Climate change, strict Pareto improvements in welfare and multilateral financial transfers

Abstract

1. Introduction

The Paris agreement establishes the ‘principle of common but differentiated responsibility and respective capabilities, in the light of different national circumstances’ (Art. 2.2). This principle calls primarily for developed countries to take the lead by undertaking ‘economy-wide absolute emission reduction targets’ (Art. 4.4) but also the obligation to ‘provide financial resources to assist developing country Parties’ (Art. 9.1, emphasis added).¹ Following this principle, the COP27 summit recently agreed to the creation of a ‘loss and damage’ fund to support poorer countries that have been affected by climate impacts. The loss and damage funding, in its current form, moves away from the earlier discussions on climate funding, which focused more on cutting carbon dioxide emissions in an effort to curb global warning, and towards the funding to cover the cost of damage to which countries cannot avoid or adapt.

Though precise estimates are difficult to come by, Jacoby et al. (2008), for example, estimate that if developed countries were to fully compensate developing countries for the costs of mitigation then their welfare costs, if shared equally, will be around 2 per cent in 2020, rising to some 10 per cent in 2050, with the implied financial transfers² being over $400 billion per year in 2020 rising to around $3 trillion in 2050. A recent report produced by fifty-five countries estimated their combined climate-linked losses over the last two decades totalled US 525 billion, or 20 per cent of their collective GDP, Vulnerable Twenty Group (2022). The EU, as part of the European Green Deal [COM (2019) 640 final] action plan, has recently announced ‘The Just Transition Mechanism’ to address the social and economic effects of the transition to a carbon-neutral EU economy. The mechanism provides targeted support of at least 150 billion Euros over the period of 2021–7 in the regions most affected by this transition. Part of this financial support constitutes financial transfers with the sole purpose to compensate those that are most affected by the move towards the green economy. The Paris agreement does also promise that developed countries will provide climate finance of up to $100 billion a year to help developing countries reduce their emissions and adapt to climate change (UNFCCC, 2010).

Explicit in the policy discussion is that in a world economy in which there are trade and climate change externalities—the latter arising from inefficient carbon pricing—multilateral financial transfers (income) can deliver welfare gains to both ‘donor’ countries and ‘recipient’ ones. The objective of this article is precisely to elaborate on the conditions that are necessary and/or sufficient to hold for financial transfers to generate strict Pareto improvements in welfare across all countries when the global economy is constrained from setting carbon and trade tax instruments at their Pareto-efficient values. This is a deceptively simple question but, as the analysis will show, with an answer that is unsurprisingly not simple.³

To address the issue, use is made of a general equilibrium model of a trading world comprising many countries and goods in which production generates (carbon) emissions that result in global negative externalities on households. Within such framework, it is shown that international transfers of income⁴ can be used to generate a strict Pareto improvement in welfare, even though the policy instrument being used is different from the ones that are causing the distortion. This will be the case if and only if the income (utility) effects generated by the financial transfers lead to an appropriate change in the value of consumption in every country, evaluated at world shadow prices, which take into account the global externality created by carbon emissions and its general equilibrium impact on world prices and households.⁵ This is the issue the article elaborates on and illustrates it through numerical examples.

The analysis builds on mainly two strands of literature: one that has discussed trade and pollution reforms and one that has discussed the possibility of immiserizing transfers arising when a recipient becomes worse off when the donor gives them resources (the latter taking place in a framework within which distortions from emissions are assumed away or, indeed, not part of the framework). The first strand of literature includes theoretical contributions that have addressed the linkages between climate (environmental, more generally) and trade policies. Some of these studies have focused on non-cooperative policy formation, characterizing nationally optimal trade and environmental policies and the interplay between them. See, for instance, the studies by Markusen (1975), Copeland (1996), Panagariya et al. (2004), Copeland (2011), and Ishikawa and Kiyono (2006). Other studies have focused on desirable directions of reform—whether for small or large economies—when one policy instrument, environment or trade, is for some reason constrained away from its optimal level. See, for example, the studies by Copeland (1994), Hoel (1996), Turunen-Red and Woodland (2004), Neary (2006), Vlassis (2013), Kotsogiannis and Woodland (2013), Michael and Hatzipanayotou (2013), Keen and Kotsogiannis (2014) and, more recently, Tsakiris and Vlassis (2022).

Part of this latter literature has, in particular, characterized Pareto-efficient allocations in which potentially three sets of policy instruments may be deployed: international lump-sum transfers, carbon pricing, and trade tariffs,⁶ focusing attention on the implications of various constraints on these policy instruments for the setting of the other policy instruments to achieve constrained Pareto-efficient or Pareto-improving welfare outcomes. Implicit in these contributions is that adjustments in the instruments translate into Pareto-improving welfare without, however, delving into the conditions necessary for the outcomes. This article elaborates on this issue.

The analysis here also relates to a second strand of literature, namely the international trade literature that has analysed the transfer problem, as in Turunen-Red and Woodland (1988). They considered the age-old question of whether a transfer of income between two countries necessarily benefits the recipient at the expense of the donor.⁷ In a general equilibrium model with many countries, they showed that interesting paradoxes can occur and, in particular, that it may be possible for multilateral transfers of income to improve the welfare of every country in the world, provided that there are trade distortions in the initial equilibrium. The transfers thus exploit the trade tax distortions to generate strict Pareto improvements. Their model, however, did not (and did not need to) consider the possibility of distortions arising from environmental externalities and policy. This is an issue that is taken up in this contribution. The article also contributes to the strand of research that investigates design issues regarding environmental agreements (for a recent survey of the literature see Pouw, Weikard and Howarth, 2022). Not surprisingly, financial transfers do emerge as a key element in countries participating in environmental agreements.

The structure of this article is as follows. Section 2 sets out the model of a world economy comprising many countries and goods and embodying global carbon emission externalities. As a preliminary analysis, Section 3 examines the basic issues concerning the welfare effects of policy reform, while Section 4 provides a general characterization of the necessary and sufficient conditions required for strict Pareto-improving international income (untied) transfers to exist. Section 5 then characterizes conditions required for international lump sum transfers not to exist. Section 6 provides a numerical example that further illustrates the mechanism at work. Finally, Section 7 provides some brief concluding remarks.

2. The structure of the model

The model is based upon those of Turunen-Red and Woodland (2004) and Keen and Kotsogiannis (2014). It is a standard perfectly competitive general equilibrium model of international trade in which there are J countries, indexed by the superscript j, that trade in N commodities the production of which generates pollution. While the model is general enough to allow the production of each commodity to generate pollution, this is not necessary. It may be that some commodities are ‘dirty’ in the sense of generating pollution, while other are ‘clean’ and do not generate pollution in their production.⁸

The N-vector of international commodity prices is denoted by p. International trade is subject to trade taxes (or subsidies), the vector of which is denoted in country j by $τj$⁠. If $τij>0$ (⁠$τij<0$⁠) and commodity i is being imported by country j, then $τij$ is an import tariff (import subsidy), and if $τij>0$ (⁠$τij<0$⁠) and commodity i is being exported by country j, then $τij$ is an export subsidy (export tax). The domestic commodity price vector in country j is thus given by the N-vector $pj=p + τj$⁠.⁹ We perform a conventional normalization of the price vector by fixing the world price of commodity 1 (the numeraire good) to unity, and assume without loss of generality that the numeraire good is freely traded. These normalization assumptions imply that $τ1j=0$ and $p1j=1,$  $j=1,…,J,$ and thus that the world price vector may be expressed as $p⊺=(1,q⊺)$ where $q⊺=(p2,…,pN)$ and the superscript $⊺$ indicates transposition. As is well known, neither normalization is of any substantive consequence, since they simply reflect the homogeneity properties of the price system.

Pollution discharges in country j are subject to pollution taxes, given by the N-vector $tj$⁠. Such pollution taxes are, in general, permitted to be sector (product)-specific.

That is, the vector of net outputs is obtained as the derivative of the revenue function with respect to the price vector, while the derivative with respect to the carbon tax vector yields the negative of the emission vector.

Equation (9) is the national budget constraint in every country j, stating that the value (at world prices) of net exports (the trade balance) must be equal to variable $bj$⁠. In the current atemporal context, without saving or borrowing from abroad, all countries would need to have zero trade balances, with $bj=0$⁠, $j=1,…,J$⁠. However, in this current article, we focus on international transfers of income as a policy instrument and, hence, allow for the possibility of transfers of income from one country to another. A country j can transfer income abroad if and only if its income from production exceeds the cost of its consumption at world prices, meaning that $bj>0$⁠. Accordingly, we reinterpret the trade balance $bj$ as a net financial/income transfer from country j. If $bj=0$⁠, then country j has a zero net transfer abroad, while $bj$ different from zero implies a financial/income transfer to, or from, country j to the rest of the world.¹⁹ When $bj>0$⁠, country j makes an income transfer to the rest of the world; when $bj<0$⁠, country j receives an income transfer from the rest of the world. Since world trade must balance in value, it follows that world net transfers must balance in value, implying that Equation (11) must hold.

The N equations in (10) are the world market equilibrium conditions for tradeable commodities, stating that the world excess supplies for these goods must be zero. Equation (12) indicates how aggregate world pollution depends on the national vectors of pollution, which depend on domestic prices for products and carbon taxes.

Given the tariff vectors $τj$⁠, $j=1,…,J$⁠, the carbon tax vectors $tj$⁠, $j=1,…,J$⁠, and the vector of multilateral financial transfers $b=(b1,…,bJ)⊺$ satisfying (11), the market equilibrium conditions (10), the national budget constraints (9) and the world pollution Equation (12) determine the competitive equilibrium world price N-vector for tradeable commodities, p, the world pollution level, Z, and the vector of country utilities $u=(u1,….,uJ)⊺$⁠.²⁰

3. Preliminary analysis

The left-hand side of this expression gives the change in the level of utility for country j multiplied by the term $p⊺Epuj=∑i=1NpjEiuj$⁠, that is, a summation of the world price weighted income effects on the consumption of the N goods. The standard normality assumption is that each such income effect is positive, meaning that an increase in income (utility) at unchanged prices will increase the consumption of each good. The Hatta (1977) normality definition, used extensively in the literature on international trade, is that the income (utility) effects lead to an increase in consumption evaluated at world prices, namely that $p⊺Epuj>0$⁠.²²

The right-hand side of Equation (13) shows that utility in country j is affected by an income transfer, $bj$⁠, a change in world prices, p, and a change in global emissions, Z. More specifically, the first effect, given by $−dbj$⁠, is the direct effect on utility in country j of an income transfer received by country j. Since $p⊺Epuj>0$⁠, assumed positive under the Hatta normality condition, a reduction in the transfer $bj$ to the rest of the world (or an increase in the transfer received by j) confers a utility gain to this country. The second effect, given by $Spj⊺dp$⁠, is the familiar terms-of-trade effect: if a change in international prices increases the terms-of-trade (⁠$Spj⊺dp>0$⁠) for country j, then its welfare increases under the assumed Hatta normality condition. The third effect, given by $−(τj⊺Sppj+tj⊺Gtpj)dp$⁠, gives the change in trade and carbon tax revenues—respectively, $−τj⊺Sppjdp$ and $−tj⊺Gtpjdp$—as the international price N-vector p changes, keeping utility, transfers and global emissions constant. If tariff/tax revenue increases as a result of the price change, then welfare increases. The final term, given by $−p⊺EpZjdZ$⁠, indicates that utility is reduced by an increase in global emissions if $p⊺EpZj>0$⁠, meaning that an increase in global emissions requires the consumer in j to increase the value, at world prices, of consumption to maintain the given level of utility. Overall, under the assumption of Hatta normality that $p⊺Epuj>0$⁠, a welfare gain requires world prices and global emissions to change in response to the change in the income transfer to make the right-hand side of Equation (13) is positive.

The negative of the term within the square brackets in (16) gives the change in import tariff and carbon tax revenues arising from a change in world prices at unchanged utility, taking into account the impact of this change upon global emissions and the impact of this upon trade tariff and carbon tax revenue. The term $Sppj+SpZjκp⊺$ is the pollution-augmented net substitution matrix in country j, which gives the responses in the net exports to changes in the terms of trade, when consumer compensated demands respond to the endogenous change in global pollution emissions; multiplication by $−τj⊺$ yields the effect on import tariff revenues. The term $Gtpj$ gives the pollution emissions response in country j due to a change in its terms of trade; multiplication by $−tj⊺$ gives the effect on carbon tax revenue. The final term on the right-hand side of (16) provides the additional expenditure on goods required to maintain utility following the effect of the change in world prices on global emissions; an increase in global emissions arising from the price change will reduce utility since $EZ>0$ by assumption.

Equation (16) is at the heart of the analysis that follows as it identifies all welfare effects that are associated with the transfers and their summation that determine total welfare. What this suggests is that, at least in principle, a multilateral financial transfer of income across countries (even in the absence of trade distortions) could reduce the welfare of every country. However, while noting this possibility, we are interested in the possibility that an income transfer increases the welfare levels of every country—a strict Pareto improvement in welfare.

Clearly, (17) shows that if $p⊺Epuj>0,$ for every country $j=1,…,J,$ then a necessary condition for a strict Pareto improvement is for the right-hand side of (17) to be positive. The first term on the right-hand side is the increase in compensated (keeping utility constant) global tariff and carbon tax revenue arising from the world price change following the multilateral income transfer. The second term on the right-hand side is the global effect on households’ expenditures needed to compensate for the change in global emissions $κp⊺dp$⁠.

It is instructive for the interpretation of (17) to consider two special cases. First, in the absence of any global emissions effect (the second term vanishes), (17) implies that for global welfare to increase it is necessary that the world price vector alters so that the compensated world tariff and carbon tax revenue increases (the first term is positive). If, in addition, all tariffs and carbon taxes are zero in the initial equilibrium, the first term on the right-hand side of (17) is zero making the whole right-hand side zero. In this case, the tax revenue channel for a global welfare improvement disappears. Secondly, in the absence of any global tax revenue effect (the first term vanishes), (17) implies that for global welfare to increase it is necessary that the world price vector alters so that global emissions fall (⁠$dZ=κp⊺dp<0$⁠) under the assumption that $∑j=1JEZj>0$ (greater emission require more global expenditure to maintain utility levels). Again, if global emissions do not alter, or the effect on global expenditures is zero, the second term vanishes and so the global emission reduction channel for a global welfare gain disappears.

If the right-hand side of (17) is zero—which would be the case if all countries trade freely and levy zero carbon taxes and there was no effect on global emissions—then a necessary (but not sufficient) condition for a strict Pareto improvement reform (⁠$duj>0, j=1,2,…,J$⁠) is that not all income effects on consumption (evaluated at world prices) $p⊺Epuj,$  $j=1,…,J,$ terms be of the same sign. The implication of this is that some commodities must be inferior in some countries but normal in others.

In summary, the above discussion has highlighted several channels through with strict Pareto improvements in welfare may arise from a multilateral transfer of income. Distortions created by trade taxes²⁴ or carbon taxes may be partially corrected via the changes in world prices so that global tariff revenue or carbon tax revenue increases. But, the discussion has also highlighted that the world price adjustments may reduce global emissions. The importance of expression (17) is in showing that at least one of these channels is necessary for a welfare improvement.

Attention is now turned to the formal characterization of necessary and sufficient conditions under which there exits a multilateral transfer of income that will raise the welfare in every country.

4. Existence of strict Pareto-improving multilateral transfers

The analysis proceeds by characterizing the conditions under which there exists a multilateral transfer of income such that there is a Pareto improvement in welfare, assuming that all tariff and carbon tax rates are given but taking into account the general equilibrium impacts of the income transfer upon world prices, world pollution, and national utility levels. Formally, the analysis proceeds by using Motzkin’s Theorem of the Alternative (Mangasarian, 1969, p.34) to characterize the necessary and sufficient conditions under which a Pareto improvement exists when multilateral transfers may be endogenously chosen.²⁵

We now proceed to establish conditions under which there exists a multilateral transfer of income that will raise the level of welfare in every country j. A strict differential Pareto-improving multilateral income transfer is defined as a transfer, db, such that $(du,dp,db,dZ)$ solves the differential system (19) with $du≫0$⁠. That is, the income transfer, along with the general equilibrium changes in world prices and global emissions, yields an increase in the utility level for every country (du is strictly positive). We follow conventional practice by ignoring the market equilibrium condition for the numeraire commodity, following Walras’ Law. Equipped with this, and our world price and trade tax normalizations (⁠$p1=1,τ1j=0$⁠), we arrive at the following result (all proofs are relegated to the Supplementary Appendix A). 

Proposition 1 involves the variable $y3$⁠, which can be thought of as the implicit social marginal value of income, evaluated at the Pareto-efficient allocation being characterized, common across countries.³⁰ It also involves the quantity $β˜j$ which, as noted above, and further explored shortly below, relates to the Hatta (1977) normality condition.³¹ It is evident from the inequalities in (31) that if all $β˜j$ have the same sign—either positive or negative—then a $y3∈R$ that solves (31) does exist. In these cases, there are no multilateral income transfers that can generate strict Pareto improvements in welfare.

On the other hand, strict Pareto-improving multilateral income transfers exist when there does not exist a scalar $y3$ (a common value for the social marginal value of income) that solves (31). This case occurs when at least two countries have non-zero $β˜j,$  $j=1,…J,$ terms that differ in sign. What this implies in practice is that the existence of strict Pareto-improving multilateral income transfers has been narrowed down to the sign structure of easily recognizable quantities defined by the country-specific scalars $β˜j,$  $j=1,…J,$ in (30). This result may be formalized as in the following corollary to Proposition 1. 

We call $β˜j≡p˜⊺Spuj<0$in (33) the Generalized Hatta Normality Emissions Condition (GHNEC) for country j. Close inspection of (36) reveals that under GHNEC the income effects on net exports are weighted by a ‘world shadow price vector’, $p˜$⁠, which accounts for the general equilibrium impacts of product prices on emissions and their subsequent effect on prices. These indirect general equilibrium effects operate through matrix $κp$⁠, which indicates how price changes affect pollution, and $SpZ$⁠, which gives the subsequent effect of the change in pollution on net exports.

Several interpretations follow from this expression. First, the inequalities provide expressions for our generalized Hatta normality term using the world shadow price vector $p˜$⁠, which embodies the distortions caused by the global pollution externality, to evaluate the income effects on demands in the two countries. These must be of opposite sign to achieve a strict Pareto improvement in welfare from an income transfer. This difference in sign is the source of the gain from a transfer. Secondly, the inequalities have an instructive geometric interpretation. What the inequalities in (38) state is that the global shadow price vector $p˜$ and the income effect vector $Epuk$ are at an acute angle (and so $p˜⊺Epuk>0$⁠), while $p˜$ and the income effect vector $Epuj$ are at an obtuse angle (in the sense of $p˜⊺Epuj<0$⁠). This means that the global shadow price vector is ‘close’ to the income effect vector (the income consumption ray) for country k, but ‘much further away’ from the income effect vector for country j.³³ The term ‘close’ is used here to mean that the two vectors point in the same direction with the angle between them being less than 90 degrees. By contrast, the requirement $p˜⊺Epuj<0$ means that the angle between the two vectors is obtuse, so that the angle is greater than 90 degrees, hence the term ‘further away’. The two consumption ray vectors $Epuj$ and $Epuk$ can be ‘close’ so the angle between them can be less than 90 degrees, but they cannot be the same. Thirdly, and following on from the second point, from an economics viewpoint the existence of a strict Pareto improvement requires ‘sufficient’ diversity. There must be some diversity³⁴ between the two countries’ income effect vectors, $Epuj$ and $Epuk$⁠. Also, there must be diversity between these two vectors and the global shadow price vector, $p˜$⁠, which incorporates the production of pollution and its evaluation by countries’ consumers. In short, differences in preferences and the nature of the externality distortions are important for the existence of a strict Pareto-improving multilateral transfer of income.³⁵

We turn now to the identification of conditions for the non-existence of strict Pareto-improving reforms.

5. Non-existence of strict Pareto-improving multilateral income transfers

For this case, we arrive at the following result. 

Proposition 2 re-confirms a result in Turunen-Red and Woodland (1988) in the present context: in the absence of pollution effects on compensated demands and if all goods are normal in all countries and there is sufficient substitutability in the world substitution matrix then income transfers across all countries do not generate a strict Pareto improvement. Substitutability allows for prices to be solved uniquely whereas the existence of normality in every country implies that the transfers will be welfare worsening for the ‘donor’.

A second special case goes in a quite different direction. Suppose now, going to the opposite extreme to the circumstances of Proposition 2, that production and consumption, on the aggregate, are unresponsive to international prices, leaving only the impact of prices on emissions. In this case, we have the following result. 

To give an example, suppose that the price of air-conditioning equipment increases (good l) and as a consequence more of this product is being supplied. Assume further that, as a result, pollution intensity (on the aggregate) increases (⁠$∂κ∂pl>0$⁠). If this increase in global emissions induces consumers to decrease aggregate compensated demand for goods other than air-conditioners (⁠$∂Epi∂Z<0$⁠), then $dEpidpl<0$ implying net-substitutability. What Proposition 3 requires is that compensated demand for goods other than air-conditioners (good i)—either for each country j or for the aggregate—decreases.³⁸

6. An illustrative example

This section presents a two-country, two-tradeable-goods illustrative example to demonstrate the multilateral income transfer mechanism at work in creating a strict Pareto improvement in welfare when carbon taxes are not set at their Pareto optimal levels. Supplementary Appendix C extends this example to three-countries and three-tradeable-goods following a more general specification of production and consumption.

Consider a world comprising two countries, producing two products under conditions of free trade and with zero carbon taxes that are clearly not Pareto optimal. One product is clean, while the other is dirty in the sense that its production generates carbon emissions that adversely affect the climate. Consumers have preferences that are, in turn, adversely affected by the level of global emissions. In this context, the numerical example demonstrates that both countries can benefit in welfare from an income transfer from one country to the other.