# **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).

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