Domain Editor-in-Chief: Anne R. Kapuscinski; Dartmouth, US
Associate Editor: Kim A. Locke; Dartmouth, US
Guest Editor: Fabio Scarano; UFRJ, FBDS, BR


1. Introduction

Environmental policy evaluation is one of the most important, yet often neglected, aspects of policy life-cycle (Crabbé and Leroy, 2008). Policy evaluation should provide two interrelated types of analysis: the measurement of impact and the development of a counterfactual scenario (Ferraro, 2009; Greenstone and Gayer, 2009; Ferraro and Miranda, 2014). In relation to the first type of analysis, to improve environmental governance practices it is crucial to determine whether a given outcome can be attributed to a driver, program, policy or intervention. In relation to the second type of analysis, a counterfactual describes something contrary to fact, used to reduce or eliminate cofounding biases from other variables. Following studies in the natural sciences, experimental research design has become standard in an increasing number of fields. It is based on the selection of a statistically significant sample of an underlying population and the separation of the sample units into two groups: a “treatment group” and a “control group”. These two groups should be statistically similar in all respects, except for exposure to the treatment. The premise is that the randomized procedure reduces the bias, and the treatment outcomes can be compared to give a credible estimate of the effect of treatment (Campbell and Stanley, 1966; Shadish et al., 2001).

Experimental designs are difficult to apply outside of controlled laboratory environments, in situations in which it is not possible to obtain a random sample. This is the case with environmental policy evaluations in which unaffected areas, that are statistically similar, cannot be found. For this reason, approaches known as quasi-experimental designs have been created to measure the effect of given treatments. These are applied in contexts in which random selection and the strict separation of effects are beyond the researchers’ control (Campbell and Stanley, 1966; Ferraro, 2009; Greenstone and Gayer, 2009). In land-use policy evaluation criteria, socio-economic indicators (Gibbs et al., 2015) such as spatial proximity (Nepstad et al., 2006) and temporal frames (Stewart-Oaten et al., 1986; Wiens and Parker, 1995; Smith, 2002) have been used to establish the similarity between areas and to evaluate differences between areas affected and unaffected by a given policy, a concept also known as before-after/control-intervention (BACI), where the design involves a control versus treatment group, and evaluates policy by comparing the situation of an area before and after the introduction of a given policy.

Quasi-experimental research designs using counterfactual analysis aim at evaluating potential outcomes under specific scenarios, or hypotheses, such as what was the most likely scenario if the area under study had not being under the influence of a given policy (Shadish et al., 2001; Ferraro, 2009). Thus, it would be possible to investigate potential environmental benefits of the policy (e.g. how much forest had been spared in a given period due to the creation of new protected areas). For example, cellular automata (Soares-Filho et al., 2006; Vega Orozco et al., 2012), econometric (Soares-Filho et al., 2010; Arima et al., 2014) and probabilistic bottom-up models (Rosa et al., 2013; Godar et al., 2014) have been used to establish counterfactual analysis and, consequently, to measure the overall effect of environmental policies in reducing deforestation and greenhouse gas emissions.

Despite the wide variety of quantitative methods available for the measurement of policy effects and counterfactual analysis, the literature does not present methods that are both general enough to be applied across different domains and sufficiently robust to provide reliable information about the effects of environmental policies. Furthermore, most of the methods mentioned above require a vast amount of economically and spatially explicit data that is often unavailable to policy-makers, especially in developing countries. In this context, this paper seeks inspiration from epidemiology to propose a set of robust yet data-light set of methods to evaluate the effect of land-use policies (Coulston and Riitters, 2003; Tonini et al., 2009; Fei, n.d.; Tuia et al., n.d.).

Statistical epidemiological models have been applied to associate the mean behavior of the number of cases of diseases to environmental or socio-economic variables or other relevant information (Jewell, 2003; Selvin, 2004). In these models, the dependent random variable can be defined as the number of cases observed among an underlying population at risk. An appropriate statistical model for this dependent random variable is the Binomial model. If the proportion of the cases with respect to the risk population is small then the Poisson distribution can be used as an approximation to the Binomial distribution. Furthermore, if further geographical information is available then spatial clustering analysis (Lawson, 2013) can be used to detect spatial clusters in which the disease rate is significantly higher. This information is crucial for early treatment of individuals and to stop the dissemination of contagious diseases.

We argue in this paper that statistical epidemiological models can also be useful for the analysis of environmental policies such as the rural environmental registry (CAR) that is part of the Brazilian Forest Code. Created in 1965, the Forest Code (FC) was transformed during the 90’s into the main Brazilian environmental federal law. The FC was revised in 2012, maintaining conservation requirements, including a Legal Reserve on at least 80% of native in private properties for the Amazon Biome. At the same time, the new FC provided an amnesty of all fines and of 58% of the areas illegally deforested in the past, while providing more flexibility for the compensation of the remaining areas with creation of the environmental reserve quota (CRA) market (Soares-Filho et al., 2014). In order to partially compensate for the amnesty and legitimization, the new FC built upon the experience of the states of Mato Grosso and Pará and created the national rural environmental registry, CAR (an acronym for Cadastro Ambiental Rural in Portuguese). CAR aims to document the degree of environmental compliance of more than 5 million rural properties in Brazil. Registry in the CAR is a voluntary initiative of the land owner, although mandatory under the FC. Benefits of joining the CAR include a lower chance of receiving fines for not complying with environmental laws, access to additional lines of credit for farmers, and the opportunity to sell to supply chains that have deforestation agreements, like those for soy and cattle (Azevedo et al., 2017).

From the perspective of epidemiology, deforestation can be conceptualized as a disease that affects an underlying population (i.e., forests), causing the decrease or death of the individuals (i.e., clearing of certain areas). Here the implementation of the CAR is assumed to be a treatment that could reduce the loss of individuals. Therefore, the proposed approach provides an example of quasi-experimental design with similarities to clinical trials and other epidemiological studies. The remainder of this paper is organized as follows: Section 2 presents the data sets for both Mato Grosso and Pará States; Section 3 presents the proposed statistical methods; Section 4 presents the results; and the discussion and conclusions are presented in Section 5.

2. The Rural Environmental Registry in Mato Grosso and Pará States

CAR is a registry implemented in the states of Mato Grosso and Pará in 2009 and 2008, respectively, with the aim to speed up the process of properties becoming compliant with Brazil’s Forest Code and to improve the monitoring capabilities of the states. Thus, CAR is part of a land-use policy aiming to reduce illegal deforestation in the Brazilian Amazon. The registry contains georeferenced data of the borders, hydrography, and land-use of individual rural properties that can be combined with deforestation data provided by PRODES, a deforestation monitoring system developed by the Brazilian Institute for Space Research (INPE, http://www.obt.inpe.br/prodes/index.php). Currently, in these states there is no other dataset of rural properties as complete as CAR, and for this reason the location and land-use of these areas were not known prior to their entry in the registry. Similarly, it would be a mistake to compare the land-use dynamics of the properties inside CAR, which tend to be active farms, with indiscriminate areas outside the registry that may include public undesignated lands and other areas that are not likely to be deforested in the near future. In order to deal with this challenge, a BACI quasi-experimental design was adopted to classify the properties, for every year of the analysis, into two groups. The properties that were already registered inside CAR in a given year were considered as part of the intervention group for the policy. Conversely, the properties that in a given year are not yet in the registry but that would join CAR in a future year are considered as part of the control group, based on the assumption that they are similar to the intervention group in all aspects except for not yet being under the influence of that policy. For instance, in 2010 for the state of Pará, the properties that joined CAR in 2008 and 2009 are part of the intervention group, whereas the control group comprises those properties that will join CAR from 2011 onwards.

To ensure the robustness of the statistical analysis, a substantial number of properties had to be excluded from the study. To account for the limitation in the spatial resolution of PRODES, which is unable to detect clearings under 6.25 hectares, all properties with areas of less than 10 ha were excluded from the dataset, as were properties outside of the Amazon Biome in Mato Grosso State. Properties with an accumulated deforestation greater than 95% per year were also excluded to eliminate the possibility of the deforestation rate being influenced by the absence of forest in a specific group of properties. Properties regularized under other land and environmental policies were also excluded to avoid possible interference in the analysis of CAR’s effects on deforestation. Among the properties influenced by activities of land regularization and excluded from the study are rural settlement projects from the Brazilian Institute for Colonization and Agrarian Reform (INCRA, from the acronym for Instituto Nacional de Colonização e Reforma Agrária, in Portuguese) that are quite different from the properties that make up most of the private land in Pará and Mato Grosso. In the specific case of Mato Grosso State, properties which began the process of licensing (LAU, from the acronym for Licença Ambiental Única in Portuguese) before the creation of CAR’s instrument were excluded, as this is a more encompassing policy that also provides authorizations for legal deforestation. Finally, to improve the spatial consistency of the dataset, properties in CAR with more than 70% of their georeferenced area overlapped by neighboring properties were excluded because it was not possible to determine which of them were correct in the registry. In cases in which the overlap was smaller than 70%, manual inspection was used to exclude the property with the oldest CAR date. Furthermore, properties without a date of registration in CAR were excluded from our analysis. Therefore, 53.4% of the properties and 29.9% of the area from Pará State were not included in our analysis, leaving 19,466 CAR properties with a total area of 11.1 million hectares. In Mato Grosso State, 54.90% of the properties and 45.72% of the area from the original data were not included in our analysis, leaving 3,559 CAR properties with a total area of 3.1 million hectares. A more detailed description of the data for each state is given in the next section.

The dataset for both states were also subdivided to control for the effect of other factors in change of land-use. Specifically, to control for the effect of property size on deforestation rates, the dataset for both states were divided into three category groups according to their areas in terms of fiscal modules (FM), a measurement that varies for each municipality and is used as a criterion for the definition of legal rights and obligations. The first group consists of properties having up to four fiscal modules (one fiscal module represents 100 ha in most municipalities in the Amazon) that are considered “small properties” by law. In the second group are medium size properties that range between 4 and 15 FM (i.e., a property in the Amazon with 401 ha belongs to the medium size properties group). The third group are the large properties with more than 15 FM (i.e., usually more than 6,000 ha). Finally, in order to control for the effect of other regional policies (e.g. law enforcement actions, governmental subsidies) and economic factors (e.g. increases in commodity prices, variations in land price) that vary over time, the analyses were carried out with comparisons only within the same year.

2.1. Pará (PA) database

The sample used for Para State is described in Table 1. In Pará the number of small properties (up to 4 FM) is 13,487, 69.3% of the sample size and accounting for 11.42% of the sample area. Medium properties total 3,453 (17.7%), while occupying 18.32% of the sample area. There are 2,527 large properties (12.98%), with 70.27% of the sample area. In terms of area, small properties accounted for 1.27 million ha, the medium properties 2.04 million ha, and large properties 7.81 million ha. Therefore, the group of properties with more than 15 FM represented 70.27% all areas inside the dataset.

Table 1

Descriptive Statistics for the Samples for Pará and Mato Grosso. DOI: https://doi.org/10.1525/elementa.260.t1

Property size group (FM) Pará Mato Grosso

Properties Sampled – qty Area Sampled Thousands ha Properties Sampled – qty Area Sampled Thousands ha

up to 4 FM 13,487 (69.3%) 1,270 (11.42%) 1,923 (54.02%) 282 (9,01%)
from 4 to 15 FM 3,453 (17.7%) 2,040 (18.32%) 1,041 (29.26%) 739 (23.62%)
over 15 FM 2,527 (12.98%) 7,810 (70.27%) 595 (16.72%) 2,109 (67.37%)
TOTAL 19,467 11,120 ha 3,559 3,130 ha (t)

The time dynamics of enrollment of properties in CAR is shown in Table 2. In general, in 2008, less than 2.54% of the properties in the different size groups had been enrolled into CAR. By 2012, more than 96.5% of the properties had been enrolled in CAR.

Table 2

Dynamics of the enrollment of properties in CAR, from 2008 to 2012 in the state of Pará. DOI: https://doi.org/10.1525/elementa.260.t2

Property size group (FM) Enrollment of the properties 2008 2009 2010 2011 2012

up to 4 FM Before CAR (control) 99.40% 96.80% 75.44% 45.08% 3.48%
CAR 0.60% 3.20% 24.56% 54.92% 96.52%
from 4 a 15 FM Before CAR (control) 99.25% 90.90% 59.58% 34.67% 3.49%
CAR 0.75% 9.10% 40.42% 65.33% 96.51%
greater than 15 FM Before CAR (control) 97.66% 87.57% 52.13% 31.55% 2.55%
CAR 2.34% 12.43% 47.87% 68.45% 97.45%

2.2. Mato Grosso (MT) database

The sample used for Mato Grosso State is described in Table 1. The database of the state of Mato Grosso has 3,559 properties divided into three groups. The first group consists of properties of up to four fiscal modules with 1,923 (54.02%) properties and 9.01% of the sample area. The second group consists of properties with 4 to 15 modules with 1,041 properties (29.26%) and 23.62% of the area. The third group consists of properties with more than 15 modules and has 595 (16.72%) properties, accounting for 67.37% of the sample area. Properties with up to four FM had 282,006 ha; the second group had 739,756 ha; and the third group had 2,109,579 ha. Therefore, the group of properties with more than 15 FM represented 67.37% of the total sample area.

The time dynamics of the enrollment of the properties in the CAR is shown in Table 3. In general, in 2009, fewer than 11% of the properties in the different size groups had not been enrolled into CAR. By 2011, more than 97% of the properties had been enrolled in the CAR.

Table 3

Dynamics of the enrollment of properties in CAR, from 2009 to 2011 in the state of Mato Grosso. DOI: https://doi.org/10.1525/elementa.260.t3

Property size group (FM) Enrollment of the properties 2009 2010 2011

up to 4 FM not CAR (control) 97.27% 41.03% 1.10%
CAR 2.73% 58.97% 98.90%
from 4 a 15 FM not CAR (control) 90.36% 35.74% 1.66%
CAR 9.64% 64.26% 98.34%
over 15 FM not CAR (control) 89.60% 40.21% 2.08%
CAR 10.40% 59.79% 97.92%

3. Statistical methods

Let Yit be a random variable representing the deforested area (in ha) of property i at time t. Fit represents the area of forest (in ha) of property i at time t. Each property can be classified into one of three groups related to size. Let j[i], j[i] ∈ {1, 2, 3} be the index related to each size group, or simply j. For properties up to 4 FM, then j = 1; for properties from 4 to 15 FM, then j = 2; and for properties greater than 15 FM, then j = 3. Furthermore, each property i can be classified through time t into the CAR or Control groups. Thus, let k[i,t] be the index representing the CAR (k = 1) or Control (k = 2) groups) of property i at time t.

Assume that Yit is a random variable that represents the number of hectares deforested in property i at time t. Let Fit be total number of hectares of forest in property i at time t. If Yit were a discrete random variable, then one may identify the potential distribution of the random variable Yit as a Binomial distribution:

Yit ~  Binomial(Yit+Fit, ρit)
(1)

where ρit represents the probability of deforestation of one ha in property i at time t, P(Yit = 1) = ρit, and Yit + Fit is the total number of forest hectares at the beginning of time t in property i. It is known that maximum likelihood estimates require the probability distribution of the observations. However, quasi-likelihood estimates (Wedderburn, 1974) requires only the relation between the mean and the variance of the observations. Thus, assuming that Yit is a continuous random variable with mean E(Yit) = (Yit + Fit) · ρit and variance of Var(Yit) = (Yit + Fit) · ρit · (1 – ρit) then Equation 1 is also a possible approximation to the stochastic behavior of the random variable Yit. However, we found that in practice, the empirical distribution of the random variable did not fit the Binomial distribution, i.e., the deviance quality-of-fit statistic (Nelder and Baker, 1972) indicated the rejection of the null hypothesis of model fit (P-value = 0.0000). Alternatives such as Poisson, Negative Binomial, Zero Inflated Poisson and Quasi-Likelihood models were also evaluated but did not fit the deforestation data.

As an alternative solution, we evaluated the first moment, i.e., the mean of the random variable, hereafter defined as E(Yit) = τjkt. Confidence intervals and prediction intervals were generated using Monte Carlo simulations and Bootstrap resampling techniques.

3.1. Statistical comparison of the effect of CAR using Monte Carlo simulations

Monte Carlo simulations (Dwass, 1957) are widely applied to provide statistical inference when the underlying distribution of the statistic of interest, or test statistic, is unknown. In many cases, the probability distribution of the test statistic given a null hypothesis cannot be calculated. Nevertheless, samples from the null distribution can be drawn using simulations. For example, in spatial disease clustering analysis (Kulldorff, 1997), the statistical inference of a cluster candidate, given the null hypothesis of spatial randomness, is conducted by randomly assigning cases to areas in proportion to their underlying at-risk populations. In sequence, the test statistic of the most likely cluster in the simulated scenario is stored. The procedure is repeated many times, say 9,999 and the p-value is the proportion of simulations in which the simulated test statistic was higher (or lower) than the observed test statistic, using the original data set. Glasserman (Glasserman, 2003), for instance, applies Monte Carlo simulations in economic settings to evaluate the performance of test statistics under simulated economic scenarios. As previously mentioned, our random variable of interest is the deforested area. We rely on statistical methods from spatial epidemiology (Lawson, 2013), since deforested areas behave similarly to observed disease cases from underlying populations, which are forests. That is, we assume that deforested areas are observed cases from an underlying continuous population of forested areas.

For each size group j and class k, the annual deforestation rates are calculated using Equation 2:

τjkt=j[i]k[i,t]Yitj[i]k[i,t](Fit+Yit)
(2)

It is of interest to test whether the deforestation rates within the different size groups (k = {1, 2}), at time t are similar. For this question, the following null hypothesis can be written:

H0:τj1t=   τj2t
(3)

In practice, we want to test the null hypothesis that the deforestation rates between properties that have adopted the CAR over the years are similar to the deforestation rates of properties that have not adopted CAR over the years. For this question, we use a Monte Carlo simulation procedure to perform hypothesis testing. The algorithm is as follows:

Monte Carlo simulation procedure to test the null hypothesis of similarity between deforestation rates among properties which adopted CAR and the properties that did not adopt CAR.

  1. For each size group and time, calculate the deforestation rates of properties that adopt CAR and properties that did not adopted CAR:
    τj1t=j[i],1  Yitij[i],1(Fit+Yit)τj2t=j[i],2  Yitij[i],2(Fit+Yit)
    (4)
  2. Let the test statistic be the difference between the deforestation rates of properties that adopt CAR and properties that did not adopted CAR:
    κjt=τj1tτj2t
    (5)
  3. Conditional on the number of properties with non-zero deforestation at time t and size group j(njt), and the total number of deforestation at time t and size group, the distribution of the test statistic under the null assumes that the number of deforested units (in hectares) in randomly selected njt properties are proportional to the total number of forested areas in these properties:
    1. njt properties are randomly selected with no replacement.
    2. Let Yt be the total number of deforested areas at time t, Yt = Σi Yit. Let pi*t=Yi*t+Fi*tYt+Ft, i* ∈ njt and Ft = Σi*Fi* t, be the proportion of deforested and forested areas in property i*. In this case, under the null, it is possible to simulate the deforestation for each property i* at time t using a multinomial distribution.
      Yit ~multinomial(Yt, π=[p1t,  ,  pit])
      (6)
  4. S simulations are generated using the multinomial distribution. For each simulation, the test statistic (Equation 5) is calculated. Thus, a sample of the test statistic under the null hypothesis is obtained, (κjt(1),κjt(2),,κjt(S)).
  5. Finally, the values of κjt(.) are ordered and if the observed statistic is less than the 2.5% percentile or greater than the 97.5% percentile of the simulated values, then the null hypothesis is rejected at the 5% level.
  6. In addition, P-value estimates are based on the rank of the observed statistic with respect to the simulated values.

3.2. Counterfactual of CAR policy using bootstrap resampling for statistical forecasting

Following the estimation of the annual deforestation rates for each size group, it is of interest to compare the observed values of the remaining forest areas with a hypothetical scenario in which all properties did not adopt CAR. In this case, we aim at providing further evidence of the effects of CAR policy in reducing the deforestation and, therefore, resulting in larger areas of remaining forest. To account for the estimates and the associated variability we propose a bootstrap resampling procedure.

The bootstrap resampling procedure (Efron, 1979) is similar to Monte Carlo simulations. However, Monte Carlo simulations generally require the specification of a null hypothesis or a scenario from which samples are drawn. The Bootstrap procedure aims at estimating the distribution function F which generated the observed random sample, Y1, Y2, …, Yn. To do so, it creates bootstrap samples, Y1*, Y2*,  ,  Yn*, which are random samples from the original data set with replacement. These bootstrap samples can be used to estimate confidence intervals of a test statistic of interest. For example, suppose we want to estimate a confidence interval for the sample mean, Y¯. Thus, we can generate B bootstrap samples of size n and, for each bootstrap sample, calculate the bootstrap sample mean, Y¯1*,  Y¯1*, ,  Y¯B*. Confidence intervals are provided using the rank of the bootstrap sample means. Further details about bootstrap estimates can be found in Efron and Tibshirani (Efron and Tibshirani, 1994) and Dekking (Dekking, 2005).

In our case, we want to get samples from the distribution of deforestation rates for properties which did not adopt CAR and use these samples to forecast the behavior of all properties, if they had never been enrolled in CAR. We do this to provide further statistical evidence regarding the effectiveness of the CAR policy. Our proposed bootstrap procedure is shown next.

Bootstrap procedure to evaluate the hypothetical scenario in which all properties had never been enrolled in CAR:

  1. First, the period of interest is held fixed: t0, t1,…, tf. For the state of Pará the period the simulation is from 2007 to 2012, and for the state of Mato Grosso period of simulation is from 2008 to 2011. Thus, t0 is the baseline. The total forest area for the baseline was set as the reference level (100%).
  2. From t1 to tf the deforestation values, and consequently, the remaining forest were estimated for all properties but assuming they had the deforestation rates of the properties which did not adopt the CAR. Thus, the forecast of remaining forest areas over the period of interest (t1 to tf), and for the different size groups is given by equation 7:
    Fj,t+1=Fj,t×(1τj2t)
    (7)

To account for uncertainties related to the estimated deforestation rates and, consequently, estimate the uncertainties in the forecasted remaining forests, the following bootstrap resampling procedure was used:

  • 3. Using the observed values of forest and deforested areas in the database (Yit, Fit), B bootstrap samples were generated (b = 1, …, B). Each replicate has the same size of the original database, and it has been generated using resampling from the original database with replacement. For each bootstrap sample, the rates of deforestation were calculated using Equation 8, but only for k = 2 (properties that did not adopt CAR):
    τjktb=j[i]k[i,t]  Yitbj[i]k[i,t](Fitb+Yitb)
    (8)
  • 4. The bootstrap deforestation rates, calculated using Equation 8, were used to forecast the deforestation and forest areas for all properties as if they had not adopted CAR in the period, starting from the original baseline forest. Equation 9 shows the forecast equation:
    Fj,t+1=Fj,t×(1τj2tb)
    (9)
  • 5. The 2.5 and 97.5 percentiles of the B bootstrap forecasts were used to create an empirical bootstrap interval with 95% confidence. These intervals represent the projection of remaining forest areas throughout the studied period, assuming a scenario in which no properties had adopted CAR.

3.3. The space-time scan statistic

The space-time scan statistic (Kulldorff et al., 1998) aims at detecting clusters in space and time in which the observed number of cases is significantly higher than the expected number of cases, under the null hypothesis of space-time randomness. It scans the 3-dimensional space defined by the spatial geographical coordinates and the time period using a cylindrical window, as shown in Figure 1. The base of the cylinder represents the spatial component whereas the height represents the time range. Both the center of the base and the height of the cylinder are varied. By changing the location of the base, its radius, the starting and stopping times (i.e., the height) of the cylinder, different configurations are created. For each configuration, the observations inside and outside the cylinder are used to calculate a likelihood ratio statistic. The base and height configuration, i.e., the cylinder configuration with the maximum value of the likelihood ratio function (see Equations 10 and 11) represents the final cluster candidate. Secondary clusters can also be evaluated by selecting non-overlapping cylinders with large likelihood ratio statistics. Statistical inference is performed using Monte Carlo simulations, which provide statistical evidence for accepting or rejecting the null hypothesis. Further details are shown below.

Figure 1 

Space-time scan statistic using a cylinder scanning windows with variations in the height (time) and location (spatial component). The space-time scan statistic that aims at detecting clusters in space and time in which the observed number of cases is significantly higher than the expected number of cases, under the null hypothesis of space-time randomness. DOI: https://doi.org/10.1525/elementa.260.f1

The space-time scan statistic is a widely-used method to detect clusters in epidemiological settings. In our case, we consider the Forest units as the at risk population and the deforested units as disease cases. Under the null hypothesis of space-time randomness, the deforested units are uniformly distributed in the population (Forest units). Therefore, the number of deforested units in property i at time t is Poisson distributed with the expected number of cases, μit, proportional to the size of Forest units in the previous year (Fi,t – 1):

H0:Yit ~Poisson(μit=λFi,t1)
(10)

where Fi,t – 1 = Fit + Yit. Under the null hypothesis, λ^=D/F, where D is the total number of cases (deforested units) in space and time, and F is the total population (forest units) in space and time. Under the alternative hypothesis, there is one space-time cluster at an unknown location. Define Z as the set of all possible cylinder clusters z. For each cluster z (z ∈ Z) let dz and Fz be the number of deforested units and Forest units inside cluster z. The likelihood ratio test statistic associated with the most likely cluster is written as:

L(z^,p^,r^)L0=sup(dzμz)dz(DdzDμz)Ddz
(11)

Where μz is the expected number of cases under the null hypothesis, μz = Ddz/F. Monte Carlo simulations (Dwass, 1957) are applied to address the statistical significance of the most likely cluster. Further details can be found in Kulldorff et al. (Kulldorff et al., 1998) and Costa and Kulldorff (Costa and Kulldorff, 2014). The R code used in all our calculations is given as Supplemental information (Data S1).

4. Results

In epidemiological settings, the number of cases of diseases can be modeled as Poisson distributed with the expected number of cases proportional to the at-risk population. Our data set has a large number of properties with zero deforested areas. For the state of Mato Grosso, 95.7% of the records have zero deforested areas. For the state of Pará 84.1% of the records have zero deforested areas. Parametric statistical models, assuming a Poisson statistical distribution or a Negative Binomial, did not fit the data., i.e., the deviance quality-of-fit statistic indicated the rejection of the null hypothesis of model fit (P-value = 0.0000). Therefore, our final analysis is based on non-parametric modeling, using Monte Carlo simulations and Bootstrap, as described in section 3.

Table 4 shows the estimated deforestation rates for each 100 ha, for each property size group and year. The Monte Carlo inference results are shown in the last column. P-values greater than 5% (0.05) indicate that the null hypothesis that the deforestation rates without CAR and with CAR are similar, was not rejected. Results show that in 2010, for properties in the state of Mato Grosso with size up to 4 FM, there is evidence that the deforestation rates between CAR and not CAR properties are different. This is also true for properties of size from 4 to 15 FM and over 15 FM in the state of Mato Grosso, in 2009. For Pará, there is statistical evidence that the deforestation rates between CAR and not CAR are different for properties of size up to 4 FM for all years, except in 2012. This is also true for properties of size from 4 to 15 FM, except in 2009. For properties of size over 15 FM there is statistical evidence that the deforestations rates are different only in 2012.

Table 4

Comparative analysis of estimated deforestation rates between properties which adopted CAR and those which did not adopt CAR for the states of Pará and Mato Grosso. DOI: https://doi.org/10.1525/elementa.260.t4

Property size group Year Estimated deforestation rates for each 100 ha
CAR effect in deforestation rates (CAR/control – 1) P-value H0: without CAR = with CAR
Control (without CAR) CAR (with CAR)

State of Mato Grosso (2009–2011)

up to 4 FM 2009 0.9444 0.5672 –39.9% 0.4688
2010 1.4685 0.5967 –59.4% 0.0137
2011 1.6609 1.7424 4.9% 0.5796

from 4 to 15 FM 2009 0.2349 0.6956 196.1% 0.0162
2010 0.9089 0.7476 –17.7% 0.3016
2011 0.4001 0.5150 28.7% 0.5675

over 15 FM 2009 0.0988 0.0046 –95.3% 0.0258
2010 0.0818 0.0954 16.5% 0.3980
2011 0.0286 0.2201 669.9% 0.3694
Pará (2008–2012)

up to 4 FM 2008 4.5769 0.9037 –80.26% 0.0002
2009 3.5037 0.5933 –83.07% 0.0001
2010 3.7155 2.4231 –34.78% 0.0001
2011 2.6247 2.2073 –15.90% 0.0071
2012 1.8443 1.6189 –12.22% 0.2600

from 4 to 15 FM 2008 2.9747 0.0196 –99.34% 0.0003
2009 2.0516 1.8890 –7.93% 0.3109
2010 1.4162 0.8856 –37.47% 0.0001
2011 0.7118 0.5689 –20.08% 0.0408
2012 0.7658 0.4002 –47.74% 0.0404

over 15 FM 2008 1.2406 1.8518 49.26% 0.1394
2009 0.5014 0.6694 33.50% 0.2722
2010 0.4425 0.5759 30.14% 0.4423
2011 0.1604 0.2239 39.58% 0.5452
2012 0.0227 0.2144 846.17% 0.0876

Figure 2 shows the deforestation rates for each size group from 2009 to 2011 in the state of Mato Grosso. For properties with sizes of up to 4 FM, the deforestation rates increase in the period for both CAR and without CAR properties. For properties with sizes from 4 to 15 FM, the deforestation rates have higher values in 2010 and a slight decrease in 2011 for both CAR and without CAR properties. For properties with sizes over 15 FM, the deforestation rates present a slight decrease for properties without CAR, whereas for properties with CAR the deforestation rates present a slight increase.

Figure 2 

Mato Grosso Deforestation. Estimated deforestation rates for the state of Mato Grosso from 2009 to 2011. DOI: https://doi.org/10.1525/elementa.260.f2

Figure 3 shows the deforestation rates for each size group from 2008 to 2012 in the state of Pará. In general, the deforestation rates decrease in time for both properties which have enrolled in CAR and for those which have not enrolled in CAR. Properties which have enrolled in CAR present deforestation rates smaller than those properties which have not enrolled in CAR.

Figure 3 

Pará Deforestation. Estimated deforestation rates for the state of Pará from 2008 to 2012. DOI: https://doi.org/10.1525/elementa.260.f3

Figures 2 and 3 shows that, in general, properties with sizes over 15 FM presented smaller deforestation rates compared to properties with sizes of up to 4MF, and properties from 4 to 15 FM.

Table 5 presents the total forest area for the different size groups, at the baseline period which is 2007 for the state of Pará and 2008 for the state of Mato Grosso. These values are the sum of deforested and forest areas at the baseline. They were used as the reference values (100%) in the bootstrap simulations. Table 6 compares the observed deforested and forest areas with the simulated forest areas as if the properties have not enrolled in CAR policy. In addition, upper and lower limits with 95% confidence are provided. These results are also presented in Figures 4 and 5. Figure 4 compares the observed forest areas with the simulated forest areas if the properties had not enrolled into CAR policy in the state of Mato Grosso. The observed values for properties of the size groups “up to 4 FM” and “from 4 to 15 FM” are within the lower and upper limits which suggests that the observed levels of forest conservation could have happened even if no property had adopted the CAR policy. For properties with sizes over 15 FM the simulation results suggest that if the properties had not adopted CAR policy then the remaining forest areas in 2011 would have been larger than the observed.

Table 5

Forest areas (in ha) for the different size groups, used as baseline in the Bootstrap deforestation simulation algorithm. DOI: https://doi.org/10.1525/elementa.260.t5

State Baseline year Properties size group
Up to 4 FM from 4 to 15 FM over 15 FM

Pará 2007 616.398 1.058.964 3.947.784
Mato Grosso 2008 101.474 359.345 1.253.688

Table 6

Forest areas (in ha) for the different size groups and simulated forest area as if the properties have not enrolled in CAR policy. DOI: https://doi.org/10.1525/elementa.260.t6

Property size group Year Deforestation area Forest area Simulated forest area (without CAR) Lower limit (2,5%) Upper limit (97,5%)

Mato Grosso (2009–2011)

Up to 4 FM 2009 947 100527 100515.7 100129.5 100859.7
2010 1000 99527 99039.6 97976.8 99739.8
2011 1733 97794 97394.6 93808.5 99039.6

from 4 to 15 FM 2009 960 358385 358500.9 357734.5 358994.7
2010 2902 355483 355242.4 350312.6 357990.9
2011 1820 353663 353821.0 350128.9 355242.4

over 15 FM 2009 1157 1252531 1252449.9 1251226.5 1253175.9
2010 1123 1251408 1251425.0 1250405.6 1252090.3
2011 2708 1248700 1251067.2 1250126.9 1251425.0
Pará (2008–2012)

Up to 4 FM 2008 28045 588353 588186.3 586690.1 589628.2
2009 19991 568362 567578.2 566071.0 569137.5
2010 19176 549186 546489.9 545100.6 547913.5
2011 13131 536055 532146.2 530709.3 533499.0
2012 8717 527338 522331.9 518833.3 525798.6

from 4 to 15 FM 2008 31350 1027614 1027463.4 1024017.9 1030687.6
2009 20974 1006640 1006383.8 1002163.0 1010135.6
2010 12374 994266 992131.2 989055.2 994627.0
2011 6208 988058 985069.0 983109.5 986736.1
2012 4092 983966 977525.5 972548.1 981816.0

over 15 FM 2008 49553 3898231 3898806.6 3886366.3 3908580.8
2009 20285 3877946 3879258.0 3872354.9 3884091.5
2010 19050 3858896 3862092.8 3856977.6 3865488.7
2011 7452 3851444 3855897.5 3851212.5 3857985.7
2012 7850 3843594 3855023.9 3851823.9 3855755.0
Figure 4 

Simulation of remaining forest in Mato Grosso if properties did not adopt CAR. Simulation results for remaining forest areas in the state of Mato Grosso assuming the hypothetical scenario in which properties did not adopt CAR. DOI: https://doi.org/10.1525/elementa.260.f4

Figure 5 

Simulation of remaining forest in Pará if properties did not adopt CAR. Simulation results for remaining forest areas in the state of Pará assuming the hypothetical scenario in which properties did not adopt CAR. DOI: https://doi.org/10.1525/elementa.260.f5

Figure 5 compares the observed forest areas with the simulated forest areas if the properties had not enrolled into CAR policy in the state of Pará. As opposed to what was observed for the state of Mato Grosso, for properties of the size groups “up to 4 FM” and “from 4 to 15 FM” the observed remaining forest areas at the end of the period are above the upper limit of the simulated confidence interval. This, suggests that the CAR policy succeeded in reducing deforestation rates and, consequently, resulting in larger forest area as compared to the scenario in which none of the properties had adopted CAR. It is worth mentioning that even though there was statistical evidence of the effectiveness of the CAR policy, there was no increase whatsoever in the forest area. Similarly to the case with Mato Grosso State, for properties with sizes over 15 FM the simulation results suggest that if the properties had not adopted CAR policy then the remaining forest areas in 2012 would have been larger than the observed.

Figures 6 and 7 show the space-time cluster analysis. For visual representation of the results, a maximum cluster size parameter of 50% of the records for the state of Mato Grosso and 20% of the records for the state of Pará were chosen. Originally, a maximum cluster size parameter of 50% were applied to both states, as suggested by and Costa (Ribeiro and Costa, 2012). However, only one large cluster was detected in the state of Pará. In this case, a smaller maximum cluster of 20% was chosen in order to improve cluster detection (Ribeiro and Costa, 2012). Detected clusters with a P-value smaller than 5% (0.05) are shown in Figures 6 and 7. The Poisson model was applied and, as previously mentioned, the Poisson distribution did not fit the data. Therefore, it is believed that the P-values are overestimated. Nevertheless, the results do provide important insights about areas which were more vulnerable to deforestation.

Figure 6 

Spatial clustering analysis for the state of Mato Grosso (MT). (a) Detected clusters in the state of Mato Grosso are quite small. Squares represent clusters which include only one property. (b) Detected clusters: 2, 4, 5, 6, 7 and 8 were found to be statistically significant in 2011. Clusters 1, 8 and 19 were statistically significant in 2010, and the remaining detected clusters were found to be statistically significant in 2009. DOI: https://doi.org/10.1525/elementa.260.f6

Figure 7 

Spatial clustering analysis for the state of Pará (PA). (a) Detected cluster in the state of Pará are larger as compared to the detect clusters in the state of Mato Grosso. DOI: https://doi.org/10.1525/elementa.260.f7

Figure 6(a) shows that detected clusters in the state of Mato Grosso are quite small. Squares represent clusters which include only one property. Therefore, there are few areas in which the deforestation rates are higher than expected under the null hypothesis of space-time randomness. Figure 6(b) shows that the detected clusters numbers 2, 4, 5, 6, 7 and 8 were found to be statistically significant in 2011. Clusters 1, 8 and 19 were statistically significant in 2010, and the remaining detected clusters were found to be statistically significant in 2009. Therefore, among the detected clusters, most of them happened in 2009 and 2010.

Figure 7(a) shows that the detected clusters in the state of Pará are larger as compared to the detect clusters in the state of Mato Grosso. Cluster one has a size which is more than 20% of the state area. This cluster was detected in years 2008 and 2009. Clusters 5, 11, 15 and 17 were active in 2011, which is the last year of data. As compared to the state of Mato Grosso, the state of Pará presented larger cluster areas. The state of Pará also presented larger deforestation rates in the clusters, as compared to its global rate.

5. Discussion and conclusion

We applied statistical epidemiological models to evaluate the deforestation rates in the states of Mato Grosso and Pará, in Brazil. Standard statistical models for count data which are the Binomial, Poisson and Negative Binomial were tested and did not fit properly the data. The data shows that most properties had zero deforestation in a given year. A zero-inflated model, was also evaluated and did not achieve a proper fit either. Thus, statistical simulation tools derived from epidemiology were developed in order to evaluate whether the governmental policy named CAR achieved its highest goal, to reduce the deforestation rates.

A statistical comparison between properties which did adopt CAR and those which did not adopted CAR in the studied period showed that the properties inside the Rural Environmental Registry have reduced their deforestation rates in some property classes and time periods, but this effect has not been systematic across time and space. This indicate that the effectiveness of CAR in reducing deforestation was only partial. For small properties, CAR seemed to have a stronger effect during the initial years of implementation but this result faded during time. For medium and high properties, alternating higher results between CAR and without CAR properties suggest that other factors than CAR may be influencing the deforestation dynamics.

Space-time cluster analysis were applied to the data in order to detect areas and time periods in which the deforestation rates were higher than the expected rate under the null hypothesis of space-time randomness. Larger clusters were found in state of Pará and smaller clusters were found in the state of Mato Grosso. The Poisson model was used in the cluster analysis but since previous statistical analysis had revealed that the Poisson model did not fit the data properly, the results represent exploratory analysis. Future works aim at developing a cluster analysis using a proper statistical model which accounts for over dispersion in the data.

As opposed to purely spatial analysis, space-time cluster analysis may indicate live clusters, i.e., clusters which comprise the last year of data, indicating that, in these clusters, deforestation may still happen in following years. Furthermore, clusters which do not comprise the last year of data indicate properties in which deforestation had decreased significantly. Results indicate smaller clusters of deforestation in the state of Mato Grosso and larger clusters in the state of Pará. Results also show live clusters in both states indicating a continuous deforestation process in some groups of properties.

This study has both policy and methodological implications. On the policy front, it indicates that CAR has not been able to reduce deforestation across the entire period and property sizes, reducing its effectiveness in small properties over time. This highlights the need of not only incentivizing farmers to join the registry but also actively use it to tackle illegal deforestation, and inform the population about the increased monitoring capabilities of the government in order to avoid deforestation. From a methodological point of view, the proposed statistical models contain some advantages over the econometric and simulation models that are currently widely applied to evaluate environmental policies. In contrast to econometric models that require detailed economic and social data (Angelsen, 1999; Pfaff et al., 2008), the proposed statistical models can be applied to situations in which such data is not available. The proposed methods also use the entire dataset without the need to calculate the difference in differences between matched subsets of samples. Similarly, the proposed statistical method provides some advantages in relation to simulation methods since it gives results that rely less on the modeler’s design choices or on the assumptions of specific statistical distributions. For these reasons, we believe that the present statistical models may find a wide application of similar policy evaluation problems, especially in data-poor contexts in developing countries.

Data Accessibility Statement

The data can be requested by contacting macosta@ufmg.br.

Supplemental File

The supplemental file for this article can be found as follows: