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