The equalty n Eq. (20) s verfed f: 22

24 Page 23 of 82 Envronmental Revews 445 Z has a clear effect on B ; 446 Z affecty only by means of the causal varable B ; 447 Z s ndependent of potental outcomes, so t s as good as f randomly assgned The consderaton of nstrumental varables allows for the causal nterpretaton ofρ. Instrumental varables are dentfed case by case from the processes determnng the varable of nterest. For the example of the relatonshp between schoolng level and earnngs, Angrst and Krueger (1992) used the school start age of pupls as an nstrumental varable. Instrumental varables solve the problem of mssng or unknown controls. In many cases, n fact, the necessary control varables are typcally unmeasured or smply unknown. In the absence of sutable nstrumental varables n the system the causal framework 454 does not hold There are some recognzed ptfalls of the nstrumental varable approach (Morgan and Wnshp 2007). In some cases the assumpton that the nstrumental varable does not have a drect effect on the response varable may be too strong. Even when such condton s verfed, an nstrumental varables estmator s based n a fnte samplesample(morgan and Wnshp 2007). These ptfalls may nfluence the possblty of drawng causal nference from the results of a study (see secton 4.1). The lmtatons of regressonbased methods should be carefully consdered for the causal analyss to be vald. A causal regresson may be nvaldated by omttng varables that both affect the dependent varable and are correlated wth the varables that are studed n the causal regresson model, by the way mssng data s handled, and by the presence of potental bases determned by measurement errors (Allson 1999) Applcatons We survey here the applcaton of regresson-based technques and combned matchng and regresson technques n the feld of sustanablty. 23

25 Envronmental Revews Page 24 of Emprcal analyses usng causal regresson technques have been wdely appled to study the relatonshp between trade openness, economc development and envronmental qualty (Stern 2004, Copeland and Taylor 2013). In the Envronment Kutznets Curve lterature, a consderable amount of studes deal wth ths relatonshp, treatng envronmental degradaton measures as the dependent varables and ncome as the ndependent varable, and provdng mxed results (Soytas et al. 2007). Antweler et al. (1998) fnd that nternatonal trade, although alterng the polluton ntensty of countres, creates small changes n polluton concentratons, especally of SO 2. The authors fnd evdence that both envronmental regulatons and captal-labor endowments determne SO 2 concentratons and conclude that openness and freer trade appear to be good for the envronment. The study concludes that f an ncrease n trade openness generates a 1% ncrease n ncome and output then, as a result of scale and technology 477 polluton does fall by approxmately 1%. Cole and Ellott (2003) confrm both envronmental regulaton effects and captal-labor effects for SO 2 and suggest that these results do not necessarly hold for other pollutants, such as NO x, bochemcal oxygen demand (BOD) and CO 2, for whch an ncrease n emssons s lkely to happen as a result of freer trade. Frankel and Rose (2005) study the effect of trade on the envronment and use exogenous geographc determnants (.e., lagged ncome, populaton sze, rate of nvestment, and human captal formaton) as nstrumental varables to account for the endogenerty of trade. The authors conclude that trade appears to have a benefcal effect on some measures of envronmental qualty. In partcular, they conclude that trade sgnfcantly tends to reduce the concentratons of SO 2 and NO 2. Manag et al. (2009) fnd that trade s benefcal for OECD countres, whle t has detrmental effects on SO 2 and CO 2 concentratons n non- OECD countres. A lower BOD s found n non-oecd countres. The detrmental mpact s found to be larger n the long term, rather than n the short term. A bulk body of research regards the accumulaton of greenhouse gases (GHGs) n the atmosphere leadng to clmate change. Regresson technques of econometrc nspraton are commonly appled for the study of the nfluence of clmate change on a number of endponts. The matter of adaptaton under clmate 24

26 Page 25 of 82 Envronmental Revews change s analyzed usng nonlnear regresson n Schlenker and Roberts (2009). The author controls for precptaton, technologcal change, sols, and locaton-specfc unobserved factors, and the results show a nonlnear relatonshp between temperature and sol yelds. The relatonshp between mortalty and changes n daly temperatures s descrbed usng regresson technques n Barreca et al. (2013). The authors document a remarkable declne n the mortalty effect of temperature extremes n the 20th century n the Unted States, and pont to ar condtonng as a central determnant n the reducton of mortalty rsks assocated wth extreme temperatures. The exposure to extreme temperatures determned by clmate change s lnked to deleterous effects on fetal health, the decrease n brth weght, and an ncrease n the probablty of low brth weght n Deschenes et al. (2009 p. 216). The analyss rests on a number of strong assumptons about data, ncludng that the clmate change predctons used n the regresson model are correct. In a smlar fashon, clmate polcy has been lnked to ncrease n mortalty and mgraton (Deschenes and Morett 2009), fluctuatons n the labor markets (Deschenes 2010), and reduced profts from agrculture n the Unted States (Deschenes and Greenstone 2007) and n Calforna (Deschenes and Kolstad 2011). Conflcts and socal nstablty have also been assocated wth clmate change (Homer- Dxon 1991). Earler studes have shown that random weather events, such as drought and prolonged heat waves, mght at tmes be correlated wth armed conflct n Afrca (Mguel et al. 2004, Smth et al. 2007, Burke et al. 2009). Hsang et al. (2011) show that a causal lnk between temperature and conflct does exst at varous scales for relatvely rcher countres as well. The ssue of causal lnks between clmate and conflct s contentous (Cane et al. 2014, Ralegh et al. 2014). Buhaug (2010 p ) nvestgated the scentfc base of the clams and concluded that a robust correlatonal lnk between clmate varablty and cvl war do not hold up to closer nspecton when alternatve statstcal models and alternatve measures of conflct are used. Hsang and Meng (2014) reproduced the analyss of Buhaug (2010) and corrected the correct the statstcal procedure for model comparson. The study concludes that the clam of Buhaug (2010) s nconsstent wth the evdence presented, thus clmate change does affect conflcts n Afrca (Hsang and Meng 2014). 25

27 Envronmental Revews Page 26 of The potental sustanable mpacts of far trade, eco-certfcaton and eco-labellng have been amply studed usng matchng technques n combnaton wth regresson technques. Ruben et al. (2009) use data from coffee and banana co-operatves n Peru and Costa Rca and fnd, usng propensty score matchng, that far trade mproves access of farmers to credt and nvestments, and also affects ther atttude towards rsk. The partcpaton n a far trade system mproved employment, as well as ther barganng power and tradng condtons. The dfference-n-dfferences dentfcaton strategy s used by Hallsten and Vllas-Boas (2013) to test the effcacy of eco-labels n promotng sustanable seafood consumpton. The study fnds evdence that n a sample of ten stores n the San Francsco Bay area the mplementaton of an eco-label led to a sgnfcant declne n sales n the range of 15%-40% of certan classes of products wth lmted envronmental sustanablty. Mller et al. (2011) use dfference-n dfferences to test the mpact of a scheme of cash transfer on food securty n Malaw. The study presents evdence that food securty s mproved by the transfer of cash by the government to rural households n Malaw. Eco-certfcaton s also the subject of the study of Blackman and Naranjo (2012). The study uses propensty score matchng to control for selecton bas and tests the mpact of eco-certfcaton on a hgh- value agrcultural commodty, organc coffee from Costa Rca. The study fnds that organc certfcaton mproves the envronmental performance of coffee growers by reducng the use of chemcals and mprovng the envronmental performance of management practces. Matchng technques have been used also to check progress on poverty reducton and on other goals n the Mllennum Development Goals (Sachs and McArthur 2005). Maertens et al. (2011) use a varety of matchng technques to test the mpact of globalzaton on poverty reducton n Senegal. The study fnds a sgnfcant postve mpact of globalzaton on poverty reducton through employment creaton and labor market partcpaton. Setboonsarng and Parpev (2008) test the mpact of mcrofnance on the MDGs usng data from a mcrofnance nsttuton n Pakstan. Usng dfference-n-dfferences, the study fnds that the lendng program of the nsttuton contrbuted to ncome generaton actvtes that have a benefcal mpact on the MDGs. Arun et al. (2006) use propensty score matchng to test whether 26

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