9 Increasing economic losses from hurricanes related to global

Transcription

1 9 Increasing economic losses from hurricanes relaed o global warming There is a growing body of evidence on he warming of he climae sysem and is impacs on biophysical and human sysems (IPCC-WGI, 2007, IPCC, 2013a). Alhough changes in he frequency and inensiy of exreme weaher evens have been documened (IPCC, 2013a; Handmer e al., 2012), he observed increases in naural disaser losses are usually hough o resul from socieal change alone (Handmer e al., 2012; Mohleji & Pielke, 2014; Pielke e al., 2008; Crompon, McAneney, Chen, Pielke, & Haynes, 2010; Barredo, 2010, 2009). Here we analyze he economic losses from hurricanes in he US and show for he firs ime he exisence of a climae change signal ha was obscured by he mehodological approach underaken in previous sudies. By 2005 climae change could already have conribued in he order of $2-$14 billion o he recorded annual losses, abou 2%-12% of he normalized losses in ha year. Empirical evidence suggess ha he upward rend in boh he number and inensiy of hurricanes in he Norh Alanic is relaed o he observed warming rend represened by he smoohed global average surface air emperaure. Hurricane losses in he U.S. could increase by $19-$88 billion for 1ºC rise in global emperaure. The presence of a warming signal in exreme evens losses could reshape he percepion of risk of boh policy-makers and he general public and have major implicaions for naional and world climae policy. Daa colleced by Munich Re (Munich Re, 2013) show ha worldwide economic losses from naural disasers have increased over he pas decades. Aribuing his rend o is causes is a complex ask because he developmen of naural disaser damages depends on an inricae inerplay of chance and changes in vulnerabiliy, he number and value of asses exposed o disasers, as well as in he hazard (Bozen, 2013). The laer can be due o eiher naural climae variabiliy or climae change. Exising sudies ypically This chaper is based on Esrada F., Bozen W.J.W., Tol R.S.J., Bouwer L.M. Increasing economic losses from hurricanes relaed o global warming. Submied for publicaion. 264

2 normalize original records of naural disaser damage by indicaors ha are assumed o reflec changes in exposure and vulnerabiliy, and use Ordinary Leas Squares (OLS) regression o es wheher a remaining (linear) ime rend is presen in normalized naural disaser damages (Bouwer, 2011). The general finding from hese sudies is ha here is no significan remaining rend in normalized naural disaser losses, from which he conclusion has been drawn ha climae change has no increased naural disaser risks (Barredo, 2009, 2010; Bouwer, 2011; Choi & Fisher, 2003; Crompon e al., 2010; Downon, Miller, & Pielke, 2005; Mohleji & Pielke, 2014; Pielke e al., 2008). However, his conclusion may be he resul of he underlying mehods. The IPCC SREX repor recenly idenified uncerainies in mehods as an imporan barrier for undersanding rends in records of losses from exreme weaher (Handmer e al., 2012). 9.1 Adjusing economic losses o accoun for socieal change Normalizaion is ypically based on an assumpion of proporionaliy (Bouwer, 2011; Pielke & Landsea, 1998). Le D denoe damage a ime due o an exreme weaher even x given exposure y. Normalized damages >D are hen: >D D = = y (, ) f y x y (9.1) where f(.) is he impac funcion. Suppose ha f ( ) is muliplicaively separable and equal o f ( y x ) = y δ h( x ) ha y grows a a consan rae r. Then ( y ) ( ) f ( y ) f y,. Assume 1 r 0 = e δ where 1 y0 δ can be inerpreed as he difference in growh raes beween acual exposure and assumed exposure (Appendix F1.1). Only if δ = 1, no rends or changes in he level will inadverenly be inroduced o he normalized damage in equaion (9.1). If 265

3 ε (,, ) = ( ) f y z x y z h x, hen normalizaion wih y will be incomplee, and he normalized damages will rend by εs, where s is he growh rae of he omied exposure variable z. Spurious rends can be inroduced in he normalized damages by an incorrec idenificaion of he relevan variables driving he increases in exposure and vulnerabiliy, which can occur because some of hem are unobservable or no measured in he available daabases, or because of he implemenaion of adapaion sraegies, e.g., when building codes improve over ime (Appendix F1.2.3 and F1.2.4 and Table F3). Inappropriae spaial resoluion may also invoke a rend (Appendix secion F1.2.1, F1.2.2, F1.2.4 and figures F1 o F6, and Tables F1 and F2). A spurious rend may incorrecly cancel ou any signal relaed o climae change, or be misaken for such a signal. Furhermore, he sandard normalizaion procedure does no es for he adequacy of he seleced normalizaion variables, nor does i provide an objecive mehod o evaluae if he losses have been correcly adjused. If a regression-based approach is used insead of proporionally normalizing he loss record, he problem of spurious rends can be minimized. Noe ha is equal o he exponenial of α +u from: >D in equaion (9.1) ln( D ) = α + δ ln( y ) + u (9.2) if he resricion δ = 1 is imposed. The validiy of his resricion, which implicily underlies he normalizaion procedure in equaion (9.1), can be empirically esed and a more appropriae value for δ can be esimaed. α + u will conain he variabiliy and nonsaionary signals ha are no explained by he scaling variable y, such as climae change. Such signals can be uncovered using rend analysis and Box-Cox ransformaions (Appendix F2). 266

4 9.2 Resuls and discussion We invesigae he presence of a climae change signal in hurricane damages in he U.S, which make up a significan proporion of worldwide naural disaser damages (Munich Re, 2013). We use he daase of Pielke (Pielke e al., 2008), which is one of he mos commonly used, publicly available daases on weaher relaed disasers. Previous analyses of his daa apply he sandard normalizaion procedure and find ha all rends in hurricanes losses can be explained by increases in populaion and wealh in coasal areas (Pielke e al., 2008; Mohleji & Pielke, 2014; Pielke & Landsea, 1999; Kaz, 2002). For comparison purposes he same normalizaion variables used in pas sudies are used here, namely coasal populaion P i, (where i denoes couny) and naional real wealh per capia RWPC defined as he curren-cos ne sock of fixed asses plus he annual producion of consumer durable goods, adjused by inflaion and populaion (all a he naional level). Applying he regression-based normalizaion approach reveals ha he ypical normalizaion approach over-adjuss losses. In paricular, he coefficien of P i, is no significanly differen from zero, and he join resricion ha boh coefficiens are equal o one is srongly rejeced (Table 9.1; Appendix F4.2. and Figure. F8). Figure 9.1 shows he regression-based normalized losses (REGN) and he adjused losses obained from he sandard normalizaion procedure (PL05) in Pielke e al. (2008). A significan linear rend is found in REGN indicaing ha losses from hurricane damages have been increasing a a rae of $136 (±$51 wo block-boosrap sandard errors) million dollars a year during he pas cenury, and ha he losses in 2005 are abou $14 (± $5.3) billion dollars larger han if here was no rend. Table 9.1. Coefficien values and -saisics of he normalizaion regression ln( D ) = µ + γ ln( P ) + δ ln( RWPC ) + ε. i i µ γ δ *** * (42.112) (-0.755) (-1.887) ***,**,* denoes saisical significance a he 1%, 5% and 10% levels, respecively. -saisics are given in parenheses. HAC sandard errors and covariance were esimaed using he Barle kernel and Newey-Wes bandwidh selecion. i 267

5 a) b) 2.0E E+11 Losses (US 2005 dollars) 1.6E E E E E Losses (US 2005 dollars) 1.0E E E E E E PL05 REGN Figure 9.1. Normalized losses per year for he period 1900 o 2005 using he sandard normalizaion (PL05, panel a) and he regression-based (REGN, panel b) procedures. In conras, a rend of $1.5 million dollars a year can be found for PL05, bu his is no saisically significan (Table 9.2). However, in boh cases, he normal, linear regression model is applied o highly skewed (non-normal) loss daa. Srong deviaions from he normaliy assumpion can render hypohesis esing on he esimaed coefficiens invalid. When an appropriae Box-Cox ransformaion is applied o PL05, resuls show ha indeed here is a saisically significan posiive (bu nonlinear) rend in he daa. This is also rue for he naural logarihm of PL05 (p-value <0.001). In oher words, he lack of evidence for a poenial climae change signal (Mohleji & Pielke, 2014; Pielke e al., 2008) is no robus o more appropriae saisical mehods. 268

6 Dependen variable REGN Table 9.2. Linear esimaes of increases in normalized losses per year and per ºC increase in global emperaure. Trend G ACE NHUR NE Increase in Increase losses by year 2005 (US$ billions) 1.36E+08 (1.89) (-7.80E06, 2.80E+08) [8.61E+07, 1.86E+08]* REGN (2.20) (8.98E+06, 1.46E+08)* [5.15E+07, 1.45E+08]* REGN (2.30) (1.03E+07, 1.40E+08) [2.35E+07, 1.23E+08]* PL (0.21) (-1.33E+08, 1.62E+08) [-8.68E+07, 1.20E+08] $14.3 (-$0.82 $29.4) [$9.03 $19.53]* (1.63) REGN E+10 (1.89) (-1.40E+09, 5.70E+10) [1.87E+10, 3.73E+10]* REGN E+10 (2.03) (4.00E+08, 4.20E+10)* [1.21E+10, 3.03E+10]* REGN E+10 (2.20) (1.72E+09, 3.59E+10)* [8.88E+09, 2.82E+10]* REGN E+10 (1.79) [-2.20E+09, 3.94E+10] [8.24E+09, 2.87E+10]* E+09 (1.35) - - $10.3 ($0.94 $19.6)* [$5.4 $15.2]* - $7.8 ($1.09 $14.65) [$2.56 $12.92]* $1.5 (-$14.02 $17.01) [-$9.04 $12.81] in losses per 1ºC increase (US$ billions) $28.0 (-$1.40 $57.40) [$18.60 $37.00]* (1.70) E+09 (1.33) - - $21.1 ($4.00 $42.00)* [$12.10 $30.30]* E+09 (1.56) - $18.80 ($1.72 $35.88)* [$8.88 $28.20]* G is he exponenially smoohed annual global surface air emperaure, ACE is he seasonal Accumulaed Cyclonic Energy, NHUR is he seasonal number of hurricanes in he Norh Alanic, NE is he number of landfalling hurricanes in he U.S. -saisics are given in parenhesis. Bold and ialic figures denoe saisical significance a he 5% and 10% levels. HAC sandard errors and covariance were esimaed when heeroskedasiciy and auocorrelaion was found using he Barle kernel and Newey-Wes bandwidh selecion. Two sandard error confidence inervals are shown in parenhesis. 95% confidence inervals using block-boosrap wih a block size of 10 observaions are shown in brackes.* indicaes ha he confidence inerval does no include zero. $18.80 (-$2.20 $39.40) [$8.24 $28.70]* The observed rend in REGN should be carefully inerpreed since i may be caused by facors oher han he effecs of climae change. Naural variabiliy, in paricular low frequency naural oscillaions, can be misaken for a rend if hese sysemaic movemens are no aken ino accoun. Linear and nonlinear rends in REGN are, however, saisically significan even when he Accumulaed Cyclonic Energy (ACE) or he annual number of hurricanes (NHUR) in he Norh Alanic are added o accoun for naural variabiliy and low-frequency oscillaions. The esimaed slope coefficiens for 269

7 he linear rend are beween $74 and $97 million dollars per year depending on wheher NHUR or ACE are included as regressors (Table 9.2). The esimaed slope coefficiens for he nonlinear rend implied by he Box-Cox ransformaion show ha losses in 2005 were $4.6 ($1.04 $14.6) billion larger han if here was no rend (Table 9.3). Including ACE and NHUR as regressors decreases he magniude of he losses explained by he rend o $2.88 ($0.66 $9.02) and $2.37 ($0.48 $8.57) billion, respecively. Boh ACE and NHUR conain posiive rends ha may be relaed o global warming and, herefore, he increase in damages accouned for a ime rend is lower when hese variables are included. Dependen variable Table 9.3. Nonlinear esimaes of increases in normalized losses in 2005 and for 1ºC increase in global emperaure. Inercep Trend G ACE NHUR Increase in losses by year 2005 (US$ billions) (US$ billions) ( λ) Increase in losses for 1ºC raise in G PL $ (5.53) (2.52) ($0.31 $20.90) ln(1+pl05) $ (6.57) (4.21) ($0.11 $4,200.00) PL 05( λ) $11.00 $54.80 (17.98) (3.59) ($2.75 $29.00) ($8.64 $204.00) PL 05( λ) $3.43 $11.50 (5.71) (1.98) (5.64) (-$0.02 $11.70) (-$0.04 $59.80) REG> ( λ) $ (5.05) (5.54) ($1.04 $14.60) REG> ( λ) $ (2.02) (4.67) (5.87) ($0.66 $9.02) REG> ( λ) $ (1.79) (3.75) (4.85) ($0.48 $8.57) REG> ( λ) $11.7 $87.70 (20.06) (6.07) ($ ) ($25.40 $240.00) REG> ( λ) $5.52 $31.80 (7.04) (4.67) (5.33) ($ ) ($7.41 $98.60) REG> ( λ) $4.76 $26.00 (5.09) (4.04) (4.49) ($1.38 $12.00) ($4.84 $90.90) -saisics are given in parenheses. Bold and ialic figures denoe saisical significance a he 5% and 10% levels. PL 05( λ), REG> ( λ) are he Box-Cox ransformaion of PL05 and REGN wih λ = and = 0.18, respecively. λ The linear rend can be replaced by he exponenially smoohed global surface air emperaure as a crude proxy for he observed warming rend, leading o esimaes of increases in losses beween abou $19 billion and $28 billion per degree Celsius of increase in global emperaures (Table 9.2; Appendix F3.2). The analysis is exended o 270

8 he appropriae Box-Cox ransformaions of he normalized losses o es he saisical significance of he explanaory variables and he saisical adequacy of hese models (see Table F8 and F10a o F10d). According o he bes models in erms of heir saisical adequacy and fi, he observed warming could have conribued in 2005 o increased hurricane losses in he range of $4.8 o $11.7 billion and a 1 ºC rise in G would increase losses by abou $26 o $88 billion (Table 9.3). Our sensiiviy analyses show ha he rend persiss when losses are normalized using he sorm caegory a he momen of landfall in addiion o he socioeconomic variables menioned above (Appendix F3.3). Some sudies (Kaz, 2002; Pielke e al., 2008) explain he lack of rend in hurricane losses by he apparen lack of a rend in he srengh and number of hurricanes in he Alanic. Oher sudies, however, repor increases in boh he number and srengh of hurricanes in he Alanic (Emanuel, 2005; Holland & Webser, 2007; Schmid, Kemfer, & Höppe, 2009; Webser, Holland, Curry, & Chang, 2005). IPCC concludes ha hurricane aciviy in he Alanic has increased since 1970, alhough here is low confidence in he human conribuion o his increase (Handmer e al., 2012). Our resuls show ha here is a sligh bu highly significan rend in NHUR, ACE and he number of landfalling hurricanes in he U.S. (NE, represened by he sum of evens per year repored in he hurricane damage daase of Pielke (Pielke e al., 2008)). This rend can be accouned for by he global mean emperaure, used as a general index of he observed warming (Tables F11, F12 and F13), also when conrolling for he Alanic Mulidecadal Oscillaion (AMO), PDO and he Souhern Oscillaion Index (SOI). 9.3 Conclusions Increases in wealh and populaion alone canno accoun for he observed rend in hurricane losses. Alhough he remaining rend can be due o an omied variable, a variey of saisical models suggess ha par of he increase in hurricane losses in he U.S. can be a consequence of observed global warming: here is subsanial evidence of a posiive rend in losses and also of posiive rends in deerminan drivers of losses such as ACE, NHUR and NE. The commonly acceped conclusion ha a climae change driven 271

9 rend in naural disaser losses is absen are likely caused by mehodological shorcomings in previous sudies. In his chaper, an improved approach is presened, and he empirical evidence suggess ha climae change may have increased pas coss of naural disasers. This finding has major implicaions for he design of climae policy in he conex of loss and damage from climae change a naional and global scales. I suggess ha a more cauious aiude is warraned when evaluaing he curren and fuure coss of climae change as well as he expeced benefis of miigaion and adapaion sraegies. 272

10 Appendix F F1.1 Effecs of he sandard normalizaion procedure on he rending behavior of he economic coss of exreme evens Invesigaing he exisence of a climae change signal in observed ime series of disaser damage is complicaed by he presence of confounding facors ha can also impar nonsaionary behavior o hese ime series. This problem, ha may be bes described as a signal exracion issue, has been commonly addressed as one relaed o properly scaling he observed damages by he variables whose nonsaionary behavior could oherwise be misakenly aribued o facors associaed wih climae change. Increases in wealh and populaion in areas prone o suffer he impacs of climae change relaed exreme weaher evens have been idenified as wo prominen drivers of hese confounding effecs. The usually applied normalizaion procedure consiss of scaling he inflaion-adjused value of he ime series of losses by an indicaor of wealh and/or populaion change (Neumayer and Barhel, 2011; Pielke and Landsea, 1998). Thus, his normalizaion inends o show losses as if all disasers occurred over he same exposed asses a a single poin in ime (Bouwer, 2011; Pielke e al., 2008). In his secion we show ha he sandard normalizaion procedure commonly used in he lieraure is likely o inadverenly inroduce rends in he normalized damages as well as o incorrecly disor or cancel a poenial climae change signal. The sandard normalizaion procedure is shown o be appropriae only under very srong assumpions abou he idenificaion of he normalizaion variables as well as changes in exposure and vulnerabiliy. We use a simple mahemaical model o illusrae he resriciveness of he commonly used normalizaion approach. The normalized damages >D adjused by he socioeconomic variable y can be described as: 273

11 1 >D = D = y ( y ) h ( x ) f y (F.1) where D are he inflaion adjused damages, ( ) f represens he poenial economic loss (i.e., acual vulnerable wealh) o a paricular exreme weaher even, y represens he chosen proxy scaling variable (e.g. a measure of wealh), x is he relevan weaher variable which is poenially influenced by climae change, and h is a general damage funcion 33. Afer applying his normalizaion procedure he mos common finding repored in he lieraure is ha here is no longer a rend in y >D, leading o he conclusion ha here is no real effec of climae change on damages or ha a leas his effec is no ye deecable. Neverheless, i should be sressed ha hese findings are condiional on he adequacy of he normalizaion procedure and in paricular on he raio ( y ) f y (i.e., he normalized poenial loss). The criical issue resides in wheher he funcion f ( y ) preserves he acual rae of growh of y. ( y ) f y acually measures if he growh of f ( y ) is "acceleraing" or "deceleraing" in comparison o ha of y. As an example, consider per capia GDP. If per capia GDP shows a posiive rend hen GDP is acceleraing wih respec o populaion. In general, if r w y = e and ( y ) e w ( y ) h( x ) = e h( x ) f = grows a some raes r and D = f, hen he normalizaion procedure yields: w and hus 33 Equaion (F.1) is used for illusraing purposes. Noe ha i could be easily exended o more han one scaling variable (e.g., wealh and populaion), as well as for a summaory of losses from differen evens and locaions. 274

12 ( y ) ( ) ( w r ) ( δ 1) r h x = e h( x ) = e h( x ) f >D = y (F.2) where δ 1 can be inerpreed as he difference in growh raes beween poenial economic losses and he scaling variable due o mismaches beween he raes of growh of f ( y ) and y. These mismaches can be caused by changes in vulnerabiliy and exposure ha are no capured by y as well as by he possible lack of a correc idenificaion of he relevan variables driving he poenial economic losses 34, and he absence of long enough daa records wih an appropriae geographic resoluion, among ohers. In general, f ( y ) is a complex funcion no only of y, bu also of several facors including exposure, vulnerabiliy and adapaion (which are no refleced by y ). Therefore, he growh raes f ( y ) and y may show emporal and/or permanen mismaches ha can lead o a wide variey of nonsaionary behaviors ha may incorrecly cancel a poenial climae change signal as well as produce a rend ha migh misakenly be aribued o his phenomenon. Only in he special case of δ = 1 for = 1,..,n, no nonsaionary behavior will inadverenly be inroduced o >D. Tha is, he sandard normalizaion procedure requires vulnerabiliy o remain consan and ha changes in exposure are solely deermined by he normalizaion variables chosen. F1.2 Differences in he rae of growh of exposed wealh and he normalizaion variables. F1.2.1 Differences in raes of growh caused by misidenificaion of he normalizaion variables. One criical problem of he normalizaion procedure is ha i relies solely on he judicious selecion of normalizaion variables, while formal esing of heir adequacy or 34 This is likely o pose a problem in pracice because he relevance of he normalizaion variables is ofen no esed, and some of he poenial loss drivers may be unobservable or unmeasured, such as changes in physical vulnerabiliy of exposed buildings. 275

13 significance is no applied. This complicaes he correc specificaion of he normalizaion procedure and precludes invesigaing if he adjusmen is correc or if he daa was under- or over-adjused. Therefore rends could have been incorrecly induced by he normalizaion procedure. For illusraing his possibiliy, consider he inflaion adjused daa series on hurricane damage in he Unied Saes for he period (Pielke e al., 2008). The lieraure proposes o selec as he normalizaion mulipliers naional level real wealh per capia RWPC and populaion i P, in he affeced coasal couny i a ime, defined as he raio of heir 2005 values and heir values in he year when he even ook place (Pielke e al., 2008). Figure F1 shows he unnormalized losses (panel A), he losses normalized by boh RWPC and i P, (panel B), he losses normalized by RWPC (panel C) and he losses normalized by P i, (panel D). Each of hese panels show large differences regarding he size of he damages per even and imply a very differen evoluion of losses during he period. The normalizaion in panel B), which is he one ha has been used in he lieraure, provides a much larger scaling of he evens occurring a he beginning of he 20h cenury, making some of hem considerably larger han hose occurring in he record season of This normalizaion has led o he conclusion ha no climae change signal is presen in hurricane losses (Pielke e al., 2008). The obvious problem is deermining which, if any, of he normalizaions in panels B), C) and D) is correcly adjusing he losses o reflec changes in vulnerabiliy and exposure. In he sandard normalizaion procedure here is no possibiliy o address his problem in a formal and objecive manner, and he final decision relies solely on he subjecive judgmen of he researcher. Furhermore, as discussed in F2, he sandard normalizaion procedure assigns he same weigh o all normalizaion variables (i.e., imposes a join resricion on he scaling coefficiens o be equal o one). Consequenly, even if he selecion of normalizaion variables is correc, hey are likely o be over- or under-represened in he adjused losses. 276

14 A) Unnormalized B) Losses (US 2005 dollars) 9E+10 8E+10 7E+10 6E+10 5E+10 4E+10 3E+10 2E+10 1E+10 0E Even Losses (US 2005 dollars) 1.6E E E E E E E E E+00 Normalized (RWPC and P) Even C) Normalized (RWPC) D) Losses (US 2005 dollars) 9E+10 8E+10 7E+10 6E+10 5E+10 4E+10 3E+10 2E+10 1E+10 0E Even Losses (US 2005 dollars) 9E+10 8E+10 7E+10 6E+10 5E+10 4E+10 3E+10 2E+10 1E+10 0E+00 Normalized (P) Even Figure F1. Unnormalized and normalized losses in he Unied Saes per even during he period Panel A) shows he unnormalized losses per even. Panel B) shows he normalized losses per even using RWPC and P i as he normalizaion variables. Panel C) shows he normalized losses per even using RWPC as he normalizaion variable. Panel D) shows he normalized losses per even using P i as he normalizaion variable. Equaion (F.2) helps explaining he differences in he normalized losses in Figure F1. When boh RWPC and i P, are used for normalizing he losses, raes of growh of hese variables are added, as shown by y e r RWPC + rp =. This leads o a much larger adjusmen facor when compared wih panels C) and D) in Figure F1. Under he sandard normalizaion procedure here is no formal way of discriminaing among hese normalizaion opions and even sligh differences in he raes of growh beween he chosen normalizaion variables and he poenial losses can lead o incorrecly inducing or cancelling rends in he normalized losses. Figure F2 uses equaion (F.2) o illusrae how he effecs of a 10% difference in he raes of growh ( δ =1. 1, δ = 0. 9) produce a rend 277

15 ha could be wrongly aribued o changes in climae variables or in vulnerabiliy, even hough boh of hem are held consan. In pracice, δ is an unobservable variable and no ess are conduced o evaluae he significance of he chosen normalizaion variables. Furhermore, noe ha r and δ are likely o vary wih ime as a funcion of several facors, such as he level of wealh, saving and invesmen raes, populaion concenraion, urbanizaion, he raio of angible/inangible wealh, as well as wih oher imporan drivers, such as axes and fiscal incenives, among ohers. If δ and r are allowed o vary wih ime, a variey of nonsaionary behavior (no only rends) can arise afer adoping he usually applied normalizaion procedure as a consequence of emporal and permanen mismaches in hese raes of growh. A) B) Moneary unis Moneary unis Years Figure F2. Trending behavior in δ = 0.9 and panel B) =1. 1 >D induced by he normalizaion procedure. Panel A) h =1. δ. The damage funcion was chosen o be ( ) % Years x Furhermore, since he normalizaion procedure is based on comparing growh raes, oher problems may arise when choosing he appropriae scaling variables. I has been noed ha GDP may no be an adequae measure of wealh given ha GDP is a flow and wealh is a sock (Barhel and Neumayer, 2012). Bu his widely used proxy for wealh (Bouwer, 2011) can lead o even more deceiving resuls: as is implied by economic growh heory, high raes of growh in GDP may indeed correspond o low levels of wealh (Barro and Sala-i-Marin, 2003). As such, poorer economies are likely o show faser increases in y han f ( ) y, while for richer economies growh in y would be 278

16 deceleraing wih respec o f ( y ). Tha is, he normalizaion procedure could produce he exac opposie scaling ha was inended o, and induce negaive/posiive rends ha will disor he analysis. In his case, even hough GDP is clearly a driver of exposed wealh, is rae of growh can be seen as ransformed by a funcion δ = f ( ) o a very differen emporal evoluion han ha of GDP. GDP, leading The Solow model provides an easy way of exemplifying possible oucomes of he normalizaion procedure when GDP is used as a normalizaion variable. In his model he oupu Y is deermined by a Cobb-Douglas producion funcion of he form: Y = A K L (F.3) α 1 α where A is he oal facor produciviy, L is populaion, α is he elasiciy of oupu wih respec o capial and K is he capial sock which is deermined by he equaion for capial accumulaion: ( 1 d ) K 1 + I 1 = ( 1 d ) K 1 + Y 1 K σ (F.4) = where d is he depreciaion rae, I is invesmen and σ is he savings rae. Populaion and oal facor produciviy are deermined by L 1 = ( 1+l) L 0 ( ) 0 + and A + 1 = 1+a A, respecively, where l and a are he corresponding growh raes. For his example, assume ha he acual exposed wealh is he per capia capial sock k and he per capia GDP y is chosen as he normalizaion variable. For he simulaions presened in Figure F3, he following parameer values were assigned: α =1 3, d = 0. 1, l = , σ = 0.1 and a = These parameer values are commonly used in he lieraure (Nordhaus and Boyer, 2000). As is shown by he example in Figure F3, he differences in growh raes of per capia GDP and per capia capial sock (used as he poenial loss measure) ha economic growh heory predics will occur can produce misleading resuls 279

17 when he normalizaion procedure is applied. The normalizaion can induce rends in he poenial losses and disor he subsequen analysis of he normalized losses. Similar resuls can occur wih oher wealh variables for which heir growh raes are expeced o decelerae as he economy ges closer o is seady sae equilibrium growh. A) B) Dollars Year y f(y)/y Year Normalized wealh Exposed wealh Figure F3. Normalizaion applied o simulaed per capia wealh and GDP using he Solow growh model. Panel A) shows he simulaed per capia GDP and panel B) shows f ( y ) he normalized poenial loss (uni free, lef axis), and per capia capial sock y (housands of dollars, righ axis) for represening exposed wealh k In he nex subsecions some special cases are examined where mismaches in he growh raes of he poenial economic losses and he normalizing variables can occur, namely geographic and secor heerogeneiy and ime evolving vulnerabiliy. F Geographic and secor heerogeneiy of growh in exposed wealh and aggregaed proxy variables of wealh. As has been discussed previously in he lieraure, noably Nuewmayer and Barhel (Neumayer and Barhel, 2011), some shorcomings of he normalizaion procedure arise because i assumes a homogeneous geographical disribuion of he raes of growh of he poenial losses and of he seleced normalizaion variables. This is a special case of equaion (F.2), which can be expressed as: 280

18 ( yi, ) ( ) ( δi, 1) r h x = e h( x ) f >Di, = y (F.5) δ + i, = δ γi, and n >D = >D i i= 1, where δ i, is he difference in growh raes beween poenial economic losses and he scaling variable, and γ i, represens he fracion of he mismach due o differences in he raes of growh of he local and aggregae scaling variable in he i-h affeced localiy ( i = 1,..., n). For illusraing he effec on he normalizaion procedure of mismaches beween he local and aggregae scaling variables, we use sae level and local income growh raes in Florida, U.S. obained from he Bureau of Economic Analysis of he US Deparmen of Commerce (hp://bea.gov/iable/). For his example δ = 0 and γ i, varies for he i counies, bu i is consan in ime, such ha ( y ) ( ) r f i, i, 1 = e γ y Figure F4a shows he raio of he local and sae level proprieors' income. While he annual average compound growh rae of sae level proprieors' income for Florida over he period is 5.88%, large differences exis among is counies, ranging from 1.38% o 9.13%. Even when imposing δ = 0, i.e., he only source of possible mismaches is he differences in he growh raes of he sae level and local normalizaion variable, he normalizaion procedure would produce a variey of posiive/negaive ime rends ha could inroduce a nonsaionary behavior on >D,. i 281

19 Given ha γ i, is unknown in mos cases due o he lack of adequae spaial resoluion of he daa, hese rends would be aribued o h ( x ) or o changes in vulnerabiliy when in fac he rending behavior is an arifac creaed by he normalizaion procedure. In addiion, if γ i, is allowed o vary wih ime, a wide variey of nonsaionary behaviors can be inroduced o he normalized wealh and, herefore, o normalized losses due o differences in local and sae level economic developmen over ime. Figure F4b shows similar resuls for he raio income. ( y ) f i, y of he couny and sae level per capia personal 282

20 A) f(y)/y B) f(y)/y Sae Florida Alachua Baker Bay Bradford Brevard Broward Calhoun Charloe Cirus Clay Collier Columbia DeSoo Dixie Duval Escambia Flagler Franklin Gadsden Gilchris Glades Gulf Hamilon Hardee Hendry Hernando Highlands Hillsborough Holmes Indian River Jackson Jefferson Lafayee Lake Lee Leon Levy Libery Madison Manaee Marion Marin Miami-Dade Monroe Nassau Okaloosa Okeechobee Orange Osceola Palm Beach Pasco Pinellas Polk Punam S. Johns S. Lucie Sana Rosa Sarasoa Seminole Sumer Suwannee Taylor Union Volusia Wakulla Walon Washingon Sae Florida Alachua Baker Bay Bradford Brevard Broward Calhoun Charloe Cirus Clay Collier Columbia DeSoo Dixie Duval Escambia Flagler Franklin Gadsden Gilchris Glades Gulf Hamilon Hardee Hendry Hernando Highlands Hillsborough Holmes Indian River Jackson Jefferson Lafayee Lake Lee Leon Levy Libery Madison Manaee Marion Marin Miami-Dade Monroe Nassau Okaloosa Okeechobee Orange Osceola Palm Beach Pasco Pinellas Polk Punam S. Johns S. Lucie Sana Rosa Sarasoa Seminole Sumer Suwannee Taylor Union Volusia Wakulla Walon Washingon Figure F4. Panel A) shows he raio of couny and sae level proprieors' personal income for Florida. Panel B) shows he raio of couny and sae level per capia personal income for Florida. Figures F5a and F5b show ha posiive and negaive rends can also be inadverenly inroduced o he normalized losses due o differences in he raes of growh of he differen secors in he affeced counies. These figures show he proprieors' personal income a he couny level for he farm (Figure F5a) and nonfarm (Figure F5b) secors normalized by he sae level proprieors' personal income. These figures sugges ha if 283

21 he proporion of damages is larger in he farm secor, hen he raio inroduce a negaive rend o he normalized losses. ( y ) f i, y will likely A) f(y)/y B) f(y)/y Sae Florida Alachua Baker Bay Bradford Brevard Broward Calhoun Charloe Cirus Clay Collier Columbia DeSoo Dixie Duval Escambia Flagler Franklin Gadsden Gilchris Glades Gulf Hamilon Hardee Hendry Hernando Highlands Hillsborough Holmes Indian River Jackson Jefferson Lafayee Lake Lee Leon Levy Libery Madison Manaee Marion Marin Miami-Dade Monroe Nassau Okaloosa Okeechobee Orange Osceola Palm Beach Pasco Pinellas Polk Punam S. Johns S. Lucie Sana Rosa Sarasoa Seminole Sumer Suwannee Taylor Union Volusia Wakulla Walon Washingon Sae Florida Alachua Baker Bay Bradford Brevard Broward Calhoun Charloe Cirus Clay Collier Columbia DeSoo Dixie Duval Escambia Flagler Franklin Gadsden Gilchris Glades Gulf Hamilon Hardee Hendry Hernando Highlands Hillsborough Holmes Indian River Jackson Jefferson Lafayee Lake Lee Leon Levy Libery Madison Manaee Marion Marin Miami-Dade Monroe Nassau Okaloosa Okeechobee Orange Osceola Palm Beach Pasco Pinellas Polk Punam S. Johns S. Lucie Sana Rosa Sarasoa Seminole Sumer Suwannee Taylor Union Volusia Wakulla Walon Washingon Figure F5. Panel A) shows he raio of farm proprieors' income per couny and sae level proprieors' income for Florida. Panel B) shows he raio of nonfarm proprieors' income per couny and sae level proprieors' income for Florida. F Effecs of ime evolving vulnerabiliy on he normalizaion procedure. The sandard normalizaion procedure ignores vulnerabiliy and does no include any correcion o ake ino accoun changes in his variable. Equaion (F.1) implicily assumes ha vulnerabiliy remains consan over ime and ha i does no vary wih changes in 284

22 exposure. A re-expression of equaion (F.2) ha allows o make vulnerabiliy explici is as follows: ( y ) ( ) ( vw r ) ( vδ 1) r h x = e h( x ) = e h( x ) f >D = y (F.6) where v acs as scaling facor and represens he effec of vulnerabiliy over he rae of growh of he poenial economic losses, leading o larger mismaches wih he growh rae of he normalizaion variable if v 1. While i is uncerain how much reducion/increase in vulnerabiliy has occurred, i is very unlikely ha he implici assumpion of consan vulnerabiliy (i.e., v is sricly equal o 1), underpinning he sandard normalizaion procedure, holds. For example, in he USA building codes o flood-proof newly buil srucures have srenghened over ime in response o severe flood evens (Burby, 2001). To illusrae he effecs of a ime varying vulnerabiliy consider he example of he proprieor's income in Walon, Florida. For his example, he normalizaion was carried ou using he sae level proprieor's income and i is assumed ha δ = 0 in equaion (F.5). When he sandard normalizaion procedure is applied and vulnerabiliy is assumed o be consan and equal o one, hen due o he differences in he raes of growh of sae and f y couny level in he proprieor's income, he resuling normalized poenial losses y conain a posiive rend induced by he normalizaion procedure (Figure F6). Neverheless, when vulnerabiliy is no fixed ( v 1), resuls can be quie differen. If in ( ) realiy for he period vulnerabiliy decreased as v = (i.e., imposing a oal reducion in he rae of growh of he poenial economic losses of 20% 285

23 by year 2011), hen incorrecly a negaive rend in normalized losses found insead (Figure F6). f ( y ) y would be Disasers are he produc of a mixure of socioeconomic and geophysical processes for which he observed economic losses associaed wih hem are jus paricular realizaions. Differen levels of vulnerabiliy and exposure would have led o very differen coss for he same geophysical even. Such differences in levels can, among ohers, arise due o differen shares of economic secors, differen proporions in ime of y ha become increases in poenial economic losses for he differen localiies affeced and echnological changes. The limiaions of he sandard normalizaion mehod discussed above preclude is correc specificaion and, in consequence, his procedure canno guaranee ha no rend will be inroduced or aken away by is applicaion. Therefore, when rying o uncover he exisence of a climae change signal in disaser losses, he sandard normalizaion procedure could lead o resuls almos as misleading as assuming ha he increases in wealh and populaion have no effec on disaser losses. 286

24 Normalized poenial losses Year Figure F6. Effecs of vulnerabiliy over he normalizaion procedure. The resuls of applying he sandard normalizaion procedure (yellow line), assuming a consan vulnerabiliy, is compared wih hose of he sandard normalizaion procedure when vulnerabiliy linearly decreases he rae of growh of he poenial economic losses by 20% in 2011 (blue line). F Simulaion experimens for illusraing he poenial failures of he normalizaion procedure when invesigaing he presence of a climae change signal on disaser losses. This subsecion provides simulaion examples for illusraing he combined effecs of he differences in growh raes beween f ( y ) and y, and ime-dependen vulnerabiliy when invesigaing he exisence of a climae change signal afer he sandard normalizaion procedure has been applied. The general simulaion model is se up as follows: ( y ) h( x ) D = f (F.7) 287

25 ( y ) h ( x ) f >D = (F.8) y h ( x ) ε = (F.9) vw ( y ) e f = (F.10) r y = e (F.11) v = v (F.12) where ε ~ ( λ) exp, λ = c + b, w is he growh rae of he poenial economic losses, which is chosen o be 3% plus a normally disribued noise of > ( 0,0.01), v is a uniform random variable ( p q) U, and he rae of growh of he normalizaion variable is r = 4.5%. In all cases he simulaion experimens consised of 1,000 realizaions and he ime horizon was chosen o be 100 years. For he firs simulaion experimen, vulnerabiliy was held fixed ( v = 0), and ε was chosen o represen a saionary climae ( b = 0, λ = ). The goal of his simulaion is o illusrae ha even under he assumpion of a saionary climae, he normalizaion procedure can lead o differen rending behaviors depending on he differences in he raes w and r. Given ha he rue value of w is unknown, in pracice wha is observed afer he normalizaion of losses is he resuling nonsaionary/saionary behavior, a resul ha is commonly inerpreed as indicaing effecs on losses of climae change, adapaion and/or changes in vulnerabiliy. Table F1 shows he percenage of significan posiive/negaive rends in he realizaions of he damage funcion, losses and normalized losses 35. The slopes and he corresponding 35 Saisical significance is evaluaed a he 5% level. 288

26 -saisics values were obained from he regression represens eiher h ( x ), D or µ + u, where Z Z = β + >D. As expeced from a saionary climae, he percenage of significan rends in h ( x ) is 5.4%, which is very close o he number of rejecions of he null hypohesis ( β = 0) ha are expeced o occur by chance. This is no he case of he un-normalized losses of which 99.2% have posiive significan rends. These rends are caused by he growh in he poenial economic losses, which is wha he normalizaion procedure aims o correc. Table F1. Percenage of significan linear rends in he realizaions of he damage funcion h ( x ), losses l and normalized losses nl obained from he firs simulaion experimen. h ( x ) D >D Posiive Negaive Toal Neverheless, afer he normalizaion procedure has been applied, he percenage of he adjused losses ha show a significan negaive rend is 75.9% of he realizaions. These rends are an arifac caused by he differences in he raes of growh of he normalizaion variable y and he poenial economic losses f ( ) y. This rend is likely o be erroneously aribued o some geophysical or socioeconomic facors (e.g., climae change, or adapaion measures) oher han an unobservable mismach of he growh raes of y and ( ) f. y The second simulaion experimen allows for a nonsaionary climae where he rend in he damage funcion is defined by λ = (Figure F7). As is shown in he Table F2, in all cases he un-normalized losses D have a significan posiive rend, while he normalized losses obscured he climae change signal conained in h ( x ) abou 64% of he simulaions for which a posiive significan rend was originally deeced and he normalizaion incorrecly induced a significan negaive rend in 11.2% of hem. Since in realiy he rue informaion abou he generaing processes of h ( x ), D and >D is 289

27 lacking, he mismach beween significan rends in h ( x ) and he lack hereof in >D could be erroneously inerpreed as he absence of a climae change signal in disaser losses, while in fac climae change has increased damage. Table F2. Percenage of significan linear rends in he realizaions of he damage funcion h ( x ), losses D and normalized losses >D obained from he second simulaion experimen. h ( x ) D >D Posiive Negaive Toal The hird simulaion experimen also allows for a nonsaionary climae ( λ = ) bu inroduces a ime-decreasing vulnerabiliy deermined by equaion (F.12) and v ~ U ( 0,0.2). Tha is, for his experimen a reducion in vulnerabiliy causes an up o 20% decrease in he rae of growh of he poenial economic losses over he simulaed 100-year period. As shown in Table F3, given ha he normalizaion procedure assumes ha vulnerabiliy remains consan in ime (more precisely i ignores i, implying v = 1 in equaion F.8), he final effec is ha an even smaller number of imes he exising climae change rend in he damage funcion will sill be deecable in he normalized losses and, in abou 14.3% of he cases, his procedure will impar a negaive rend o hem. 290

28 h(x) Years Figure F7. Realizaions of he damage funcion h ( x ) represening he nonsaionary climae for simulaion experimen number wo. Table F3. Percenage of significan linear rends in he realizaions of he damage funcion h ( x ), losses D and normalized losses >D obained from he hird simulaion experimen. h ( x ) D >D Posiive Negaive Toal In general, hese simulaion experimens sugges ha when invesigaing he exisence of a climae change signal in disaser losses he curren normalizaion pracice could lead o resuls which are almos as misleading as if no correcion was applied for he increasing wealh and populaion. The exisence of unobserved variables precludes he possibiliy of verifying he validiy of he normalizaion and no firm conclusion abou he exisence of a climae change can in fac be drawn, alhough his has been common pracice o do (Bouwer, 2011). Evidenly, depending on he values chosen for he raes of growh r and w as well as he evoluion of he climae variable and vulnerabiliy, differen rends and percenages of significance can arise. This simulaion experimen shows ha only in very special cases, 291

29 he sandard normalizaion procedure can be successfully applied wihou inadverenly inroducing or aking away rends in he normalized losses. Even if he normalizaion variables are chosen correcly, i is quie likely ha hey will provide a poor represenaion of he acual growh in he poenial economic losses. If his is he case, he normalizaion procedure would impar a nonsaionary behavior o >D ha could blur any climae change signal or creae a false one. This is furher complicaed by he effecs of vulnerabiliy and adapaion which are largely deermined by socioeconomic facors and mosly unobservable, bu can hardly be considered o remain consan over ime. F2 A modificaion of he sandard normalizaion procedure o esimae he presence of a climae change signal in disaser losses. Observed losses from disasers represen a mixure of differen socioeconomic and geophysical processes ha are inherenly random, uncerain and in some cases unobservable. As shown in he previous secions, he sandard normalizaion procedure consising of scaling he observed losses by some wealh proxy variable is only adequae under very resricive condiions. In his secion a regression-based normalizaion procedure is presened which provides a way o es he significance of he chosen normalizaion variables, o esimae he coefficiens for scaling he rae of growh of he normalizaion variables and o es for he significance of climae variables ha may be considered as direc or indirec drivers of he observed losses. Equaion (F.1) can be expressed as: ( y ) ( y ) f >D = α h( x ) (F.13) g g y γr where ( ) ( ) = y e is a power funcion and γ = 1 in he sandard normalizaion γ = procedure. Noe ha when γ 1 he rae of growh of he normalizaion variable is scaled. This coefficien can be esimaed using he observed daa o preven he mismach 292

30 in he growh raes of f ( y ) and y. he exponenial of α + ε from: >D in equaions (F.1) and (F.13) is equivalen o - ln( D ) = α + γ ln( ) + ε (F.14) y when he resricion γ = 1 is imposed. The validiy of his resricion can be empirically esed and a more appropriae value for γ can be esimaed. Moreover, he saisical significance of y can be evaluaed, providing an objecive crierion for selecing he relevan normalizaion variables. signals ha are no explained by he scaling variable y. α + ε will conain he variabiliy and nonsaionary Invesigaing he exisence of a poenial climae change signal in >D is usually done by esing for a linear rend by means of a normal linear regression and ignoring ha losses are usually highly skewed and non-normally disribued. Srong deviaions from he normaliy assumpion can render hypohesis esing on he esimaed coefficiens invalid. Alernaive approaches like Box-Cox ransformaions are required in such cases. The Box-Cox ransformaion is a class of power ransformaions such ha: y * λ ( y 1) = ln λ if λ 0 ( y ) if λ = 0 where λ is commonly esimaed by maximizing he log-likelihood funcion or by minimizing he skewness coefficien. Furhermore, as is ofen discussed in he lieraure (Emanuel, 2011; Nordhaus, 2010; Pielke, 2007), h( x ) is likely o be a nonlinear funcion of x (e.g. a power funcion). Therefore, invesigaing he exisence of a climae change signal should no be limied o linear rends, bu should allow for a variey of sysemaic behavior ha could be consisen wih i. 293

31 A more efficien esimaion of equaion (F.13) ha allows for esimaing h ( x ) can be achieved if he regression model in (F.14) is exended o include a proxy variable for he climae driver x : ln( D ) = µ + γ ln( y ) + θ ln( x ) + u (F.15) In his case he damage funcion ( ) ( ) θ h x = α x (a power funcion) and he normalizaion funcion g ( y ) ( ) γ = y are esimaed joinly. As in he case of he normalizaion variables, he saisical significance of he chosen climae variable x can be assessed and he saisical adequacy of he model evaluaed. Noe ha he proposed regression-based approach encompasses he sandard normalizaion procedure, as he laer is a special case of he former. F3. Invesigaing he exisence of a climae change signal in he hurricane damage in he Unied Saes during he period The exisence of a climae change signal in he economic losses from hurricane landfalls in he U.S. has been ruled ou by previous sudies (Barredo, 2010; Choi and Fisher, 2003; Crompon e al., 2010; Downon e al., 2005; Pielke e al., 2008). Here we es if his conclusion is robus o using he regression-based normalizaion procedure described in he previous secion. Moreover, we examine if his conclusion sill holds when he loss daa is ransformed o be approximaely normally disribued before esing for he presence of a linear rend. F3.1. Socioeconomic and climae daa sources. All socioeconomic daa used here are aken from he Cener for Science and Technology Policy Research and cover he period (hp://sciencepolicy.colorado.edu/publicaions/special/normalized_hurricane_ damages.hml). The ime series of he inflaion adjused economic losses relaed o 294