Johan Eyckmans, Sam Fankhauser and Snorre Kverndokk Development aid and climate finance

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1 Johan Eyckans, a Fankhauser and norre Kverndokk Developent aid and cliate finance Article (Accepted version) (Refereed) Original citation: Eyckans, Johan, Fankhauser, a and Kverndokk, norre (2015) Developent aid and cliate finance. Environental and Resource Econoics. IN DOI: /s pringer cience+business Media Dordrecht This version available at: Available in LE Research Online: Noveber 2015 LE has developed LE Research Online so that users ay access research output of the chool. Copyright and Moral Rights for the papers on this site are retained by the individual authors and/or other copyright owners. Users ay download and/or print one copy of any article(s) in LE Research Online to facilitate their private study or for non-coercial research. You ay not engage in further distribution of the aterial or use it for any profit-aking activities or any coercial gain. You ay freely distribute the URL ( of the LE Research Online website. This docuent is the author s final accepted version of the journal article. There ay be differences between this version and the published version. You are advised to consult the publisher s version if you wish to cite fro it.

2 Developent Aid and Cliate Finance Johan Eyckans a, a Fankhauser b and norre Kverndokk c Noveber 2014 Abstract This paper discusses the iplications of cliate change for official transfers fro rich countries (the North) to poor countries (the outh) when the otivation for transfers is ethical rather than strategic. Traditional developent transfers to increase incoe and reduce poverty are copleented by new financial flows to reduce greenhouse gas eissions (itigation transfers) and becoe cliate-resilient (adaptation transfers). We find that in the absence of barriers to adaptation, itigation or developent, cliate change will ake isolated transfers less efficient: A large part of their intended effect (to increase incoe, reduce eissions, or boost cliateresilience) dissipates as the outh reallocates its own resources to achieve the itigation, adaptation and consuption balance it prefers. Only in the case of least-developed countries, which are unable to adapt fully due to incoe constraints, will adaptation support lead to ore cliate resilience. In all other cases, if the North wishes to change the balance between itigation, adaptation and consuption it should structure its transfers as atching grants, which are tied to the outh s own level of funding. Alternatively, the North could provide an integrated cliate-copatible developent package that recognizes the cobined cliate and developent requireents of the outh. If the ai is to increase both itigation and adaptation in the outh, developent assistance that increases the incoe level, can an effective easure, but only if there is an international agreeent and the recipient country is not incoe constrained. If the recipient country is very poor, developent aid ay reduce adaptation effort. Keywords: inequality aversion; itigation; adaptation; cliate finance; developent assistance; institutional barriers JEL classification: D63, Q50, Q54, Q56 Acknowledgeents: The project was supported financially by the MILJØ2015 progra at the Research Council of Norway. Fankhauser also acknowledges financial support by the Grantha Foundation for the Protection of the Environent and the UK Econoic and ocial Research Council. We are indebted to discussions with cott Barrett and to coents fro two anonyous referees, Katinka Holtsark, Torben Mideksa, Linda Nøstbakken and various seinar participants. The authors are associated with CREE - the Oslo Centre for Research on Environentally Friendly Energy - which is supported by the Research Council of Norway. a KU Leuven capus Brussels, Center for Econoics and Corporate ustainability. b Corresponding author: Grantha Research Institute and Centre for Cliate Change Econoics and Policy, London chool of Econoics (s.fankhauser@lse.ac.uk). c Ragnar Frisch Centre for Econoic Research, Oslo. 1

3 1. Introduction The twin needs of poverty alleviation and environental protection have long been recognized as copleentary challenges. There is by now an extensive body of work that docuents the close links between environent and developent, a literature to which Anil Markandya has ade wide-ranging contributions (e.g. Pearce et al. 1990; Markandya and Pearce 1991; Markandya 1998, 2002, 2008; Markandya and Nurty 2004). Perhaps less appreciated in the acadeic literature is the fact that environent-developent links also extend to questions of finance. Official developent assistance has been subject to extensive research in particular about aid effectiveness (e.g., Dollar and Easterly 1999; Collier and Dollar 2002, 2004; Bourguignon and undberg 2007), but environental finance has becoe a topic of wider acadeic interest only recently in the context of cliate change. Under the Copenhagen Accord of 2009 (UNFCCC, 2010), and reaffired in subsequent negotiation docuents, developed countries have proised to provide additional cliate finance of up to $100 billion a year to help developing countries reduce their eissions and adapt to cliate change. Cliate finance is to be explicitly provided on top of conventional developent assistance, which developed countries have pledged to increase to 0.7% of GDP as part of the Millenniu Developent Goals. Fankhauser and Pearce (2014) offer a conceptual discussion of sustainable developent finance, while Haites (2013) provides an overview of cliate finance issues. Tol (2005) argued early on that developent aid can reduce vulnerability to cliate change. However, there has been no systeatic analysis up to now of how environental finance and developent aid interact, either fro a donor perspective (e.g., in ters of overlapping or copeting donor objectives) or fro a recipients point of view (e.g., in ters of the incentives that ultiple funding streas provide). The ai of this paper is to close this gap, using cliate change as a pertinent exaple. The paper offers a theoretical odel to analyze the ethical otivation of donors in providing three kinds of funding to developing countries: funding to alleviate poverty (developent aid), funding to reduce greenhouse gas eissions (itigation finance) and funding to prepare for unavoidable cliate change (adaptation finance). The odel also studies how the three funding 2

4 streas affect the ability and inclination of recipient countries to increase consuption, reduce eissions and strengthen resilience to cliate change. We specify a two period odel (present and future), with a rich region (North) and a poor region (outh). They play a leader-follower gae, where the North calculates the behavior of the outh before deciding on the optial level of transfers. We are not concerned with optiizing global social welfare. Rather, we take the point of view of donor and recipient countries and ask what their social welfare functions iply for the ipact of different financial transfers. The ain difference between our study and earlier papers on international transfers is threefold: (i) the explicit ethical otivation for giving transfers, (ii) the broad set of transfers we study and (iii) the treatent of arket iperfections and institutional barriers for transfers. It is worth elaborating on each of these features. First, in ters of the ethical otivation of transfers, ost of the existing literature on financial transfers focuses on their strategic value, that is, their erit in securing an international agreeent (see e.g., Barrett, 2003, 2007 and Hong and Karp, 2012, on foring international environental agreeents). Already in the 1990s, Carraro and iniscalco (1993) and Kverndokk (1994) argued that side payents ainly fro OECD countries to non-oecd countries would be an effective policy instruent for aking a liited treaty significant. Eyckans and Tulkens (2003) show that a proportional surplus- sharing rule can stabilize a grand coalition and secure the first-best global cliate policy, and Carraro et al. (2005) deonstrate the iportance of onetary transfers as strategic instruents to foster stability of voluntary cliate agreeents. Further, Hoel (2001) argues that onetary transfers are also iportant to reduce carbon leakage, while Chatterjee et al. (2003) and Bretschger and uphaphiphat (2014) study transfers that proote econoic growth. In contrast, the basic tenet in our paper is that transfers reflect the ethical beliefs of those aking the. That is, transfers are not ade priarily for strategic reasons, but because people in developed countries care about the welfare of people in developing countries. 1 We also assue 1 The Copenhagen Accord describes transfers that should address the needs of developing countries, see UNFCCC (2010). 3

5 that these beliefs can be expressed in an appropriately specified welfare function, and study how the level and coposition of financial flows depend on the ethical beliefs of developed countries. Fairness issues related to cliate finance have been studied by, e.g., Grasso (2010) and Pittel and Rübbelke (2013a). Grasso (2010) studies adaptation finance fro the fraework of procedural and distributive justice. Pittel and Rübbelke (2013a) focus on how cliate finance ay support an optial cliate outcoe, arguing that international adaptation transfers could help address the perceived unfairness associated with historical eissions. Hence, such transfers ay help achieving an international cliate agreeent. For a further discussion of the ethical diensions of cliate change see Kolstad et al. (2014), tern (2014a, b) and Kverndokk and Rose (2008). A second distinguishing feature of our paper is that it analyzes the full range of available transfers, including transfers for itigation, adaptation and developent. In that respect the paper is part of a recent literature on the interplay between adaptation and itigation (see for instance Ingha et al. 2007; Tulkens and van teenberghe 2009; Buob and tephan 2011, 2013; Ebert and Welsch 2012; Heuson et al., 2012; Bréchet et al. 2013). A recurring insight fro this body of work is that while the benefits of itigation are non-excludable, the benefits of adaptation are often excludable. This eans adaptation is priarily a private good and the benefits accrue only to the nation doing the adaptation investent (Kane and hogren, 2000; Barrett, 2008). 2 Thus, nations should have the incentives to do the appropriate adaptation investent theselves in contrast to itigation. We should thus expect at least soe crowding out of adaptation transfers as countries pursue their optial adaptation strategies. Another issue in this literature is whether adaptation and itigation are substitutes or copleents (Buob and tephan, 2013). If the two easures are substitutes, a reduction in the cost of one (say, lower adaptation costs) will reduce deand for the other (less itigation, since additional low-cost adaptation can reduce the effects of cliate change). If the two easures are copleents, a reduction in costs will increase deand for both easures. There are exaples where this is the case, such as the preservation of peat lands and angrove forests, which siultaneously sequesters carbon and reduces ipacts. However, in ost cases itigation and 2 There are exaples of adaptation actions with regional public goods features, such as the anageent of international water systes, and global public good features, such as easures to deal with cliate refugees (Heuson et al., 2012), but we can treat these as exceptions fro the rule. 4

6 adaptation see to be substitutes (Tol, 2005; Ingha et al., 2005), which is the assuption we ake in this paper. 3 A third iportant feature of our paper lies in its assuptions about barriers and arket iperfections. In the absence of any arket iperfections the cliate change externality is fully addressed, there are no financing barriers, transfers are cost-free etc. the optial transfer strategy is easy. Donor countries transfer incoe in accordance with their ethical beliefs and recipient countries allocate funds between incoe, itigation and adaptation to axiize their welfare. We take this (unrealistic) case as the starting point, before exploring financing and institutional constraints (see also Bretschger and uphaphiphat 2014). The abition of the international cliate negotiations is to achieve a legally binding and universal cliate agreeent for all nations. An interesting question is how this abition interacts with itigation transfers both fro the recipient side and the donor side. A universally binding international agreeent is therefore a preise for our analysis, although we do not prescribe how constraining the eissions liits ight be. An alternative to a carbon constraint is studied by Pittel and Rübbelke (2013b), who develop a two-region odel, siilar to ours, to explore the erit of financial adaptation transfers that are conditional on itigation efforts. Conditional transfers are also studied in this paper. However, we also ask whether transfers ay be optial for donor countries without being conditional. We then introduce financing constraints. Dividing the world into only two regions, rich and poor, is of course a siplification as the developing region consists of countries at different incoe levels, which ay face different financing barriers. We study the case of low incoe countries, which ay face a consuption constraint as they seek to fulfill a subsistence level condition. If they are constrained in available resources we find that the effects of transfers are different. While credit constraints are also studied in Bretschger and uphaphiphat (2014), they do not study adaptation transfers. 3 If itigation and adaptation are copleents, the poor region will boost its itigation when it receives ore adaptation support. This additional itigation is beneficial for the rich region, given the public good nature of itigation. o in that case, there are strong incentives for the rich region to voluntarily support adaptation in the poor region. Note that this arguent is valid when there is no binding cliate agreeent. 5

7 The paper is structured as follows. ection 2 sets out our theoretical odel. It features a twoperiod leader-follower gae of transfers fro North to outh with utility functions that include the welfare in the other region. We then use this fraework to study a series of questions relating to the interplay of developent aid and official finance for itigation and adaptation. The gae is solved by first analyzing the proble of the follower, that is, decision aking in the outh. ection 3 studies the effect of official transfers on the itigation decisions of the outh, while section 4 studies the ipact on adaptation. ection 5 introduces a financing constraint and analyzes the special case of a (least-developed) country whose ability to spend oney on cliate change is constrained by the need to aintain a subsistence level of consuption. We turn to the leader and study decision aking in the North in section 6, where we analyze the incentive of the North to offer adaptation, itigation and developent transfers, bearing in ind the strategic reaction of the outh observed in sections 3 and 4. ection 7 studies the sae question but with an institutional constraint: the efficiency of transfers varies, that is, a varying fraction of funding is lost in the course of the transfer. Finally, section 8 concludes. 2. A two-period odel of transfers Our odel is structured as a leader-follower gae between two regions over two periods ( t 0,1 ). The two regions are called North ( j N) and outh ( j ), where North is a rich region and outh is poor. Each region produces an exogenous output eissions t y j, which results in greenhouse gas t e j. 4 The cobined eissions fro both regions result in cliate change daage, which reduces output in period 1. Daage in period 0 is assued to be negligible. In period 0 each region chooses the aount it wishes to invest in itigation technology j and adaptation technology a j. The benefit of adaptation is reduced ipacts fro cliate change in period 1. We assue that cliate change daage in country j, D j, increases in aggregated 4 Thus, we iplicitly assue that real capital investents are ade optially. 6

8 eissions, is proportional to output, and a fraction, j, of this daage can be avoided through adaptation. Investing in adaptation has decreasing returns: ja j 0 1 with 0 and 0. This specification, while siple,is in line with the literature on integrated assessent j odelling (see, e.g., Fankhauser, 1994; Kverndokk, 1994; Tol, 2002; Nordhaus, 2008; de Bruin, Dellink and Tol, 2009; de Bruin, Dellink and Agrawala, 2009; for a critique see Pindyck, 2013), and covers both arket and non-arket daages. 5 j Mitigation capital is long-lived so that the choice of j deterines eissions over both periods. t t Eissions are proportional to output, that is, e j j j y j, where j j can be interpreted as the eission-to-output ratio. Thus, the benefit of investing in itigation is a lower eission intensity of output. We assue that itigation investent has decreasing returns (equivalently, the abateent costs functions is convex): j 0 and j 0. 6 Each region has its own eission constraints, which one ay think of as being part of an international agreeent to constrain eissions over both regions: (1) e e eˆ ; e e eˆ ; eˆ eˆ eˆ N N N N For siplicity we assue that there is no interaction (e.g., through carbon trading) between the two eission spaces. The respective eissions constraints apply separately to each region, although eissions are fungible across tie periods For a discussion of the case where consuption and the environent are specified as two different goods in the utility function, see Hoel and terner (2007). 6 Buob and tephan (2013) define itigation and adaptation as substitutes if adaptation negatively affects the arginal productivity of itigation. To see that this is the case in our odel, we define a green GDP function as F( y, a, ) y 1 ( a) D ( ) y y. Based on this, the condition for substitution is in Buob and tephan; 2 2 fulfilled as F( y, a, ) a ' D' ' y 0. 7 This is not iportant for the conclusions in this paper, but it siplifies the analyses as we get only one shadow price of carbon in the region, see section 3 below. 8 Eyckans et al (2014) explore a global carbon constraint where carbon is traded between regions, thus introducing a strategic eleent into the gae. Another alternative would be to associate the benefit of itigation directly with reduced daage. This too would introduce strategic considerations into the odel and ake it difficult to distinguish the equity case for transfers fro the strategic case. Moreover, our representation is not unrealistic. Very 7

9 The North can ake three types of transfer in period 0: a productive capital transfer (developent assistance), available output (and eissions) of the outh in period 1, a itigation transfer, an adaptation transfer, i T, which will increase the T, which helps the outh reduce its eissions in both periods, a T, which augents the adaptation capital available to the outh. The transfers introduce soe intra- and intergenerational tradeoffs. Mitigation (and itigation support) has an iediate and lasting ipact because it lowers the eission intensity in both periods. Adaptation and productive capital support however, are subject to a tie delay. Today s investent only pays off in the next period. Hence, we assue that changing the productive capital base of a country requires ore tie than curbing its eission intensity. Increasing the adaptation capacity only affects the future as the daage is only felt in the longer ter. 9 The output that is left after transfers and investents in itigation and adaptation in period 0 is consued. The consuption levels in each region and period, eissions, t e j, can be specified as shown in Table 1. t c j, and the corresponding Table 1: Consuption and eissions levels in each region and period. Period 0 (now) Period 1 (future) 0 0 a i N (North) c y a T T T N N N N e y 0 0 N N N N 0 0 (outh) c y a e T y 0 0 ˆ c 1 1 a D e y 1 1 N N N N N e y 1 1 N N N N a ˆ i c a T D e y T e T y T 1 1 i few countries are large enough to influence global eissions significantly. For ost, the incentive to reduce eissions coes fro an exogenously agreed target, rather than the possibility to reduce daage directly. 9 In reality, there will also be quick wins in iproving adaptation capacity and productivity. At the sae tie, soe itigation efforts will only curb eission intensity in the long run. We abstract fro these possibilities ainly because it allows us to keep the odel tractable. 8

10 The final, crucial eleent of the odel is each region s utility function. We assue that both regions gain utility fro consuption (that also includes feedback fro the environent). For siplicity we assue linear utility functions, and we can write the interteporal utility function of the outh as: 10 (2), U c c c c where is the consuption discount factor of the outh, expressing the intergenerational equity preferences of the region. To be able to study transfers fro North to outh that are not otivated by strategic reasons, we assue that the North has social preferences. It cares about the intragenerational distribution of consuption, that is, the distribution of consuption between the regions. One way of doing this is to follow Fehr and chidt (1999) and assue that the North expresses inequality aversion in consuption; 11 people in the North dislike that the outh is poorer than the, but would dislike it even ore if the outh were richer. 12 In representative deocracies, these preferences get reflected in the actions of policy akers (Lee et al. 2004). We can therefore assue that the Fehr-chidt utility functions of voters work through in the welfare function of the country as a whole (Kverndokk et al. 2014). Obviously, as North is the richer region, we have cn then be written as: c. The utility function of the North can 10 A linear utility function is of course a siplification. However, we ay argue that transfers are not so big that they lead to large changes in the consuption levels of the regions, thus the arginal utility is relatively constant. With this representation, the arginal utility fro a change in consuption is equal to one. 11 We could also introduce the inequality preferences in the welfare function of the outh as in Kverndokk et al. (2014). This would give preferences for a higher consuption level in the outh. However, as will be obvious fro the discussions in ections 3 and 5 below, equity preferences will not affect the optial itigation and adaptation levels, and inequality aversion in the outh would not atter for our analysis The general case would be U c, c c ax c c,0 ax c c,0, c c c, j N,, N N N N N j j j j where is a paraeter representing the negative feeling of being worse off than the outh, while μ is the paraeter representing the negative feeling of being better off. We then have. The second part of the welfare function equals zero as cn c. 9

11 (3) 0 1 U c, c c ( c c ) (1 ) c c, c c c, j N, N N N N N j j j j where 0 is a paraeter expressing the intragenerational preferences of the North, while N is the discount rate of the North, expressing its intergenerational preferences. Fro (3) we see that 1 is required for consuption in the North to add to the North s welfare. In addition, it is reasonable to assue that consuption in the North adds ore to the utility of the North than consuption in the outh. Thus, we set Financial transfers and itigation in the outh The gae is solved by backward induction; we first look at decisions by the follower, that is, the outh. The odel is structured so that the outh s adaptation and itigation decisions are independent fro each other, and we start with itigation. That is, we first explore how the need to reduce eissions affects how the outh reacts to official financial flows fro the North. All optiization probles and first order conditions are specified in Annex 1. Let be the shadow price on carbon for the outh. Assuing the eissions constraint is binding, we find the optial level of itigation in the outh fro the necessary first-order condition (FOC) for an interior solution: (4) 0 1 i 1 / y y T 13 We could also introduce a consuption transfer fro North to outh in both periods as a eans to reduce consuption inequality. However, as we have assued that 12, no interior solution would be possible fro the optiization proble, and there would not be any consuption transfer between the two regions. This is because utility is linear in consuption, and the North will always prefer one extra consuption unit to itself than to the outh. A transfer is only welfare iproving for the North if it increases consuption ore in the outh than it reduces consuption in the North. To be ore precise: C 1 C. Note, however, that with a concave utility N function, it ay be welfare iproving for the North to transfer consuption to the outh if the consuption level is so high that the direct arginal utility of consuption (not considering inequality aversion) is very sall. Thus, in this case we ay find an optial consuption transfer. Also, if 0 so that North does not care about the welfare level of the outh, there will not be any consuption transfer. The reason is that the consuption transfer has no strategic effect. The only reason to transfer consuption is that the North cares about the welfare of the outh. 10

12 The FOC tells us that the shadow price of carbon, λ, is deterined by the arginal cost of itigation, easured over both periods. Equation (4) together with the binding eissions 0 1 constraint e e eˆ fro equation (1) constitute a two-equation syste with two endogenous variables 0 1 i and, which are functions of incoe y, y, transfers T, T and the eissions constraint e ˆ. Note that adaptation is not present in the FOC for itigation effort, which is why we can study the itigation decision separately. We solve the syste by totally differentiating the two equations. Expressed in atrix for this yields: (5) dt 2 1/ 0 y d y i dt 0 d y 1 y deˆ 0 1 i where y y y T is total undiscounted incoe over both periods. We find that: (6) d 1 d d 0; 1 ; 0. i deˆ y dt dt y The first expression confirs that a ore lenient eissions constraint in the outh leads to reduced itigation effort. The second expression suggests that a dedicated itigation transfer copletely crowds out the outh s own itigation efforts. ince the cap on eissions is fixed, the transfer allows the outh to free up its own resources for consuption. As a corollary there is no additional itigation in the outh. A binding eissions constraint in the outh renders itigation transfers ineffective, i.e. 14 de (7) d y 1 0 dt dt. 14 It sees likely that a global agreeent would be heterogeneous. oe countries ay have restrictions on absolute eission levels as in equation (1), while other countries ay have restrictions on carbon intensity, i.e. σ. If the latter is true, we have ( ). However, this will not change conclusions in the no-trade case as this also defines j j j the itigation level as a function of the exogenous target. 11

13 The final expression in equation (6) shows the effect of developent assistance on itigation in the outh. It suggests that additional aid will trigger further itigation. This is because a productive incoe transfer leads to higher output and therefore ore eissions, and additional itigation is needed to reain within the carbon constraint. Again, the presence of an eissions constraint akes the transfer less effective, in the sense that developent assistance now leads to a lower increase in utility in the outh, and therefore also the North. 15 To see this we differentiate the utility function of the outh with respect to developent assistance: du dt a (8) a T i d 1 1 ( ˆ D e) i dt The second ter of the equation represents the increase in period 1 consuption that a productive transfer would norally have. The first ter is negative and reflects the reduction in consuption due to the need for ore itigation. Because wellbeing in the outh features in the utility function of the North, utility in the North is affected in the sae way. Note that the effect on period 1 consuption depends on cliate daages. We will return to this issue in the next section. Equations (6) to (8) give rise to the following proposition: Proposition 1: Mitigation and developent transfers becoe less effective if the outh has a binding eissions constraint, in the sense that the transfers result in less additional itigation or additional consuption, respectively, than the sae transfer in the absence of a constraint. This is because each of the transfers focuses on only one objective (eissions cuts and higher output, respectively), and the outh will redeploy its own resources to establish its preferred balance between the two goals. 15 However, Bretschger and uphaphiphat (2014) find that a itigation transfer ay be better for the outh than developent aid due to its effects on econoic growth. 12

14 If the North wishes to preserve the full effect of developent transfers 16 it will have to recognize the twin iportance of both output growth and eissions cuts. The North ay then devise a cobined package of transfers T that includes both developent and itigation assistance. In particular, a package that cobines each dollar of developent assistance with y dollars of itigation transfer (see equation (6) and recall that is negative), would be eissions-neutral and not require any further adjustents in the outh: i de d (9) T T T 0; 0 y dt dt We can think of such a package as low-carbon developent assistance (say, rural electrification based on renewable energy) rather than traditional, high-carbon developent aid (access to fossil fuel-based energy), where the increental cost of the clean solution constitutes the itigation transfer. The presence of an eissions constraint in the outh thus strengthens the case for lowcarbon developent aid, and raises questions about developent support for high-carbon projects like coal. If the North is intent on increasing itigation in the outh beyond the eissions constraint e ˆ, it ay wish to structure itigation transfers as atching grants, where for each dollar the outh spends on itigation, the North would pay an additional dollars for further itigation. 17 This would provide an incentive to reduce eissions in the outh beyond what its carbon constraint requires. Defining 1 that there is still crowding out but at a lower rate: as the total itigation level in the outh, it is easy to show (10) d d d d d. Hence, the effect of a slight increase of the atching grant rate (fro say 10% to 11%) is a decrease in itigation expenditure in the outh of 1. In order to ake this 16 Note that this will not necessarily follow fro the optiization proble of the North, see ection Again, this ay not necessarily be an optial policy for the North. 13

15 coparable to the effect of the direct grant (which is easured in onetary ters), we have to divide by in equation (10). Therefore, the effect of a slight change in the atching grant is given by 1 1 1,0 grant case., showing that there is incoplete crowding out in the atching An incoplete crowding out iplies that ore is spent on itigation easures and eissions fall. As the eissions constraint is no longer binding, the shadow price of the constraint is zero and additional itigation is undertaken if arginal itigation costs are less than the arginal benefit, which is τ, i.e., the additional revenue the outh gets fro the atching grant. 18 However, unlike in the case of low-carbon developent assistance, the atching grant will not result in a welfare axiizing allocation of resources fro the perspective of the outh as it would allocate resources differently without the atching grant restriction. We suarize these findings in the following proposition: Proposition 2: The North can respond to the ipact that an eissions constraint in the outh has on the effectiveness of transfers by switching to a low-carbon for of developent assistance and / or by offering itigation assistance in the for of a atching grant. The forer would ensure that the twin objectives of output growth and eissions cuts are et siultaneously. The latter would encourage the outh to undertake additional itigation beyond what its eissions constraint requires. 4. Financial transfers and adaptation in the outh We now turn to the adaptation decision of the outh and explore how the adaptation in the outh depends on transfers fro the North. Fro the optiization specified in Annex 1, we find the following FOC: i ˆ a T D e y T 1 a 1 (11) 18 Note that there is an additional effect as the daage in period 1 is no longer given. However, for an individual country this effect will probably be negligible, see footnote 8. 14

16 The optial adaptation effort is found by equalizing the arginal benefits of adaption (the left hand side) and its arginal costs (the right hand side). The FOC deterines adaptation effort as an iplicit function of adaptation and developent transfers and the global eission cap, a i a T, T, e ˆ. To deterine the signs of the exogenous factors (that is, the ipacts of transfers and the eissions constraint on the adaptation level in the outh), we totally differentiate equation (11): (12) a 1 i 1 i i ˆ da dt D y T D y T de DdT 0 It follows straightforwardly that a i da D ˆ,, 0 eˆ deˆ D (13) a e T T A higher global cap on eissions will cause the outh to adapt ore as the arginal benefit to adaptation is higher. An interpretation of this is that a region would adapt less if a cliate agreeent is reached. Thus ore itigation would ean less adaptation as in our odel itigation and adaptation are substitutes. If follows also that T (14) a e T T a a i da ˆ,, 1. a dt That is, additional adaptation support copletely crowds out the outh s own adaptation effort the outh decreases its own adaptation effort by the sae aount. In the sae way as for itigation, additional adaptation support frees up resources that the outh prefers to use for consuption. The reason for this is seen fro the first order condition given by equation (11). Adaptation transfers do not address any exogenous constraints to adaptation but siply offer 15

17 additional adaptation resources. But since the benefit fro adaption is the sae before and after the transfer, it will be optial for the outh to aintain its original adaptation level. This is in line with the literature claiing that the benefits of adaptation are excludable, see, e.g., Buob and tephan (2013). As in the case of itigation transfers, the North could increase adaptation in the outh, and thus reduce daage in the outh, by using a atching grant for of support. As before this would lead to incoplete crowding out, but as it changes the allocation of resources, it would result in a welfare loss for the outh. This gives us the following proposition: Proposition 3: Adaptation capital transfer fro the North to outh will copletely crowd out adaptation investents in the outh, unless a atching grant support function is used, but this will not be a welfare axiizing allocation of resources for the outh. To study the effect of developent assistance on adaptation, it follows fro (12) that a i da D ˆ,, 0, i i 1 i 1 i T dt D y T y T (15) a e T T That is, productive capital support leads the outh to increase its adaptation effort. Intuitively, by increasing incoe in the outh, ore value is at risk in the region due to cliate change. 19 This gives an incentive to increase adaptation efforts. Note that this effect hinges on the assuption that daages are proportional to output, a standard assuption in econoic studies as entioned in ection 2. The result can be stated in a Proposition: Proposition 4: An increase in developent assistance will increase the adaptation level of the outh. 19 In addition, higher incoe ay lead to higher deand for cliate protection, but we do not odel this incoe effect. 16

18 As seen fro equations (6) and (15), increasing developent assistance has a positive ipact on both itigation and adaptation effort in the outh. This is in contrast to cliate finance, which does not alter overall adaptation and itigation levels. However, the result is due to the assuption that there are no barriers. There are no liits to the outh s ability to allocate resources between itigation, adaptation and consuption. We review this assuption in the next section. Institutional barriers in the North will be discussed further in ection Financial transfers when the outh is incoe-constrained Up to now, we have assued that the outh is sufficiently affluent that it can invest soe of its resources in adaptation or itigation. We now relax this assuption by requiring that consuption in the initial period should be at least equal to soe inial subsistence level c. This condition ay be binding for a least-developed country. The outh s optiization proble is now given by: (16) ax s.t. and ˆ, a U c c c c e e e Associating a Lagrange ultiplier to the inial consuption requireent and with the eission constraint as before, we can write the FOC for optial itigation (assuing an interior solution 20 ) as follows: (17) 0 1 i 1 y y T 0 The first ter denotes the arginal cost of a dollar invested in itigation in the first period: one unit of consuption forgone plus the shadow price of the subsistence requireent. The second ter easures the arginal return of that extra itigation investent which depends on the shadow value of the eissions constraint. The FOC for optial adaptation efforts is given by: 20 We can do this because we have assued that the arginal benefits of the first units of itigation- and adaptation investents are unbounded. 17

19 i 1 D y T 0 (18) 1 Now, the first ter stands for the arginal adaptation cost and the shadow price of the inial subsistence consuption level. The second ter stands for the arginal benefit, i.e., reduction in reaining cliate change daages. Copared to the unconstrained case (equation (4) for itigation and equation (11) for adaptation), we see that arginal cost of investent will be higher in the constrained case (given that the constraint is binding). Hence, the outh will itigate and adapt less if it is constrained in consuption in the initial period which is very intuitive. They would like to itigate and adapt ore but they cannot because otherwise they would starve to death. The coparative statics and derivations are shown in Annex 2. When both the eissions and consuption constraints are binding, we find exactly the sae results for itigation as in the unconstrained case discussed earlier. In particular, itigation support is copletely crowded out, adaptation support has no ipact on itigation efforts, productive capital support leads to higher itigation (in order to copensate for higher eissions), a ore lenient eission constraint iplies less itigation, and the inial consuption level (and hence a pure transfer of consuption) has no ipact on the itigation decision. The coparative statics for adaptation by the outh are, however, different fro the unconstrained case. First, extra itigation support leads to ore adaptation in the constrained case (reeber it did not affect adaptation in the unconstrained case). The transfer of itigation capital leads to coplete crowding out of itigation as the outh will lower its own effort by exactly the sae aount. However, this frees resources that can be invested in adaptation which was previously constrained. econdly, extra adaptation support has no ipact on the adaptation choice of the outh in the sense that the outh does not change its own adaptation investents. The reason is that the outh 18

20 was constrained in adaptation. Hence, the support alleviates the constraint and increases to total adaptation capital of the outh. Thirdly, productive capital support leads to higher second period eissions which have to be copensated by higher itigation if the eission constraint is binding. This iplies that resources should be drained away fro adaptation in order to satisfy the consuption constraint. Note that itigation investents have to be ade in the first period and, therefore, have to be at the expense of adaptation investents as the consuption constraint is binding. In the second period, production will increase, but that will only have an ipact on consuption as no investents are ade in the second period. Thus, in our odel, traditional developent assistance leads to lower adaptation investents in the poorest countries. Recall that this was different in the unconstrained case, in which the outh reacted with extra adaptation efforts when receiving developent assistance. Fourthly, a ore lenient global carbon constraint results in ore adaptation investent in the outh because the arginal benefit of adaptation increases. This effect is the sae as in the unconstrained case. A final result is that siply transferring consuption goods (i.e., relaxing the consuption constraint) would lead to higher adaptation. The additional consuption is used to direct ore resources to constrained adaptation investents. 21 Proposition 5: If the outh is very poor (i.e. constrained to subsistence consuption in the initial period), adaptation can be boosted by providing (1) targeted adaptation support, (2) itigation support, or (3) direct consuption transfers. All three routes are equally efficient at boosting adaptation. Productive capital support leads however to lower adaptation. 21 Thus, as opposed to the result in the ain odel in ection 2, a consuption transfer ay be optial in this case. 19

21 6. The financial transfer decisions of the North To coplete the solution to our leader-follower gae, we now turn to the proble of the North. First, note that the eissions constraint in the North given by equation (1) deterines the need for itigation in the North, i.e., the optial level of eissions follows directly fro the eissions constraint and is unaffected by the transfers to the outh. Next, to decide on its adaptation level and the transfers to the outh, the North wants to axiize its interteporal welfare function, given all restrictions fro ection 2 and subject to a i its adaptation level ( a N ) and transfers ( T, T, T ). The North takes the optial responses of the outh into account when deciding on the transfers, see also Buob and tephan (2013). That is, the North decides on transfers, and the outh responds to these transfers. The North has the inforation to calculate the responses of the outh. The optiization probles and the FOCs are given in Annex 1. The first order condition for adaptation transfers can be written as: a 1 1 a T 1 i (19) y T D eˆ This shows that the arginal cost of the transfer in the North, weighted with the equity weight (left hand side), should equal the benefit of increased consuption in the outh in the next period, also weighted with the equity weight (right hand side). But fro (14) we know that a T a 1 and the adaptation transfer copletely crowds out the outh s adaptation effort if there are no other constraints. In this case we see that (19) does not hold, and there is no interior solution. Thus, it will not be optial for the North to transfer adaptation capital to the outh Note that an adaptation transfer in this case would be equal to a pure consuption transfer. As discussed in footnote 13, a consuption transfer will not be optial with a linear utility function. However, with a concave utility function we would get an interior solution, and it would be optial with an adaptation transfer even if the adaptation level in the outh did not increase. The reason is that consuption in outh would increase and the inequality between the two sectors would be lower. This would increase the utility of the North as they express inequality aversion. 20

22 However, if there are constraints attached to the adaptation transfers, such that for every dollar used on adaptation in the outh, the North transfers τ a dollars (a atching grant), we know fro ection 3 that the crowding out is not coplete. Using a atching grant ay, therefore, give an interior solution of the optiization proble and a positive adaptation transfer fro the North to the outh will occur. The agnitude of this transfer is increasing with the equity weight put on the utility of the outh, and the transfer would be zero if the weight is set to zero. da If the outh is constrained in consuption (ection 5), we know that 0, see Annex 2. a dt Equation (19) now becoes: 1 i (20) 1 y T D eˆ Thus, as we do not have crowding out, it ay be optial for the North to transfer adaptation capital to the outh. We know fro ection 3 that there is full crowding out of itigation transfers to the outh. Using this in the first order condition for itigation transfers in Annex 1, we get the sae result as for adaptation transfers; there is no interior solution to itigation transfers and the optial level is equal to zero. The itigation transfer would just work as a consuption transfer, which is not optial with the linear utility function. This also holds if the outh is incoe-constrained. This gives us the following proposition: Proposition 6: Due to the coplete crowding out of adaptation and itigation in the outh fro adaptation and itigation transfers respectively, these would work as pure incoe transfers, which will not be optial with a linear utility function. However, if the outh is incoeconstrained, adaptation transfers would be optial for the North as they will increase the total adaptation capital in the outh. 21

23 The optial level of developent assistance follows fro its FOC in Annex 1: 23 a i i s T T 1 i a (21) 1 1 y T D eˆ 1 1 a T D eˆ Developent assistance has ipacts on the utility of the North via changes in the itigation and adaptation efforts in the outh, as well as the incoe increase in the outh as the region gets richer. Thus, there ay be an interior solution, eaning there ay exist an optial level of developent assistance. For the case where the outh is incoe-constrained, we ay still have an interior solution, but should note that the sign of a T i now turns fro positive to negative, which has an ipact on the size of the transfer. Whether, transfers increase or decrease is undeterined as adaptation in the outh has both a positive (reduces utility in the first period) and negative (increases utility in the second period) ipact on the interteporal utility of the poor region. 7. The decisions of the North when financial transfers are inefficient We next introduce an institutional barrier. In particular we study the case where international transfers are subject to leakage, that is, a fraction of transfers does not reach the intended beneficiary. With weak or corrupt institutions, which are prevalent in any developing countries, oney ay disappear along the road. In our odel, the efficiency of transfers can be odeled in different ways. For instance, the α- and σ-functions describe how adaptation easures and itigation easures are transferred into reduced daage and eissions respectively. Thus, these functions also describe the efficiency of these transforations. As an exaple, the α-function ay describe the costs of adaptation. 23 Note again that the transfer is only welfare iproving, i.e., there exists an interior solution, if the cost of the transfer in the North (reduced consuption) is less than the increased consuption in the outh that follows fro the transfer. 22

24 To odel how uch oney actually reaches the targets, we can introduce efficiency paraeters j 0 b 1, j a, i,. This eans that the North ay pay for ore than what reaches the outh. Thus, while the North s optiization proble is unchanged, these paraeters need to be incorporated in outh s optiization proble. The introduction of these efficiency paraeters only has a odest ipact on the qualitative conclusions. However, there will be less crowding out of adaptation and itigation capital if less oney reaches the outh, i.e., there is only crowding out of the actual transfer that reaches the target. The optial sizes of transfers will of course be affected by leakage. It is also worth exploring to what extent our conclusions hinge on the assuption that developent assistance is efficient. In our odel developent assistance has a positive effect on production in the outh; the growth potential of developent aid is not crowded out. oe studies suggest that aid does not necessary raise capital stocks in developing countries, and that the outcoe depends on doestic policies and institutions, see e.g., Dollar and Easterly (1999); Easterly and Pfutze (2008), but there are also ore optiistic views on the effects of developent aid (e.g. achs (2005); Banerjee and Duflo (2011)). Teple (2010) exaines the conditions under which foreign aid will be effective in raising growth. Based on the evidence, he finds that aid can be effective, and that a hypothesis that aid ay be harful does not have backing. Thus, while we have odeled the effect of aid in a siple way, we can conclude that as long as aid is given in a way that prootes growth (not coplete crowding out), the effect on itigation and adaptation effort in the developing countries will be positive in our ain odel. Another of our assuptions is ore crucial. In the ain odel with linear utility functions, it is not optial for the North to transfer itigation and adaptation capital as we have full crowding out and the transfers go to consuption. With concave utility functions, in contrast, the option for the North would be to increase outhern consuption by either transferring consuption goods directly, or transferring adaptation or itigation capital. The choice would depend on the transaction costs for each transfer, akin to the leaky bucket proble; i.e., the relative efficiency loss in distribution. As a consequence, transferring adaptation or itigation capital ay give 23

25 different effects on consuption and on who receives the consuption good than a direct transfer of the good itself. 8. Conclusions This paper discusses the interplay of different types of donor assistance to developing countries: developent assistance to boost output and incoe, itigation support to reduce greenhouse gas eissions, and adaptation support to increase resilience to cliate risks. We assue that the otivation for these transfers is derived solely fro the North s concern about well-being in the outh. Our odel does not include any strategic reasons for itigation and adaptation transfers, such as the need to secure a global agreeent on eissions, or concerns about international trade where countries specializing in an adaptation or itigation technology seek to expand their arket. The ain odel does not contain any arket distortions that are not internalized. In particular, there are no barriers (such as poor institutions) to effective adaptation, effective econoic anageent and the transfer of funds, and we assue a binding global eissions constraint to address the cliate change externality. We ay associate this situation with iddle incoe countries, which tend to have fairly advanced institutions. We find that under these assuptions isolated transfers aied solely at developent, itigation or adaptation are relatively inefficient: A large part of their intended effect (to increase incoe, reduce eissions, or boost cliate-resilience) dissipates as the outh reacts to the transfers by reallocating its own resources until it has established the itigation, adaptation and consuption balance that optiizes its welfare. In essence, cliate change finance works as a pure incoe transfer and any ipacts on itigation and adaptation are indirect, triggered by the softer budget constraint. The ain otivation for transfers in this context would have to be strategic, a topic not studied in this paper. If the North wishes to change the balance between itigation, adaptation and consuption in the outh it needs to structure its transfers as atching grants, which vary according to the outh s own level of funding. In our odel such conditional funding would not lead to a welfare 24