Keywords: Deforestation, Mining, Protected areas, Panel data, Spatial econometrics, Sub-Saharan Africa. JEL codes C23, L70, O13, N57, Q23, Q32

African countries are natural resource-rich. The continent has natural forests, homes of endemic biodiversity and various ores. This richness brings hope for sustainable and inclusive development in a continent whose population is rapidly growing. It also raises fears of environmental degradation. This article studies mining-driven deforestation using unique finescale data from 2001 to 2019. The dataset covering all Sub-Saharan African countries entails 2,207 polygons with an average size of about 12,000 square kilometres. 926 polygons were forested in 2001, of which 198 hosted industrial mines. A spatial autoregressive model allows taking dependence between deforestation decisions at the polygon level. The econometric results show that an additional mine increases deforestation by about 155 square kilometres.

Protected areas mitigate deforestation poorly. One hundred square kilometres under protected areas enable only a 9.7 square kilometres reduction in forest loss. More than doubling protected areas would be necessary to offset mining-driven forest loss. Protected areas cannot alone mitigate the adverse effects of mining on forest loss and other environmental consequences. Moreover, the effectiveness of protected areas is not uniform across space: it vanishes in highly conflicted regions.

Introduction

Many African countries are rich in natural resources and aspire to better livelihoods. With a steadily growing population expected to be just under four billion by the end of the 21st century,1 African countries face a challenge: achieving inclusive and sustainable development.

Tapping natural resources, particularly ores, can generate significant income and reduce poverty. Today, according to the World Development Indicators, mineral and forest rents are above the world averages as a percentage of GDP. Still, natural resource extraction can also irreversibly damage essential natural assets for sustainable development, especially the forest.

21.7% of tropical African forests have been deforested since 1900 [START_REF] Aleman | Forest extent and deforestation in tropical Africa since 1900[END_REF]. West and East African forests have practically vanished. In recent years, while deforestation has slowed down worldwide, it seems to have accelerated in Africa, with a net forest loss of 3.94 million ha per year from 2010 to 2020 against 3.4 million ha per year in the previous decade [START_REF] Mansourian | Review of Forest and Landscape Restoration in Africa 2021. Accra: The Food and Agriculture Organization of the United Nations & the African Union Development Agency-NEPAD[END_REF]. The deforestation and forest degradation drivers are multiple. The literature [START_REF] Geist | Proximate causes and underlying driving forces of tropical deforestation[END_REF] distinguishes between the proximate causes of deforestation (agriculture and pastoral expansion, wood extraction, infrastructure extension, mining activities) and underlying causes (macroeconomic variables, societal factors). On a global scale, agriculture is the main proximate driver of deforestation. A meta-analysis concludes that deforestation is more likely when the economic returns of agriculture are higher [START_REF] Busch | What Drives Deforestation and What Stops It? A Meta-Analysis[END_REF].

Africa is on the verge of a mining boom [START_REF] Edwards | Mining and the African Environment[END_REF]. With its promise of high incomes, the mining sector is expected to grow in Africa. The 5th edition of the mining contribution index of the International Council on Mining and Metals (ICMM) evidences that five African countries, including the Democratic Republic of Congo and Madagascar, rank high in the list of mining-dependent countries. This dependency will likely endure as 30% of the world's total mineral reserves is in Africa [START_REF] Adu | Africa's mineral economies : breaking their dependence on mining[END_REF]. The existing literature evidence several effects of mining development in Sub-Saharan African (SSA) countries. For instance, mining positively impacted African agricultural sectors though the authors also This article studies the link between mining activities and deforestation and questions the effectiveness of protected areas in response to mining-induced deforestation. More precisely,

we aim to answer the two following questions. How do mining activities contribute to deforestation? How do conservation instruments such as protected areas dampen miningdriven deforestation?

We estimate a deforestation spatial econometric model that allows us to consider interactions between neighbouring spatial units. Each spatial unit covers 12,070 square kilometres on average. Overall, we have 2,207 spatial units, namely polygons, from 2001 to 2019, of which 926 are forested at the beginning of the study period. The dataset gathers information on deforestation, mining activities, protected areas and other relevant socioeconomic variables affecting deforestation. To our knowledge, our study is the first to address mining-driven deforestation using sub-national data. This level of analysis is the most relevant because clearing and land use conversion both take place at a fine spatial scale. Existing studies are conducted at the national level [START_REF] Azomahou | Strategic Environmental Commitment and Climate Change in Africa: Evidence on Mining and Deforestation[END_REF]. We contribute to the literature on the effectiveness of protected areas in curbing deforestation since we examine the role of protected areas as a lever for mitigating deforestation induced by mining activity, which has never been investigated in SSA. The estimation results show that mining activities increase deforestation while protected areas reduce deforestation. Moreover, it does not appear that the presence of protected areas dampens the impact of mining on deforestation. We highlight a spatial heterogeneity: the negative t impact of mines on forests and the poor effect of protected areas occur when the local institutional quality is poor.

The remainder of the article is as follows. Section 2 reviews the existing literature. We present the econometric framework in Section 3. We detail the elaboration of the fine-scale data set from which we extract descriptive statistics in section 4. Section 5 successfully gives the main results and estimates how much mining drives forest losses in Sub-Saharan Africa.

We provide concluding remarks in section 6.

Literature review

We will first present the studies devoted to the impact of mining activities on deforestation.

We will then review the main findings of studies dealing with the relationship between protected areas (and forest management) and deforestation. Finally, we will describe the few studies focusing on the role of protected areas as a tool for mitigating the effects of mining on forest cover and present our hypotheses.

Mining activity and deforestation

Several studies have studied the link between mining activities and deforestation. Most of them focus on the Amazonian forest and use high-resolution geospatial data. For instance, mining significantly increased deforestation in the Brazilian Amazon [START_REF] Sonter | Mining drives extensive deforestation in the Brazilian Amazon[END_REF].

Moreover, forest losses extend well beyond the mining lease boundaries and account for 9% of deforestation between 2005-2015. In Colombia, the contribution of legal mining activities inside concessions to deforestation grew during the 2010s and reached a 5.6% peak in 2017.

The two minerals mainly causing deforestation are gold and coal [START_REF] González-González | Growing mining contribution to Colombian deforestation[END_REF]. Some artisanal-scale gold mining activities would be particularly detrimental to forest conservation. Indeed, these activities are often illegal and therefore do not comply with environmental regulations. This phenomenon is reported in several Latin American countries, for instance: Suriname [START_REF] Peterson | Deforestation and forest regeneration following small-scale gold mining in the Amazon: the case of Suriname[END_REF] or Peru [START_REF] Caballero Espejo | Deforestation and Forest Degradation Due to Gold Mining in the Peruvian Amazon: A 34-Year Perspective[END_REF].

In the case of the Brazilian Amazon, deforestation of illegal gold mining increased by more than 90% from 2017 to 2020 [START_REF] Siqueira-Gay | The outbreak of illegal gold mining in the Brazilian Amazon boosts deforestation[END_REF]. Furthermore, once abandoned, the mining area is not correctly restored, and therefore the regeneration of the primary forest is hampered. Periods of rising gold prices are particularly detrimental to forest conservation in the Peruvian Amazon [START_REF] Swenson | Gold Mining in the Peruvian Amazon: Global Prices, Deforestation, and Mercury Imports[END_REF]. In Latin America, the increase in the demand for gold after the international financial crisis fueled deforestation from 2007 to 2013 [START_REF] Alvarez-Berríos | Global demand for gold is another threat for tropical forests[END_REF].

Only a few studies have examined the impact of mining activities on deforestation in Asia.

For instance, there is evidence of adverse effects of mining activities on forest cover at the district level in India [START_REF] Ranjan | Assessing the impact of mining on deforestation in India[END_REF]. The effect is heterogeneous and depends on the mineral involved. In Indonesia, mining activities are increasingly responsible for the loss of forest cover from 2001 to 2016 [START_REF] Austin | What causes deforestation in Indonesia?[END_REF]. However, palm oil plantations encroachments outweigh mining activities since the former represents 23% of deforestation compared to 2%.

Africa has experienced lower deforestation rates than South America and South and South East Asia for several decades. For instance, oil and gas receipts substantially reduced deforestation from 2000 to 2005 [START_REF] Rudel | The national determinants of deforestation in sub-Saharan Africa[END_REF]. The extractive sector's contribution to urbanisation may have hampered deforestation's proximate drivers. However, a recent study relying on panel data from 2001 to 2017 found a positive effect: a one-point percentage of GDP increase in mineral rents generated about 50 square kilometres of forest loss [START_REF] Azomahou | Strategic Environmental Commitment and Climate Change in Africa: Evidence on Mining and Deforestation[END_REF]). An oil and mineral-fueled forest transition may have started in Africa, especially in the Congo Basin humid forest. Indirect effects of deforestation in the surroundings of mining areas are likely at work. Direct deforestation within the mining areas concerns few countries, while indirect deforestation is a problem for two-thirds of tropical countries. The indirect deforestation impact is remarkably high in some African countries, such as Gabon and Zambia [START_REF] Giljum | A pantropical assessment of deforestation caused by industrial mining[END_REF].

Protected areas and deforestation

"A protected area is a clearly defined geographical space, recognised, dedicated and managed, through legal or other effective means, to achieve the long-term conservation of nature with associated ecosystem services and cultural values." (IUCN Definition 2008). 2 14.6% of the land area was designated as protected, and 16% of the forest fell within a legally established protected area in 2015. In Africa (Democratic Republic of Congo), the proportion of forest areas with legally protected areas was 23.37% (12.38%) in 2000 and 25.73% (18.45%) in 2020 [START_REF] Ritchie | Biodiversity, Our World in Data[END_REF].

A bulk of econometric studies study the effectiveness of protected areas. Early studies date back to the early 2000s [START_REF] Joppa | Global protected area impacts[END_REF][START_REF] Nelson | Effectiveness of Strict vs. Multiple Use Protected Areas in Reducing Tropical Forest Fires: A Global Analysis Using Matching Methods[END_REF]. The main challenge is the location bias of protected areas (Cropper, Puri and Griffiths, 2001; Joppa and Pfaff, 2 Protected areas can also be managed locally, nationally, or internationally. Moreover, the degree of legal protection provided by the protected area depends on their category. The different categories are the following: strict nature reserve (Ia); wilderness area (Ib); national park (II); natural monument of feature (III); habitat/species management area (IV); protected landscape/seascape (V); protected areas with sustainable use of natural resources (VI). The most restrictive categories are I, II and III. Categories IV, V and VI allow a sustainable use of resources. Source: IUCN available at https://www.iucn.org/theme/protected-areas/about.

2009

). Authors usually address this issue by implementing matching methods with control groups. Once the location bias is controlled for, the authors found that protected areas reduce deforestation. Most existing results pertain to Latin America: Costa Rica [START_REF] Andam | Measuring the effectiveness of protected area networks in reducing deforestation[END_REF][START_REF] Pfaff | Park Location Affects Forest Protection: Land Characteristics Cause Differences in Park Impacts across Costa Rica', The B.E[END_REF][START_REF] Robalino | Evaluating Interactions of Forest Conservation Policies on Avoided Deforestation[END_REF][START_REF] Robalino | Heterogeneous Local Spillovers from Protected Areas in Costa Rica[END_REF], Guatemala and Mexico [START_REF] Bray | Tropical deforestation, community forests, and protected areas in the Maya Forest[END_REF], the Brazilian state of Acre [START_REF] Pfaff | Governance, Location and Avoided Deforestation from Protected Areas: Greater Restrictions Can Have Lower Impact, Due to Differences in Location[END_REF] or Sumatra in South East Asia [START_REF] Gaveau | Evaluating whether protected areas reduce tropical deforestation in Sumatra[END_REF].

Heterogeneity effects in the impact of protected areas on deforestation may occur. For example, in the case of the legal Amazon, the protected areas with the highest impact are those located near cities and roads [START_REF] Pfaff | Protected area types, strategies and impacts in Brazil's Amazon: public protected area strategies do not yield a consistent ranking of protected area types by impact[END_REF]. Strictly protected areas are more effective. Existing studies on Brazil support that claim once accounting for location bias [START_REF] Nolte | Governance regime and location influence avoided deforestation success of protected areas in the Brazilian Amazon[END_REF][START_REF] Kéré | Addressing Contextual and Location Biases in the Assessment of Protected Areas Effectiveness on Deforestation in the Brazilian Amazônia[END_REF]. The results hold with considering contextual bias and spatial dependence [START_REF] Kéré | Addressing Contextual and Location Biases in the Assessment of Protected Areas Effectiveness on Deforestation in the Brazilian Amazônia[END_REF]. Spatial interactions are another critical issue. Deforestation in one location could impact deforestation in neighbouring areas, for instance, through transportation infrastructure development [START_REF] Angelsen | Playing games in the forest: State-local conflicts of land appropriation[END_REF][START_REF] Schwartz | Optimal protected area implementation under spillover effects[END_REF]. These spatial interactions are likely at work in the "arc of deforestation" in Brazil. In addition, protected areas can foster deforestation leakages. Deforestation leakage occurred into forests from concession areas in the Peruvian Amazon [START_REF] Oliveira | Land-Use Allocation Protects the Peruvian Amazon[END_REF]. Parks facing tremendous deforestation pressure show more significant leakage in Costa Rica [START_REF] Robalino | Heterogeneous Local Spillovers from Protected Areas in Costa Rica[END_REF]. However, the proximity to a protected area can also contribute to reducing forestry activity, for example, by creating more difficulties in accessing the forest resource. Indigenous lands raise deforestation nearby, contrary to federal-protected areas in the Brazilian Pará State [START_REF] Herrera | Impacts of protected areas vary with the level of government: Comparing avoided deforestation across agencies in the Brazilian Amazon[END_REF]. Strictly protected areas and indigenous lands allow reducing deforestation, unlike sustainable protected areas in the Brazilian Legal Amazonia [START_REF] Amin | Neighborhood effects in the Brazilian Amazônia: Protected areas and deforestation[END_REF]. Moreover, these two types of protected areas generate a positive spillover effect: they reduce deforestation in their vicinity.

There are similar questions about the effectiveness of forest management plans which are considered a step towards sustainable forest management, particularly in the Congo Basin (Democratic Republic of Congo), which represents the second largest primary forest in the world [START_REF] Karsenty | Regulating industrial forest concessions in Central Africa and South America[END_REF]. These plans entail selective logging to ensure maximum harvest rates while at the same time preserving the resource. Protected areas surrounded by logging concessions operated with a forest management plan ("unified conservation landscape") could be considered as means to both achieve economic development and biodiversity conservation [START_REF] Brandt | Deforestation and timber production in Congo after implementation of sustainable forest management policy[END_REF]. Deforestation and timber production are higher in concessions with registered forest management (Brandt, Nolte andAgrawal, 2016, 2018) though the results are questioned [START_REF] Karsenty | Deforestation and timber production in Congo after implementation of sustainable management policy: A reaction to the article by J.S. Brandt[END_REF]. Between 2000 and 2010, deforestation was also found to be significantly lower in concessions operating under a forest management plan [START_REF] Tritsch | Do forest-management plans and FSC certification help avoid deforestation in the Congo Basin?[END_REF].

Mining, protected areas and deforestation

A very understudied issue is the effectiveness of protected areas in the face of mininginduced deforestation. [START_REF] Weisse | Conservation Beyond Park Boundaries: The Impact of Buffer Zones on Deforestation and Mining Concessions in the Peruvian Amazon[END_REF] studied the effect of protected area buffer zones on formal and informal mining extent in the Peruvian Amazon. These buffer zones have been poorly studied because of the ambiguity of their management rules and their sometimes-informal status. Nevertheless, these buffer zones cover more than 10% of the country and positively impact forest cover by limiting the extent of mining concessions.

However, they could be more efficient in mitigating the development of illegal mining activities.

Expanding mining concessions increased the forest cover loss from 1990 to 2010 in the Democratic Republic of Congo (DRC) [START_REF] Butsic | Conservation and conflict in the Democratic Republic of Congo: The impacts of warfare, mining, and protected areas on deforestation[END_REF]. One of the particularities of the Congo Basin is the prevalence of conflicts. It appears that they fuel deforestation, but in times of conflict, the impact of mining concession on deforestation was mitigated. Moreover, protected areas reduced deforestation, even in times of conflict.

In this article, we seek to answer two questions. Is mining a driver of deforestation in Sub-Saharan Africa? Are protected areas an effective tool for mitigating the effects of mining on deforestation? These questions are relevant in the SSA context, where low institutional quality prevails and where mining companies can use corruption to circumvent environmental regulation.

Methodology

We present first the econometric framework. It takes advantage of fine-scale data, allowing the investigation of spatial dependence in activities potentially contributing to deforestation.

Then we discuss the identification of neighbours and how we intend to interpret the results.

Econometric framework

The spatial lag model is theoretically appropriate for investigating spatial dependence (e.g. [START_REF] Ndiaye | Road tax interactions among local governments: a spatial panel data analysis of the French case over the period 1984-2000[END_REF]. 3 In this paper, we claim that deforestation in one area interacts with neighbours' deforestation. Following the literature, the spatial dependence of deforestation between polygons is theoretically interpreted as evidence that the decisions conducing to deforestation are strategic complements (Brueckner, 2003; Schwartz et al., 2022). 4 Deforestation in one area favours deforestation in its vicinity by facilitating access to the forest and thus reducing the costs of deforestation.

Building on this theoretical intuition, we estimate a spatial panel data model in which the level of deforestation in a spatial unit (see the definition of spatial units, namely polygons in Where 𝐹𝑜𝑟𝑒𝑠𝑡_𝑙𝑜𝑠𝑠 𝑖𝑡 refers to the level of forest loss observed for the spatial unit 𝑖 at period 𝑡. 𝑤 𝑖𝑗 corresponds to the spatial weight's matrix that is an 𝑁 × 𝑁 pre-specified rownormalised weights matrix with zeros on the diagonal. ∑ 𝑁 𝑗=1,𝑗≠𝑖 𝑤 𝑖𝑗 𝐹𝑜𝑟𝑒𝑠𝑡_𝑙𝑜𝑠𝑠 𝑗𝑡 thus refers to the spatially lagged deforestation variable and represents the average deforestation of neighbouring spatial units. The spatial scalar parameter 𝜌 reflects the endogenous spatial interaction between a spatial unit and its neighbours. 𝜌 = 0 means no spatial interaction. If 𝜌 is positive, the level of deforestation in a spatial unit tends to mimic the neighbours', suggesting a complementarity effect. On the other hand, a negative 𝜌 means a substitution in deforestation levels that may result from deforestation leakage.

𝐿𝑎𝑔𝑃𝐴 𝑖𝑡 and 𝑀𝑖𝑛𝑒 𝑖𝑡 are respectively the one-year-lagged value of protected areas and the number of mines for unit 𝑖 at period 𝑡. The interactive variable 𝐿𝑎𝑔𝑃𝐴 𝑖𝑡 × 𝑀𝑖𝑛𝑒 𝑖𝑡 assesses the specific influence of protected areas on mining-driven forest loss. 𝑥 𝑖𝑡 𝑘 is the 𝑘-th control variable for unit 𝑖 at period 𝑡. We add spatial unit-fixed effects 𝜇 𝑖 to capture time-invariant spatial unit-specific attributes such as natural endowments or distance to markets, and period-fixed effects 𝜂 𝑡 to capture common trends in deforestation or the influence of other variables, such as international commodity prices. The omission of these characteristics might bias the estimates in a panel data analysis [START_REF] Elhorst | Applied Spatial Econometrics: Raising the Bar[END_REF][START_REF] Baltagi | Econometric Analysis of Panel Data[END_REF].

Besides the simultaneity bias generated by the spatial lag of the dependent variable, namely the lagged forest loss, another issue comes from potential additional endogenous variables. In particular, we use the one-year-lagged value of the protected areas variable to avoid simultaneity bias between protected areas and forest loss.6 𝜀 𝑖𝑡 is the spatially correlated error term such as 𝜀 𝑖𝑡 = λ ∑ 𝑁 𝑗=1,𝑗≠𝑖 𝑤 𝑖𝑗 𝜀 𝑗𝑡 + 𝑢 𝑖𝑡 where 𝑢 𝑖𝑡 represents idiosyncratic shocks uncorrelated across spatial units and over time.

According to our hypotheses, one should observe the following: 𝛽 1 > 0 namely mining activities favour deforestation; 𝛽 2 < 0, namely protected areas dampen deforestation. Moreover, if protected areas mitigate mining-induced deforestation, then we have 𝛽 3 < 0, which means that the impact of mining on deforestation should be lower in the larger protected areas.

The previous specification is the benchmark model to uncover spatial interactions in the deforestation process. We add another specification to check the validity of the results by allowing for strong cross-sectional dependence under the form of common factors [START_REF] Pesaran | Estimation and Inference in Large Heterogeneous Panels with a Multifactor Error Structure[END_REF][START_REF] Chudik | Weak and strong cross-section dependence and estimation of large panels[END_REF]. 7 As a robustness check, we, therefore, have the following equation:

𝐹𝑜𝑟𝑒𝑠𝑡_𝑙𝑜𝑠𝑠 = 𝜌 ∑ 𝑁 𝑗=1,𝑗≠𝑖 𝑤 𝑖𝑗 𝐹𝑜𝑟𝑒𝑠𝑡_𝑙𝑜𝑠𝑠 𝑗𝑡 + 𝛽 1 𝑀𝑖𝑛𝑒 𝑖𝑡 + 𝛽 2 𝐿𝑎𝑔𝑃𝐴 𝑖𝑡 + 𝛽 3 𝐿𝑎𝑔𝑃𝐴 𝑖𝑡 𝑀𝑖𝑛𝑒 𝑖𝑡 + 𝛾 𝑘 𝑥 𝑖𝑡 𝑘 + Γ 1 𝐹𝑜𝑟𝑒𝑠𝑡_𝑙𝑜𝑠𝑠 ̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅ 𝑡 + Γ 2 𝑀𝑖𝑛𝑒 ̅̅̅̅̅̅̅ 𝑡 + Γ 3 𝐿𝑎𝑔𝑃𝐴 ̅̅̅̅̅̅̅̅̅ 𝑡 + Γ 4 𝐿𝑎𝑔𝑃𝐴 × 𝑀𝑖𝑛𝑒 ̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅ 𝑡 + Γ 5 𝑥̅ 𝑡 𝑘 + 𝜇 𝑖 + 𝜂 𝑡 + 𝜀 𝑖𝑡 (2)
where 𝐹𝑜𝑟𝑒𝑠𝑡_𝑙𝑜𝑠𝑠 ̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅ 𝑡 = 1/𝑁 ∑ 𝑁 𝑖=1 𝐹𝑜𝑟𝑒𝑠𝑡_𝑙𝑜𝑠𝑠 𝑖𝑡 is the cross-sectional average of the deforestation variable. 𝑀𝑖𝑛𝑒 ̅̅̅̅̅̅̅ 𝑡 , 𝐿𝑎𝑔𝑃𝐴 ̅̅̅̅̅̅̅̅̅ 𝑡 , 𝐿𝑎𝑔𝑃𝐴 × 𝑀𝑖𝑛𝑒 ̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅ 𝑡 and 𝑥̅ 𝑡 𝑘 are the cross-sectional averages of the independent variables at time 𝑡. These common factors are parameters to be estimated [START_REF] Shi | A spatial panel data model with time varying endogenous weights matrices and common factors[END_REF].

Identification of neighbours and interpretation of the results

Building the spatial weight matrix is crucial in identifying spatial neighbours. We rely on the 𝑘-nearest matrix with 𝑘 = 5. Hence, 𝑤 𝑖𝑗 is equal to 1 if 𝑗 is one of 𝑖's five nearest neighbours 7 Initially, in panel data, a common strategy to deal with unobservable heterogeneity set about (i) using a transformation of variables (fixed effects model) or (ii) by setting out assumptions about the structure of the error term (random effects model). However, in these both cases, a restriction is made on the form of heterogeneity for each individual that is constant in the temporal dimension. By definition, common factors and spatial panels make it possible to capture interactions between individuals (Bouayad Agha, Le Gallo and Védrine, 2018). In addition, the presence of common factor allows to considering residual unobserved effects. In spatial econometrics, [START_REF] Shi | A spatial panel data model with time varying endogenous weights matrices and common factors[END_REF] proposed a decomposition of the error term in SAR panel into a common factor component (strong spatial dependence) and an idiosyncratic component (weak spatial dependence). In our study, as additive individual and time effects can potentially not be explained entirely the heterogeneity effects, we also add common factor component in order to verify the robustness of our results in presence of weak and strong cross-section dependence [START_REF] Chudik | Weak and strong cross-section dependence and estimation of large panels[END_REF].

and 0 otherwise. We also consider two alternative weight matrices: Gabriel neighbours and the inverse distance. 8The spatial lag variable does not allow directly interpreting the coefficients from equations

(1) and ( 2). We, therefore, compute partial derivatives, i.e. marginal effects [START_REF] Lesage | Introduction to Spatial Econometrics[END_REF]. The matrix of partial derivatives of 𝐹𝑜𝑟𝑒𝑠𝑡_𝑙𝑜𝑠𝑠 𝑖𝑡 with respect to an explanatory variable 𝑧 𝑖𝑡 is:

𝜕𝐹𝑜𝑟𝑒𝑠𝑡_𝑙𝑜𝑠𝑠 𝑖𝑡 𝜕𝑧 𝑖𝑡 = ((𝐼 -𝜌 ∑ 𝑁 𝑗=1,𝑗≠𝑖 𝑤 𝑖𝑗 ) -1 ) δ (3)
Where 𝛿 is the coefficient of the explanatory variable 𝑧 𝑖𝑡 .

A change in an explanatory variable in a spatial unit directly affects that spatial unit and indirectly affects the neighbouring ones. The total effect of the variable on deforestation is the sum of the direct and indirect effects.9

4 Data

We build an original panel dataset. The following subsections describe the observation units, namely the spatial units that are polygons. We then present the variables and give descriptive statistics.

Polygons in Africa

We relied on geolocalised data from [START_REF] Hansen | High-Resolution Global Maps of 21st-Century Forest Cover Change[END_REF] to build the most comprehensive dataset from 2000 to 2019. These data define the spatial units of study that are square polygons covering all SSA countries. 10 Each polygon has an area of approximately 12,070 square kilometres. It is the finest possible subdivision which allows obtaining units with available observations. Overall we have 2,207 polygons in SSA, 926 of which were forested in 2001. Forested polygons in 2001 had at least 10% of their area covered by the forest (Figure A.1 in Appendix). We take advantage of the time dimension to define four five-year periods.

We eventually have 926 × 4 = 3,704 observations.

We use raster files containing the necessary information for each variable to extract the geolocated data belonging to each polygon. These high-definition image files containing geolocated information for each variable came from various sources. Table A-1 in Appendix overviews our variables and their sources.

Study variables

We present below the dependent variable, our interest variables and other controls.

Dependent and interest variables

𝐹𝑜𝑟𝑒𝑠𝑡_𝑙𝑜𝑠𝑠 is our measure of deforestation that we borrow from the Hansen et al.

database [START_REF] Hansen | High-Resolution Global Maps of 21st-Century Forest Cover Change[END_REF]. 11 The variable covers the 2000 to 2019 period. Measures are 10 Gridded data is quite widespread in econometrics when faced with a lack of data at the micro level. For example, [START_REF] Buys | Determinants of a Digital Divide in Sub-Saharan Africa: A Spatial Econometric Analysis of Cell Phone Coverage[END_REF] at an approximately 30 × 30-meter resolution. In this database, tree cover is any vegetation taller than 5 metres. Thus, the tree cover could represent natural forests or plantations. The loss of vegetation cover can refer to deforestation due to human activities or natural causes such as extreme weather events or forest fires. The deforestation variable is the cumulated tree cover loss over each period in the polygon.

The World Database on Protected Areas (WDPA) gives the surface of protected areas. 12 It allows identifying other effective area-based conservation measures (OECM). 13 These databases are products of the UN Environment Program and IUCN (International Union for Conservation of Nature).

The Minex Consulting 14 database delivers information about the geolocalisation of each industrial mining operation, its state of operation, and its year of opening or discovery. Thus, for each unit, we have the number of industrial mines present for each period, irrespective of their status. 15

Control variables

We control for other drivers of deforestation, such as climate conditions (𝑇𝑒𝑚𝑝 and 𝑅𝑎𝑖𝑛), night-time luminosity (𝐴𝑐𝑡𝑖𝑣𝑖𝑡𝑦) population density (𝑃𝑜𝑝) and violence (𝐹𝑎𝑡𝑎𝑙𝑖𝑡𝑖𝑒𝑠). Climatic conditions influence the profitability of agricultural activity and, thus, land use [START_REF] Nelson | Effectiveness of Strict vs. Multiple Use Protected Areas in Reducing Tropical Forest Fires: A Global Analysis Using Matching Methods[END_REF]. It is also possible that temperatures and rainfall affect the occurrence and intensity of forest fires. Economic activity and population density are underlying drivers of deforestation. Night-time luminosity is a proxy of economic activity at the subnational level [START_REF] Chen | Using luminosity data as a proxy for economic statistics[END_REF]. The effect of the population could be ambiguous: on the one side, population density fuels the demand for cultivated land, but on the other side, it could favour the demand for forest products [START_REF] Amin | Neighborhood effects in the Brazilian Amazônia: Protected areas and deforestation[END_REF]. The impact of violence and conflicts on deforestation is also ambiguous. On the one hand, insecurity could lead to more deforestation: the poor institutional quality that translates into violent events fosters 12 https://www.iucn.org/theme/protected-areas/our-work/world-database-protected-areas 13 https://www.iucn.org/commissions/world-commission-protected-areas/our-work/oecms 14 https://minexconsulting.com/useful-links/ 15 The number of artisanal mines is unknown.

deforestation while downgrading environmental protection. Furthermore, deforestation provides a source of funding for armed insurrection. On the other hand, insecurity penalises economic activity, which can slow down deforestation [START_REF] Prem | End-of-conflict deforestation: Evidence from Colombia's peace agreement[END_REF].

𝑇𝑒𝑚𝑝 is the absolute value of the temperature deviation from the period average. It comes from the GISS Surface Temperature Analysis (GISTEMPv4) database. We extract 𝑅𝑎𝑖𝑛 from the Climate Hazards Group InfraRed Precipitation with Station data (CHIRPS) database.

𝐴𝑐𝑡𝑖𝑣𝑖𝑡𝑦 comes from the Defense Meteorological Program -Operational Line-Scan System (DMSP-OLS) dataset. 𝑃𝑜𝑝 is the population density from the Gridded Population of the World, Version 4 (GPWv4) database. We consider the death toll related to conflicts from the ACLED database to build 𝐹𝑎𝑡𝑎𝑙𝑖𝑡𝑖𝑒𝑠.

Descriptive statistics

Figure 1 provides the location of forested polygons, protected areas and mining activities.

We report descriptive statistics in Table 1 andTable 2.

Table 1 gives the essential characteristics of our dataset. The statistics pertain to the 3,704 polygons. Namely, they cover all polygons over the four-year periods. Considering that a polygon's average area is 12,070 square kilometres, the forest loss amounts to 1.1% of the polygon's surface, while the figure for protected areas is 11.4%. It aligns with the percentages of protected areas released in the literature [START_REF] Chape | Measuring the extent and effectiveness of protected areas as an indicator for meeting global biodiversity targets[END_REF].

In Table 2, we report the total number of observations, the number of polygons on which these variables are observed, the probability of observing a non-zero value of the variable, the totalled and disaggregated values over the four periods, the mean of the variable per polygon.

The probability of forest loss close to one tells us that forest loss concerns almost all polygons over the period. When we break down by sub-period, we also see an increase in forest loss. One-fifth of the polygons contain mines. Protected areas are present in threequarters of the observed units. In the last six rows, we see the level of deforestation in the spatial units below and above the protected areas (mines) median. We observe that the polygons with an area of protected areas above the median experience less deforestation on average. Deforestation is higher in polygons with mining activities on average. This observation concerning the deforestation impact of mining activities is still valid even in polygons where protected areas are above the median.

Considering the pairwise correlations (Table A-2 in Appendix), we observe a significant and positive correlation between the number of mines and the extent of deforestation. Moreover, the surface of protected areas correlates negatively with mining activities and deforestation.

Results

We first evidence the relevance of the spatial econometric model. Then, we assess the marginal impact of mines and protected areas on forest loss. Finally, we implement a robustness check and consider different heterogeneities.

5.1

The relevance of the spatial econometric model We estimate equations (1) and (2). We gradually introduce explanatory variables in the model to control for multicollinearity bias (Models 1 to 8). Table 4 reports the estimated spatial parameters 𝜌 and  for the standard spatial autoregressive model (Eq. 1). The spatial autocorrelation is positive and statistically significant, corroborating that deforestation decisions are complements. The coefficients range from 78.9% to 79.1%. The smallness of the finest spatial units, namely the polygon, could explain this high level of interaction. When including strong cross-sectional dependence with common factors (Table 5), the autoregressive coefficients are unchanged results. Overall, our spatial interaction results align with previous studies on deforestation determinants outside Sub-Saharan African countries [START_REF] Amin | Neighborhood effects in the Brazilian Amazônia: Protected areas and deforestation[END_REF]. The evidence in Africa is scanter. Interestingly, [START_REF] Heß | Environmental effects of development programs: Experimental evidence from West African dryland forests[END_REF] found that Community-Driven Development (CDD) programs generated positive spillover effects of deforestation in West African drylands.

Impact measures

We find that all explanatory variables' estimated direct, indirect and total effects are very similar without (Table 6) or with common factors (Table 7). We only interpret the total effects.

As expected, 𝐴𝑐𝑡𝑖𝑣𝑖𝑡𝑦 has a positive and significant impact on deforestation (Models 4 to 8 in 16 Following [START_REF] Pesaran | Testing Weak Cross-Sectional Dependence in Large Panels[END_REF], we find evidence for strong spatial dependence while computing the correlation coefficients between the observations of each pair of spatial polygons in SSA. Pesaran's null hypothesis of crosssectional dependence is that the values are only weakly cross-sectionally dependent. The test yields a statistic value of 442.28, which is strongly significant. We conclude that the spatial estimator should include both weak and strong spatial dependence. Although the coefficients vary slightly, the results are robust when common factors are included. In particular, significance and the sign of both the spatial parameters and the marginal effects of the different specifications remain broadly the same.

Table 6 andTable 7). 𝑇𝑒𝑚𝑝, 𝑅𝑎𝑖𝑛, 𝐹𝑎𝑡𝑎𝑙𝑖𝑡𝑖𝑒𝑠 and 𝑃𝑜𝑝 remain statistically insignificant (Models 5 to 8 in Table 6 andTable 7). 17 , 18

Protected areas (𝐿𝑎𝑔𝑃𝐴) have a significant negative effect at the 5% or 1% level, depending on the specification) on forest loss: models 4 to 8 in Table 6 andTable 7. Second, regarding mining activity, estimation results show a positive and significant (at the 0.1% level) effect of 𝑀𝑖𝑛𝑒 on deforestation, regardless of the specification. This result is consistent with previous findings in DRC [START_REF] Butsic | Conservation and conflict in the Democratic Republic of Congo: The impacts of warfare, mining, and protected areas on deforestation[END_REF]. This result also suggests that mines impact deforestation in their location polygons and neighbouring polygons. An additional mine leads to a forest loss of 39.8 km2 directly and 115.5 km2 indirectly (Table 6, model 4). The total effect is, therefore, impressive since an additional mine leads to a 155.4 km2 increase in forest loss. It is interesting to compare this result with that obtained for protected areas. An additional mine results in 155.4 km2 of forest loss in a polygon, whereas 1 km2 of an additional protected area only prevents 0.097 km2 of forest cover loss. Put differently, an additional 1598 km2 in a protected area would be required to offset the effect of an additional mine. Avoiding mining-driven forest loss, therefore, would at least necessitate a twice-fold increase in the average protected area if we assume that each extra square kilometre of protected area delivers the same reduction in forest loss.

We can assess whether protected areas dampen the harmful role of mining activities by considering the interactive variable: 𝐿𝑎𝑔 𝑃𝐴 × 𝑀𝑖𝑛𝑒. The sign of the interactive variable is 17 We regress the error terms of our benchmark model (Eq. 1) on the set of explanatory variables. Results validate the hypothesis of no correlation between the error term and explanatory variables suggesting the effectiveness of our procedure in controlling for endogeneity. These results are presented in Table A-5 in Appendix. 18 In addition, to (i) Moran test for spatial autocorrelation and (ii) Pesaran test for cross-section dependence, we also perform additional tests in order to validate our empirical specification (Table A-6 in Appendix for the full model including spatially lagged independent variables). First, using the robust version of the Hausman test to spatial autocorrelation of errors, the result leads to rejection of the null hypothesis of absence of correlation between individual effects and explanatory variables. Hence this test confirms that fixed effect models are statistically required. Second, we also test for spatial autocorrelation into account by SAR (LM_lag) or SEM (LM_error), the results confirm the rejection of the null hypothesis (taken independently) suggesting the inclusion of spatial parameter in lag form of the dependent variable (forest loss level) or via a spatial error component. In a more credible way, we also add robust versions of LM_lag, LM_error to test for the absence of a spatial autoregressive term when the model already contains a spatial autoregressive term in the error (Robust LM_lag), or vice versa (Robust LM_error). These robust versions are highly significant suggesting the choice of a fixed-effect model with both an autoregressive spatial process in the dependent variable and in the errors (SARAR). However, it should be noted that the test statistic for a Robust LM_lag version is higher than that for a Robust LM_error version.

negative but not significant, regardless of the specification used. In other words, the impact of mining on the forest does not decrease with protected areas. However, interpreting the coefficients on the mines and protected variables as the average effect of these variables on deforestation can be questioned [START_REF] Brambor | Understanding Interaction Models: Improving Empirical Analyses[END_REF]. We decided to study the evolution of the impact of mines on deforestation according to the distribution of protected areas. We consider here the model including all explanatory variables (model 8 in Table 6).

Figure 2. Marginal effect of mine on forest loss according to the distribution of protected areas

Note: The grey area represents the confidence interval at the 5% level.

Robustness check

To handle omitted variables in the spatial context, we also perform the spatial Durbin

model (SDM) (Table A-7 and Table A-8 in Appendix

). The main outcomes remain stable across specifications. The coefficients of the variables of interest retain the same sign, and most spatially lagged exogenous variables are insignificant. In addition, comparing the Akaike information criterion (AIC) and Bayes' information criterion (BIC), results show that models without including spatially lagged independent variables are better than those with the spatially lagged exogenous explanatory variables (Table A-9 in Appendix).

Testing Heterogeneities

Because of its importance, we estimate a SARAR model with spatial units and time-fixed effects only on the Congo Basin. 19 Table A-10 in Appendix reports the marginal effects. A noticeable result is the lack of significance of the protected area variable. Therefore, the unstable institutional context of the region likely makes this environmental protection instrument ineffective. This result is also in line with (Brandt, Nolte andAgrawal, 2016, 2018) though it was challenged by [START_REF] Karsenty | Deforestation and timber production in Congo after implementation of sustainable management policy: A reaction to the article by J.S. Brandt[END_REF].

We continue to explore the heterogeneity driven by local institutional variability. Poor institutional quality leads to many conflicts and violence. Hence, we split the sample into two sub-samples according to a threshold depending on the number of conflict deaths measured at the polygon level (Fatalities). We assume institutions are "good" when this number is below the sample median. 20 Protected areas reduce deforestation significantly only in polygons characterised by "good" institutional quality (Table A-11 in Appendix: compared column 1 versus column 2; total effect). In addition, the impact of mines on deforestation is higher in polygons with "weak" institutions.

We also studied the impact of mines according to mining status. 21 We consider the category of pre-operating mines as it concerns many polygons (163). The results are qualitatively unchanged (Table A-11 in Appendix: column 3, total effect). In particular, protected areas do not mitigate mining-driven deforestation. In addition, an additional pre-operating mine appears to lead to a forest loss of 202.4 km2. This effect is more important than the one obtained with all the mines regardless of their status (155.4 km2; Table 6, model 4). Therefore, during the pre-operating phase, mining activity appears to have the highest impact on land use in the area surrounding the mine.

Although the results favour the effectiveness of protected areas, these highlighted effects can also depend on the more or less strict character of the protected areas following the IUCN classification. We, therefore, break down protected areas into two groups. Both less stringent protected areas (𝐿𝑎𝑔 𝐿𝑎𝑟𝑔𝑒_𝑃𝐴) and strictly protected areas (𝐿𝑎𝑔 𝑆𝑡𝑟𝑖𝑐𝑡_𝑃𝐴) preserve the forest from deforestation (Table A-3 and Table A-4 in Appendix). Nevertheless, it is not possible to highlight the greater effectiveness of strictly protected areas. Moreover, even when we decompose protected areas into two groups, the interactive variable is still nonsignificant.

21 There are three mining status, namely (1) operating mines, (2) pre-operating mines and (2) closed mines.

Pre-operated mines include mines in the feasibility study phase, mines under construction and mines awaiting commissioning.

Concluding remarks

This article studies mining-driven deforestation using fine-scale data from 2001 to 2019.

We run spatial panel models controlling for spatial interactions. Mining activities harm the forest, and protected areas allow for reduced deforestation. We also find that protected areas do not dampen the impact of mining activities on deforestation. The result is robust to several econometric specifications. In addition, spatial heterogeneity prevails: the lower the institutional quality of the polygon, the greater the impact of the mine on deforestation.

Furthermore, the effectiveness of protected areas is lost in areas characterised by low institutional quality.

The interpretation of the results may raise several questions. First, satellite data does not distinguish forest loss resulting from human actions or natural disasters. We cope with this issue with temperature and rainfall variables. Second, the presence of endogenous variables on the right-hand side is a common occurrence in econometric work. In particular, including variables related to protected areas could lead to localisation bias [START_REF] Joppa | High and Far: Biases in the Location of Protected Areas[END_REF].

Nevertheless, the panel structure with period and polygon fixed effects and the one-year lagged value of protected areas address the bias.

It is feared that the likely development of mining activities in Africa in the coming years will increase the pressure on the forest resource. Smart mining attracts increasing attention, but offsets' contribution to forest preservation depends on many factors, such as enabling institutions and support of local communities [START_REF] Maddox | Forest-Smart Mining. Identifying Factors Associated with the Impacts of Large-Scale Mining on Forests[END_REF]. It is not realistic to hope that protected areas alone will be able to preserve the forest from mining activities. The weight of mining activity must be contained by increased diversification, thus reducing the dependence on primary commodities. Lower dependence on natural resources and higher diversification is not only an economic imperative but also an environmental one.

7 Appendix

  section 4.1) depends on the level of deforestation in neighbouring units and on a set of observed local characteristics. Formally, let the index 𝑖 = 1, … , 𝑁 denotes a spatial unit and 𝑡 = 1, … , 𝑇 denotes a time period. 𝑡 = 2005 for the 2001-2005 period, 𝑡 = 2010 for the 2006-2010 period, 𝑡 = 2015 for the 2011-2015 period and 𝑡 = 2019 for the 2016-2019 period. Using average years rather than yearly data allows us to grasp the medium-term effects of mining activities and protected areas on deforestation. 5 Our identification strategy is based on a panel spatial autoregressive model (SAR) with spatial units and period-fixed effects. This model writes as follows:

Figure 1 .

 1 Figure 1. Forest losses, Protected areas and Mines 2000 2019

Figure 2 (

 2 Figure 2(A) shows that the impact of mining on deforestation does not change significantly with the size of protected areas whose distribution is given in Figure 2(B). The impact of mining on forest loss is only slightly decreasing according to the distribution of protected areas, with values ranging between 155 to 150 km². Mining activities do not condition the dampening effect of protected areas on deforestation.

Figure A- 1 .

 1 Figure A-1. Polygons and the 926 forested polygons in 2001

  , studying the determinants of digital division in SSA countries, used 993,401 square polygons. Interplay between pastoralism, climate change and conflict in Africa is another example[START_REF] Mcguirk | Nomadic Pastoralism, Climate Change, and Conflict in Africa. w28243[END_REF].

11 https://glad.earthengine.app/view/global-forest-change#dl=1;old=off;bl=off;lon=20;lat=10;zoom=3. The data set comes from a collaboration between the GLAD (Global Land Analysis Discovery) lab, USGS, Google, and NASA. The global database consists of files with a spatial resolution of one arc-second per pixel, corresponding to approximately 30 meters per pixel at the equator. The data was generated using multispectral satellite imagery from Landsat 5, Landsat 7, and Landsat 8 satellites.

Table 1 .

 1 Descriptive Statistics -Overview

	Variables	Observations Mean	Standard Deviation	Min Max	Measurement unit
	𝐹𝑜𝑟𝑒𝑠𝑡_𝑙𝑜𝑠𝑠 3,704	139.640	184.698	0	1,927	Square kilometres
	𝑃𝐴	3,704	1,371.197 2,276.034	0	11,793 Square kilometres
	𝑀𝑖𝑛𝑒	3,704	0.423	1.160	0	12	Integer
	𝑇𝑒𝑚𝑝	3,704	297.211	2.586	286	303	Kelvin degrees
	𝑅𝑎𝑖𝑛	3,704	1,202.968 559.936	0	3,321	Millimetres
	𝐴𝑐𝑡𝑖𝑣𝑖𝑡𝑦	3,704	0.313	1.285	0	15	Pixel (luminosity)
	𝐹𝑎𝑡𝑎𝑙𝑖𝑡𝑖𝑒𝑠 3,704	22.584	210.191	0	7,630	Units, number of deaths
	𝑃𝑜𝑝	3,704	57.063	113.776	0	1,562	Inhabitants per square kilometer

Table 2 .

 2 Descriptive Statistics -Mines and Protected Areas in the Forest

	Whole	Sub-
	period	periods

Table 3 .

 3 Table3displays the evolution of the standardised value of Moran's I statistic over the period for each spatial weight matrix. These results suggest that immediate proximity matters more for deforestation interactions. In particular, the Moran's I statistic is increasing over time, thus suggesting that the levels of deforestation are positively and significantly clustered in SSA areas. The computed statistics are consistent with the hypothesis of a positive spatial clustering of deforestation among nearby SSA polygons. Standardised Moran's I statistics

	Year	std_nn5	std_dinverse	std_gabriel
	2005	1,233.179 * * *	1,327.680 * * *	1,438.183 * * *
	2010	1,081.750 * * *	1,187.847 * * *	1,261.682 * * *
	2015	1,345.908 * * *	1,431.672 * * *	1,544.010 * * *
	2019	1,438.017 * * *	1,534.271 * * *	1,663.758 * * *
	*** p<0.001, ** p<0.01, * p<0.05

Table 4 .

 4 Estimation results for the benchmark spatial autoregressive model. 𝐹𝑜𝑟𝑒𝑠𝑡_𝑙𝑜𝑠𝑠; *** 𝑝 < 0.001, ** 𝑝 < 0.01, * 𝑝 < 0.05; Standard errors in parentheses; the list of variables in the different specifications are given in Table 6

		Model1	Model2	Model3	Model4	Model5	Model6	Model7	Model8
	𝜌	0.798***	0.791***	0.790***	0.790***	0.789***	0.789***	0.789***	0.789***
		(0.019)	(0.019)	(0.019)	(0.019)	(0.019)	(0.019)	(0.019)	(0.019)
		-0.228***	-0.228***	-0.230***	-0.230***	-0.228***	-0.228***	-0.226***	-0.228***
		(0.050)	(0.050)	(0.050)	(0.050)	(0.050)	(0.050)	(0.050)	(0.050)
	Dependent variable:

Table 5

 5 reports estimated 𝜌 and  for the spatial autoregressive model with common factors (Eq. 2). The estimated values of 𝜌 and  are consistent, whatever the specifications (Table4 and Table 5).16

Table 5 .

 5 Estimation results for the spatial autoregressive model with common factors Dependent variable: Deforestation 𝐹𝑜𝑟𝑒𝑠𝑡_𝑙𝑜𝑠𝑠; *** 𝑝 < 0.001, ** 𝑝 < 0.01, * 𝑝 < 0.05; Standard errors in parentheses; the list of variables in the different specifications are given inTable 7

		Model1	Model2	Model3	Model4	Model5	Model6	Model7	Model8
	𝜌	0.798***	0.791***	0.790***	0.790***	0.789***	0.789***	0.789***	0.789***
		(0.019)	(0.019)	(0.019)	(0.019)	(0.019)	(0.019)	(0.019)	(0.019)
		-0.229*** -0.229*** -0.230*** -0.230*** -0.229*** -0.228*** -0.226*** -0.228***
		(0.050)	(0.050)	(0.050)	(0.050)	(0.050)	(0.050)	(0.050)	(0.050)
	Dependent variable:

Table 6 .

 6 Marginal effects of covariates on deforestation; Spatial autoregressive model without common factors

		Model1	Model2	Model3	Model4	Model5	Model6	Model7	Model8
		Direct
	𝐿𝑎𝑔_𝑃𝐴	-0.014	-0.019	-0.017	-0.025**	-0.025*	-0.026**	-0.026*	-0.026*
		(0.012)	(0.012)	(0.013)	(0.013)	(0.014)	(0.012)	(0.012)	(0.012)
	𝑀𝑖𝑛𝑒		39.052***	40.670***	39.834***	39.843***	39.771***	39.550***	39.488***
			(5.788)	(6.335)	(6.721)	(6.068)	(6.690)	(6.709)	(5.970)
	𝐿𝑎𝑔_𝑃𝐴 × 𝑀𝑖𝑛𝑒			-0.002	-0.001	-0.001	-0.001	-0.001	-0.001
				(0.003)	(0.003)	(0.003)	(0.003)	(0.003)	(0.003)
	𝐴𝑐𝑡𝑖𝑣𝑖𝑡𝑦				16.328***	16.148***	16.362***	16.274***	15.343***
					(4.577)	(4.825)	(4.495)	(4.233)	(5.008)
	𝑇𝑒𝑚𝑝					2.297	2.420	2.374	2.522
						(5.829)	(5.844)	(5.963)	(5.498)
	𝑅𝑎𝑖𝑛						-0.011	-0.011	-0.012
							(0.010)	(0.010)	(0.010)
	𝐹𝑎𝑡𝑎𝑙𝑖𝑡𝑖𝑒𝑠							-0.008	-0.007
								(0.008)	(0.007)
	𝑃𝑜𝑝								0.041
									(0.082)
		Indirect
	𝐿𝑎𝑔_𝑃𝐴	-0.042	-0.055	-0.048	-0.072**	-0.074*	-0.076*	-0.075*	-0.074*
		(0.036)	(0.035)	(0.038)	(0.037)	(0.041)	(0.037)	(0.037)	(0.039)
	𝑀𝑖𝑛𝑒		112.167***	117.210***	115.540***	115.508***	114.494***	113.648***	113.450***
			(21.455)	(23.046)	(25.093)	(22.638)	(24.060)	(23.373)	(21.875)
	𝐿𝑎𝑔_𝑃𝐴 × 𝑀𝑖𝑛𝑒			-0.004	-0.004	-0.004	-0.004	-0.003	-0.003
				(0.009)	(0.010)	(0.010)	(0.009)	(0.009)	(0.009)
	𝐴𝑐𝑡𝑖𝑣𝑖𝑡𝑦				47.359***	46.813***	47.104***	46.763***	44.080***
					(14.089)	(15.118)	(3.916)	(12.550)	(16.078)
	𝑇𝑒𝑚𝑝					6.658	6.966	6.821	7.246
						(17.517)	(16.951)	(16.963)	(15.985)
	𝑅𝑎𝑖𝑛						-0.031	-0.032	-0.033
							(0.029)	(0.028)	(0.029)
	𝐹𝑎𝑡𝑎𝑙𝑖𝑡𝑖𝑒𝑠							-0.023	-0.021
								(0.022)	(0.021)
	𝑃𝑜𝑝								0.120
									(0.248)
		Total
	𝐿𝑎𝑔_𝑃𝐴	-0.056	-0.074	-0.065	-0.097**	-0.0990*	-0.102*	-0.101*	-0.100*
		(0.042)	(0.047)	(0.052)	(0.050)	(0.054)	(0.049)	(0.049)	(0.051)
	𝑀𝑖𝑛𝑒		151.219***	157.880***	155.374***	155.351***	154.265***	153.198***	152.937***
			(26.528)	(28.7748)	(31.181)	(27.993)	(30.126)	(29.455)	(27.018)
	𝐿𝑎𝑔_𝑃𝐴 × 𝑀𝑖𝑛𝑒			-0.006	-0.005	-0.005	-0.005	-0.004	-0.005
				(0.012)	(0.013)	(0.013)	(0.012)	(0.012)	(0.012)
	𝐴𝑐𝑡𝑖𝑣𝑖𝑡𝑦				63.687***	62.961***	63.466***	63.037***	59.423***
					(18.415)	(19.742)	(18.202)	(16.596)	(20.888)
	𝑇𝑒𝑚𝑝					8.955	9.386	9.195	9.767
						(23.319)	(22.772)	(22.900)	(21.454)
	𝑅𝑎𝑖𝑛						-0.041	-0.043	-0.045
							(0.040)	(0.038)	(0.039)
	𝐹𝑎𝑡𝑎𝑙𝑖𝑡𝑖𝑒𝑠							-0.031	-0.029
								(0.029)	(0.029)
	𝑃𝑜𝑝								0.160
									(0.329)

*** 𝑝 < 0.01, ** 𝑝 < 0.05, * 𝑝 < 0.1; standard errors in parentheses.

Table 7 .

 7 Marginal effects of covariates on deforestation; spatial autoregressive model with common factors

		Model1	Model2	Model3	Model4	Model5	Model6	Model7	Model8
		Direct
	𝐿𝑎𝑔_𝑃𝐴	-0.0140	-0.019*	-0.017	-0.025*	-0.025**	-0.026**	-0.026**	-0.026**
		(0.011)	(0.011)	(0.013)	(0.013)	(0.012)	(0.014)	(0.012)	(0.013)
	𝑀𝑖𝑛𝑒		39.057***	40.707***	39.874***	39.883***	39.812***	39.590***	39.526***
			(5.202)	(6.333)	(6.100)	(6.720)	(6.321)	(5.819)	(6.339)
	𝐿𝑎𝑔_𝑃𝐴 × 𝑀𝑖𝑛𝑒			-0.001	-0.001	-0.001	-0.001	-0.001	-0.001
				(0.003)	(0.003)	(0.003)	(0.003)	(0.003)	(0.003)
	𝐴𝑐𝑡𝑖𝑣𝑖𝑡𝑦				16.351***	16.171***	16.383***	16.295***	15.369***
					(4.715)	(4.442)	(4.520)	(4.659)	(5.386)
	𝑇𝑒𝑚𝑝					2.290	2.411	2.365	2.513
						(6.169)	(6.112)	(6.265)	(5.405)
	𝑅𝑎𝑖𝑛						-0.011	-0.011	-0.011
							(0.009)	(0.009)	(0.010)
	𝐹𝑎𝑡𝑎𝑙𝑖𝑡𝑖𝑒𝑠							-0.008	-0.007
								(0.007)	(0.008)
	𝑃𝑜𝑝								0.041
									(0.081)
		Indirect
	𝐿𝑎𝑔_𝑃𝐴	-0.042	-0.056*	-0.048	-0.073*	-0.074**	-0.077*	-0.076*	-0.075**
		(0.034)	(0.033)	(0.039)	(0.038)	(0.036)	(0.043)	(0.038)	(0.041)
	𝑀𝑖𝑛𝑒		113.523***	118.723***	117.066***	117.033***	116.004***	115.155***	114.945***
			(19.420)	(23.819)	(22.638)	(22.667)	(23.000)	(21.479)	(24.452)
	𝐿𝑎𝑔_𝑃𝐴 × 𝑀𝑖𝑛𝑒			-0.004	-0.004	-0.004	-0.004	-0.003	-0.004
				(0.009)	(0.010)	(0.009)	(0.010)	(0.009)	(0.009)
	𝐴𝑐𝑡𝑖𝑣𝑖𝑡𝑦				48.005***	47.451***	47.738***	47.400***	44.693***
					(14.742)	(13.594)	(14.941)	(14.251)	(16.552)
	𝑇𝑒𝑚𝑝					6.720	7.026	6.880	7.307
						(17.943)	(18.158)	(18.717)	(16.223)
	𝑅𝑎𝑖𝑛						-0.031	-0.031	-0.033
							(0.027)	(0.026)	(0.030)
	𝐹𝑎𝑡𝑎𝑙𝑖𝑡𝑖𝑒𝑠							-0.023	-0.022
								(0.022)	(0.022)
	𝑃𝑜𝑝								0.112
									(0.241)
		Total
	𝐿𝑎𝑔_𝑃𝐴	-0.056	-0.075*	-0.065	-0.097*	-0.099**	-0.103*	-0.102**	-0.101**
		(0.045)	(0.043)	(0.042)	(0.050)	(0.048)	(0.056)	(0.051)	(0.054)
	𝑀𝑖𝑛𝑒		152.580***	159.430***	156.939***	156.916***	155.815***	154.745***	154.471***
			(23.984)	(23.436)	(28.076)	(28.715)	(28.469)	(26.548)	(30.159)
	𝐿𝑎𝑔_𝑃𝐴 × 𝑀𝑖𝑛𝑒			-0.006	-0.006	-0.005	-0.005	-0.005	-0.005
				(0.012)	(0.013)	(0.012)	(0.013)	(0.012)	(0.013)
	𝐴𝑐𝑡𝑖𝑣𝑖𝑡𝑦				64.356***	63.622***	64.121***	63.692***	60.062***
					(19.242)	(17.865)	(19.234)	(18.681)	(21.750)
	𝑇𝑒𝑚𝑝					9.009	9.437	9.245	9.820
						(24.089)	(24.844)	(24.955)	(21.599)
	𝑅𝑎𝑖𝑛						-0.041	-0.042	-0.045
							(0.036)	(0.035)	(0.040)
	𝐹𝑎𝑡𝑎𝑙𝑖𝑡𝑖𝑒𝑠							-0.031	-0.0291
								(0.029)	(0.030)
	𝑃𝑜𝑝								0.160
									(0.032)

*** 𝑝 < 0.01, ** 𝑝 < 0.05, * 𝑝 < 0.1; standard errors in parentheses.

Table A -

 A

	Variable name Description	Source
	𝐹𝑜𝑟𝑒𝑠𝑡_𝑙𝑜𝑠𝑠	Forest loss	Hansen's database
	𝑀𝑖𝑛𝑒	Number of industrial mines present in each	MinEx database
		cell
	𝑃𝐴	Surface of protected area for each study	World Database on Protected Areas and world database
		unit.	on other effective area-based conservation measures
	𝑇𝑒𝑚𝑝	Absolute deviation of the temperature	GISS Surface Temperature Analysis (GISTEMPv4)
			database
	𝑅𝑎𝑖𝑛	Rainfall	Climate Hazards Group InfraRed Precipitation with
			Station data (CHIRPS)
	𝐴𝑐𝑡𝑖𝑣𝑖𝑡𝑦	Night-time luminosity	Defense Meteorological Program -Operational Line-
			Scan System (DMSP-OLS) dataset
	𝐹𝑎𝑡𝑎𝑙𝑖𝑡𝑖𝑒𝑠	Number of deaths due to conflicts	ACLED database
	𝑃𝑜𝑝	Population density	The Gridded Population of the World, Version 4
			(GPWv4)

1. Variables description

Table A

 A Table A-3. Marginal effects of covariates on deforestation for heterogeneity PA; spatial autoregressive model without common factors

			-2. Pairwise correlations
	Variables		(1)		(2)	(3)	(4)	(5)	(6)	(7)	(8)
			𝐹𝑜𝑟𝑒𝑠𝑡_𝑙𝑜𝑠𝑠 Model1 Model2	𝑃𝐴 Model3	𝑀𝑖𝑛𝑒 Model4	𝑇𝑒𝑚𝑝 Model5	𝑅𝑎𝑖𝑛 Model6	𝐴𝑐𝑡𝑖𝑣𝑖𝑡𝑦 𝐹𝑎𝑡𝑎𝑙𝑖𝑡𝑖𝑒𝑠 𝑃𝑜𝑝 Model7 Model8 Model9	Model10
	(1)		1.000 Direct
	Lag_Strict_PA 𝐹𝑜𝑟𝑒𝑠𝑡_𝑙𝑜𝑠𝑠 (2) 𝑃𝐴 (3) 𝑀𝑖𝑛𝑒 Lag_Large_PA	-0,004 -0.069*** -0,018 (0.005) (0.018) 0.167*** -0,016 (0.021)	-0.035** (0.019) 1.000 -0.034* -0.057*** 1.000 -0.029 (0.020) -0.033* (0.020) (0.021)	-0.037 (0.025) -0.042 (0.026)	-0.043** (0.022) -0.050** (0.023)	-0.043** (0.024) -0.050** (0.026)	-0.044* (0.022) -0.050* (0.023)	-0.044** (0.024) -0.050** (0.026)	-0.044* (0.022) -0.051* (0.024)
	(4) 𝑇𝑒𝑚𝑝 Mine (5) 𝑅𝑎𝑖𝑛 Lag_Strict_PA x	0.043*** 0.210***	0.050*** -0.011 39.908*** 41.890*** (5.891) (5.972) -0.055*** 0.040** 0.172*** 1.000 40.034*** 39.009*** 1.000 (6.463) (6.550) -0.009 -0.008 -0.008	39.023*** (6.429) -0.008	38.961*** (7.412) -0.008	38.718*** (6.859) -0.008	38.626*** (6.787) -0.008
	(6) 𝐴𝑐𝑡𝑖𝑣𝑖𝑡𝑦 Mine (7) 𝐹𝑎𝑡𝑎𝑙𝑖𝑡𝑖𝑒𝑠 -0.028* 0.056*** Lag_Large_PA x (8) 𝑃𝑜𝑝 0.086*** Mine Activity	-0.029* -0.018 -0.100*** 0.079*** -0.067*** -0.074*** 0.620*** 0.072*** 0.058*** -0.026* (0.007) (0.007) (0.007) (0.007) (0.007) (0.007) -0.109*** 1.000 0.006 -0.024 0.013 0.018 0.002 0.003 0.003 0.003 0.003 1.000 (0.004) (0.004) (0.004) (0.004) (0.004) 15.271*** 15.211*** 15.377*** 15.304*** 1.000	(0.007) 0.003 (0.004) 14.023***
	Temp	*** 𝑝 < 0.01, ** 𝑝 < 0.05, * 𝑝 < 0.1		(4.262)	(4.468) 0.628	(4.756) 0.687	(4.459) 0.657	(4.470) 0.890
									(5.843)	(5.888)	(5.953)	(6.071)
	Rain									-0.010	-0.010	-0.011
										(0.009)	(0.010)	(0.010)
	Fatalities										-0.008	-0.007
											(0.008)	(0.008)
	Pop											0.058
												(0.077)
			Indirect
	Lag_Strict_PA		0,001	0,003	-0.103**	-0.084	-0.106	-0.127*	-0.126*	-0.128*	-0.128**	-0.129*
			(0.001)	(0.004)	(0.057)	(0.059)	(0.075)	(0.068)	(0.072)	(0.066)	(0.074)	(0.068)
	Lag_Large_PA			0,003	-0.100*	-0.097*	-0.121	-0.143**	-0.143**	-0.146*	-0.145**	-0.147*
				(0.004)	(0.060)	(0.061)	(0.081)	(0.073)	(0.080)	(0.069)	(0.106)	(0.074)
	Mine				116.168***	121.996***	116.341***	114.058***	114.081***	113.150***	112.224***	112.003***
					(22.832)	(22.236)	(23.880)	(23.904)	(23.856)	(25.787)	(23.807)	(23.787)
	Lag_Strict_PA x				-0.027	-0.024	-0.023	-0.023	-0.023	-0.023	-0.024
	Mine					(0.020)	(0.019)	(0.021)	(0.021)	(0.021)	(0.022)	(0.020)
	Lag_Large_PA x					0.006	0.008	0.008	0.008	0.008	0.008
	Mine						(0.011)	(0.011)	(0.012)	(0.012)	(0.012)	(0.012)
	Activity							44.650***	44.468***	44.658***	44.359***	40.662***
								(14.582)	(14.526)	(14.758)	(14.174)	(13.910)
	Temp								1.837	1.995	1.906	2.580
									(17.1888)	(17.675)	(17.398)	(18.039)
	Rain									-0.030	-0.030	-0.0331
										(0.028)	(0.031)	(0.029)
	Fatalities										-0.024	-0.023
											(0.023)	(0.022)
	Pop											0.168
												(0.232)
			Total
	Lag_Strict_PA		-0,003	-0,015	-0.139**	-0.113	-0.143	-0.170*	-0.170*	-0.172*	-0.172**	-0.174*
			(0.004)	(0.015)	(0.075)	(0.079)	(0.099)	(0.089)	(0.096)	(0.088)	(0.097)	(0.090)
	Lag_Large_PA			-0,013	-0.134*	-0.130*	-0.162	-0.193**	-0.192**	-0.196*	-0.196**	-0.198*
				(0.017)	(0.079)	(0.081)	(0.107)	(0.096)	(0.106)	(0.091)	(0.106)	(0.098)
	Mine				156.076***	163.887***	156.376***	153.067***	153.105***	152.111***	150.942***	150.628***
					(28.041)	(27.364)	(29.638)	(29.793)	(29.708)	(32.535)	(29.963)	(29.884)
	Lag_Strict_PA x				-0.036	-0.033	-0.031	-0.031	-0.031	-0.031	-0.032
	Mine					(0.026)	(0.026)	(0.028)	(0.028)	(0.028)	(0.029)	(0.027)
	Lag_Large_PA x					0.001	0.010	0.010	0.011	0.011	0.011
	Mine						(0.014)	(0.015)	(0.016)	(0.016)	(0.016)	(0.015)
	Activity							59.921***	59.679***	60.036***	59.664***	54.685***
								(18.629)	(18.822)	(19.334)	(18.452)	(18.200)
	Temp								2.465	2.683	2.563	3.470
									(23.008)	(23.538)	(23.326)	(24.083)
	Rain									-0.040	-0.041	-0.045
										(0.038)	(0.041)	(0.038)
	Fatalities										-0.033	-0.030
											(0.030)	(0.030)
	Pop											0.226
												(0.309)
		*** p<0.001, ** p<0.01, * p<0.05; standard errors in parentheses

Table A -

 A 4. Marginal effects of covariates on deforestation for heterogeneity PA; spatial autoregressive model with common factors

		Model1 Model2 Model3	Model4	Model5	Model6	Model7	Model8	Model9	Model10
		Direct
		-0.004	-0.018	-0.036*	-0.029	-0.037*	-0.043**	-0.043*	-0.044**	-0.044**	-0.047*
	Lag_Strict_PA	(0.005)	(0.018)	(0.017)	(0.019)	(0.021)	(0.023)	(0.024)	(0.021)	(0.021)	(0.025)
			-0.016	-0.0345	-0.033*	-0.041*	-0.049**	-0.049**	-0.050**	-0.050**	-0.051**
	Lag_Large_PA		(0.019)	(0.019)	(0.019)	(0.022)	(0.026)	(0.025)	(0.023)	(0.023)	(0.025)
				39.923***	41.914***	40.047***	39.045***	39.060***	38.998***	38.754***	38.661***
	Mine			(5.475)	(6.455)	(6.490)	(6.699)	(6.611)	(6.381)	(6.284)	(6.486)
					-0.009	-0.008	-0.008	-0.008	-0.008	-0.008	-0.008
	Lag_Strict_PAxMine				(0.007)	(0.007)	(0.007)	(0.007)	(0.007)	(0.006)	(0.007)
						0.002	0.003	0.003	0.003	0.003	0.003
	Lag_Large_PAxMine					(0.004)	(0.004)	(0.004)	(0.004)	(0.004)	(0.004)
							15.288***	15.229***	15.393***	15.321***	14.042***
	Activity						(4.071)	(4.154)	(4.294)	(4.426)	(4.609)
								0.619`	0.680	0.647	0.880
	Temp							(5.854)	(6.162)	(6.181)	(6.037)
									-0.010	-0.010	-0.011
	Rain								(0.009)	(0.009)	(0.009)
										-0.009	-0.008
	Fatalities									(0.007)	(0.008)
											0.058
	Pop										(0.078)
		Indirect
		0.001	0.004	-0.105*	-0.086	-0.108*	-0.128**	-0.128*	-0.130*	-0.130*	-0.131*
	Lag_Strict_PA	(0.001)	(0.004)	(0.053)	(0.059)	(0.065)	(0.072)	(0.075)	(0.065)	(0.064)	(0.074)
			0.003	-0.102	-0.098*	-0.123*	-0.146**	-0.146*	-0.150**	-0.150**	-0.150**
	Lag_Large_PA		(0.004)	(0.058)	(0.059)	(0.069)	(0.078)	(0.078)	(0.071)	(0.070)	(0.076)
				117.600***	123.524***	117.779***	115.575***	115.598***	114.654***	113.722***	113.482***
	Mine			(20.877)	(26.425)	(23.912)	(25.354)	(24.723)	(23.318)	(24.504)	(22.484)
					-0.027	-0.025	-0.024	-0.024	-0.024	-0.024	-0.024
	Lag_Strict_PAxMine				(0.021)	(0.022)	(0.021)	(0.021)	(0.022)	(0.020)	(0.020)
						0.007	0.008	0.008	0.008	0.008	0.008
	Lag_Large_PAxMine					(0.011)	(0.013)	(0.012)	(0.012)	(0.012)	(0.011)
							45.253***	45.071***	45.257***	44.959***	41.217***
	Activity						(13.473)	(14.078)	(14.290)	(13.976)	(15.346)
								1.832	1.990	1.899	2.582
	Temp							(17.469)	(18.417)	(18.026)	(18.158)
									-0.029	-0.030	-0.033
	Rain								(0.027)	(0.027)	(0.029)
										-0.025	-0.023
	Fatalities									(0.021)	(0.024)
											0.170
	Pop										(0.234)
		Total
		-0.003	-0.015	-0.140*	-0.115	-0.145*	-0.172**	-0.172*	-0.174**	-0.174*	-0.176*
	Lag_Strict_PA	(0.004)	(0.014)	(0.070)	(0.078)	(0.085)	(0.095)	(0.098)	(0.086)	(0.085)	(0.098)
			-0.013	-0.136	-0.132*	-0.166*	-0.195**	-0.195*	-0.198**	-0.198*	-0.201**
	Lag_Large_PA		(0.015)	(0.076)	(0.078)	(0.090)	(0.104)	(0.103)	(0.094)	(0.093)	(0.101)
				157.523***	165.438***	157.826***	154.620***	154.658***	153.651***	152.476***	152.143***
	Mine			(25.689)	(32.244)	(29.687)	(31.345)	(30.625)	(29.061)	(30.195)	(28.296)
					-0.037	-0.033	-0.032	-0.032	-0.032	-0.032	-0.032
	Lag_Strict_PAxMine				(0.085)	(0.030)	(0.028)	(0.028)	(0.029)	(0.026)	(0.027)
						0.009	0.010	0.010	0.010	0.011	0.011
	Lag_Large_PAxMine					(0.015)	(0.017)	(0.016)	(0.016)	(0.016)	(0.015)
							60.542***	60.300***	60.650***	60.280***	55.259***
	Activity						(17.323)	(17.999)	(18.285)	(18.180)	(19.828)
								2.451	2.667	2.546	3.461
	Temp							(23.306)	(24.551)	(24.180)	(24.171)
									-0.039	-0.041	-0.044
	Rain								(0.036)	(0.036)	(0.038)
										-0.033	-0.031
	Fatalities									(0.028)	(0.031)
											0.228
	Pop										(0.312)
	*** p<0.001, ** p<0.01, * p<0.05; standard errors in parentheses

Table A -

 A 5. Regression of error terms of Table6on the explanatory variables.

		Table A-7. Estimation results for the spatial Durbin model with additive PA
				error1 Model 1	error2 Model 2	error3 Model 3	error4 Model 4	error5 Model 5	error6 Model 6 error7 Model 7 error8 Model 8
		𝐿𝑎𝑔_𝑃𝐴	0.004 0.799*** 0.791*** 0.792*** 0.792*** 0.791*** 0.794*** 0.793*** 0.794*** 0.003 0.005 0.005 0.006 0.007 0.007 0.006 (0.019) (0.019) (0.019) (0.019) (0.019) (0.019) (0.019) (0.019)
				(0.010) -0.229*** -0.229*** -0.231*** -0.231*** -0.230*** -0.236*** -0.234*** -0.239*** (0.010) (0.011) (0.011) (0.011) (0.011) (0.011) (0.011) (0.050) (0.050) (0.050) (0.050) (0.050) (0.049) (0.049) (0.049)
	Lag_PA	𝑀𝑖𝑛𝑒	-0.011	0.940 -0.015	2.202 -0.014	1.455 -0.015	1.483 -0.015	1.562 -0.021** 1.578	1.595 -0.021**	-0.021**
	Mine			(0.009)	(4.682) (0.009) 31.429*** 32.500*** 32.513*** 32.529*** 31.894*** 31.715*** 31.514*** (5.428) (5.425) (5.425) (5.425) (5.426) (0.010) (0.010) (0.010) (0.010) (0.010) (0.010) (5.430)
		𝐴𝑐𝑡𝑖𝑣𝑖𝑡𝑦		(4.458)	(5.225)	2.052 (5.226)	2.474 (5.228)	2.274 (5.206) 2.269	1.755 (5.210)	(5.203)
	Temp						(3.893) 4.600 (5.559)	(3.910) 4.835 (5.572)	(3.913) 3.167 (5.554) (3.914) 3.042 (4.206) (5.563)	2.586 (5.545)
	Rain	𝑇𝑒𝑚𝑝					-6.435 -0.008	-6.548 -0.008	-6.562	-6.531 -0.009	-0.009
	Activity							(5.853) (0.008)	(5.854) (0.008) (5.854) (0.008) (5.860) 12.857*** 12.786*** 12.593*** (0.008)
	Fatalities	𝑅𝑎𝑖𝑛							0.012 (3.609) 0.012	(3.612) 0.011 -0.006	(3.869) -0.006
										(0.009)	(0.009) (0.006) (0.009)	(0.006)
	Pop	𝐹𝑎𝑡𝑎𝑙𝑖𝑡𝑖𝑒𝑠								0.0001	0.0003	0.009 (0.064)
	SlagW_Lag_PA	0.0002	0.001	0.001	0.001		0.001		0.001	(0.006) 0.001 (0.006)	0.001
	SlagW_Mine	𝑃𝑜𝑝	(0.002)	(0.002) 3.928	(0.002) 3.914	(0.002) 4.052		(0.002) 3.968		(0.002) 3.389	(0.002) 0.024 3.461	(0.002) 3.115
					(3.771)	(5.055)	(5.058)		(5.060)		(5.044)	(0.072) (5.046)	(5.041)
	SlagW_Temp 𝐿𝑎𝑔_𝑃𝐴 × 𝑀𝑖𝑛𝑒 SlagW_Rain			-0.001	5.250 -0.001 (16.210)	5.898 -0.001 (16.240) -0.001 4.659 (16.166) -0.001 -0.002 0.004	4.100 (16.195) -0.001 0.004	1.942 (16.176) 0.004
	SlagW_Activity			(0.003)	(0.003)	(0.003) (0.009)	(0.003) (0.009) (0.003) (0.009) (0.003) 7.638** 7.607**	(0.009) 15.105***
		Standard errors in parentheses; *p< 0.1; **p<0.05; ***p<0.01			(3.477)	(3.477)	(4.447)
	SlagW_Fatalities								0.008	0.008
		Table A-6. Standard tests in spatial panel models				(0.014)	(0.014)
	Statistics 3906.8*** 3502.4*** 410.32*** 5.9003** 290.45*** *** p<0.01, ** p<0.05, * p<0.10 LM_lag LM_error Lag_PA x Mine SlagW_Pop Robust LM_lag Robust LM_error SlagW_Lag_PAxMine Hausman *** p<0.01, ** p<0.05, * p<0.1; standard errors in parentheses Df 1 -0.001 -0.001 1 (0.003) (0.003) 1 -0.0001 -0.0002 1 (0.003) (0.003) 16	-0.001 (0.003) -0.0001 (0.003)		-0.001 (0.003) -0.00002 (0.003)	-0.001 (0.003) -0.0001 (0.003)	-0.132*** (0.049) -0.001 (0.003) 0.0001 (0.003)

Table A -

 A 8. Estimation results for the spatial Durbin model with heterogeneity PA

		Model 1	Model 2	Model 3	Model 4	Model 5	Model 6	Model 7	Model 8	Model 9	Model 10
		0.799***	0.799***	0.794***	0.794***	0.794***	0.796***	0.796***	0.795***	0.795***	0.796***
		(0.019)	(0.019)	(0.019)	(0.019)	(0.019)	(0.019)	(0.019)	(0.019)	(0.019)	(0.019)
		-0.229*** -0.229*** -0.232*** -0.234*** -0.230*** -0.236*** -0.236*** -0.234*** -0.232*** -0.238***
		(0.050)	(0.050)	(0.050)	(0.050)	(0.050)	(0.049)	(0.049)	(0.049)	(0.049)	(0.049)
	Lag_Strict_PA	-0.004	-0.018	-0.028*	-0.023	-0.030	-0.034*	-0.034*	-0.035*	-0.036*	-0.035*
		(0.005)	(0.018)	(0.015)	(0.015)	(0.019)	(0.019)	(0.019)	(0.019)	(0.019)	(0.019)
	Lag_Large_PA		-0.015	-0.027*	-0.026	-0.034*	-0.039**	-0.039**	-0.040**	-0.040**	-0.040**
			(0.020)	(0.016)	(0.016)	(0.020)	(0.020)	(0.020)	(0.020)	(0.020)	(0.020)
	Mine			32.021*** 33.644*** 31.874*** 31.290*** 31.321*** 31.281*** 31.090*** 30.983***
				(4.494)	(4.633)	(5.306)	(5.287)	(5.288)	(5.290)	(5.294)	(5.288)
	Activity						11.915*** 11.827*** 12.102*** 12.049*** 11.535***
							(3.533)	(3.562)	(3.577)	(3.580)	(3.824)
	Temp							1.565	1.616	1.493	1.076
								(5.514)	(5.524)	(5.534)	(5.511)
	Rain								-0.008	-0.008	-0.008
									(0.008)	(0.008)	(0.008)
	Fatalities									-0.007	-0.007
										(0.006)	(0.006)
	Pop										0.024
											(0.065)
	Slag_Lag_Strict_PA 0.001	0.001	0.001	0.001	0.001	0.002	0.002	0.002	0.002	0.001
		(0.002)	(0.002)	(0.003)	(0.003)	(0.003)	(0.003)	(0.003)	(0.003)	(0.003)	(0.003)
	Slag_Lag_Large_PA		-0.002	0.0001	-0.0001	-0.0001	0.0002	0.0002	0.0002	0.0002	-0.001
			(0.002)	(0.003)	(0.003)	(0.003)	(0.003)	(0.003)	(0.003)	(0.003)	(0.003)
	Slag_Mine			3.561	3.476	3.747	3.074	3.110	3.060	3.103	2.688
				(4.992)	(4.991)	(5.006)	(4.993)	(4.994)	(4.995)	(4.996)	(4.991)
	Slag_Activity						7.415**	7.422**	7.611**	7.575**	14.986***
							(3.437)	(3.444)	(3.482)	(3.482)	(4.449)
	Slag_Temp							3.407	3.773	3.153	0.838
								(16.162)	(16.189)	(16.219)	(16.194)
	Slag_Rain								0.004	0.004	0.004
									(0.009)	(0.009)	(0.009)
	Slag_Fatalities									0.007	0.007
										(0.014)	(0.014)
	Slag_Pop										-0.131***
											(0.049)
	Lag_Strict_Pa x				-0.008	-0.007	-0.007	-0.006	-0.006	-0.006	-0.007
	Mine
					(0.005)	(0.005)	(0.005)	(0.005)	(0.005)	(0.005)	(0.005)
	Lag_Large_PA x					0.002	0.002	0.002	0.002	0.002	0.002
	Mine
						(0.003)	(0.003)	(0.003)	(0.003)	(0.003)	(0.003)
	Slag_Lag_Strict_PA			-0.00005	-0.00002	-0.0001	-0.001	-0.001	-0.0004	-0.001	-0.001
	x Slag_Mine
				(0.003)	(0.003)	(0.003)	(0.003)	(0.003)	(0.003)	(0.003)	(0.003)
	Slag_Lag_Large_PA			0.0005	0.001	0.001	0.001	0.001	0.001	0.001	0.002
	x Slag_Mine
				(0.003)	(0.003)	(0.003)	(0.003)	(0.003)	(0.003)	(0.003)	(0.003)
	*** p<0.001, ** p<0.01, * p<0.05; standard errors in parentheses

Table A -

 A 10. Marginal effects of covariates on deforestation focusing on Congo Basin countries; spatial autoregressive model without common factors

		Model 1	Model 2	Model 3	Model 4	Model 5	Model 6	Model 7	Model 8
	Direct		.	.	.	.	.	.	.
	Lag_PA	-0.099	-0.094	-0.092	-0.079	-0.081	-0.089	-0.086	-0.086
		(0.134)	(0.129)	(0.126)	(0.143)	(0.130)	(0.129)	(0.128)	(0.138)
	Mine		14.734*** 12.633**	12.182*	11.882** 11.842**	11.699**	11.650*
			(5.617)	(5.869)	(6.064)	(6.298)	(6.032)	(5.511)	(6.663)
	Lag_PAxMine			0.00291	0.00293	0.00299	0.00297	0.00286	0.00286
				(0.0036)	(0.0040)	(0.0035)	(0.0035)	(0.0036)	(0.0034)
	Activity				9.976	9.689	9.584	8.810	8.203
					(7.569)	(7.163)	(7.110)	(7.615)	(7.884)
	Temp					35.936*	36.351*	36.341*	36.527*
						(20.353)	(19.726)	(20.502)	(19.347)
	Rain						-0.0182	-0.0180	-0.0178
							(0.0189)	(0.0170)	(0.0166)
	Fatalities							-0.009	-0.009
								(0.0059)	(0.0058)
	Pop								0.035
									(0.099)
	Indirect		.	.	.	.	.	.	.
	Lag_PA	-0.029	-0.023	-0.022	-0.020	-0.020	-0.024	-0.022	-0.022
		(0.0788)	(0.0456)	(0.047)	(0.052)	(0.053)	(0.063)	(0.053)	(0.055)
	Mine		3.550	2.987	3.047	2.964	3.139	3.046	3.007
			(4.034)	(3.6413)	(3.415)	(3.826)	(4.013)	(3.689)	(3.284)
	Lag_PAxMine			0.00068	0.00073	0.00074	0.00079	0.00075	0.00074
				(0.0013)	(0.0017)	(0.0013)	(0.0017)	(0.0015)	(0.0015)
	Activity				2.495	2.417	2.541	2.294	2.117
					(3.604)	(3.854)	(4.044)	(3.8259)	(4.146)
	Temp					8.964	9.637	9.462	9.426
						(11.875)	(12.469)	(10.637)	(10.537)
	Rain						-0.0048	-0.0047	-0.0046
							(0.0089)	(0.0072)	(0.0071)
	Fatalities							-0.0024	-0.0024
								(0.0029)	(0.00313)
	Pop								0.009
									(0.041)
	Total		.	.	.	.	.	.	.
	Lag_PA	-0.128	-0.116	-0.114	-0.099	-0.10	-0.112	-0.109	-0.108
		(0.195)	(0.165)	(0.162)	(0.187)	(0.172)	(0.177)	(0.173)	(0.183)
	Mine		18.285**	15.620*	15.229*	14.846*	14.981*	14.745*	14.657*
			(8.132)	(8.193)	(8.351)	(8.962)	(8.661)	(8.0512)	(8.821)
	Lag_PAxMine			0.0036	0.0037	0.0037	0.0038	0.0036	0.0036
				(0.0046)	(0.0054)	(0.0045)	(0.0048)	(0.0049)	(0.0045)
	Activity				12.472	12.106	12.125	11.104	10.320
					(10.347)	(9.882)	(10.025)	(10.422)	(11.171)
	Temp					44.901	45.99*	45.803*	45.954*
						(28.975)	(27.71)	(26.759)	(26.529)
	Rain						-0.023	-0.023	-0.022
							(0.0258)	(0.0223)	(0.0221)
	Fatalities							-0.012	-0.0116
								(0.0079)	(0.008)
	Pop								0.0439
									(0.134)

*** p<0.01, ** p<0.05, * p<0.10; standard errors in parentheses

Table A -

 A 11. Marginal effects of covariates on deforestation, Heterogeneities; spatial autoregressive model without common factors

		Quality of institutions		Status of mines
		(Fatalities)
		Weak (1)	Strong
		(1)	(2)	(3)
		Direct
	Lag_PA	-0.022	-0.023*	-0.022*
		(0.018)	(0.014)	(0.012)
	Mine	64.261***	42.238***
		(9.737)	(6.719)
	Activity	12.0342**	18.092***	15,075***
		(5.511)	(5.994)	(4.854)
	Temp	1.225	2.754	2,229
		(8.267)	(6.477)	(5,976)
	Rain	-0.0226	-0.00428	-0.011
		(0.014)	(0.010)	(0.009)
	Pop	0.040	-0.035	0.040
		(0.093)	(0.113)	(0.079)
	Lag_PA x Mine	-0.00112	-0.00117
		(0.004)	(0.003)
	Pre_Operating Mine			52.182***
				(7,531)
	Fatalities			-0.009
				(0.008)
	Lag_PA×Pre_Operating mine			-0.0064
				(0.004)
		Indirect
	Lag_PA	-0.064	-0.057*	-0,063*
		(0.055)	(0.035)	(0.037)
	Mine	189.263***	104.197***	.
		(38.570)	(21.877)
	Activity	35.444**	44.631***	43.384***
		(17.494)	(16.094)	(15.112)
	Temp	3.607	6.793	6,415
		(24.792)	(16.415)	-17,501
	Rain	-0.067	-0.010	-0.0308
		(0.0439)	(0.025)	(0.028)
	Pop	0.118	-0.0872	0,115
		(0.279)	(0.285)	(0.231)
	Lag_PA×Mine	-0.0033	-0.0029	.
		(0.0124)	(0.008)
	Pre_Operating mine			150.177***
				(28.404)
	Fatalities			-0.026
				(0.023)
	Lag_PA×Pre_Operating mine			-0.0185
				(0.012)
		Total
	Lag_PA	-0.085	-0.080*	-0.084***
		(0.072)	(0.049)	(0.049)
	Mine	253.524***	146.434***	.
		(47.029)	(27.74)
	Activity	47.478**	62.723***	58.459***
		(22.868)	(21.842)	(19,792)
	Temp	4.832	9.5461	8.644
		(33.022)	(22.857)	(23,454)
	Rain	-0.0892	-0.0146	-0,042
		(0.058)	(0.035)	(0.037)
	Pop	0.158	-0.123	0,155
		(0.371)	(0.397)	(0.310)
	Lag_PA x Mine	-0.0044	-0.0041	.
		(0.0165)	(0.0115)
	Pre_Operating mines			202,359***
				(35,029)
	Fatalities			-0.035
				(0.030)
	Lag_PA x Pre_Operating mines			-0.0133162
				(0.016)

*** 𝑝 < 0.01, ** 𝑝 < 0.05, * 𝑝 < 0.1; standard errors in parentheses

United Nations, Department of Economic and Social Affairs, Population Division (2022). World Population Prospects

2022, Online Edition.

Early examples of the spatial econometric models date back to the 2000s[START_REF] Brueckner | Do Local Governments Engage in Strategic Property-Tax Competition?[END_REF][START_REF] Solé Ollé | Electoral accountability and tax mimicking: the effects of electoral margins, coalition government, and ideology[END_REF].

Providing theoretical foundations for spatial interactions allows addressing the criticisms of the last 10 years concerning these models[START_REF] Mcmillen | Issues in Spatial Data Analysis[END_REF][START_REF] Corrado | Where Is the Economics in Spatial Econometrics?[END_REF][START_REF] Gibbons | Mostly Pointless Spatial Econometrics?*[END_REF].

Moreover, five-year panel data are justified for other reasons: i) Some observations are not available every year. ii) This strategy allows to smooth out yearly variations in deforestation data that may be driven by measurement issues; iii) The inter-annual variability of some variables is low; iv) Not using annual data allows to neutralize the problems specific to time series: presence of a cointegration relationship or unit roots.

In the robustness check, we consider a spatial lag for each explanatory variable to reduce the finite-sample bias of endogeneity implied by measurement error and simultaneity[START_REF] Fingleton | Endogeneity in a Spatial Context: Properties of Estimators[END_REF].

Gabriel neighbours are defined by a Gabriel graph[START_REF] Gabriel | A New Statistical Approach to Geographic Variation Analysis[END_REF]. Inverse distance weight matrix is a geographical definition of neighbourhood based on the inverse geographical distance between spatial units.

From a technical point of view, the direct effects are measured by the average of the diagonal entries of the spatial weight matrix whereas the average of non-diagonal elements measures the indirect effects.

The Congo Basin countries are: Angola, Burundi, Central African Republic, Cameroon, Democratic Republic of Congo, Congo Republic, Gabon, Rwanda, Tanzania, and Zambia. The number of polygons is 537.

The sample was also split on the basis of the mean of the variable Fatalities. The results are unchanged.

Acknowledgements

We thank the online Séminaire d'Economie Géographique (SecGo) participants, especially L. Védrine and J. Le Gallo, for their comments and suggestions.


S Chabanet
email: sylvain.chabanet@univ-lorraine.fr

M Dumas

H Bril El-Haouzi

Philippe Thomas

In-person: ☒ Virtual in Zoom

Keywords: Machine Learning, applied artificial intelligence Sawmills, ICP dissimilarity, Ensemble of shape functions, k nearest neighbors, simulation metamodeling

In the sawmill industry, to predict the set of lumber that would be sawed from specific wood logs is a difficult problem. Even if they exist many sawmill simulators able to simulate the sawing process in order to predict these quantities, they can be too slow for large scale industrial problems. Replacing these simulators with machine learning surrogate models, or metamodels, is a promising avenue of research to speed up predictions. One such research direction is based on the computation of pairwise dissimilarities between logs, used, for example, by k-nearest neighbor algorithms. Interesting results have been obtained with the so-called iterative closest point (ICP) dissimilarity who has, however, several undesirable properties. This paper explores another alternative based on ensemble of shape functions.

Introduction

Sawmills are key elements of the forest product industry transforming wood logs into various lumber. Several factors, including heterogeneity of the raw material, introduce uncertainty on the mix of lumber that can be obtained from sawing a batch of logs. For this reason, academics and industrials have developed sawing simulators that are able to simulate the sawing of individual logs based on a description of their shapes, and sometimes internal defects. Shape information commonly comes in the form of 3D scans of the full profile of the logs, obtained using laser scanners (Fig. 1). Fig. 1 Full profile 3D scan of a log. The scale is in centimeters.

These simulators can be used to support decisionmaking by alleviating the uncertainty associated with the sawing process, by predicting sets of lumber that might be obtained from every individual log [START_REF] Morin | Machine learning-based models of sawmills for better wood allocation planning[END_REF]. In the following of this article, this set of lumber sawed from one log is called its basket of products (BoP).

However, the time taken by such simulation can be too long for practical use for decision problems involving thousands of logs. A single simulation can, indeed, take several minutes, or even more than one hour in some cases.

For this reason, researchers have proposed to replace these simulators with machine learning metamodels, i.e, surrogate models based on machine learning algorithms trained on past simulation results to predict BoP of new logs [START_REF] Morin | Machine Learning-Based Metamodels for Sawing Simulation[END_REF].

Few machine learning algorithms, however, allow making predictions based directly on 3D scans. These scans are, indeed, 3D points cloud, containing unordered points spanning the log surface. The number of points also varies from one scan to another.

Two main approaches have been proposed in past works to predict BoP of logs. The first one, introduced in [START_REF] Morin | Machine Learning-Based Metamodels for Sawing Simulation[END_REF], builds a structured representation of the logs based on a collection know-how features commonly used in the forest-product industry. The second approach, introduced in [START_REF] Selma | An Iterative Closest Point Method for Measuring the Level of Similarity of 3D Log Scans in Wood Industry[END_REF], is to compute a pairwise dissimilarity between 3D logs scans. These dissimilarities can then be used to predict BoP using, for example, a k nearest neighbors (kNN) algorithm.

Such a dissimilarity is a real-valued function 𝑑(𝑥 1 , 𝑥 2 ), with 𝑥 1 , 𝑥 2 two log scans, that intuitively measure how alike the two scans are. It is, in its usage, similar to a distance, but does not necessarily respect the properties of one, such as symmetry or positivity.

The dissimilarity used in previous works [START_REF] Selma | An Iterative Closest Point Method for Measuring the Level of Similarity of 3D Log Scans in Wood Industry[END_REF]- [START_REF] Chabanet | Dissimilarity to Class Medoids as Features for 3D Point Cloud Classification[END_REF] to predict logs BoP is the so-called Iterative Closest Point (ICP) dissimilarity. This dissimilarity is a consequence of the Iterative Closest Point algorithm [START_REF] Besl | Method for registration of 3-D shapes[END_REF], which is classically used to align 3D point clouds. While this The remaining of this paper is structured as follows. Section 2 first introduces both the ICP and ESF-based dissimilarities, as well as their advantages. Numerical experiments comparing the performances of these dissimilarities to predict logs baskets of products are presented section 3. Section 4 concludes and proposes future research directions.

Dissimilarities computation 2.1. ICP dissimilarity

The ICP dissimilarity is a consequence of the Iterative Closest Point algorithm, which is an iterative algorithm for the fine registration of 3D shapes. This algorithm starts with two points clouds; one usually called the source and the other the target. It then searches for a rotation and a translation to minimize a position-dependent dissimilarity between the point clouds and align the source on the target.

The main steps of an iteration are as follows:

• Pair every point in the sources with its closest neighbor in the target. Points from the target may be selected several times or not at all. This step yield 𝑁 𝑆 pairs (𝑠, 𝑡 𝑠 ), with 𝑁 𝑆 the number of points in the source, s a point from the source and 𝑡 𝑠 its closest neighbor in the target. • Find a rotation R and a translation T minimizing 𝐷(𝑅, 𝑇) = ∑ (𝑅𝑠 + 𝑇 -𝑡 𝑠 ) 2

𝑠

. A closed-forms solution of this minimization problem can, in particular, be efficiently computed using quaternion theory [START_REF] Besl | Method for registration of 3-D shapes[END_REF].

• Apply the transformation obtained, go back to the first step, and loop until some ending criterium, such as a maximum number of iterations, is obtained. It can be shown that the value of 𝐷(𝑅, 𝑇) decreases at every iteration of the algorithm. It, therefore, converges to a local minimum. The value of 𝐷(𝑅, 𝑇) obtained at the end of the last iteration of the algorithm is what is kept as the ICP dissimilarity 𝑑 𝐼𝐶𝑃 . Several inconveniences of this dissimilarity should, however, be noticed. Firstly, due to the non-symmetric roles of the target and source in the ICP algorithm, the ICP dissimilarity isn't symmetric, and in general 𝑑 𝐼𝐶𝑃 (𝑥 1 , 𝑥 2 ) is not equal to 𝑑 𝐼𝐶𝑃 (𝑥 2 , 𝑥 1 ). Secondly, the computation of 𝑑 𝐼𝐶𝑃 is highly dependent on the number of points in the source 𝑁 𝑆 and target 𝑁 𝑇 . More precisely, the complexity of one iteration of the ICP algorithm ranges from 𝑂(𝑁 𝑆 𝑁 𝑇 ) to 𝑂(𝑁 𝑆 log(𝑁 𝑇 ))

depending on the implementation of the closest neighbor search.

ESF dissimilarity

The ESF dissimilarity, 𝑑 𝐸𝑆𝐹 , is based on the representation of the logs scan as a collection of q normalized histograms ℎ 1 , … , ℎ 𝑞 . These histograms have to be computed only once for every log, and can be stored and reused for multiple dissimilarities computation.

Every histogram ℎ 𝑗 approximates the distributions of values taken by a shape function 𝑓 𝑗 evaluated over groups of points sampled at random from a scan. Various shape functions can be used. Three common functions were selected to be used in this paper. The first is the Euclidean distance between 2 points, the second is the angle defined by three points, and the third is the area of the triangle defined by three points. An example of these three histograms computed for one log is presented The ESF dissimilarity between two logs is then defined as the sum of the 𝐿 2 distance between the histograms of both logs:

𝑑 𝐸𝑆𝐹 (𝑥 1 , 𝑥 2 ) = ∑ ∥ h 1j -ℎ 2𝑗 ∥ 2 𝑞 𝑗=1 , (1)
with h 1j and h 2j the histograms of the first and second log respectively. Interestingly, the complexity of computing 𝑑 𝐸𝑆𝐹 does not depend on the number of points in the scans. It is, instead, governed by two selected by the user. The first one is the number of pair or triplet of points selected at random to estimate the histogram representation of the scan. This parameter was set to 2 17 ,in this paper, by trial and error in order to stabilize the histogram estimates. The second is the number of bins in the histograms, fixed to 64 here.

Experiments

This section presents numerical experiments comparing the performances of kNN algorithms based on either the ESF or ICP dissimilarity to predict BoP of logs. The dataset and evaluation scores are presented first, followed by the results.

Dataset

The dataset used for the experiments described in this paper originates from the Canadian sawmill industry. It contains information over 2219 real softwood logs. The 3D scan of every log is available, as well as their basket of products simulated by the sawing simulator optitek [START_REF] Goulet | Optitek -User's Manual[END_REF].

The scans of logs are composed of rough ellipsoids spanning the log surface. All scans are i initially oriented around the z-axis, with the first ellipsoid starting at z=0. This original orientation was kept as initial position when running the ICP algorithm to compute dissimilarities.

The sawmill modeled by the simulator could produce up to 74 types of lumber, characterized by their length, width, thickness, and grade (an evaluation of their quality). To simplify the prediction problem, the products were aggregated by grade, which reduce their number to 47, characterized only by their dimensions. A basket of products is, therefore, modeled as a vector of size 47. The i th component represents the number of lumber of type I presents in the basket of products.

For experimental purpose, this dataset was repeatedly divided into a training set containing 1500 logs and a test set containing the remaining 719 logs. This dividing was repeated independently 30 times, the training set used as examples set by a kNN regressor algorithm, which is then evaluated on the test set.

Considering that the prediction problem is, here, modeled as a regression problem, the kNN prediction is the average of the baskets of the input log neighbors, and not necessarily a feasible basket. In particular, the kNN can predict non integer lumber quantities. This might not be a problem depending on the usage of the prediction, especially if, has done in [START_REF] Morin | Machine learning-based models of sawmills for better wood allocation planning[END_REF], the predictions of individual logs are aggregated and used as input to a mix-integer programming problem.

Evaluation scores

Several evaluation scores are used in this study to evaluate and compare the predictive performances of the kNN algorithms using either dissimilarity. The first one is the usual root mean squared error between real and predicted baskets:

𝑅𝑀𝑆𝐸 = √ 1 𝑁 ∑ ∑ (𝑦 ̂𝑙𝑖 -𝑦 𝑙𝑖 ) 2 47 𝑖=1 𝑁 𝑙=1 , (2)
with N the size of the training set, 𝑦 ̂𝑙𝑖 the predicted quantity of lumber of type i for the log l, and 𝑦 𝑙𝑖 the real quantity. Several researchers, however, have stressed that such classic evaluation scores would be difficult to interpret for field experts from the industry and have proposed alternatives, in particular, the predictionproduction score (𝑠 𝑝𝑟𝑒×𝑝𝑟𝑜 ) [START_REF] Morin | Machine Learning-Based Metamodels for Sawing Simulation[END_REF] and a variation of the 𝐹 1 score adapted to this problem [START_REF] Martineau | Neural Network Architectures and Feature Extraction for Lumber Production Prediction[END_REF].

In order to define the prediction-production scores, both the prediction score 𝑠 𝑝𝑟𝑒 and production score 𝑠 𝑝𝑟𝑜 need to be defined. Both are defined on a log-perlog basis.

The prediction score, 𝑠 𝑝𝑟𝑒 , is the per-product average of the predicted lumber quantity over the real lumber quantity:

𝑠 𝑙 𝑝𝑟𝑒 = 1 𝑝 ∑ min(1, 𝑦 ̂𝑙𝑖 max(𝑦 𝑙𝑖 , 𝜀) ) 𝑝 𝑖=1 . (3)
𝜀 is, here, a very small quantity introduced to avoid dividing by 0. The index l in 𝑠 𝑙 𝑝𝑟𝑒 is added to stress the dependency over a specific log. Considering that this score is extremely sensible to (0, 0) predictedproduced pairs which might make this score too optimistically biaised due to the sparsity of the produced and predicted basket of product, all such pairs are removed before computing this score. 𝑝 is the number of non filtered products, which can vary from one log to another. The production score, 𝑠 𝑝𝑟𝑜 , is similarly defined as the per-product average of the real lumber quantity over the predicted lumber quantity:

𝑠 𝑙 𝑝𝑟𝑜 = 1 𝑝 ∑ min(1, 𝑦 𝑙𝑖 max(𝑦 ̂𝑙𝑖 , 𝜀) ) 𝑝 𝑖=1 . ( 4
)
The prediction-production score is then naturally defined as:

𝑠 𝑝𝑟𝑒×𝑝𝑟𝑜 = 1 𝑁 ∑ 𝑠 𝑙 𝑝𝑟𝑒 × 𝑠 𝑙 𝑝𝑟𝑜 𝑁 𝑙=1 . (5)
Similarly to the prediction-production scores, a variant of the 𝐹 1 score has been defined by [START_REF] Martineau | Neural Network Architectures and Feature Extraction for Lumber Production Prediction[END_REF] based on redefinitions of the numbers of True Positive (TP), 19-21 October 2022, Corfu, Greece False Positive (FP) and False Negative (FN) computed on a log per log basis.

• The number of true positives 𝑇𝑃 𝑙 is the number of lumber predicted and produced. 𝑇𝑃 𝑙 = ∑ min(𝑦 ̂𝑙𝑖 , 𝑦 𝑙𝑖 ) 47 𝑖=1

. • The number of false positives 𝐹𝑃 𝑙 is the number of lumber predicted but not produced. 𝐹𝑃 𝑙 = ∑ max(𝑦 ̂𝑙𝑖 -𝑦 𝑙𝑖 , 0) 47 𝑖=1 • The number of false negatives 𝐹𝑁 𝑙 is the number of lumber produced but not predicted. 𝐹𝑁 𝑙 = ∑ max(𝑦 𝑙𝑖 -𝑦 ̂𝑙𝑖 , 0) 47 𝑖=1

.

The 𝐹 1 score is then redefined as:

𝑠 𝑝𝑟𝑒×𝑝𝑟𝑜 = 1 𝑁 ∑ 2 × 𝑇𝑃 𝑙 2 × 𝑇𝑃 𝑙 + 𝐹𝑃 𝑙 + 𝐹𝑁 𝑙 𝑁 𝑙=1 . (6)

Results

As detailed previously, the dataset was divided 30 times into a training and a test sets. For every dividing, two kNN algorithms searching neighbors with the ICP dissimilarity and ESF dissimilarity were trained on the train set and evaluated on the test set. In each case, the parameter k was tuned by 5 folds cross-validation on the training set, using the RMSE as basis for comparisons. k was selected among [START_REF] Morin | Machine learning-based models of sawmills for better wood allocation planning[END_REF][START_REF] Chabanet | Dissimilarity to Class Medoids as Features for 3D Point Cloud Classification[END_REF]10,20]. All experiments were run on an Intel Core i7 vPRO 10 th generation CPU at 2.70 GHz.

Experimental results are exposed Table 1. This table exposes the average and standard deviation over the repetitions of the experiments of the RMSE, prediction-production and F 1 scores for the kNN algorithms based on the ICP and on the ESF dissimilarities respectively.

The kNN based on the ESF dissimilarity has, in average, lower RMSE and higher predictionproduction score and F 1 than the kNN based on the ICP dissimilarity. The poor performances of the ICP dissimilarity is, in part, due to the fact that it is not symmetric. In particular, replacing 𝑑 𝐼𝐶𝑃 (𝑥 1 , 𝑥 2 ) by 𝑑 𝐼𝐶𝑃 (𝑥 1 , 𝑥 2 ) + 𝑑 𝐼𝐶𝑃 (𝑥 2 , 𝑥 1 ) give a far lower RMSE, at 2.17. It, however, double the number of ICP computations needed to yield a prediction and is, therefore, not considered in the following.

To comfirm this difference between ICP and ESF dissimilarities, scores of both methods were compared by using student statistical test with Nadeau and Bengio correction [START_REF] Bouckaert | Evaluating the Replicability of Significance Tests for Comparing Learning Algorithms[END_REF]. This correction aim to take into account the dependency between results obtained for various dividing of the same dataset into a training and test sets. Given two prediction method A and B yielding evaluations 𝑎 𝑗 and 𝑏 𝑗 over J independent dividing of a dataset, the statistic of this test is:

𝑡 = ∑ 𝑎 𝑗 -𝑏 𝑗 𝑗 √( 1 𝐽 + 𝑛 2 𝑛 1 )𝜎 ̂2, (7)
with 𝑛 1 the size of the training set, 𝑛 2 the size of the test set and 𝜎 ̂2 an estimate of the variance of the differences 𝑎 𝑗 -𝑏 𝑗 . The p-value of the test is then computed from the usual student distribution with J-1 degrees of freedom. This test yield, here, a p-value of 3 × 10 -3 when applied to the RMSE, 0.6 when applied to the prediction-production scores, and 5 × 10 -15 when applied to the F 1 . Therefore, the difference can be considered statistically significant for two of the three evaluation scores. The ESF dissimilarity might also appear interesting in terms of computational cost. The scan of logs used during the experiments exposed in this paper contains, in average, 18 452 points, and the average ICP dissimilarity computation time is 0.1 seconds, with 10 iterations of the algorithm. The implementation was based on Open3D library for python. The ESF dissimilarity was implement from scratch using the numpy python library. The computation of the collection of histograms for each logs took, in average, 5.8s per scan. These histograms, however, need to be computed only once for every log. In particular, when predicting the BoP of a log, only its own histograms need to be computed, because the others can be considered to have been computed and stored previously. Computing the ESF dissimilarity from precomputed histograms is, then, extremely fast. In particular, it tooks only 0.0014s in average for the implementation used during experiments. Whether the ICP or ESF dissimilarities would be faster in practice would then depends on the specific user implementation, ability to parallelize the ICP computations and size of the kNN algorithm example set. The ESF dissimilarity appears, however, preferable for large example sets.

Conclusion

This paper explores an alternative to the ICP dissimilarity to predict BoP of logs based on their 3D scans. More precisely, it proposes the use of the ESF dissimilarity, based on the computation of an intermediary representation of the scans as an ensemble of histograms. The computation of this representation can take several seconds, but only needs to be computed once for every log. Computation of the distance between the histograms is then far faster than computation of the ICP dissimilarity, which is advantageous for kNN algorithms with large example sets.

Additionally, when predicting BoP of logs with a kNN algorithm, the ESF dissimilarity leads to lower RMSE error and higher F 1 than the ICP dissimilarity.

Others machine learning algorithms, however, have been explored to predict BoP of logs from their 3D scans. These algorithms use a representation of a scan as a vector of dissimilarity toward a small set of preselected representative scans. Whether or not the ESF would still compare favorably for these algorithms needs to be explored in future works.

  Fig 2.

Fig 2 .

 2 Fig 2. Histograms of the three shapes functions of a log scan used to compute the ESF dissimilarities.

Table 1 .

 1 Average and standard deviation of the evaluation scores of kNN regressors based on the ICP and ESF dissimilarities, taken over the 30 dividing of the datasets. The best model for each score is highlighted in bold.

	Dissimilarity	RMSE	𝐬 𝐩𝐫𝐞×𝐩𝐫𝐨	𝐅 𝟏
	ICP	3.05 (0.34)	34.8 (7.1)	35.3 (1.2)
	ESF	2.18 (0.25)	39.3 (8.0)	50.2 (1.0)

rd International Conference on Advances in Signal Processing and Artificial Intelligence (ASPAI' 2022), 19-21 October 2022, Corfu, Greece

Acknowledgements

The authors gratefully acknowledge the financial support of the ANR-20-THIA-0010-01 Projet LOR-AI (lorraine intellgence artificielle) and région Grand EST.

We are also extremely grateful to FPInnovation who gathered and processed the dataset we are working with.