metadata: authors: 0: author: Wang,Dieter
1: author: O'Reilly Gurhy,Bryan
2: author: Hanusch,Marek
3: author: Kollenda,Philipp
count: Brazil
docna: 0: docna: Could Sustainability-Linked Bonds
            Incentivize Lower Deforestation in Brazil’s Legal Amazon ?
docty: Policy Research Working Paper
abstracts: cdata!: This paper proposes a new relative
            evaluation and benchmarking framework for performance linked
            financing instruments. It argues that the carrots and sticks
            of sustainability-linked bonds should not use key
            performance indicators which are solely tied to outcomes.
            Instead, they should be based on its issuer&#x2019;s
            level of performance with respect to a target. The paper
            defines performance as the part of the outcome that the
            issuer can influence. Otherwise, the issuer may be rewarded
            or penalized for factors outside their control. In such a
            case, principal-agent theory would predict a dilution of the
            performance-based instrument&#x2019;s incentives. This
            framework is then applied to deforestation in
            Brazil&#x2019;s Legal Amazon and estimate performance by
            accounting for the real effective exchange rate, global
            commodity prices, and prevalent deforestation trends. The
            results show that policy efforts helped lower deforestation
            in the 2000s, even after accounting for external factors.
            The trend reversal and acceleration in deforestation since
            2012 are partly due to weaker policy and macroeconomic
            factors. Based on these results, the paper proposes an
            Amazon sustainability-linked bond, which could allow for a
            more effective mechanism to incentivize policy efforts. The
            paper also introduces the feasibility and ambitiousness
            matrix to set sustainability performance targets. The matrix
            is used to define the terms low-hanging fruits and long
            shots and to discuss why such targets are subject to the
            risk of greenwashing.
display_title: Could Sustainability-Linked Bonds
            Incentivize Lower Deforestation in Brazil’s Legal Amazon ?
listing_relative_url: /research/2023/09/34155746/sustainability-linked-bonds-incentivize-lower-deforestation-brazil’s-legal-amazon
topicv3: Deforestation m1503714 3386,Sustainable Development Goals m1504460 3134
publishtoextweb_dt: 2023-09-04T00:00:00Z
dois: 10.1596/1813-9450-10558
origu: Off of Sr VP Dev Econ/Chief Econ (DECVP)
author_keys: 0: author_key: 1624437
1: author_key: 1804310
2: author_key: 1045860
3: author_key: 2230471
model_extractions: Policy Research Working Paper 10558 Could Sustainability-Linked Bonds Incentivize Lower Deforestation in Brazil’s Legal Amazon?

_Dieter Wang Bryan Gurhy Marek Hanusch Philipp Kollenda_ Macroeconomics, Trade and Investment Global Practice & Finance, Competitiveness and Innovation Global Practice September 2023
Policy Research Working Paper 10558

# **Abstract**

This paper proposes a new relative evaluation and benchmarking framework for performance linked financing instruments. It argues that the carrots and sticks of sustainability-linked bonds should not use key performance indicators which are solely tied to outcomes. Instead, they should be based on its issuer’s level of _performance_ with respect to a target. The paper defines performance as the part of the outcome that the issuer can influence. Otherwise, the issuer may be rewarded or penalized for factors outside their control. In such a case, principal-agent theory would predict a dilution of the performance-based instrument’s incentives. This framework is then applied to deforestation in Brazil’s Legal Amazon and estimate performance by accounting for the real effective exchange rate, global commodity prices, and prevalent deforestation trends. The results show that policy efforts helped lower deforestation in the 2000s, even after accounting for external factors. The trend reversal and acceleration in deforestation since 2012 are partly due to weaker policy and macroeconomic factors. Based on these results, the paper proposes an Amazon sustainability-linked bond, which could allow for a more effective mechanism to incentivize policy efforts. The paper also introduces the feasibility and ambitiousness matrix to set sustainability performance targets. The matrix is used to define the terms _low-hanging fruits_ and _long shots_ and to discuss why such targets are subject to the risk of greenwashing.

This paper is a product of the Macroeconomics, Trade and Investment Global Practice and the Finance, Competitiveness and Innovation Global Practice. It is part of a larger effort by the World Bank to provide open access to its research and make a contribution to development policy discussions around the world. Policy Research Working Papers are also posted on the Web at http://www.worldbank.org/prwp. The authors may be contacted at dwang5@worldbank.org.

_The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent._ Produced by the Research Support Team
# Could Sustainability-Linked Bonds Incentivize Lower Deforestation in Brazil’s Legal Amazon?

Dieter Wang<sup>*1</sup> , Bryan Gurhy<sup>1</sup> , Marek Hanusch<sup>1</sup> , and Philipp Kollenda<sup>1</sup>

> 1World Bank Group

**JEL codes** : G23, H63, Q23, Q56.

**Keywords** : Sustainability-linked bonds, performance-based finacing, benchmarking, Amazon deforestation, feasibility and ambitiousness.

**Executive summary** : English, Portuguese.

> * Corresponding author. E-mail: dwang5@worldbank.org.

> This paper is a further refined version of a technical background paper for (Hanusch, 2023) "A Balancing Act for Brazil’s Amazonian States: An Economic Memorandum". The authors are grateful for insightful comments provided by André Rodrigues de Aquino, Steen Byskov, Rodrigo Silveira Veiga Cabral, Doerte Doemeland, Jose Antonio Gragani, Farah Hussain, David James Kaczan, Werner Kornexl, Paul Jonathan Martin, Habib Rab, James Seward, Anderson Caputo Silva, Daniel Navia Simón, Fiona Stewart, Claudia Tufani, Carla Cristina Solis Uehara, Niraj Verma, Paolo Verme, Thales Pupo West. We also thank the participants of the “Measuring Development 2023” conference for their feedback.
# **1 Introduction**

With sustainability becoming mainstream in financial markets, some investors are increasingly keen to align traditional investment goals with those of responsible or impact investing. Since the European Investment Bank issued the first green bond in 2007, the World Bank in 2008, and the International Finance Corporation in 2013, the green, social, sustainable bonds (GSSB) market has grown exponentially. With GSSBs, also called use-of-proceeds bonds, the proceeds are earmarked to fund predefined projects. However, these instruments face criticism from both issuers and investors, including concerns about “greenwashing” when targets are set too low, the rigidity of the use-of-proceeds model (especially for sovereign issuers), and the lack of measurable additionality. In this environment, issuers and investors are considering alternative mechanisms that tie financing to impact on the ground. A key question is how the investment’s impact should be measured, which is particularly challenging at the sovereign level.

Sustainability-linked bonds (SLBs)1 have emerged as promising instruments to meet this demand (Flugge et al., 2021; Lindner et al., 2023). The instrument is already well established in the corporate market, with US$225 billion SLBs outstanding as of March 2023. The experience of SLBs in the corporate debt asset class provides a motivation to start with high standards for the public sector, given the potential of these instruments to induce changes in public policy (Silva et al., 2023; SSDH, 2023). While market standards for sovereign SLBs (in terms of structure) have not been established, two successful issuances of sovereign SLBs exist as of the time of writing. Chile issued an SLB in March 2022 with a step-up coupon structure linked to greenhouse gas emissions targets and non-conventional renewable energy generation (Ministry of Finance of Chile, 2022). Chile’s structure, with a coupon step-up of 25 basis points, has been the standard in corporate markets (Lindner et al., 2023). However, in October 2022 Uruguay issued an SLB with both a step-up and step-down coupon structure (Ministry of Economy and Finance of Uruguay, 2022). Which payoff structures will become standard in sovereign SLB issuances remains to be seen.

**The case for sustainability-linked bonds** A key difference between SLBs and labeled bonds is that the proceeds of SLBs are not earmarked. Instead, their proceeds can be accounted for like conventional bonds and added to the general government budget. The main stipulation is that the SLB’s coupons are linked to a key performance indicator (KPI), which tracks the issuer’s progress towards a sustainability performance target (SPT). The issuer is incentivized to perform2 through financial carrots and sticks: missing the target leads to an interest rate penalty (step-up), while achieving the target leads to an interest rate reward (step-down).3

The less restrictive use of proceeds gives SLBs distinct advantages over labeled bonds. First, the issuer can use the proceeds to fund policies and programs that are not directly linked to an SPT but may benefit it indirectly (Lindner et al., 2023). For instance, a labeled bond intended to curb deforestation in the Amazon may have its proceeds earmarked to support local law enforcement. In contrast, the proceeds of an SLB could be used partly to enhance forest governance and partly to boost productivity, which will foster economic development and shift the economy away from resource extraction, including deforestation, in the longer run (Hanusch, 2023; World Bank

> 1In this paper we focus on sustainability-linked bonds but the same insights hold for sustainability-linked loans.

> 2We use the term perform to describe efforts the issuer undertakes to reach the SPT. These can include passing necessary legislation, enforcing existing regulations, investing in structural reforms or diversifying the economy.

> 3Step-ups and step-downs refer to the practice of increasing or lowering coupon payments of bonds. A step-down means that the debtor pays a lower interest rate, which serves as an incentive to achieve the SPT. Conversely, a step-up would entail higher interest payments. SLBs could be issued with either or both incentive structures, depending on the case.

2
Group, 2023). Such performance-based financing can both be effective in setting incentives and an attractive addition to governments’ fiscal instruments. Second, the possibility to scale the labeled bond market depends on the number of eligible projects. This is not the case for SLBs, which gives them more scalability and also the ability to mobilize more private capital.

The financial incentives in the SLB structure assure that issuers have “skin-in-the-game” as achieving the SPT is in their financial interest. This gives SLBs a third powerful advantage: they allow issuers to adapt and explore policy measures during the SLB’s lifetime. From the point of view of economic theory, the SLB structure is an elegant solution to the problem of incomplete contracts. Since it is impossible to completely specify how the issuer should act in all future scenarios to reach the targets, theory suggests that targets can also be achieved if the decision power is delegated to the issuer, as long as the issuer’s incentives are aligned with the target. This decision delegation ensures that issuers will react to a changing environment and adapt policies to achieve the SPT, without having to stipulate how the funds should be used ex-ante.

**Choosing the appropriate KPI** The effectiveness of an SLB in incentivizing issuer performance rests upon the choice of KPIs. We differentiate between _outcome_ KPIs, where performance is measured only using the outcome indicator of interest, and _benchmarked_ KPIs, where performance is assessed relative to a benchmark model. The idea behind a benchmark is to decompose an observed outcome into a performance part, which can be attributed to the issuer’s actions, and an exogenous part that is not in the issuer’s control. In Section 4, for example, lower deforestation may be due to effective government policies, e.g. designating protected areas, or the consequence of exogenous factors that render deforestation unprofitable, e.g. lower global commodity prices or unfavorable effective exchange rates (Arcand et al., 2008; Carvalho et al., 2019; Hanusch, 2023), or both. The benchmark level of deforestation reflects the expected amount of forest loss if the issuer would not undertake any additional efforts to avoid deforestation (see Figure 5).

In Section 2, we introduce the Relative Evaluation And benCHmarking (REACH) framework. We discuss the three requirements (R1)-(R3) that benchmarks ideally satisfy in order to facilitate both goals: setting strong performance incentives for the issuer and obtaining evidence-based additionality metrics for the investor. We further explain why all three requirements are necessary in the context of the _informativeness principle_ (Holmström, 2016).

An SLB whose KPIs are assessed relative to a benchmark will also have sustainable performance targets that are defined in relative terms. We acknowledge that giving up absolute targets in favor of relative targets may lead to some level of unease as absolute SPTs are simple and easy to understand. However, they dilute performance incentives and hamper impact evaluation, which in turn weakens the SLB’s effectiveness and signaling effect. Moreover, absolute targets pose practical challenges. Suppose we target zero deforestation by 2030. How ambitious or feasible is this target? To answer this question, one would need deforestation predictions until 2030 under the business-as-usual scenario. Since deforestation is path-dependent and influenced by natural and economic factors with feedback effects, this exercise is far from trivial. This does not mean that absolute targets are irrelevant and as we will demonstrate in Section 5 they can for example be used to evaluate near-term targets.

Using a benchmark model to deduce performance may not be common in sustainability finance, but the concept is widely used in other areas of finance. Our proposed way of benchmarking performance finds conceptual similarities in factor attribution and empirical asset pricing. For example, the financial performance of investment funds is not assessed in absolute terms. Instead, actively managed funds or passive index funds are evaluated with respect to a benchmark index 3
## **Figure 1: The components of the REACH framework**

The framework defines key performance indicators (dark green bars) as the difference between the observed outcome (black, solid line) and the benchmark outcome (blue, dashed line). The difference is zero if the issuer did not perform and generated no additional impact. In this example, the issuer performed consistently (except for period 4) and reaches the benchmarked SPT after five periods.

<!-- Start of picture text --> Component Example<br>Benchmark outcome Expected deforestation<br>Observed outcome Observed deforestation<br>= outcome KPI<br>Benchmark – observed Avoided deforestation<br>= benchmarked KPI<br>Sustainability performance Forest preservation goal<br>target (SPT) over five years<br>Note: The benchmark outcome is a counterfactual and<br>is not observed. It needs to be estimated by a<br>statistical benchmark model.<br>0 1 2 3 4 5<br><!-- End of picture text --> Source: Authors.

(e.g. the “market portfolio” in the capital asset pricing model), such as the S&P500 or the MSCI World Index in the equity space. Good performance then means over-performing the benchmark (generating “alpha”), which is very similar to our benchmarking approach. However, while portfolio managers are concerned with risk-adjusted returns, we are interested in additionality and measurable impact.

The remainder of this paper is structured as follows. Section 2 introduces the REACH framework and gives examples for each of its components. It stipulates the three requirements for the benchmarking approach. Section 3 lays the theoretical foundation and formalizes the rationale behind paying for performance instead of outcomes. Section 4 shows an application of the REACH framework to Brazil’s Legal Amazon. Section 5 introduces the feasibility and ambitiousness matrix (FAB) and illustrates how to identify ambitious but feasible targets to curb deforestation. Section 6 discusses how the REACH framework and FAB matrix can be used for other instruments and support the development of SLBs in general.

# **2 The REACH framework**

The REACH framework consists of five components, as shown in Figure 1: (1) observed outcome, (2) benchmark outcome, (3) benchmark model, (4) benchmarked KPIs, and (5) benchmarked SPTs. This framework is consistent with the International Capital Markets Association (ICMA) guidelines for SLBs and can be seen as a special case of it, where benchmarking takes up a much more central role. In this section, we describe each component and provide examples in the 4. context of deforestation, which sets the stage for the subsequent application in Section

## **2.1 Observed outcome**

The observed outcomes are indicators, variables, or measurements that constitute the basic building blocks of the framework. These indicators are objective measures of the sustainability issue 4
of interest. They are usually collected by national statistical offices, government ministries, universities, international organizations or private corporations. Observed outcomes need to meet minimum data quality standards such as sufficient coverage, availability of historical data, accessibility to the wider public and transparency about their methodology.

**Example** Annual primary forest loss in km<sup>2</sup> .

# **2.2 Benchmark outcome**

The benchmark outcomes represent what outcome we would expect without policy intervention in the absence of the SLB issuance. However, the benchmark outcome is not observed because we only observe the outcome with policy intervention. Therefore, this _counterfactual_ outcome has to be estimated using a statistical model, possibly incorporating data from other countries or other indicators. An appropriate, interpretable, robust and transparent benchmark model is essential for the credibility and effectiveness of the REACH framework.

**Example** Expected annual primary forest loss in km<sup>2</sup> , controlling for existing policy, earlier deforestation, previous exchange rates and commodity prices.

# **2.3 Benchmark model**

To produce a credible counterfactual, the benchmark model needs to provide clear and convincing reasoning why its results can be used for performance evaluation.4 We suggest that benchmark models should fulfill the following three requirements:

- (R1) **Transparent benchmark model.** The benchmark model should articulate which factors it considers as being in the issuer’s control and which it considers exogenous. This clarifies immediately how the SLB defines performance towards the SPT. A transparent model specification is also beneficial for communication and instrument pricing and allows the desired level of performance to be specified by choosing the cutoffs and/or step sizes (see Table 1) given historical performance.

- (R2) **Benchmark probability distribution.** The estimated benchmark outcome should be accompanied by a probability distribution around the preferred estimate to understand the likelihood of alternative outcomes. This is necessary to clarify whether the measured performance is due to chance or constitutes actual performance beyond a reasonable statistical doubt. It is worth emphasizing that the benchmark distribution is not merely a tool for performance evaluation. A good understanding of uncertainty around the performance measure is also necessary for accurately setting performance incentives (see Section 3).

- (R3) **Justification for additionality.** The benchmark model needs to be supported by a rigorous, evidence-based justification for why it can be used to measure performance and additionality. Ideally, these claims are supported by historical evaluations and back-testing results. Two possible justifications for additionality can be derived from the _informativeness principle_ (see Section 3.4): first, using the _controllability principle_ which stipulates that incentives should only depend on influenceable factors, and second, through _relative performance evaluation_ , where the performance can be gauged through the behavior of relevant peers.

> 4Antle et al. (1988) define performance evaluation in their model as being about “producing information relevant to the question of whether the desired behavior was supplied”.

5
**Example** The benchmark model in Section 4 recognizes the fact that deforestation is not only determined by the government’s policy efforts but also by factors outside the government’s control. This provides a justification via the controllability principle, satisfying (R3). The econometric model (7) articulates which and how external factors are incorporated in the counterfactual benchmark calculation, which satisfies (R1). Finally, Figure 6 demonstrates how the model can produce a benchmark distribution, as required by (R2).

# **2.4 Key performance indicator**

KPIs in REACH serve a more fundamental purpose than only tracking the issuer’s progress towards the SPT. They also measure impact and additionality with a claim to causality (see Section 3.5). More importantly, a well-chosen KPI sets strong incentives for the issuer to act. In Section 3 we will explain why KPIs that only depend on the observed outcome (what we call _outcome KPIs_ ) may not set the strongest incentives for the issuer to perform.

## outcome KPI = observed outcome

Instead, the REACH framework advocates for benchmark model-based KPIs, or simply _benchmarked KPIs_ , which are defined as the difference between the observed outcome and the estimated benchmark outcome.

## benchmarked KPI = observed outcome − benchmark outcome

Consequently, benchmarked KPIs have a natural interpretation: The KPI is zero, if there is no evidence of performance. If the observed outcome is better than the benchmark, the KPI will be positive. If it is worse, the KPI will be negative. While we introduced the benchmarking concept in the context of an SLB, the ability to estimate performance can be used for any performance-based financing instrument.

**Example** for _outcome KPI_ : Annual avoided primary forest loss in km<sup>2</sup> . **Example** for _benchmarked KPI_ : Annual avoided primary forest loss in km<sup>2</sup> _above_ the benchmark.

## **2.4.1 What differentiates performance from chance?**

A positive KPI suggests performance, but it does not imply that it is _significant_ enough to warrant a financial reward. For instance, if observed deforestation is only slightly below the benchmark, it is difficult to interpret this as a strong signal for additionality. An investor may argue that this minor improvement was merely the result of chance rather than policy efforts. Similarly, if observed forest loss is only slightly worse than expected, it does not necessarily mean that the issuer did not exert sufficient effort. The issuer can credibly attribute the negative KPI to chance. Clear identification of effort is important to generate time-consistent government incentives. Without it, governments may not feel sufficiently incentivized at times when exogenous deforestation pressures are strong and deforestation rises in spite of their efforts to prevent even worse outcomes.

In the REACH framework, the terms “slightly” and “chance” can be defined in statistical terms thanks to requirement R2, because each benchmark model should be accompanied a benchmark distribution. While the benchmark outcome describes the outcome level we would expect, the benchmark distribution tells us how likely alternative outcomes are. We can then use the benchmark distribution to assess whether the signal from the KPI is weak (within the 50% confidence 6
# **Figure 2: Actual performance or coincidence?**

In Section 2.4.1 we described the need for benchmark models to be able to produce benchmark distributions. These distributions are centered around the benchmark outcome and help us understand if an observed outcome and its associated KPI could be due to chance (within the buffer zone) or constitutes a significant signal for additional performance beyond any reasonable doubt. The 50% and 95% cutoffs are illustrative and can be adjusted in practice.

<!-- Start of picture text --> Outcome is Outcome is<br>worse significantly better<br>than benchmark than<br>95% confidence Outcome<br>interval variable<br>50% confidence<br>interval Very strong KPI<br>Weak negative KPI<br>Strong negative KPI<br>Very strong negative KPI<br><!-- End of picture text --> Source: Authors.

interval) or significant (outside the 95% confidence interval).5 A KPI that falls inside the 50% confidence interval does not make a strong case for either financial reward or penalty because its signal is too weak to rule out the possibility of chance. When a KPI falls outside the 50% confidence interval, it is much harder to attribute the result to chance. Hence, a step-up or step-down may be warranted. A KPI that falls outside the 95% confidence interval is a statistically significant signal for over- or underperformance beyond a reasonable doubt. A step-up or step-down is certainly warranted. Table 1 shows a possible incentive structure, where the size of the step-up or step-down scales with the strength of statistical evidence for performance.

# **2.5 Sustainability performance target**

An SLB reaches its SPT when the cumulative benchmarked KPIs cross a specific threshold (see lower panel of Figure 1). Targets, therefore, share the same unit as benchmarked KPIs and are expressed in relation to the benchmark outcome. Note that while benchmarked SPTs are set in absolute numbers, they are not interpreted in absolute terms since they are a sum of benchmarked KPIs.6 The key challenge is how to set targets that are ambitious and feasible. We return to this question in Section 5.

**Example** 10,000 km<sup>2</sup> of avoided primary forest loss above benchmark over the next five years.

> 5While confidence intervals of 50% and 95% are common reference points in statistical analysis, the precise boundaries may differ for each SLB issuance and change during the structuring process.

> 6Some financial products may evaluate social or environmental performance on a yearly basis, combined with a yearly payout structure. SPTs would then also be annual, rather than cumulative. In practice, most instruments will define periodic evaluation windows that are less frequent than annually which necessitates expressing SPTs as cumulative benchmarked KPIs.

7
## **Table 1: Linking step-up and step-downs to KPI strength**

This table illustrates how different KPI strengths can be translated into correspondingly sized financial incentives in terms of basis points (bps) changes. Practical implementations may choose cutoffs other than the symmetric 50% and 95% points and/or adjust the step sizes to reflect the goals of the instrument.

|Cutofs|Within 50%|Between 50% and 95%|Outside of 95%|
|---|---|---|---|
|Description|Observed outcome is|Observed outcome is|Observed outcome is|
||**slightly worse/better**<br>than benchmark|**worse/better**<br>than benchmark|**signifcantly worse/better**<br>than benchmark|
|KPI strength|Weak|Strong|Very strong|
|Step-up/-down|+/−0 bps|+/−25 bps|+/−50 bps|

# **3 Paying for performance, not outcomes**

The terms “performance-based financing”, “outcome-based financing” or “results-based financing” are often used interchangeably. In the REACH framework, however, _performance_ and _outcome_ represent fundamentally different concepts. _Outcome_ is the observed value (e.g. forest loss), which is the result of the government’s efforts combined with a set of external circumstances, such as weather conditions, existing policies or global exchange rates. The _effort_ is, however, unobserved. But, as we will do in Section 4, it is possible to decompose the observed outcome and estimate the share of avoided deforestation that can be attributed to government efforts. This share is called _performance_ .

<!-- Start of picture text --> effort outcome<br>e y ( e, θ )<br>external factors<br>θ<br><!-- End of picture text --> In this section, we discuss why it is in both the issuer’s and investor’s interest to make this decomposition as clear as possible. From the _controllability principle_ (see Section 3.4) we derive that the better the distinction, the stronger the incentives for the issuing government to perform, and the more attractive the SLB is to investors.

**The issuer’s perspective** Let us consider the case where rewards are linked to observed outcomes instead of performance. Since the outcome does not only depend on the issuer’s performance, the issuer faces two risks. On the one hand, deforestation could slow down because global beef prices drop and logging forests to expand pastureland becomes less profitable. On the other hand, the El Niño-Southern Oscillation could lead to abnormally dry and hot weather, which could drastically accelerate deforestation due to wildfires. However, since neither weather nor global beef prices are under the issuer’s control, the issuer may be rewarded or penalized based on a KPI that is largely unrelated to how much effort they put in. Why, then, should the issuer put in any effort at all?

**The investor’s perspective** A responsible investor is unlikely to be interested in investing in a performance-based product if its returns do not reflect the issuer’s performance. Not only is this against an impact investor’s goal of funding efforts to curb deforestation. Moreover, the investor’s return will depend on weather conditions, exchange rate fluctuations or commodity price swings.

8
Hence, the investor would be exposed to additional risk factors without adequate compensation, effectively raising the SLB’s costs.

# **3.1 Should the end justify the means?**

One could argue that investors may be less interested in how much effort the issuer exerted and more interested in the actual outcome on the ground. After all, what should matter is how many hectares of primary forests were protected and how many tons of emissions were avoided. However, we argue that this perspective has three important drawbacks.

First, if we maintain the assumption that enacting laws, enforcing conservation policies and reducing the economy’s dependence on extracting natural resources are the most reliable ways to avoid deforestation, then incentivizing the government to act accordingly remains the best bet for the investor. While this does not guarantee a measurable improvement in absolute terms, it certainly raises its _likelihood_ .

Second, having a reliable measure of the issuer’s efforts and understanding what share of actual deforestation can be attributed to the government has implications for setting targets in the future. If the SLB targets are set using observed deforestation, but all the issuer can control is their own efforts, then it is likely that targets lie outside the range of outcomes to which the issuer can credibly commit.

Finally, the purpose of a performance-based instrument such as an SLB is to promote actions and create conditions to facilitate efforts towards sustainable development goals. Designating protected areas or passing legislature to diversify the economy will have long-lasting effects, beyond the lifetime of the SLB, and affect the economy as a whole. Focusing only on observed deforestation may overly narrow the attention to outcomes in the short term and only to one particular sector.

# **3.2 Theoretical framework**

To formalize the lines of reasoning behind REACH, we anchor our analysis using insights from economic theory. In particular, let us consider a simple moral hazard framework in the spirit of Holmström (1979), Mirrlees (1999), and Shavell (1979) to model the principal-agent relationship behind an SLB, or any other performance-linked instrument.7 The principal (the investor) lends capital to the agent (the issuer), whose actions influence the success probability of the underlying project. Both parties agree on the project target and on the state-contingent instrument. Different from a conventional debt contract, the interest rate _i_ of an SLB is not fixed. Instead, depending on the results, the interest rate can either be adjusted with a step-up, Δ<sup>_u_</sup> _>_ 0, in case the target is missed or a step-down, Δ<sup>_d_</sup> _<_ 0, if the target is reached. The agent can choose an unobservable level of effort _e_ that incurs private costs. The agent is risk-averse and has a utility that depends on the effort and contractual payoff, _U_ = _U_ ( _e,_ Δ) with _dU_ / _de <_ 0 and _U_ ( _e,_ Δ<sup>_u_</sup> ) _< U_ ( _e,_ Δ<sup>_d_</sup> ). The principal is also risk-averse with utility function, _V_ = _V_ ( _d_ ), that satisfies _V_ (Δ<sup>_u_</sup> ) _> V_ (Δ<sup>_d_</sup> ).

For a given set of external factors _θ_ (also called the “state of nature”) which captures the business cycle, existing legislature, and other factors the agent cannot control, the agent’s effort induces a change in the observable outcome _y_ = _y_ ( _e, θ_ ). We assume that _dy_ / _de >_ 0 for all states of nature _θ_ , so exerting effort always improves the outcome. However, neither _e_ nor _dy_ / _de_ can be

> 7One could look at a green bond contract as a moral hazard problem as well. Namely, after the debt contract is issued, the performance of the issuer is incentivized through monitoring, reporting and verification. This could be modeled through the costly state verification approach (Townsend, 1979).

9
# **Figure 3: Performance measures with and without additional information**

The two figures depict the difference between an outcome-based KPI (left), which only uses the outcome _y_ to estimate the unobserved effort. The benchmark model-based KPI (right) also incorporates the external factors _θ_ . Since the observed outcome is determined jointly by unobserved efforts and external factors, including _θ_ leads to a more accurate estimate of effort.

<!-- Start of picture text --> (a) Outcome-based KPI (b) Benchmark model-based KPI<br>effort outcome kpi outcome effort benchmarked kpi outcome<br>e E[ e | y ] y ( e, θ ) e E[ e | y, θ ] y ( e, θ )<br>external factors external factors<br>θ θ<br><!-- End of picture text -->

directly observed. Instead, we must estimate a key performance indicator _kpi_ , which is a noisy signal of the agent’s effort _e_ . Thus, while effort itself cannot be observed, it is possible to obtain a statistical distribution that helps determine “whether [the agent’s] supply of inputs is able to affect the probability distribution of the output statistic” (Antle et al., 1988).8 It is therefore important to accurately characterize the probability distribution around the _kpi_ , and how it depends the included factors, _θ_ .

# **3.3 The value of information**

One could argue that the observed outcome _y_ alone is sufficiently informative about the agent’s efforts. This can be expressed as a conditional expectation, where _η_ is mean zero and with variance _ση_<sup>2.Inthespecialcasewhere</sup><sup>_y_istreatedasaperfect</sup> measure of effort, that is by assuming _kpi_ = _e_ = _y_ and _ση_<sup>2=0,weobtainan</sup><sup>_outcome-basedKPI_,</sup> or simply an _outcome KPI_ . However, _y_ alone would typically be an insufficient measure of _e_ , since the outcome is jointly determined by the agent’s efforts and the state of nature, _y_ = _y_ ( _e, θ_ ). Not using _θ_ in calculating the _kpi_ would be wasting valuable information about the agent’s effort. As both issuer and investor are risk-averse, both prefer a more accurate and informative performance measure. It is therefore always desirable to include _θ_ in the performance estimation, Not conditioning on the additional information _θ_ would increase the estimation uncertainty, i.e. _ση_<sup>2</sup><sup>_>σ_</sup> _u_<sup>2and give the principal a less informative signal about the agent’s performance, which in</sup> turn reduces the risk-averse agent’s incentive to exert effort.

# **3.4 Informativeness principle**

Our argumentation for why we advocate benchmarked KPIs over outcome KPIs is consistent with the _informativeness principle_ . As outlined in Holmström’s (2016) Nobel Prize lecture on “Pay For

> 8Concretely, Holmström (1979) describes the joint distribution _F_ ( _x, a_ ), where the outcome is _x_ and the effort _a_ , as being induced on _x_ through the relationship _x_ = _x_ ( _a, θ_ ) where _θ_ denotes the state of nature. Shavell (1979) introduces the notion of the principal’s observation of effort _z_ = _z_ ( _e, θ_ ). Hence, for a given _θ_ , the outcome distributions of different effort levels will differ in the sense of first-order stochastic dominance.

10
Performance and Beyond”, the principle states that an “additional signal [ _θ_ ] is valuable if and only if it carries additional information about what the agent did given the signal [ _y_ ]”.

How the additional signal _θ_ should enter the _kpi_ cannot be stated in general as it depends on the use case, time period, issuer and the type of effort the SLB intends to incentivize. Nevertheless, the implications of the informativeness principle provide guidance for possible approaches to define E[ _e_ | _y, θ_ ]. In particular, the _controllability principle_ and the _relative performance evaluation_ approaches provide statistical frameworks to estimate an unobserved counterfactual benchmark outcome, _y_<sup>_B_</sup> , which describes the hypothetical outcome if the issuer does not undertake any additional effort. Both approaches can be expressed as a difference between the observed outcome _y_ and the benchmark outcome _y_<sup>_B_</sup> .

Inserting this equation into (2) yields Equation 4 shows the decomposition of the observed outcome into a part attributed to the agent’s performance, a part attributed to exogenous factors and a component that represents statistical uncertainty. We discuss how _y_<sup>_B_</sup> could be specified for both approaches in the following.

## **3.4.1 Controllability principle**

The application in Section 4 follows the _controllability principle_ , which states that an agent’s incentives should only depend on factors under their control. We implement this by estimating the counterfactual benchmark outcome _y_<sup>_B_</sup> which reflects how much deforestation would have occurred due to external factors alone. In this case, the benchmark model could be expressed as a conditional expectation _y_<sup>_B_</sup> = _E_ [ _y_ | _X_ ] where _X_ ⊆ _θ_ is a set of exogenous predictors. Thus, equation (4) becomes a regression model of the form

## **3.4.2 Relative performance evaluation**

Alternatively, one could follow the _relative performance evaluation_ approach and obtain a benchmark outcome by using observed deforestation levels in peer countries. Synthetic control methods (Abadie, 2021) provide a suitable econometric framework. In this case, the benchmark model could be expressed as _y_<sup>_B_</sup> = _E_ [ _y_ | _YP_ ] where _YP_ denotes the observed outcomes of a set of relevant peers _P_ , e.g. similar geographic region or comparable income levels. Correspondingly, equation (4) becomes a regression model of the form

# **3.5 Measuring impact through counterfactuals**

Setting the right incentives through better performance measurement is a primarily theoretical concern. In practice, the rigorous assessment and quantification of impact are far from trivial and require a sound statistical framework. One fundamental concept, known as the Neyman-Rubin causal model, is that of potential outcomes (Rubin, 1974). It describes the counterfactual situation 11
**Figure 4: Annual deforestation in the Legal Amazon (km**<sup>2</sup> **)**

<!-- Start of picture text --> 30,000<br>25,000<br>20,000<br>15,000<br>10,000<br>5,000<br>0<br>1990 1995 2000 2005 2010 2015 2020<br><!-- End of picture text --> Source: Instituto Nacional de Pesquisas Espaciais (INPE) PRODES.

that would have occurred in the absence of the evaluated intervention. The fundamental problem of causal inference is that "it is impossible to _observe_ the [potential outcome] on the same unit and, therefore, it is impossible to _observe_ the [treatment] effect" (Holland, 1986). However, researchers across different fields have developed empirical strategies to estimate these counterfactual outcomes, using randomized controlled trials, difference-in-differences, synthetic controls (Abadie, 2021) or matching.

While the optimal estimation strategy in any given context depends on the assumptions the researcher or practitioner is willing to make, all methods share the fundamental insight that the causal impact of a program cannot be observed, but needs to be estimated. Relevant for our application of deforestation in Brazil’s Legal Amazon are Baylis et al. (2016), Ferraro (2009), and Ferraro et al. (2014), who review the available causal inference methods and their suitability for applications in environmental policy.

# **4 Deforestation in Brazil’s Legal Amazon**

We apply the REACH framework to deforestation and construct an econometric benchmark model that accounts for macroeconomic factors. We study deforestation in the nine Brazilian states which comprise the Legal Amazon: Acre, Amapá, Amazonas, Mato Grosso, Pará, Rondônia, Roraima, Tocantins, and (parts of) Maranhão. The rate of deforestation in Brazil’s Legal Amazon is alarming (Figure 4) and constitutes one of the main sources of Brazil’s GHG emissions as well as a major source of biodiversity loss (Hanusch, 2023). Most deforestation in the area is illegal, so resourcing and incentivizing governments to enforce existing laws to protect forests (“Command and Control”) is critical.

Whether legal or illegal, deforestation is an economic choice (Hanusch, 2023). Macroeconomic factors can be key determinants of the costs and benefits of that choice and therefore, ultimately, of deforestation outcomes (de Souza Ferreiro Filho et al., 2022). On a local level, deforestation may have different immediate causes (for example cattle ranching, timber extraction, land grabbing, or mining), but on a regional or national level, the literature has found that macroeconomic factors that capture the demand for commodities (e.g. commodity prices) and the external competi12
# **Figure 5: Illustration of the benchmarked KPI for deforestation**

This figure depicts schematically how observed deforestation (grey) can be attributed to macroeconomic factors (blue), weather variables (orange), and outlier events (red). Most importantly, we also show how much of the forest was at risk of deforestation (green) but the loss never materialized thanks to policy efforts. Incentives should be aligned with the benchmarked KPI (green) rather than the observed outcome KPI (grey). This is only possible if we know the benchmark outcome (dark grey).

<!-- Start of picture text --> Forest loss<br>Macroeconomic factors Weather Outlier events Policy efforts<br>Rising commodity prices, favorable exchange rates Extremely dry weather Strict pandemic The “forest at risk” that was<br>and macroeconomic conditions that benefit the lowers agricultural lockdowns leads to not lost due to conservation<br>profitability of the extractive sector over other yields and raises risks migration from urban efforts, law enforcement and<br>sectors of the economy. of wild fires. to rural areas a diversified economy<br>Observed outcome = Outcome KPI Benchmarked KPI<br>Benchmark outcome<br>Attribution<br><!-- End of picture text --> Source: Authors.

tiveness of domestic producers (e.g. inflation or the exchange rate) can partly explain the loss of primary forests (Arcand et al., 2008; Assunção et al., 2015; Curtis et al., 2018). While global prices and Brazil’s macroeconomic condition likely influence deforestation outcomes in Brazil’s Legal Amazon, the economy of the corresponding Brazilian states only accounts for 9 percent of national GDP in 2019 (de Souza Ferreiro Filho et al., 2022) and 13 percent of the population in 2021 (Hanusch, 2023), so deforestation patterns are unlikely to influence global or national outcomes. This makes deforestation in the Legal Amazon an ideal case to illustrate a benchmarked KPI.

Macroeconomic factors matter — but policy matters, too. In many cases, the literature is divided over the effectiveness of different policies over vast territories like the Legal Amazon, as policies’ effectiveness in one area may displace deforestation to other areas. Such displacement effects have been shown, for example, for protected areas and voluntary private sector commitments such as the soy and beef moratoria for the Amazon (Carvalho et al., 2019). Other policies may be more effective at a larger scale, such as satellite-supported law enforcement or the blacklisting of municipalities in high deforestation areas (West et al., 2021). An ideal deforestation baseline would exclude any policy effects, as they are necessary for the performance that is supposed to be rewarded.

13
# **4.1 Data**

**Observed deforestation for Brazil’s Legal Amazon** We use deforestation data from PRODES9 for the Legal Amazon between 1989 and 2021 for the annual model (Figure 4), and from DETER10 between May 2015 and January 2021 for the monthly model (see Appendix A). This serves as the outcome variable, _yt_ . We explore sub-annual and sub-national deforestation data using remotesensed data with ex-post attribution of deforestation drivers in subsequent research.

As discussed in Section 2.4, benchmarked KPIs are defined with respect to the benchmark outcome, which is an estimate from the benchmark model. The main ingredient of the approach in this _X_ . application is a set of exogenous factors From the literature, we can identify a set of possible factors that are both exogenous to the Brazilian economy as well as predictive of the deforestation dynamics. However, it is harder to know ex-ante exactly which factors should be included and in what form. We describe the candidate variables below.

**Real effective exchange rate (REER)** As the exchange rate determines a country’s competitiveness on the world stage, a weakening exchange rate will accelerate deforestation for wood production and the export of timber products, and/or advance the forest to land conversion for agricultural exports (Arcand et al., 2008; Hanusch, 2023; Richards, 2021).

**Global commodity prices.** Globally, Curtis et al. (2018) estimate that "27±5% of all forest disturbance between 2001 and 2015 was associated with commodity-driven deforestation". For our application, we use global market prices of beef, coffee, soy, corn, sugar, soy oil, hardwood logs, and iron ore in Brazilian real. In line with the previous point, higher commodity prices will drive Brazilian deforestation. However, the reverse does not hold, i.e. it is very unlikely that Brazilian forest loss will drive global commodity prices, esp. in the short-run (Arcand et al., 2008; Hanusch, 2023; Richards, 2021). Since commodity prices are highly correlated, we compute their principal components instead of using the variables directly.

**Previous deforestation rate.** To reflect deforestation trends that precede the policy actions defined as performance we include lagged deforestation. This variable could be argued to be not fully exogenous. For example, policy decisions about forest conservation affect not only deforestation in a given year but also in subsequent years. These variables are weakly exogenous or predetermined, meaning that previous deforestation trends determine current deforestation, but not vice versa, especially in the short run.

# **4.2 Econometric benchmark model**

Equation (7) shows how the benchmark model under the controllability principle from Section 3.4.1, equation (5), is operationalized in this application. The definition holds for the annual model

> 9The PRODES project carries out satellite monitoring of clear-cut deforestation in the Legal Amazon and produces, since 1988, annual deforestation rates in the region, which are used by the Brazilian government to establish public policies. For more information, please see the official website and Valeriano et al. (2004).

> 10Developed by the National Institute for Space Research (INPE) as one of the key changes from the Action Plan for the Prevention and Control of Deforestation in the Legal Amazon, DETER is a satellite-based system that captures and processes georeferenced imagery on forest cover in 15-day intervals. See the official website and Assunção et al. (2023).

14
using PRODES data as well as the monthly version which uses DETER data.11 Here, _c_ is the intercept, _φp_ is the autocorrelation coefficient of lag _p_ , _xt_<sup>_k_</sup> − _q_<sup>arethepredictors</sup> described in the previous section, lagged at least one and up to three years. _dt_<sup>_s_</sup> [ _t_ ≥ _s_ ]<sup>arelevel-</sup> shifting policy dummies that account for known past policy interventions and which remain active for all years after the intervention. The years for which policy dummies are permissible are selected based on knowledge of past policy actions – in this application we choose 2004, 2009 and 2012 (see Figure 6). These dummies are necessary to model the generalizable relationship between exogenous deforestation drivers and benchmark predictors, untainted by known policy effects. This leaves us with a large set of possible predictors. Using a variable selection method (LASSO) we select the most relevant predictors for deforestation (see Figure 12). Policy dummies are not subject to penalization. The model is estimated for annual and monthly deforestation rates. We impose a _L_<sup>1</sup> penalty on the coefficients _φp_ and _βq_<sup>_k_for variable selection (Tibshirani, 1996), where</sup> the penalty strength is determined through cross-validation.

The selection results show that four variables matter the most: previous deforestation, lagged REER percentage change, and lagged commodity prices (see Figure 12). The second and fourth principal components mostly capture the prices of beef, iron ore, sugar12 and hardwood logs (see Table 3). After selecting the variables, we refit a linear regression model with only the most important predictors (see Table 4) as an illustration. Jointly, they explain about 90% of the variation in the annual model and around 80% for the monthly model. Note that we also include level-shifting policy dummies for the years 2004, 2009 and 2012 for the annual model and seasonal dummies for the monthly model (see Table 5).

# **4.3 Benchmarking avoided deforestation performance**

Using the benchmark model (Equation 7) we can ex-post calculate the benchmark level of deforestation in the Legal Amazon. Figure 6 shows the results. The bars show observed deforestation levels _yt_ , similarly to the bars in Figure 4. However, they have now been colored to reflect whether _yt_ was better or worse than the expected benchmark _yt_<sup>_B_, shown as blue horizontal dashed lines.</sup> Since the model also produces a benchmark distribution, we can calculate the confidence intervals for each prediction. Interestingly, for the four years where new policies were introduced, we can observe lower than expected deforestation levels: Amazon Region Protected Areas Program (2000), Plan for Prevention and Control of Deforestation in the Legal Amazon (PPCDAm, 2004) and Soy Moratorium (2005), the blacklisting of municipalities and beef moratorium (2009), and the update of the Forest Code (2012). For the blacklisting moratorium and Forest Code, measured deforestation is outside the 95% confidence interval, such that it would constitute a strong KPI (see Table 1).

Since 2018, and especially 2019, deforestation has picked up to a rate that exceeds what can be expected given the macroeconomic conditions. However, the increase in the benchmark outcome suggests that not the entire increase in observed deforestation can be attributed to (a lack of) policy

> 11The time periods and frequencies of relevant variables are then changed from annual to monthly, accordingly. See Appendix A for monthly results.

> 12Though sugar is not grown in the Legal Amazon, its cultivation in other parts of Brazil can lead to displacement effects and affect land choices across the country.

15
# **Figure 6: Better or worse than expected?**

This figure shows the expected outcomes (center of distributions, blue dashed lines) and the observed deforestation levels (colored bars), which are red if deforestation is worse and green if better than expected. The text boxes demarcate the years when a policy was introduced to combat deforestation. For monthly results, see Figure 13, Appendix.

<!-- Start of picture text --> 35,000<br> Amazon Region Protected Areas Program (2002)<br>30,000 Plan for Prevention and Control of Deforestation in the Legal Amazon (2004)<br>25,000<br> Amazon Soy moratorium (2006)<br>20,000 Blacklisting of municipalities (2008)<br> Cattle moratorium (2009)<br>15,000<br> Updated forest code (2012)<br>10,000<br>5,000<br>0<br>1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 2020 2021<br>Benchmark deforestation Observed deforestation<br>benchmark outcome slightly below benchmark: weak KPI slightly above benchmark: weak KPI<br>50% confidence interval below benchmark: strong KPI above benchmark: strong KPI<br>95% confidence interval significantly below benchmark: very strong KPI significantly above benchmark: very strong KPI<br>2)<br>Annual Amazonian deforestation (km<br><!-- End of picture text --> Source: Instituto Nacional de Pesquisas Espaciais (INPE) PRODES, calculation by authors.

action under the federal government. This finding is in line with (de Smit, 2022) who also finds a mostly positive but not significant effect using synthetic control methods.

# **4.4 Incentives under constant benchmarks**

The main argument behind the above analysis is that estimating benchmark outcomes requires robust and transparent empirical methods instead of simple extrapolation of historical trends. In this section we explore a hypothetical method for setting constant benchmarks and discuss the implications of those.

for results-based financing that penalizes emissions from deforestation and forest degradation, rewards forest carbon stock conservation and enhancement, and sustainable forest management (UNFCCC, 2011, paragraph 70). Payments are contingent upon the observed difference between FRLs/FRELs and the observed deforestation (Granziera et al., 2021). This is consistent with our suggestion not to use observed outcomes as KPIs, but instead compare the outcomes with a benchmark. In fact, the guidelines in UNFCCC (2014) assess how historical data were taken into account when establishing the FRLs/FRELs.

However, some reference levels discussed in Granziera et al. (2021) are simple historical averages over 4-year to 20-year periods, reassessed periodically. Various reference levels were used for results-based financing (see Figure 7), which correspond to historical averages over an expanding window since 1996. These remain constant for 5-year periods, after which the FRELs are updated. Within the 5-year periods, the results were evaluated against the prevalent benchmark. This approach to estimating a baseline scenario has been criticized in the past as too simplistic (Fletcher 16
# **Figure 7: Brazil’s forest reference emissions levels (FRELs)**

This figure depicts Brazil’s submitted FRELs for the Amazonia biome (Ministry of the Environment of Brazil, 2018; Ministry of the Environment of Brazil et al., 2014), and reflects how the benchmarks are computed as historical averages over an expanding window since 1996, which remain constant within 5-year periods.

<!-- Start of picture text --> FREL A, reference period: 1996 2005<br>1,400 FREL B, reference period: 1996 2010<br>FREL C, reference period: 1996 2015<br>1,200 FREL A, reference level: 2006 2010<br>FREL A FREL B, reference level: 2011 2015<br>FREL C, reference level: 2016 2020<br>1,000<br>FREL B<br>800 FREL C<br>600<br>400<br>200<br>0<br>1996 2000 2004 2008 2012 2016 2020<br><!-- End of picture text --> Source: Ministry of the Environment; Ministry of Science, Technology and Innovation of Brazil.

et al., 2016; Huettner et al., 2009; Mertz et al., 2018), see Arts et al. (2019) for an overview.

From a principal-agent perspective, a constant benchmark that does not satisfy the _controllability principle_ (see Section 3.4.1) will weaken the performance incentives for the issuer. If the benchmark does not reflect external factors, then the issuer’s rewards or penalties will be decoupled from its performance. Moreover, funding providers may end up rewarding results which may have taken place regardless of the issuer’s efforts.

For instance, the spike in deforestation in Brazil’s Legal Amazon until 2004 implies a high baseline deforestation rate for all FRELs used in projects that started in subsequent years, as shown in Figure 7. As a result, West et al. (2020), West et al. (2023) argue that a significant part of the carbon credits claimed through such projects do not reflect additional emissions reductions. This highlights the importance of appropriate and robust benchmark choices, also for the credibility of carbon offsets. The authors also show that during the implementation phase of such projects, deforestation decreased in most areas of the Brazilian Amazon (in part) due to macroeconomic conditions.

# **4.5 Discussion**

If we compare the FREL benchmarks described Figure 7 with the benchmarked KPI in Figure 6, we can make several observations with respect to the REACH framework. Both approaches satisfy the requirement of a “transparent benchmark model”. In the case of FRELs, the benchmark is a historical average over a reference period, updated every five years. For our proposed benchmarked KPIs, the econometric benchmark model is described in Section 4.2. However, different from the benchmarked KPI approach, FRELs do not provide any probability distributions for their benchmarks. This makes it difficult to assess if the outcomes were due to chance or actual efforts.

17
Most importantly, the FRELs do not provide a clear justification for additionality. From Brazil’s submissions under the UNFCCC13 we can gather a potential justification, since the submissions explicitly state that the FRELs “[do] not include assumptions on potential future changes to domestic policies.” This is different for the benchmarked KPIs, which satisfies the informativeness principle. The benefit of the latter is that it disentangles which part of deforestation was under the issuer’s control and which part was not, which in turn satisfies the controllability principle.

An alternative approach that satisfies the relative performance evaluation is the work of GuizarCoutiño et al. (2022) and West et al. (2020) who used statistical methods based on matching to estimate the additionality of conservation projects on a sub-national project level. While GuizarCoutiño et al. (2022) find that deforestation in 40 conservation projects areas in nine countries was reduced by 47%, on average, compared to matched control pixels, West et al. (2020) find little evidence that such projects in the Brazilian Amazon “have mitigated forest loss” compared to matched control regions using synthetic control methods. This method was also explored by de Smit (2022) on a country level, though the author did not find any statistically significant results.

# **5 Setting ambitious, yet feasible targets**

A promising SPT strikes a good balance between ambitiousness and feasibility.14 So far, we have described how the framework assesses performance and sets incentives through benchmarked KPIs. In this section, we discuss another essential aspect of the framework: setting ambitious SPTs that remain feasible to achieve. The ICMA guidelines define ambitious targets as those that “represent a material improvement [...] beyond a ‘Business as Usual’ trajectory” (ICMA, 2020). At the same time, the guidelines emphasize the need for feasible targets based on “benchmarking approaches” such as the past performance of the issuer, their peers, or science-based scenarios.

The Feasibility-Ambitiousness (FAB) matrix summarizes how we assess sustainability performance targets. Figure 8 shows the interplay between feasibility and ambitiousness. The ideal targets are those that are highly ambitious and become increasingly feasible due to SLB funding. Such targets imply additionality and thereby send the strongest signals for both issuers and investors.

## **5.1 Low-hanging fruits and long shots**

**Low-hanging fruits** Issuers of SLBs with unambitious targets are vulnerable to greenwashing allegations. If little to no effort is necessary to reach the SPT, then such targets would have likely been realized without the SLB financing. This is especially true for SPTs that the issuer was already making good progress towards. Additionally, in the event of reaching an SPT, investors will face lower financial returns due to the triggered step-down. Responsible or impact investors may find such an SLB unattractive since they would have to justify the financial and reputational consequences if the social or environmental impact achieved was only a low-hanging fruit.

**Long shots** If achieving the SPT would require an unrealistic improvement, projects may be regarded as unattainable and overzealous. Issuers would likely have to pay a penalty fee since the SLB structure stipulates a step-up in the case of missing the SPT. Such overambitious SPTs may be therefore only look good on paper and never translate into reality, leading to possible greenwashing allegations. Investors that buy such an SLB face two types of reputational risks.

> 13See Ministry of the Environment of Brazil (2018) and Ministry of the Environment of Brazil et al. (2014).

> 14Visit https://esgdata.worldbank.org/tools/fab to analyze indicators and countries on the Sovereign ESG Data Portal.

18
# **Figure 8: The Feasibility–Ambitiousness (FAB) matrix**

The FAB shows that setting promising targets requires the consideration of both ambitiousness and feasibility. Neither low-hanging fruits nor long shots are desirable as they may lead to greenwashing allegations (see Section 5.1) The ideal targets are both feasible and ambitious but require additional SLB funding to become realizable.

<!-- Start of picture text --> forward-looking<br>extrapolates business-as-usual<br>Ambitiousness trends with no policy changes<br>Feasibility Low High Very high<br>Highly ambitious<br>backward-looking but low chance<br>based on historical Low Long Shots of success<br>precedents of Target unlikely to<br>relevant peers be achieved given<br>High lack of historical<br>precedence<br>Reachable<br>Low-Hanging Targets<br>Very high Fruits<br>Highly feasible but unambitious<br>Target requires little to no effort and Source: Wang, Gurhy,<br>may have been reached in any case Hanusch, Kollenda (2023)<br><!-- End of picture text --> Source: Authors.

The first type stems from funding unrealistic projects whose targets may never be reached. This is compounded by the second risk, namely that they will need to justify benefiting from a stepup when the issuer fails to meet an unrealistic SPT – especially, if it was known that the SPT’s feasibility was low.

We illustrate how SPTs for reduced deforestation in Brazil’s Legal Amazon could be set using the FAB matrix. The methodology to evaluate feasibility relies on a peer country comparison with other tropical forest countries. For these countries, we use country-level primary forest loss data from the Global Forest Watch rather than INPE’s data, which is only available for Brazil’s Legal Amazon. We set the SPT horizon to four years for this application. From a collection of all tropical forest countries, we selected 19 comparable peer countries with non-negligible deforestation rates in the past.15 Because of the disproportional size of Brazil’s forest area, our deforestation indicator is standardized to represent annual forest loss relative to the forest area in the year 2000. Figure 9 shows the selected countries and annual relative forest losses since 2000. In the two decades until 2021, Brazil’s Legal Amazon has lost 7 percent of its primary forest area – a loss of 261,567 square kilometers, almost the total land area of Ecuador.

# **5.2 Ambitiousness**

Ambitiousness is a _forward-looking_ concept based on projecting a business-as-usual (BAU) scenario. Given the discussion on macroeconomic drivers of deforestation in Section 4 we construct a BAU scenario by applying equation (7) to predict deforestation with forecasted macroeconomic conditions from 2022-2025 from the World Bank’s Macro-Fiscal Model (Burns et al., 2019).16 Figure 10 shows that given forecasted macroeconomic conditions, deforestation in Brazil’s Legal Amazon

> 15Angola, Argentina, Bolivia, Brazil, Cameroon, Republic of Congo, Colombia, Ecuador, Gabon, Guyana, Indonesia, India, Mexico, Peru, Suriname, Tanzania, Uganda, República Bolivariano de Venezuela, and Zambia.

> 16Alternative modeling choices for BAU scenarios could be based on computable general equilibrium models, time series econometrics or dynamic factor models. The best choice will depend on the indicator of interest.

19
<!-- Start of picture text -->
1.60%<br>' Angola (2021=0.99%)<br>% Zambia (2021=0.88%)<br>x 1.40% Uganda (2021=0.74%)<br>° . Bolivia (2021=0.71%)<br>8 1.20% Cameroon (2021=0.47%)<br>3 | Mexico (2021=0.38%)<br>7 1.00% vA . Brazil (Legal Amazon) (2021=0.37%)<br>> r k V/\ . Argentina (2021=0.27%)<br>i} 0.80% ai r , |. f . | Tanzania (2021=0.26%)<br>2 ' . nls LVS rod Colombia (2021=0.23%)<br>w " i HN A </ \A oe Peru (2021=0.22%)<br>© 0.60% oe ie VA N\A India (2021=0.22%)<br>4 TT NENT A Vans pK A Indonesia (2021=0.22%)<br>= \> Lt A OW YT WX |X» ak 7 Congo, Rep. (2021=0.09%)<br>5 0.40% . x} 1 Kz asSy Ecuador (2021=0.12%)<br>S 0.20% 4 Sti w—s 1] tte Li > v4 Suriname (2021=0.08%)<br>= OL a Ze SS NG “we BR Venezuela, RB (2021=0.06%)<br>x o.00% SS 3S 5 = = —— Guyana (2021=0.04%)<br>Gabon (2021=0.04%)<br>2000 2004 2008 2012 2016 2020 2024<br><!-- End of picture text -->
<!-- Start of picture text --> 0.60% —- Average Forecast<br>90% forecast interval<br>S 0.50% 50% forecast interval<br>oF ° — Brazil Legal Amazon<br>a 0.40%<br>©<br>LLv i<br>0.30% HH<br>S<br>S<br>J i<br>N<br>(0.20%<br>-i<br>v<br>2<br>~ '<br>® 0.10%<br>v i<br>v2021 (0.37% ~ 0%)<br>2 0.00% —<br>y iy \<br>n iN \.<br>v i WA<br>2 -0.10% a i<br>= N Low ambitiousness<br>5 ' ae Ambitious<br>c<br>& -0.20% High ambitiousness<br>2000 2004 2008 2012 2016 2020 2024<br><!-- End of picture text -->
<!-- Start of picture text --> 0.60% | —m— Median development path<br>< 90% feasibility interval /<br>° 50% feasibility interval ff<br>-<br>S — Brazil Legal Amazon H<br>XN 0.40% Peer countries j/<br>o i /<br>ro) } vA<br>ro) i<br>=] if<br>Oo : wa<br>£ 0.20% 2005 i High feasibility<br>= i H<br>aad H<br>& 2001 if<br>o O iLt<br>w2021 (0.37% ~ 0%)<br>2 0.00%<br>Ywn ityiy<br>2 7<br>nam iN rN Feasible<br>© 2009 aa\ “oe<br>c bows |<br>E -0.20% ?<br>xc‘ 2017 i Low feasibility<br>-20 -18 -16 -14 -12 -10 -8 -6 -4 -2 Base +1 +2 +3 +4<br><!-- End of picture text -->
# **Table 2: FAB analysis for Brazil’s Legal Amazon until 2025**

This table shows an illustration of the FAB matrix analysis. It shows the values from the ambitiousness and feasibility categories and how the two analyses can inform a target setting exercise. Values are expressed as annual forest loss relative to the forest area in the year 2000 and converted into square kilometers in parentheses. For feasibility, relative forest loss is transformed to square kilometers using the forest area of Brazil’s Legal Amazon.

|2021|2022|2023|2024|2025|
|---|---|---|---|---|
|**Most recent value**<br>0.37%<br>(13,235 km<sup>2</sup>)|||||
|**Ambitiousness**|||||
|Average BAU scenario forecast|0.31%<br>(11,178 km<sup>2</sup>)|0.25%<br>(8,738 km<sup>2</sup>)|0.24%<br>(8,469 km<sup>2</sup>)|0.24%<br>(8,470 km<sup>2</sup>)|
|Cutof: low ambitiousness / ambitious|0.30%<br>(10,640 km<sup>2</sup>)|0.25%<br>(8,749 km<sup>2</sup>)|0.24%<br>(8,461 km<sup>2</sup>)|0.24%<br>(8,426 km<sup>2</sup>)|
|Cutof: ambitious / highly ambitious|0.28%<br>(9,802 km<sup>2</sup>)|0.23%<br>(8,122 km<sup>2</sup>)|0.23%<br>(8,016 km<sup>2</sup>)|0.23%<br>(8,083 km<sup>2</sup>)|
|**Feasibility**|||||
|Median development path|0.40%<br>(14,235 km<sup>2</sup>)|0.37%<br>(13,108 km<sup>2</sup>)|0.46%<br>(16,464 km<sup>2</sup>)|0.43%<br>(15,169 km<sup>2</sup>)|
|Cutof: feasible / highly feasible|0.30%<br>(10,689 km<sup>2</sup>)|0.30%<br>(10,636 km<sup>2</sup>)|0.31%<br>(11,260 km<sup>2</sup>)|0.30%<br>(10,769 km<sup>2</sup>)|
|Cutof: low feasibility / feasible|0.21%<br>(7,549 km<sup>2</sup>)|0.21%<br>(7,392 km<sup>2</sup>)|0.26%<br>(9,361 km<sup>2</sup>)|0.21%<br>(7,321 km<sup>2</sup>)|

outcome ranges should be transparent and use evidence-based methodologies. For example, Assunção et al. (2023) describe how recent advances in satellite technology have contributed to monitoring and environmental enforcement in the Amazon. They find that “increasing monitoring and law enforcement by half decreases municipal deforestation by an estimated 25 percent”. The authors used cloud coverage as an instrument for law enforcement and were thereby able to construct a model to estimate counterfactuals for different scenarios. This framework could serve as a benchmark for feasible improvements for other tropical forest countries that consider deforestation-related SPTs paired with similar policy efforts.

# **5.4 Discussion**

We end the exercise in target setting by combining our insights along the ambitiousness and feasibility dimensions into the feasibility-ambitiousness matrix and identifying a promising target. Table 2 summarizes the relevant values from the ambitiousness (Figure 10) and feasibility (Figure 11) analyses. From the ambitiousness analysis, we considered the lower bound of the 90% forecast interval as a potential ambitious target. This translates to a target of an annual forest loss between 0.28% (9,802 km<sup>2</sup> ) in 2022 and 0.23% (8,083 km<sup>2</sup> ) in 2025. From the feasibility analysis, we can see that such a trajectory would lie within the range of feasible outcomes, which taking 2025 as an example ranges from 0.21% (7,321 km<sup>2</sup> ) to 0.30% (10,769 km<sup>2</sup> ).

Hence, the trajectory laid out by the lower bound of the 90% ambitiousness forecast interval is a _reachable_ (ambitious and feasible) target (see Figure 8). So far, we have expressed the target in absolute annual values and not in relation to a baseline outcome. To set a relative target, one would have to define an appropriate ex-ante benchmark and then take the difference between the benchmark trajectory and the absolute target path to calculate the target in relation to the benchmark. In our example, an appropriate benchmark could be the average BAU forecast (see 23
Table 2.

# **6 Conclusion**

In this paper we provided a new way of looking at sustainability-linked financing instruments and investigated how SLBs could be an effective tool to curb deforestation in Brazil’s Legal Amazon. We introduce the REACH framework – relative evaluation and benchmarking – which makes the crucial distinction between outcome measurement and performance measurement through the use of benchmarking methods. The key insight is that it is in both the issuer’s and the investor’s interests to reward the issuer’s performance and not the observed outcomes. This follows directly from principal-agent theory and the _controllability principle_ . To give the strongest incentives for the issuer to perform, the carrots and sticks of an SLB should only be linked to factors the issuer can control, e.g. passing legislation to curb deforestation, supporting the forest police or diversifying the economy. Conversely, external factors which the issuer cannot control but determine the ultimate outcome, e.g. weather conditions or global commodity prices, should be stripped away from the performance metric.

The use of benchmarks is in line with the guidelines proposed by ICMA, which suggest that KPIs should be measured with respect to a benchmark, which can be in the form of “an external reference or definitions” (ICMA, 2020). REACH imposes stricter requirements on benchmarks, since they determine what qualifies as impact or additionality. In other words, benchmarks are necessary to quantify the causal effect beyond any statistical doubt. We discuss why this cannot be done without knowing counterfactual outcomes, i.e. how much deforestation would have happened if the issuer did not perform any better or worse than expected. The REACH framework lists three requirements for the benchmarks: (R1) transparent model specification, (R2) benchmark probability distribution, and (R3) justification for additionality.

Using the REACH framework we turn our attention to Brazil’s Legal Amazon. We specify a benchmark model that satisfies the requirements (R1)-(R3) and estimate this historical performance of a hypothetical SLB. The analysis shows the difference between outcome KPIs, which equate performance with outcomes (“20,000 km<sup>2</sup> of observed forest loss”), and benchmarked KPIs, which calculate performance relative to the effect of external factors (“2,000 km<sup>2</sup> less deforestation than would be expected given the prevalent macroeconomic conditions”). We also discuss why benchmarks which do not fulfil the REACH requirements, such as forest reference emissions levels, dilute the incentives that benchmarked KPIs preserve.

To complement REACH, which is primarily about performance measurement, we introduce the Feasibility-Ambitiousness (FAB) matrix which is about target setting. SLBs specify which sustainability goals they aim to achieve and within which time frame. However, it is difficult to assess whether a target is ambitious. Issuers have used second-party opinions to answer this question. We argue that one must also consider the feasibility of the targets to avoid greenwashing accusations. According to the FAB, one should avoid _low hanging fruits_ – which are highly feasible but not ambitious – and _long shots_ – which are highly ambitious but not feasible. The FAB delineates statistical methods to assess both dimensions and we give an example of an SPT that would be feasible and ambitious in Brazil’s Legal Amazon.

While we introduced the frameworks in the context of SLBs, the REACH and FAB can be applied more widely. For instance, it can be used to assess the impact of labeled bonds or to track the additionality of nature-based solutions or debt-for-nature swaps. SLBs just happen to be ideally suited to connect the evaluation with performance incentives. For issuers and investors, REACH 24
and FAB can form the basis of discussions and roadshows, while also facilitating the subsequent structuring and pricing process.

# **6.1 Practical considerations**

**State-contingent debt instruments** The structure of SLBs is reminiscent of state-contingent debt instruments (SCDIs), which share the fundamental idea to link debt service with a state variable.20 Traditionally, SCDIs were attractive to investors due to their counter-cyclical, diversification and hedging properties. They were also appealing to issuers since debt repayments are linked to the fiscal capacity and because SCDIs could broaden the country’s investor base (IMF, 2017). However, SCDIs enjoyed limited uptake due to liquidity and pricing concerns, and measurement issues such as delayed reporting.

In the current climate of sovereign debt distress and associated debt restructuring negotiations, linking debt repayments to a state variable could be worth exploring, especially for sovereigns exposed to climate change risks and environmental degradation (Volz, 2023). The benchmarked KPIs developed under the REACH framework could inform debt (re-)structuring decisions. Similar to catastrophe bonds or other disaster risk financing instruments, SLBs could thereby provide downside protection in the case of natural disasters, since the benchmarked KPIs account for external factors. At the same time, SLBs could expand governments fiscal space and aid in their mission to reach their Sustainable Development Goals (SDGs) or Nationally Determined Contributions (NDCs).

**Geospatial deforestation data** It is worth emphasizing that the viability of both evidence-based frameworks hinges on the data environment. In the application, annual data was sufficient to demonstrate the framework. However, for model validation and reliability, more granular data would be needed. For deforestation, remote-sensed satellite data is a highly promising way to provide objective, regular and reliable observations. Subannual and subnational geospatial data on land use and land cover transitions can help us understand the drivers, locations and trends in deforestation and degradation, which could in turn produce more sophisticated and effective KPIs. An SLB that targets deforestation due to cropland expansion may necessitate a different set of government entities than an SLB that targets deforestation due to urban expansion. The World Bank and the European Space Agency are currently exploring how SLBs may leverage new deforestation monitoring technologies with cloud-penetrating capabilities.

**Private capital mobilization** Multilateral development banks (MDBs) have a clear and essential role to play to mobilize private capital. The REACH framework aims at setting better performance incentives by accounting for what the issuer can be reasonably expected to achieve. The size of the step-ups or step-downs could then be scaled beyond the commonly used 25 basis points. However, while this sends strong signals about the commitment of both issuer and investor, the interest rate differentials may be difficult to stomach, especially when the market for sovereign SLBs is still nascent. MDBs can help derisk the transaction on either side through concessional finance or guarantees.21 Moreover, SPTs are often aligned with existing development operations and MDBs can provide technical assistance, capacity building and knowledge transfer to support issuers in reaching their goals. A strong coupling of incentives to performance, as in the REACH

> 20The SLBs discussed in the REACH framework could be seen as _floater_ -type SCDIs, which have a fixed principal and a variable coupon. For the SLB, the coupon would be linked to the benchmarked KPI, the state variable. 21In the context of contract theory, MDBs can help relax the participation constraints for issuers.

25
framework, only strengthens the case for accompanying non-financial support as these efforts are now more directly liked to financial rewards.

**Use-of-proceeds with exclusions** We have argued that, in theory, one of the SLB’s strengths is that a well-chosen KPI obviates the need for identifying a basket of eligible projects and tag the expenses as is common for GSSBs. In practice, however, an entirely unrestricted use of proceeds may lead to greenwashing concerns as well. For instance, when proceeds are used to fund activities that pollute the environment or violate human rights. In order to conserve room for sovereigns to navigate, on the one hand, and preventing reputational concerns due to the use of proceeds, on the other hand, it may be prudent to stipulate which activities SLB funds cannot be used for. The UN Global Compact principles could serve as a reference for exclusionary criteria.

**Pricing of SLBs** Since SLBs are still new, pricing is a particular hurdle. For instance, it would be difficult to find comparable instruments to serve as references. Conventional fixed income pricing approaches may not be appropriate given the SLB’s state-contingent repayment mechanisms. Instead, SLBs constructed using REACH can leverage the (R2) requirement of always providing a benchmark probability distribution. This opens up the toolbox of insurance or derivative pricing. Concretely, benchmarked KPIs are the underlying, SPTs define the strike price, and the benchmark distributions provide the necessary moments to compute variance, skewness and kurtosis. Closely related is also the literature on real option pricing, which could inform the price of forest carbon offsets. We leave the pricing exercise to future research.

# **6.2 Outlook**

REACH and FAB together pave the way for the standardization of SLB issuances in the future. While the selection of KPIs, definition of benchmark models and target-setting procedures will need to be tailored for each country and instrument, the structured approach of both REACH and FAB can be generalized. Moreover, since statistical models underpin the frameworks, discussions about whether or not a particular KPI constitutes actual performance can be easily supported or disproved with empirical evidence. Making the data and code publicly accessible will further reduce information asymmetries, foster uptake, support coordination between ministries, encourage critical discussion, and ultimately lead to better SLBs.

26