THE HEALTH BENEFITS OF CONTROLLING CARBON EMISSIONS IN CHINA 1. by Richard F. GARBACCIO; Mun S. HO; and Dale W. JORGENSON

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1 THE HEALTH BENEFITS OF CONTROLLING CARBON EMISSIONS IN CHINA 1 by Rchard F. GARBACCIO; Mun S. HO; and Dale W. JORGENSON 1. Inroducon Ar polluon from rapd ndusralzaon and he use of energy has been recognzed o be a cause of serous healh problems n urban Chna. For example, he World Bank (1997) esmaed ha ar polluon caused 178,000 premaure deahs n urban Chna n 1995 and valued healh damages a nearly 5% of GDP. The same sudy esmaed ha hospal admssons due o polluon-relaed respraory llness were 346,000 hgher han f Chna had me s own ar polluon sandards, here were 6.8 mllon addonal emergency room vss, and 4.5 mllon addonal person-years were los because of llnesses assocaed wh polluon levels ha exceeded sandards. Much of hs damage has been arbued o emssons of parculaes and sulfur doxde. Furhermore, hs problem s expeced o grow n he near fuure as rapd growh oupaces effors o reduce emssons. Whle parculae and sulfur doxde emssons from burnng fossl fuel conrbues o local polluon, he use of fossl fuels also produces carbon doxde, a greenhouse gas hough o be a major conrbuor o global clmae change. The ssue of clmae change has engaged polcy makers for some me now and s he focus of much curren research. As par of hs research, n a prevous paper, we examned he effecs of lmng CO 2 emssons n Chna hrough he use of a carbon ax. In hs paper we make a frs aemp a esmang he local healh benefs of such polces. Unlke many oher effors amed a esmang healh effecs, whch focus on specfc echnologcal polces o reduce polluon, here we examne broad based economc polces whn a framework whch ncludes all secors of he economy. We presen a prelmnary effor, ulzng a number of smplfcaons, o llusrae he procedure. We plan o use more sophscaed ar qualy modellng echnques n fuure work. 1 Ths research s fnancally suppored by he U.S. Deparmen of Energy and he U.S. Envronmenal Proecon Agency. Gordon Hughes and Ksenya Lvovsky of he World Bank generously shared daa and esmaes from her work on he healh coss of fuel use. Karen Fsher-Vanden and Gerno Wagner conrbued o hs projec. The auhors may be conaced a: mun_ho@harvard.edu and garbacco.rchard@epa.gov. 1

2 Our smple esmaes, neverheless, are nsrucve. We fnd ha a polcy whch reduces carbon emssons by 5% every year from our base case wll also reduce premaure deahs by some 3.5 o 4.5%. If we apply commonly used valuaon mehods, he healh damage caused by ar polluon n he frs year s abou 5% of GDP. A polcy o modesly reduce carbon emssons would herefore reduce local healh losses by some 0.2% of GDP annually. 2. The economy-energy-healh model Our economc modelng framework s descrbed n Garbacco, Ho, and Jorgenson (1999). We summarze only key feaures of he model here. Insead, we descrbe n some deal he healh aspecs of our model. Our approach s o frs esmae he reducon n emssons of local polluans due o polces o reduce CO 2 emssons. These changes n emssons are ranslaed no changes n concenraons of varous polluans n urban areas. Dose-response funcons are hen used o calculae he effec of reducons n concenraons of polluans on healh oucomes. These nclude reduced premaure moraly, fewer cases of chronc bronchs, and oher healh effecs. Fnally, we ulze commonly used valuaon mehods o ranslae he reduced damages o healh no yuan values whch may be compared o he oher coss and benefs of such polces. 2.1 The economc model Our model s a sandard mul-secor Solow growh (dynamc recursve) model ha s modfed o recognze he wo-er plan-marke naure of he Chnese economy. The equaons of he model are summarzed n Appendx A. As lsed n Table 1, here are 29 secors, ncludng four energy secors. Oupu s produced usng consan reurns o scale echnology. Enerprses are gven plan oupu quoas and he governmen fxes prces for par of her oupu. They also receve some plan npus a subsdzed prces. Margnal decsons, however, are made usng he usual prce equals margnal cos condon. Domesc oupu compees wh mpors, whch are regarded as mperfec subsues. The household secor maxmzes a uly funcon ha has all 29 commodes as argumens. Income s derved from labor and capal and supplemened by ransfers. As n he orgnal Solow model, he prvae savngs rae s se exogenously. Toal naonal savngs s made up of household savngs and enerprse reaned earnngs. These savngs, plus allocaons from he cenral plan, fnance naonal nvesmen (and he exogenous governmen defc and curren accoun). Ths nvesmen ncreases he socks of boh marke and plan capal. Labor s suppled nelascally by households and s moble across secors. The capal sock s parly owned by households and parly by he governmen. The plan par of he sock s mmoble n any gven perod, whle he marke par responds o relave reurns. Over me, plan capal s deprecaed and he oal sock becomes moble across secors. The governmen mposes axes on enerprse ncome, sales, and mpors, and also derves revenue from a number of mscellaneous fees. On he expendure sde, buys commodes, makes ransfers o households, pays for plan nvesmen, makes neres paymens on he publc deb, and provdes varous subsdes. The governmen defc s se exogenously and projeced for he duraon of he smulaon perod. Ths exogenous arge s me by makng governmen spendng on goods endogenous. 2

3 Fnally, he res-of-he-world supples mpors and demands expors. World relave prces are se o he daa n he las year of he sample perod. The curren accoun balance s se exogenously n hs one-counry model. An endogenous erms of rade exchange rae clears hs equaon. The level of echnology s projeced exogenously,.e. we make a guess of how npu requremens per un oupu fall over me, ncludng energy requremens. For he laer, hs s somemes called he AEEI (auonomous energy effcency mprovemen). In he model, here are separae secors for coal mnng, crude peroleum, peroleum refnng, and elecrc power. Non-fossl fuels, ncludng hydropower and nuclear power, are ncluded as par of he elecrc power secor. Table 1. Secoral characerscs for Chna, 1992 Gross Energy Use Emsson Oupu (ml. n. coal Hegh Secor (bl. yuan) equvalen) Class 1 Agrculure low 2 Coal Mnng medum 3 Crude Peroleum medum 4 Meal Ore Mnng 24 6 medum 5 Oher Non-meallc Ore Mnng medum 6 Food Manufacurng medum 7 Texles medum 8 Apparel & Leaher Producs medum 9 Lumber & Furnure Manufacurng medum 10 Paper, Culural, & Educaonal Arcles medum 11 Elecrc Power hgh 12 Peroleum Refnng medum 13 Chemcals medum 14 Buldng Maeral medum 15 Prmary Meals medum 16 Meal Producs medum 17 Machnery medum 18 Transpor Equpmen medum 19 Elecrc Machnery & Insrumens medum 20 Elecronc & Communcaon Equpmen medum 21 Insrumens and Meers 24 1 medum 22 Oher Indusry 75 7 medum 23 Consrucon low 24 Transporaon & Communcaons low 25 Commerce low 26 Publc Ules low 27 Culure, Educaon, Healh, & Research low 28 Fnance & Insurance low 29 Publc Admnsraon low Households low Governmen - Toals 6, Source: Developmen Research Cener Socal Accounng Marx for 1992; Sae Sascal Bureau; and auhor s esmaes. 3

4 A carbon ax s a ax on fossl fuels a a rae based on her carbon conen. Ths ax s appled o he oupu of hree ndusres coal mnng, crude peroleum, and peroleum refnng. I s appled o mpors whle expors are excluded. In he base case hs ax s zero. In he polcy smulaons he carbon ax rae s se o acheve a desred reducon n carbon emssons. Snce he applcaon of hs ax wll rase revenues above hose n he base case, o manan comparably, we keep governmen spendng and revenues he same by reducng oher exsng axes. 2.2 The envronmen-healh aspecs Emssons of local polluans comes from wo dsnc sources, he frs s due o he burnng of fossl fuels (combuson emssons), he oher from non-combuson processes (process emssons). A grea deal of dus s produced n ndusres lke cemen producon and buldng consrucon ha s no relaed o he amoun of fuel used. In hs paper we concenrae on wo polluans, parculae maer less han 10 mcrons (PM-10) and sulfur doxde (SO 2 ). The analyss of he healh effecs of oher polluans, such as nrogen oxdes and lead, are lef for fuure work. PM-10 and SO 2 boh have her orgns n combuson and non-combuson sources. Our specfcaon of emssons, concenraons, and dose-response follows Lvovsky and Hughes (1997). 2 Toal emssons from ndusry j s he sum of process emssons and combuson emssons from burnng coal, ol, and gas. Le EM jx denoe he emssons of polluan x from ndusry j n perod. Then we have: (1) EM = QI + ( ψ AF ) jx σ, jx j f jxf where x = PM-10, SO 2, f = coal, ol, gas, j = 1,2,.., 29, H, G. jf σ jx s process emssons of polluan x from a un of secor j oupu and ψ jxf s he emssons from burnng one un of fuel f n secor j. QI j s he quany of oupu j and AF jf s he quany of fuel f (n ons of ol equvalen (oe)) consumed by secor j n perod. The model generaes nermedae npus, denoed A j, whch are measured n consan yuan. For he cases where s one of he fuels, hese A j s are ranslaed o AF jf whch are n ons of ol equvalen of coal, ol, and naural gas. The j ndex runs over he 29 producon secors and he non-producon secors (household and governmen). For he wo non-producon secors here are zero process emssons ( σ = 0 ). jx 2 Lvovsky and Hughes (1997) dscuss he choce of PM-10 raher han oal suspended parculaes (TSP). The daa currenly colleced by he Chnese auhores are mosly n TSP. Healh damage, however, s beleved o be manly due o fner parcles. Lvovsky and Hughes make an esmae of he share of PM-10 n TSP and kep ha consan. Improved daa would obvously refne hs and oher analyses. 4

5 The amoun of emssons per yuan of oupu, or emssons per oe of fuel used, depends on he echnology employed and wll change as new nvesmens are made. A proper sudy should ake no accoun he coss of hese new echnologes and how much hey reduce emssons and energy use. 3 Esmaes of hese facors have no ye been assembled for many ndusres n Chna and we use a smple mechansm o represen such changes. Lvovsky and Hughes (1997) make an esmae of he emsson levels of new echnology and wre he acual emsson coeffcens as a weghed sum of he coeffcens from he exsng and new echnologes. Usng superscrps O and N o denoe he old and new coeffcens we have: (2) ψ = k ψ + ( 1 k ) ψ, jxf O jxf N jxf where he wegh, k, s he share of old capal n he oal sock of capal. 4 Whn each of he secors here s consderable heerogeney n plan sze, vnage, ec. Unforunaely, we are unable o ncorporae such a hgh level of deal no hs work. However, we do noe ha, on average, dfferen ndusres emssons ener he amosphere a dfferen levels. Followng Lvovsky and Hughes we classfy emsson sources as low, medum, and hgh hegh. As a frs approxmaon, emssons from he elecrc power secor are classfed as hgh hegh, mos of he manufacurng ndusres are classfed as medum, and he non-manufacurng and household secors as low. The exac desgnaons by secor are gven n Table 1. Denong he emssons of polluan x a hegh c by E we have: cx (3) E =, where c = low, medum, hgh. cx EM jx j c The nex sep s o esmae concenraons of polluans n populaon ceners due o hese emssons. A good approach would be o dsaggregae he emssons by geographc locaon and feed he daa no an ar dsperson model a each locaon. Ths would generae he concenraons a each populaon cener from all sources of emssons. Such an elaborae exercse wll have o be deferred o fuure work. Agan we follow Lvovsky and Hughes and use reduced form coeffcens o esmae he concenraons. Unlke Lvovsky and Hughes, who dsngush beween large and oher ces, we make a furher smplfcaon here and express he naonal average urban amben concenraon as: N (4) C x = γ low, xelow, x + γ medum, xemedum, x + γ hgh, xehgh, x, where he γ cx coeffcens ranslae emssons a hegh c o concenraon of x. 5 3 For example, Jorgenson and Wlcoxen (1990) suded he economc effecs of regulaons n he U.S. usng daa on capal and operang coss of equpmen ha were nsalled n response o EPA regulaons. 4 Ths smple approach gnores he fac ha cleaner equpmen wll lkely cos more han dry equpmen. Furhermore, he exogenous energy effcency mprovemens descrbed above are se ndependenly of hese emsson facors. An negraed approach would of course be preferred when such daa becomes avalable. 5 Indexng hs equaon by ces would be more approprae f we had a model ha calculaed economc acvy regonally. A a mnmum we would need o have projecons of populaon by cy o make use of such a dsaggregaon. 5

6 The formulaon descrbed above s raher crude and so we now brefly dscuss he effecs of msspecfcaon of dfferen pars of he procedure. An error n he γ cx reduced form coeffcens has a frs-order effec on he level of concenraon, whch as we descrbe nex, wll have a frs-order effec on he esmae of healh damage. Ths has an mporan drec mpac on he esmaes of he absolue level of he value of damages. However, when we dscuss he effecs of polcy changes (e.g. wha s he percenage reducon n moraly due o a parcular polcy?), hen an error n γ cx would have only a second-order effec. (In hs model hs parameer only eners lnearly, and wh no feedback, so here are no second-order effecs. However, n a more general specfcaon, here wll be.) Ths s llusraed numercally n secon sx below. Much debae and research s ongong abou he magnude of he effec a parcular level of concenraon of a polluan has on human healh and on how he effecs of varous polluans nerac. Snce much of he exsng research has been done n developed counres, quesons have been rased as o how hese dose-response relaonshps should be ranslaed o counres lke Chna wh very dfferen polluon mxes and populaons wh dfferen demographc and healh characerscs. Ths s dscussed n Wang and Smh (1999b, Appendx E) who also ce a range of 3 esmaes for moraly effecs rangng from 0.04% o 0.30% for a one µ g / m ncrease n PM-10 (see her Table 5). In addon, here s he ssue of dfferenal age mpacs of hese polluans and he assocaed dffculy of measurng he qualy of lfe-years. We wll no be able o address hese mporan ssues here and choose only a smple formulaon. In our base case we follow Lvovsky and Hughes (1997) who denfy egh separae healh effecs for PM-10 and wo for SO 2. The mos mporan of hese effecs are moraly and chronc bronchs. These effecs, ndexed by h, are gven n Table 2 ogeher wh he dose-response relaonshp, DR hx. The 7.1 number for moraly s nerpreed as he number of excess deahs per 3 mllon people due o an ncrease n he concenraon of PM-10 of one µ g / m. Ths s equvalen o a 0.1% moraly effec, whch s also he cenral esmae n Wang and Smh (1999b, Table 5). We use an alernave esmae n our sensvy analyss n secon sx. Wh hese dose-response relaonshps, he number of cases of healh effec h n perod s hen gven by: N u (5) HE = ( DR C ) POP er) h x hx ( α h = Moraly, RHA,..., x x u where α x s he WHO reference concenraon, POP s he urban populaon (n mllons), and er s he exposure rae (he share of he urban populaon exposed o polluon of concenraon C ). N x 6

7 Varous approaches have been used o value hese damages. We use he wllngness o pay mehod. The valuaon of hese damages s a conroversal and dffcul exercse, wh argumens over he dea self [Henzerlng (1999)], wheher he conngen valuaon mehod works [Hamm and Graham (1999)], and how o aggregae he wllngness o pay [Pra and Zeckhauser (1996)]. For hs prelmnary effor we agan follow Lvovsky and Hughes (1997) and use esmaes for wllngness o pay n he U.S. and scale hem by he rao of per capa ncomes n Chna and he U.S. 6 Usng hs smple scalng means ha we are assumng a lnear ncome effec. The U.S. values assocaed wh each healh effec are gven n he hrd column of numbers n Table 2. The nex column gves he values scaled usng per capa ncomes n Mos sudes of healh damage valuaon would use hese esmaes for all years of her analyss. However, Chna s experencng rapd ncreases n real ncomes. For example f ncome rses a an annual rae of 5%, would have rsen 3.4 mes n 25 years. In he base case, our model projecs an average growh rae of 4-5% n per capa ncomes over he nex 40 years. Gven hs rae of ncrease, we have chosen a valuaon mehod ha changes every perod n lne wh ncome growh, agan assumng a lnear ncome effec. The values for 2020 are gven n he las column of Table 2. The naonal value of damage due o effec h s gven by: (6) Damage h = Vh HEh, x where he valuaons for 1995, V h, 1995, are n he hrd column of Table 2. The value of oal damages s smply he sum over all effecs: (7) TD = Damage h. h We should pon ou ha hese are he valuaons of people who suffer he healh effec. Ths s no he same as calculang he medcal coss, he cos of los oupu of sck workers, he cos of parens me o ake care of sck babes, ec. The personal wllngness-o-pay may, or may no, nclude hese coss, especally n a sysem of publcly provded medcal care. 6 These esmaes are from Chaper 2 of World Bank (1997), whch also dscusses he use of wllngness o pay valuaon versus human capal valuaon, he mehod mos commonly used n Chna. 7

8 Table 2. Dose-Response and Valuaon Esmaes for PM-10 and SO 2 Cases per 1 ml. people wh Valuaon Valuaon Valuaon a 1 µg/m 3 n 1995 n 1995 n 2020 Healh Effec ncrease U.S. $ yuan yuan Due o PM-10: ,600,000 82, , Respraory hospal admssons (cases) , Emergency room vss (cases) Resrced acvy days (days) 57, Lower respraory nfecon/chld ashma Ashma aacks (cases) 2, Chronc bronchs (cases) ,000 1, , Respraory sympoms (cases) 183, Due o SO 2 : 9 10, Respraory sysems/chld Sources: Dose-response daa are from World Bank (1997), updaed. Valuaon n U.S. $ are from Lvovsky and Hughes (1997). Valuaon n yuan are auhor s esmaes. 2.3 Daa Obvously, o mplemen he model descrbed above, a grea deal of economc and healh relaed daa s requred. We need economc daa for he base year, he parameers of he varous behavoral funcons (e.g. elasces of subsuon n he producon funcons), and projecons of he exogenous varables. Ths ncludes projecons of he populaon, he savngs rae, producvy growh, mpor prces, he governmen defc, ec. These daa and forecass for he economc componen of he model are descrbed n Garbacco, Ho, and Jorgenson (1999). A parcularly mporan daa source s he 1992 Chnese npu-oupu able. 8

9 For he healh componen descrbed n secon wo above we obaned he oupu and energy use from he 1992 npu-oupu able and Snon (1996). The process emssons coeffcens are calculaed from he secoral non-combuson emssons daa n Snon (1996). The energy relaed emsson coeffcens ( ψ jxf ) are derved from hose n Lvovsky and Hughes (1997) and scaled o equal he combuson emssons daa. 7 Daa s gven n deal for he mnng, manufacurng, and elecrc power secors, wh summary esmaes for he oher secors (agrculure, servces, and fnal demand). We dsrbue he oal for he oher secors n proporon o fuel use and scale Lvovsky and Hughes esmaes of hese σ and ψ jxf coeffcens. Lvovsky and Hughes also provded separae esmaes of O ψ jxf and jx N ψ jxf and for process coeffcens, O N σ jx and σ jx. The esmaes for PM-10 for curren and low-cos mproved echnology are gven n Table 3a for combuson emssons and n Table 3b for process emssons. Lvovsky and Hughes (1997) gve coeffcens ha ransform emssons o concenraons separaely for each of 11 major ces. We use hs nformaon o calculae a naonal average se of γ cx s. In he 1992 base year, wh emssons calbraed o he daa from Snon (1996), he esmaed urban 3 concenraon averaged over he ces s 194 µ g / m. Esmang he number of people affeced by ar polluon nvolves esmang and projecng he sze of he urban populaon. Boh he fuure oal populaon and he urbanzed poron have o be projeced. We ake oal populaon projecons he from World Bank (1995). The rae of urbanzaon n Chna for s ploed n Fgure A1. For comparson we also plo he rae of urbanzaon n he U.S. over he perod The medum urbanzaon projecon s produced by leng he urbanzaon rae rse a 0.5% per year, whle n he low urbanzaon projecon, he rae s assumed o be 0.3% per year. The medum projecon s very close o U.S. hsorcal raes. Lvovsky and Hughes (1997) assume a rae of urbanzaon slghly hgher han our medum projecon. 2.4 The base case smulaon I s no he am of hs paper o provde esmaes of he damage caused by urban ar polluon, bu raher he changes n he damage caused by some polcy. I s only o gve a clear dea of how our approach works ha we descrbe our base case smulaon,.e. a smulaon of he economy and healh effecs usng curren polcy parameers. 7 Snon (1996) provdes a convenen Englsh complaon from varous Chnese sources ncludng he Chna Envronmenal Yearbook. Page 18 gves he energy converson coeffcens. Table VIII-4 gves he emssons by secor from boh combuson and noncombuson sources. 8 From U.S. Census Bureau publcaon CPH-2-1, a hp:// 9

10 We sar he smulaon n 1995 and so we nalze he economy o have he capal socks ha were avalable a he sar of 1995 and he workng age populaon of 1995 supplyng labor. The economc model descrbed n he appendx calculaes he oupu of all commodes, consumpon by households and he governmen, expors, and he savngs avalable for nvesmen. Ths nvesmen augmens he capal sock for he nex perod and we repea he exercse. The level of oupu (specfc commodes and oal GDP) hus calculaed depends on our projecons of he populaon, savngs behavor, changes n spendng paerns as ncomes rse, he ably o borrow from abroad, mprovemens n echnology, ec. Our resuls are repored n Table 4 and Fgure A2. The 5.9% growh rae of GDP over he nex 25 years ha resuls from our assumpons s slghly less opmsc han he 6.7% growh rae projeced recenly for Chna by he World Bank (1997), bu sll mples a very rapd growh n per capa ncome. The populaon s projeced o rse a a 0.7% annual rae durng hese 25 years. 10

11 Table 3a. Combuson parculae emssons Curren Emssons by Fuel Secor Coal Ol Emssons wh Low Cos Improvemens by Fuel Naural Gas Coal Ol Naural Gas 1 Agrculure 42, , Coal Mnng 38, , Crude Peroleum 38, , Meal Ore Mnng 38, , Oher Non-meallc Ore Mnng 38, , Food Manufacurng 32, , Texles 18, , Apparel & Leaher Producs 7, , Lumber & Furnure 25, , Manufacurng 10 Paper, Culural, & Educaonal 25, , Arcles 11 Elecrc Power 32, , Peroleum Refnng 7, , Chemcals 17,898 1, ,966 1, Buldng Maeral 13,454 1, ,485 1, Prmary Meals 6, , Meal Producs 8, , Machnery 11, , Transpor Equpmen 11, , Elecrc Machnery & 11, , Insrumens 20 Elecronc & Communcaon 11, , Equpmen 21 Insrumens and Meers 11, , Oher Indusry 46, , Consrucon 42, , Transporaon & 42,560 5, ,280 2, Communcaons 25 Commerce 42, , Publc Ules 42, , Culure, Educaon, Healh, & 42, , Research 28 Fnance & Insurance 42, , Publc Admnsraon 42, , Households 21, , O N Noe: Coeffcens ψ jxf and ψ jxf n ons of PM-10 per mllon ons of ol equvalen (oe). 11

12 Table 3b. Process Parculae Emssons Emssons Curren wh Low Cos Secor Emssons Improvemen s 1 Agrculure Coal Mnng Crude Peroleum Meal Ore Mnng Oher Non-meallc Ore Mnng Food Manufacurng Texles Apparel & Leaher Producs Lumber & Furnure Manufacurng Paper, Culural, & Educaonal Arcles Elecrc Power Peroleum Refnng Chemcals Buldng Maeral Prmary Meals Meal Producs Machnery Transpor Equpmen Elecrc Machnery & Insrumens Elecronc & Communcaon Equpmen Insrumens and Meers Oher Indusry Consrucon Transporaon & Communcaons Commerce Publc Ules Culure, Educaon, Healh, & Research Fnance & Insurance Publc Admnsraon Households O N Noe: Coeffcens σ jx and σ jx n ons per mllon 1992 yuan. 12

13 Table 4. Seleced Varables from Base Case Smulaon Varable Populaon (ml.) 1, , , GDP (bl yuan) 3, , , Energy Use (ml. ons sce) 1, , , Coal Use (ml. ons) 1, , , Ol Use (ml. ons) Carbon Emssons (ml. ons) , , Parculae Emssons (ml. ons) From Hgh Hegh Sources From Medum Hegh Sources From Low Hegh Sources SO 2 Emssons (ml. ons) Premaure Deahs (1,000) , Healh Damage (bl. yuan) , , Healh Damage/GDP 5.10% 9.80% 15.30% The dashed lne n Fgure A2 shows he fossl fuel based energy use n sandard coal equvalens (sce) on he rgh-hand axs. Our assumpons on energy use mprovemens are farly opmsc and ogeher wh changes n he srucure of he economy, resul n an energy-gdp rao n 2030 ha s almos half ha n The carbon emssons from fossl fuels are also ploed usng he rgh-hand axs. The rae of growh of carbon emssons s even slower han he growh n energy use. Ths s manly due o our assumpons on he shf from coal o ol. 13

14 Wh he ndusry oupus and npu requremens calculaed for each perod we use equaons (1)-(7) o calculae oal emsson of polluans, he urban concenraon of polluans, and he healh effecs of hese polluans. The growh of PM-10 emssons s much slower han he growh n energy use and carbon emssons. Ths s due o he sharp dfference n he assumed coeffcens for new and old capal (see Table 3). All sources of PM-10 ncrease emssons, wh he larges rse comng from low-hegh sources. Projeced SO 2 emssons rse much faser han parculaes due o a less opmsc esmae of he mprovemen n he σ jx and ψ jxf coeffcens. 9 In hs base case we assume no ncrease n emsson reducon effors over me. Ths dffers from Lvovsky and Hughes (1997) BAU case whch assumes ha he larges 11 ces wll choose wha hey call he hgh nvesmen opon. The resul s ha our esmae of curren premaure moraly s hgher, 320,000 versus 230,000. The growh rae of healh effecs from our smulaons, however, are que close. By 2020 our esmaed excess deahs are 3.1 mes he 1995 level, compared o he 3.7 mes calculaed n Lvovsky and Hughes BAU case. Of course he fac ha our esmaes are close does no mean ha eher esmae s good. We repor he level esmaes o explan our smulaon procedure and o llusrae he magnudes nvolved. To reerae, hs s no a forecas of emssons, bu raher a projecon f no changes n polcy are made. We expec boh he governmen and prvae secors o have polces and nvesmens ha are dfferen from oday s. The mporan ssue s polcy choces and he esmaon of he effecs of dfferen polces. Ths s where we urn nex. 2.5 Healh effecs of a carbon ax As descrbed n he prevous secon, our projeced growh of carbon emssons n he base case, whle lower han he growh of GDP, s sll very hgh. The level of emssons doubles n 15 years. A number of polces have been suggesed o reduce he growh of emssons of hs global polluan, rangng from specfc, dealed polces lke mporng naural gas or shung down small coal plans, o broader approaches, such as carbon axes and emssons radng. In hs paper we concenrae on he smples broad based polcy by mposng a carbon ax,.e. a ax on fossl fuels based on her carbon conen. 10 The specfcs of hs ax, and he dealed economc effecs, are dscussed n Garbacco, Ho, and Jorgenson (1999). In our smulaons we rase he prce of crude peroleum and coal, boh domesc and mpored, by hs carbon ax. In hs paper, wo carbon arges are examned, 5% and 10% reducons n annual carbon emssons. The level of he ax s calculaed endogenously such ha emssons n each perod are 5% or 10% less han n he base case. Ths s shown n Fgure 1. The revenues from hs new ax are used o reduce oher exsng axes. The amoun of reducon s such ha he publc defc (exogenous) and real governmen expendures (endogenous) were kep he same as he base case. 9 The emsson coeffcens for sulphur doxde are no repored here bu are avalable from he auhors. Gven he relavely mnor role n human healh (as shown n Table 2), we do no emphasze SO 2 n hs sudy. I s of course an mporan cause of oher damages, e.g. acd ran. 10 In hs sudy we gnore boh oher sources of carbon doxde and oher greenhouse gases. 14

15 The resuls of hese carbon ax smulaons are gven n Table 5 and Fgures 1-4. The amoun of carbon ax needed o acheve hese reducons s ploed n Fgure 2. In he frs year, a ax of 8.8 yuan per on s requred o acheve a 5% reducon n emssons. 11 Ths s equvalen o a 6% ncrease n he facory gae prce of coal and a 1% ncrease n he prce of crude peroleum. These hgher energy prces reduce demand for fuels and rase he relave prces of energy nensve goods. We assume ha he governmen does no compensae he household secor for he hgher prces and so consumpon falls n he shor run. Because he labor supply s assumed fxed, real wages fall slghly. The compensang reducon n enerprse axes, however, leaves frms wh hgher afer-ax ncome, and gven our specfcaon, hs leads o hgher nvesmen. Over me, hs leads o a sgnfcanly hgher capal sock,.e., hgher han n he base case, and hus hgher GDP. Ths hgher oupu allows a level of consumpon ha exceeds ha n he base case soon afer he begnnng of he smulaon perod. As can be seen n Table 5, n he frs year of he 5% carbon reducon case, he mposon of he carbon ax leads o a reducon n oal parculae emssons of 3.5%. Ths, however, s an average over hree dfferen changes. Hgh hegh emssons from he elecrc power secor fell by 5.6%, medum hegh emssons from manufacurng fell 2.7%, whle low hegh emssons fell 3.7%. Secoral emssons of sulfur doxde fell by smlar amouns. The elecrc power secor s he mos fossl fuel nensve and hence experences he larges fall n oupu and emssons. 11 There are ons of carbon emed per on of average coal. The average prce of coal oupu n 1992, derved by dvdng he value n he npu-oupu able by he quany of coal mned, s abou 68 yuan per on. Ths mples a ax on coal of abou 7 percen. 15

16 Table 5. Effecs of a Carbon Tax on Seleced Varables (Percenage Change from Base Case) Effec n 1s Year wh: Effec n 15h Year wh: 5% CO 2 10% CO 2 5% CO 2 10% CO 2 Emssons Emssons Emssons Emssons Varable Reducon Reducon Reducon Reducon GDP -0.00% -0.00% 0.21% 0.42% Prmary Energy -4.72% -9.45% -4.68% -9.35% Marke Prce of Coal 6.03% 12.80% 6.29% 13.40% Marke Prce of Ol 0.95% 2.01% 0.71% 1.53% Coal Oupu -5.93% % -6.14% % Ol Oupu -0.81% -1.71% -0.59% -1.29% Parculae Emssons -3.50% -6.97% -3.11% -6.20% From Hgh Hegh Sources -3.67% -7.37% -3.09% -6.21% From Medum Hegh Sources -2.66% -5.29% -2.22% -4.40% From Low Hegh Sources -5.59% % -5.44% % Parculae Concenraon -3.45% -6.92% -2.95% -5.92% SO 2 Concenraon -3.43% -6.88% -2.78% -5.59% Premaure Deahs -4.52% -9.04% -3.55% -7.10% Cases of Chronc Bronchs -4.52% -9.04% -3.55% -7.10% Value of Healh Damages -4.52% -9.04% -3.55% -7.11% 16

17 Fgure 1. Carbon emssons n base case and smulaons Base Case 5% Emssons Reducon 10% Emssons Reducon Bllon Tons Fgure 2. Carbon axes requred o aan a gven reducon n emssons 5% Emssons Reducon 10% Emssons Reducon Yuan per Ton

18 Fgure 3. Reducon n PM-10 emssons and concenraons relave o base -9 10% CO2 Reducon Case - Emssons 10% CO2 Reducon Case - Concenraon 5% CO2 Reducon Case - Emssons 5% CO2 Reducon Case - Concenraon Percenage Change Fgure 4. Reducon n excess deahs relave o base case 5% CO2 Emssons Reducon 10% CO2 Emssons Reducon Percenage Change

19 Ths reducon n emssons resuls n a fall n he average urban concenraon of PM-10 by 3.4%. As a consequence, cases of varous healh effecs fall by abou 4.5% (.e. he number of premaure deahs, he number of cases of chronc bronchs, ec.). The reducon n healh effecs s bgger han he change n concenraon due o he non-proporonal naure of equaon 5. If we apply hese percen changes o he base case esmaes n Table 4, hs ranslaes o 14,000 fewer excess deahs, and 126,000 fewer cases of chronc bronchs. Snce he valuaons are smple mulples (see equaon 6) he percen change n yuan values of hs healh damage s also -4.5%. Over me, as he revenue rased hrough he carbon ax reduces he ncome ax burden on enerprses, hgher nvesmen leads o a larger capal sock and hence a hgher level of GDP. The hgher level of oupu means greaer demand for energy and hence requres a hgher carbon ax rae o acheve he 5% reducon n carbon emssons. Ths s shown n he 15h year column of Table 5 and n Fgure 2. The lower ax on crude peroleum n he 15h year s due o our assumpon on he prce of world ol. If we had assumed no mpors, he ax on crude peroleum would also have been hgher. Ths ws n fossl fuel prces resuls n a bgger fall n coal consumpon compared o crude peroleum consumpon for an unchanged GDP. However, he hgher demand has a bgger effec han hs ws n fuel prces and hence he reducon n emssons n he 15h year s smaller han he nal reducon, 3.1% versus 3.5%. The reducon n concenraons over me s correspondngly smaller, as shown n Fgure 3. Anoher feaure of he resuls ha should be poned ou s ha he change n concenraon s smaller han he change n emssons n fuure years (see Fgure 3). Ths s due o our classfyng emssons by hegh and ha low level emssons are he bgges conrbuors o concenraon (.e. he bgges γ cx s). Dfferen secors of he economy are growng a dfferen raes (sources of low hegh emssons are growng he mos rapdly), and respond dfferenly o he mposon of he carbon ax. The mos responsve secor (.e. he one ha shrnks he mos) s elecrc power generaon, whch produces hgh hegh emssons wh he lowes conrbuon o concenraons. Fnally, hs pah of concenraon changes leads o healh effecs ha become smaller over me, from a 4.5% reducon n he frs year, o a 3.6% reducon n he 15h year, o 3.2% n he 25h year. When we rase he argeed carbon emssons reducons from 5% o 10% of he base case he effecs are approxmaely lnear. In he 15h year column of Table 5 we see ha he effecs on coal prces are less han doubled whle he effecs on ol prces are more han doubled. The end resul on emssons, concenraons, and healh effecs s a smple doublng of he percenage change. Ths seemng lneary would no hold for larger changes. 2.6 Sensvy analyss In secon hree above we dscuss frs- and second-order effecs of an error n a parameer. To llusrae hs we use an alernave assumpon abou an exogenous varable, he fuure urbanzaon rae. Ths varable, POP, eners n equaon 4. The base case ploed n Fgure A1 has he urban u share of oal populaon rsng a 0.5% per year, he low case rses a 0.3% per year. We ran he model agan wh hs lower esmae of he exposed populaon. The number of premaure deahs n boh he base case and n hs alernave smulaon are ploed n Fgure A3. Ths s an example of a frs-order effec of an error n a parameer or exogenous varable. 19

20 Fnally, we ran he model wh he lower urban populaon growh rae and agan mposed a carbon ax o acheve a 5% reducon n carbon emssons. In he orgnal smulaon, hs resuled n excess deahs ha were 4.5% lower n he frs year (see Table 5 and Fgure 4). Usng he alernave urbanzaon esmae, moraly agan falls by 4.5%. The percenage reducons n premaure moraly over me for boh cases are ploed n Fgure A4. They are almos dencal. The wde range of esmaes for he dose-response relaonshp was noed n secon hree above. For 3 moraly, Lvovsky and Hughes (1997) use 7.14 excess deahs per mllon per µ g / m. If we use a coeffcen ha s 1.5 mes hgher, well whn he range ced by Wang and Smh (1999b), hen he projeced excess deahs are smply 50% hgher. Ths s shown n Fgure A5. The above llusraes he effec of changng a varable or parameer ha has no feedback effec. However, f we change exogenous varables ha do have feedbacks, here wll be second-order effecs. For example, an alernave guess abou he me pah of he governmen defc wll change revenue requremens and axes and wll have an effec on he esmaed percenage change. Ths effec wll, however, be mnor, merely a second-order effec on he percenage change. The really crucal parameers have a frs-order effec on he percenage change. These nclude he elascy of subsuon beween capal and energy, he elascy of subsuon beween coal and ol, and oher behavoral parameers. In he case of healh effecs, f he concenraon and dose responses (equaons 4 and 5) were no lnear hen here would be sgnfcan changes. Two oher examples come o mnd. If he healh of workers s a facor n he effecveness of labor npu or f urbanzaon s modeled explcly, hen somehng lke a carbon ax would have a more complex neracon wh GDP and healh benefs. Examnaon of hese ssues s deferred o fuure sudes. 2.7 Conclusons Ths paper presens a prelmnary effor o negrae a model of healh effecs from fossl fuel use wh a mul-secor economy-wde CGE model. In our nal analyss, we look a how polces nended o reduce emssons of greenhouse gasses mgh smulaneously affec emssons of local polluans and ulmaely human healh. Our nal specfcaons of he lnkages beween fuel use and emssons of local polluans and beween emssons of hese polluans and her concenraons n urban areas are very smple. Effors o mprove hese specfcaons are currenly under way. However, o he exen ha he effecs are lnear (as descrbed n equaons 4 and 5), our esmaes of he percen changes n concenraons and moraly would be as good (or bad) as our esmaes of secoral oupu changes. The am of a more dealed modelng effor would be o provde gudance for polcy makng. One goal of hs prelmnary effor s o lay ou explcly he assumpons ha need o go no makng such an analyss, even wh beer daa and more elaborae model specfcaon. A complex regonal ar polluon model would sll requre ha projecons be made abou oal and urban populaon sze, fuure world ol prces, energy effcency mprovemens, and all he oher me-dependen exogenous varables dscussed prevously. 20

21 Anoher goal of hs prelmnary modellng effor s o hghlgh n whch areas mprovemens n daa collecon and modellng would brng he greaes benef o even a lmed analyss. Issues beyond hose assocaed wh he economc par of he model nclude: () Healh damage from ar polluon s beleved o be due o very fne parcles. Daa on ha would be mporan. () Daa on concenraons n dfferen urban areas and he modellng of hese concenraons n a sample of ces would gve a sense of he range of he reduced form coeffcens. () We have crudely classfed emssons by low, medum, and hgh heghs for dfferen ndusres. Havng more refned daa on ndusry emssons characerscs would mprove he modellng n em (). (v) Geng beer dose-response funcons s already a recognzed prory. We would urge consderaon of ncludng an age dmenson n he research. Ths would be especally mporan n aempng o lnk worker s healh back o labor producvy. 21

22 REFERENCES Garbacco, Rchard F., Mun S. Ho and Dale W. Jorgenson. (1997). A Dynamc Economy-Energy-Envronmen Model of Chna. Unpublshed Manuscrp, Harvard Unversy. Garbacco, Rchard F., Mun S. Ho, and Dale W. Jorgenson (1999). Conrollng Carbon Emssons n Chna. Envronmen and Developmen Economcs, 4(4), Hamm, James K. and J. D. Graham (1999). Wllngness o Pay for Healh Proecon: Inadequae Sensvy o Probably? Journal of Rsk and Uncerany, 18(1), Henzerlng, Lsa (1999). Dscounng Lfe. Yale Law Journal, 108, Jorgenson, Dale W. and Peer J. Wlcoxen (1990). Envronmenal Regulaon and U.S. Economc Growh. Rand Journal of Economcs, 21(2), Lvovsky, Ksenya and Gordon Hughes (1997). An Approach o Projecng Amben Concenraons of SO 2 and PM-10. Unpublshed Annex 3.2 o World Bank (1997). Maddson, Davd, Ksenya Lvovsky, Gordon Hughes, and Davd Pearce (1998). Ar Polluon and he Socal Cos of Fuels. Mmeo, World Bank, Washngon, D.C. Pra, John W. and Rchard J. Zeckhauser (1996). Wllngness o Pay and he Dsrbuon of Rsk and Wealh. Journal of Polcal Economy, 104(4), Snon, Jonahan ed. (1996). Chna Energy Daabook. Lawrence Berkeley Naonal Laboraory, LBL-32822, Rev. 3. Wang, Xaodong and Krk R. Smh (1999a). Secondary Benefs of Greenhouse Gas Conrol: Healh Impacs n Chna. Envronmenal Scence and Technology, 33(18), Wang, Xaodong and Krk R. Smh (1999b). Near-erm Healh Benefs of Greenhouse Gas Reducons. World Healh Organzaon, Geneva, WHO/SDE/PHE/99.1. World Bank (1994). Chna: Issues and Opons n Greenhouse Gas Emssons Conrol. Washngon, D.C. World Bank (1995). World Populaon Projecons. Washngon, D.C. World Bank (1997). Clear Waer, Blue Skes: Chna s Envronmen n he New Cenury. Washngon, D.C. 22

23 APPENDIX A: DESCRIPTION OF THE ECONOMIC MODEL The man feaures of he model for Chna are dscussed n hs appendx, furher deals are gven n Garbacco, Ho, and Jorgenson (1997). We descrbe he modelng of each of he man agens n he model n urn. Table A1 lss a number of parameers and varables whch are referred o wh some frequenly. In general, a bar above a symbol ndcaes ha s a plan parameer or varable whle a lde ndcaes a marke varable. Symbols whou markngs are oal quanes or average prces. To reduce unnecessary noaon, whenever possble, we drop he me subscrp,, from our equaons. 23

24 Table 1A. Seleced Parameers and Varables n he Economc Model Parameers e s c k L r x expor subsdy rae on good carbon ax rae on good ax rae on capal ncome ax rae on labor ncome ne mpor arff rae on good ne ndrec ax (oupu ax less subsdy) rae on good un ax per on of carbon Endogenous Varables G_I G_INV G_IR G_ransfer KD P * PE PI PI PL PL PM PM * PS PT QI QS * rb ( ) R_ransfer neres on governmen bonds pad o households nvesmen hrough he governmen budge neres on governmen bonds pad o he res of he world governmen ransfer paymens o households renal prce of marke capal by secor expor prce n foregn currency for good producer prce of good purchaser prce of good ncludng axes average wage wage n secor mpor prce n domesc currency for good mpor prce n foregn currency for good supply prce of good renal prce of land of ype oal oupu for secor oal supply for secor paymens by enerprses o he res of he world ransfers o households from he res of he world 24

25 A.1 Producon Each of he 29 ndusres s assumed o produce s oupu usng a consan reurns o scale echnology. For each secor j hs can be expressed as: (A1) QI = f ( KD, LD, TD, A,..., A, ) j j j j 1 j nj, where KD j, LD j, TD j, and A j are capal, labor, land, and nermedae npus, respecvely. 12 In secors for whch boh plan and marke allocaon exss, oupu s made up of wo componens, ~ he plan quoa oupu (QI j ) and he oupu sold on he marke (QI j ). The plan quoa oupu s sold a he sae-se prce ( PI j ) whle he oupu n excess of he quoa s sold a he marke prce ~ ( PI j ). A more dealed dscusson of how hs plan-marke formulaon s dfferen from sandard marke economy models s gven n Garbacco, Ho, and Jorgenson (1999). In summary, f he consrans are no bndng, hen he wo-er plan/marke economy operaes a he margn as a marke economy wh lump sum ransfers beween agens. The reurn o he owners of fxed capal n secor j s: ~ ~ ~ ~ KD (A2) prof = PI QI + PI QI P KD PL LD PT TD j j j j j j ~ ~ PS A PS A j j j j j j For each ndusry, gven he capal sock K j and prces, he frs order condons from maxmzng equaon A2, subjec o equaon A1, deermne he marke and oal npu demands. Gven he lack of a conssen me-seres daa se, n hs verson of he model, we use Cobb-Douglas producon funcons. Equaon A1 for he oupu of ndusry j a me hen becomes: α α α α α j j j j j j (A3) QI = g() KD LD TD E M Kj Lj Tj Ej Mj, where j. loge j logm j E = α log A and k = coal, ol, elecrcy, and refned peroleum, k kj kj M = α log A and k = non-energy nermedae goods. k kj kj 12 QI j denoes he quany of ndusry j s oupu. Ths s o dsngush from, QC j, he quany of commody j. In he acual model each ndusry may produce more han one commody and each commody may be produced by more han one ndusry. In he language of he npu oupu ables, we make use of boh he USE and MAKE marces. For ease of exposon we gnore hs dsncon here. 25

26 Here α Ej s he cos share of aggregae energy npus n he producon process and α E kj s he share of energy of ype k whn he aggregae energy npu. Smlarly, α Mj s he cos share of aggregae non-energy nermedae npus and α M kj s he share of nermedae non-energy npu of ype k whn he aggregae non-energy nermedae npu. To allow for based echncal change, he α Ej coeffcens are ndexed by me and are updaed exogenously. We se α Ej o fall gradually over he nex 40 years whle he labor coeffcen, α Lj, rses correspondngly. The composon of he aggregae energy npu (.e. he coeffcens α E kj ) are also allowed o change over me. These coeffcens are adjused gradually so ha hey come close o resemblng he U.S. use paerns of The excepon s ha he Chnese coeffcens for coal for mos ndusres wll no vansh as hey have n he U.S. 13 The coeffcen g() n equaon A3 represens echncal progress and he change n g() s deermned hrough an exponenal funcon ( g& ( ) = A exp( µ ) ). Ths mples echncal change ha s rapd nally, bu gradually declnes j j j oward zero. The prce o buyers of hs oupu ncludes he ndrec ax on oupu and he carbon ax: c (A4) PI = ( 1 + ) PI +. A.2 Households The household secor derves uly from he consumpon of commodes, s assumed o supply labor nelascally, and owns a share of he capal sock. I also receves ncome ransfers and neres on s holdngs of publc deb. Prvae ncome afer axes and he paymen of varous non-ax fees (FEE), Y p, can hen be wren as: p (A5) Y = YL + DIV + G_ I + G_ ransfer + R_ ransfer FEE, where YL denoes labor ncome from supplyng LS uns of effecve labor, less ncome axes. YL s equal o: (A6) YL = ( 1 L ) PL LS. 13 We have chosen o use U.S. paerns n our projecons of hese exogenous parameers because hey seem o be a reasonable anchor. Whle s unlkely ha Chna s economy n 2032 wll mrror he U.S. economy of 1992, s also unlkely o closely resemble any oher economy. Oher projecons, such as hose by he World Bank (1994), use he npu-oupu ables of developed counres ncludng he U.S. We have consdered makng exrapolaons based on recen Chnese npu-oupu ables, bu gven he shor sample perod and magnude of he changes n recen years, hs dd no seem sensble. 26

27 The relaonshp beween labor demand and supply s gven n equaon A31 below. LS s a funcon of he workng age populaon, average annual hours, and an ndex of labor qualy: w L (A7) LS = POP hr q. Household ncome s allocaed beween consumpon (VCC ) and savngs. In hs verson of he model we use a smple Solow growh model formulaon wh an exogenous savngs rae ( s ) o deermne prvae savngs ( S p ): p p p (A8) S = s Y = Y VCC. Household uly s a funcon of he consumpon of goods such ha: C (A9) U = U( C1,..., Cn) = α logc. Assumng ha he plan consrans are no bndng, hen as n he producer problem above, gven marke prces and oal expendures, he frs order condons derved from equaon A9 deermne household demand for commodes, C, where C = C + C ~. Here C and C ~ are household purchases of commodes a sae-se and marke prces. The household budge can be wren as: ~ ~ (A10) VCC = ( PS C + PS C ). We use a Cobb-Douglas uly funcon because we currenly lack he dsaggregaed daa o esmae an ncome elasc funconal form. However, one would expec demand paerns o change wh rsng ncomes and hs s mplemened by allowng he α C coeffcens o change over me. These fuure demand paerns are projeced usng he U.S. use paerns of A.3 Governmen and axes In he model, he governmen has wo major roles. Frs, ses plan prces and oupu quoas and allocaes nvesmen funds. Second, mposes axes, purchases commodes, and redsrbues resources. Publc revenue comes from drec axes on capal and labor, ndrec axes on oupu, arffs on mpors, he carbon ax, and oher non-ax receps: j j j j j j j j k KD L r * (A11) Rev = ( P KD D ) + PL LD + PI QI + PM M j + c ( QI X + M) + FEE, j j 27

28 where D j s he deprecaon allowance and X and M are he expors and mpors of good. The carbon ax per un of fuel s: c x (A12) = θ, where x s he un carbon ax calculaed per on of carbon and θ s he emssons coeffcen for each fuel ype. Toal governmen expendure s he sum of commody purchases and oher paymens: e (A13) Expend = VGG + G_ INV + s PI X + G_ I + G_ IR + G_ ransfer Governmen purchases of specfc commodes are allocaed as shares of he oal value of governmen expendures, VGG. For good : (A14) PS G G = α VGG. We consruc a prce ndex for governmen purchases as log PGG quany of governmen purchases s hen: G = α log PS. The real (A15) GG VGG =. PGG The dfference beween revenue and expendure s he defc, G, whch s covered by ncreases n he publc deb, boh domesc ( B ) and foregn ( B G* ): (A16) G = Expend Rev, G* G* (A17) B + B = B 1 + B 1 + G. The defc and neres paymens are se exogenously and equaon A16 s sasfed by makng he level of oal governmen expendure on goods, VGG, endogenous. A.4 Capal, nvesmen, and he fnancal sysem We model he srucure of nvesmen n a farly smple manner. In he Chnese economy, some sae-owned enerprses receve nvesmen funds drecly from he sae budge and are allocaed cred on favorable erms hrough he sae-owned bankng sysem. Non-sae enerprses ge a neglgble share of sae nvesmen funds and mus borrow a wha are close o compeve neres raes. There s also a small bu growng sock marke ha provdes an alernave channel for prvae savngs. We absrac from hese feaures and defne he capal sock n each secor j as he sum of wo pars, whch we call plan and marke capal: (A18) Kj = Kj + K ~ j. 28

29 The plan poron evolves wh plan nvesmen and deprecaon: (A19) K = ( δ ) K + I, = 1, 2,, T. j 1 j 1 j In hs formulaon, K j 0 s he capal sock n secor j a he begnnng of he smulaon. Ths poron s assumed o be mmoble across secors. Over me, wh deprecaon and lmed governmen nvesmen, wll declne n mporance. Each secor may also ren capal from he oal sock of marke capal, K ~ : (A20) ~ ~ K = K, where j j ~ K j > 0. The allocaon of marke capal o ndvdual secors, ~ K j, s based on secoral raes of reurn. As n equaon A2, he renal prce of marke capal by secor s P ~ KD j. The supply of K ~ j, subjec o equaon A20, s wren as a ranslog funcon of all of he marke capal renal prces, ~ ( ~ KD K K P,..., P ~ KD = 1 ). j j n In wo secors, agrculure and crude peroleum, land s a facor of producon. We have assumed ha agrculural land and ol felds are suppled nelascally, absracng from he complex propery rghs ssues regardng land n Chna. Afer axes, ncome derved from plan capal, marke capal, and land s eher kep as reaned earnngs by he enerprses, dsrbued as dvdends, or pad o foregn owners: ~ (A21) profs P KD ~ * + K + PT T = ax( k) + RE + DIV + r( B ) j j j j j j j j, where ax( k) s oal drec axes on capal (he frs erm on he rgh hand sde of equaon A11). 14 As dscussed below, oal nvesmen n he model s deermned by savngs. Ths oal, VII, s hen dsrbued o he ndvdual nvesmen goods secors hrough fxed shares, α I : I (A22) PS I = α VII. Lke he α C coeffcens n he consumpon funcon, he nvesmen coeffcens are ndexed by me and projeced usng U.S. paerns for A poron of secoral nvesmen, I, s allocaed drecly by he governmen, whle he remander, I ~, s allocaed hrough oher channels. 15 The oal, I, can be wren as: In Chna, mos of he dvdends are acually ncome due o agrculural land. I should be noed ha he ndusres n he Chnese accouns nclude many secors ha would be consdered publc goods n oher counres. Examples nclude local rans, educaon, and healh. 29