Global Environmental Risks

f our aal of Er ononi c Gl obal Pei spr ai ves- I ' ol unt e 7, Number Env i r onment al 9- Fal l 1993- Pages 6J- 86 Ri sks Gr aci el a Chi chi l ni sky and Geof f r ey Heal / 1 anagi ng cl i mat e r i sk i s not a new act i vi t y . I n medi eval Engl and, a peasant f ar mer ' s l and was br oken i nt o many wi del y- di sper sed par cel s . M V Economi c hi st or i ans i nt er pr et t hi s as a way of hedgi ng cl i mat e r i sk ( see r ef er ences i n Br oml ey, 199?) . Land i n di f f er ent l ocat i ons woul d be af f ect ed di f f er ent l y by dr ought s, f l oods and f r ost s . By spr eadi ng l and hol di ngs over di f f er ent l ocat i ons, as wel l as by or gani zi ng agr i cul t ur al cooper at i ves and buyi ng i nsur ance, f ar mer s have managed cl i mat e r i sk f or many cent ur i es . Today' s concer ns about gl obal cl i mat e change br eak new gr ound i n t wo ways . One i s t he gl obal scope of t he pot ent i al changes consi der ed, such as changes i n t he at mospher e of t he pl anet . The second i s t hat t hese changes appear t o be dr i ven by human act i vi t y, whi ch has now r eached l evel s at whi ch i t can af f ect t he gl obal cl i mat e . Cl i mat e has al ways been unpr edi ct abl e, but t he i ncl usi on of t hese t wo new el ement s has ext ended t hi s uncer t ai nt y bot h qual i t at i vel y and quant i t at i vel y . Cl assi cal f or mul at i ons of uncer t ai nt y i n economi cs no l onger suf f i ce . Ther e i s uncer t ai nt y about basi c sci ent i f i c r el at i onshi ps, such as t he l i nk bet ween gaseous emi ssi ons and gl obal mean t emper at ur e. Ther e i s al so uncer t ai nt y about t he connect i on bet ween gl obal mean t emper at ur e and cl i mat e . Cl ear l y i t i s cl i mat e, a var i abl e encompassi ng wi nd pat t er ns, humi di t y and r ai n pat t er ns, and not j ust t emper at ur e, t hat mat t er s f r om a soci oeconomi c per spect i ve . The f l oods of 1993 i n t he Uni t ed St at es and Bangl adesh have r emi nded us of t he pr of ound vul ner abi l i t y of human set t l ement t o cl i mat e . Cl i mat ol ogi st s l i nk t hese t o El Ni f i o, t he ocean cur r ent of f t he coast of Chi l e, conf i r mi ng t he gl obal l i nkages wi t hi n t he ear t h' s cl i mat e syst em. Fut ur e emi ssi ons of gr eenhouse gases and f ut ur e cl i mat e ar e al so hi ghl y uncer t ai n . I n addi t i on, t hese emi ssi ons can be dr i ven by economi c act i vi t y and by pol i cy measur es : hence t he r i sks f aced ar e endogenous . w Gr aci el a Chi chi l ni sky i s Pr of essor of Economi cs, Heal i s Pr of essor and Seni or Vi ce Dean, Ci t y, New Yor k . Col umbi a Uni ver si t y, ar ul Geof f r ey Col umbi a Busi ness School , bot h i n Neu , Yor k 66 Jour nal of Economi c Per spect i ves Gr aci el a Chi chi l ni sky and Geof f r ey Heal Ther e ar e t wo st andar d ways i n whi ch soci et i es can r espond t o t i l e r associ at ed wi t h such uncer t ai nt y . One way i s r ni l i gr al i on . The ot her i s i nsur a 11' e can t hi nk of t hem as br oadl y equi val ent t o pr event i on and cur e r espect i , i n t he medi cal f i el d . Mi t i gat i on means t aki ng measur es t o r educe t he possi bl e damage . One mi ni mi ze t he damage i f t i l e har mf ul es of doi ng t hi s i s t o t ake st eps t hat occur s . Bui l di ng l evees, canal s ; i n( ] f l ood dr ai nage syst er ns t o r educe t i l e i r nl of f l ood wat er s i s an exampl e . An al t er nat i ve appr oach t o mi t i gat i on i ! r educe t he i nci dence of I r ar r nf ul event s . Of cour se, i f st eps ar e t aken t o r ed t i l e r i sk of cl i mat e change, t hen t i l e r i sks bec ome endogenous, det er mi nec our pol i cy measur es . Thi s cont r ast s wi t h most model s of r esour ce- al l ocat under uncer t ai nt y . i n whi ch pr obabi l i t i es ar e about act s of nat ur e and t her ef or e exogenous . r The pr obabi l i t i es of st at es i n an Ar r ow- Debr eu f r a The second i ssue i s endogeni t y of r i sks . The r i sks t hat we f ace ar e af f ect ed by our act i ons . 3 The t hi r d i ssue i s cor r el at i on of r i sks . Cl i mat e changes wi l l I r r ever si bi l i t y i s t he f i nal i ssue . I n t hi s ar ea, man) maj or economi c deci si ons and t hei r consequences ar e l i kel y t o be i r r ever si bl e . Cl i mat e changes, t i l e mel t i ng of i ce caps, deser t i f i cat i on, speci es ext i nct i on, ar e al l pr ocesses not r ever si bl e, or at l east not on r el evant t i me scal es . I n summar y, we ar e deal i ng wi t h r i sks t hat cannot be al t er ed by agent s : t her e i s no scope f or mi t i gat i on i n t he second st of i mpr ovi ng odds . The s ame i s t r ue i n t he cl assi cal model s of i nsur ance ( see domi nat ed by t wo quest i ons : What 1972, 1970, wher e t he i nci dence of har mf ul event endogenous . I nsur ance by cont r ast does not hi ng t o r educe t he chances oI t o cl i mat e change . I t onl y ar r anges f or damage l ar ge sense of r i sk- pool i ng wor ks best f or l ar ge number s of smal l st at i st i cal l y i ndependent r i sks . W e t hus have t o ask what t ypes of mar ket s wor k best when r i sks ar e connect ed and col l ect i ve . nous, agai n t aken t o be exogenous . Mi t i gat i on acqui r es a new meani ng when r i sks af f ect number s of peopl e i n t he same way . A r i se i n sea l evel , f or exampl e, wi l l af f ect l ow- l evel coast al communi t i es i n most count r i es . I nsur ance i n t he t r adi t i onal wor k may be subj ect i ve and an agent ' s subj ect i ve pr obabi l i t i es may be .- t i r e by l ear ni ng . Howev er t he act ual f r equency of i nci dence of har mf ul evt exampl e Mal i nvaud . 67 col l ect i ve and uncer t ai nt y about i r r ever si bl e . In pol i cy t er ms, ar e poor l y under st ood, t he nat ur e gl obal cl i mat e change i mpl i es t hat and endoge- ext ent of soci et y' s posi t i on wi l l be cost i s i t wor t h i ncur r i ng t o r educe t i l e poor l y- under st ood r i sk of cl i mat e change, or t o i mpr ove our under st andi ng of t he r i sk .-" ' How may exi st i ng soci al i nst i t ut i ons, such as i nsur ance cont r act s and secur i t i es mar ket s, be used t o pr ovi de t he most ef f i ci ent al l ocat i on of t he r i sks associ at ed wi t h gl obal cl i mat e change% t hose who ar e adver sel y af i ect e( r ecei ve compensat i on af t er t he event , as i n t he case of f eder al di sast er r el i ef U. S. f l ood vi ct i ms . I nsur ance i s a maj or economi c act i vi t y, i nvol vi ng ber t h i nsur ance i ndust r y and l ar ge par t s of t he secur i t i es i ndust r y . Can t he exi s and ver y ext ensi ve pr i vat e sect or or gani zat i ons pr ovi de t hose at cl i mat e change wi i h adequat e i nsur ance cover % i f not , i n mar ket 6 i nst i t ut i ons mi ght be appr opr i at e i n t hi s c as e Thi s paper i s about t hem, r i sk why not % What char t hese and r el at ed quest i ons . I n at t empt i ng t o ans we deal wi t h many di f f er ent aspect s of t he t heor y of r i sk- bear i ng . F key i ssues r ecur i n our anal ysi s . The f i r st i ssue concer ns t he di f f i cul t y i n assessi ng r i sks . Most cl i m r el at ed r i sks ar e di f f i cul t t o quant i f y . I ndeed, i n a cl assi cal st at i st i cal sense pr obabi l i t i es descr i bi ng t hem ar e unk nowabl e . W e may never be abl e t o obst enough exper i ment s t o appr oxi mat e t he pr obabi l i t y of gl obal cl i mat e chang t he r el at i ve f r equency sense : such event s ar e i nher ent l y uni que . I t i s possi bl eval uat e t he f r equency of occur r ence of a heal t h r i sk f r om mor bi di t ) Ri sk- Al l ocat i on i n a Gener al Equi l i br i um Fr amewor k Economi st s have t wo st andar d model s of r i sk- al l ocat i on i n a mar ket omy . The mor e gener al i s t hat of Ar r ow and Debr eu, econ- i n whi ch agent s t r ade " cont i ngent commodi t i es . " The al t er nat i ve i s t he model of i nsur ance vi a r i sk pool i ng i n l ar ge popul at i ons . Nei t her case addr esses t i l e i ssue of mi t i gat i on vi a a r educt i on i n t he i nci dence of har mf ul event s . I n t he Ar r ow- Debr eu f r amewor k t her e i s a set of exogenous " st at es of nat ur e" whos e val ues ar e r andom and r epr esent t he sour ces of uncer t ai nt y . Cl assi cal l y one t hi nks of event s such as ear t hquakes and met eor st r i kes . Agent s i n t he ec onomy ar e al l owed t o t r ade commodi t i es cont i ngent on t he val ues of t hese exogenous var i abl es . Thes e ar e cal l ed " st at e- cont i ngent commodi t i es . " As exampl es, t hi nk of " wat er i n a dr ought " and " wat er i n a f l ood . " Wi t h a compl et e set . of mar ket s f or st at e- cont i ngent commodi t i es, t he f i r st t heor em of mor t al i t y dat a, as t he out comes of r epeat ed exper i ment s ar e avai l abl e . How, wel f ar e economi cs hol ds f or economi es under uncer t ai nt y : a Par et o ef f i ci ent way . " we cannot eval uat e t he r i sks f r om COzyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA emi ssi ons i n t hi s al l ocat i on of r esour ces can be at t ai ned by a compet i t i ve ec onomy wi t h uncer t ai nt y , about exogenous var i abl es. I I ; ur z ( 1974) set out a f r amewor k f or endogenous uncer t ai nt y : r ecent l y t hi s has been an f i el d, e . g. , Kur z ( 1990, f or t hcomi ng 1993) , Chi chi l ni sky and Wi t ( 1991) , Chi chi l ni sky, Dut t a 3 Endogenei t y of r i sks l eads t o mor al hazar d when r i sks t o agent s depend on t hei r act i ons, whi ch Heal ( 1992) , Chi chi l ni sky ( 1992) , Chi chi l ni sky . Hahn and Heal ( 1992) . cannot be obser ved by t i l e i nsur er s and wi l l be i nf l uenced by t i l e i nsur ance of f er ed . Thi s l eads t o ' I n t hi s r espect t her e may be a di f f er ence bet ween t he var i ous aspect s of cl i mat e r i sk . Th( ar gument s f or coi nsur ance ( see f or exampl e St i gl i t z, 1983) . I n t he pr esent cont ext such mor al hi st or i cal dat a on t he r el at i on bet ween at mospher i c C: ( ) _ and cl i mat e f r om t r ee r i ng and i ce hazar d pr obl ems ar e not cent r al t o t he anal ysi s : asymmet r i c i nf or mat i on i s not a char act er i st i c of st udi es . Wi t h ozone depl et i on t i l e phenomenon i s so new t hat such dat a i s not avai l abl e . cl i mat e r i sks . Endogenous uncer t ai nt y i s mor e gener al t han mor al hazar d . 68 _I our nai of Ecoi i ovt i c Per spect i ve .% Ar r ow ( 1953) showed t hat ef f i ci ency can i n f act be at t ai ned by usi ng mi xt ur e of secur i t i es mar ket s and mar ket s f or non- cont i nent commodi t i es, s( t hat a compl et e set of cont i ngent commodi t y mar ket s i s not r equi r ed . Thi obser vat i on pr ovi des a nat ur al and i mpar t ant . r ol e f or secur i t i es mar ket s i n 01al l ocat i on of r i sk- bear i ng . The secur i t i es used ar e cont r act s t hat pay one uni t i and onl y i f a par t i cul ar st at e occur s . Whi l e t he cont i ngent cont r act appr oach i i n pr i nci pl e al l - i ncl usi ve and cover s most concei vabl e cases of uncer t ai nt y, i t pr act i cal t er ms t her e ar e cases wher e i t can be i mpossi bl e t o i mpl ement . I t ca ; be ver y demandi ng i n t er ms of t he number of mar ket s r equi r ed ( Chi chi l ni sk and Heal , 1992) . For exampl e, i f agent s f ace i ndi vi dual r i sk ( i . e . , r i sks who% pr obabi l i t i es var y f r om i ndi vi dual t o i ndi vi dual ) , t hen i n a popul at i on of 10 si mi l ar agent s each of whom f aces t wo possi bl e st at es, t he number of mar ket r equi r ed woul d be 2 t ° " . ' The number of mar ket s r equi r ed i s so l ar ge as t o ni ak t he cont i ngent cont r act appr oach unr eal i st i c . The use of i nsur ance mar ket s f or pool i ng r i sks i s a l ess gener al but mcn pr act i cal al t er nat i ve . Thi s r equi r es t hat popul at i ons be l ar ge and t hat t he r i l l be smal l , si mi l ar and st at i st i cal l y i ndependent . The l aw of l ar ge number s t he oper at es and t he f r equency of occur r ence of an i nsur ed event i n a l ar ge samp of agent s appr oxi mat es i t s i nci dence i n t he popul at i on as a whol e . Ther e i s t i l t a r ol e f or i nsur ance compani es t o act as i nt er medi ar i es and pool l ar ge numbe of si mi l ar but st at i st i cal l y i ndependent r i sks . I n so doi ng t hey ar e abl e y aggr egat i on and t he use of t he l aw of l ar ge number s t o neut r al i ze t i l e r i sl f aced by many si mi l ar agent s . The mai n r ef er ences on t hi s ar e Ar r ow and Li r ( 1970) and Ni al i nvaud F1972, 1973) . ' The i nsur ance appr oach i s at a di sadvant age when r i sks ar e cor r el at e When l ar ge number s ar e l i kel y t o be af f ect ed at once, r i sk- pool i ng wi l l n Gl obal Envi r onment al Ri sks 69 t hem. They r ecogni ze t hat t her e ar e sever al di f f er ent opi ni ons about " , f l at t hese ar e, but f eel unabl e t o choose def i ni t i vel y bet ween t hese al t er nat i ves . I f t hey wer e expect ed ut i l i t y maxi mi zer s, t hey woul d be uncer t ai n about t hei r own pr ef er ences . I n such a case, i t i s nat ur al t o t hi nk, of t he f r equency di st r i but i on over cl i mat e changes as a st at e of t he wor l d, a r i sk, i n t he Savage sense : we do not know what val ue i t wi l l assume, and what ever val ue t hi s i s, i t af f ect s economi c act i vi t y . As shown bel ow, i gnor ance t hen assumes t he r ol e of a col l ect i ve r i sk, and can be t r eat ed by t he use of st at e- cont i ngent mar ket s . One somet i mes t hi nks of uncer t ai nt y about pr obabi l i t i es bei ng r esol ved by l ear ni ng . Thi s i s an avenue whi ch i s not open when sci ent i f i c knowl edge i s i ncompl et e and exper i ment s ar e not possi bl e . I n t hi s case an al t er nat i ve appr oach i s t he openi ng of l i es%, mar ket s ( Chi chi l ni sky and Heal , 1992, and t he di scussi on bel ow) . I n SUM: t he Ar r ow- Debceu appr oach t o r i sk al l ocat i on vi a st at e- cont i ngent mar ket s i s i n pr i nci pl e uni ver sal l y appl i cabl e . However , i t i s cumber some and per haps unr eal i st i c i n t he case of r i sks wi t h i ndi vi dual component s . I nsur ance mar ket s ar e mor e manageabl e, but l eave uncover ed col l ect i ve or cor r el at ed r i sks such as t he r i sk i nduced by i gnor ance of t he t r ue f r equency di st r i but i on of har mf ul event s . So i t woul d be nat ur al t o al l ow agent s t o t r ade secur i t i es cont i ngent on such col l ect i ve r i sks, and cover t he i ndi vi dual component s of r i sks by mut ual i nsur ance cont r act s . Thi s i s pr eci sel y t he appr oach t hat we devel op bel ow. Al t hough new t o t he economi cs l i t er at ur e, i t i s by no means new i n pr act i ce ; we ar gue bel ow t hat some of t he ol dest r i sk- bear i ng i nst i t ut i ons r ecor ded, agr i cul t ur al cooper at i ves, have exact l y t hi s st r uct ur e . wor k . However i t does have t he advant age r el at i ve t o t he cont i ngent mar k appr oach of economi zi ng dr amat i cal l y on t he number of mar ket s needed . I gnor anc e as Col l ect i ve Ri s k t he above exampl e, onl y t wo mut ual i nsur ance cont r act s and 2809 secur i t i 2i " " woul d be needed i nst ead of cont i ngent cont r act s ( Chi chi l ni sky and He . 1992 ; Cass, Chi chi l ni sky and Wu, 1991) . Consi der an economy i n whi ch agent s f ace r i sks whose r el at i ve f r equenci es t hey know t hat t hey cannot eval uat e . Such r i sks coul d der i ve f r om t he i mpact of gl obal cl i mat e change on i ncome l evel s vi a f l oods, st or ms or dr ought s, or f r om t he ef f ect s on heal t h of ozone depl et i on, aci d r ai n, or ai r pol l ut i on . What mar ket st r uct ur e woul d suf f i ce t o assur e ef f i ci ent al l ocat i ons i n t hi s si t uat i on? " Ther e ar e wi del y di f f er i ng opi ni ons about t hese i mpact s, on whi ch t her e i s i nadequat e i nf or mat i on . When r i sks ar e al l ocat ed by t r adi ng st at e- cont i ngent secur i t i es, or r i sk- pool i ng and i nsur ance, i t i s ver b i mpor t ant t hat agent s know, or bel i eve t hat d knnu! , t he r el at i ve f r equenci es of ci t e st at es of nat ur e, at l east appr oxi mat el y . Thi s obvi ous when t r adi ng i nsur ance cont r act s. The act uar i al cal cul at i ons needed set i nsur ance pr emi a can onl y be per f or med i f t he par t i es bel i eve t hat t r el at i ve f r equenci es of t he i nsur ed event s ar e appr oxi mat el y known. I n t he Ar r ow- Debr eu appr oach, i t suf f i ces t o t hi nk of agent s maxi mi zi expect ed ut i l i t y t o appr eci at e t he need f or t hem t o know, or at l east behave a : t hey know, t he r el at i ve f r equenci es of exogenous st at es . These f r equenci es t he wei ght s pl aced on t hei r ut i l i t i es f r om st at e- dependent consumpt i on. T poi nt i s si mpl e : i f agent s cannot assi gn r el at i ve f r equenci es t hen t hei r pr ef ences ar e not wel l - def i ned and t hey cannot act t o maxi mi ze expect ed ut i l i t y . 1n t he cont ext of cl i mat e change t hi s may be t oo demandi ng . Agent s do t know t he f r equenci es of di f f er ent st at es, and r ecogni ze t hat t hey do not kn Chi chi l ni sky and Heal ( 1992) f or mal i ze t hi s t ype of si t uat i on i n a gener al equi l i br i um model . Each agent f aces t he r i sk of bei ng i n one of sever al st at es ( e . g . heal t hy or si ck, pr oduct i ve or unpr oduct i ve) . No one knows what wi l l be t he t r ue f r equency di st r i but i on of af f ect ed agent s . A pr obabi l i t y i s assi gned t o each possi bl e f r equency . A t ypi cal pr obabi l i t y di st r i but i on of t hi s t ype mi ght st at e f or exampl e t hat t her e i s a 10 per cent chance t hat 9( 1 per cent of t he popul at i on wi l l be har med by gl obal war mi ng, a 25 per cent chance t hat 50 per cent of t he popul at i on wi l l be har med, and so on . The pr obabi l i t y di st r i but i on over al t er nat i ve f r equency di st r i but i ons may be di f f er ent f r om i ndi vi dual t o i ndi vi dual . 70 Gr aci el a Chi chi l nt sky and Geof f r ey Heal f nur nal of Econonuc 1' er sf ) ect i aes we have t wo l evel s of uncer t ai nt y . The f i r st l evel of uncer t ai nt y i s col l ect i ve : what i s t i l e di st r i but i on of agent s who ar e har med i n t he economy% Wi l l 90 per cent be har med, or onl y 3( 1 per cent - Thi s i s a Havi ng deal t I n t hi s f r amewor k, quest i on about t i l e aggr egat e i nci dence of t he phenomenon over t he popul at i on as a whol e . The second l evel of uncer t ai nt 3 i s i ndi vi dual : i t i s uncer t ai nt y about whet her a gi ven agent about quest i ons such by cl i mat e change . I t devol ve i s har med or not as : gi ven t hat 90 per cent t he popul at i on of wi l l be wi t h i ndi vi dual col l ect i ve r i sks . W e need r i sks by mut ual Ar r ow secur i t i es t o deal i nsur ance, wi t h we st i l l 71 f ace t hese col l ect i ve r i sks i nduced by uncer t ai nt y about t he over al l di st r i but i on of adver se ef f ect s . Ar r ow secur i t i es ar e usual l y def i ned as secur i t i es t hat pay one dol l ar i f and onl y i f a par t i cul ar st at e of t he wor l d occur s . Her e t i l e) , pay one dol l ar i f and onl y i f t her e i s a par t i cul ar f r equency of af f ect ed par t i es i n t he popul at i on . As al r eady not ed, t he i nci dence of i mpact s on t he popul at i on as a whol e i s bei ng t r eat ed as t i l e depl et i on of t he ozone l ayer or cancer or t he i mpact of cl i mat e change on agr i cul t ur al pr oduct i vi t y, t i l e t w( l evel s of uncer t ai nt y ar e : f i r st , uncer t ai nt y about t i l e t r ue r el at i onshi p bet ween t he wor l d" i n t he Ar r ow- Debr eu sense . W e t r eat each possi bl e di st r i but i on of adver se af f ect s as a di st i nct col l ect i ve st at e, and use secur i t i es mar ket s t o enabl e par t i es t o t r ansf er weal t h bet ween t hese st at es . One Ar r ow secur i t y i s needed f or each possi bl e di st r i but i on of adver se ef f ect s wor l dwi de, ozone depl et i on and t i l e i nci dence of i ndi vi dual di sease i n t he popul at i on as t whol e, or about t he t r ue r el at i onshi p bet ween cl i mat e change and agr i cul t ur a because t o at t ai n Par et o ef f i ci ency each separ at e st at e must secur i t y . har med, wi l l I n our a par t i cul ar agent exampl es of t he i mpact pr oduct i vi t y ; and secondl y, a " st at e of be har med or mot = of whet her uncer t ai nt y about any gi ven per son of c ommuni t y wi l l be af f ect ed . Our i gnor ance of sci ent i f i c pr ocesses ( l i ke t i l e r el at i on bet ween oz om emi ssi on and cl i mat e change) cause , depl et i on and ski n cancer or bet ween M t he col l ect i ve f r equency of r i sk, by whi ch we har med agent s i n quency i s cent r al mean uncer t ai nt y about but we wi l l t hi s . Onc e f r equenci es ar e known, tile Uncer t ai nt y about t o t i l e pr obl em. When t hi s i s r esol ved we wi l l who i s damaged and who i s not , descr i bi ng t he t he popul at i on . at l east act uar i al r el at i v , t hi s f r e st i l l not knos k now t he f r equent cal cul at i ons can b conduct ed and t he pr obl em i s i nsur abl e . Vt i ' e pr opose an i nst i t ut i onal st r uct ur e whi ch uses t wo t ypes of f i n : ul ci .- i nst r ument s whi ch ar e t ai l or ed t o t hese t wo aspect s of t i l e pr obl em. Thes e ca e f ol l ow a f r at newor l ead t o ef f i ci ent al l ocat i on i n t he f ace of such r i sks . W est abl i shed by Cass, Chi chi l ni sky and \ 1 ' u ( 1991) and Chi chi l ni sky and He: be cover ed by a The f ol l owi ng exampl e wi l l hel p t o mak e t hi s f r amewor k concr et e . Consi der a wor l d of t wo count r i es 1 and 2, i n whi ch t i l e cl i mat e may be i n one of t wo st at es a or / 3 . Ther e ar e t wo possi bl e pr obabi l i t y di st r i but i ons over t hese t wo cl i mat e st at es . These di st r i but i ons ar e cal l ed A and B, wi t h di st r i but i on A gi vi ng a pr obabi l i t y of 0 . 1 t o cl i mat e st at e a and a pr obabi l i t y of 0 . 9 t o cl i mat e st at e 6 . Di st r i but i on B gi ves t i l e r ever se pr obabi l i t i es . i . e . , i t gi ves pr obabi l i t y 0 . 9 t o cl i mat e st at e a and pr obabi l i t y 0 . 1 t o cl i mat e st at e ( 3 . The endowment s of t he t wo count r i es depend on t he cl i mat e st at e, and ar e as f ol l ows : t o, ( a) i s count r y 1' s endowment vect or i f t he cl i mat e i s i n st at e a, and W2( a) i s t he cor r espondi ng endowment f or count r y 2 . Si mi l ar l y, endowment s i n cl i mat e st at e / 3 ar e gi ven by t o, ( Q) and o) , ( / 3) r espect i vel y . Endowment s sat i sf y m, ( a) > w, ( a) and eu, ( f 3) < w10) , so t hat count r y I i s r el at i vel y bet t er of f i n st at e a and count r y 2 i n st at e / 3 . To r each an ef f i ci ent al l ocat i on of r i sks we need t wo Ar r ow secur i t i es . One, pays $1 mi l l i on i f and onl y i f t he pr obabi l i t y di st r i but i on over st at es of t he cl i mat e i s A . The ot her , SB, pays $1 mi l l i on i f and onl y i f t he pr obabi l i t y di st r i but i on over st at es of t i l e cl i mat e i s B. I n pr act i ce of cour se, pr obabi l i t y di st r i but i ons ar e not obser vabl e, and we cannot condi t i on cont r act s on unobSA, ( 1992) . One i nst r ument i s a mut ual i nsur ance cont r act t o deal wi t h t he r i sks f aced E communi t i es cont i ngent on each possi bl e di st r i but i on of har mf i ef f ect s wor l dwi de . A mut ual i nsur ance cont r act i s an agr eement bet ween par t i ( agent s or subj ect t o si mi l ar r i sks t hat t hose who ar e har med wi l l be compensat ed by t l - ot her s . Exampl es ar e agr i cul t ur al cooper at i ves of t he t ype r ecor ded i n Eur or at l east si nce t he f i f t eent h cent ur y, and t he ni net eent h cent ur y U . K. wor ker associ at i ons and f r i endl y soci et i es . Thes e i nvol ved agr eement s bet ween a gr ou i f one wer e si ck and unabl e t o wor k, t hat wor ker woul d I compensat ed by t he ot her s who wer e not har med . I n t he pr esent cont ext , of coul d t hi nk of gr oups of communi t i es subj ect t o t he possi bl e i mpact of cl i ma of wor ker s t hat change, wi t h t hose unhar med compensat i ng t he ot her s . Mak i ng t he t er ms such a mut ual i nsur ance cont r act cont i ngent on t he di st r i but i on of har mf ser vabl e event s . So condi t i oni ng on a pr obabi l i t y di st r i but i on means condi t i oni ng on f r equency di st r i but i ons consi st ent wi t h t hat pr obabi l i t y di st r i but i on i n a sampl i ng sense . Count r i es can spr ead t he r i sk ar i si ng f r om not k nowi ng whi ch i s t he t r ue st at es of t i l e cl i mat e by t r adi ng t hese t wo secur i t i es . I n addi t i on t hey mak e mut ual i nsur ance cont r act s condi t i onal on st at es of t i l e cl i mat e. Such a cont r act coul d t ake t he f ol l owi ng f or m. I f t he di st r i but i on over cl i mat e st at es i s A ( di st r i but i on A gi ves pr obabi l i t y 0 . 1 t o cl i mat e st at e a and di st r i but i on over t her e bet ween t he par t i es f or each possi bl e aggr egat e di st r i but i on of har mf ul ef f ec To k now what compensat i on i s due i n any par t i cul ar case, t he par t i es have f i t pr obabi l i t y 0 . 9 t o cl i mat e st at e ( 3) t hen count r y I mak es a t r ansf er Ai , 2 t o count r y 2 i f t he st at e of t he cl i mat e i s a, and count r y 2 mak es a t r ansf er A2, t o t count r y 1 i f t he cl i mat e st at e i s f 3 . Thes e t r ansf er s sat i sf y O" A, , 2 + 0 . 9A2, t = 0 so t hat t i l e expect ed t r ansf er i s zer o and t he mut ual i nsur ance cont r act i s t o assess t he di st r i but i on of har mf ul ef f ect s gl obal l y, deci de whi ch mut ual i nsur ance cont r act t o appl y . act uar i al l y f ai r . Ther e woul d be a si mi l ar cont r act t o cover t he case when t he di st r i but i on over cl i mat e st at es i s B . ef f ect s wor l dwi de means t hat i s a di f f er ent compensat i on agr eeme and on t he basi s of t i 72 J 0111 ) - / Gl obal Euvi r onr nenl al Ri sks of Er anout i c Per sJsecl i r t es To susnwl ar i ze t he ar gument : Our i gnor ance of t he f r equency of t he i mpact s of cl i mat e change const i t ut es a col l ect i ve r i sk . Thi s col l ect i ve r i sk can be al l ocat ed t hr ough mar ket s f or secur i t i es t hat pay of f cont i ngent on t hat f r e quency . For t he i ndi vi dual r i sks t hat r emai n, i t i s mor e pr act i cal t o use mut ual i nsur ance cont r act s : t hi s i s done by havi ng a di f f er ent i ndi vi dual i nsur ance cont r act f or each possi bl e f r equency of i mpact s . Ther e ar e t wo f eat ur es of t he r esul t s whi ch ar e of gener al i nt er est . One i s t he devel opment of ' a f r amewor k f or achi evi ng ef f i ci ent al l ocat i ons i n t he f ace of uncer t ai n i ndi vi dual r i sks . Gi ven r api d changes i n t echnol ogy wi t h pot ent i al l y f ar - r eachi ng envi r onment al i mpact s and heal t h ef f ect s, t he pr obl em of pr ovi di ng i nsur ance agai nst such r i sks i s par t i cul ar l y i mpor t ant . I t i s a mat t er of ver y act i ve concer n i n t he i nsur ance i ndust r y . The second i nt er est i ng f eat ur e i s t he way a combi nat i on of secur i t i es mar ket s and i nsur ance mar ket s can be used t o pr ovi de a r el at i vel y si mpl e i nst i t ut i onal st r uct ur e f or deal i ng wi t h unknowabl e al l ( ] cor r el at ed r i sks . An I nst i t ut i onal Fr amewor k Our anal ysi s suggest s t hat al t hough t he r i sks associ at ed wi t h gl obal cl i mat e change ar e ver y di f f i cul t t o eval uat e, t her e i s never t hel ess a mar ket f r amewor k wi t hi n whi ch i nsur ance can be pr ovi ded . I t i nvol ves f i r st i dent i f yi ng t he set of 73 si nce t hen, ' and have pr ovi ded mut ual i nsur ance cont r act s f or t hei r member s, i n t hat t hey have ar r anged t r ansf er s f r om t he l ess t o t he mor e f or t unat e i n any gi ven season, t he si ze of t he t r ansf er dependi ng on t he over al l l evel of pr osper i t y . They al so hedge agai nst t he over al l f r equency of poor cr op yi el ds i n t hei r communi t l by bui l di ng up r eser ves t o car r y over f r om good t o had year s . So t he} , have act ual l y , f ul f i l l ed bot h of t he i nsur ance f unct i ons out l i ned above- snaki ng t r ansf er s bet ween agent s cont i ngent on t he over al l i nci dence of negat i ve event s, and al l owi ng a mechani sm f or t r ansf er r i ng weal t h bet ween st at es i n t he sense of hi gh or l o" , over al l i nci dences of negat i ve event s i n t he popul at i on . Tr adi ng Ri sks . An i nt er est i ng aspect of t he mar ket s j ust descr i bed i s t hat t i l e) - can pr ovi de a nat ur al mechani sm f or r econci l i ng di f f er ences i n assessment s of t he l i kel i hood of i mpor t ant cl i mat e changes bet ween count r i es, and f or t est i ng t he convi ct i on behi nd publ i cl y- st at ed posi t i ons . Suppose f or exampl e t he Uni t ed St at es bel i eves i t most l i kel y t hat t her e wi l l he l i t t l e cl i mat e change, and t he Eur opean Communi t y bel i eves ot her wi se . Then t hr ough t he mar ket f or secur i t i es whose payof f s depend on whi ch descr i pt i on of cl i mat e change i s cor r ect , t he Uni t ed St at es wi l l nat ur al l y sel l i nsur ance t o t he E. C. The Uni t ed St at es woul d wi sh t o be a sel l er of secur i t i es whi ch pay i f cl i mat e change i s ser i ous, because of i t s bel i ef t hat t hi s event wi l l not occur , and a buyer of secur i t i es t hat pay i f i t i s not , because of i t s bel i ef t hat t hi s wi l l be t he out come . The E . C . woul d be on t he opposi t e si des of t hese possi bl e descr i pt i ons of t he col l ect i ve r i sks . Nat ur al descr i pt i ons of r i sk ar e f r equenci es of occur r ence of cl i mat e- r el at ed event s such as f l oods, t r opi cal st or ms or cer t ai n t emper at ur e pat t er ns . Next t hi s f r amewor k i nvol ves i nt r oduci ng secur i t i es whose payof f s depend on whi ch descr i pt i on of t he r i sk i s cor r ect . Thi s amount s t o al l owi ng agent s t o bet on whi ch model of t he r i sk i s cor r ect . Bet t i ng on whi ch of sever al al t er nat i ve descr i pt i ons of t he way t he wor l d wor ks i s cor r ect , i s i n ef f ect what one does when choosi ng one r esear ch st r at egy over anot her . Cor por at i ons, i ndi vi dual s and gover nment s al l do t hi s r egul ar l y . For exampl e, a mar ket f or t he secur i t i es of hi gh- t echnol ogy f i r ms pur sui ng di f f er ent r esear ch st r at egi es t owar ds t he I nt er nat i onal mar ket s f or t he r i sks of cl i mat e change woul d al so pr ovi de an obj ect i ve t est of t he ser i ousness wi t h whi ch count r i es adher e t o t hei r publ i cl ypr of essed posi t i ons on t he r i sk of cl i mat e change . I t i s possi bl e t hat a count r y mi ght publ i cl y pr of ess t o a l ack of concer n about t he r i sks of cl i mat e change, i n spi t e of act ual l y bei ng concer ned about t hese r i sks, i n or der t o f r ee r i de on CO. , same goal i s a f i nanci al mar ket i n whi ch t hese bet s ar e made . An addi t i onal exampl e i s pr ovi ded by t he Chi cago Boar d of Tr ade, whi ch i s i n t he pr ocess of i nt r oduci ng secur i t i es cal l ed " cat ast r ophe f ut ur es" whose payof f s depend i nt er al i a oi l t he i nci dence of t r opi cal st or ms i n t he Uni t ed St at es, as measur ed by t he I nsur ance Ser vi ce Or gani zat i on' s i ndex . Thi s i s a par t i cul ar exampl e of t he i nst r ument s i ni t i al l y pr oposed i n Chi chi l ni skv and Heal ( 1992) . Fi nal l y, our appr oach i nvol ves est abl i shi ng compensat i on agr eement s bet ween har med and unhar med r egi ons t hat depend on whi ch descr i pt i on of t he change not bei ng ser i ous, and buy t hose payi ng of f i f i t i s ser i ous . Consi st ency wi t h i t s publ i c posi t i ons woul d r equi r e t hat i t be on exact l y t he opposi t e si des of t hese mar ket s . Ther e woul d t her ef or e be a cash cost t o convi nci ng and consi st ent mi sr epr esent at i on of t r ue bel i ef s . These cash cost s coul d of f set some of t he r i sk t ur ns out t o be cor r ect . Mut ual i nsur ance cont r act s or mut ual compensa t i on agr eement s ar e al r eady par t of our i nst i t ut i onal f r amewor k . I n f act , t hey dat e back t o t i l e ni net eent h cent ur y and beyond, and wer e t he f oundat i ons of many cur r ent i nsur ance compani es and t r ade uni ons . Consi der f or exampl e agr i cul t ur al cooper at i ves, pr obabl y t he ol dest r i sk- al l ocat i on i nst i t ut i ons i n t he wor l d . I n f act , one of t he l ar gest banks i n I t al y, t he Mont e dei Paschi di Si ena, was l bunded t o pl ay t hi s r ol e i n 1473 . The) - have i nsur ed agai nst weat her r i sks mar ket s . abat ement pol i ci es i nt r oduced by ot her s . These i ssues ar e di scussed i n det ai l i n Heal ( 1993) and t he r ef er ences ci t ed t her e . The exi st ence of mar ket s f or t he r i sks of cl i mat e change woul d pl ace such a count r y i n a di l emma . The count r y' s t r ue bel i ef s woul d i ncl i ne i t t o sel l secur i t i es payi ng of f i n t he event of cl i mat e i ncent i ve t o f r ee emi ssi ons . r i de on ot her count r i es' ef f or t s to r educe gr eenhouse Not e t hat t r adi ng r i sks i s di f f er ent f r om t he t r adi ng of emi ssi on per mi t s, as di scussed i n t he ar t i cl es by Pot er ba and Weyant i n t hi s vol ume . The r ecogni t i on of uncer t ai nt y suggest s t he need t o consi der st at e- cont i ngent emi ssi on per mi t s, " i ' l t ey al so suppor t ed par t of t hi s r esear ch and pr ovi ded access to t hei r r ecor t l s. 74 f or awt l of Economi c Per sl ) ecl i r a"zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA s wher e t i l e st at e i s def i ned i n t er ms of t he f r equency of cl i mat e- change r el at ed event s . Per mi t s t o emi t CO._ woul d f or ex ampl e be cont i ngent on t he i nci dence of i ndi cat or s of cl i mat e change . Such cont i ngent emi ssi on per mi t s coul d pl ay Gr aci ekr Chi chi l ni sky and Geof f r ey Heal Fossi l out put , f uel s, capi t al equi pment 75 and t he at mospher e ar e used t o pr oduce st ock . whi ch may be c ons umed or r ei nvest ed t o augment t i l e capi t al Pr oduct i on gener at es emi ssi ons, whi ch af f ect t i l e pr obabi l i t y of a change i n t he t he r ol e of secur i t i es whose payof f s depend on t he col l ect i ve r i sk . I n t he cont ext of emi ssi on per mi t s, i t i s wor t h not i ng t he publ i c good nat ur e of t he cl i mat e . Cl i mat e i s a publ i c good . However , i t does not f i t f ul l y t i l e convent i onal par adi gm because emi ssi on abat ement , whi ch i s t he pr oduct i on of t he publ i c good " unc hanged cl i mat e, " i s conduct ed i ndependent l y i n t i l e st at e of var i ous count r i es of t he wor l d . I t i s not pr oduced i n a cent r al pr oduct i on f aci l i t y, as assumed i n t i l e usual t r eat ment s' of publ i c goods : i t i s a pr i vat el y pr oduced publ i c good . A consequence i s t hat economi c ef f i ci ency wi l l onl y i mpl y equal i zat i on of t he mar gi nal cost s of emi ssi on abat ement acr oss count r i es use of an exhaust i bl e r esour ce i n pr oduct i on . The r emai ni ng i nput i f l ump- s um t r ansf er s bet ween count r i es ar e made t o equal i ze t i l e mar gi nal ut i l i t y of i nc ome i n al l count r i es, a s omewhat unl i kel y cont i ngency . Equal i zat i on of t i l e mar gi nal cost s of emi ssi on abat ement acr oss count r i es i s of t en t aken as pr esent di scount ed ut i l i t y of consumpt i on . Ther e i s a const r ai nt amount of t he r esour ce t hat can be used, as t hi s i s exhaust i bl e : t her e i s al so a j ust i f i cat i on of t i l e super i or i t y of t r adeabl e per mi t s as a met hod f or cont r ol l i ng emi ssi ons . Thi s poi nt i s devel oped i n Chi chi l ni sky ( 1993) and Chi chi l ni sky and f l ea] ( 1993) . Mor e gener al l y, a key i ssue i s t hat an ef f i ci ent al l ocat i on of a publ i c good such as unc hanged cl i mat e must be suppor t ed by a Li ndahl equi l i br i um expect ed ut i l i t y subj ect t o t he r esour ce and nat i onal i ncome const r ai nt s, wher e and not ar e opt i mal a compet i t i ve equi l i br i um. I n gener al abl e emi ssi on per mi t s may not decent r al i ze compet i t i ve mar ket s f or t r adePar et o ef f i ci ent al l ocat i ons of abat ement . t i l e at mospher e . The at mospher e i s a r esour ce t hat st at e . I ni t i al l y t i l e at mospher e i s i n t he f avor abl e st at e but may change st ochast i cal l ) , t o t i l e unf avor abl e st at e, and once i n t hi s st at e wi l l r emai n t her e f or ever . The sour ce of emi ssi ons whi ch af f ect s t he pr obabi l i t y of cl i mat e change i s t he t o pr oduc- t i on i s t he capi t al st ock . An obvi ous exampl e of t hi s st r uct ur e i s t he emi ssi on of CO. , by t he use of f ossi l f uel s . Cons umpt i on yi el ds ut i l i t y and t i l e obj ect i ve i s t o maxi mi ze t i l e expect ed nat i onal i ncome i dent i t y . The over al l on t he t ot al pr obl em sol ved i nvol ves maxi mi zi ng t he expect at i on i s over t he pr ocess gover ni ng cl i mat e change . Heal ( 1984) char act er i zes opt i mal pat hs of consumpt i on, capi t al accumul at i on and use of f ossi l f uel f or t hi s pr obl em. He compar es t hese wi t h t hose t hat i mpact i n t he absence of an at mospher i c i mpact , of changes i n par amet er s such as t he di scount and al so st udi es t he r at e and degr ee of r i sk aver si on and uses t hi s t o i sol at e t he key par amet er s i n det er mi ni ng t he opt i mal r at e of use of f ossi l f undament al Opt i mal ent er s i nt o t he economy' s pr oduct i on f unct i on, whi ch may be i n a f avor abl e or an unf avor abl e Al l oc at i on wi t h Endogenous Ri s k s f uel s . The i nt r oduct i on of at mospher i c i mpact mak es a di f f er ence . The t i me pr of i l e of r esour ce use whi ch emer ges i s f l at t er t han t hat whi ch emer ges f r om an opt i mal depl et i on pr obl em wi t h no at mospher i c i mpact . I ni t i al l evel s of r esour ce use ar e l ower , and t hey f al l mor e " ' hat i s i t wor t h . spendi ng t o r educe t he pr obabi l i t y of har mf ul cl i mat e changes Onl y i f we can answer t hi s quest i on can we j udge pr oper l y pr oposal s f or car bon t axes, al t er nat i ve ener gy st r at egi es, and CO. - r educt i on pr ot ocol s . Car ef ul j udgment i s cr uci al , as al l of t hese i nvol ve ver y consi der abl e cost s, as sl owl y, t han i n t i l e no- at mospher i c- i mpact case . The di f f er ence depends on t i l e i ndi cat ed by Weyant ' s paper i n t hi s symposi um, Cl i ne ( 1992) and ot her s . Her e we shal l s ummar i z e one appr oach t o t hi s pr obl em, based on Heal ( 1984, 1990) . Thi s i s a model t hat exami nes t i l e ext ent t o whi ch t he consumpt i on of f ossi l pur e depl et i on case t hi s pr i ce r i ses at t he r at e of di scount : i n Heal ( 1984) i t may f uel s shoul d be cur t ai l ed because i t i ncr eases t he pr obabi l i t y of a change i n cl i mat e . The model i n Heal ( 1984) i s based on t hr ee assumpt i ons . Fi r st , t i l e at mospher e may be i n one of t wo st at es, one f avor abl e t o economi c act i vi t y and one unf avor abl e ( t her e i s a possi bi l i t y of a f ut ur e cl i mat e cat ast r ophe) . Secondl y, t he at mospher e mov es st ochast i cal l y f r om t he f avor abl e st at e to tile unf avor abl e, and once t her e r emai ns t her e f or ever , so t hat at mospher i c change cur r ent i s i r r ever si bl e . Fi nal l y, t he pr obabi l i t y of a t r ansi t i on f r om t i l e f avor abl e t o tile unf avor abl e- st at e i s endogenous and i ncr eases wi t h t i l e l evel of cumul at i ve emi ssi ons f r om t i l e use of f ossi l f uel s . The pr obabi l i t y t hat t hi s change wi l l def i ni t el y occur at s ome dat e i s l ess t han one, so t her e i s a posi t i ve pr obabi l i t y of t he change never occur i ng . char act er i zat i on i n t er ms of t he i nt er nal i zat i on of pr obabi l i st i c i nt er gener at i onal degr ee of r i sk aver si on and on t i l e par amet er s of t he pr obabi l i t y di st r i but i on r el at i ng cumul at i ve emi ssi on t o cl i mat e change . The behavi or of t he shadow pr i ce of t he r esour ce i s al so of i nt er est . I n t he f al l and even bec ome negat i ve . W e can i nt er pr et t he di f f er ence bet ween t he s hadow pr i ce of t he r esour ce i n t he no- at mospher i c- i mpact case and t he car bon t ax . Thi s t ax depends on t he count r y' s case as an opt i mal degr ee of r i sk aver si on and on t he par amet er s of t i l e pr obabi l i t y di st r i but i on descr i bi ng t i l e r i sk of cl i mat e change as a f unct i on of car bon emi ssi ons, as wel l as on t i l e damage r esul t i ng f r om cl i mat e change . The model t hus l eads t o a di st i nct i ve appr oach t o char act er i zi ng an opt i mal car bon t ax and i t s evol ut i on over t i me . ext er nal i t i es . Because it is Har t wi ck ( 1992) an i nt er t empor al model , gi ves an anal ysi s of it pr ovi des t hi s car bon t axes usi ng t hi s f r amewor k . The l i kel i hood of cl i mat e change as a f unct i on of economi c act i vi t y i s a key r el at i onshi p i n eval uat i ng t he choi ces posed i n t hi s model . Thi s i s a f unct i onal 76 Gl obal Envi r onment al Ri sks Jour nal of Economi c Per s1kchves 77 r el at i onshi p r at her t han a par amet er . Gl obal change R&D l eads us t o a bet t er under st andi ng of t hi s r el at i onshi p . I t i s wor t h st r essi ng t hat pr oper economi c anal ysi s r equi r es not j ust t he l i kel i hood of cl i mat e change as a r esul t of one par t i cul ar emi ssi on scenar i o, whi ch i s what most sci ent i f i c anal yses ar e pr ovi d- have sought t o capt ur e t hi s i n a f r amewor k f or cost - benef i t anal ysi s . Thi s has l ed t o t he concept of " opt i on val ue : " pr eser vi ng a uni que asset i n i t s pr esent st at e al l ows us t i l e possi bi l i t y of changi ng our mi nds l at er . Al t er i ng i t i r r ever si bl y does not . Pr eser vi ng i t has t hus t o be cr edi t ed wi t h an " opt i on i al ue" i ng, but r at her a syst emat i c eval uat i on of how t he nat ur e and l i kel i hood of cl i mat e change var i es wi t h t he pat t er n of economi c act i vi t y . The st udy and char act er i zat i on of t hi s l i kel i hood f unct i on i s an i mpor t ant t opi c f or i nt er di sci pl i nar y r esear ch . I t i s not sur pr i si ng t hat what i t i s wor t h payi ng t o r educe t i l e r i sk of cl i mat e because i t keeps open t he opt i on of r econsi der i ng t he deci si on . A concept r el at ed t o opt i on val ue i s t hat of non- use val ue or exi st ence val ue . We may val ue envi r onment al goods f or whi ch we have no i mmedi at e economi c use . The exi st ence of cer t ai n speci es i s i n t hi s cat egor y : t he Cal i f or change depends i nt er al i a on a soci et y' s degr ee of r i sk aver si on and di scount r at e . However , t hi s has an i nt er est i ng and i mpor t ant i mpl i cat i on . Even i f t her e wer e compl et e agr eement about al l of t he sci ent i f i c aspect s of t he gl obal change pr obl em, t her e coul d st i l l be di sagr eement about pol i cy r esponses . Because of t i l e i nt er nat i onal ext er nal i t i es associ at ed wi t h cl i mat e, so t hat al l count r i es " consume" t he same cl i mat e . CO_, abat ement pol i ci es onl y make sense i f coor di nat ed i nt er nat i onal l y ( Pot er ba' s paper i n t hi s symposi um; Bar r et t , 1990 ; Car r ar o and Si ni scal co, 1991 ; Heal , 1993b) . The f act t hat di f f er ent count r i es need not agr ee on pol i cy choi ces even i f t i r e) , agr ee on t he sci ent i f i c eval uat i on of t he pr obl em coul d cl ear l y make such agr eement di f f i cul t t o obt ai n . Di f f er ent count r i es' posi t i ons wi t h r espect i o measur es t o r est r i ct gr eenhouse gas emi ssi ons depend on t hei r di scount r at es and degr ees of r i sk aver si on . Ti l e Uni t ed St at es, f or exampl e, has been agai nst gl obal abat ement agr eement s, whi l e Ger many has been i n f avor . Thi s f i t s wi t h t he convent i onal wi sdom t hat t he f i nanci al and i ndust r i al communi t y i n t he Uni t ed St at es has bot h a hi gher di scount r at e and a l ower degr ee of r i sk aver si on ( gr eat er wi l l i ngness t o t ake r i sks) t han t hat i n Ger many . The di f f er ences i n pol i cy posi t i ons coul d t hen be at t r i but ed t o di f f er ences i n pr ef er ences r at her t han, or i n addi t i on t o, di f f er ent i nt er pr et at i ons of t he cur r ent sci ent i f i c evi dence . Di f f er ent per cept i ons of t he r i sk i nvol ved do not however pr ecl ude ef f i ci ent sol ut i ons . Economi cs i s about di f f er ences i n pr ef er ences l eadi ng t o t r ade . I n t hi s case di f f er ences i n at t i t udes t owar ds r i sk coul d be gr ounds f or t he i nt r oduct i on of mar ket s i n whi ch di f f er ent ef f i ci ency gai ns, as di scussed ear l i er . r i sk posi t i ons ar e t r aded, wi t h Opt i on Val ues and I r r ever si bi l i t y I n val ui ng envi r onment al r esour ces such as cur r ent cl i mat e condi t i ons, bi odi ver si t y, or compl ex ecol ogi cal syst ems, t i l e i r r ever si bi l i t y of deci si ons and event s can be cent r al . A key aspect of t hese r esour ces i s t hat once al t er ed t hey cannot easi l y be r est or ed t o t hei r cur r ent condi t i ons, at l east on a r el evant t i mescal e . The deci si on not t o pr eser ve a r i ch r eser voi r of bi odi ver si t y such as t i l e 60 mi l l i on- year - ol d Kor up f or est i n Ni ger i a i s i r r ever si bl e . The al t er at i on or dest r uct i on of a uni que asset of t hi s t ype has an awesome f i nal i t y, and anal yst s ni an condor , t i l e spot t ed owl , and var i ous snai l s and f i sh come t o mi nd . Ther e i s no sense i n whi ch we can cur r ent l y use t hese speci es : possi bl y one coul d ar gue t hat t he condor and t he owl have consumpt i on val ue f or t hose wi l l i ng t o make t he ef f or t needed t o see t hem, but f ew peopl e come i nt o t hi s cat egor y . One doubt s t hat t hi s i s a si gni f i cant i ssue wi t h t i l e snai l . The t wo concept s, opt i on val ue and non- use val ue, seem t o over l ap . Many goods whi ch exempl i f y one al so exempl i f y t he ot her . At t i l e same t i me, t her e ar e no doubt di f f er ences . Non- use val ues st em i n some degr ee f r om et hi cal consi der at i ons, f r om a r ecogni t i on t hat a speci es has a r i ght t o exi st even i f humani t y pl aces no di r ect val ue on i t . But one suspect s t hat behi nd man non- use val uat i ons t her e l ur ks an opt i on val ue : many non- use val uat i ons st em f r om an unst at ed bel i ef t hat a use val ue may emer ge . I n t hi s sect i on we r evi ew t wo di st i nct f or mul at i ons of t hi s i ssue, one i n whi ch t he r et ur ns t o a pr eser vat i on pr oj ect ar e uncer t ai n at pr esent but wi l l be r eveal ed i n t he f ut ur e, and one i n whi ch t he pr ef er ences of f ut ur e gener at i ons f or envi r onment al f aci l i t i es ar e uncer t ai n . The f i r st f r amewor k i s t he one i n whi ch t he i ssue of opt i on val ues has t r adi t i onal l y been st udi ed . We pr ovi de an out l i ne of t he ar gument i n t hi s case and i l l ust r at e t he f act t hat one needs t hr ee condi t i ons f or an opt i on val ue t o exi st . These ar e i r r ever si bi l i t y, t he acqui si t i on of i nf or mat i on wi t h t i l e passage of t i me, and an asymmet r y of t he under l yi ng pr obabi l i t y di st r i but i on . Si mi l ar r esul t s appl y t o t he case of uncer t ai nt y about t he pr ef er ences of f ut ur e gener at i ons . Wai t i ng f or I nf or mat i on The opt i on val ue of pr eser vi ng an envi r onment al or ecol ogi cal asset has been expl or ed i n t i l e cont ext of uncer t ai nt y about t he f ut ur e benef i t s associ at ed wi t h i t s exi st ence. A r evi ew of t i l e l i t er at ur e i s i n Fi sher and Kr ut i l l a ( 1985) . 5 The cent r al i ssue i s t hat benef i t s wi l l accr ue i n t he f ut ur e f r om t i l e pr eser vat i on of a r esour ce, but t hese ar e cur r ent l y unknown . I f t he r esour ce i s pr eser ved i nt o t i l e f ut ur e, t hen i n t he f ut ur e t he deci si on about whet her t o pr eser ve i t can be r econsi der ed i n t he l i ght of bet t er i nf or mat i on t hen avai l abl e about t he benef i t s f r om i t s exi st ence . I f i t i s not pr eser ved, t hen t her e i s no chance of r econsi der at i on when we have bet t er i nf or mat i on . I n t hi s case convent i onal deci si on r ul es wi l l under est i mat e t he val ue of pr eser vi ng t he asset . The f ol l ow' Amongs t t he st udi es of t hi s i ssue ar e Wei s br od ( 1964) , Kr ut i l l a ( 1967) , Ci chet t i and Fr eeman ( 1971) , Sc hmal ens ee ( 1972) , Ar r ow and Fi sher ( 1974) , Henr y ( 1974a, b) and Bohnt ( 1975) . 78 j our nal of Economi c Per sf ) ecl i nes Gr aci el a Chi chi l ni sky and Geof f r ey Heal Fi gur e 1 79 expect ed benef i t f r om devel opment ( assumi ng a zer o di scount r at e) i s b t , c o + Uncer t ai n Benef i t s f r om Pr eser vat i on i n Per i od 2 pb, c, + ( 1 - p) b 2 c, . W e have t o choose conser vat i on l evel s c t St at e s, : choose conser vat i on l evel Payof f i s b, c, . < 0. c, and c_, t o maxi mi ze ( t he expect ed benef i t ) . We f ocus on t he i nt er est i ng case i n whi ch t her e i s cur r ent l y no benef i t t o pr eser vat i on, 6 b t , < 0, nor i s t her e any benef i t i n st at e 1 i n t he f ut ur e, b, < 0 . However , t her e i s t i l e f ut ur e possi bi l i t y of st at e 2 i n whi ch t her e ar e posi t i ve benef i t s f r om pr eser vat i on, b 2 > 0 . I f deci si ons ar e r ever si bl e, we pr eser ve not hi ng at t i me t = 0, i . e . , we set c t , = 0. Then at t i me t = 1, we conser ve not hi ng i n st at e 1 and ever yt hi ng i n st at e 2, i . e . , we set c, = 0 and c_, = 1 . I n t he r ever si bl e case we can set c_, = I because by assumpt i on deci si ons made at 1 = 0 ar e r ever si bl e . t =0 zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA Choos e conser vat i on l evel c : benef i t i s b, ; < ( 1 . St at e s . , : c hoos e conser vat i on l evel c ._, . Payof f i s b, , > 0 . i ng exampl e ( f r om Dasgupt a and Heal , si mpl e f r amewor k . 1979) i l l ust r at es t he key poi nt i n a We shal l show t hat wi t h i r r ever si bl e deci si ons t her e i s an opt i on val ue t o conser vat i on i n t he i ni t i al per i od i f and onl y i f t her e i s a posi t i ve expect ed payof f f r om conser vat i on i n t hat per i od gi ven t hat we f ol l ow an opt i mal pol i cy . We cont r ast t hi s wi t h t he r ever si bl e case, i n whi ch we never conser ve i n t i l e f i r st per i od and t her e i s no opt i on val ue . Consi der t wo dat es, t he pr esent t = 0 and t he f ut ur e t = 1 . W e have one uni t of an envi r onment al asset . The benef i t f r om pr eser vi ng t hi s now at t i me t = 0 i s bt , . At t i me t = I i n t he f ut ur e t her e ar e t wo possi bl e st at es of nat ur e s, and s2 . The st at e of nat ur e i s r eveal ed at t i me t = 1 . I f t he st at e i s s, , t i l e benef i t of pr eser vi ng t he asset i s b, : i f s i s t he st at e, t he benef i t i s h- The s pr obabi l i t i es of s, and s, ar e p and ( 1 - p) r espect i vel y . Deci si ons about pr eser vat i on ar e made bot h cur r ent l y at t i me t = 0 and i n t he f ut ur e at i = l . At t = 0 a deci si on i s made on how much of t he asset t o pr eser ve unt i l I = l : at t hat dat e we may ei t her conser ve ever yt hi ng conser ved at I = 0, or conser ve l ess . Gi ven t hat dest r uct i on i s i r r ever si bl e, we cannot of cour se at 1 = I conser ve mor e t han was conser ved at t = 0. Our opt i ons at l = 1 ar e t her ef or e const r ai ned by t he deci si on made at l = 0. Thi s si t uat i on i s summar i zed i n Fi gur e 1 . We shal l compar e t he case al r eady descr i bed wher e t he deci si on made at t i me t = 0 i s i r r ever si bl e wi t h a hypot het i cal al t er nat i ve case i n whi ch t hi s deci si on can i n f act be r ever sed . I n t hi s case t he deci si on made at t i me t = 0 no l onger const r ai ns t he opt i ons avai l abl e at t i me t = I . We l ook at t hi s al t er nat i ve case f i r st , as i t i s si mpl er and pr ovi des a benchmar k . Let c t , be t he amount of t he r esour ce conser ved now at t i me I = 0, and c, and c 2 be t he amount s conser ved i n t he f ut ur e at t i me I = 1 i n st at es 1 and 2 r espect i vel y . The Now consi der t he r eal case i n whi ch t he deci si on at t i me I = 0 cannot be r ever sed l at er . I n t hi s case t he choi ce made at t = ( 1 does const r ai n t i l e choi ces open at t = 1 . We have t o sat i sf y t i l e const r ai nt t hat what i s conser ved at t i me I = 1 cannot exceed t hat whi ch Was conser ved i ni t i al l y, t hat i s, 0 < c, , C 2 < C O < l . I n par t i cul ar , i f ever yt hi ng i s dest r oyed i n t he f i r st per i od, t hen we have no opt i ons i n t he second . What pol i ci es now maxi mi ze ( t he expect ed benef i t ) ' I s t her e a val ue t o car r yi ng t he opt i on t o conser ve i nt o t he second per i od% Cl ear l y i f i n t he second per i od t he st at e of t he wor l d i s one i n whi ch t her e ar e posi t i ve benef i t s t o conser vat i on, t hen i n t hat per i od we wi l l conser ve ever yt hi ng l ef t t o us by our ear l i er deci si on, t hat i s we wi l l al ways set C . _ = C . I f however t he st at e i n t i l e f ut ur e i s unf avor abl e t o conser vat i on, t hen Ave wi l l conser ve not hi ng and set C, = 0. ' I t i s opt i mal t o conser ve i n t he f i r st per i od i f and onl y i f t her e i s a posi t i ve expect ed payof f t o f ut ur e conser vat i on, gi ven t hat r ye choose opt i mal l y l at er , i . e . , l ye Set C, = 0 and c_, = c . Cont r ast t hi s wi t h t he deci si on i n t he r ever si bl e case, i n whi ch we never conser ve and al ways chose c = 0. These t wo deci si ons ar e di f f er ent i f t he expect ed payof f t o conser vat i on i n t he f i r st per i od i s posi t i ve . " I n t hi s case t her e i s an opt i on val ue t o conser vat i on as a means of car r yi ng t he r esour ce i nt o t he second per i od and t aki ng advant age of f ut ur e i nf or mat i on . Opt i on Val ues Not e t hat t i l e exi st ence of an " opt i on val ue" does not depend on r i sk aver si on, as we assumed t hr oughout t he pr evi ous subsect i on t hat t he maxi f i l f bo > 0, t her e ar e benef i t s t o conser vat i on i n t he f i r st per i od, so t hat c t he f i r st per i od . Nt i e concent r at e conser ve i n per i od Not i ng t hat t op C, t he i nt er est i ng case of = 0 and C, + (I l evel - p) b 2) > = 1, i . e . , we conser ve i n b < ( 1, when, t i l e onl y i ncent i ve t o I i s t he possi bi l i t y of a posi t i ve r et ur n i n per i od 2 . = Ct , i n t he i r r ever si bl e case, t he expr essi on f or expect ed benef i t at t i l e of t hi s page r educes t o ( b t , + ( I - p) b z) c . As t he conser vat i on (b on is posi t i ve i f and onl y expr essi on i f t he der i vat i ve wi t h is l i near r espect to in C: C: , t i l e i ni t i al i s posi t i ve, i .e. 0 . The i nequal i t y has a si mpl e i nt er pr et at i on : t he l ef t - hand si de i s t he expect ed payof f f r om conser vat i on i n t he f i r st per i od . I t i s t he cer t ai n payof f i n t he f i r st per i od pl us t he expect ed payof f f r om conser vat i on i n t he second, gi ven t hat i f t he st at e unf avor abl e t o conser vat i on occur s t her e wi l l be no conser vat i on i n t he second per i od . I t i s t he expect ed payof f t o conser vat i on i n per i od one gi ven t hat an opt i mal " An i mpor t ant pol i cy i s f ol l owed subsequent l y . si mpl i f yi ng assumpt i on i n t hi s ex ampl e i s t he l i near i t y of payof f s pr eser vat i on . Fi sher and Kr ut i l l a ( 1985) di scuss t he r ol e of l i near i t y . i n t he l evel of 80 6I obal Eni dr onment al Ri sl u Jour nal of Economi c Per spect i ves 81 t nand i s t he expect ed val ue of benef i t s . ' The key i ssues her e ar e : f i r st , t he Because t hey mi ght val ue t hem snor e, we shoul d, i t i s ar gued, at t r i but e a val ue i r r ever si bi l i t y of t he deci si on ; second, t he f act t hat del ayi ng a deci si on can l et t o l eavi ng t hem t he opt i on of hi gh consumpt i on l evel s . Sol ow ( 1992) ar gues one t ake advant age of bet t er i nf or mat i on, and t hi r d, t hat on aver age t her e wi l l t hat an i mpor t ant el ement i n t he def i ni t i on of sust ai nabi l i t y i s r ecogni zi ng t he be benef i t s f r om conser vat i on i n t he f i r st possi bi l i t y t hat per i od, pr ovi ded t hat we choose opt i mal l y l at er ( as s hown i n not e 7) . t he pr ef er ences of f ut ur e gener at i ons about asset s may be ver y di f f er ent f r ot h our s ( see al so Chi chi l ni sky, envi r onment al 19931) ; Bel t r at t i , Ther e ar e i mpor t ant pr act i cal i mpl i cat i ons of t he anal ysi s t hat we have j ust Chi chi l ni sky and f l ea[ , f or t hcomi ng 1993) . Thi s seems cl ose t o t he concept of compl et ed . Cl i mat e change i s l i kel y t o be i r r ever si bl e i f i t occur s . So i n a cost - benef i t anal ysi s of pr event i ng cl i mat e change ( i . e . , pr eser vi ng t he at mo opt i on val ue set out above, and i ndeed i t i s, t hough t her e ar e s ome di f f er ences spher i c envi r onment ) , i t may be appr opr i at e t o cr edi t pr eser vat i on ( pr event i ng t hat ar e r eveal i ng . 1Ne next st udy t hi s pr obl em, dr awi ng heavi l y on r esul t s i n and usi ng Bel t r at t i , Chi chi l ni sky and Heal ( 1992) , a hi ghl y - si mpl i f i ed ver si on of cl i mat e change) t hat model . " wi t h an opt i on val ue . Thi s coul d be t he case i f t he passage a1; t i me i s l i kel y t o br i ng si gni f i cant new i nf or mat i on about t he l i kel i hood cl i mat e change or about i t s consequences . Ti l e most t hor ough st udy of t he cost s and benef i t s of r educi ng cl i mat e change i s Cl i ne ( 1992) . ) t seems wor t h not i ng t hat NNe shal l i l l ust r at e t he concl usi on t hat uncer t ai nt y about f ut ur e pr ef er ences of al t hough t hi s st udy r ef er s al one i s not suf f i ci ent r esour ce l ef t t o t i l e next t o pr oduce an " opt i on val ue" case f or i ncr easi ng t i l e gener at i on . I n addi t i on t o pur e uncer t ai nt y, be asymmet r y i n t he di st r i but i on must of t her e possi bl e changes i n [ ) r ef er ences . many t i mes t o t he sci ent i f i c uncer t ai nt i es associ at ed wi t h pr edi ct i ng cl i mat e Neut r al uncer t ai nt y ( i ncr eases and decr eases i n t i l e i nt ensi t y of pr ef er ences ar e change, i t at no poi nt at t r i but es an opt i on val ue t o pr event i ng cl i mat e change . equal l y l i kel y) does not gener at e a case f or l eavi ng mor e t o t he f ut ur e i n case Thi s means t hat Cl i ne' s st udy may syst emat i cal l y under est i mat e t he benef i t - cost t hey val ue t he r esour ce mor e hi ghl y t han us . Uncer t ai nt y r at i o of conser vat i on onl y when t he expect ed r et ur n t o pos t ponement pr eser vat i on of anal ysi s i n t he at mospher e i n i t s st at us quo . Ther e i s al so an Mar i ne and Ri chel s ( 1992) of t he val ue of wai t i ng f or sci ent i f i c mak es a case f or of consumpt i on i s posi t i ve . i nf or mat i on about t he gr eenhouse ef f ect . They consi der t wo possi bi l i t i es : act i ng Consi der a t wo per i od wor l d wher e t her e i s a f i xed t ot al st ock of a nat ur al st r ongl y now t o r educe t he emi ssi on of gr eenhouse gases, or t aki ng ver y l i mi t ed r esour ce t o be c ons umed i n t he t wo per i ods . The i ni t i al st ock i s k nown t o be s o . act i on now and wai t i ng unt i l t her e i s f ur t her sci ent i f i c evi dence . Taki ng maj or The amount s c ons umed i n t he f i r st and second per i ods ar e c, st eps t owar ds emi ssi on abat ement now amount s t o conser vi ng t he at mospher i c t i vel y : t hese must envi r onment i n i t s pr esent st at e, and shoul ct agai n be cr edi t ed wi t h an opt i on anyt hi ng t hat i s c ons umed i n t he f i r st per i od i s not avai l abl e i n t he second, val ue . Mar i ne and Ri chel s f ai l t o do t hi s, and so agai n under est i mat e t he val ue t hat consumpt i on her e i s an i r r ever si bl e depl et i on of t he st ock . The ut i l i t y f r om of buyi ng i nsur ance agai nst per i od one consumpt i on i s u( c, ) , whi ch i s an i ncr easi ng st r i ct l y concave f unc- t he gr eenhouse ef f ect by act i ng st r ongl y now. As and c . , r espec obvi ousl y sat i sf y c, + c 2 = s ( , . As t he st ock i s i r r epl aceabl e, so t he val ue of an opt i on gener al l y i ncr eases wi t h i ncr easi ng uncer t ai nt y about t he t i on . The ut i l i t y f r om second per i od consumpt i on i s unk nown : i t may be ei t her f ut ur e, ( 1 + a) u( c 2 ) wi t h pr obabi l i t y p or ( I and as uncer t ai nt y l ooms l ar ge i n any pr oj ect i ons war mi ng, t he ext ent r egar di ng gl obal of t he under est i mat e coul d be i mpor t ant . I t coul d f or exampl e be deci si ve i n t he endor sement of a gl obal car bon t ax . - l 6) l i ( c, , , ) wi t h pr obabi l i t y ( 1 - p) . Her e 0 < a, P < 1 . So t her e i s a pr obabi l i t y p t hat t he ut i l i t y der i ved f r om f ut ur e consumpt i on wi l l be " scal ed up" by a f act or a, and a pr obabi l i t y ( 1 - p) t hat i t wi l l be " scal ed down" by a f act or / 3 . Uncer t ai nt y about Fut ur e Gener at i ons Ther e ar e sever al Consi der f i r st as a benc hmar k t he case i n whi ch t her e wi l l be no change i n ways of gener al i zi ng or r ef i ni ng t i l e concept of opt i on pr ef er ences, so t hat we j ust have t o pi ck c, and c . , t o maxi mi ze u( c, ) + t t ( e! ) . val ue . A key consi der at i on seems t o be t he possi bi l i t y t hat f ut ur e gener at i ons Fi gur e 2 shows t hi s si t uat i on : t he l engt h of t he hor i zont al wi l l st ock of t he r esour ce . Cons umpt i on i n t he f i r st per i od c, val ue st at ement mar gi n, envi r onment al t hat t hen anal ysi s ( Heal , It may, r esour ces t hese r esour ces wi l l t hi s ef f ect mor e t han be scar cer , i s capt ur ed we do. If t hi s i s si mpl y a and so mor e val uabl e on t he i n t he usual appr oach t o cost - bet l ef i t 1993a) . however , st at ement t hat f ut ur e gener at i ons coul d have i s meas ur ed t o t he r i ght f r om t he l ef t - hand or i gi n and consumpt i on i n t he second per i od t o t he l ef t f r om t he r i ght - hand or i gi n . Mar gi nal t he opt i mal l evel s of be a axi s i s s ot , t he i ni t i al c, ut i l i t y i n each per i od i s pl ot t ed, and and c . , ar e t hose at whi ch t he mar gi nal ut i l i t y cur ves cr oss . I n t he absence of di scount i ng, and wi t h ut i l i t y f unct i ons t he s ame i n each di f f er ent pr ef er ences f r om us, and mi ght val ue envi r onment al asset s di f f er ent l y . per i od, t hese cur ves wi l l of cour se be symmet r i c, as s hown i n Fi gur e 2 . ` ' ! ' i ndyck ( 1991) consi der s a si mi l ar exampl e i n t he case of i r r ever si bl e i nvest ment deci si ons, and shows t hat t he opt i on val ue of del ayi ng an i nvest ment deci si on t o t ake advant age of i nf or mat i on t hat wi l l become avai l abl e i n t he f ut ur e, can be comput ed usi ng t he f or mul a used i n f i nance f or val ui ng an opt i on t o bi t ) a st ock . See al so Di xi t ( 1992) . " ' The f ul l model i s r adi cal l y di f f er ent f r ont most ot her model s i n whi ch opt i on val ues have been st udi ed . I t i s an i nf i ni t e- hor i zon st ochast i c dynami c opt i mi zat i on model i n whi ch t he maxi mand i s t he expect ed pr esent val ue of ut i l i t y and f ut ur e pr ef er ences evol ve st ochast i cal l c . 82 f our ual of Economi c Per specl i zt e., Gr aci el a Cl uchi l ni skY and Geof f r ey Heal Fi gur e 2 r at e and t he degr ee of r i sk aver si on ( Bel t r at t i , Unc er t ai nt y about Fut ur e Pr ef er enc es Chi chi l ni sky and Heal , 83 1992) . Does t hi s r educt i on i n per i od one c ons umpt i on r ef l ect an " opt i on val ue" i n t he sense of t he pr ev i ous sect i on% Mar gi nal ut i l i t y To under s t and t hi s, pos ed i ni t i al l y . " Second per i od mar gi nal ut i l i t y wi t h asymmet r i c uncer t ai nt y and / 6 - 0 . we hav e t o consi der Suppos e f i r st t hat ences but on av er age we expect Fi r st per i od mar gi nal t ai l i t y . decr eases bal anc e out t he mor e gener al case t hat we t her e i s uncer t ai nt y about f ut ur e pr ef er - no net c hange, i n t he s ens e t hat i ncr eases and i n pr obabi l i t y t er ms . Then t he s ec ond per i od mar gi nal ut i l i t y c ur v e i s unal t er ed by t i l e uncer t ai nt y about f ut ur e pr ef er enc es . I n t hi s case uncer t ai nt y about f ut ur e pr ef er ences wi l l not l ead t o a r educ t i on i n pr es ent c ons umpt i on . I ndeed i t wi l l l ead t o no c hanges i n an) , c ons umpt i on l evel s, ev en Second per i od mar gi nal ut i l i t y - ' t i l t cer t ai r uc . i f agent s ar e st r i ct l y r i sk aver se i n t he s ens e t hat t hei r ut i l i t y f unct i ons ar e st r i ct l y c onc av e. t 1.t I f on t he ot her hand t her e i s an expect at i on of an i ncr ease i n t i r e ut i l i t y of c ons umpt i on i n tile ut i l i t y c ur v e wi l l l i e abov e t hat s ec ond per i od, t hen t he per i od t wo ex pec t ed mar gi nal under cer t ai nt y and c ons equent l y t i l e opt i mal per i od one c ons umpt i on l evel wi l l be l ower t han under cer t ai nt y . Conv er s el y , i f t her e i s an expect at i on of a dec r eas e i n t he ut i l i t y of c ons umpt i on i n t he s ec ond per i od, t hen t her e wi l l be a decr ease i n t i l e per i od one c ons umpt i on r el at i ve t o i t s l evel under cer t ai nt y . rt I n concl usi on, uncer t ai nt y about Opt i mal f i r st per i od consumpt i on f al l s i t expect ed second per i od mar gi nal ut i l i t y r i ses . t o pr oduc e an " opt i on val ue" Opt i mal consumpt i on i n each per i od i s s / 2 wi t h no uncer t ai nt y . zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA gener at i on . t her e i s uncer t ai nt y about r esul t of f i r st per i od c ons umpt i on l evel t he possi bi l i t y of a shi f t in in t he second possi bl e c hanges t her e mus t pr ef er ences . Neut r al be as y mmet r y i n t he unc er t ai nt y wi t h i n- t o t he f ut ur e i n case t hei r pr ef er ences f or t he r esour ce ar e st r onger t han our s . Uncer t ai nt y mak es a case f or conser vat i on onl y when t he ex pec t ed r et ur n t o pos t ponement One f i nal of c ons umpt i on i s posi t i ve . obser vat i on and an i ndi cat i on of possi bl e f ut ur e Bel t r at t i . Chi chi l ni sky and Heal model r esear ch : tile of opt i on val ues s ummar i z ed her e i s one i n whi c h ut i l i t y i s der i v ed onl y f r om t he f l ow of c ons umpt i on of t i l e env i r on ment al r es our c e . I n pr act i ce t i r e st ock ut i l i t y f unct i on . For ex ampl e, f ut ur e pr ef er enc es as a may al so ent er as an ar gument of t he we val ue t he c ur r ent c l i mat e as an asset : we v al ue t wo qual i t at i vel y di f f er ent t ypes of opt i mal c ons umpt i on pat h, dependi ng on t owar ds t i l e nat ur al " Equal i zat i on of expect ed mar gi nal ut i l i t i es i n t i l e t wo per i ods r equi r es i n t hi s case t hat tt au 11( t I ) + p( 1 + a) u( c q ) + ( I ar t Now we have t o choose r , and r _, t o maxi mi ze t he expect at i on of ut i l i t y, whi ch as p = 0 i s - p) t t ( r _, ) . The sol ut i on t o t hi s r equi r es t hat t i l e mar gi nal ut i l i t ) of consumpt i on i n t i l e f i r st per i od equal s t i l e expect ed mar gi nal ut i l i t y i n t i l e second, i . e ., al l ar , in t i r e c ur r ent st ock of speci es or of r ai nf or est s . I n t hi s case t her e ar e l i kel y t o be i s now l ower t han bef or e, r esour ce . Gener al l y one c an s how t hat t i l e amount of t hi s r educt i on depends on t he pr obabi l i t y di st r i but i on gov er ni ng t i l e c hange i n pr ef er ences, t he di scount - suf f i ci ent t o t he next cr eases and decr eases equal l y l i kel y does not gener at e a case f or l eavi ng mor e pr ef er ences per i od- t hi nk of t hi s as uncer t ai nt y about t he pr ef er ences of a f ut ur e gener at i on . Al so si mpl i f y mat t er s by as s umi ng t hat f 3 = ( l , so t hat t i l e onl y possi bl e c hange i n pr ef er ences i s a " scal i ng up" of t i l e ut i l i t y of c ons umpt i on . Thi s c or r es ponds t o t he case t hat we ment i oned at t i l e st ar t of t hi s sect i on, namel y t he possi bi l i t y of an . i ncr ease i n t he appr eci at i on t hat peopl e hav e f or t i l e r esour ce . t t The ex pec t ed mar gi nal ut i l i t y c ur v e f or s ec ond per i od c ons umpt i on i s no%v abov e t he cer t ai n s ec ond per i od mar gi nal ut i l i t y cur ve, as s hown i n Fi gur e 2. The opt i mal case f or i ncr easi ng t he r es our c e l ef t I n addi t i on t o pur e uncer t ai nt y, di st r i but i on of Now s uppos e t hat f ut ur e pr ef er ences al one i s not r2 °( pa+1) al- l at ., +a) +( 1 - h) ( I - p) ) er -., . Now t he per i od t wo expect ed mar gi nal ut i l i t y cur ve may i n gener al l i e above or bel ow t i l e f i r st per i od cur ve: i t wi l l be exact l y t he same as t i l e f i r st per i od cur ve, i . e . , t i l e cur ve i n t i l e absence of uncer t ai nt y, i f and onl y i f t i l e coef f i ci ent of al l / a( 2 i s one, i . e . , ( p( 1 + a) + ( I - p) ( I - 9) ) = I . Thi s condi t i on means t hat t he expect ed shi f t i n per i od t wo ut i l i t y i s zer o . 13 Cl ear l y ( pa + 1) > 1, so t hat t he per i od t wo mar gi nal ut i l i t y cur ve i s mov ed t i l l I , uncer t ai nt y and per i od one ( ousunt pt i on f al l s, as i n Pi gur c ° . al l =W l Techni cal l y, t hi s i s because uncer t ai nt y her e i s about t i l e ut i l i t y f unct i ons, and t he maxi mand i s l i near i n t hese . Soci et y i s not r i sk- aver se about ut i l i t y l evel s . even t hough i t i s about consumpt i on l evel s . 84 j our nal of Ecouunr i c f er sper l i ves t he si ze of t he i ni t i al st ock of t he r esour ce . I f t hi s i s l ar ge, t he opt i mal pat h wi l l i nvol ve t he mai nt enance of posi t i ve st ocks of f i l e r esour ce i ndef i ni t el y : i f i t i s Gl obal Envi r onment al Ri sks Ref er ences Ar r ow, Kennet h J . , " The Rol e of Secur i t i es i n an Opt i mal Al l ocat i on of Ri sk- bear i ng . " Ecor t omel ne, Pr oceedi ngs of t he Cal l cpue sur l es Fondement s el Appl i cat i ons de i s Theone du Ri sque pr ef er ences . I n t hi s case, i t i s possi bl e t hat a change i n uncer t ai nt y about f ut ur e en Economei ne, Cent r e Nat i onal de t o Recher che pr ef er ences wi l l t i p t i r e ec onomy f r ot h one opt i mal consumpt i on r egi me t o Scl ent i f i que, Par i s, 1953 . Engl i sh t r ansl at i on i n " t i l e c ompuanot her . Such a p henomenon woul d mak e a dr amat i c di f f er ence t ezyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA Revi ew of Economi c St udi es, Apr i l 1964 . 31, t at i on of t he opt i on val ue . 91- 96 . Ar r ow, Kennet h J . , and Ant hony C. Fi sher , " Envi r onment al Pr eser vat i on . Uncer t ai nt y Concl usi ons and Open Quest i ons and I r r ever si bi l i t y, " Quar t er l y Jour mt l of F. conomcs, Mar 1974, 88 : 2, 312- 19 . Ar r ow, Kennet h) . , and Rober t C. Li nd, Whi l e s ome of t he f oundat i ons ar e i n pl ace f or an under st andi ng of ( l i e " Uncer t ai nt y and t he Eval uat i on of Publ i c I neconomi cs of gl obal envi r onment al r i sks, t her e ar e cer t ai n aspect s t hat r equi r e vest ment s Deci si ons . " Amer i can Economi c Bevi ew, June 1970, 60 : 3, 364- 78 . mor e at t ent i on . Fr om a pol i cy per spect i ve, t he eudogenci t y of t he r i sk f aced i s Bar r et t , Scot t , " Ti r e Par adox of I nt er nai mpor t ant . The pur pose of many r ec ommended pol i ci es i s pr eci sel y t o change t i onal Envi r onment al Agr eement s . " Par i s : Ent i r e r i sks t hat we f ace . An exampl e i s t he gl obal car bon t ax pr oposed by t he vi r onment Di r ect or at e, OECD, 1990 . OECD and r evi ewed i n Chi chi l ni sky ( 1993a) . Onl y r ecent l y has t her e been Bel t r at t i , Andr ea, Gr aci el a Chi chi l ni sky, and Geof f r ey, M. Heal , " I r r ever si bi l i t y, Uncer syst emat i c st udy of t he wel f ar e economi cs of mar ket s wi t h endogenous r i sks . t ai n Fut ur e Pr ef er ences and Opt i on \ ' al oes, " and many quest i ons r emai n open . St anf or d I nst i t ut e f or Theor et i cal Economi cs, Ti l e pol i cy i mpl i cat i ons of many of t he i ssues t hat we have r evi ewed need Techni cal Repor t No . 53, St anf or d Uni ver si t y, 1992 . f ur t her at t ent i on . 1- l ow i mpor t ant , f or exampl e, ar e t he opt i on val ues associ at ed Bel t r at t i , Andr ea, Gr aci el a Chi chi l ni sky wi t h gl obal changes= I t woul d be i nt er est i ng t o see s ome of t i r e l ar ge model s and Geof f r ey M. Heal , " Sust ai nabl e Gr owt h i n sym posi um addr ess t hi s quest i on . W e need t o st udy r evi ewed by Nl t evant t hi s and t he Gr een Gol den Rul e . " wor ki ng paper , f ur t her t he , i nst i t ut i onal i mpl i cat i ons of t r adi ng envi r onment al r i sks on f i nanci al Col umbi a Busi ness School , 1993 . I n Gol di n, I an and L . Al an Wi nt er s, Economi c Appr oaches mar ket s such as cont i ngent cl ai ms mar ket s and mut ual i nsur ance mar ket s . The t o Sust ai nabl e Devel opment , OECD, Par i s, f or t hpubl i c good aspect of t he gl obal cl i mat e has not been anal yzed adequat el y . The comi ng 1993 . st r uct ur e of emi ssi ons per mi t mar ket s needed f or ef f i ci ency i s st i l l not under Bohm, Pet er , " Opt i on Demand and Const ood . Our anal yses of opt i on val ues ar e st i l l based on ver y l i mi t ed assumpt i ons, sumer ' s Sur pl us : Comment , " Amencan Economi c Revi ew, Sept ember 1975, 65 : 4, 733- 36 . i n spi t e of a l ong and di st i ngui shed l i t er at ur e i n t hi s ar ea . Fi nal l y, economi st s Br oml ey, Dani el W., Maki ng t he Commons exchange of i nf or m at i on wi t h physi cal sci ent i st s : i t i s f ai r t o cl ear l y need mor e Wor k . San Fr anci sco: I CS Pr ess, 1992 . say t hat t i r e t wo ar eas f ai l t o snake any si gni f i cant cont act i n a f i el d t hat needs Car r ar o, Car l o, and Domeni co Si ni scal co, t he ski l l s of bot h . " St r at egi es f or I mer nat i or al Pr snect i on of t he Envi r onment , " wor ki ng paper , Fondazi one The pr ospect of cl i mat e change i nduced by human act i vi t y f aces soci et i es Eni Enr i co Mat t el , Mi l ano, 1991 . wi t h demandi ng i ssues i n r i sk management and r i sk assessment : at t he same Cass, Davi d, Gr aci el a Chi chi l ni sky, and Wu t i me, i t f aces economi cs wi t h chal l enges and oppor t uni t i es . The chal l enge i s t o Ho- Mot , " I ndi vi dual Ri sks and Mut ual I nsur ance . " CARESS Wor ki ng Paper #91- 27, Dedevel op i nt el l ect ual t ool s, c ommuni c at e t hem t o soci et y at l ar ge and pr ove t hat par t ment of Economi cs, Uni ver si t y, of Pennsyl t hey can add val ue t o t he anal ysi s of a compl ex and possi bl y f undament al vani a, 1991 . pr obl em. Chi chi l ni sky, Gr aci el a, and Wu Ho- Mot , " Fi nanci al I nnovat i on and Def aul t i n I nconi l i t Bot h Chi chi l ni sky and Heal acknowl edge f i nanci al suf t j r or 1 f i or m t he AI SF f gr ar t l s pl et e Mar ket s, " wor ki ng paper , Col umbi a Uni ver si t y, Depar t ment of Economi cs, 1991 . 92- 16028 and 91- 0460 r esl oect i vel y) , t he Fonda. zi one Al al l ei and t he Al onl e dei Paschi Chi chi l ni sky, Gr aci el a, " Exi st ence and Opdi Si er r a . Bot h aut hor s aj r j r r eci al e val uabl e comni enl s f r ont l i en Ar r ow, Andr ea Bel t r at t i , t i mal i t y of Equi l i br i um wi t h Endogenous UnMor decai Kur z, Ri char d Sandor , and Bob Sol ow. l Fe ar e par l i cul ar l Y gr at ef ul t o t he cer t ai nt y, " wor ki ng paper , Col umbi a Uni ver edi t or s of t hi s i ssue, Di ck Schi nal ensee, Car l Shapi r o and Ti r nol hl Tayl or , f or val uabl e si t y, Depar t ment of Economi cs, 1992 . 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