Declining Discount Rates: Evidence from the UK

Declining Discoun Ra es: E idence om he UK Ben G oom∗Phoebe Koundou i†Eka e ini Panopoulou‡ Theologos Pan elidis§ Janua y 31, 2005 Abs ac We es ima e schedules o declining discoun a es o cos bene i analysis in he UK. We highligh he impo ance o model selec ion o his ask and hence o he e alua ion o long- e m in es men s, namely clima e change p e en ion and nuclea build. JEL classi ica ion: C13, C53, Q2, Q4 Keywo ds: long- un discoun ing, s a e-space models, egime-swi ching models, clima e change policy, nuclea build Acknowledgmen s: We a e g a e ul o Ch is ian Gollie , Came on Hepbu n, Dimi ios Mallia op- ulos, Da id Pea ce and Niki as Pi is o help ul commen s and sugges ions. Panopoulou and Pan elidis hank he EU o inancial suppo unde he “PYTHAGORAS: Funding o esea ch g oups in he Uni e si y o Pi aeus” h ough he G eek Minis y o Na ional Educa ion and Religious Affai s. ∗Depa men o Economics, Uni e si y College London, UK. †Depa men o Economics, Uni e si y o Reading, UK and Depa men o Economics, Uni e si y College London, UK. ‡Depa men o Banking and Financial Managemen , Uni e si y o Pi aeus, G eece and Depa men o Eco- nomics, Na ional Uni e si y o I eland Maynoo h. Co espondence o: Eka e ini Panopoulou, Depa men o Economics, Na ional Uni e si y o I eland Maynoo h, Co.Kilda e, Republic o I eland. E-mail: [email protected]. Tel: 00353 1 7083793. Fax: 00353 1 7083934. §Depa men o Banking and Financial Managemen , Uni e si y o Pi aeus, G eece. 1 1 In oduc ion The discussion o discoun ing in Cos Bene i Analysis (CBA) has come o he o e once mo e as policy make s a e inc easingly equi ed o app aise in es men s whose cos s and bene i s acc ue in he a dis an u u e. Clima e change and nuclea build exempli y his long- e m policy a ena. La gely in esponse o he d ama ic effec s o con en ional exponen ial discoun ing on wel a e changes in he dis an u u e, he discussion has u ned o discoun a es ha decline wi h he ime ho izon, Declining Discoun Ra es o DDRs, and he e is now an e ol ing body o heo y.1Fo example, Wei zman (1998) shows ha unce ain y and pe sis ence o he discoun a e i sel p o ides a a ionale o DDRs and o all he heo e ical app oaches his app oach has p o en mo e amenable o implemen a ion, mainly because he in o ma ional equi emen s s op a he cha ac e isa ion o he unce ain y su ounding he discoun a e.2In his espec , Newell and Pize (2003) (N&P, hence o h) cha ac e ise in e es a e unce ain y by he pa ame e unce ain y ypically encoun e ed in any econome ic model. Thei model o US in e es a es, hough simple, yields a wo king de ini ion and es ima ion o he Ce ain y Equi alen o wa d Ra e (CER) o use in CBA. The au ho s con i m he declining pa e n o discoun a es and i s ela ion o unce ain y and pe sis ence. Ou iew in his pape is ha such a simple model is no sufficien ly e sa ile o ep oduce he empi ical egula i ies ypically ound in in e es a e se ies. Ou aim he e o e is o de elop ela i ely simple econome ic models ha cha ac e ize he pas as accu a ely as possible and offe a lexible amewo k o he u u e due o hei ime-he e ogenei y p ope ies. We discuss he in-sample p ope ies o al e na i e econome ic models o he UK in e es a es, commen on he p ope ies o he simula ed dis ibu ion and inally selec among hem based on hei ou -o -sample o ecas ing pe o mance. We exempli y he policy ele ance o DDRs and model selec ion wi h wo UK case s udies wi h long- e m impac s: he alue o ca bon seques a ion and he app aisal o nuclea build. 2 Discoun ing and in e es a e models Discoun ing u u e consequences in pe iod back o he p esen is ypically calcula ed using he discoun ac o P ,whe e P =exp(− P i=1 i).When is s ochas ic, he expec ed discoun ed alue o a dolla deli e ed a e yea s is: E(P )=EÃexp(− X i=1 i)!(1) Following Wei zman (1998) we de ine (1) as he ce ain y equi alen discoun ac o ,and he co esponding ce ain y-equi alen o wa d a e o discoun ing be ween adjacen pe iods a ime as equal o he a e o change o he expec ed discoun ac o : E(P ) E(P +1)−1=e (2) whe e e is he o wa d a e om pe iod o pe iod +1a ime in he u u e. Ou ocus is on he de e mina ion o he s ochas ic na u e o e h ough he obse ed dy- namics o he p ocess. Ou s a ing poin is he ela i ely simple AR(p)model employed by N&P, speci ied as ollows: =η+e ,e = p X i=1 aie −i+ξ (3) 1See e.g. Pea ce e al. (2003) and he e e ences he ein o a de ailed discussion o he DDR li e a u e. 2Fo example, he in o ma ional equi emen s do no ex end o speci ic a ibu es o u u e gene a ions’ isk p e e ences as would be una oidable in he case o Gollie (2002a, 2002b). 2 whe e ξ ∼N(0,σ2 ξ),η∼N¡η,σ2 η¢and p P i=1 ai<1. Howe e , modeling he in e es a e o he e y long un h ough cons an coefficien models is likely o be an un ealis ic assump ion, since a numbe o ac o s, such as he economic cycle, oil c ises, s ock ma ke c ises, p oduc i i y and echnology shocks may accoun o a ime- a ying beha io in he da a gene a ion p ocess o he in e es a e. In his espec , we in oduce wo models ha a e ime-he e ogeneous in he sense ha hey accoun o he possibili y o ime a ying pa ame e s and egime changes. Ou Regime-Swi ching (RS) model is one wi h wo egimes as ollows: =ηk+e ,e = p X i=1 ak ie −i+ξ (4) whe e ξ ∼IIDN(0,σ2 k),k=1,2 o he i s and second egime, espec i ely. Each egime inco po a es a diffe en speed o mean- e e sion, along wi h a diffe en pe manen componen , ηk,and e o a iance. The p obabili y o being in each egime a ime is speci ied as a Ma ko 1 p ocess, i.e. i depends only on he egime a ime −1,wi h he ma ix o he ansi ion p obabili ies assumed o be cons an .3A mo e con enien way o accoun o in ini e egimes in he in e es a e p ocess is h ough a ime a ying coefficien model, such as an AR(1) model wi h an AR(p)coefficien , namely a S a e Space (SS) model, gi en by he ollowing sys em o equa ions: =η+α −1+e ,α = p X i=1 ηiα −i+u ,µe u ¶∼Nµ·0 0¸,·σ2 e0 0σ2 u¸¶ (5) 3 Empi ical Resul s 3.1 Da a and Es ima ion Resul s Ou da ase consis s o nominal in e es a es ans o med o eal in e es a es by sub ac ing he annual change in he Consume P ice Index o he pe iod 1800 o 2001.4To smoo h e y sho - e m luc ua ions, a 3-yea mo ing a e age o he eal in e es a e se ies is employed and in o de o a oid nega i e in e es a es, we use he na u al loga i hms o he se ies. A a ie y o uni oo es s con i med ha he UK eal in e es a e is a s a iona y p ocess.5 Ou AR(4) model displays ela i ely apid e e sion o he implied uncondi ional mean o 3.32% (see Table 1, Panel A). Howe e , ou es ima es o he RS model (see Table 1, Panel B) indica e he p esence o wo dis inc egimes (modelled as AR(2) p ocesses). The uncondi ional means o each a e 2.14% and 3.70% and mean e e sion is as e in he la e . The i s egime has an es ima ed du a ion o 4 yea s, while he second one is mo e pe sis en wi h a du a ion o 15 yea s. O e all, he es ima es o his model sugges ha low in e es a e pe iods a e quickly mean- e e ing, su ounded by g ea e unce ain y and ansi mo e o en o high in e es a es pe iods which a e mo e pe sis en and less unce ain. Tu ning o ou SS model, he pa ame e es ima es (see Table 1, Panel C) sugges ha he s a e p ocess is highly pe sis en , almos a andom-walk p ocess, as indica ed by he es ima e o he au o eg essi e coefficien . The cons an o ou model sugges s a minimum o 1.31% o he in e es a e p ocess. 3The ma ix o p obabili ies is as ollows: P ob(R =1|R −1=1)=P, P ob(R =2|R −1=2)=Q P ob(R =2|R −1=1)=1−P, P ob(R =1|R −1=2)=1−Q whe e R e e s o he egime a ime . 4The nominal in e es a e is he Uni ed Kingdom 2 1/2% Consol Yield. Da a p o ided by he Global Financial Da a, Inc, a ailable a h p://www.global inda a.com. 5Uni oo es s a e no epo ed o b e i y bu a e a ailable upon eques . 3 3.2 Simula ion esul s and model selec ion Based on he es ima es p esen ed in Table 1, we simula e 100.000 possible u u e discoun a e pa hs o each model s a ing in 2002 and ex ending 400 yea s in o he u u e.6The expec ed discoun ac o s and CERs a e calcula ed om equa ions (1) and (2) and a e epo ed in Tables 2 and 3. We also commen on he empi ical dis ibu ion o in e es a es. The SS model yields he highes discoun ac o s ollowed by he RS and AR(4) model. These diffe ences a e mo e p onounced du ing he i s hal o he o ecas ho izon. Only SS sus ains some alue in he dis an u u e (400 yea s). Na u ally, he co esponding ce ain y- equi alen discoun a es e eal la gely he opposi e pic u e. The AR (4) model yields he highe a es du ing he i s hal o he sample, while he RS model yields he highe a es in he second hal . The SS model gi es consis en ly lowe CERs ha luc ua e in he ange o 2.2% o 1.4%. Tu ning o he simula ed dis ibu ion o discoun ac o s, he model wi h he lowes coefficien o a ia ion (i.e. he a io o s anda d de ia ion o e mean) is SS, whe eas he AR(4) model yields he highes coefficien .7Al e na i ely, as a measu e o unce ain y, we employ he 5% and 95% empi ical pe cen iles. This measu e seems o a o he RS model, which has he igh es con idence in e als, sugges ing ha unce ain y o e he expec ed discoun ac o is conside ably educed. On he o he hand, he pe cen iles o he SS model a e ela i ely wide. E alua ing he o ecas ing pe o mance o ou models o he long un is impossible due o limi a ion o da a. Howe e , since o wa d a es exis o a pe iod o 30 yea s we unde ake a compa ison o o ecas ing pe o mance o e his ime ho izon using a ailable eal da a. Speci i- cally, we make use o he e m s uc u e o he in la ion-indexed UK go e nmen bonds and use he Mean Squa e Fo ecas E o (MSFE) as ou selec ion c i e ion. Fo comple eness we calcu- la e ou modi ied MSFE c i e ia by inco po a ing ou ke nels8which a ach diffe en weigh s o obse a ions based on hei p oximi y o he p esen . The esul s a e p esen ed in Table 4. In e es ingly, he a ious speci ica ions o he MSFE c i e ion unanimously ank he SS model i s ollowed by he RS model and hen he AR(4) model. In sum, i we selec he models on he basis o hei abili y o cha ac e ize he pas and hei accu acy conce ning o ecas s o he u u e we a e inclined o p e e he SS model. 4 Policy Implica ions In his sec ion we highligh he policy implica ions o DDRs and model selec ion by looking a he long- e m policy a ena. Fi s ly we ollow N&P and conside he p esen alue o ca bon seques a ion: he emo al o 1 on o ca bon om he a mosphe e. Secondly, we look a nuclea build in he UK. The wo a e di ec ly ela ed since nuclea powe can bene i omca bonc edi s unde a sys em o join implemen a ion and ca bon ading (see Pea ce e al. 2003). Rega ding ou i s cases udy,wees ablish hep esen alueo he emo alo 1 ono ca bon om he a mosphe e, and hence he p esen alue o he bene i s o he a oidance o clima e change damages o each o ou models.9The esul s, epo ed in Table 5, sugges ha he lowe alua ion is gi en by he con en ional 3.5% discoun ing, ollowed by he AR(4) model. In e es ingly, when employing he SS model, he p esen alue o ca bon emissions educ ion is o e 200% la ge compa ed o he case o cons an discoun ing. Ou second case s udy highligh s a sense in which DDRs a e limi ed in accoun ing o in e gene a ional equi y. We, speci ically, conside new nuclea build in he UK which is s ill being conside ed as an op ion o ensu e secu i y o ene gy supply and adhe ence o Kyo o a ge s 6The p ocess o picking pa ame e s and shocks is a ailable om he au ho s upon eques . Ini ial alues o any lags o he eal in e es a e necessa y o he simula ion a e se a 3.5 pe cen , he a e used o CBA by he UK T easu y (HM T easu y 2003). 7The ele an ables a e no epo ed o b e i y, bu a e a ailable upon eques . 8The Ba le , he Pa zen, he Quad a ic-Spec al (QS) and he Tukey-Hanning (TK) ke nels a e he weigh ing unc ions used in ou e alua ion. 9See N&P o he assump ions conce ning he modeling o ca bon emissions damages. 4 (UK Pe o mance and Inno a ion Uni , 2002). Bo h decommission cos s and ca bon c edi s a e na u ally sensi i e o he use o DDRs and in Table 6 we compa e he NPV o in es men in a nuclea powe s a ion using ou es ima ed DDRs.10 The app aisal shows ha al hough he SS model has signi ican consequences o he p esen alue o e enues and ca bon c edi s, hep esen alueo decommissioningandope a ing cos s is also inc eased conside ably. In his espec , he NPV o nuclea build is affec ed only ma ginally when e alua ed using DDRs, al hough he SS and he RS models inc ease he NPV o he p ojec by mo e han 8%. 5 Conclusions This pape builds on N&P’s econome ic app oach o de e mining DDRs and emphasises he policy ele ance o model selec ion when dealing wi h leng hy ime ho izons. Using UK in e es a e da a we show ha he econome ic speci ica ion should allow he da a gene a ing p ocess o change o e ime and ha he b oad class o s a e space models is app op ia e. The policy ele ance o ou p ocedu e is highligh ed in he alua ion o ca bon seques a ion he p esen alue o which is inc eased by o e 200%. Re e ences [1]Gollie , C. (2002a). Time Ho izon and he Discoun Ra e. Jou nal o Economic Theo y 107 (2), 463-473. [2]Gollie , C. (2002b). Discoun ing an Unce ain Fu u e. Jou nal o Public Economics 85, 149- 166. [3]HM T easu y, (2003). The G een Book: App aisal and E alua ion in Cen al Go e nmen : London: HM T easu y. [4]Newell, R. and W. Pize (2003). Discoun ing he Bene i s o Clima e Change Mi iga ion: How Much do Unce ain Ra es Inc ease Valua ions? Jou nal o En i onmen al Economics and Managemen 46 (1), 52-71. [5]Pea ce, D., B. G oom, C. Hepbu n and P. Koundou i (2003). Valuing he Fu u e: Recen Ad ances in Social Discoun ing. Wo ld Economics 4 (2), 121-141. [6]Pe o mance and Inno a ion Uni (2002). The Ene gy Re iew - Feb ua y. [7]Wei zman, M. (1998). Why he Fa Dis an Fu u e Should be Discoun ed a i s Lowes Possible Ra e. Jou nal o En i onmen al Economics and Managemen 36, 201-208. 10We ollow he same cos and p ice assump ions and ime ho izons o cons uc ion, ope a ion and decommis- sioning as Pea ce e al. (2003). 5 Table 1: Es ima ion Resul s PanelA:AR(4)model Coefficien Es ima e S d. E o -s a . n1.201 0.177 6.777 a11.054 0.058 18.165 a2-0.125 0.089 -1.392 a3-0.443 0.070 6.308 a40.368 0.035 10.452 σ2 ξ0.064 0.005 13.733 Panel B: Regime Swi ching model Coefficien Es ima e S d. E o -s a . n10.760 0.244 3.117 a1 10.700 0.312 2.249 a1 2-0.212 0.312 -0.679 n21.306 0.082 15.892 a2 11.397 0.079 20.573 a2 2-0.530 0.058 -9.094 σ2 10.219 0.047 4.694 σ2 20.014 0.002 8.106 P0.767 0.101 7.543 Q0.933 0.033 28.617 Panel C: S a e Space model Coefficien Es ima e S d. E o -s a . n0.266 0.044 6.091 n10.991 0.002 438.82 ln(σ2 e)-2.503 0.104 -24.049 ln(σ2 u)-6.462 0.594 -10.884 Table 2. Ce ain y Equi alen Discoun Fac o s Model 3.5% AR(4) Regime S a e Yea Cons an Swi ching Space 10.96618 0.96618 0.96618 0.96618 20 0.50257 0.48208 0.51472 0.61857 40 0.25257 0.23676 0.26746 0.40678 60 0.12693 0.11778 0.13981 0.27722 80 0.06379 0.05912 0.07354 0.19368 100 0.03206 0.02997 0.0389 0.13775 150 0.00574 0.00569 0.00813 0.06172 200 0.00103 0.00115 0.00177 0.02882 250 0.00018 0.00027 0.00041 0.01379 300 0.00003 0.00008 0.0001 0.00669 350 0.00001 0.00003 0.00003 0.00328 400 0.00000 0.00002 0.00001 0.00161 6 Table 3. Ce ain y Equi alen Discoun Ra es Yea / Model AR(4) Regime S a e Swi ching Space 13.50 3.50 3.50 20 3.68 3.35 2.22 40 3.58 3.31 2.02 60 3.52 3.28 1.87 80 3.48 3.25 1.76 100 3.43 3.22 1.68 150 3.33 3.14 1.57 200 3.13 3.05 1.51 250 2.77 2.93 1.47 300 2.17 2.75 1.45 350 1.12 2.45 1.43 400 0.39 2.14 1.44 Table 4. A e age MSFEs Model AR(4) Regime S a e C i e ion Swi ching Space AMSFE 2.330 1.486 0.195 AMSFE (B) 0.875 0.527 0.135 AMSFE (P) 0.562 0.332 0.132 AMSFE (QS) 0.659 0.407 0.071 AMSFE (TH) 0.818 0.480 0.137 No es: The weigh ing unc ions a e as ollows: Ba le (B), Pa zen(P), Quad a ic-Spec al (QS) and Tukey-Hanning (TH). Table 5: Value o Ca bon Damages Ca bon Values Rela i e o Model (£/ c) Cons an Ra e Cons an (3.5%) 5.35 – AR(4) 5.78 7.9% Regime Swi ching 6.21 16.1% S a e Space 16.73 212.6% Table 6: The Cos s and Bene i s o Nuclea Build in he UK (£/KW) CAPEX OPEX DECOM Re /es C C NPV Rela i e o 3.5% 3.5% 2173 2336 427 4062 228 -646 – AR(4) 2167 2245 396 3904 215 -689 -6.6% RS 2178 2401 479 4176 249 -633 8.0% SS 2196 2973 1126 5170 547 -577 8.9% 7