Vikas Kumar
email: vikas.kumar@uwe.ac.uk

Archana Kumari
email: archana.kumari@uwe.ac.uk

Ximing Ruan
email: ximing.ruan@uwe.ac.uk

Jose Arturo Garza-Reyes

Supalak Akkaranggoon

Investigating Key Antecedents of Customer Satisfaction in B2B information Service Firms

Keywords: Information Services, FSQ, TSQ, Corporate Image, Customer Satisfaction, B2B, Service Management e-business, e-government

Service sector has grown significantly over the years and now is one of the major contributors of the Gross Domestic Product (GDP) of most of the developed and developing economies. Within the service sector, information economy has grown significantly with the rapid developments in the Internet and Communication Technologies (ICTs). However, the research so far has focused on the manufacturing sector rather than the service sector. This paper, therefore, aims to fill this void by testing the service management and Service Quality (SERVQUAL) theories in Businesses to Business (B2B) information services context. An empirical investigation with secondary data is carried out to explore the relationship between three key antecedents of Customer Satisfaction (CS) namely; Functional Service Quality (FSQ), Technical Service Quality (TSQ) and Corporate Image (CI). This re-search also aims to investigate the interrelationship between the three key antecedents of customer satisfaction. The findings show that FSQ, TSQ, and CI are positively correlated with customer satisfaction. Results also show that CI is positively correlated with TSQ and FSQ.

Introduction

Over the years, the manufacturing sector has dominated the world economy; however, the world economy is now slowly transforming to a service based economy. The growing importance of services to the economy can be realized by the fact that service sector nowadays is a major contributor to the Gross Domestic Product (GDP) of most of the developed and developing nations [START_REF] Lovelock | Services Marketing: People, technology, strategy[END_REF] [START_REF] Kumar | Dependability a Key Element for Achieving Competitive Advantage: A Study of Information Service Firms[END_REF]. For example, the contribution of services to the U.S. GDP is around 80%, UK around 73%, Japan around 74%, France around 73% and Germany is around 68% [START_REF] Lovelock | Services Marketing: People, technology, strategy[END_REF] [2] [START_REF] Paulson | Services Science: A New Field for Today's Economy, Industry Trends[END_REF]. The growth in service sector is primarily attributed to the rapid advancements and implementations of the Internet and Communication Technologies (ICTs). ICT growth has led to the emergence of the information sector as a strong contributor in the service dominant economy. The significance of information economy was firstly highlighted by Machlup [4] and then later by Porat and Rubin [START_REF] Porat | The Information Economy (9 Volumes)[END_REF] who attempted to measure the US information economy. In the late 70s, Porat and Rubin [START_REF] Porat | The Information Economy (9 Volumes)[END_REF] measured the size and structure of the US information economy. Their findings reveal that the information sector contributed to around 46% of the US Gross National Product (GNP) in 1967. A research by Apte and Nath [START_REF] Apte | Size, structure and growth of the US information economy[END_REF] concluded that the contribution of the information sector to US GNP rose to around 63% in 1997. The significance of information economy was further verified by [START_REF] Godin | The Information Economy: the History of a Concept through it Measurement, 1949-2005[END_REF] and [START_REF] Kumar | An Empirical Investigation of the Linkage between Dependability, Quality and Customer Satisfaction in Information Intensive Service Firms[END_REF], who point out that during the last fifty years, developed or developing economies have evolved from a goods or manufacturing-oriented economy to a service oriented and now have moved on to the information-oriented economy.

Information economy has become integral part of the economy and their contribution cannot be ignored. However, the research so far has primarily focused on the manufacturing sector. In light of the growing significance of information services in the worldwide economy and the lack of enough research evidence, this paper sets out to test some of the service management and SERVQUAL theories in the context of information service settings, particularly, in Business to Business (B2B) information service firms. Literature identifies Service Quality and Corporate Image as key indicators of Customer Satisfaction [START_REF] Grönroos | Service quality: the six criteria of good perceived service quality[END_REF] [10] [START_REF] Srivastava | Service Quality, Corporate Brand Image, and Switching Behavior: The Mediating Role of Customer Satisfaction and Repurchase Intention[END_REF] [12] [START_REF] Ishaq | Role of corporate image, product quality and customer value in customer loyalty: Intervening effect of customer satisfaction[END_REF]. Nevertheless, quality is often treated as multidimensional construct in services which can be understood from two main dimensions: Technical Service Quality (TSQ) and Functional Service Quality (FSQ) [START_REF] Kumar | An Empirical Investigation of the Linkage between Dependability, Quality and Customer Satisfaction in Information Intensive Service Firms[END_REF] [9] [START_REF] Levesque | Determinants of customer satisfaction in retail banking[END_REF] [15] [START_REF] Kumar | Alternative Perspectives on Service Quality and Customer Satisfaction: The Role of BPM[END_REF]. Existing literature has identified a number of antecedents of customer satisfaction, such as; quality, trust, dependability, corporate image and waiting time [START_REF] Chi | Examining the structural relationships of destination image, tourist satisfaction and destination loyalty: An integrated approach[END_REF] [18] [START_REF] Kumar | The impact of operations performance on customer loyalty[END_REF]. However, this research will primarily investigate the linkages between three key antecedents of customer satisfaction: Technical Service Quality, Functional Service Quality, and Corporate Image and their impact on customer satisfaction in the context of B2B information service organizations. The choice of three antecedents is restricted by the availability of the secondary data provided by the case organization. In addition, the interrelationship between the three key antecedents of customer satisfaction has not been fully explored in literature and this study aims to also bridge this gap.

The rest of the paper is organized as follows. Next section reviews a number of research papers to set out the context of the research and identify the linkages among the variables. Section 3 delineates the research objectives and proposes the research framework. Section 4 elaborates the research methodology. The findings of the research are presented in section 5. Section 6 concludes this study and sets out the direction for future research

Theoretical Background

Earlier discussion indicates that with the rapid advancement in ICTs, economy is slowly moving towards a more information based economy. However, very few researchers have looked at the information service sector [START_REF] Lovelock | Services Marketing: People, technology, strategy[END_REF] [2] [6] [7] [START_REF] Kumar | An Empirical Investigation of the Linkage between Dependability, Quality and Customer Satisfaction in Information Intensive Service Firms[END_REF]. Literature also indicates that the growth in information technology, inter-net and web technologies has revolutionized the way in which Business to Business (B2B) and Business to Customers (B2C) organizations interact and offer services to their customers [START_REF] Zhao | Using Semantic Web Technologies for Representing E-science Provenance, The Semantic Web -ISWC[END_REF] [START_REF] Bhappu | The Role of Relational and Operational Performance in Business-to-Business Customers' Adoption of Self-Service Technology[END_REF]. B2B and B2C firms have different characteristics that set them apart from each other, for example, different types of purchases and authorizations; unique contracts, terms, and conditions for different business customers; variety of customer sizes, demands and requirements; and different level of participation in customer's supply chain [START_REF] Kumar | An Empirical Investigation of the Linkage between Dependability, Quality and Customer Satisfaction in Information Intensive Service Firms[END_REF] [START_REF] Minett | B2B Marketing[END_REF] [23] [START_REF] Homburg | How organizational complaint handling drives customer loyalty: an analysis of the mechanistic and the organic approach[END_REF]. Due to these differences, the strategies adopted by B2B and B2C firms vary [START_REF] Mithas | Why Do Customer Relationship Management Applications Affect Customer Satisfaction[END_REF]. A study by Rauyruen and Miller [START_REF] Rauyruen | Relationship quality as a predictor of B2B customer loyalty[END_REF] further suggests that B2B service providers need to understand the nature and the circumstances of their customers. Therefore, B2B service-providers should pay attention to the quality control of their service delivery systems and must put a lot of effort into creating high-level perception of the service quality [START_REF] Kumar | An Empirical Investigation of the Linkage between Dependability, Quality and Customer Satisfaction in Information Intensive Service Firms[END_REF]. Tang et al. [START_REF] Tang | B2B brand extension to the B2C market-The case of the ICT industry in Taiwan[END_REF] argues that perceived service quality is an important factor in the B2B. This was also noted in the study of Bhappu and Schultze [START_REF] Bhappu | The Role of Relational and Operational Performance in Business-to-Business Customers' Adoption of Self-Service Technology[END_REF], where they found that in the B2B environment, both the relational (soft quality) and operational performance (hard quality) are of prime significance particularly for achieving customer satisfaction. However, apart from the study by Bhappu and Schultze [START_REF] Bhappu | The Role of Relational and Operational Performance in Business-to-Business Customers' Adoption of Self-Service Technology[END_REF] there are limited studies that aim to investigate the significance of the service quality dimensions in the B2B environment [27] [28] [29]. This study, therefore, aims to empirically provide further evidence of the relationship between FSQ, TSQ and Customer Satisfaction in a B2B service setting.

The drivers of customer satisfaction are well highlighted in the operations management literature, which identifies service quality, speed, flexibility, cost, corporate image and dependability as critical drivers [START_REF] Grönroos | Service quality: the six criteria of good perceived service quality[END_REF] [18] [19] [START_REF] Gonzalez | Assessing tourist behavioural intensions through perceived service quality and customer satisfaction[END_REF]. One of the popular frameworks that identify the linkage between quality and customer satisfaction is the service profit chain proposed by Heskett et al. [START_REF] Heskett | Putting the service-profit chain to work[END_REF]. In brief, it proposes a positive linear relationship between staff satisfaction, service quality and customer satisfaction leading, ultimately, to profitability [START_REF] Kumar | Alternative Perspectives on Service Quality and Customer Satisfaction: The Role of BPM[END_REF]. Gonzalez et al. [START_REF] Gonzalez | Assessing tourist behavioural intensions through perceived service quality and customer satisfaction[END_REF] also identify perceived service quality as an antecedent of satisfaction. This was also further verified in the work of [START_REF] Kumar | Dependability a Key Element for Achieving Competitive Advantage: A Study of Information Service Firms[END_REF] [19] [START_REF] Sohail | Service quality in hospitals than you might think[END_REF] [START_REF] Chiou | Service Quality, Trust, Specific Asset Investment, and Expertise: Direct and Indirect Effects in a Satisfaction-Loyalty Framework[END_REF]. These SERVQUAL studies show that a strong link exists between customer satisfaction and service quality. Parasuraman et al. [START_REF] Parasuraman | A conceptual model of service quality and its implications for future research[END_REF] differentiate the service quality construct as Functional Service Quality (FSQ) (doing things nicely) and Technical Service Quality (TSQ) (doing things right). Grönroos [START_REF] Grönroos | A service quality model and its marketing implications[END_REF] suggests that dissatisfaction occurs if expectations are greater than actual performance. As a result, evaluations are not based solely on the outcome of the service, the technical quality; they also involve the process of service delivery or functional quality. A number of published researches emphasize the relationship between the two dimensions of service quality (i.e. technical and functional) and customer satisfaction [START_REF] Kumar | Alternative Perspectives on Service Quality and Customer Satisfaction: The Role of BPM[END_REF] [START_REF] Lassar | Service quality perspectives and satisfaction in private banking[END_REF] [36] [START_REF] Bell | Customer Relationship Dynamics: Service Quality and Customer Loyalty in the Context of Varying Levels of Customer Expertise and Switching Costs[END_REF]. A study by Rosenzweig and Roth [START_REF] Rosenzweig | Towards a theory of competitive progression: Evidence from High-Tech Manufacturing[END_REF] shows that an interrelationship exists between the two dimensions of service quality, i.e., TSQ and FSQ. They further provide empirical evidence of their impact on profit-ability. Lai and Yang [START_REF] Lai | Effects of employees perceived dependability on success of enterprise applications in e-business[END_REF] also demonstrate that TSQ affects user satisfaction positively. Apart from the service quality dimensions, corporate image has also emerged as one of the drivers of customer satisfaction and loyalty. Andreassen and Lindestad [START_REF] Andreassen | Customer loyalty and complex services: the impact of corporate image on quality, customer satisfaction and loyalty for customers with varying degrees of service expertise[END_REF] based on data from 600 individual customers, reported that corporate image impacts customer satisfaction and loyalty. Their study also reports that corporate image impacts customer loyalty directly. This relationship was also reported in the study of Martenson [41] where they showed that corporate image is a key driver of customer satisfaction. Cameran et al. [START_REF] Cameran | Customer satisfaction, corporate image, and service quality in professional services[END_REF] in their study of the professional service firms show that corporate image and service quality impacts customer satisfaction. Wu et al. [START_REF] Wu | An empirical analysis of synthesizing the effects of service quality, perceived value, corporate image and customer satisfaction on behavioral intentions in the transport industry: A case of Taiwan high-speed rail[END_REF] show that higher perceptions of service quality have a positive influence on corporate image. The study also indicates that higher perceptions of corporate image influences customer satisfaction positively. The literature review clearly indicates that service quality dimensions (FSQ and TSQ) and corporate image influence customer satisfaction and customer loyalty positively. Moreover, there is an interrelationship between service quality dimensions (FSQ and TSQ) and corporate image.

The information sector has shown rapid growth in the last few decades and has started showing the dominance in today's economy. The literature review further indicates that FSQ, TSQ, and Corporate Image influences Customer Satisfaction. However, literature investigating these relationships in a B2B information service environment is scarce. Realizing the gap in the literature, this paper sets out to fill this void by empirically investigating the service management and SERVQUAL theories that links these variables together in B2B information services. The next section provides the research framework and propositions to be tested in this research.

Research Model and Propositions

The literature review highlights that functional service quality (FSQ); technical service quality (TSQ); and corporate image (CI) affect customer satisfaction (CS) and loyalty. This investigation is a confirmatory study which aims to test the findings of service management and SERVQUAL literature in the context of B2B information service settings. This study looks beyond the traditional linkages between these variables and sets out to understand their interrelationships. Apart from highlighting the linkages, this study also stresses that performing well on these dimensions can help B2B information service firms to successfully meet customer satisfaction levels which in the longer run can lead to customer loyalty and ultimately benefit firms to achieve sustainable competitive advantage. The study primarily focuses on identifying the significance of Functional Service Quality, Technical Service Quality, Corporate Image and Customer Satisfaction. The investigation involves assessing these relationships in a large B2B information intensive firm operating in the UK. Customer loyalty is not included in the framework due to the restrictions imposed by the secondary data. This research sets out to test the following relationships in the context of information service settings:

 Functional Service Quality (FSQ) affects Customer Satisfaction  Technical Service Quality (TSQ) affects Customer Satisfaction  Corporate Image (CI) affects Customer Satisfaction  An interrelationship exists between FSQ, TSQ, and CI The research framework tested in this research comprises of three key antecedents of customer satisfaction namely, FSQ, TSQ, and CI (see Fig. 1). As mentioned above, the literature review indicates that a number of papers link these individual key indicators with customer satisfaction, however, studies investigating their interrelation-ships in information service setting is limited. The study proposes a number of propositions derived from the framework based on the review of literature. This study sets out to test following propositions: P1: Functional Service Quality affects with Customer Satisfaction positively P2: Technical Service Quality affects Customer Satisfaction positively P3: Corporate Image affects Customer Satisfaction positively P4: Functional Service Quality and Technical Service Quality are positively correlated P5: Functional Service Quality and Technical Service Quality are also positively correlated with Corporate Image

The next section elaborates the research methodology and data collection method followed in this research.

Research Methodology

In management research, positivism has traditionally been much more dominant than phenomenology [START_REF] Kumar | An Empirical Investigation of the Linkage between Dependability, Quality and Customer Satisfaction in Information Intensive Service Firms[END_REF], [START_REF] Meredith | Alternative Research Paradigms in Operations[END_REF], [START_REF] Riege | Validity and Reliability Tests in Case Study Research: a Literature Review with "hand-on" Applications for each Research Phase[END_REF]. In this study the selection of the quantitative approach is not motivated by its dominance in management research; rather that the choice has been based purely on the research aims. This research therefore supports the positivist approach. A hypothetico-deductive approach has been followed where the hypotheses are constructed and guided by previous theories and later these hypotheses are tested, based on the gathered empirical data, and accepted or rejected as a part of the theorytesting. The explanatory nature of the research demanded that, in order to explore the causality, the variables need to be studied over time. Longitudinal time series data collected over 48 months' time frame was made available for researchers. Secondary data used in this research was collected by the B2B service firm by applying the collection and analysis protocols consistently. Bryman [START_REF] Bryman | Social Research Methods[END_REF] points out that secondary data are usually of high quality, as rigorous sampling procedures are employed and experienced researchers or data collection agencies are involved, following a structured approach and control procedures to ensure the quality of the collected data. Bryman [START_REF] Bryman | Social Research Methods[END_REF] further identifies that it offers the opportunity of longitudinal analysis and is less time-consuming, thus providing more time to the researcher for the data analysis. Thus, this study relies on the secondary longitudinal time series data for the analysis.

This research paper investigates a large information intensive B2B service firm operating in the UK. The case example studied is from the network branch of the B2B power supplier in the UK. The network branch is a distribution company that operates and maintains the electrical supply system for organizations with large energy needs and spends. The network branch currently provides energy to more than 30,000 organisations that together spend over £2bn on electricity and gas. For the B2B network branch the customers are mainly the Small and Medium scale Enterprises (SMEs) and large business firms. The firm offers a range of agreements for their business customers, such as fixed term contract, flexible purchasing contracts and specialist customer contracts. The firm measures and collects data through telephone interviews and surveys to monitor its performance over time. The secondary data set for a 48 months' time frame (48 data points) was made available for this research that comprised monthly measurements of variables considered as proxies for Functional Service Quality, Technical Service Quality, Corporate Image and Customer Satisfaction.

In this research, Functional Service Quality (FSQ) refers to soft quality or relational element of the quality whereas Technical Service Quality (TSQ) is referred as a hard quality or an ability to perform the promised service dependably and accurately, including time commitments [START_REF] Newman | Interrogating SERVQUAL: a critical assessment of service quality measurement in a high street retail bank[END_REF] [15] [START_REF] Kumar | Alternative Perspectives on Service Quality and Customer Satisfaction: The Role of BPM[END_REF]. The B2C service firms used a multi-dimensional scale to measure the FSQ and TSQ. The firm did not employ SERVQUAL scale to measure the quality construct. However, the measures used by the firm resemble to some of the items of the SERVQUAL scale including the empathy, access, assurance, and responsiveness dimensions. Corporate Image was also measured on a multi-dimensional scale. How-ever, Customer Satisfaction was measured on a single item scale as an overall satisfaction with the level of services provided. The constructs studied in this study were measured on a 5 point Likert scale and conform to the reliability and validity tests. FSQ, TSQ and CI were finally converted to a single scale item as Cronbach's Alpha value was > 0.70. The detailed scales of the variables studied are presented below: FSQ (Cronbach's Alpha = 0.90) FSQ_1: Staff were polite and helpful FSQ_2: They were able to provide sufficient information about the problem FSQ_3: I was able to easily contact them to find out about the problem TSQ (Cronbach's Alpha = 0.81) TSQ1: Overall, how would you rate the non-half hourly bills and billing service? TSQ2: Overall, how would you rate the non-half hourly meter reading service? TSQ3: Overall, how would you rate the half hourly statements and invoicing service?

TSQ4 The next section discusses the analysis findings.

Research Findings

Data analysis firstly involved running a correlation analysis (see Fig. 2). The analysis shows there is a positive correlation (0.615) between functional service quality and customer satisfaction with a significance level of P<0.01. This verifies our first proposition (P1). A positive correlation (0.601) was also evident between technical service quality and customer satisfaction significant at P<0.01 level. This verifies our second proposition (P2). Corporate image was also positively correlated with customer satisfaction (0.478) significant at P<0.05 level. This verified our third proposition (P3). The next step of the analysis was aimed at investigating the interrelationship between the three key antecedents studied in this research. A positive correlation was found between TSQ and CI (0.565) as well as between CI and FSQ (0.687) both significant at P<0.01 level. This verifies our fifth (P5) proposition. Interestingly, no significant correlation (0.310) was found between FSQ and TSQ. Thus, our proposition P4 could not be verified.

Conclusions

The paper shows that Functional Service Quality (FSQ), Technical Service Quality (TSQ) and Corporate Image (CI) are key antecedents of Customer Satisfaction (CS). The findings are interesting as these relationships were tested in a new context of B2B information services. The outcome shows that for B2B information service firms performing well on both quality dimensions (FSQ and TSQ) is very important to maintain a satisfied customer base. This counter argues some of the SERVQUAL findings (such as Grönroos [START_REF] Grönroos | Service quality: the six criteria of good perceived service quality[END_REF]) that prioritize FSQ over TSQ in achieving customer satisfaction by indicating that both dimensions are equally important. This verifies the earlier findings of Bhappu and Schultze [START_REF] Bhappu | The Role of Relational and Operational Performance in Business-to-Business Customers' Adoption of Self-Service Technology[END_REF], who emphasized the significance of both quality dimensions. Findings suggest that failure to meet quality expectations of customers can lead to dissatisfaction and ultimately customers can move on to other competitors. Another important finding of this study is the importance of corporate image in building customer satisfaction. The research also shows that FSQ and TSQ are positively correlated with corporate image thus suggesting an interrelation-ship between these three variables. While the literature tends to treat these three variables independently, the outcome of this research shows that the elements are closely linked. This also suggests that if firms perform well on quality dimensions their corporate image can be improved. However, analysis showed that FSQ and TSQ are not correlated. This is an interesting finding as, first it points out that both quality dimensions are distinct, an argument that has been widely argued in SERVQUAL literature. Secondly, a lack of correlation between these two variables also suggests that performing well on one dimension of service quality not necessarily improves the other dimension. Hence, B2B information service firms must focus on both dimensions of service quality to satisfy their customers. However, more evidence is required before generalizing the relationship between FSQ and TSQ in B2B information service setting. It is important to bear in mind that the findings presented in this paper are based on a single case example from a B2B information services context. Therefore, generalizations that we infer are limited to just B2B information services. We also intend to test these relationships using more case examples to support our findings and extend this study further by also investigating these relationships in B2C information services. Looking at these relationships over a longer time frame is also vital and this requires alternative methods of research. Longitudinal studies are necessary to test out some cause-effect phenomena.

Future studies should involve testing these relation-ships using more robust statistical methods such as multiple regressions and structural equation modeling in B2C information sector. Additionally, more case examples should be investigated to broaden the generalizations of the findings across the information services sector. Moreover, future studies should also aim to investigate the differences in the relationships among the variables between the SMEs and the large business firms.

Figure 1 .

 1 Figure 1. Research Framework

Figure 2 .

 2 Figure 2. Correlations

  : Overall, how would you rate the half hourly meter reading service?

	CI (Cronbach's Alpha = 0.80)
	CI. They are well-known
	CI. They have a good reputation
	CI. They are environmentally responsible
	CI. They support local communities
	CI. They recognize and reward your loyalty
	CI. They offer competitive prices
	CS: Overall, how would you rate their level of customer service?


Sébastien Desbureaux
email: sebastien.desbureaux@udamail.fr

Eric N Kéré

Motel Pascale Combes
email: pascale.combes-motel@udamail.fr

Catherine Araujo Bonjean

Keywords: Land use patterns, Deforestation, Environmental policies, Agricultural innovation. JEL codes O12, O13, Q15, Q23, R14

This paper analyzes deforestation leakages from natural rainforests to anthropized habitats following the creation of Protected Areas in Madagascar. A simple theoretical framework highlights that a conservation constraint does not necessarily create deforestation leakages on secondary forests. An original dataset is built combining fine scale vegetation cover images and spatialized census data over the period 2000 to 2012. Cover images allow us to distinguish a mosaic of landscapes. Multilevel panel regressions and matching techniques indicate a causal effect of Protected Areas on deforestation leakages. Though Protected Areas reduce deforestation in protected natural forests, forest clearing is mostly reported on other types of anthropized forests. Our results demonstrate the limitations of Porter-like mechanism in agricultural innovation. They also support the hypothesis of a conservation dilemma: protecting biodiversity may come at the expense of the welfare of locals who rely on local (provisioning) ecosystem services.

Introduction

Human beings have been modifying tropical forests for tens of thousands of years. Between 2000 to 2012 alone, an estimated 2.3 million square kilometers of forests have been lost worldwide [START_REF] Hansen | High-Resolution Global Maps of 21st-Century Forest Cover Change[END_REF]). These forests have been transformed mainly into agricultural lands [START_REF] Kissinger | Drivers of deforestation and forest degradation[END_REF] but also into anthropized forested landscapes that supply direct ecosystem services to locals (construction wood, fueldwood, charcoal etc), resulting in the development of many human-modified mosaic landscapes. Today 410 million people to depend highly on the access to natural and anthropized forests to support their livelihoods (WRI 2005).

International efforts to tackle tropical deforestation have increased since the early 1990s, partly in the name of the global ecosystem services forests provide to human beings, such as biodiversity conservation, carbon storage and sequestration [START_REF] Costanza | The value of the world's ecosystem services and natural capital[END_REF][START_REF] Mea | Ecosystems and human well-being[END_REF][START_REF] Costanza | Changes in the global value of ecosystem services[END_REF]. Protected Areas (PAs) remain the dominant policy answer to stopping deforestation of natural forests and have proven to be effective at attaining this objective [START_REF] Miteva | Evaluation of biodiversity policy instruments: what works and what doesn't?[END_REF]). Yet locals may simply displace deforestation from the created PA to elsewhere in the landscape. This phenomenon is known in the literature as deforestation leakage 1 . This paper examines the possibility of deforestation leakages from natural forests to anthropized forested areas following the creation of PAs in the context of Madagascar's rainforests. Madagascar is one of the top three countries worldwide in terms of mega-biodiversity [START_REF] Goodman | Natural history of Madagascar[END_REF]. Most of its terrestrial biodiversity is concentrated in natural forests. Over the last 60 years, the country has probably lost around 50% of its natural forest cover [START_REF] Harper | Fifty years of deforestation and forest fragmentation in Madagascar[END_REF][START_REF] Mcconnell | Protecting lemurs: Madagascar's forests[END_REF], making Madagascar one of the hottest spots for global biodiversity conservation [START_REF] Myers | Biodiversity hotspots for conservation priorities[END_REF]. Approximately 9 million hectares of natural forests remain in Madagascar, of which about 5.6 million are rainforest, located in the eastern ecoregion. According to our calculations, around 1.5 million people live in highly forested areas in Madagascar. Family agriculture is the principal economic activity of about 90% of these forest inhabitants, with slash and burn being the dominant agricultural technique for rice production (ed, the staple food in Madagascar). In a context of rapid population growth (2.9% average according to the World Bank), of an observed sharp decrease of fallow lengths [START_REF] Styger | Influence of slash-and-burn farming practices on fallow succession and land degradation in the rainforest region of Madagascar[END_REF])and of limited adoptions of agricultural innovations (Minten 1 The possibility of leakages also appears for other types of conservation instruments such as Payments for Environmental Services [START_REF] Shapiro | Forest conservation and slippage: Evidence from Mexico's national payments for ecosystem services program[END_REF][START_REF] Velly | PES Impact and Leakages over Several Cohorts: The Case of PSA-H in Yucatan, Mexico[END_REF] ; reforestation policies [START_REF] Meyfroidt | Forest transition in Vietnam and displacement of deforestation abroad[END_REF]Lambin 2009, forest concessions in Brazil (Oliveira et al. 2007) or REDD+ initiatives [START_REF] Aukland | A conceptual framework and its application for addressing leakage: the case of avoided deforestation[END_REF] and [START_REF] Minten | Agricultural Technology, Productivity, and Poverty in Madagascar[END_REF], slash and burn is the primary driver of deforestation, despite its practice on natural forests being prohibited since 1881 [START_REF] Jarosz | Defining and Explaining Tropical Deforestation: Shifting Cultivation and Population Growth in Colonial Madagascar (1896-1940)[END_REF]. As a result, a growing network of PAs now covers around 40% of the remaining forests (3.6 million hectares) and appear to have been effective in slightly reducing (but not in halting) deforestation on natural forests [START_REF] Gimenez | Impact of Protected Areas on Forests in Madagascar[END_REF][START_REF] Desbureaux | The impact of Protected Areas on Deforestation? An Exploration of the Economic and Political Channels for Madagascar's Rainforests[END_REF].

In addition to natural forests, vegetation data from satellite images clearly illustrate that a large part of the Malagasy landscape is now covered by anthropized forested areas (Figure 1).

These can be degraded remains of past natural forests, eucalyptus and pine plantations, and agro-forestry systems such as shaded cocoa or coffee groves. In the eastern ecoregion alone, the dataset we constructed reveals the presence of about 6.5 million hectares of anthropized forested areas with moderate or highly degraded tree cover. These areas are not of primary interest for biodiversity conservation or for carbon sequestration. They do however supply many provisioning ecosystem services to the local population. As soils' fertility in these degraded forests tends to be poor (particularly after eucalyptus plantation), most of these areas are often unsuitable for agriculture. However, anecdotal evidence from our field visits reveals a significant transformation of anthropized forests -namely the conversion of eucalyptus plantations into rice plantations at the edge of some PAs where we have previously worked (see Figure A1 in the Appendix). Some villagers repeatedly stated during informal discussions that they had decided to cultivate rice on eucalyptus parcels because clearing natural [ed, protected] forests was illegal. Thus, they simply displace rice production and deforestation elsewhere in the landscape rather than investing in more intensive agricultural techniques as predicted in a Porter-like hypothesis [START_REF] Porter | Toward a new conception of the environmentcompetitiveness relationship[END_REF]. By contrast, a recent study by geographers has reported notable intensification of agricultural practices in the north-east part of Madagascar where large PAs have been established [START_REF] Zaehringer | Beyond deforestation monitoring in conservation hotspots: Analysing landscape mosaic dynamics in north-eastern Madagascar[END_REF]. The authors hypothesize that this intensification may have been propelled by the establishment of PAs. Our deforestation dataset indicates that 57,000 hectares of highly degraded forested areas and 260,000 hectares of moderately degraded forested in the eastern ecoregion were lost lost between 2000 and 2012. Part of these losses may correspond to deforestation leakages from natural protected forests. If so, the protection of natural forests to conserve global ecosystem services may negatively impact local inhabitants who would experienced a weakening of provisioning ecosystem services provided by antrhopized areas.

The paper begins by theoretically highlighting via an agricultural household model taking into account ecosystem services how and under what conditions leakages from natural habitats to anthropized forests can occur after the establishment of PAs. In our model, the household can produce an agricultural commodity (rice) by clearing natural forests or by clearing anthropized forested areas (e.g., plantations). Standing anthropized forests provide the household provisioning ecosystem services (e.g. charcoal) when associated with some labor time. The household thus faces a land use conflict over anthropized forests: either it converts plantations in agricultural lands, harvests rice but loses direct ecosystem services, or it keeps the plantation and enjoys the ecosystem services. We show that conservation constraints on natural forests such as the creation of PAs if effective, release labor time for the household. Whether the household reallocate this time to agricultural production (the leakage effect), or to the production of ecosystem service will in the end depend on differences in marginal labor productivities for the two activities. Second, we empirically test for the presence of leakages from natural to human impacted forests between 2000 and 2012 for the entire Malagasy rainforest. We use a panel of 13 years of fine scale Landsat vegetation cover images to distinguish between three types of anthropized habitats: natural forests, a slightly degraded habitat and a highly degraded one. We spatialize census data then use multi-level panel regressions and matching techniques to exhibit a potential causal leakage effect of PAs. This study contributes to the impact evaluation literature regarding nature conservation policies. Recent studies converge to show that PAs have allowed for a reduction in deforestation of about 10% to 20%2 . These studies have mainly focused on a small number of countries in Latin America and South East Asia, but few concern Africa with the exception of [START_REF] Gimenez | Impact of Protected Areas on Forests in Madagascar[END_REF] and [START_REF] Desbureaux | The impact of Protected Areas on Deforestation? An Exploration of the Economic and Political Channels for Madagascar's Rainforests[END_REF] that look at Madagascar. We add to this literature by focusing on leakages. Previous studies find both close to no leakages [START_REF] Macedo | Decoupling of deforestation and soy production in the southern Amazon during the late 2000s[END_REF][START_REF] Soares-Filho | Role of Brazilian Amazon protected areas in climate change mitigation[END_REF], particularly negative leakages (Ewers and A. S. Rodrigues 2008) or positive leakages (Honey-Roseés, Baylis, and Ramirez 2011; [START_REF] Gaveau | Evaluating whether protected areas reduce tropical deforestation in Sumatra[END_REF][START_REF] Robalino | Contagious development: Neighbor interactions in deforestation[END_REF]. Our findings suggest that PAs have allowed for decreased deforestation in Madagascar within the protected natural forests themselves but have caused negative leakages: after the creation of PAs, deforestation in adjacent areas has increased.

To our knowledge, this papers is the first to examine leakages in a landscape, i.e. leakages from natural habitats to already anthropized areas instead of leakages from protected natural forests to other natural yet unprotected forests. In Madagascar, PAs are large in sizes. New PAs cover areas of up to more than 600,000ha. Thus, leakages from protected natural forests to other unprotected natural forests would involve population migrations and resettlement, and would be a mid-to long-term phenomenon. By studying leakages from the protected natural forests to anthropized forests within a municipality, our approach emphasizes a more short-term adaptation of the behaviors of farmers. We show that the leakages on anhropized areas have surpassed the observed decrease in deforestation within protected natural forests during the period studied.

Additionaly, the idea of negative leakages is closely related to the literature focused on the adoption of agricultural innovations: instead of innovating to comply with new land use restrictions as in a Porter-like hypothesis of a forced innovation (Porter and Van der Linde 1995), farmers stick with the same land-extensive agricultural practice and fulfill their needs for fertile lands by displacing deforestation to unprotected areas. The hypothesis of contextual-driven innovation has been proposed for long in the case of agrarian transitions [START_REF] Boserup | The Conditions of Agricultural Growth: The Economics of Agrarian Change Under Population Pressure[END_REF]. This hypothesis of adjustment remains debated today, as in Madagascar [START_REF] Zaehringer | Beyond deforestation monitoring in conservation hotspots: Analysing landscape mosaic dynamics in north-eastern Madagascar[END_REF]. We discuss our results in the light of this literature to provide thoughts on why an agricultural transition has not yet emerged for Malagasy family farmers.

The paper proceeds as follows: Section 2 provides the theoretical foundations for our analysis, Section 3 describes the data, Section 4 describes the empirical strategy and Section 5 presents the empirical results of leakages for Madagascar's rainforests. We discuss our results in Section 6 and then conclude.

Theoretical Framework

In Madagascar, 80% of the population live in rural areas and rely on subsistence agriculture for their living (Instat -EPM 2010) Rice is the staple food and the dominant crop in the country: 87% of agricultural households grow rice as the dominant commodity (Instat -EPM 2010). They are probably about 1.5 million individuals living directly in highly forested areas. These forests provide them with a stock of potential fertile lands for their agricultural activities with slash and burn being the dominant agricultural technique.

Households' welfare also depends on local forest ecosystem services (ES hereafter) whether they come from natural forests or anthropized forested areas. Local ES do not obviously embed global ES such as forest carbon storage which can represent the main part of the value of standing forests (e.g. [START_REF] Bulte | Forest conservation in Costa Rica when nonuse benefits are uncertain but rising[END_REF]. Local ES are rather privately appropriated by households. They mainly consist in the provision of charcoal and construction woods. All subsistence generating activities depend on land and labor inputs.

The Setup

We model the production choice of a welfare maximizing agricultural household in the presence of multiple types of lands that provide different ES. Motivated by the Malagasy context and following several authors (e.g. [START_REF] Janvry | Peasant household behaviour with missing markets: some paradoxes explained[END_REF], it is assumed that the labor market is shallow (i.e. households are self-sufficient in labor), and that labor cannot be traded on the market. There is neither off-farm labor nor rented labor. We denote L the stock of labor held by the household.

We assume that the household produces a single agricultural commodity, let's say rice, for subsistence purposes. Subsistence cropping is mainly conducted on cleared land, through slash-and-burn agriculture (only 12% of agricultural lands are irrigated rice parcels in the eastern eco-region, Table 1). Land can be cleared either on natural forests (practiced known as tavy in Madagascar) or on secondary forested areas (teviala). We call A 1 the amount of converted lands by the household on natural forests. When no conservation effort is implemented, natural forests are de facto freely accessible. The implementation of protected areas is modeled as an upper constraint Ā on land converted from natural forests. Secondary forests are constituted for instance by eucalyptus plantations. Since they stem from previously converted forests, it is assumed that their surfaces Ā2 is fixed. Two types of activities can take place in secondary forests: A 2 can be cleared once again for subsistence purposes (rice production) while Ā2 -A 2 can be kept in place for the provision of ES (e.g., charcoal production).

The household therefore faces a double trade-off: (i) Producing rice on land plots encroached either on natural or secondary forests; and (ii) Allocating secondary forested areas to rice or ES provision.

We call Y 1 (A 1 , L 1 ) the return on rice grown on A 1 units of cleared natural forests with L 1 units of labor. Y 2 (A 2 , L 2 ) is the return on rice grown on A 2 units of cleared secondary forests with L 2 units of labor. Y 3 ( Ā2 -A 2 , L -L 1 -L 2 ) stands for the return on the provision of local ES which rely on remained secondary forested areas Ā2 -A 2 and on remained labor

L -L 1 -L 2 . Y i are net of labor and other input costs.
The question is whether an increase i, conservation effort such as the implementation of PAs will induce deforestation leakages i.e., an increase in deforestation on secondary forests A 2 ?.

Our model shares several features with the agricultural household models' literature initiated by [START_REF] Singh | Agricultural household models: Extensions, applications, and policy[END_REF]. It is however different in several ways. First, production and consumption decisions are separable. Consequently labor allocation decisions do not depend on household composition (see e.g. [START_REF] Benjamin | Household composition, labor markets, and labor demand: testing for separation in agricultural household models[END_REF]. Second, the model does not address the question of market failures (e.g. [START_REF] Janvry | Peasant household behaviour with missing markets: some paradoxes explained[END_REF]. There exists several examples of models of land conversion (among several authors: [START_REF] Angelsen | Rethinking the Causes of Deforestation: Lessons from Economic Models[END_REF][START_REF] Barbier | Valuing ecosystem services as productive inputs[END_REF][START_REF] Delacote | Reducing Deforestation and Forest Degradation: Leakage or Synergy?[END_REF] but to the best of our knowledge, none explicitly modeled deforestation leakages induced by the implementation of PAs.

The household maximization program

Once the Y i are aggregated, they constitute the net return from agricultural production and local ES provision, denoted π. π is supposed to be strictly quasi-concave. Cross derivatives are assumed to be strictly positive. More generally, it is supposed to be well-behaved so that all solutions are interior. Formally, the problem is:

max A 1 ,A 2 ,L 1 ,L 2 π ≡ Y 1 (A 1 , L 1 ) + Y 2 (A 2 , L 2 ) + Y 3 ( Ā2 -A 2 , L -L 1 -L 2 ) such that A 1 < Ā
The inequality constraint A 1 < Ā corresponds to the conservation constraint: a decrease in Ā denotes an increase in the conservation effort i.e. an increase in natural forests included in PAs. The corresponding Lagrangean function writes as:

L A 1 ,A 2 ,L 1 ,L 2 ,µ; Ā, Ā2 ,L ≡ Y 1 (A 1 , L 1 ) + Y 2 (A 2 , L 2 ) + Y 3 ( Ā2 -A 2 , L -L 1 -L 2 ) -µ(A 1 -Ā)
where µ is the non-negative multiplier. It represents the implicit additional cost born by households when PAs are implemented. This theoretical setting allows taking into account local benefits extracted from standing forests but without internalizing global benefits such as carbon storage. The potential conflict between local and global benefits from conservation initiatives is not taken into account [START_REF] Perrings | Conserving biodiversity: Reconciling local and global public benefits[END_REF].

First order necessary conditions (FONC) for an interior solution are:

FONC :                              ∂L ∂A 1 = 0 ⇔ ∂Y 1 ∂A 1 -µ = 0 ∂L ∂A 2 = 0 ⇔ ∂Y 2 ∂A 2 -∂Y 3 ∂A = 0 ∂L ∂L 1 = 0 ⇔ ∂Y 1 ∂L 1 -∂Y 3 ∂L = 0 ∂L ∂L 2 = 0 ⇔ ∂Y 2 ∂L 2 -∂Y 3 ∂L = 0 ∂L ∂µ ≥ 0, µ ≥ 0 and µ ∂L ∂µ = 0 i.e. -A 1 + Ā ≥ 0, µ A 1 -Ā = 0
From the envelope theorem, the overall effect of the conservation effort is shown to have a non-positive impact on the maximized profit:

∂π ∂ Ā = ∂L * ∂ Ā = µ > 0.
The quasi-concavity of π ensures the existence of a maximum (Appendix B1). As a consequence, FONC allows defining A 1 , A 2 , L 1 and L 2 as implicit functions of exogenous parameters. In the following, we are particularly interested in the effect of Ā on the demands for agricultural factors.

Remark 1: For the sake of simplicity it is assumed that conservation effort is linear in Ā.

However, one hectare of PA often does not mean one hectare effectively protected because of imperfect law enforcement in tropical countries. See in the appendix the discussion on that.

Remark 2: It would be possible to refine the maximization problem so as to consider subsistence requirements. This can be made by explicitly introducing a minimum level for rice production. The Lagrangean function would be:

L A 1 ,A 2 ,L 1 ,L 2 ,µ; Ā, Ā2 ,L,Y ≡ Y 1 (A 1 , L 1 ) + Y 2 (A 2 , L 2 ) + Y 3 ( Ā2 -A 2 , L -L 1 -L 2 ) -µ(A 1 -Ā) -λ(Y -Y 1 -Y 2 )
where Y is a minimum level of rice production return. It would deliver an additional FONC written as: ∂L ∂λ ≥ 0, λ ≥ 0 and λ ∂L ∂λ = 0. Another possibility would be to maximize the indirect utility function V of the returns from rice production and local SE provision:

V(Y 1 (A 1 , L 1 ) + Y 2 (A 2 , L 2 ) + Y 3 ( Ā2 -A 2 , L - L 1 -L 2 )) under the additional constraint V(Y 1 (A 1 , L 1 ) + Y 2 (A 2 , L 2 ) + Y 3 ( Ā2 -A 2 , L -L 1 - L 2 )) ≥ V 0 .
This idea was explored by [START_REF] Pagiola | The effect of subsistence requirements on sustainable land use practices[END_REF] in a dynamic setting.

Remark 3:

We present here a static model. As highlighted by Porter, in a dynamic model the establishment of environmental regulations might incite the household to invest in new and more intensive agricultural practice to comply with the law, and in our case, thus ensure the provision of ES. However in Madagascar, we observe a limited adoption of agricultural practices in general [START_REF] Minten | Agricultural Technology, Productivity, and Poverty in Madagascar[END_REF]. We thus believe that our static framework is sufficient to capture insights in the Malagasy context.

Comparative Statics

The comparative statics exercise allows establishing two propositions highlighting how and when leakages can occur. We denote |H| the positive determinant of the bordered hessian matrix. Following the FONC, we first study how L 1 varies for a change in the amount of protected forests Ā:

|H| ∂L 1 ∂ Ā = ∂ 2 Y 1 ∂A 1 ∂L 1   ∂ 2 Y 2 ∂A 2 2 + ∂ 2 Y 3 ∂A 2 (∂ 2 Y 2 ∂L 2 2 + ∂ 2 Y 3 (∂L 2 - ∂ 2 Y 2 ∂A 2 ∂L + ∂ 2 Y 3 ∂A∂L 2   (1)
Because of the concavity of production functions, Equation 1 will be positive if the direct second order derivatives dominates cross derivatives i.e. when "own-effects dominates cross effects" [START_REF] Silberberg | The Structure of Economics: A Mathematical Approach[END_REF]:

|H| ∂L 1 ∂ Ā > 0 iif ∂ 2 Y 2 ∂A 2 2 + ∂ 2 Y 3 ∂A 2 ∂ 2 Y 2 ∂L 2 2 + ∂ 2 Y 3 ∂L 2 > ∂ 2 Y 2 ∂A 2 ∂L + ∂ 2 Y 3 ∂A∂L 2
In this condition, a decrease in Ā (ndlr, a tightening of conservation efforts) results in a decrease in L 1 . This result holds even if the conservation constraint is not slack. When

PAs are implemented, land conversion from natural forests is relatively costlier and induces household labor reallocation towards other activities located in secondary forests. This result is summarized in the following proposition:

Proposition 1: An increase in PAs incites households to reallocate labor towards other activities under rapidly decreasing marginal productivity of labor on secondary forests.

Regarding the effect of a change on conservation efforts on deforestation leakages on Ā2 , it follows from FONC that:

|H] ∂A 2 ∂ Ā = - ∂ 2 Y 1 ∂A 1 ∂L 1 ∂ 2 Y 3 ∂A∂L ∂ 2 Y 2 ∂L 2 2 - ∂ 2 Y 3 ∂L 2 ∂ 2 Y 2 ∂A 2 ∂L (2)
The sign of Equation 2 is a priori unknown without additional assumptions. Following

|H| ∂A 2 ∂ Ā < 0 iff ∂ 2 Y 3 ∂L 2 ∂ 2 Y 2 ∂L 2 2 > ∂ 2 Y 3 ∂A∂L ∂ 2 Y 2 ∂A 2 ∂L
We synthesized this result in Proposition 2:

Proposition 2: An increase in surfaces under PAs does not necessarily induce deforestation leakages on secondary forests. This will occur only when the provision of local ES services is subjected to more rapidly decreasing marginal productivities of labor than rice production (-

∂ 2 Y 3 ∂L 2 -∂ 2 Y 2 ∂L 2 2 )
The full derivations of propositions 1 and 2 as well as additional results are provided in Appendix B. In the following sections, we are going to test the empirical validity of the propositions related to the possibility of leakages from natural forests to anthropized forested areas summarized in propositions 1 and 2.

Data

To test our predictions, we build a spatially explicit dataset combining vegetation data, the last PAs' spatial census and socio-economic census surveys at the municipality level.

Vegetation Data: Defining Forests

We want to track deforestation dynamics over different type of forested landscapes. We define three types of forested areas using vegetation data from [START_REF] Hansen | High-Resolution Global Maps of 21st-Century Forest Cover Change[END_REF] v1.0. We rely on two spatial layers: tree cover in 2000 and annual tree cover losses between 2001 and 2012. The Tree cover layer indicates for each pixel of 30m × 30m in 2000 the density of tree cover of a potential size higher than 5m. Values range from 0% to 100% of vegetation density cover for each pixel. The annual tree cover losses layer indicates whether a pixel has been deforested

and if so, in what year.

Madagascar is divided into three ecologically diverse areas, each with its own forest and vegetation types. There are rainforests in the eastern ecoregion, savannah and dry forests in the western ecoregion and spiny forests in the southern ecoregion (Figure 2). Each natural habitat presents different level of tree cover density. To distinguish between natural habitats and anthropized habitats pixels, we overlap our vegetation layer with a map from the BioSceneMada project delimitating natural forests (Figure 2). This us to identify the minimal vegetation density within natural habitats. We find that southern spiny natural forests are dominantly composed of areas with a tree cover density of at least 6%, western dry natural forests are characterized by tree cover density of at least 20%, and eastern natural rainforests are composed of areas with tree cover density of at least 78%. From these thresholds, we define natural forest as the pixels that present at least this minimal tree cover density. We then define anthropized areas as the pixels with less than this minimal tree cover density.

For the purpose of this study, we focus on the eastern ecoregion in order to get a large enough spectrum of anthropized vegetation (< 78% of tree cover density per pixel). We define natural forests as the pixels with a tree cover density larger than or equal to 78%. We consider two strata of degraded forests: a first strata of highly degraded forest with a tree cover density between 30% and 53%, and a second strata of moderately degraded forest with a tree cover density between 54% and 77% (Figure 2). We do not include pixels with a tree cover density lower than 30% as doing so would require us to define the whole eastern ecoregion as forests, which is not the case3 . Our geographical unit of analysis is municipalities. We thus aggregate pixel data within municipalities and compute the deforestation rate within the forest strata j in municipality i at date t as: De f ijt = Forest i,j,t -Forest i,j,t-1 Forest i,j,t-1 The other 88 are NPAs.

Treatment: Protected Areas

In this study, we consider all PAs and NPAs from the eastern ecoregion that were officially included in the SAPM in 2012. Our database includes 24 historic PAs and 31 NPAs impacting 109 and 126 municipalities, respectively.

Control Variables

Finally, we construct a set of control covariates. First, we use census data from the ILO Cornell project (2001). The census includes information on economic, social and political characteristics for 1,385 of the country's 1,392 municipalities, known in Madagascar as communes. Particularly, we use information regarding the size of the population, the share of irrigated rice parcels (i.e., the alternative to slash and burn) and the share of impoverished people (people who face recurrent food shortage every years). These three variables will have a direct impact on deforestation. We spatialize the census and match it with official municipality' boundaries.

Second, we construct a set of bio-physical covariates for each municipality: average slope, average elevation, average Euclidean distance to nearest road [START_REF] Deininger | Determinants of deforestation and the economics of protection: An application to Mexico[END_REF].

Within each municipality, we determine the same bio-physical measures for each of the three vegetation strata. To compute them, we draw a random sample of 60,000 pixels for each strata and average the values inside each municipality.

At the end, we have a sample of 688 municipalities of which 561 have a natural forest cover larger than 50 hectares4 . Data sources and summary statistics are provided in Table 1.

Empirical Strategy

For each municipality, we consider the three main categories of forest cover: natural forest (more than 78% forest cover density), slightly degraded anthropized forest (forest cover between 54 and 78% density) and highly degraded anthropized forest (between 30 and 54% of forest cover density). We seek to determine if the establishment of a PA within a given municipality has decreased deforestation on natural forests but has caused an increase in deforestation on anthropized areas in the same municipality.

To avoid confounding effects, we control for other determinants of deforestation. These include both the location characteristics of forest cover (altitude, slope and distance to the nearest road of each type of forest within a municipality) and the characteristics of the municipality itself. For example, two natural forests with similar characteristics may have very different rates of deforestation if the municipal context is not the same. The context can be captured here by including demographic or agricultural pressures. The characteristics of the municipality allow for capturing contextual effects [START_REF] Manski | Identification of endogenous social effects: The reflection problem[END_REF]). The hierarchical nature of the determinants (forest strata and municipal) allows us to estimate a multilevel model.

Multilevel models provide a natural framework for accounting for the correlation of observations within the municipalities. This correlation refers to correlated effects [START_REF] Manski | Identification of endogenous social effects: The reflection problem[END_REF], and according to [START_REF] Anselin | Under the hood issues in the specification and interpretation of spatial regression models[END_REF] and [START_REF] Wendland | Regional-and district-level drivers of timber harvesting in European Russia after the collapse of the Soviet Union[END_REF] they allow for taking into account the spatial correlation of the error term in municipalities. However, multilevel models assume that the explanatory variables and random effects are independent. If this assumption is violated the estimation results may be biased. This problem of correlation can be dealt with by a within (-group) transformation of the explanatory variables.

The econometric model has the following specification:

De f ijt = β 0 + β 1 Cover54 ijt + β 2 Cover30 ijt + β 3 PA jt + β 4 Cover54 ijt × PA jt + β 5 Cover30 ijt × PA jt + β 6 X ijt -Xijt + β 7 Xijt + β 8 Z j + ν t + µ j + i jt
where index i represents the forest cover category, j refers to the municipality and t is a time index. De f ijt is the deforestation rate of each forest cover category i in municipality j in year t, Cover54 ij and Cover30 ij are the fixed effects associated with forest cover. They are set to 1 when the forest cover is between 54 and 78% and between 30 and 54% respectively. PA jt is a binary variable equal to 1 if the natural forest is protected in the municipality j in year t. X ijt are location variables measured for each forest cover category i in municipality j at year t and Z j are contextual variables. We crossed the protected area variable with forest cover categories (Cover54 ijt × PA jt and Cover30 ijt × PA jt ) in order to capture the leakage effect of deforestation of protected natural forests protected on secondary forests within municipalities. Parameters β 0 , β 1 , β 2 , β 3 , β 4 , β 5 , β 6 , β 7 and β 8 are the regression coefficients to be estimated.

The error term is broken down into three parts. The first component ν t ∼ N(0, σ ν 2 ) is specific to the year and constant between forest cover categories and municipalities. The second component is µ j ∼ N(0, σ µ 2 ) which is specific to the municipality and constant between forest cover categories of the same municipality. The last component varies between year, forest cover categories and municipalities, and is designated as ijt ∼ N(0, σ 2 ).

Empirical Results

Compared to natural forests, anthropized forests are found at a lower altitude and on flatter areas, closer to roads. In other words, Anthropized forests are in areas more prone to economic activities [START_REF] Angelsen | Rethinking the Causes of Deforestation: Lessons from Economic Models[END_REF] and consequently were the first to be converted into productive areas. However, the average annual deforestation rate on natural forests is significantly higher than the ones on already antrhopized forests as natural forests offer more fertile soils and provide less direct ES to locals. 18% of the observations were impacted by a PA over the period (Table 1). We now turn to the impact of PAs on deforestation and leakages. 5.048 Note: Superscripts *, ** and *** correspond to 10%, 5% and 1% levels of significance. Student test measuring differences between natural forests and slightly degraded forests, and between natural forests and highly degraded forests are presented. In addition, deforestation rates, tree cover and slope are statistically different at 1% between slightly and highly degraded forests, distance to nearest road is significant at 10% level and elevation is not statistcally different

The relevance of the multilevel model and the existence of contextual effects are first assessed with a Hausman test. The χ 2 statistic (Table 2) does not allow us to reject the null hypothesis of independence between errors and explanatory variables. It therefore favors multilevel modeling. Second, we implement a likelihood ratio test between the multilevel model without contextual effects (restricted model) and the full model with contextual effects (unrestricted model). The statistics of the likelihood ratio test allows us to reject the joint null hypothesis of contextual effects at the 1% level for all multilevel models. The portion of the total variability accounted for at the municipal level calculated as the intra-class correlation coefficient ρ = σ 2 µ / σ 2 µ +σ 2 is at least equal to 7%. In other words, at least 7% of the total variance in the deforestation rate is explained at the municipal level. These results justify the inclusion of both contextual and correlated effects.

Table 2 shows the results of the estimations. Three separate estimates have been run: the fixed effects model, the multilevel model with years' fixed effects and the full multilevel model with municipality and year random effects. All of these results show that the establishment of a protected natural forest contributes to a reduction in deforestation by at least 1.1%. According to Proposition 1, the effectiveness of PAs in reducing deforestation will lead to a reallocation of household labor time.Proposition 2 stipulates that a leakage effect of de-forestation is not automatic. Here, the coefficients associated with multiplicative variables (Cover30 ijt × PA jt and Cover54 ijt × PA jt ) are positive and significant. This indicates that deforestation increases by about 1% in each of the two categories of anthropized forests that are located in the municipalities where the natural forest is protected. In other words, there is a leakage of deforestation from protected natural forests to anthropized forests in the same municipality. Based on Proposition 2, this leakage effect can partly be explained by more rapidly decreasing marginal productivity of labor in the provision of local ES over rice production.

Taken globally, because of the leakage effect, PAs seem ineffective or even counterproductive in terms of vegetation cover changes. Indeed, one can define the net impact of PAs on cover changes is the sum of avoided deforestation and the induced leakages. Tests on the sum of the coefficients (β 3 + β 4 + β 5 ) presented in Table 1 show that PAs generate a net increase of 1% in vegetation clearing. Indeed, as the anthropized forests are less fertile, households must clear more land for the same level of agricultural productivity. Therefore, the leakage of deforestation from natural forests to anthropized forests exceeds avoided deforestation. We would, however, need to convert these physical land use changes in economically more relevant values (ecosystem services, rice production) to get a broader view of the welfare impact of PAs [START_REF] Vincent | Impact Evaluation of Forest Conservation Programs: Benefit-Cost Analysis, Without the Economics[END_REF].

Finally, our results show that forest cover, slope, elevation, distance from roads and the percentage of land devoted to rice production are associated with lower deforestation. For better efficiency, conservation policies must be supported by rural development policies in particular the promotion of agricultural intensification techniques (use of fertilizers or irrigation land), processing of agricultural products and the development of non-agricultural income generating activities.

Robustness Check: Evidence from Matching Techniques

The regression results may be biased if treated and non-treated municipalities do not have the same average deforestation rate. For example, if treated municipalities are intrinsically exposed to lower deforestation than those from the control group, traditional models would overestimate the impact of PAs (Ferraro 2009;[START_REF] Joppa | High and Far: Biases in the Location of Protected Areas[END_REF]. Therefore, we need to find an acceptable counterfactual group to estimate an unbiased effect of protected areas and their leakage effects. We use a reweighting technique, entropy balancing [START_REF] Hainmueller | Entropy balancing for causal effects: A multivariate reweighting method to produce balanced samples in observational studies[END_REF], in order to ensure that the distribution of covariates is the same in the control group and in the treated group. Entropy balancing attains more effective results than propensity score or mahanolobis methods when reducing covariate imbalances. In practice in a first step, we (0.00269) (0.00272) Note: Superscripts *, ** and *** correspond to 10%, 5% and 1% levels of significance respectively. Standard errors in Model 1 are clustered within each municipality. Standard errors in the multilevel models account for potential correlations within municipalities. The difference between Model 2 and Model 3 consists in the way yearly variations are taken into account: Model 2 relies on year fixed effects, Model 3 treats years as a third level. determine a set of entropy weights that allows us to match the means of the covariates in the treatment group with those in the reweighted control group. In a second step, we perform the multilevel model by weighting this regression with the entropy weights. The coefficient associated with the treatment variable can be considered as the average treatment effect. Table C.1 in Appendix C presents the mean of the distribution of covariates before and after the reweighting. This table shows that after the reweighting procedure, the control and treated group are very similar in terms of the observed characteristics. The estimation results after reweighting remain qualitatively unchanged (Table 3). We still observe a negative and significant effect of protected natural forest on deforestation and leakage of deforestation displaced to anthropized forests. The net effect of protected areas on deforestation is approximately 0.7% and positive.

Discussion

The literature has highlighted the possibility of leakages following the implementation of conservation restrictions and these leakages have been empirically found in a few studies. In this present work, we have extended the conception of leakages by studying deforestation displacement from protected natural forests to already anthropized forested areas.

A large body of literature is devoted to studying the opportunity cost of conservation policies for local inhabitants [START_REF] Shyamsundar | Tropical forest protection: an empirical analysis of the costs borne by local people[END_REF][START_REF] Ferraro | The local costs of establishing protected areas in low-income nations: Ranomafana National Park, Madagascar[END_REF]. Studying leakages with an ES framework allows us to cast a new look at this question by highlighting the possibilities of farmers' coping strategies in response to the creation of PAs. In our approach, the local cost of conservation does not correspond to the raw income losses on now protected lands but rather is a loss net of leakages. Leakages themselves have a dual composition: on the one hand, locals minimize the raw income loss following PAs' creation by harvesting agricultural commodities on previously anthropized lands, but on the other hand, they lose the direct provisioning ES these lands provided. Our results, nonetheless, confirm a salient point of the literature through an ES approach: an important part of the cost of protecting the provision of global ES is borne by locals and subsequent conservation policies may displace deforestation onto lands that provide locals important provisioning ES.

The types of leakages we capture in our study probably corresponds to a short-term adjustment of farmers' behavior. Farmers first reap economic profit in their neighborhoods by continuing to clear some (but less) natural forest despite prohibitions, and by reporting some deforestation on anthropized forested areas. Once these economic opportunities are exploited, we can expect mid-to long-term adjustments possibly involving migration or the intensification of current agricultural techniques (eg, terrace cultivation).

Distinguishing between Anthropized Forests

In order to study the displacement of deforestation from protected natural forests to anthropized habitats, we use vegetation data and distinguish the two types of habitats based on differences in their tree cover density. In our case, natural rainforests present a higher percentage of tree cover density than anthropized habitats. We set up a threshold between natural and anthropized areas (ed, 78% of tree cover density) using official forest maps. Then, in order to differentiate between slightly degraded and highly degraded habitats, we cut our anthropized forested areas (30% to 77%) into two equal parts (30% to 53% and 54% to 77%).

However, in doing that, we can't precisely determine the composition of the two strata of anthropized forested areas, i.e. eucalyptus or pine plantation, agri-forestry systems, old fallows etc. Official land use maps would have allowed us to distinguish between each land use. Yet no such recent and precise maps are available for Madagascar.

An alternative to official land use maps would have been to conduct some ground checking for the vegetation data that we have: for each category of tree cover density, we could go observe to which they correspond. Nonetheless, [START_REF] Hansen | High-Resolution Global Maps of 21st-Century Forest Cover Change[END_REF] vegetation data provide percent of tree cover density only for the year 2000. Field observation 15 years later would clearly not informative. Therefore, we believe there is still room for future research to better understand the interaction between conflicting land use with the help of land use maps, perhaps in the context of a country with richer data than Madagascar.

Understanding the Absence of Agricultural Intensification in Madagascar

Whether forests are protected or not, slash-and-burn agriculture on natural forests in Madagascar is illegal5 . Yet it remains the principal agricultural technology used and few farmers have invested in new practices to comply with the law. In conservationists' theory of change relative to the creation of PAs, a Porter-like hypothesis (Porter and Van der Linde 1995) is implicit: new legal restrictions will incite farmers to invest in order to comply with the rule [START_REF] Phalan | Reconciling food production and biodiversity conservation: land sharing and land sparing compared[END_REF]). Yet, the adoption of innovations has remained extremely limited in Madagascar [START_REF] Moser | The disappointing adoption dynamics of a yield-increasing, low external-input technology: the case of SRI in Madagascar[END_REF] and our results show that people have chosen to displace deforestation and continue the practice of slash and burn even on anthropized forested areas, despite the fact that it it might impede the provision of local ES and despite lower yields. Understanding the reasons why little agricultural innovation has occurred in Madagascar remains a key policy challenge.

The economic literature has pointed out several factors that limit the adoption of new practices in the agricultural domain. They are the lack of access to credits and information, insufficient human capital and aversion to risk among others [START_REF] Feder | Adoption of agricultural innovations in developing countries: A survey[END_REF][START_REF] Abdulai | The diffusion of new agricultural technologies: the case of crossbred-cow technology in Tanzania[END_REF]Moser and Barrett 2006;[START_REF] Foster | Microeconomics of technology adoption[END_REF]. Among these factors, risk aversion appears as a key explanation in the specific context of Madagascar's eastern ecoregion [START_REF] Brimont | Achieving Conservation and Equity amidst Extreme Poverty and Climate Risk: The Makira REDD+ Project in Madagascar[END_REF]. Madagascar is among the countries most vulnerable to climate risks and high levels of poverty make Malagasy farmers particularly risk-averse [START_REF] Nielsen | Poverty and attitudes towards time and risk: Experimental evidence from Madagascar[END_REF]. Even if it provides low yields, slash and burn on uplands is an efficient risk-management strategy to cope with climatic vulnerability [START_REF] Aubert | Déforestation et systèmes agraires à Madagascar: les dynamiques des tavy sur la côte orientale[END_REF][START_REF] Delille | Perceptions et stratégies d'adaptation paysannes face aux changements climatiques à Madagascar[END_REF] as opposed to many alternative practices.

Recent findings have also highlighted the role of social interactions in the adoption of new agricultural practices [START_REF] Bandiera | Social networks and technology adoption in northern mozambique*[END_REF][START_REF] Conley | Learning about a new technology: Pineapple in Ghana[END_REF]. This stream of literature somehow echoes the findings of Moser and Barrett (2006) that underline the research of social conformity as a determinant of technological adoption (or non-adoption) of agricultural innovations in Madagascar. The authors argue that people may adopt (or not) an innovation so as to comply with the group's social norms. As slash and burn is at the basis of the social organization of forests community in Madagascar, it serves as a mechanism to establish the elders' authority in collective decision processes and as a support of cultural and religious rites [START_REF] Aubert | Déforestation et systèmes agraires à Madagascar: les dynamiques des tavy sur la côte orientale[END_REF][START_REF] Desbureaux | Between economic loss and social identity: The multi-dimensional cost of avoiding deforestation in eastern Madagascar[END_REF]. Conformity with the dominant social norm then requires local farmers to continue the practice of slash and burn instead of adopting alternative practices.

In order to reduce deforestation leakages from protected natural forests to anthropized ones, it might be useful to put in place policies for intensification of agricultural production oriented toward peers (elderly, traditional and religious authorities) and based on the access to credit, training and insurance to manage risks. Indeed, a policy supported by the peers would help to break down social barriers. Access to credit and training would enable populations to switch to more intensive techniques.

Concluding Remarks

This paper presents evidence that deforestation leakages have constituted a significant adaptation strategy of Malagasy farmers to the creation of PAs in the eastern rainforest. We use fine scale vegetation satellite images to distinguish natural forests from already anthropized forested areas and construct a panel dataset of annual deforestation between 2000 and 2012 for each vegetation type. We found that PAs contributed to decrease deforestation of natural forests in Madagascar. This decrease, however, has resulted in an increase in deforestation of already anthropized forested areas despite the fact that anthropized forested areas provide crucial provisioning ecosystem services to locals' inhabitants. This result confirms the idea through a ecosystem services approach that locals bear an important cost of conservation policies. In addition, this deforestation leakage contradicts a Porter hypothesis reasoning which suggests that a change in institutional rules, herethe creation of PAs, should have increased the adoption of new more land-intensive agriculture practices. Risk aversion in a context of a highly risky environment and collective action dynamics appear as a possible explanation for the absence of adoption of alternate agricultural practices.

Appendix A: Rice Plantation After Eucalyptus

B: Maths Appendices B1: Second Order Necessary Conditions

The second order sufficient condition for a maximization problem with four decision variables subjected to one constraint depends on the properties of the bordered hessian matrix H. From FONC, H is such that:

H =             π 11 0 π 13 0 -1 0 π 22 π 23 π 24 0 π 13 π 23 π 33 π 34 0 0 π 24 π 34 π 44 0 -1 0 0 0 0             where π 11 = ∂ 2 Y 1 ∂A 2 1 < 0 ; π 22 = ∂ 2 Y 2 ∂A 2 2 + ∂ 2 Y 3 ∂A 2 < 0 ; π 33 = ∂ 2 Y 1 ∂L 2 1 + ∂ 2 Y 3 ∂L 2 < 0 ; π 34 = ∂ 2 Y 3 ∂L 2 < 0 ; π 44 = ∂ 2 Y 2 ∂L 2 2 + ∂ 2 Y 3 ∂L 2 < 0. Moreover, π 13 = ∂ 2 Y 1 ∂A 1 ∂L 1 > 0 ; π 23 = ∂ 2 Y 3 ∂A∂L > 0 and π 24 = ∂ 2 Y 2 ∂A 2 ∂L + ∂ 2 Y 3 ∂A∂L < 0.
The sufficient condition for a maximum is that the principal minors M k of order k (which have k + 1 rows and columns), k = 2, 3 and 4, alternate in sign with M 4 = |H| > 0. Under the assumption that π is quasi-concave the sufficient second order condition for a maximization is fulfilled (Arrow & Enthoven 1961).

B2: Full derivation of propositions 1 and 2 and additional results

Generally speaking the effect of Ā on all endogenous variables is obtained while solving the following system:

H             ∂A 1 ∂ Ā ∂A 2 ∂ Ā ∂L 1 ∂ Ā ∂L 2 ∂ Ā ∂µ ∂ Ā             =                0 0 0 0 0 -1               
It can be calculated that |H| = -

f 22 f 23 f 24 f 23 f 33 f 34 f 24 f 34 f 44 > 0.
B2-1: Effect of an increase in Ā on A 1

The effect is obtained while calculating: decrease in cleared natural forests even if the conservation constraint is slack. This results holds under the proviso that protected areas are effectively implemented. This is obviously not the case in Madagascar. This institutional feature may be easily handled while slightly modifying the conservation constraint as A 1 ≤ g( Ā) with g > 0 and g ≤ 0 as suggested in [START_REF] Delacote | Reducing Deforestation and Forest Degradation: Leakage or Synergy?[END_REF].

B2-2: Effect of an increase in Ā on L 1 (Proposition 1)

The effect is obtained while calculating:

∂L 1 ∂ Ā =
π 11 0 0 0 -1 0 π 22 0 π 24 0 π 13 π 23 0 π 34 0 0 π 24 0 π 44 0

-1 0 -1 0 0 |H| It comes that |H| ∂L 1 ∂ Ā = ∂ 2 Y 1 ∂A 1 ∂L 1 ∂ 2 Y 2 ∂A 2 2 + ∂ 2 Y 3 ∂A 2 ∂ 2 Y 2 ∂L 2 2 + ∂ 2 Y 3 ∂L 2 -∂ 2 Y 2 ∂A 2 ∂L + ∂ 2 Y 3 ∂A∂L 2 > 0 iif ∂ 2 Y 2 ∂A 2 2 + ∂ 2 Y 3 ∂A 2 ∂ 2 Y 2 ∂L 2 2 + ∂ 2 Y 3 ∂L 2 > ∂ 2 Y 2 ∂A 2 ∂L + ∂ 2 Y 3 ∂A∂L 2
. This property reads as when "own-effects dominate cross effects" (Silberberg 1990, p.164), then the expression in parentheses is positive.

B2-3: Effect of an increase in Ā on A 2 (Proposition 2)

|H| ∂A 2 ∂ Ā = ∂ 2 Y 1 ∂A 1 ∂L 1 ∂ 2 Y 3 ∂A∂L ∂ 2 Y 2 ∂L 2 -∂ 2 Y 3 ∂L 2 ∂ 2 Y 2 ∂A 2 ∂L ∂A 2 ∂ Ā < 0 (leakage) iif ∂ 2 Y 3 ∂A∂L ∂ 2 Y 2 ∂L 2 -∂ 2 Y 3 ∂L 2 ∂ 2 Y 2 ∂A 2 ∂L > 0 that is ∂ 2 Y 3 ∂L 2 / ∂ 2 Y 2 ∂L 2 2 > ∂ 2 Y 3 ∂A∂L / ∂ 2 Y 2 ∂A 2 ∂L
. In other words, providing -∂ 2 Y 3 ∂L 2 is "sufficiently" high with respect to -∂ 2 Y 2 ∂L 2 , i.e., -

∂ 2 Y 3 ∂L 2 -∂ 2 Y 2 ∂L 2 , such that ∂ 2 Y 3 ∂L 2 / ∂ 2 Y 2 ∂L 2 2 > ∂ 2 Y 3 ∂A∂L / ∂ 2 Y 2 ∂A 2 ∂L
. It follows that an increase in the conservation effort represented by a decrease in Ā induces an increase in land converted from secondary forests A 2 .

B2-4: Effect of an increase in Ā on L 2

The intuitive result holds:

sign ∂L 2 ∂ Ā = sign - ∂L 1 ∂ Ā with: ∂L 2 ∂ Ā = - ∂ 2 Y 1 ∂A 1 ∂L 1   ∂ 2 Y 2 ∂A 2 2 + ∂ 2 Y 2 ∂A 2 ∂ 2 Y 3 ∂L 2 - ∂ 2 Y 3 ∂A∂L ∂ 2 Y 2 ∂A 2 ∂L + ∂ 2 Y 3 ∂A∂L  
Using the same kind of arguments than for the effect of Ā on L 1 , it can be established that

∂ 2 Y 2 ∂A 2 2 + ∂ 2 Y 2 ∂A 2 ∂ 2 Y 3 ∂L 2 > ∂ 2 Y 3 ∂A∂L ∂ 2 Y 2 ∂A 2 ∂L + ∂ 2 Y 3
∂A∂L and therefore ∂L 2 ∂ Ā < 0 6 .

B2-5: Effect of an increase in Ā on µ

At last, it is shown that:

C: Empirical Additional Details

∂L 2 ∂ Ā + ∂L 1 ∂ Ā = 1 |H| ∂ 2 Y 1 ∂A 1 ∂L 1 ∂ 2 Y 2 ∂A 2 + ∂ 2 Y 3 ∂A 2 ∂ 2 Y 2 ∂L 2 2 -∂ 2 Y 2 ∂A 2 ∂L ∂ 2 Y 2 ∂A 2 ∂L + ∂ 2 Y 3 ∂A∂L > 0.
It evidences the reallocation of labor, say

∂L 1 ∂ Ā > -∂L 2 ∂ Ā .
The intensity of decreasing marginal productivities on land and labor for Y 2 and Y 3 allows gauging the magnitude of labor reallocation towards Y 2 and Y 3 .

Figure 1 :

 1 Figure 1: Vegetation Mosaic in Eastern Madagascar

Figure 2 :

 2 Figure 2: Defining Forests for Each Ecoregion

  PAs aim to protect natural habitats of rich biodiversity and important carbon sinks in the context of REDD+. As such, PAs cover natural habitats but not degraded forests. PAs began to be established in Madagascar in 1927 and covered 1.7 million hectares in 2000. In 2003, an ambitious plan to triple the network of PAs was launched so that PAs now cover about 40% of the remaining natural forests in Madagascar. PAs and New PAs (NPAs) are all included in Madagascar's network of protected areas (SAPM -Système des Aires Protégées de Madagascar).Currently, there are 138 PAs in Madagascar. Fifty of them are the "historic" PAs created between 1927 and 1999. They are managed by the Madagascar National Parks public agency.

Figure 3 :

 3 Figure 3: Rice cultivation after eucalyptus plantation

  quite straightforward. An increase in the conservation effort induces a 100%

  π 23 π 24 π 13 π 23 π 33 π 34 0 π 24 π 34 π 44|H|The numerator is the determinant of the hessian of the net return function. If π is assumed to be strictly concave then the numerator is negative and therefore ∂µ ∂ Ā < 0. The net agricultural return function is concave in Ā.

  Proposition 1, conservation efforts reallocate labor in favor of Y 2 and Y 3 which are obtained on secondary forested areas. The household is therefore facing a dilemma: either it chooses to increase rice production Y 2 which is detrimental to the the provision of local ES, or it chooses to increase the local ES provision which positively depends on secondary forest. The net effect of Ā on A 2 is thus dependent on the relative magnitude of decreasing marginal labor productivities. For Equation 2 to be negative, we indeed need to have:

Table 1 :

 1 Descriptive Statistics

	Forest strata regressors (level one, Obs= 5,886 /strata)
		Natural Forests	Slightly Degraded Forests	Highly Degraded Forests
		Mean	S.D.	Mean	S.D.	Mean	S.D.
	Deforestation rate 0.0234 0.0683	0.00695***	0.0147	0.00217***	0.00560
	Tree Cover 0.0795	0.175	0.0638***	0.0695	0.0402***	0.0406
	Elevation 0.585	0.542	0.554***	0.552	0.546***	0.549
	Slope 9.955	5.610	8.676***	4.348	7.884***	3.773
	Distance to Nearest Road 5.504	5.422	5.205***	5.068	5.033***	5.034
	Municipal level regressors (level two, Obs: 561)
	Share of municipalities with a PA at Year t	18.3	38.7
	Population in 2001 13,600	8730
	Share of Irrigated Paddy Rice 13.52	24.58
	Share of Impovrished People 8.847	12.96
	Average Elevation 0.562	0.520
	Average Slope 8.839	3.994
	Average Dist to Nearest Road 5.248

Table 2 :

 2 Deforestation, Protected Areas and Leakages

		(1)		(2)		(3)
		Full fixed effect	Multilevel model	Full multilevel model
				with year fixed effects
		Estimates Std. Err.	Estimates	Std. Err.	Estimates	Std. Err.
	Level one regressors
	PA			-0.01265*** (0.00189)	-0.01167***	(0.00188)
	Cover 30	-0.02557*** (0.00174)	-0.02557*** (0.00082)	-0.02558***	(0.00080)
	Cover 54	-0.01978*** (0.00157)	-0.01978*** (0.00079)	-0.01977***	(0.00077)
	Cover 30 x PA	0.01183*** (0.00183)	0.01183*** (0.00193)	0.01173***	(0.00189)
	Cover 54 x PA	0.01062*** (0.00156)	0.01062*** (0.00191)	0.01053***	(0.00188)
	Forest-C	-0.01048** (0.00424)	-0.01047*** (0.00394)	-0.01122***	(0.00387)
	Elevation-C	-0.01795*** (0.00674)	-0.01795*** (0.00214)	-0.01792***	(0.00210)
	Slope-C	-0.00028	(0.00029)	-0.00028*	(0.00015)	-0.00028*	(0.00015)
	Road-C	-0.00104* (0.00058)	-0.00104*** (0.00028)	-0.00103***	(0.00028)
	Municipal level regressors
	Forest-M			-0.01703** (0.00828)	-0.02031**	(0.00837)
	Elevation-M			0.01262*** (0.00121)	0.01263***	(0.00123)
	Slope-M			-0.00049*** (0.00016)	-0.00054***	(0.00016)
	Road-M			-0.00022*	(0.00013)	-0.00022*	(0.00013)
	Population 2001			0.10156	(0.06344)	0.11338*	(0.06412)
	Irrigated rice paddy			-0.00005** (0.00002)	-0.00005**	(0.00002)
	Impoverished people			0.00005	(0.00004)	0.00005	(0.00004)
	σ µ			0.01034*** (0.00043)	0.01023***	(0.00044)
	σ ν					0.00882***	(0.00067)
	σ			0.03776*** (0.00020)	0.03705***	(0.00024)
	Municipality fixed effects	Yes
	Year fixed effects	Yes		Yes
	Constant	0.06385*** (0.00427)	0.23002*** (0.01278)	0.23002***	(0.01278)
	Observations	17,658	17,658	17,658
	Hausman test
	χ 2 statistic			2.95		0.87
	p-value			1.000	0.999
	Net deforestation
	β 3 + β 4 + β 5			0.01005***	0.00979***
	Std. Err.

Table 3 :

 3 Matching with reweighting

		(1)		(2)
		Multilevel model	Full multilevel model
		with year fixed effects
		Estimates	Std. Err.	Estimates	Std. Err.
	Level one regressors
	PA	-0.01071*** (0.00150)	-0.00960*** (0.00145)
	Cover 30	-0.02083*** (0.00157)	-0.02087*** (0.00270)
	Cover 54	-0.01530*** (0.00132)	-0.01533*** (0.00213)
	Cover 30 x PA	0.00981*** (0.00160)	0.00982*** (0.00149)
	Cover 54 x PA	0.00825*** (0.00133)	0.00825*** (0.00137)
	Forest-C	-0.01125*** (0.00389)	-0.01148*** (0.00157)
	Elevation-C	-0.01604*** (0.00488)	-0.01600*** (0.00536)
	Slope-C	-0.00010	(0.00020)	-0.00011	(0.00012)
	Road-C	-0.00000	(0.00035)	0.00000	(0.00009)
	Municipal level regressors
	Forest-M	-0.00929** (0.00450)	-0.00846*** (0.00097)
	Elevation-M	0.00674*** (0.00169)	0.00439*** (0.00082)
	Slope-M	-0.00027*** (0.00010)	-0.00016*** (0.00005)
	Road-M	-0.00022*** (0.00008)	-0.00018*** (0.00005)
	Population 2001	-0.01495	(0.03857)	-0.01875** (0.00847)
	Irrigated rice paddy	-0.00003*	(0.00002)	-0.00003*** (0.00000)
	Impoverished people	0.00005*	(0.00003)	0.00003*** (0.00001)
	σ µ	0.00001	(0.00001)	0.07446	(0.08406)
	σ ν			0.05945**	(0.02130)
	σ	0.00047**	(0.00021)	0.00037*** (0.00016)
	Year fixed effect	Yes
	Constant	0.02228*** (0.00228)	0.03810	(0.10549)
	Observations	17658	17658
	Net deforestation
	β 3 + β 4 + β 5	0.00734***	0.00846***
	Std. Err.	(0.00152)	(0.00145)
	Note: Superscripts *, ** and *** correspond to 10%, 5% and 1% levels of
	significance. The difference between Model 1 and Model 2 consists in the
	way yearly variations are taken into account: Model 1 relies on year fixed
	effects, Model 2 treats Years as a third level.

Table 4 :

 4 Entropy Matching Sample Mean

		Before-Reweighting	After-Reweighting
		Treat	Control	Treat	Control
	Level one regressors
	Forest-C	3.38E-10 0.0002504	3.38E-10 3.38E-10
	Elevation-C	1.84E-09 -1.03E-09	1.84E-09 1.84E-09
	Slope-C	-1.77E-09 -3.91E-09	-1.77E-09 -1.77E-09
	Road-C	1.51E-08	7.13E-09	1.51E-08 1.51E-08
	Municipal level regressors
	Forest-M	0.1089	0.0509	0.1089	0.1089
	Elevation-M	0.6480	0.5430	0.6480	0.6480
	Slope-M	10.9500	8.3850	10.9500	10.9500
	Road-M	6.6260	4.9570	6.6260	6.6260
	Population 2001	0.0116	0.0141	0.0116	0.0116
	Irrigated rice paddy	15.0900	13.1700	15.0900	15.0900
	Destitute people	6.1500	9.4500	6.1500	6.1500

6

Again, the same argument allows establishing the ancillary result:

Études et Documents n°13, CERDI, 2016

Examples of recent studies are[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[END_REF] Arriagada et al. 2012 in Costa Rica ;[START_REF] Gaveau | Evaluating whether protected areas reduce tropical deforestation in Sumatra[END_REF] in Indonesia ;Nolte et al. 2013 in Brazil ; Sims 2010 in Thaïland ;[START_REF] Sims | Only One Tree from Each Seed? Environmental Effectiveness and Poverty Alleviation in Mexico's Payments for Ecosystem Services Program[END_REF][START_REF] Blackman | Paper park performance: Mexico's natural protected areas in the 1990s[END_REF] in Mexico and Nelson and Chomitz 2011 for a set of tropical countries but using fire data instead of direct deforestation data.

The FAO for example may consider as forest a plot with a tree cover density from 10%. In such case, the plot should not have another land use, which would not be the case in the context of eastern Madagascar. Despite being arbitrary, 30% is also used in other studies, e.g. the Global Forest Watch platform.

We drop municipalities with less than

hectares of natural forest cover as PAs aim at protecting large paths of remaining natural forests. Hence, including localities with almost no forest would bias estimates as these municipalities are structurally different from those still covered by important areas of natural forests.

Actually, some permits may be accorded to farmers to clear forests. However, permits are never requested by locals making the clearing of forest illegal.

This work was supported by the LABEX IDGM+ (ANR-10-LABX-14-01) within the program "Investissements d'Avenir" operated by the French National Research Agency (ANR). http://www.cerdi.org/Sébastien Desbureaux thanks the DP Forêts et Biodiversité for its institutional support in Madagascar and Emilson Rakotorisoa for his research assistance; and acknowledges the financial support of the National Geographic Society through the Young Explorer Program (#C293-15). Eric Kéré was supported by the French government's Agence Nationale de la Recherche through the "Investissements d'avenir" program (ANR-10-LABX-14-01). This project started while he was a Research Fellow at CERDI. Viewpoints and any errors are our own.