Development Aid and Climate Finance

Transcription

1 Development Ad and Clmate Fnance Johan Eyckmans, am Fankhauser and norre Kverndokk August 2013 Centre for Clmate Change Economcs and Polcy Workng Paper o. 143 Grantham Research Insttute on Clmate Change and the Envronment Workng Paper o. 123

2 The Centre for Clmate Change Economcs and Polcy (CCCEP) was establshed by the Unversty of Leeds and the London chool of Economcs and Poltcal cence n 2008 to advance publc and prvate acton on clmate change through nnovatve, rgorous research. The Centre s funded by the UK Economc and ocal Research Councl and has fve nter-lnked research programmes: 1. Developng clmate scence and economcs 2. Clmate change governance for a new global deal 3. Adaptaton to clmate change and human development 4. Governments, markets and clmate change mtgaton 5. The Munch Re Programme - Evaluatng the economcs of clmate rsks and opportuntes n the nsurance sector More nformaton about the Centre for Clmate Change Economcs and Polcy can be found at: The Grantham Research Insttute on Clmate Change and the Envronment was establshed by the London chool of Economcs and Poltcal cence n 2008 to brng together nternatonal expertse on economcs, fnance, geography, the envronment, nternatonal development and poltcal economy to create a worldleadng centre for polcy-relevant research and tranng n clmate change and the envronment. The Insttute s funded by the Grantham Foundaton for the Protecton of the Envronment and the Global Green Growth Insttute, and has fve research programmes: 1. Global response strateges 2. Green growth 3. Practcal aspects of clmate polcy 4. Adaptaton and development 5. Resource securty More nformaton about the Grantham Research Insttute on Clmate Change and the Envronment can be found at: Ths workng paper s ntended to stmulate dscusson wthn the research communty and among users of research, and ts content may have been submtted for publcaton n academc journals. It has been revewed by at least one nternal referee before publcaton. The vews expressed n ths paper represent those of the author(s) and do not necessarly represent those of the host nsttutons or funders.

3 Development Ad and Clmate Fnance Johan Eyckmans a, am Fankhauser b and norre Kverndokk c revsed verson, February 2014 Abstract Ths paper dscusses the mplcatons of clmate change for offcal transfers from rch countres (the orth) to poor countres (the outh). The concern s no longer just about poverty allevaton (.e. ncome n the outh), but also about global emssons and reslence to clmate rsk. Another mplcaton s that tradtonal development transfers to ncrease ncome are complemented by new fnancal flows to reduce greenhouse gas emssons (mtgaton transfers) and become clmate-reslent (adaptaton transfers). We fnd that n the absence of nsttutonal barrers to adaptaton, mtgaton or development, clmate change wll make solated transfers less effcent: A large part of ther ntended effect (to ncrease ncome, reduce emssons, or boost clmate-reslence) dsspates as the outh reallocates ts own resources to acheve the mtgaton, adaptaton and consumpton balance t prefers. Only n the case of least-developed countres, whch are unable to adapt fully due to ncome constrants, wll adaptaton support lead to more clmate reslence. In all other cases, f the orth wshes to change the balance between mtgaton, adaptaton and consumpton t should structure ts transfers as matchng grants, whch are ted to the outh s own level of fundng. However, the orth can also provde an ntegrated transfer package that recognzes the combned clmate and development requrements of the outh. Keywords: nequalty averson; mtgaton; adaptaton; clmate change fnance; development assstance; ad effectveness JEL classfcaton: D63, Q50, Q54, Q56 Acknowledgements: The project was supported fnancally by the MILJØ2015 program at the Research Councl of orway. Fankhauser also acknowledges fnancal support by the Grantham Foundaton for the Protecton of the Envronment and the UK Economc and ocal Research Councl. We are also ndebted to ntal dscussons wth cott Barrett and to comments from Katnka Holtsmark, Torben Mdeksa, Lnda østbakken and semnar partcpants at the Frsch Centre. The authors are assocated wth CREE - the Oslo Centre for Research on Envronmentally Frendly Energy - whch s supported by the Research Councl of orway. a Katholeke Unverstet Leuven, Center for Economcs and Corporate ustanablty. b Correspondng author: Grantham Research Insttute and Centre for Clmate Change Economcs and Polcy, London chool of Economcs (s.fankhauser@lse.ac.uk). c Ragnar Frsch Centre for Economc Research, Oslo.

4 1. Introducton The twn needs of poverty allevaton and envronmental protecton have long been recognzed as complementary challenges. There s by now an extensve body of work that documents the close lnks between envronment and development, a lterature to whch Anl Markandya has made wderangng contrbutons (e.g. Pearce et al. 1990; Markandya and Pearce 1991; Markandya 1998, 2002, 2008; Markandya and urty 2004). Perhaps less apprecated n the academc lterature s the fact that envronmentdevelopment lnks also extend to questons of fnance. Offcal development assstance has been subject to extensve research n partcular about ad effectveness (e.g., Bourgugnon and undberg 2007; Coller and Dollar 2002, 2004; Dollar and Easterly 1999). Envronmental fnance has become a topc of wder academc nterest only recently n the context of clmate change. ee Hates (2013) for an overvew and Fankhauser and Pearce (2014) for a more conceptual dscusson. There has been no systematc analyss up to now of how envronmental fnance and development ad nteract, ether from a donor perspectve (e.g., n terms of overlappng or competng donor objectves) or from a recpents pont of vew (e.g., n terms of the ncentves that multple fundng streams provde). The am of ths paper s to close ths gap, usng clmate change as a pertnent example. Under the Copenhagen Accord of 2009, and reaffrmed n subsequent negotaton documents, developed countres have promsed to provde addtonal clmate fnance of up to $100 bllon a year from 2020 to help developng countres to reduce ther emssons and adapt to the consequences of clmate change. The offer needs to be seen n a broader context of fnancal assstance to developng countres, whch also ncludes development ad: Clmate fnance s to be explctly provded on top of conventonal development assstance, whch developed countres have pledged to ncrease to 0.7% of GDP as part of the Mllennum Development Goals. Ths paper offers a theoretcal model to analyze the motvaton of donors n provdng three knds of fundng to developng countres: fundng to allevate poverty

5 (development ad), fundng to reduce greenhouse gas emssons (mtgaton fnance) and fundng to prepare for unavodable clmate change (adaptaton fnance). The model also studes how the three fundng streams affect the ablty and nclnaton of recpent countres to ncrease ncome, reduce emssons and strengthen reslence to clmate change. The basc tenet s that transfers reflect the ethcal belefs of those makng them. That s, transfers are not made prmarly for strategc reasons, but because people n developed countres care about the welfare of people n developng countres. We also assume that these belefs can be expressed n an approprately specfed utlty functon, and study how the level and composton of fnancal flows depend on the ethcal belefs of developed countres (whch, wth apologes to the antpodes, we shall call the orth). For a more detaled dscusson of the ethcal dmensons of clmate change see tern (2012) and Kverndokk and Rose (2008). Most of the exstng lterature on fnancal transfers focuses on ther strategc value, that s, ther mert n securng an nternatonal agreement (see e.g., Barrett, 2003, 2007 and Hong and Karp, 2012, on formng nternatonal envronmental agreements; an excepton s Grasso 2010). Already n the 1990s, Carraro and nscalco (1993) and Kverndokk (1994) argued that sde payments manly from OECD countres to non- OECD countres would be an effectve polcy nstrument for makng a lmted treaty sgnfcant. Eyckmans and Tulkens (2003) show that a proportonal surplus- sharng rule can stablze a grand coalton and secure the frst-best global clmate polcy, and Carraro et al. (2005) demonstrate the mportance of monetary transfers as strategc nstruments to foster stablty of voluntary clmate agreements. Further, Hoel (2001) argues that monetary transfers are also mportant to reduce carbon leakage, whle Chatterjee et al. (2003) study transfers to promote economc growth and contrast the effects of a transfer ted to publc nfrastructure nvestments wth a tradtonal pure transfer. Our paper s also part of a more recent lterature on the nterplay between adaptaton and mtgaton (see for nstance Buob and tephan 2011, Ebert and Welsch 2012; Tulkens and van teenberghe 2009; Ingham et al. 2007; Bréchet et al. 2013). A recurrng nsght from ths body of work s the followng. Whle the benefts of

6 mtgaton are non-excludable, the benefts of adaptaton are often excludable, meanng that adaptaton s prmarly a prvate good and the benefts accrue only to the naton dong the adaptaton nvestment (Kane and hogren, 2000; Barrett, 2008). 1 Thus, natons should have the ncentves to do the approprate adaptaton nvestment themselves n contrast to mtgaton. Another ssue n ths lterature s that adaptaton and mtgaton can be substtutes (Ingham et al., 2005). Thus, by reducng the effects of clmate change, the ncentve to mtgate may be lower and gve a negatve feedback to the donors. To bypass ths ssue, Pttel and Rübbelke (2013) develop a two-regon model, smlar to ours, to explore the mert of fnancal adaptaton transfers that are condtonal on mtgaton efforts. Also Heuson et al. (2013) consder a stylzed two-regon model of mtgaton and adaptaton wth dfferent types of transfers from the ndustralzed regon to compensate for mtgaton and adaptaton costs and expected and potental clmate change damages n the developng regon. In contrast to these approaches, we allow for development assstance (n the form of productve captal transfers) as an addtonal transfer channel and, more mportantly, we consder a more general preference structure that allows for ethcally motvated behavor. Ths paper departs from the exstng lterature n other respects. Frst, unlke the sde payment lterature we treat fnancal transfers as an equty ssue rather than a strategc queston. Transfers are determned by ethcal preferences and not by the need to secure cooperaton (although there are, nevtably, some strategc effects). econd, we are not concerned wth optmzng global socal welfare. Rather than a global perspectve, we take the pont of vew of donor and recpent countres and ask what ther socal welfare functons mply for the mpact of dfferent fnancal transfers. The type of transfers we consder consttutes the thrd dfference. Whle the lterature focuses predomnantly on mtgaton fnance, our model offers a choce between mtgaton fnance, development ad and adaptaton fnance. The paper s structured as follows. ecton 2 sets out our theoretcal model. It features a two-perod game of transfers from orth to outh wth utlty functons that nclude 1 There are examples of adaptaton actons wth regonal publc goods features, such as the management of nternatonal water systems, but we can treat these as exceptons from the rule.

7 the welfare n the other regon. We then use ths framework to study a seres of questons relatng to the nterplay of development ad and offcal fnance for mtgaton and adaptaton. The frst three questons concern decson makng n the outh: ecton 3 studes the effect of offcal transfers on the mtgaton decsons of the outh, whle secton 4 studes the mpact on adaptaton. ecton 5 analyses the specal case of a leastdeveloped country, whose ablty to spend money on clmate change s constraned by the need to mantan a subsstence level of consumpton. The next two sectons concern decson makng n the orth. ecton 6 analyses the ncentve of the orth to offer adaptaton, mtgaton and development transfers, bearng n mnd the strategc reacton of the outh observed n sectons 3 and 4. ecton 7 studes the same queston but n a more general set up where the effcency of transfers vares. That s, a varyng fracton of fundng s lost n the course of the transfer. ecton 8 concludes. 2. A two-perod model of transfers Our model s structured as a smple game between two regons, j, over two perods (t = 0,1). The two regons are called orth (j = ) and outh (j = ), where orth s a rch regon and outh s poor. Each regon produces an exogenous output results n greenhouse gas emssons t y j, whch t e j. 2 The combned emssons from both regons result n clmate change damage, whch reduces avalable output n perod 1. Damage n perod 0 s assumed to be neglgble. In perod 0 each regon chooses the amount t wshes to nvest n mtgaton technology m j and adaptaton technology a j. The beneft of adaptaton s reduced mpacts from clmate change n perod 1. We assume that clmate change damage n country j, D j, s a constant share of output, and that a fracton, α j, of ths damage can be avoded through adaptaton. Investng n adaptaton has decreasng returns: ( a j ) 0 α 1 wth α 0 and α 0. These are hghly smplstc assumptons but j j j 2 Thus, we mplctly assume that real captal nvestments are made optmally.

8 they are common n the lterature (e.g., Fankhauser, 1994; Kverndokk, 1994; Tol, 2002; ordhaus and Boyer, 2000; de Brun, Dellnk and Tol 2009; de Brun, Dellnk and Agrawala 2009; for a crtque see Pndyck 2013). The beneft of nvestng n mtgaton s lower emssons for a gven level of producton. Mtgaton captal s long-lved so that the choce of m j determnes emssons over both perods. Emssons are proportonal to output, that s, e j t = σ j (m j )y j t, where σ j (m j ) can be nterpreted as the emsson-to-output rato. We assume that mtgaton nvestment has decreasng returns (equvalently, the abatement costs functons s convex): σ j < 0 and σ j 0. We assume that each regon has ts own emsson constrants, whch one may thnk of as beng part of an nternatonal agreement to constran emssons over both regons: (1) e + e eˆ ; e + e eˆ ; eˆ + eˆ eˆ For smplcty we assume that there s no nteracton (e.g. through carbon tradng) between the two emsson spaces. The respectve emssons constrants apply separately to each regon, although emssons are fungble across tme perods. We wll lft the restrcton on carbon tradng brefly n secton 3 to study the mpact of a global carbon market on offcal fnancal flows. 3 The orth can make three types of transfer n perod 0: a productve captal transfer (development assstance), T, whch wll ncrease the avalable output (and emssons) of the outh n perod 1, a mtgaton transfer, T m, whch helps the outh reduce ts emssons n both perods an adaptaton transfer, T a, whch augments the adaptaton captal avalable to the outh. 3 An alternatve formulaton would be to assocate the beneft of mtgaton drectly wth reduced damage. However, ths would ntroduce clmate change as a strategc externalty nto the model and make t dffcult to dstngush the equty case for transfers from the strategc case. Moreover, our representaton s not unrealstc. Very few countres are large enough to nfluence global emssons. For most, the ncentve to reduce emssons comes from an exogenously agreed target and/or the prospect of carbon market revenues, rather than the possblty to reduce damage drectly.

9 The transfers ntroduce some ntra- and ntergeneratonal tradeoffs. Mtgaton (and mtgaton support) has an mmedate and lastng mpact because t lowers the emsson ntensty n both perods. Adaptaton and productve captal support however, are subject to a tme delay. Today s nvestment only pays off n the next perod. Hence, we assume that changng the productve captal base and adaptaton capacty of a country requres more tme than curbng ts emsson ntensty. 4 The output that s left after transfers and nvestments n mtgaton and adaptaton n perod 0 s consumed. The consumpton levels n each regon and perod, c t j, and the correspondng emssons, e t j, can now be specfed, as shown n Table 1. Table 1: Consumpton and emssons levels n each regon and perod. Perod 0 (now) Perod 1 (future) (orth ) (outh ) c = y m a T T T 0 0 m a ( ) e = σ m y 0 0 c = y m a 0 0 m ( ) e = σ m + T y 0 0 ( ) ( ˆ) c = 1 1 α a D e y 1 1 ( ) e = σ m y 1 1 a ( ) ( ˆ) c = α a + T D e y + T m ( ) 1 1 = σ + + e m T y T The fnal, crucal element of the model s each regon s utlty functon. We assume that both regons gan utlty from consumpton (that also ncludes feedback from the envronment). For smplcty we assume lnear utlty functons, and we can wrte the ntertemporal utlty functon of the outh as: (2) (, ) U c c = c + δ c where δ s the consumpton dscount factor of the outh, expressng the ntergeneratonal equty preferences of the regon. 4 In realty, there wll also be quck wns n mprovng adaptaton capacty and productvty. At the same tme, some mtgaton efforts wll only curb emsson ntensty n the long run. We abstract from these possbltes manly because t allows us to keep the model tractable.

10 To be able to study transfers from orth to outh that are not motvated prmarly by strategc reasons, we assume that the orth also cares about the ntrageneratonal dstrbuton of consumpton, that s, consumpton n the outh. One way of dong ths s to follow Fehr and chmdt (1999) and assume that the orth expresses nequalty averson n consumpton; 5 people n the orth dslke that the outh s poorer than them, but would dslke t even more f the outh were rcher. 6 Obvously, as orth s the rcher regon ntally, and would not make transfers that make the outh rcher than them, we have c > c. The utlty functon of the orth can then be wrtten as: (3) ( ) 0 1 U c, c = c µ ( c c ) = (1 µ ) c + µ c, c = c + δ c, j =, j j j j where µ > 0 s a parameter expressng the ntrageneratonal preferences of the orth, whle δ s the dscount rate of the orth, expressng ts ntergeneratonal preferences. From (3) we see that µ < 1 s requred for consumpton n the orth to add to the orth s welfare. In addton, t s reasonable to assume that consumpton n the orth adds more to the utlty of the orth than consumpton n the outh. Thus, we set µ < We could also ntroduce the nequalty preferences n the welfare functon of the outh as n Kverndokk et al. (2014). Ths would gve preferences for a hgher consumpton level n the outh. However, as wll be obvous from the dscussons n ectons 3 and 5 below, equty preferences wll not affect the optmal mtgaton and adaptaton levels, and nequalty averson n the outh would not matter for our analyss. 6 The general case would be U c, c = c η max c c,0 µ max c c,0, c = c + δ c, j =,, where η s a parameter ( ) { } { } 0 1 j j j j representng the negatve feelng of beng worse off than the outh, whle μ s the parameter representng the negatve feelng of beng better off. We then have η μ. The second part of the welfare functon equals zero as c > c. 7 We could also ntroduce a consumpton transfer from orth to outh n both perods as a means to reduce consumpton nequalty. However, as we have assumed that µ < 1/2, no nteror soluton would be possble from the optmzaton problem, and there would not be any consumpton transfer between the two regons. Ths s because utlty s lnear n consumpton, and the orth wll always prefer one extra consumpton unt to tself than to the outh. ote, however, that wth a concave utlty functon, we would get an nteror soluton, and the margnal utlty of consumpton as well as the equty weghts wll determne the outcome. If µ = 0 so that orth does not care about the welfare level of the outh, there wll not be any consumpton transfer even n ths case. The reason s that the consumpton transfer has no strategc effect. The only reason to transfer consumpton s that the orth cares about the welfare of the outh.

11 3. Fnancal transfers and mtgaton n the outh The frst ssue to whch we apply our model s the queston of how the need to reduce emssons affects how the outh treats offcal fnancal flows from the orth. The optmal transfers from the orth wll be dscussed n ecton 5 below. For the tme beng we also gnore the need for adaptaton and focus on mtgaton only. Frst, note that as long as there s no emssons tradng, the emssons constrant n the orth gven by equaton (1) determnes the need for mtgaton n the orth,.e., the optmal level of m follows drectly from the emssons constrant and s unaffected by the transfers to the outh. We return to the case wth emssons tradng below. The optmzaton problem of the outh wth respect to mtgaton s gven by maxmzng the followng Lagrangan, (4) max L = c + δ c + λ [ eˆ e e ] m a m {[1 [1 ( )] ( ˆ)][ ]} { ˆ ( )[ ]} = y m a + δ α a + T D e y + T + λ e σ m + T y + y + T where λ s the shadow prce on carbon. Assumng the emssons constrant s bndng, the necessary frst-order condton (FOC) for an nteror soluton s (5) L m = + + = λ σ y y T / σ y + y + T = λ That s, the shadow prce of carbon,, s determned by the margnal cost of mtgaton, measured over both perods. Equaton (5) together wth the bndng emssons constrant e + e = eˆ from equaton (1) consttutes a two-equaton system 0 1 wth two varables and, whch are functons of ncome, transfers

12 and the emssons constrant. ote that adaptaton s not present n the FOC for mtgaton effort, whch allows us to study the mtgaton decson separately. We solve the system by totally dfferentatng the two equatons. Expressed n matrx form ths yelds: (6) m ( 2 ( dt σ 1/ 0 y λ dm σ y σ ( dt σ 0 d y 1 y = λ ( σ σ deˆ where that: s total undscounted ncome over both perods. We fnd (7) dm 1 dm dm σ = ( < 0; = 1 ; = 0. m ( > deˆ σ y dt dt σ y The frst expresson confrms that a more lenent emssons constrant n the outh leads to reduced mtgaton effort. The second expresson suggests that a dedcated mtgaton transfer completely crowds out the outh s own mtgaton efforts. nce the cap on emssons s fxed the transfer allows the outh to free up ts own resources for consumpton. As a result there s no addtonal mtgaton n the outh. A bndng emssons constrant n the outh renders mtgaton transfers neffectve,.e. de dm (8) = σ 1 0 m + m =. dt dt The fnal expresson n equaton (7) shows the effect of development assstance on mtgaton n the outh. It suggests that addtonal ad wll trgger further mtgaton. Ths s because a productve ncome transfer leads to hgher output and therefore more emssons, and addtonal mtgaton s needed to reman wthn the carbon constrant. Agan, the presence of an emssons constrant makes the transfer less effectve, n the sense that development assstance now leads to a lower ncrease n utlty n the outh, and therefore also the orth. To see ths we dfferentate the utlty functon of the outh wth respect to development assstance:

13 du dt {[1 1. D ( e ˆ )]} (9) = + δ α ( ) dm dt The second term of the equaton represents the ncrease n perod 1 consumpton that a productve transfer would normally have. The frst term s negatve and reflects the reducton n consumpton due to the need for more mtgaton. Because wellbeng n the outh features n the utlty functon of the orth, utlty n the orth s affected n the same way. ote that the effect on perod 1 consumpton depends on clmate damages. We wll return to ths ssue n the next secton. Equatons (7) to (9) gve rse to the followng proposton: Proposton 1: Mtgaton and development transfers become less effectve f the outh has a bndng emssons constrant, n the sense that the transfers result n less addtonal mtgaton or addtonal consumpton, respectvely, than the same transfer n the absence of a constrant. Ths s because each of the transfers focuses on only one objectve (emssons cuts and hgher output, respectvely), and the outh wll redeploy ts own resources to establsh ts preferred balance between the two goals. If the orth wshes to preserve the full effect of development transfers 8 t wll have to recognze the twn mportance of both output growth and emssons cuts. The orth may then devse a combned package of transfers that ncludes both development and mtgaton assstance. In partcular, a package that combnes each dollar of σ development assstance wth ( σ dollars of mtgaton transfer (recall that s y negatve, see equaton (7)), would be emssons-neutral and not requre any further adjustments n the outh: ( σ m de dm (10) T = T + ( T ( = 0; ( = 0 σ y dt dt 8 ote that ths wll not necessarly follow from the optmzaton problem of the orth, see ecton 5.

14 We can thnk of such a package as low-carbon development assstance (say, access to renewable energy) rather than tradtonal, hgh-carbon development ad (access to fossl fuel-based energy), where the ncremental cost of the clean soluton consttutes the mtgaton transfer. The presence of an emssons constrant n the outh thus strengthens the case for low-carbon development ad, and rases questons about development support for hgh-carbon projects lke coal. If the orth s ntent on ncreasng mtgaton n the outh beyond the emssons constrant, t may wsh to structure mtgaton transfers as matchng grants, where for each dollar the outh spends on mtgaton, the orth would pay an addtonal dollars for further mtgaton. 9 Ths would provde an ncentve to reduce emssons n the outh beyond what ts carbon constrant requres. Defnng as the total mtgaton level n the outh, t s easy to show that there s stll crowdng out but at a lower rate: ( (11) dm 1 m m 0 m 1 m = dm + τ + mdτ = dm dτ = m + τ. Hence, the effect of a slght ncrease of the matchng grant rate (from say 10% to m 11%) s a decrease n mtgaton expendture n the outh of m 1+ τ. In order to make ths comparable to the effect of the drect grant (whch s measured n monetary terms), we have to dvde by m n equaton (11). Therefore, the effect of a slght change n the matchng grant s gven by τ a [ 1,0] there s ncomplete crowdng out n the matchng grant case., showng that An ncomplete crowdng out mples that more s spent on mtgaton measures and emssons fall. However, unlke n the case of low-carbon development assstance, the matchng grant wll not result n a welfare maxmzng allocaton of resources from the perspectve of the outh as the outh would allocate resources dfferently wthout the matchng grant restrcton. We summarze these fndngs n the followng proposton: 9 Agan, ths may not necessarly be an optmal polcy for the orth.

15 Proposton 2: The orth can respond to the mpact that an emssons constrant n the outh has on the effectveness of transfers by swtchng to a low-carbon form of development assstance and / or by offerng mtgaton assstance n the form of a matchng grant. The former would ensure that the twn objectves of output growth and emssons cuts are met smultaneously. The latter would encourage the outh to undertake addtonal mtgaton beyond what ts emssons constrant requres. An nterestng extenson to consder s how the possblty of carbon tradng mght affect the case for offcal development and mtgaton assstance. To explore ths we replace the separate regonal emssons constrants of equaton 1 wth a global emssons target, (12) e + e + e + e eˆ, where. Countres are allowed to trade n devatons between actual and target emssons, whch gves rse to an addtonal fnancal flow that affects utlty n both regons:, where s the nternatonal prce of carbon. The consumpton levels n each regon and at each tme perod s now specfed n Table 2. Table 2: Consumpton levels n each regon and perod. Permt tradng. Perod 0 (now) Perod 1 (future) (orth ) (outh ) c = y m a T T T 0 0 ( ) e = σ m y 0 0 c = y m a p eˆ0 e m ( ) e = σ m + T y 0 0 m a + p e e 0 ˆ0 ( ) ( ˆ) c = 1 1 α a D e y 1 1 ( ) e = σ m y p e ˆ e 1 1 a ( ) ( ˆ) c = α a + T D e y + T p e ˆ e

16 m ( ) 1 1 = σ + + e m T y T The presence of carbon tradng ntroduces a strategc element to the orth s decson about development and mtgaton transfers, snce the mpact these have on outhern emssons may feed back to the orth n the form of dfferent carbon market dynamcs: Proposton 3: When emssons are controlled through a global carbon market, a transfer of mtgaton captal completely crowds out mtgaton n the outh. The transfer has no mpact on the optmal mtgaton level n the orth. Development assstance that ncreases output and emssons n the outh wll ncrease the mtgaton effort n the outh, whle the mtgaton effort n the orth s also lkely to ncrease. We demonstrate these results n Annex 1. It shows that most results also carry over to the case wth emssons tradng. The man dfference s that mtgaton n the outh affects the permt prce. When development assstance s gven, southern emssons ncrease and the outh needs to mtgate more to meet ts target, or to buy permts from the orth. In the Annex we show that both are lkely to happen, whch means that mtgaton wll ncrease n both regons and the prce for permts goes up. 4. Fnancal transfers and adaptaton n the outh We now turn to the adaptaton decson of the outh and explore how the adaptaton n the outh depends on transfers from the orth. The maxmzaton problem of the outh s gven by: (13) max L = c + δ c + λ [ eˆ e e ] a a m {[1 [1 ( )] ( ˆ)][ ]} { ˆ ( )[ ]} = y m a + δ α a + T D e y + T + λ e σ m + T y + y + T

17 The necessary frst-order condton for a maxmum (nteror soluton 10 ) wth respect to adaptaton effort, a, s gven by: + δ α + = 1 1 D y j T 0. Thus, we get δ ˆ α a + T D e y + T = 1 a 1 (14) ( ) ( ) The optmal adaptaton effort s found by equalzng the margnal benefts of adapton (the left hand sde) and ts margnal costs (the rght hand sde). The FOC determnes adaptaton effort as an mplct functon of adaptaton and productve nvestment and the global emsson cap: ( a a,, ˆ T T e) %. In a smlar way, we can fnd the optmal adaptaton level n the orth: 11 (15) δ y D ( eˆ ) α = 1. 1 ' Thus, as for the outh, the dscounted margnal benefts of adaptaton should equal the margnal cost of adaptaton. The optmal adaptaton level follows from economc consderatons only, whch means that both the mtgaton level and adaptaton level of the orth s unaffected by ts equty preferences. In addton, they are also unaffected by transfers to the outh. To see the mpact of transfers on the adaptaton level n the outh, we fnd from equaton (14): (16) a 1 1 α ˆ da + dt D y + T + α D y + T de + α DdT = 0 It follows straghtforwardly that 10 uffcent condtons for an nteror soluton are that the frst unt of nvestment n adaptaton has a very large effect on the resdual damages ( α ( 0) = + ) and that ths effect vanshes for very large nvestments lm α a = 0). ( ( ) a + 11 ee equaton (23) for the optmzaton problem.

18 a da D ˆ,, = = > 0 eˆ % α deˆ α (17) a ( e T T ) A hgher global cap on emssons wll cause the outh to adapt more as the margnal beneft to adaptaton s more mportant. If follows also that T (18) a ( e T T ) a a da % ˆ,, = = 1. a dt That s, addtonal adaptaton support completely crowds out the outh s own adaptaton effort. Drect adaptaton support funded by the orth does not lead to addtonal adaptaton because the outh decreases ts own adaptaton effort by the same amount. In the same way as for mtgaton, addtonal adaptaton support frees up resources that the outh prefers to use for consumpton. The reason for ths s seen from the frst order condton gven by equaton (14). Adaptaton transfers do not address any exogenous constrants to adaptaton but smply offer addtonal adaptaton resources. But snce the beneft from adapton s the same before and after the transfer, t wll be optmal for the outh to stck to ts orgnal adaptaton level. Thus, ths s n lne wth the lterature dscussed n the ntroducton clamng that the benefts of adaptaton are excludable, so the poor regon has the rght ncentves to adapt even before the transfer. As for mtgaton transfers dscussed above, the orth could ncrease the adaptaton n the outh, and thus reduce damage n the outh, by agan usng a matchng grant form of support. As before ths would lead to ncomplete crowdng out, but as ths gves a dfferent allocaton of resources than wthout the matchng grant restrcton, t would result n a welfare loss for the outh. Ths gves us the followng proposton: Proposton 4: Adaptaton captal transfer from the orth to outh wll completely crowd out adaptaton nvestments n the outh, unless a matchng grant support

19 functon s used, but ths wll not gve the welfare maxmzng allocaton of resources for the outh. To study the effect on adaptaton of development assstance, t follows from (16) that a da δ α D α ˆ,, = = = > 0, 1 1 T dt δ [ α ] D y + T [ α ] y + T (19) a% ( e T T ) hence, productve captal support leads to the desred result that the outh ncreases ts adaptaton effort. Intutvely, by promotng GDP growth n the outh, more value s at rsk n the regon due to clmate change. 12 Ths gves an ncentve to ncrease adaptaton efforts. ote that ths effect hnges on the assumpton that damages are proportonal to output, a standard assumpton n economc studes as mentoned n ecton 2. The result can be stated n a Proposton: Proposton 5: An ncrease n development assstance wll ncrease the adaptaton level of the outh. As seen from equatons (7) and (19), ncreasng development assstance that ncreases producton n developng countres has a postve mpact on both mtgaton and adaptaton effort n the developng countres. Ths s n contrast to clmate fnance that gves transfer of adaptaton and mtgaton captal. These results hnge on the assumpton that development assstance has a postve effect on producton n the poor countres, and that we do not have a complete crowdng out of nvestments n real captal. We wll dscuss ths n further detal n ecton 5 below Fnancal transfers when the outh s ncome-constraned Up to now, we have assumed that the outh s suffcently affluent that t can nvest some of ts resources n adaptaton or mtgaton. We now relax ths assumpton by requrng that consumpton n the ntal perod should be at least equal to some 12 In addton, hgher ncome may lead to hgher demand for clmate protecton, but we do not model ths ncome effect. 13 ote that the results for adaptaton depend on a gven level of accumulated emssons n the second perod. That s, t does not matter whether the permts are tradable or not.

20 mnmal subsstence level c. We can thnk of ths as the stuaton of a least-developed country. The outh s optmzaton problem s now gven by: (20) max s.t. and ˆ m, a U = c + δ c c c e + e e Assocatng a Lagrange multpler θ to the mnmal consumpton requrement and λ wth the emsson constrant as before, we can wrte the FOC for optmal mtgaton (assumng an nteror soluton 14 ) as follows: 0 1 (21) [ ] 1 + θ λ σ y y T + + = 0 The frst term denote the margnal cost of a dollar nvested n mtgaton n the frst perod: one unt of consumpton forgone plus the shadow prce of the subsstence requrement. The second term measures the margnal return of that extra mtgaton nvestment whch depends on the shadow value of the emssons constrant. The FOC for optmal adaptaton efforts s gven by: (22) [ ] 1 1+ θ + δ α D y + T = 0 The frst term stands for the margnal adaptaton cost and the shadow prce of the mnmal subsstence consumpton level. The second term stands for the margnal beneft,.e., reducton n remanng clmate change damages. Compared to the unconstraned case (equaton (5) for mtgaton and equaton (14) for adaptaton), we see that margnal cost of nvestment wll be hgher n the constraned case. Hence, the outh wll mtgate and adapt less f t s constraned n consumpton n the ntal perod whch s very ntutve. They would lke to mtgate and adapt more but they cannot because otherwse they would starve to death. 14 We can safely do ths because we have assumed that the margnal benefts of the frst unts of mtgaton- and adaptaton nvestments are unbounded.

21 The comparatve statcs and dervatons are shown n Annex 2. When both the emssons and consumpton constrants are bndng, we fnd exactly the same results for mtgaton as n the unconstraned case dscussed earler. In partcular, mtgaton support s completely crowded out, adaptaton support has no mpact on mtgaton efforts, productve captal support leads to hgher mtgaton (n order to compensate for hgher emssons), a more lenent emsson constrant mples less mtgaton, and the mnmal consumpton level (and hence a pure transfer of consumpton) has no mpact on the mtgaton decson. The comparatve statcs for adaptaton by the outh are however dfferent from the unconstraned case. Frst, extra mtgaton support leads to more adaptaton n the constraned case (remember t dd not affect adaptaton n the unconstraned case). The transfer of mtgaton captal leads to complete crowdng out of mtgaton as the outh wll lower ts own effort by exactly the same amount. However, ths frees resources that can be nvested n adaptaton whch was prevously constraned. econdly, extra adaptaton support has no mpact on the adaptaton choce of the outh n the sense that they do not change ther own adaptaton nvestments. The reason s that they were constraned n adaptaton. Hence, the support allevates the constrant and ncreases to total adaptaton captal of the outh. Thrdly, productve captal support leads to hgher second perod emssons whch have to be compensated by hgher mtgaton f the emsson constrant s bndng. Ths mples that resources should be draned away from adaptaton n order to obey the consumpton constrant. Thus, tradtonal development assstance leads to lower adaptaton nvestments n the poorest countres. Recall that ths was dfferent n the unconstraned case, n whch the outh reacted wth extra adaptaton efforts when recevng development assstance. Fourthly, a more lenent global carbon constrant results n more adaptaton nvestment n the outh because the margnal beneft of adaptaton ncreases. Ths effect s the same as n the unconstraned case.

22 A fnal result s that smply transferrng consumpton (.e., relaxng the consumpton constrant) would lead to hgher adaptaton. The addtonal consumpton s used to drect more resources to constraned adaptaton nvestments. 15 Proposton 6: If the outh s very poor (.e. constraned to subsstence consumpton n the ntal perod), adaptaton can be boosted by provdng (1) targeted adaptaton support, (2) mtgaton support, or (3) drect consumpton transfers. All three routes are equally effcent at boostng adaptaton. Productve captal support leads however to lower adaptaton. 6. The fnancal transfer decsons of the orth To decde on ts adaptaton level and the transfers to the outh, the orth wants to maxmze ts ntertemporal welfare functon, gven all restrctons from ecton 2 and a m subject to ts adaptaton level ( a ) and transfers ( T, T, T ). The optmal mtgaton level ( m ) s found n ecton 3. The optmzaton problem for the orth can then be wrtten as (23) a m T, T, T 0 a m 0 µ ( y m a T T T ) µ ( y m a ) 1 (1 µ )( y ( 1 (1 ( ))) ( ˆ α a D e) ) 1 a + µ (( y )( 1 (1 ( ))) ( ˆ + T α a + T D e) ) 0 1 { eˆ σ ( m )[ y y ]}, max L = (1 ) + + δ + λ + where λ s the shadow prce of carbon n the orth. The Kuhn-Tucker condtons, where the choces of the outh are taken as gven, are L T a = (1 µ ) + µδ ( ˆ y + T D e) α a T 1 (24) ( ) a L m (25) = (1 µ ) µ 0 m m T T 15 Thus, as opposed to the result n the man model n ecton 2, a consumpton transfer may be optmal n ths case.

23 (26) a 1 ( ( )) ˆ ( ) L m a a (1 µ ) µ δ 1 1 ( ) ( ) ( ˆ µ α a s T D e y T α = D e) 0, T T T T where equalty holds for nteror solutons of the respectve endogenous varables. Before dscussng the frst order condtons, note that by settng µ = 0, the only reasons for transfers from orth to outh would be strategc. Thus, ethcal reasons such as to do good would not apply. As s obvous from equatons (24) to (26), there are no strategc reasons for transfers n ths model. However, as we wll dscuss below, ths wll change when we ntroduce tradable permts. To fnd the optmal levels of transfers, we need to work wth the frst-order condton. Let us start wth the adaptaton transfers. For an nteror soluton, we fnd from (24): a 1 µ = µδ ( ˆ y + T D e) α + 1 a T 1 (27) ( ) Ths shows that the margnal cost of the transfer n the orth, weghted wth the equty weght (left hand sde), should equal the beneft of ncreased consumpton n the outh n the next perod, also weghted wth the equty weght (rght hand sde). a But from (18) we know that = 1 and the adaptaton transfer completely crowds a T out outh s adaptaton effort f there are no constrants to the transfer. In ths case we see that (27) does not hold, and there s no nteror soluton. Thus, t wll not be optmal for the orth to transfer adaptaton captal to the outh ote that an adaptaton transfer n ths case would be equal to a pure consumpton transfer. As dscussed n footnote 7, a consumpton transfer wll not be optmal wth a lnear utlty functon. ote, however, that wth a concave utlty functon, we would get an nteror soluton, and t would be optmal wth an adaptaton transfer even f the adaptaton level n the outh dd not ncrease. The reason s that consumpton n outh would ncrease and the nequalty between the two sectors would be lower. Ths would ncrease the utlty of the orth as they express nequalty averson.

24 However, f there are constrants attached to the adaptaton transfers, such that for every dollar used on adaptaton n the outh, the orth transfers τ a dollars (a matchng grant), we know from ecton 3 that there s crowdng out, but t s not necessarly complete. Usng a matchng grant may, therefore, gve an nteror soluton of the optmzaton problem and a postve adaptaton transfer from the orth to the outh wll occur. The magntude of ths transfer s ncreasng wth the equty weght put on the utlty of the outh, and the transfer would be zero f the weght s set to zero. da If the outh s constraned n consumpton (ecton 5), we know that 0 dt =, see a Annex 2. Ths has mplcatons for the adaptaton transfers as equaton (27) now becomes: 1 µ µδ y T D ( eˆ ) α 1 (28) = ( + ) Thus, as we do not have crowdng out, t may be optmal for the orth to transfer adaptaton captal to the outh. To study the optmal mtgaton transfers we combne (25) and (7) and fnd L (29) = (1 µ ) + µ < 0 m T As for adaptaton transfers, there s no nteror soluton to mtgaton transfers and the optmal level s equal to zero. The mtgaton transfer would just work as a consumpton transfer, whch s not optmal wth the lnear utlty functon. Ths also holds f the outh s ncome-constraned. Ths gves us the followng proposton: Proposton 7: Due to the complete crowdng out of adaptaton and mtgaton n the outh from adaptaton and mtgaton transfers respectvely, these would work as pure ncome transfers, whch wll not be optmal wth a lnear utlty functon. The transfers could be optmal f they are desgned as a matchng grant functon. Also, f

25 the outh s ncome-constraned, adaptaton transfers would be optmal for the orth as they wll ncrease the total adaptaton captal n the outh. The optmal level of development assstance follows from equaton (26). Assumng an nteror soluton, t can be re-organzed as: (30) 1 a ( ( ) ˆ ) ( ) ( ) 1 µ m a 1 ( ) 1 1 ( ) ( ˆ y T D e a s T D e) T µ = T µ δ + α + δ µ α + As seen from (30), the development assstance has mpacts on the utlty of the orth va changes n the mtgaton and adaptaton efforts n the outh, as well as the ncome ncrease n the outh as the regon gets rcher. Thus, there may be an nteror soluton meanng that there may exst an optmal level of development assstance. For the case where the outh s ncome-constraned, we may stll have an nteror soluton, but note that the sgn of a T now turns from postve to negatve, whch has an mpact on the sze of the transfer. Whether, t ncreases or decreases s undetermned as adaptaton n the outh has both a postve (reduces utlty n the frst perod) and negatve (ncreases utlty n the second perod) mpact on the ntertemporal utlty of the poor regon. If there s a permt market, the development assstance has addtonal mpacts on the utlty of the orth va changes n the permt prce, see Annex 1. Ths has agan mpacts for the mtgaton effort n both countres. Thus, even f the orth does not care about the welfare of the outh, the regon may stll be nterested n transferrng development assstance for strategc reasons as the transfer has mpacts on the fnancal flows from the permt market and ts mtgaton effort. ote, however, that the strategc and ethcal ncentves may go n dfferent drectons. For nstance, even f the orth cares about the outh, t may stll refran from transferrng development assstance or reduce the ethcally optmal level due to the effect of the transfer on ts mtgaton and the fnancal flows from the emsson permt market.

26 7. The decsons of the orth when fnancal transfers are neffcent In addton to the ncentve effects studed so far, the effects of nternatonal transfers also depend on leakage,.e., the extent to whch transfers do not reach ther ntended benefcary. Wth weak or corrupt nsttutons, whch are prevalent n many countres, money may dsappear along the road. In our model, the effcency of transfers can be modeled n dfferent ways. For nstance, the α- and σ-functons descrbe how adaptaton measures and mtgaton measures are transferred nto reduced damage and emssons respectvely. Thus, these functons also descrbe the effcency of these transformatons. As an example, the α- functon may descrbe the costs of adaptaton. To model what actually reaches the targets, we can ntroduce effcency parameters j 0 b 1, j = a,, m. Ths means that the orth may pay more than what reaches the outh. Thus, whle the orth s optmzaton problem s unchanged, these parameters need to be ncorporated n outh s optmzaton problem. The ntroducton of effcency parameters only has modest mpacts for the qualtatve conclusons of the model. In the case of permt tradng, the permt prce wll be affected by the effectveness of development ad. Also, crowdng out of adaptaton and mtgaton captal wll be less f less reaches the outh,.e., there s only crowdng out of the actual transfer that reaches the target. Our conclusons on the effect of development ad hnges on the assumpton that development assstance has a postve effect on producton n the poor countres, and that we do not have a complete crowdng out of nvestments n real captal. In our model, we have assumed that nvestments n real captal are exogenous, so that the growth potental of development ad s not crowded out. ome studes suggest that ad does not necessary rase captal stocks n developng countres, and that the outcome depends on domestc polces and nsttutons, see e.g., Dollar and Easterly (1999); Easterly and Pfutze (2008), but there are also more optmstc vews on the effects of development ad (e.g. achs (2005); Banerjee and Duflo (2011)). Temple (2010)

27 examnes the condtons under whch foregn ad wll be effectve n rasng growth. Based on the evdence, he fnds that ad can be effectve, and that the hypothess that ad may be harmful does not have backng. Thus, whle we have modeled the effect of ad n a smple way, we can conclude that as long as ad s gven n a way that promotes growth (not complete crowdng out), the effect on mtgaton and adaptaton effort n the developng countres wll be postve. The leakages do not change the qualtatve conclusons for mtgaton and adaptaton transfers. In the man model, t s not optmal for the orth to transfer mtgaton and adaptaton captal as we have full crowdng out and the transfers go to consumpton. However, ths s based on the assumpton of lnear utlty functons. Wth concave utlty functons, the opton for the orth would be to ncrease the outhern consumpton by ether transferrng consumpton goods drectly, or transferrng adaptaton or mtgaton captal. The choce would depend on transacton costs akn to the leaky bucket problem;.e., effcency loss n dstrbuton. As a consequence, transferrng adaptaton or mtgaton captal may gve dfferent effects on consumpton and on who receves the consumpton good than a drect transfer of the good tself. 8. Conclusons Ths paper dscusses the nterplay of dfferent types of donor assstance to developng countres: development assstance to boost output and ncome, mtgaton support to reduce greenhouse gas emssons, and adaptaton support to ncrease reslence to clmate rsks. The motvaton for these transfers s derved solely from the orth s concern about well-beng n the outh. Our man model does not nclude any strategc reasons for mtgaton and adaptaton transfers, such as the need to secure a global agreement on emssons, or concerns about nternatonal trade, where countres specalzng n an adaptaton or mtgaton technology may expand ther market f others apply that technology. The man model does not contan any market dstortons that are not nternalzed. In partcular, there are no barrers to ether effectve adaptaton or effectve economc management (such as poor nsttutons), and we assume a bndng global emssons

28 constrant to address the clmate change externalty. We may assocate ths stuaton wth mddle ncome countres, whch tend to have farly advanced nsttutons. We fnd that under these assumptons solated transfers amed solely at development, mtgaton or adaptaton are relatvely neffcent: A large part of ther ntended effect (to ncrease ncome, reduce emssons, or boost clmate-reslence) dsspates as the outh reacts to the transfers by reallocatng ts own resources untl t has establshed the mtgaton, adaptaton and consumpton balance that optmzes ts welfare. In essence, clmate change fnance works as a pure consumpton transfer and any mpacts on mtgaton and adaptaton are ndrect, trggered by the softer budget constrant. If the orth wshes to change the balance between mtgaton, adaptaton and consumpton n the outh t needs to structure ts transfers as matchng grants, whch vary accordng to the outh s own level of fundng. In our model such condtonal fundng would not lead to a welfare maxmzng allocaton of resources. Matchng grants could only be justfed f the orth cares partcularly about clmate securty n the outh, rather than welfare more broadly. Ultmately f the orth wants to preserve the full effect of development transfers, t may recognze how clmate change complcates welfare maxmzaton and provde an ntegrated transfer package that addresses the combned clmate and development requrements of the outh. The development communty has started to call ths clmate-smart development or, more catchly green growth (Jacobs 2013; World Bank 2012; Bowen and Fankhauser 2011). The result changes f we ntroduce a bndng ncome constrant. We can thnk of ths as the stuaton of least-developed countres, whch have to secure a subsstence level of ncome before money can be allocated for clmate change purposes. In ths stuaton fnancal transfers can have some unexpected consequences. For example, a mtgaton transfer may lead to hgher levels of adaptaton because the outh s own mtgaton budget s freed up and can be reallocated. But more expectedly, an adaptaton transfer wll have the desred effect by easng the constrant on adaptaton and ncreasng clmate reslence.