Bio-based and Applied Economics BAE Copyright: © 2023 Moukam C.Y., Atewamba C. Open access, article published by Firenze University Press under CC-BY-4.0 License. Firenze University Press | www.fupress.com/bae Bio-based and Applied Economics 12(3): 197-220, 2023 | e-ISSN 2280-6172 | DOI: 10.36253/bae-13534 Citation: Moukam C.Y., Atewamba C. (2023). Incorporating expert knowledge in the estimate of farmers’ opportunity cost of supplying environmental ser- vices in rural Cameroon. Bio-based and Applied Economics 12(3): 197-220. doi: 10.36253/bae-13534 Received: August, 16 2023 Accepted: June 9, 2023 Published: October 15, 2023 Data Availability Statement: All rel- evant data are within the paper and its Supporting Information files. Competing Interests: The Author(s) declare(s) no conflict of interest. Editor: Simone Cerroni ORCID CYM: 0000-0001-8926-0906 AC: 0000-0001-7609-0397 Incorporating expert knowledge in the estimate of farmers’ opportunity cost of supplying environmental services in rural Cameroon Claudiane Yanick Moukam1,*, Calvin Atewamba2 1 Department of Public Economics, University of Douala, Cameroon 2 College Boreal, Canada *Corresponding author. E-mail: yanickmclaudiane@yahoo.fr Abstract. This paper applies a Bayesian approach to incorporate non-data information in estimating the opportunity cost for farmers in rural Cameroon to engage in biodi- versity conservation and carbon sequestration efforts. Findings from our field survey reveal that only a small percentage of farmers are willing to participate in environ- mental protection programmes without compensation. A multidimensional preferenc- es analysis indicates that this behavior may be attributed to a disconnection between environmental values and socioeconomic values. Bayesian analysis of the Tobit model, examining Willingness to Accept (WTA) compensation for agroforestry participation, highlights that factors such as aging, higher educational attainment, and higher socio- economic status are highly likely to promote pro-environmental behaviors. The esti- mated opportunity cost of supplying environmental services is 10,775 CFA francs with a standard deviation of 333.6 CFA francs per farmer. These results differ qualitatively from the existing literature, underscoring the relative significance of considering expert knowledge in the interpretation of environmental policies. Keywords: Bayesian analysis, environmental services, stated preferences, opportunity cost, rural Cameroon. JEL codes: Q57, C34, C11. 1. INTRODUCTION Nature plays a crucial role in supporting human development; howev- er, the increasing demand for the Earth’s resources is leading to accelerated extinction rates and a decline in global biodiversity and ecosystem services. According to the International Panel on Biodiversity and Ecosystem Services (IPBES, 2019), the average abundance of native species in major land-based habitats has decreased by at least 20%, primarily since 1900. Additionally, more than 40% of amphibian species, nearly 33% of reef-forming corals, and over one-third of marine mammal species are currently facing threats. Recognizing this global challenge, governments worldwide are taking action to incorporate biodiversity and ecosystem services into their development plans, policies, and strategies (IPBES, 2019). These initiatives include targets http://creativecommons.org/licenses/by/4.0/legalcode https://doi.org/10.36253/bae-13534 https://doi.org/10.36253/bae-13534 https://orcid.org/0000-0001-8926-0906 https://orcid.org/0000-0001-7609-0397 198 Bio-based and Applied Economics 12(3): 197-220, 2023 | e-ISSN 2280-6172 | DOI: 10.36253/bae-13534 Claudiane Yanick Moukam, Calvin Atewamba such as regenerating vegetative cover in the agricultural sector, enhancing agricultural productivity, and reduc- ing the amount of land used for agriculture through the implementation of intensive agricultural systems. Farmers, being at the forefront of environmen- tal conservation in agriculture, play a crucial role. The effectiveness and efficiency of government incentive mechanisms depend not only on the specific design of the schemes (Bareille et al., 2023) but also on the val- ues farmers associate with ecosystem services and the opportunity costs associated with adopting sustainable agricultural practices (Karsenty et al., 2010; Bessie et al., 2014; Kernecker et al., 2021). By taking into account farmer preferences and expectations in the design of government incentive schemes, we can identify the fac- tors that determine the social acceptability and eco- nomic efficiency of these schemes. Conducting research to assess farmer preferences and expectations, as well as estimating farmers’ willingness to accept compensation (WTA) for providing environmental services, is essential in this context. Farmers’ WTA to participate in envi- ronmental protection programmes reflects the opportu- nity cost of supplying environmental services. In other words, farmers express their preferences by assigning selling prices to environmental services, which can be used for their valuation (Brown and Gregory, 1999; Han- ley and Czajkowski, 2019). The economic literature on the adoption of pay- ment for ecosystem services (PES) schemes using a Stat- ed Preference (SP) approach is extensive (Carson, 2012; Villanueva et al., 2017; Johnston et al., 2017; Hanley and Czajkowski, 2019; Wang and Nuppenau, 2021; Raina et al., 2021; Viaggi et al., 2022). However, most SP stud- ies rely on respondents’ hypothetical choices as data to infer their preferences and, consequently, their WTA for changes in environmental services. As noted by Haghani et al. (2021), the hypothetical nature of SP choice set- tings introduces a hypothetical bias, leading people to systematically over or understate their WTA values in SP exercises. This bias arises because no actual pay- ment is made or received in exchange for a change in the quantity or quality of environmental services. Current research on hypothetical bias in SP approaches focuses on understanding its causes and developing methods to mitigate it. One approach to mitigate hypothetical bias is the use of “cheap talk” scripts, which aim to improve the realism of hypothetical sce- narios and reduce the influence of social desirability biases. However, the effectiveness of cheap talk as a bias mitigation tool varies depending on the context and the specific script used, as highlighted by Bosworth and Tay- lor (2012) and Doyon et al. (2015). Another approach to mitigating hypothetical bias is to use “non-hypothetical” or “real” choice experi- ments (Menapace and Raffaelli, 2020; Fang et al., 2021; Cerroni et al., 2023). These experiments involve asking participants to make actual choices rather than hypo- thetical ones, and they can be conducted in laboratory or field settings. Real-choice experiments have been found to reduce hypothetical bias in some contexts, although they can be more expensive and logistically challenging to implement compared to hypothetical choice experi- ments. In addition to these methodological approaches, researchers are exploring the use of behavioral interven- tions to reduce hypothetical bias. Vossler and Holladay (2016, 2018) suggests that framing survey questions in a way that emphasizes the importance of the decision or providing feedback on the accuracy of participants’ responses may encourage more truthful and accurate responses. However, it is important to note that survey- based welfare measures for public environmental goods are often sensitive to elicitation methods, such as wheth- er the elicitation is framed as an up-or-down vote or an open-ended willingness-to-pay question. Controlling for economic incentives, Vossler and Zawojska (2020) show that most survey response formats, including single bina- ry choice, double-bounded binary choice, payment card, and open-ended formats, elicit statistically identical WTP distributions. This finding highlights that behavioral fac- tors may not be the primary drivers of elicitation effects. Overall, research on hypothetical bias in SP approaches is an active and evolving field, with ongo- ing efforts to understand its causes and develop effec- tive mitigation strategies. Reducing hypothetical bias in choice experiments requires not only careful sur- vey design but also the integration of non-survey data information and expert knowledge. Non-data informa- tion refers to prior knowledge or assumptions derived from sources other than observed or survey data, such as expert opinions, previous studies, or theoretical con- siderations (Knuiman and Speed, 1988; Gelman et al., 2013; Mahmoud et al., 2020; Awwad et al., 2021; Hegazy et al., 2021). Incorporating non-data information in SP studies is particularly valuable when survey data is lim- ited, noisy, biased, or when complex problems demand additional information for accurate analysis. By account- ing for non-data information, we can improve analysis accuracy, mitigate the impact of outliers or measure- ment errors, and enhance understanding of economic agent preferences and behaviors (Kadane and Lazar, 2004; Gelman et al., 2013; Kruschke, 2013). However, it should be noted that incorporating non-data informa- tion poses challenges compared to analyzing survey data alone. Despite its potential, there have been limited https://doi.org/10.36253/bae-13534 199Incorporating expert knowledge in the estimate of farmers’ opportunity cost of supplying environmental services in rural Cameroon Bio-based and Applied Economics 12(3): 197-220, 2023 | e-ISSN 2280-6172 | DOI: 10.36253/bae-13534 studies explicitly considering expert knowledge or non- data information to address hypothetical bias in choice experiments. This is partly explained by the difficulty to capture expert knowledge in current WTA modelling frameworks, which usually rely exclusively on survey data to estimate the unknown parameters of agent preferences. This paper explores an approach that utilizes non-data information to constrain the range of unknown parameters of agent preferences and aims to reduce hypothetical bias in estimating WTA values. To achieve our objective, we start by conducting a field survey in Barombi Mbo, a rural area in Cameroon, to gather data on the socio-economic and environmental conditions of farmers. The survey includes information on farmers’ willingness to accept (WTA) compensation for participating in agroforestry and afforestation pro- grammes. Additionally, we employ a Multidimensional Preferences Analysis (MPA), a technique used to develop spatial representations of proximities among psychologi- cal stimuli or other entities (Carroll and Chang, 1970; Wish and Carroll, 1982; Davison, 1983), to gain insights into the contextual socio-economic and environmen- tal values of the farmers in Barombi Mbo. This analy- sis helps us understand the various factors influencing farmers’ decision-making processes. We then extend a Tobit model, originally proposed by Tobin in 1958, to estimate the WTA values. The Tobit model accounts for the presence of censoring or truncation in the WTA data. Furthermore, we incorporate stochastic constraints in the model’s parameters using prior distributions. These prior distributions capture our expert knowl- edge or expectations regarding agent preferences when engaging in environmental protection programmes. By adopting a Bayesian approach, we update our knowledge based on the data and obtain posterior estimates of the model parameters. The results of our analysis indicate that a significant majority of farmers in Barombi Mbo are willing to participate in agroforestry and afforesta- tion programmes if their financial constraints are allevi- ated. Furthermore, we find that a higher socio-economic status is likely to promote pro-environmental behaviors among farmers, while increased knowledge on environ- mental protection strategies alone does not necessarily lead to eco-friendly behaviors. Based on our Bayesian estimation, the distribution of farmers’ WTA is found to be normally distributed with a mean of 10,775CFA franc and a standard deviation of 323.59CFA franc. Moreo- ver, we estimate the opportunity cost of providing envi- ronmental services for farmers in our study area to be approximately 3,290,448CFA fanc per year. Our research findings demonstrate qualitative dif- ferences from the existing literature (Moukam, 2021; Gou et al., 2021; P érez-S ánchez et al., 2021). While previous studies have acknowledged the potential of employing a Bayesian approach for modeling ecosystem services (Landuyt et al., 2013; Ban et al., 2014; Uusitalo et al., 2015; Hofer et al., 2020), a review of these stud- ies reveals that the technique is not yet fully utilized. It has been highlighted in Hofer et al. (2020); Moukam (2021); Gou et al. (2021); P érez-S ánchez et al. (2021) that the standard approach for modeling ecosystem ser- vice delivery relies solely on data, without incorporat- ing expert knowledge, which can lead to controversial results regarding the drivers of economic agent behavior for environmental protection. In contrast to the afore- mentioned studies, our approach incorporates expert knowledge through the utilization of prior distributions for the model parameters. By doing so, we not only pro- vide mean- ingful insights into the determinants of econom- ic agent preferences but also significantly improve the estimation of WTA compensation for participation in environmental conservation efforts. This allows us to account for situations where the available data may not adequately capture the tangible and intangible benefits of the environment. Our results suggest that the con- ditional probability of the parameters provides the best summary of the knowledge we can gain from the data. The remaining sections of the paper are structured as follows. Section 2 provides a description of the study area, emphasizing its agroecological characteristics and the availability of agricultural extension services. In Sec- tion 3, we outline the research methodology, including details on the survey design, data collection process, and analytical methods employed. The obtained descriptive statistics, research findings, and their discussions are presented in Section 4. Finally, Section 5 serves as the conclusion of the paper, summarizing the key points and providing policy implications based on the findings. 2. BAROMBI MBO AREA IN CAMEROON 2.1. Agro-ecological characteristics The rural area Barombi Mbo is located in the Meme Division of the Southwest region of Cameroon and is one of the villages near the periphery of Lake Barombi Mbo, just after the Forest Reserve (indicated by a black line in Figure 1). It was created in 1940 by the colonial government to protect the Lake, and the local inhabit- ants (natives) were granted the rights to fish in the Lake and harvest cocoa in existing farms within the Reserve (RIS, 2008). However, over the years, the resourc- es attracted an increasing number of people, leading https://doi.org/10.36253/bae-13534 200 Bio-based and Applied Economics 12(3): 197-220, 2023 | e-ISSN 2280-6172 | DOI: 10.36253/bae-13534 Claudiane Yanick Moukam, Calvin Atewamba to the exploitation of illegal farming, hunting, tim- ber, and non-timber forest products (NTFPs), coupled with uncontrolled fishing (Agbor, 2008; Sounders and Kimengsi, 2011; Tchouto et al., 2015). The major food crops grown in the region include cassava (Manihot esculenta), plantain (Musa paradisi- aca), Egusi melon (Cucumis sativus), maize, cocoyams, and taro (Colocasia antiquorum). Cocoa, palm oil, and rubber are the major cash crops in the zone, which is characteristic of the humid forest agro-ecological zone of the Southwest region of Cameroon. Barombi Mbo experiences a typical equatorial climate with a long rainy season from March to November and a short dry season from December to February. The village is known for its hot weather, with an average annual temperature ranging from 20°C to 30°C, as reported by the Delega- tion of Agriculture of Kumba. However, according to the most recent survey (RIS, 2008), the mean annual tem- perature is approximately 18°C or even lower at higher altitudes, with annual precipitation ranging from 1825 to 3000mm. The area has undergone significant climate change, with rains sometimes starting earlier in March and unexpected rainfall occurring during the dry sea- sons. In 2010, the rainy season extended until Decem- ber, disrupting the planting and production of cash and food crops, as well as other economic activities, which typically end in October-November in previous years (Sounders and Kimengsi, 2011; Lebamba et al., 2012; Tchouto et al., 2015). Furthermore, the area consists of steep slopes that are prone to erosion, and it is characterized by a mix- ture of soils, including limon, laterite, sandy, clay, and volcanic soils. These soils, which have a high content of andosols, are predominantly composed of dark volcanic materials. They are generally fertile and suitable for cul- tivating both food and cash crops. However, in deforest- ed and degraded areas, soils are gradually losing fertility due to increased slash and burn practices, soil exposure, pollution, and overcropping (Sounders and Kimengsi, 2011; Tchouto et al., 2015). Agriculture is increasingly encroaching on the area, leading to the reduction of for- ested areas. As a result, the intensified use of fertilizers in agriculture has led to the pollution of the lake. 2.2. Agricultural extension services Several types of sustainable agricultural practices have been promoted among farmers in the Meme Divi- sion by the Ministry of Agriculture and Rural Develop- ment (MINADER), including farmer field school and farmer business school. Through farmer field school, MINADER trains farmers on good agricultural prac- tices in collaboration with cooperatives, while farmer business school focus on promoting agroforestry as a source of income. MINADER provides farmers with improved corn seedlings, maize seeds, cassava cuttings, as well as some pesticides and fertilizers. However, farm- ers face difficulties in adopting agroforestry practices due to the scarcity of improved agroforestry species or nurseries and limited access to productive agricultural land for planting. It is important to note that Barombi Mbo village is not one of the communities targeted by MINADER due to its proximity to the forest reserve, which is managed by the Ministry of Forestry and Wild- life (MINFOF). Due to the lack of collaboration between these two government institutions at the field level, Barombi Mbo farmers are unable to learn about or bene- fit from agroforestry practices supported by MINADER. 3. METHODOLOGY This section outlines the methodology employed to estimate the opportunity cost for farmers in the Barombi Mbo area of Cameroon to adopt agroforestry and afforestation practices. We present the conceptual framework, survey design and data collection meth- ods, modeling framework, and the integration of expert knowledge. 3.1. Conceptual framework – Contingent valuation Sustainable agricultural systems, such as agrofor- estry, deliver and maintain a range of valuable positive environmental externalities, including wildlife habitat and climate mitigation. They have been proven to be less vulnerable to shocks and stresses (VERMA et al., 2016; Gama-Rodrigues et al., 2021). Since these environ- mental benefits are typically considered public goods, private ranches are often less motivated to supply them at their optimal levels. Additionally, a standing forest typically represents a potential source of income that can be accessed through logging or farming in the case of sudden need (Bacon et al., 2012; Gama-Rodrigues et al., 2021). Farmers may thus be unwilling to introduce changes in their production systems that involve a loss of these potential income sources. Therefore, a valuable approach to promoting biodiversity conservation and carbon sequestration is the PES, which provides finan- cial transfers to landowners, farmers, and communities whose land-use decisions may affect the biodiversity val- ues and climate change. PES creates incentives for the conservation of plant and animal species, as well as the soil quality (Engel et al., 2008; Ito, 2022). https://doi.org/10.36253/bae-13534 201Incorporating expert knowledge in the estimate of farmers’ opportunity cost of supplying environmental services in rural Cameroon Bio-based and Applied Economics 12(3): 197-220, 2023 | e-ISSN 2280-6172 | DOI: 10.36253/bae-13534 Although PES is an economic incentive mechanism for the provision of environmental services, the effec- tiveness and efficiency of its implementation, especially in the agricultural sector, largely depend on their social acceptability (Todorova, 2019; Viaggi et al., 2021). In addition, it is relatively difficult, and even impossible, to value environmental services through market mecha- nisms due to their public goods nature. Therefore, the compensation for supplying environmental services is usually based on the opportunity cost of changing practices or restricting use rights. In other words, an eco- nomic agent may seek a monetary amount to ensure that their activities protect or deliver a range of environmen- tal services (Divinski et al., 2018; Sheng et al., 2019). The Figure 1. Location of the study area in South West region of Cameroon. https://doi.org/10.36253/bae-13534 202 Bio-based and Applied Economics 12(3): 197-220, 2023 | e-ISSN 2280-6172 | DOI: 10.36253/bae-13534 Claudiane Yanick Moukam, Calvin Atewamba contingent valuation methodology helps reveal the mon- etary amount an economic agent would like to receive to secure the value of goods or services when prices are not available (Carson, 2012; Johnston et al., 2017). If an economic agent, such as a farmer, has exclusive proper- ty or user rights over a good, such as a standing forest, and is being asked to give up or restrict that entitlement in terms of exclusivity or transfer of user rights, then the correct measurement within a contingent valuation framework is the WTA (Brown and Gregory, 1999; Car- son et al., 2001; McFadden and Train, 2017). There is evidence suggesting that farmers, through their exposure to agri-environmental schemes, have become familiar with the tradeoff between agricultural production and the provision of environmental pub- lic goods (Buckley et al., 2012; McGurk et al., 2020). According to McFadden and Train (2017), the SP meth- odology involves conducting surveys to elicit economic agents’ preferences and their WTA for the provision of public goods, such as environmental services. The devel- opment of SP surveys aims to maximize the validity and reliability of the resulting value estimates. Validity refers to minimizing bias in estimates, while reliability per- tains to reducing variability (Mitchell and Carson, 1989; Bateman et al., 2002; Bishop and Boyle, 2019). Therefore, as emphasized by Johnston et al. (2017), well-designed surveys and proper implementation procedures are cru- cial for achieving these goals and are necessary when extrapolating model estimates from a survey sample to an intended population. 3.2. Survey design and data collection We design a survey instrument that clearly explains the current conditions and presents a consequential val- uation question. Additionally, we select a random sam- ple from the potentially affected population and choose a survey mode that ensures complete questionnaire responses. Scenario description We define a hypothetical scenario to assess agro- forestry development in Barombi Mbo, capturing the impacts of current agricultural practices and potential changes. We present both the baseline or status quo con- ditions and the proposed changes relative to the base- line to the farmers. This approach ensures that farmers understand and accept the valuation scenario (Schultz et al., 2012; Johnston et al., 2017). Our hypothetical sce- nario, along with its consequential value question, is as follows: “Studies conducted in the Barombi Mbo forest reserve have observed that approximately 90% of the for- est reserve, particularly the forest near the lake, has been destroyed. If the current level of activities in the reserve continues, there will be no trees left to provide fuelwood, wood, climate stabilization, wildlife habitat, and water quality and quantity for future generations, as well as for eco-tourism in the watershed. To restore the forest reserve, the government plans to implement an afforesta- tion programme. Your participation in this programme will assist the government in estimating the cost of afforestation.” Questionnaire testing As recommended by Johnston et al. (2017), we con- ducted a focus group discussion with 28 farmers from Barombi Mbo to test our questionnaire. This allowed us to assess the impacts of the information provided on farmers’ responses to the valuation questions, the fram- ing of the valuation questions, as well as the respondents’ prior experience and knowledge. The testing of the ques- tionnaire helped us clarify the questions and informa- tion with the farmers, and also enabled us to determine the monetary amounts (bids) that farmers are willing to accept for adopting agroforestry. This process is crucial not only for ensuring the validity and reliability of our estimates but also for avoiding respondent fatigue caused by the provision of unnecessary details (Mitchell and Carson, 1989; Bateman et al., 2002; Champ et al., 2017). Value elicitation We utilize an open-ended elicitation format to gather pilot data during the survey pretesting phase. This format enables us to collect point estimates of dif- ferent monetary amounts that farmers are willing to accept for agroforestry adoption (Vossler and Zawojska, 2020). Following the presentation of the hypothetical scenario for agroforestry development, our open-ended valuation question is as follows: “What annual compen- sation would you expect to plant trees in or out of the Reserve?” The responses obtained from the participants provide us with a range of monetary amounts, allowing us to determine the distribution of the WTA and select a finite set of monetary amounts to be proposed to farm- ers in the final survey. Instead of choosing monetary amounts between the 15th and 85th percentiles or from the tail of the distribution, as recommended by Kanninen (1995) for WTP, we retain the first two lowest monetary amounts, https://doi.org/10.36253/bae-13534 203Incorporating expert knowledge in the estimate of farmers’ opportunity cost of supplying environmental services in rural Cameroon Bio-based and Applied Economics 12(3): 197-220, 2023 | e-ISSN 2280-6172 | DOI: 10.36253/bae-13534 specifically 10,000CFA franc and 15,000CFA franc. This approach helps to reduce hypothetical bias, as economic agents often tend to overstate their WTA, as highlighted by Kahneman and Tversky’ (1979). Alberini (1995) and Terra (2010) suggest that including approxi- mately two monetary amounts for estimating WTA is theoretically optimal. Having a small number of bids is preferred over a large number as it increases estima- tion efficiency and the power of statistical tests. After conducting the field pilot survey, we revise the ques- tionnaire to incorporate the monetary amounts/WTA for the provision of environmental services, as well as farmers’ suggestions regarding the types and levels of activities carried out in the farm and forest reserve, as presented in Section 4.1. The final survey employs a dichotomous-choice elicitation format. Specifically, we use a WTA question to determine the minimum amount of cash a farmer is willing to accept as compensation for changing their current land-use practices to more productive and envi- ronmentally friendly ones. This question is presented to farmers using a single binary choice format (Carson and Groves, 2007; Carson et al., 2014; Vossler and Holladay, 2018). Our single binary choice question is as follows: “Would you be willing to receive ‘X amount’ per year for your participation in the afforestation programme?” The ‘X amount’ represents either 10,000CFA franc or 15,000CFA franc. The farmer is asked to respond with either “yes” or “no.” Population and sampling procedure The population of Barombi Mbo was estimated to be 595 inhabitants in March 2015, with 349 males and females above 15 years old (Tchouto, 2015). Limiting the age of respondents to 15 years and older allows us to account for farms owned or managed by youths when one or both of their parents are still alive or have passed away. To obtain a sample size that represents the popu- lation of Barombi Mbo, we use the following formula (Yamane, 1967): (1) In this formula, N = 349 represents the number of individuals older than 15 years old, and c = 4.6% is the margin of error. By plugging these values into the for- mula, we calculate a sample size of 200 farmers. The selection of farmers for face-to-face interviews is done randomly within the village. Data collection For data collection, we assign 50% of the sample to each of the two monetary amounts to ensure an equal distribution of bids. The responses to the single binary choice question mentioned earlier are obtained through face-to-face or in-person interviews. Our questionnaire includes auxiliary or support- ing questions to aid in understanding responses to value elicitation questions and ensure construct validity (Krup- nick and Adamowicz, 2006; Mitchell and Carson, 1989; Bateman et al., 2002; Champ et al., 2017; Johnston et al., 2017; Vossler and Holladay, 2018). These auxiliary ques- tions serve multiple purposes, such as identifying demo- graphic, household, or other relevant characteristics of the respondents. Additionally, a subset of these ques- tions may provide covariates, which are used in valuation models to explain the variation in responses to the value elicitation questions (Johnston et al., 2017; Vossler and Holladay, 2018). To account for factors that may influ- ence the WTA, our questionnaire collects information on the socioeconomic characteristics of farmers, farm characteristics, and environmental variables. This infor- mation helps deconstruct farmer preferences and iden- tify factors that affect the WTA. Previous studies, such as Chatterjee et al. (2021), have shown that the adoption of conservation agriculture is related not only to ecologi- cal factors but also to adopters’ characteristics, their per- ceptions, and the decision-making process. Specifically, our questionnaire includes questions regarding the age, gender, education level, family size, and origin of farm- ers. We also inquire about the location and size of farms because the ownership of large and strategically posi- tioned agricultural land may influence farmers’ participa- tion in environmental protection programmes (Ajayi et al., 2012). Furthermore, we include questions about the current agricultural income and the use of fertilizers and pesticides to examine how the land opportunity cost or on-farm income could make compensation or payments more attractive within a PES scheme. Existing evidence suggests that farmers with higher profit levels from their existing activities generally demand higher levels of com- pensation to participate in a conservation scheme (Bate- man, 1996; Ajayi et al., 2012). Furthermore, our questionnaire includes ques- tions to capture farmers’ perceptions of the potential development outcomes associated with unsustainable agricultural practices, such as the heavy use of chemi- cal fertilizers and slash and burn techniques. The poor performance of these unsustainable practices may moti- vate farmers to seek sustainable alternatives, such as agroforestry. As highlighted by Gama-Rodrigues et al. https://doi.org/10.36253/bae-13534 204 Bio-based and Applied Economics 12(3): 197-220, 2023 | e-ISSN 2280-6172 | DOI: 10.36253/bae-13534 Claudiane Yanick Moukam, Calvin Atewamba (2021), agroforestry has positive effects on both income and the environment. In agroforestry systems, habitats are provided for species that can tolerate a certain level of disturbance, and the rate of natural habitat conversion is reduced compared to traditional agricultural systems (Jose, 2009). Agroforestry also contributes to biodiver- sity conservation as trees, crops, and/or animals enhance soil fertility, improve water quality, increase aesthetics, and sequester carbon. For instance, multi-strata cocoa agroforestry systems that incorporate timber, fruit, and native forest species create improved wildlife habitats by increasing plant diversity, enhancing landscape con- nectivity, and reducing edge effects between forests and agricultural land (Jose, 2009; Gama-Rodrigues et al., 2021; Bareille et al., 2023). However, it is important to acknowledge that seeking more sustainable alternatives also involves costs and potential income losses for farm- ers. Therefore, they may require compensation for imple- menting agri-environmental protection solutions (Raina et al., 2021). Moreover, our questionnaire includes questions aimed at capturing the social, environmental, and cul- tural values associated with agroforestry. These val- ues encompass the importance of non-timber forest products (NTFPs), environmental sensitivity, access to information and knowledge about agroforestry and bio- fertilizer technologies, as well as awareness of the PES mechanism. Recognizing and understanding these cul- tural and environmental values is crucial for promoting biodiversity conservation through agroforestry in the long term. These values provide justification for farmers to conserve native forest habitat within cocoa production landscapes, maintain or restore diverse and structurally complex shade canopies within cocoa agroforestry systems, and retain other forms of on-farm tree cover to enhance landscape connectivity and habitat availability (Schroth and Harvey, 2007; Gama-Rodrigues et al., 2021; Bareille et al., 2023; Ito, 2022). However, our field survey reveals a lack of knowledge about the benefits of agroforestry in the Barombi zone. This issue will be discussed further in Section 4.1. Non-data information or expert knowledge In situations where the available data are limited, noisy, or biased, or when the empirical problem is com- plex and requires additional information to determine the WTA, non-data information can be particularly val- uable. Non-data information refers to any prior knowl- edge or assumptions about the WTA that are not derived from observed or survey data (Knuiman and Speed, 1988; Gelman et al., 2013; Mahmoud et al., 2020; Awwad et al., 2021; Hegazy et al., 2021). Such information can be obtained from various sources, including: • Expert opinion: Prior knowledge can be informed by the insights and expertise of professionals in the field who possess relevant experience and knowl- edge. • Previous studies: Prior knowledge can be based on the findings of previous research that has investigat- ed similar or related problems. • Empirical data: Prior knowledge can be derived from data collected from sources other than the cur- rent study, such as pilot studies or surveys. • Theoretical considerations: Prior knowledge can be based on theoretical frameworks and considerations regarding the relationships between the variables of interest. Accounting for non-data information can indeed enhance the accuracy and precision of WTA estimates and mitigate the influence of outliers or measurement errors (Kadane and Lazar, 2004; Gelman et al., 2013; Kruschke, 2013). However, it is crucial to approach the use of non-data information with caution and provide adequate justification, as it introduces subjectivity into the analysis. In our study, we rely on prior knowledge derived from theoretical considerations regarding the relationship between WTA and psychological stimuli experienced by farmers. Further details on this aspect are discussed in Section 3.4. 3.3. Modeling farmer’s willingness to accept The use of a Tobit model is appropriate in our study to model farmers’ WTA compensation. The Tobit model is a regression model commonly employed when the dependent variable is censored within a certain range. In our case, the WTA lies within the interval [0, ∞[ since there is no negative compensation observed in our experiment (as discussed in Section 3.2). Therefore, the Tobit model can effectively capture the behavior of the WTA. In the context of the Tobit model, the choice of a farmer to participate in the agroforestry programme with compensation can be represented as a dichoto- mous outcome. A farmer either agrees to participate (indicating WTA > 0) or does not agree to partici- pate (indicating WTA = 0). The Tobit model has been widely used in studies investigating technology adop- tion and participation in conservation programmes, as mentioned in prior research (e.g., (Buckley et al., 2012; Thompson et al., 2021)). https://doi.org/10.36253/bae-13534 205Incorporating expert knowledge in the estimate of farmers’ opportunity cost of supplying environmental services in rural Cameroon Bio-based and Applied Economics 12(3): 197-220, 2023 | e-ISSN 2280-6172 | DOI: 10.36253/bae-13534 The conceptual model can be described in terms of a latent variable WTA* and an observed variable WTA as follows: (2) (3) where, Xi is a row vector of explanatory variables that determine the respondent i’s WTAi or participation in a sustainable agriculture or conservation programme, β is a column vector of parameters to be estimated, and εi is an error term with a normal distribution N (0, σ2). The Tobit model consists of two parts: a continu- ous part, represented by the linear regression equation 2, and a discrete part, represented by the censored point equation 3. The continuous part, equation 2, models the underlying relationship between the latent variable WTA*i and the explanatory variables Xi. It assumes a lin- ear relationship, where the value of WTA*i is determined by the values of Xi multiplied by the parameter vector β, along with the error term εi. The censored point equa- tion 3 introduces the censoring mechanism. It states that the observed WTA value WTAi is determined based on the value of WTA*i. If WTA*i is greater than zero, indi- cating that the respondent agrees to participate, the observed WTA value equals WTA*i. However, if WTA*i is less than or equal to zero, indicating that the respondent does not agree to participate, the observed WTA value is censored at zero. The Tobit model combines these two parts to esti- mate the parameters β that determine the relationship between the explanatory variables and the WTA, taking into account the censoring mechanism. The estimation procedure accounts for both the continuous and cen- sored parts simultaneously, providing insights into the factors influencing farmers’ WTA and their decision to participate in the agroforestry programme with compen- sation. From (2), we derive that WTA*i follows a normal dis- tribution; and the probability to reject an offer to partici- pate in a sustainable agriculture programme is given by: (4) where φ is the standard normal density function. It fol- lows that the probability for WTA*i to take on positive values is given by: (5) We derive the log-likelihood function of WTA from (3), (4) and (5) as follows: (6) To determine the components of the explanatory variables Xi, we draw insights from existing literature on empirical research on farmers’ valuation of envi- ronmental services, adoption of agricultural technolo- gies, and participation in conservation programmes in both developed and developing countries. These studies include research by Adesina et al. (2000); Jose (2009); Scognamillo and Sitko (2021), Chatterjee et al. (2021) and Raina et al. (2021), among others. These studies provide valuable information on the factors influenc- ing farmers’ WTA. Additionally, some of these studies offer guidance on designing a relevant questionnaire to explore the key determinants of farmers’ WTA (refer to Table 1). From (2) and (3), it can be shown that: E(WTAi/Xi) = (1 − Φ(α))(µ − σλ(α)) (7) where α = −µ/σ, λ(α) = ϕ(α)/(1−Φ(α)), ϕ and Φ are the standard normal density and distribution functions respectively, and µ = Xiβ, with Xiβ = β1 + β2AGE + β3GEND + β4ORIGIN + β5EDU + β6FHSIZE + β7ONFINC + β8LOFARM + β9FASIZE + β10ENVSTY + β11AWPES + β12BIOFERT + β13OUTCPRA + β14NTFPs (8) Denote by θ = (β, σ) the parameter of the empirical model (2). Using data to estimate θ, we can predict the WTA from (7). In this paper, we are interested in pre- dicting the WTA of a representative farmer character- ized by X– = E(Xi). In the following section, we propose an approach to estimate θ. 3.4. Incorporating expert knowledge into farmer’s willing- ness to accept In most SP studies, data on farmers’ hypothetical choices of the WTA are utilized to deduce their prefer- ences for various levels of environmental services (John- ston et al., 2017; Hanley and Czajkowski, 2019; Wang https://doi.org/10.36253/bae-13534 206 Bio-based and Applied Economics 12(3): 197-220, 2023 | e-ISSN 2280-6172 | DOI: 10.36253/bae-13534 Claudiane Yanick Moukam, Calvin Atewamba and Nuppenau, 2021). However, the hypothetical nature of the WTA choices introduces a bias, as individu- als tend to systematically overstate or understate their WTA values. This bias arises because no actual payment is made or received in exchange for an actual change in the quantity or quality of environmental services (Haghani et al., 2021). As suggested in Section 3.2, one way to correct the bias and improve the accuracy and precision of the WTA estimates is to incorporate expert knowledge. Expert knowledge can be utilized to constrain the range of possible values for the unknown parameters, θ, related to agent preferences. The most commonly employed statistical methods for estimating the parameter θ are referred to as fre- quentist (or classical) methods. Specifically, the maxi- mum likelihood method is often utilized, making use of the log-likelihood function (6) (Xu and Lee, 2015; Xu and fei Lee, 2018; Toker et al., 2021). These meth- ods assume that the unknown parameter θ is a fixed constant and determine the probability of its estimator through limiting relative frequencies. As a result of these assumptions, it is not possible to provide a probabilistic statement regarding the unknown parameter θ since it is considered fixed. Consequently, the frequentist approach is not suitable for incorporating expert knowledge in the estimation of the unknown parameter θ. Bayesian estimation provides an alternative approach, treating θ as a random variable and allow- ing for the expression of uncertainty through prob- ability statements and distributions known as priors (Mahmoud et al., 2020; Awwad et al., 2021; Hegazy et al., 2021). Priors are designed to incorporate any relevant information the researcher possesses before observ- ing the data. Therefore, priors can take various forms, accommodating the inclusion of expert knowledge in the estimation of the unknown parameter θ. By leveraging our expert knowledge of farmer preferences, as captured by the prior distribution of θ, Bayesian analysis enables us to learn from data and update our knowledge accord- ingly. It emphasizes that the conditional probability of the unknown parameter θ serves as the optimal means of summarizing the information derived from the data (Chan et al., 2019). The Bayesian approach provides a comprehensive probabilistic framework for empirical modeling. It ena- bles us to address hypothetical bias in the estimates of sample characteristics such as E(WTAi/Xi) by leverag- ing our prior knowledge of the unknown parameters (Kadane and Lazar, 2004; Gelman et al., 2013; Krusch- ke, 2013). As stated by Chan et al. (2019), Bayesian analy- sis involves the calculation of the posterior distribu- tion of the parameter θ, denoted as p(θ/WTA). It can be expressed, up to an arbitrary constant, in a proportional form as: p(θ/WTA) ∝ Log L × π(θ) (9) Here, Log L represents the log-likelihood function of the censored regression model for WTA (refer to (6)), and π(θ) is referred to as the prior distribution of θ, or Table 1. Description of explanatory variables and their expected signs. Variables Description Expected signs AGE Age of farmer (CONTINUOUS) (±) GEND Sex of farmer (DUMMY): 1 if male and 0 if female (±) ORIGIN Origin of farmers (DUMMY): 1 if native and 0 if non-native (+) EDU Education level of farmers (CATEGORICAL): 0 if None (never been to school), 1 if primary and 2 if high level (secondary, high school) (−) FHSIZE Size of farm households (CONTINUOUS) (±) ONFINC Average yearly on-farm income (CONTINUOUS) (+) LOFARM Location of the farm (DUMMY): 1 if out of the reserve and 0 if otherwise (+) FASIZE Size of the farm (DUMMY): 1 if more than 5ha and 0 if not (−) ENVSTY Environmental sensitivity of farmers (DUMMY): 1 if sensitive to the role of forest to protect the environment and 0 if not (−) AWPES Awareness of PES scheme (DUMMY): 1 if yes and 0 otherwise (±) OUTCPRA Perception of the output of current practices by farmers (DUMMY): 1 if average (average, bad) and 0 if good (good, very good) (±) BIOFERT Knowledge of Bio-fertilizers (DUMMY): 1 if farmers have knowledge and 0 otherwise (±) NTFPs Importance of NTFPs to the farmer: 1 if important and 0 otherwise (−) Source: Authors’ definitions https://doi.org/10.36253/bae-13534 207Incorporating expert knowledge in the estimate of farmers’ opportunity cost of supplying environmental services in rural Cameroon Bio-based and Applied Economics 12(3): 197-220, 2023 | e-ISSN 2280-6172 | DOI: 10.36253/bae-13534 simply the prior. As mentioned earlier, the prior distri- bution reflects our expert knowledge about the param- eter θ before examining the data. It can assume various forms, such as uniform, normal, gamma, or other dis- tributions, depending on the problem’s nature and the available prior information. In equation (9), the prior knowledge is incorporated into the posterior distribu- tion using Bayes’ theorem. As more data is collected, the influence of the prior distribution diminishes, and the posterior distribution becomes increasingly shaped by the likelihood function. This process is known as updat- ing the prior distribution. As discussed in Section 3.2, there are various sourc- es of prior knowledge. When expert opinions, previous studies, or empirical data about the parameters are lack- ing, theoretical considerations can be employed to gen- erate prior knowledge. Theoretical considerations are particularly valuable for specifying uninformative pri- ors. Chan et al. (2019) defines an uninformative, flat, or diffuse prior as any distribution that expresses vague or general information about a parameter. The use of non- informative priors in Bayesian analysis offers several advantages, including: • Objectivity: Non-informative priors aim to mini- mize the influence of prior knowledge on posterior results by expressing ”objective” information, such as ”the parameter is positive” or ”the parameter is less than a certain limit.” They strive to be as objec- tive as possible, allowing the data to exert the great- est influence on the final inference. This can help address concerns about subjectivity or bias in the analysis. • Robustness: Non-informative priors can be valuable when prior knowledge or information is limited or unreliable. They provide a default assumption that avoids strong assumptions or bias based on incom- plete or uncertain information. This is particularly beneficial in situations where there is a lack of prior knowledge or when multiple analysts with different perspectives are involved. • Simplicity: Non-informative priors are often simple and unrestrictive, facilitating a more straightforward analysis. They simplify the modeling process and reduce the computational burden associated with estimating complex prior distributions. • Sensitivity analysis: Non-informative priors are use- ful for conducting sensitivity analyses. By compar- ing the results obtained with non-informative priors to those obtained with informative priors, research- ers can assess the impact of prior assumptions on the final inference. This helps identify the extent to which the results depend on prior specifications. • Communicating uncertainty: Non-informative priors offer a means to quantify and communi- cate uncertainty when little or no prior knowledge is available. They enable the estimation of credible intervals or posterior distributions that reflect the uncertainty in the parameters of interest based sole- ly on the observed data. However, it’s important to acknowledge that non- informative priors have their limitations. In certain cases, they may not fully capture all available informa- tion, resulting in less efficient inference or potentially misleading results. Table 1 outlines the expected signs for the parameters in our model based on theoretical considerations, representing the necessary prior knowl- edge for specifying noninformative priors. However, for robustness, we assume that all explanatory variables may have both positive and negative effects on WTA. The principle of indifference, which assigns equal probabilities to all possibilities, is the simplest and old- est rule for determining a non-informative prior. In this study, we adopt a non-informative prior for β, specifical- ly a uniform prior distribution, π(β) ∝ 1. Additionally, it is common in the literature to use a gamma distribution as a prior for the standard deviation of a normal distri- bution (Chan et al., 2019). Therefore, we assume that σ follows a gamma distribution, π(σ) ∝ G(a, b), where a = 0.01 represents the shape parameter and b = 0.01 denotes the inverse-scale parameter. The choice of hyper-param- eters a and b ensures convergence of the posterior dis- tribution sampling. Furthermore, we assume that β and σ are independently distributed, giving π(θ) = π(β)π(σ). To perform a Bayesian analysis of the Tobit model (2) and (3), we can utilize the LIFEREG procedure in the Statistical Analysis Software (SAS). This procedure incorporates an Adaptive Rejection Metropolis Sampling (ARMS) algorithm based on the programme provided by Gilks (2003) to draw a sample θk = (βk, σk)k=1...m from the full-conditional distribution (9). The Bayesian esti- mate of the mean WTA of agent i, denoted as E(WTAi/ Xi), is then calculated as: (E(WTAi/Xi)/Y) ≈ (1 − Φ(αk))(µk – σkλk(αk)), as m approaches infinity, (10) where, Y = {WTAi, Xi}i=1,..,n represents the data, αk = −µk/ σk, λk(αk) = ϕ(αk)/(1 − Φ(αk)), ϕ and Φ denote the stand- ard normal density and distribution functions, respec- tively, and µk = Xiβk. https://doi.org/10.36253/bae-13534 208 Bio-based and Applied Economics 12(3): 197-220, 2023 | e-ISSN 2280-6172 | DOI: 10.36253/bae-13534 Claudiane Yanick Moukam, Calvin Atewamba 4. RESULTS AND DISCUSSION In this section, we provide the results of implement- ing the methodology outlined in the previous section. Firstly, we provide a brief overview of the descriptive statistics pertaining to both traditional and eco-innova- tive farming practices in the study area. Subsequently, we employ a multidimensional preferences analysis to examine contextual behavior patterns that could eluci- date farmer preferences. Finally, we analyze the empiri- cal estimates of farmer willingness to accept compensa- tion for environmental services. 4.1. Descriptive statistics of traditional and eco-innovative farming practices Throughout generations, farmers have continu- ously strived to enhance agricultural land productivity through the utilization of available technologies. Table 2 provides an overview of the traditional and eco-inno- vative farming practices employed by farmers in the study area. It is observed that approximately 85 percent of farmers utilize chemical inputs, such as fertilizers and pesticides, to improve soil fertility and manage cocoa farms. Among the pesticides used, fungicides and insec- ticides are the most commonly employed, both within and outside the reserve. Regarding soil preparation techniques, 53.5% of farmers employ crop rotation, fol- lowed by a slash and burn method (34%). Despite facing challenges related to limited land availability for crop cultivation, a majority (50.5%) of farmers employ vari- ous durations of bush fallow systems to enhance land productivity. While 24.5% of farmers have their farms located within the reserve, a significant proportion of respondents (70.5%) attribute most of the observed deforestation in the reserve to the exploitation of fuel- wood, timber, and NTFPs. To mitigate the adverse impacts of deforestation, chemical fertilizers, and pesticides in the vicinity of the lake, farmers have adopted various eco-innovative prac- tices to protect the environment. A significant number of farmers prioritize conservation by preserving old and large trees within their own farms. For example, approx- imately 52% of farmers have planted fruit trees, NTFPs, and other species on their land. These seedlings are typically sourced from their own nurseries or purchased from external suppliers. The planting of trees serves the dual purpose of preventing soil erosion and safeguard- ing the environment. However, agroforestry practices are not widely implemented, primarily due to limited aware- ness regarding their significance. Only a small propor- tion of farmers (16%) have heard about agroforestry or bio-agriculture, with information dissemination occur- ring through various channels, including schools, vil- lage meetings, and the farmers field school initiative of MINADER (Ministry of Agriculture and Rural Devel- opment). It is worth noting that the majority of farmers believe that chemical fertilizers are the most effective solution to combat declining soil fertility. This inclina- tion can be attributed to the lack of awareness regarding indigenous knowledge pertaining to soil erosion pre- vention, soil demineralization, and the production and application of organic manure. In fact, when asked to explain their understanding of bio-fertilizers, only 30.5% of farmers demonstrated some knowledge on the subject. Moreover, it is noteworthy that only 48% of farmers consider the outputs from their current farming prac- tices to be good or satisfactory (see Table 2). Almost all farmers (95.5%) acknowledge the significance of forests in providing vital ecosystem services, including climate regulation, flood control, erosion control, wildlife habi- tat, landscape beauty, and cultural/spiritual value. Con- cerning watershed protection, the majority of farmers (97.5%) recognize the positive correlation between for- Table 2. Traditional and eco-innovation farming practices. Description Frequency of ”yes” % of the respondents Chemical use Overall 170 85 Fungicides 94 55.29 Insecticides 22 12.94 Soil preparation techniques Slash and burn 68 34 Rotation 107 53.50 Bush fallow practice 101 50.50 Tree conservation NTFPs 47 43.12 Timber 31 28.44 Fruit trees 21 19.27 Reforestation Fruit trees 70 67.31 NTFPs 27 27.96 Origin of seedlings From own nursery 48 46.15 Buy 29 27.88 Donation 22 21.15 Forest cover destroyed in the reserve More than 75% of forest destroyed 141 70.50 Agro-forestry knowledge 32 16 Bio-fertilizers knowledge 61 30.50 Source: Authors’ calculations from survey data. https://doi.org/10.36253/bae-13534 209Incorporating expert knowledge in the estimate of farmers’ opportunity cost of supplying environmental services in rural Cameroon Bio-based and Applied Economics 12(3): 197-220, 2023 | e-ISSN 2280-6172 | DOI: 10.36253/bae-13534 est cover and water quality. However, only 27% of farm- ers are familiar with the PES mechanism (see Table 2). Nonetheless, considering the farmers’ willingness to plant diverse tree species on their own land, it is rea- sonable to expect their active participation in the PES scheme if they are provided with incentives to plant and preserve trees. 4.2. Adoption of agro-forestry and multidimensional prefer- ences analysis According to the data presented in Table 3, a signifi- cant proportion of farmers (87.5%) are willing to accept compensation in order to participate in an afforestation programme both within and outside the reserve, as well as along the border of the lake. While the benefits of agroforestry are discussed with farmers during the sur- vey, only a small percentage (8.5%) of farmers residing near the lake express their willingness to adopt agrofor- estry practices. However, among those who are willing to adopt agroforestry, a majority also demonstrate their commitment to refrain from using chemicals within an 8-meter distance from the lake, provided that they receive seedlings for agroforestry and receive training on best agroforestry practices. In conducting a multidimensional preferences anal- ysis (MPA), we aim to identify the primary dimensions of farmer preferences that can explain their willingness to adopt agroforestry practices. While Principal Com- ponent Analysis (PCA) focuses on reducing complexity and identifying patterns in large datasets, MPA delves into understanding individual or group preferences and priorities. It can be seen as a PCA of a data matrix, with columns representing individuals and rows representing variables or objects. As depicted in Figure 2, the determinants of farm- ers’ willingness to participate in an afforestation pro- gramme are classified into three groups: • The first group comprises variables such as aware- ness of PES schemes (AWPES), knowledge of bio- fertilizers (BIOFERT), the importance of non-timber forest products (NTFPs), and education level (EDU). This group reflects the extent to which farmers pos- sess knowledge about environmental management. It is reasonable to assume that farmers with higher levels of education are more likely to be aware of PES programmes, have knowledge of bio-fertilizers, and understand the importance of NTFPs. • The second group consists of variables related to environmental sensitivity (ENVSTY), the origin of the farmer (ORIGIN) (whether native or non-native to the study area), and the location of the farm (LOFARM) (whether inside or outside the reserve). This group captures the farmers’ connection (sensi- tivity, origin, and location) to the study area and the local community. It is evident that farmers who are native to the study area and have farms within the reserve exhibit a higher sensitivity to the role of for- ests in environmental protection. • The third group includes variables such as age (AGE), gender (GEND), farm size (FASIZE), farm household size (FHSIZE), and yearly on-farm income (ONFINC). This group reflects farmers’ soci- oeconomic status and demographic characteristics. The strong correlation between on-farm income and farm size suggests the existence of an extensive agri- cultural system, which often exerts significant pres- sure on the environment. By analyzing these three groups of variables, mul- tidimensional preferences analysis helps uncover the underlying dimensions driving farmers’ preferences and their willingness to adopt agroforestry practices. The perfect negative correlation between the first group of variables (related to knowledge and awareness of environmental management) and the second group of variables (related to connections with the local commu- nity) reveals an interesting pattern. It suggests that farm- ers who have weak connections with the local commu- nity tend to be more knowledgeable about environmental management, while those with strong connections are less informed in this regard. This finding has important implications as it may help explain why rural areas are more susceptible to environmental degradation. In rural areas, where strong community ties and social networks are prevalent, farmers who have close connections with the local community may rely on tra- ditional practices and knowledge passed down through generations. However, these practices may not always align with sustainable agricultural practices or modern environmental management strategies. On the other hand, farmers who have weaker connections with the local community, such as migrants or individuals with limited social integration, may have more exposure to Table 3. Distribution of the willingness to accept. Response FCFA10,000 FCFA15,000 Total No 14 11 25 Yes 86 89 175 Total 100 100 200 Percentage of yes 86% 89% 87.5% Source: Authors’ calculations from survey data. https://doi.org/10.36253/bae-13534 210 Bio-based and Applied Economics 12(3): 197-220, 2023 | e-ISSN 2280-6172 | DOI: 10.36253/bae-13534 Claudiane Yanick Moukam, Calvin Atewamba external information and knowledge regarding sustain- able agriculture and environmental management. This finding highlights the need for capacity building and training initiatives targeting local and indigenous com- munities, as well as natural resources owners in rural areas like Barombi Mbo. By providing them with appro- priate knowledge and skills related to sustainable agri- cultural practices and environmental management, we can promote behavior change and the adoption of more sustainable practices. Recognizing the ownership of natural resources, coupled with empowering individuals with the necessary knowledge, can serve as a catalyst for positive changes and contribute to the reduction of envi- ronmental degradation in the area. The non-correlation between the third group of variables (related to socio-economic status and demo- graphic characteristics) and both the first and second groups of variables suggests that farmers’ knowledge of environmental management practices and their con- nections with the local community are independent of their socio-economic and demographic conditions. In other words, farmers can enhance their understanding of environmental management or improve their commu- nity connections regardless of their socio-economic sta- tus or demographic characteristics. This finding implies that efforts to build farmers’ capacity in environmental management will not significantly impact their socio- economic and demographic conditions. While farmers may possess knowledge about sustainable agricultural practices, they may lack the socio-economic incentives or motivations to translate that knowledge into concrete actions that protect the environment. This may explain why farmers, despite having knowledge of sustainable practices, appear to be less sensitive to environmental degradation. To address this gap between knowledge and action, it becomes imperative to introduce economic incentive schemes such as PES programmes. These programmes Figure 2. Multidimensional Preferences Analysis. https://doi.org/10.36253/bae-13534 211Incorporating expert knowledge in the estimate of farmers’ opportunity cost of supplying environmental services in rural Cameroon Bio-based and Applied Economics 12(3): 197-220, 2023 | e-ISSN 2280-6172 | DOI: 10.36253/bae-13534 create an enabling business environment where farmers can be rewarded for their efforts in reducing environ- mental deterioration. By providing economic incentives, farmers are more likely to be motivated to adopt and implement sustainable agricultural practices that contrib- ute to environmental protection. Integrating economic incentives with farmers’ existing knowledge of sustain- able practices, we can bridge the gap between awareness and action, ensuring that farmers are actively engaged in protecting the environment. This approach recognizes the need to align environmental goals with socio-eco- nomic conditions and provides a practical mechanism for incentivizing sustainable practices among farmers. Overall, combining knowledge-building initiatives with economic incentive schemes can effectively encour- age farmers to apply their knowledge and contribute to environmental conservation while considering their socio-economic and demographic realities. 4.3. Determinants of the WTA for the provision of environ- mental services Geweke diagnostics are commonly used to assess the convergence of parameters drawn from the posterior distribution in Bayesian analysis. The fact that Geweke diagnostics (Table 4) indicate no evidence to reject the convergence suggests that the estimation process has been successful and the sample of parameters obtained from the posterior distribution (9) is representative. By using this sample of parameters, statistical inferences can be made about the effects of farmers’ socio-eco- nomic, environmental, and demographic values on their WTA for environmental services. The probabilities Pr(θi ≤ 0) provide a basis for determining the likely direction of influence of each variable on WTA. The influence is likely negative if Pr(θi <= 0) ≥ 0.5, whereas it is positive if Pr(θi <= 0) < 0.5. Based on the given information, it appears that variables such as the sex of farmers (GEND), origin of farmers (ORIGIN), location of farms (LOFARM), out- put of current practices (OUTCPRA), awareness of PES scheme (AWPES), and knowledge of bio-fertilizers (BIOFERT) have a positive inf luence on WTA. This means that these factors are likely to increase farmers’ WTA for environmental services. On the other hand, variables such as the age of farmers (AGE), education level of farmers (EDU), size of farm households (FHSIZE), size of the farm (FASIZE), yearly on-farm income (ONFINC), and importance of non-timber forest products (NTFPs) are likely to have a negative effect on WTA. This suggests that these varia- bles are expected to decrease farmers’ WTA for environ- mental services. These findings provide valuable insights into the fac- tors that shape farmers’ preferences and willingness to accept compensation for environmental services. Under- standing these determinants can inform policy and deci- sion-making processes related to the design and imple- mentation of effective incentive schemes, such as pay- ment for environmental services, to promote sustainable agricultural practices and environmental conservation. The negative effect of farmers’ age (AGE) on their WTA participation in an afforestation programme can Table 4. Bayesian Parameter Estimates. Parameters (θi) Estimates Std. Dev. Equal-Tail Interval Pr(θi ≤ 0) Geweke Diagnostics Lower Upper z Pr ≥ |z| Intercept 12060.4 1843.8 8529.4 15674.5 0 -1,237 0.216 AGE (age of farmer) -79.680 36.286 -151.5 -9.6776 0.987 0.171 0.865 GEND (sex of farmer) 1276.7 732.4 -172.5 2691.3 0.043 1,422 0.155 EDU (education level of farmer) -871.7 549.2 -1942.4 211.5 0.944 -0.101 0.920 ORIGIN (origin of farmer) 1546.9 967.3 -344.2 3469.9 0.054 0.880 0.379 FHSIZE (size of farm household) -109.7 163.4 -436.2 206.4 0.748 -0.124 0.901 LOFARM (location of farm) 346.9 820.5 -1251.8 11973.7 0.336 -0.235 0.814 FASIZE (size of farm) -255.3 772.2 -1749.9 1272.6 0.630 -1,505 0.133 ONFINC (yearly on-farm income) -0.00013 0.000208 0.000281 0.000273 0.736 0.678 0.498 OUTCPRA (output of current practices) 444.7 675.8 -875.5 1770.6 0.254 -0.154 0.877 AWPES (awareness of PES scheme) 1751.6 782.2 218.3 3271.9 0.012 -0.852 0.394 BIOFERT (knowledge of bio-fertilizers) 2923.6 765.1 1416.1 4434.5 0.000 0.766 0.443 NTFPs (importance of non-timber forest products) -538.0 746.3 -2025.3 912.9 0.763 0.236 0.814 Scale 4595.2 222.5 4182.7 5054.6 0 1,202 0.229 https://doi.org/10.36253/bae-13534 212 Bio-based and Applied Economics 12(3): 197-220, 2023 | e-ISSN 2280-6172 | DOI: 10.36253/bae-13534 Claudiane Yanick Moukam, Calvin Atewamba be explained by several factors. As individuals grow older, they tend to prioritize existential values over eco- nomic values. Existential values encompass fundamen- tal questions regarding human existence, such as “To be or not to be?”, as well as practical concerns related to protecting human life and avoiding threats to existence (Lipiec, 2000). This shift in focus towards existential val- ues may lead older farmers to be less inclined to accept compensation in exchange for adopting eco-innovations that protect the environment and, consequently, human existence. Additionally, the aging process often fosters a great- er concern for the well-being of others, beyond one’s own self-interest. As individuals age, they become more attuned to the collective and the welfare of the broader community. Older individuals may view the realiza- tion of environmental values as a means to establish the foundational basis for other values. Consequently, elder- ly farmers are less likely to be receptive to compensation offers aimed at incentivizing their adoption of agrofor- estry practices, especially when the central question revolves around human existence. Overall, the negative relationship between age and WTA for participation in an afforestation programme can be attributed to the prioritization of existential val- ues over economic values among older individuals. Aging prompts individuals to care not only for them- selves but also for the collective well-being. Elderly farm- ers may view the pursuit of environmental values as cru- cial for establishing the existential foundation necessary to support other values. Consequently, they may be less inclined to accept compensation to adopt agroforestry practices, given the overarching importance they place on human existence. The positive effect of farmers’ origin (ORIGIN) on their WTA compensation to participate in an afforesta- tion programme may seem counterintuitive at first. One would expect that native farmers, who have a stronger connection to the local area and a better understanding of the importance of protecting their natural heritage, would be more inclined to adopt agroforestry practices voluntarily, without requiring compensation. However, to interpret this unexpected result, we need to consider the relationship between farmers’ origin and the location of their farms. As illustrated in Figure 2 and Table 4, native farm- ers tend to have farms located outside the reserve. It is important to note that farmers with farms outside the reserve are more likely to demand higher compensa- tion to participate in an afforestation programme. This can be attributed to the fact that farms located outside the reserve generally have fewer trees compared to those within the reserve. Consequently, the opportunity cost of adopting agroforestry practices on farms outside the reserve is likely to be higher than on farms within the reserve. Native farmers, therefore, may be requesting compensation to offset the higher opportunity cost asso- ciated with implementing agroforestry on their farms. Additionally, the observed behavior of native farm- ers could be influenced by their lower level of educa- tion and their limited valuation of NTFPs, as indicated in Figure 2. Farmers with lower levels of education or those who do not recognize the importance of NTFPs are more likely to demand higher compensation to adopt agroforestry practices, as demonstrated in Table 4. This finding aligns with the well-established understanding that higher educational attainment promotes pro-envi- ronmental behavior (Tianyu and Meng, 2020; Zhou et al., 2021). In summary, the positive effect of farmers’ origin on their WTA for participation in an afforestation pro- gramme can be explained by several factors. Native farm- ers, despite their stronger connection to the local area, may request compensation due to the higher opportu- nity cost associated with adopting agroforestry on farms located outside the reserve. Furthermore, their lower level of education and limited recognition of the importance of NTFPs may contribute to their demand for higher compensation. These findings emphasize the complex interplay between farmers’ origin, farm location, educa- tion, and value orientations in shaping their willingness to accept compensation for agroforestry adoption. The variables representing farmers’ socio-economic status, namely the size of farm households (FHSIZE), size of the farm (FASIZE), and yearly on-farm income (ONFINC), are found to have a negative effect on farm- ers’ WTA compensation for participating in an affores- tation programme, as indicated in Table 4. This implies that higher socio-economic status is associated with a greater propensity for pro-environmental behavior. Two theoretical perspectives in the literature can help explain this important finding. The first perspective revolves around the concept of post-materialism, which suggests that individuals with higher socio-economic status are more likely to adopt values that prioritize self-expression, subjective well- being, and quality of life. As highlighted by Pampel (2014), post-materialist values are associated with con- cerns for issues such as environmentalism, feminism, and equality. In our context, the size of farm house- holds, which serves as an indicator of farmers’ social status, can be seen as reflecting their adherence to post- materialist values. Farmers who value self-expression and quality of life are more inclined to prioritize envi- https://doi.org/10.36253/bae-13534 213Incorporating expert knowledge in the estimate of farmers’ opportunity cost of supplying environmental services in rural Cameroon Bio-based and Applied Economics 12(3): 197-220, 2023 | e-ISSN 2280-6172 | DOI: 10.36253/bae-13534 ronmental protection and are thus more willing to par- ticipate in afforestation programmes. The second perspective is based on the notion of affluence, suggesting that environmental quality is con- sidered an amenity that high-income individuals can more readily afford (Franzen and Meyer, 2010). In this view, the size of the farm and yearly on-farm income, as indicators of prosperity, can positively influence farmers’ inclination to protect the environment, particularly when the associated economic costs are perceived as insig- nificant. Higher-income farmers may be more willing to invest in environmental conservation measures because they have the financial means to do so without compro- mising their livelihoods. This affluence argument aligns with the observation that higher socio-economic status promotes pro-environmental attitudes and behaviors. Both theories, post-materialism and affluence, can be applied in our context to explain why farmers with higher socio-economic status exhibit a greater willing- ness for participating in afforestation programmes. The size of farm households ref lects post-materialist val- ues related to self-expression, while the size of the farm and yearly on-farm income capture the affluence aspect, indicating that farmers with greater financial resources are more likely to prioritize environmental protection when the associated costs are perceived as manageable. Overall, these findings highlight the role of socio- economic status in shaping farmers’ pro-environmental behavior and suggest that individuals with higher socio- economic status are more inclined to support environ- mental initiatives. The variables representing farmers’ knowledge of environmental management, namely the awareness of PES scheme (AWPES) and knowledge of bio-fertilizers (BIOFERT), are found to have a positive influence on farmers’ WTA compensation for participating in an afforestation programme, as shown in Table 4. This indi- cates that having greater knowledge about environmen- tal management does not necessarily translate into eco- friendly behavior among farmers. There seems to be a significant gap between farmers’ knowledge of environ- mental risk management and their actual on-the-ground actions in dealing with environmental issues. This disparity between knowledge and behavior highlights the need to understand the factors that con- tribute to the “knowledge-behavior gap” in the context of sustainability. Merely providing additional informa- tion to farmers is unlikely to lead to significant improve- ments in environmental conditions unless certain key factors are addressed. As emphasized by Knutti (2019), securing political will and implementing simple solu- tions that provide immediate and local co-benefits are crucial. It is not enough for farmers to possess knowl- edge; they also require support, incentives, and clear pathways for action. While environmental management strategies exist, their implementation is often hindered by various fac- tors, including attitudes towards environmental pro- tection, short-term and medium-term implementation costs, and doubts about the effectiveness and efficiency of proposed policy instruments. Farmers who have a positive attitude towards environmental management may perceive compensation for participating in an afforestation programme as a means to bridge the gap between their knowledge and their behavior in the con- text of sustainability. Offering financial incentives can serve as a motivating factor for farmers to align their behavior with their environmental knowledge. Overall, the presence of a “knowledge-behavior gap” among farmers indicates that simply increasing their knowledge of environmental management strategies is insufficient to drive eco-friendly behavior. Addressing this gap requires a comprehensive approach that goes beyond information provision and tackles other barriers such as attitudes, costs, and doubts about the effective- ness of policy instruments. Offering compensation as a reward for participating in environmental programmes can incentivize farmers and help bridge the gap between their knowledge and their actions in a sustainability context. 4.4. The opportunity cost of environmental services Bayesian estimation provides us with a sample of parameters {θk = (βk, σk)}k=1...m from the full conditional distribution (9), where θk represents the parameters of farmer preferences. Using this sample, we can derive a distribution of the mean WTA using equation (7) for a representative farmer.1 The resulting distribution of the mean WTA, as depicted in Figure 3, exhibits a normal shape. To for- mally test the normality of the distribution, we use the Anderson-Darling statistic, which confirms that the mean WTA follows a normal distribution with a mean of 10,775CFA franc and a standard deviation of 333.6CFA franc, as shown in Table 5. To estimate the mean WTA using a Bayesian approach, we apply formula (10). The Bayesian estimate of the mean WTA is calculated to be 10,775CFA franc, with a 95% confidence interval of 10,769-10,781CFA franc, as presented in Table 5. The narrow confidence 1 The characteristics of the representative farmer are obtained by taking the mean of each explanatory variable. https://doi.org/10.36253/bae-13534 214 Bio-based and Applied Economics 12(3): 197-220, 2023 | e-ISSN 2280-6172 | DOI: 10.36253/bae-13534 Claudiane Yanick Moukam, Calvin Atewamba interval indicates that the estimate of the mean WTA has low volatility or high precision, suggesting a more reliable estimate. Overall, the Bayesian estimation allows us to obtain a distribution of the mean WTA, which is found to fol- low a normal distribution. The Bayesian estimate of the mean WTA, along with its confidence interval, provides a precise estimation of the mean WTA value, contribut- ing to a better understanding of farmers’ preferences in the context of willingness to accept compensation for participating in an afforestation programme. Based on the survey design outlined in Section 3.2, we can deduce that the probability for a farmer in the Barombi Mbo community to accept compensa- tion and participate in an afforestation programme is P = 175/200. To estimate the total willingness to accept (WTA) or the community opportunity cost to partici- pate in the afforestation programme using a Bayesian approach, we can use the following formula: E(Total WTA/Y ) ≈ N × P × Mean_WTAk, (11) where Y = {WTAi, Xi}i=1,..,n represents the observed data, N = 349 denotes the size of the eligible population in Barombi Mbo, and {Mean–WTAk} represents the sam- ple of the mean WTA obtained from the Bayesian esti- mation. In this formula, m represents the number of samples drawn from the Bayesian estimation. As m approaches infinity, the estimate becomes more accurate. By multiplying the probability P with the popula- tion size N and the average of the sample mean WTA values, we can estimate the total WTA or the commu- nity opportunity cost to participate in the afforestation programme. It is important to note that this estima- tion assumes that the sample of farmers in the survey is representative of the entire eligible population in Barombi Mbo. The results reported in Table 5 indicate that the Bayesian estimate of the total WTA or the community opportunity cost to participate in the afforestation pro- gramme is 3,290,448CFA franc with a 95% confidence interval of 3,288,511-3,292,385CFA franc. The small con- fidence interval suggests that the estimate of the total WTA exhibits low volatility or high precision. We can also derive a sample of the distribution of the community opportunity cost of providing envi- ronmental services from the sample distribution of the mean WTA using the relationship Total WTA = N ×P ×Mean WTA. Furthermore, a test of normality using the Anderson-Darling statistic confirms that the com- munity opportunity cost of providing environmen- tal services follows a normal distribution with a mean of 3,290,448CFA franc and a standard deviation of 98,818CFA franc. Comparing these results with those obtained by Moukam (2021) using a Maximum Likelihood meth- od to estimate the Tobit model, it can be observed that the estimated values of the mean and total WTA obtained from the Bayesian approach are almost three times higher. Specifically, the Bayesian estimate of the mean WTA is 10,775CFA franc, whereas the estimate obtained using the Maximum Likelihood method is 4,488CFA franc. Similarly, the Bayesian estimate of the total WTA is 3,290,448CFA franc, while the Maximum Likelihood estimate is 1,370,491CFA franc. This differ- ence highlights the potential of the Bayesian approach to account for both tangible and intangible values of ecosystem services. Overall, the results suggest that the Bayesian approach provides a more comprehensive and precise estimation of the WTA and community opportunity cost, incorporating both economic and noneconomic factors associated with environmental services. In Bayesian analysis, sensitivity analysis is usually recommended to assess the impact of prior assump- tions on the final inference using non-informative priors as the counterfactual. However, in our case, since our results are primarily based on non-informative priors, conducting a sensitivity analysis is not feasible. Conse- quently, our results can be interpreted as a quantification of the uncertainty in the parameters of interest based solely on the observed data. Table 5. Opportunity Cost of Supplying Environmental Services (Fcfa). Parameter Estimate Std. Dev. 95% Confidence Limits Anderson-Darling Lower Upper Stat. P. Value Mean WTA 10,775 323.59 10,769 10,781 0.587 0.131 T otal WTA 3,290,448 98,818 3,288,511 3,292,385 0.587 0.131 Note. Aderson-Darling is a Goodness-of-Fit Test for Normal Distribution. https://doi.org/10.36253/bae-13534 215Incorporating expert knowledge in the estimate of farmers’ opportunity cost of supplying environmental services in rural Cameroon Bio-based and Applied Economics 12(3): 197-220, 2023 | e-ISSN 2280-6172 | DOI: 10.36253/bae-13534 5. CONCLUSION AND IMPLICATIONS In this paper, we incorporate non-data information and expert knowledge into the estimation of farmers’ opportunity cost for providing environmental services through agroforestry and forest regeneration in the rural area of Cameroon. To achieve this, we begin by conduct- ing a survey to gather information on farmers’ WTA and factors that may influence their preferences to par- ticipate in an environmental protection programme in Barombi Mbo, a rural region in Cameroon. Subsequent- ly, we adjust a Tobit model of the WTA by incorporat- ing expert knowledge through the specification of prior distributions for model parameters. Finally, a Bayes- ian approach is employed to estimate both the model parameters and the farmers’ opportunity cost of sup- plying environmental services, accounting for both data and non-data information. The paper contributes to the important economic literature on the valuation of environmental goods and services using a SP approach. Specifically, we propose a two-step survey design to determine a limited number of bids that farmers can choose from, which allows them to highlight their preferences and their WTA for changes in environmental services. Additionally, we conduct a mul- tidimensional preference analysis to identify the primary dimensions of farmer preferences that may explain their willingness to participate in environmental conservation programmes. Furthermore, we expand the well-known Tobit model of WTA by incorporating non-data infor- mation or expert knowledge through the specification of parameter distributions. To estimate a comprehensive probabilistic model of WTA for changes in environmen- tal services, we employ a Bayesian approach. Compared to the related literature (Moukam, 2021; Pérez-Sánchez et al., 2021), our approach to WTA modeling has the poten- tial to significantly reduce potential hypothetical bias in data collection and analysis.2 This reduction in hypo- thetical bias is achieved through an improved estimate of farmers’ opportunity cost of supplying environmen- tal services, resulting in more realistic and interpretable results. Our results align with the findings of previous authors Kadane and Lazar (2004); Gelman et al. (2013); Kruschke (2013) who have demonstrated that Bayesian methods provide more accurate estimates, better model comparison, and improved inferences compared to tra- ditional frequentist methods. However, it is worth not- ing that conducting a Bayesian analysis requires a careful specification of prior distributions that incorporate our expert knowledge. As more data are collected, the influ- ence of the prior distribution decreases, and the posterior distribution becomes increasingly influenced by the like- lihood function (Chan et al., 2019). An important result of this paper is that the major- ity of farmers (87.5%) are unlikely to voluntarily engage in environmental management without economic incen- tives. Our multidimensional preference analysis suggests that farmers’ behavior may be attributed to the lack of correlation between environmental and socio-economic dimensions of their preferences. Therefore, it is crucial to implement economic incentive mechanisms, such as PES, to facilitate the alignment of environmental and socio- economic values. The Bayesian analysis reveals that aging is likely to promote pro-environmental behavior, indicat- ing that older individuals are more sensitive to existential values compared to the youth (Lipiec, 2000). Addition- ally, natives are more inclined to accept compensation for adopting sustainable agricultural practices compared to migrants. This controversial finding can be partly explained by the observation that natives generally have lower educational attainment than migrants. This aligns with the widely accepted understanding that higher levels of education promote pro-environmental behavior (Tian- yu and Meng, 2020; Zhou et al., 2021). A significant finding of this paper is that higher socio-economic status, as indicated by factors such as the size of farm households, farm size, and yearly on- farm income, positively inf luences proenvironmen- tal behavior. This observation can be explained by the affluence argument (Franzen and Meyer, 2010), which suggests that high-income farmers are more capable of affording environmental quality as an amenity good. Moreover, farmers with higher socio-economic status are more likely to have embraced postmaterialist values, which prioritize self-expression, subjective well-being, 2 Hypothetical bias arises from the tendency of people to systematically overor understate their WTA in SP studies. Figure 3. Distribution of Mean WTA. https://doi.org/10.36253/bae-13534 216 Bio-based and Applied Economics 12(3): 197-220, 2023 | e-ISSN 2280-6172 | DOI: 10.36253/bae-13534 Claudiane Yanick Moukam, Calvin Atewamba and quality of life, leading to increased concerns for environmental issues (Pampel, 2014). Furthermore, our analysis reveals that an increase in knowledge of envi- ronmental management strategies is less likely to pro- mote eco-friendly behavior. This finding aligns with the research by Knutti (2019), who identified several barriers contributing to the observed knowledge-behavior gap. These barriers include attitudes towards environmental protection, implementation costs in the short and medi- um term, and skepticism regarding the effectiveness of proposed policy instruments. Another important finding of this paper is that farmers’ WTA follows a normal distribution with a mean of 10,775CFA franc and a standard deviation of 333.6CFA franc. Additionally, the community opportu- nity cost of supplying environmental services also exhib- its a normal distribution, with a mean of 3,290,488CFA franc and a standard deviation of 98,818CFA franc. These distributions have significant implications for policy-making, as they enable us to make probabilis- tic statements about the value of environmental servic- es. For instance, considering the significance of WTA in cost-benefit analysis (CBA), our results provide an effective means to incorporate uncertainty when assess- ing the welfare effects of regulatory and investment interventions that impact the environment. This allows expected outcomes in CBA, such as financial and eco- nomic net present values (NPVs), to incorporate risk and uncertainty associated with environmental management. Furthermore, our estimation of the distribution of WTA plays a crucial role in understanding the intricate finan- cial trade-off involved in the Cameroonian government’s engagement in international financial mechanisms for biodiversity conservation and climate change mitigation. This paper presents a significant empirical frame- work for estimating the value of environmental services and evaluating the inf luence of socio-economic and demographic factors on that value. Considering that farmers in developing countries often exhibit compara- ble socio-economic and demographic characteristics, along with similar con- cerns regarding environmental degradation, our estima- tion of the WTA distribution can serve as valuable prior knowledge or information regarding the value of envi- ronmental services in other rural areas of Cameroon or the developing world. REFERENCES Adesina, A. A., D. Mbila, G. B. Nkamleu, and D. Enda- mana (2000, 9). Econometric analysis of the determi- nants of adoption of alley farming by farmers in the forest zone of southwest cameroon. Agriculture, Eco- systems and Environment 80, 255–265. Agbor, E. (2008). Building capacity for sustainable pay- ment for environmental service schemes (pes) in cameroon. Ajayi, O. C., B. K. Jack, and B. Leimona (2012). Auc- tion design for the private provision of public goods in developing countries: Lessons from payments for environmental services in malawi and indonesia. World Development 40, 1213–1223. Alberini, A. (1995). Board of regents of the university of wisconsin system testing willingness-to-pay models of discrete choice contingent valuation survey data. Source: Land Economics 71, 83–95. Awwad, R. R. A., O. M. Bdair, and G. K. Abufoudeh (2021). Bayesian estimation and prediction based on rayleigh record data with applications. Statistics in Transition New Series 22. Bacon, C. M., C. Getz, S. Kraus, M. Montenegro, and K. Holland (2012). The social dimensions of sustainabil- ity and change in diversified farming systems. Ecol- ogy and Society 17. Ban, S. S., R. L. Pressey, and N. A. Graham (2014). Assessing interactions of multiple stressors when data are limited: A bayesian belief network applied to cor- al reefs. Global Environmental Change 27. Bareille, F., M. Zavalloni, and D. Viaggi (2023, 1). Agglom- eration bonus and endogenous group formation. Amer- ican Journal of Agricultural Economics 105, 76–98. Bateman, I., R. T. G. B. D. for Transport., B. Day, M. Hanemann, N. Hanley, T. Hett, M. Jones-Lee, G. Loomes, I. Bateman, R. Carson, B. Day, M. Hane- mann, N. Hanley, T. Hett, M. Jones-Lee, and G. Loomes (2002). Economic valuation with stated pref- erence techniques : a manual. Edward Elgar. Bateman, I. J. (1996, 3). Household willingness to pay and farmers’ willingness to accept compensation for establishing a recreational woodland. Journal of Envi- ronmental Planning and Management 39, 21–44. Bessie, S., F. Beyene, B. Hundie, G. Goshu, and Y. Menge- sha (2014). Local communities’ perceptions of bam- boo deforestation in benishangul gumuz region, ethi- opia. Journal of Economics and Sustainable Develop- ment www.iiste.org ISSN 5. Bishop, R. C. and K. J. Boyle (2019, 2). Reliability and validity in nonmarket valuation. Environmental and Resource Economics 72, 559–582. Bosworth, R. and L. O. Taylor (2012). Hypothetical bias in choice experiments: Is cheap talk effective at elimi- nating bias on the intensive and extensive margins of choice? https://doi.org/10.36253/bae-13534 217Incorporating expert knowledge in the estimate of farmers’ opportunity cost of supplying environmental services in rural Cameroon Bio-based and Applied Economics 12(3): 197-220, 2023 | e-ISSN 2280-6172 | DOI: 10.36253/bae-13534 Brown, T. C. and R. Gregory (1999). Why the WTA- WTP disparity matters. Technical report. Buckley, C., S. Hynes, and S. Mechan (2012). Supply of an ecosystem service-farmers’ willingness to adopt riparian buffer zones in agricultural catchments. Environmental Science and Policy 24, 101–109. Carroll, J. D. and J.-J. Chang (1970). Analysis of indi- vidual differences in multidimensional scaling via an n-way generalization of eckart-young decomposition. Carson, R. T. (2012, nov). Contingent Valuation: A Prac- tical Alternative when Prices Aren’t Available. Journal of Economic Perspectives 26 (4), 27–42. Carson, R. T., N. E. Flores, and N. F. Meade (2001). Con- tingent valuation: controversies and evidence. Envi- ronmental and Resource Economics 19. Carson, R. T. and T. Groves (2007, 5). Incentive and informational properties of preference questions. Environmental and Resource Economics 37, 181–210. Carson, R. T., T. Groves, and J. A. List (2014, 3). Conse- quentiality: A theoretical and experimental explo- ration of a single binary choice. Journal of the Asso- ciation of Environmental and Resource Economists 1, 171–207. Cerroni, S., D. W. Derbyshire, W. G. Hutchinson, and R. M. Nayga (2023, 2). A choice matching approach for discrete choice analysis: An experimental investiga- tion in the laboratory. Land Economics 99, 80–102. Champ, P. A., K. J. Boyle, and T. C. T. C. Brown (2017). A primer on nonmarket valuation. Chan, J. C. C., G. Koop, D. J. Poirier, and J. L. Tobias (2019). Bayesian econometric methods, Volume 2. Chatterjee, R., S. K. Acharya, A. Biswas, A. Mandal, T. Biswas, S. Das, and B. Mandal (2021). Conservation agriculture in new alluvial agro-ecology: Differential perception and adoption. Journal of Rural Studies 88. Davison, M. L. (1983, 9). Introduction to multidimen- sional scaling and its applications. Applied Psychologi- cal Measurement 7, 373–379. Divinski, I., N. Becker, and P. B. (Kutiel) (2018). Oppor- tunity costs of alternative management options in a protected nature park: The case of ramat hanadiv, israel. Land Use Policy 71. Doyon, M., L. Saulais, B. Ruffieux, and D. Bweli (2015). Hypothetical bias for private goods: Does cheap talk make a difference? Theoretical Economics Letters 05. Engel, S., S. Pagiola, and S. Wunder (2008). Designing payments for environmental services in theory and practice: An overview of the issues. Ecological Eco- nomics 65. Fang, D., R. M. Nayga, G. H. West, C. Bazzani, W. Yang, B. C. Lok, C. E. Levy, and H. A. Snell (2021). On the use of virtual reality in mitigating hypothetical bias in choice experiments. American Journal of Agricul- tural Economics 103. Franzen, A. and R. Meyer (2010, apr). Environmental Attitudes in Cross-National Perspective: A Multilevel Analysis of the ISSP 1993 and 2000. European Socio- logical Review 26 (2), 219–234. Gama-Rodrigues, A. C., M. W. Müller, E. F. Gama-Rodri- gues, and F. A. T. Mendes (2021). Cacao-based agro- forestry systems in the atlantic forest and amazon biomes: An ecoregional analysis of land use. Gelman, A., J. B. Carlin, H. S. Stern, D. B. Dunson, A. Vehtari, and D. B. Rubin (2013, 11). Bayesian Data Analysis. Chapman and Hall/CRC. Gilks, W. R. (2003). Adaptive Metropolis Rejection Sam- pling (ARMS). Gou, M., L. Li, S. Ouyang, N. Wang, L. La, C. Liu, and W. Xiao (2021, 7). Identifying and analyzing ecosys- tem service bundles and their socioecological drivers in the three gorges reservoir area. Journal of Cleaner Production 307, 127208. Haghani, M., M. C. Bliemer, J. M. Rose, H. Oppewal, and E. Lancsar (2021). Hypothetical bias in stated choice experiments: Part i. macro-scale analysis of literature and integrative synthesis of empirical evidence from applied economics, experimental psychology and neuroimaging. Hanley, N. and M. Czajkowski (2019, aug). The Role of Stated Preference Valuation Methods in Understand- ing Choices and Informing Policy. Review of Environ- mental Economics and Policy 13 (2), 248–266. Hegazy, M. A., R. E. A. El-Kader, A. A. El-Helbawy, and G. R. Al-Dayian (2021). Bayesian estimation and pre- diction of discrete gompertz distribution. Journal of Advances in Mathematics and Computer Science. Hofer, S., A. Ziemba, and G. E. Serafy (2020, 3). A bayes- ian approach to ecosystem service trade-off analysis utilizing expert knowledge. Environment Systems and Decisions 40, 67–83. IPBES (2019). Summary for policymakers of the global assessment report on biodiversity and ecosystem servic- es of the Intergovernmental Science-Policy Platform on Biodiversity and Ecosystem Services. IPBES secretariat. Ito, J. (2022). Program design and heterogeneous treat- ment effects of payments for environmental services. Ecological Economics 191. Johnston, R. J., K. J. Boyle, W. V. Adamowicz, J. Ben- nett, R. Brouwer, T. A. Cameron, W. M. Hanemann, N. Hanley, M. Ryan, R. Scarpa, R. Tourangeau, and C. A. Vossler (2017, 6). Contemporary guidance for stated preference studies. Journal of the Association of Environmental and Resource Economists 4, 319–405. Jose, S. (2009, 5). Agroforestry for ecosystem services and https://doi.org/10.36253/bae-13534 218 Bio-based and Applied Economics 12(3): 197-220, 2023 | e-ISSN 2280-6172 | DOI: 10.36253/bae-13534 Claudiane Yanick Moukam, Calvin Atewamba environmental benefits: An overview. Kadane, J. B. and N. A. Lazar (2004, 3). Methods and criteria for model selection. Journal of the American Statistical Association 99, 279–290. Kahneman, D. and A. Tversky’ (1979). Prospect theory: An analysis of decision under risk. Econometrica XLVII, 263–91. Kanninen, B. J. (1995, 1). Bias in discrete response con- tingent valuation. Journal of Environmental Econom- ics and Management 28. Karsenty, A., T. Sembres, and M. Randrianarison (2010). Paie- ments pour services environnementaux et biodiversit´e dans les pays du sud. Revue Tiers Monde 202, 57. Kernecker, M., V. Seufert, and M. Chapman (2021). Farmer-centered ecological intensification: Using innovation characteristics to identify barriers and opportunities for a transition of agroecosystems towards sustainability. Agricultural Systems 191. Knuiman, M. W. and T. P. Speed (1988, 12). Incorporat- ing prior information into the analysis of contingen- cy tables. Biometrics 44, 1061. Knutti, R. (2019, sep). Closing the Knowledge-Action Gap in Climate Change. One Earth 1 (1), 21–23. Krupnick, A. and W. Adamowicz (2006). Supporting questions in stated-choice studies. Kruschke, J. K. (2013). Bayesian estimation supersedes the t test. 142, 573–603. Landuyt, D., S. Broekx, R. D’hondt, G. Engelen, J. Aerts- ens, and P. L. Goethals (2013). A review of bayesian belief networks in ecosystem service modelling. Envi- ronmental Modelling and Software 46. Lebamba, J., A. Vincens, and J. Maley (2012). Pollen, vegetation change and climate at lake barombi mbo (cameroon) during the last ca. 33 000 cal yr bp: A numerical approach. Climate of the Past 8, 59–78. Lipiec, J. (2000). Existential Values. In Life the Human Being between Life and Death, pp. 173–182. Dordrecht: Springer Netherlands. Mahmoud, M., M. M. Nassar, and M. A. Aefa (2020). Bayesian estimation and prediction based on pro- gressively first failure censored scheme from a mix- ture of weibull and lomax distributions. Pakistan Journal of Statistics and Operation Research 16. McFadden, D. and K. Train (2017). Contingent Valuation of Environmental Goods. McGurk, E., S. Hynes, and F. Thorne (2020). Participation in agri-environmental schemes: A contingent valua- tion study of farmers in ireland. Journal of Environ- mental Management 262. Menapace, L. and R. Raffaelli (2020, 8). Unraveling hypo- thetical bias in discrete choice experiments. Journal of Economic Behavior & Organization 176, 416–430. Mitchell, R. C. and R. T. Carson (1989). Using surveys to value public goods : the contingent valuation method. Resources for the Future. Moukam, C. Y. (2021). Supplying environmental services through sustainable agriculture in rural cameroon: An estimation of farmers’ willingness to accept in barombi mbo. International Journal of Innovation and Applied Studies 33, 222–233. Pampel, F. C. (2014, mar). The varied influence of SES on environmental concern. Social science quarterly 95 (1), 57–75. Pérez-Sánchez, D., M. Montes, C. Cardona-Almeida, L. A. Vargas-Marín, T. Enríquez-Acevedo, and A. Suarez (2021, 5). Keeping people in the loop: Socio- economic valuation of dry forest ecosystem services in the colombian caribbean region. Journal of Arid Environments 188, 104446. Raina, N., M. Zavalloni, S. Targetti, R. D’Alberto, M. Rag- gi, and D. Viaggi (2021, 10). A systematic review of attributes used in choice experiments for agri-envi- ronmental contracts. Bio-based and Applied Econom- ics 10, 137–152. RIS (2008). Information sheet on ramsar wetlands, 2006- 2008 version. Schroth, G. and C. A. Harvey (2007, 7). Biodiversity con- servation in cocoa production landscapes: An over- view. Schultz, E. T., R. J. Johnston, K. Segerson, and E. Y. Besedin (2012, 5). Integrating ecology and economics for restoration: Using ecological indicators in valua- tion of ecosystem services. Restoration Ecology 20, 304–310. Scognamillo, A. and N. J. Sitko (2021). Leveraging social protection to advance climate-smart agri- culture: An empirical analysis of the impacts of malawi’s social action fund (masaf) on farmersˆa€™ adoption decisions and welfare outcomes. World Development 146. Sheng, J., H. Qiu, and S. Zhang (2019). Opportunity cost, income structure, and energy structure for landhold- ers participating in payments for ecosystem services: Evidence from wolong national nature reserve, china. World Development 117. Sounders, N. B. and J. N. Kimengsi (2011). Sustainable management of lake barombi mbo as a source of drinking water to the population of kumba, came- roon. African Journal of Social Sciences 2, 76–94. Tchouto, P., E. E. S., and M. K. N (2015). Report of the socioeconomic survey of the lake barombi mbo forest reserve, south west region, cameroon. Terra, S. (2010). Guide de bonnes pratiques pour la mise en oeuvre de la m´ethode d’evaluation contingente serie methode 05-m04. Thompson, N. M., C. J. Reeling, M. R. Fleckenstein, L. https://doi.org/10.36253/bae-13534 219Incorporating expert knowledge in the estimate of farmers’ opportunity cost of supplying environmental services in rural Cameroon Bio-based and Applied Economics 12(3): 197-220, 2023 | e-ISSN 2280-6172 | DOI: 10.36253/bae-13534 S. Prokopy, and S. D. Armstrong (2021). Examining intensity of conservation practice adoption: Evidence from cover crop use on u.s. midwest farms. Food Pol- icy 101. Tianyu, J. and L. Meng (2020, dec). Does education increase pro-environmental willingness to pay? Evidence from Chinese household survey. Journal of Cleaner Production 275, 122713. Todorova, K. (2019). Factors affecting adoption behavior of farmers in bulgaria-agri-environment public goods for flood risk management. Journal of Central Euro- pean Agriculture 20. Toker, S., N. A˜–zbay, G. A˜œstA˜¼ndaA¨ Y¨ ˚Aˇziray, and A¨ °smail Yenilmez (2021). Tobit liu estimation of censored regression model: an application to mroz data and a monte carlo simulation study. Journal of Statistical Computation and Simulation 91. Uusitalo, L., A. Lehikoinen, I. Helle, and K. Myrberg (2015). An overview of methods to evaluate uncer- tainty of deterministic models in decision support. Environmental Modelling and Software 63. VERMA, S., V. SINGH, D. VERMA, and S. GIRI (2016). Agroforestry practices and concepts in sustainable land use systems in india. International Journal of Forestry and Crop Improvement 7. Viaggi, D., F. Bartolini, and M. Raggi (2022, 1). The bio- economy in economic literature: looking back, look- ing ahead. Bio-based and Applied Economics 10, 169– 184. Viaggi, D., M. Raggi, A. J. Villanueva, and J. Kantelhardt (2021). Provision of public goods by agriculture and forestry: Economics, policy and the way ahead. Villanueva, A. J., K. Glenk, and M. Rodr´ıguez-Entrena (2017, sep). Protest Responses and Willingness to Accept: Ecosystem Services Providers’ Preferences towards Incentive-Based Schemes. Journal of Agricul- tural Economics 68 (3), 801–821. Vossler, C. A. and J. S. Holladay (2016). Alternative value elicitation formats in contingent valuation: A new hope. Journal of Public Economics. Vossler, C. A. and J. S. Holladay (2018). Alternative value elicitation formats in contingent valuation: Mecha- nism design and convergent validity. Journal of Public Economics 165. Vossler, C. A. and E. Zawojska (2020). Behavioral drivers or economic incentives? toward a better understand- ing of elicitation effects in stated preference stud- ies. Journal of the Association of Environmental and Resource Economists 7. Wang, X. and E.-A. Nuppenau (2021, jun). Modelling payments for ecosystem services for solving future water conflicts at spatial scales: The Okavango River Basin example. Ecological Economics 184, 106982. Wish, M. and J. D. Carroll (1982, 1). 14 multidimensional scaling and its applications. Handbook of Statistics 2, 317–345. Xu, X. and L. fei Lee (2018). Sieve maximum likelihood estimation of the spatial autoregressive tobit model. Journal of Econometrics 203. Xu, X. and L. F. Lee (2015). Maximum likelihood estima- tion of a spatial autoregressive tobit model. Journal of Econometrics 188. Yamane, T. (1967). Statistics: An Introductory Analysis (2nd ed.). Harper and Row. Zhou, M., F. Chen, and Z. Chen (2021, may). Can CEO education promote environmental innovation: Evi- dence from Chinese enterprises. Journal of Cleaner Production 297, 126725. https://doi.org/10.36253/bae-13534 220 Bio-based and Applied Economics 12(3): 197-220, 2023 | e-ISSN 2280-6172 | DOI: 10.36253/bae-13534 Claudiane Yanick Moukam, Calvin Atewamba A. APPENDIX Figures. 4 and 5 show the draws, the autocorrela- tion of draws, and the empirical posterior distribution of two parameters: the Intercept and the Biofertilizer (BIOFERT) from the implementation of the Adapta- tive Rejection Metropolis Sampling (ARMS) algorithm based on a programme provided by Gilks (2003) using the procedure LIFEREG of the Statistical Analysis Soft- ware (SAS). We can see that the draws are randomly dis- tributed and exhibit low correlation. This is an indica- tion that the Bayesian estimation has converged for these two parameters. A similar result is obtained for other parameters. Figure 4. Bayesian diagnostics for Intercept. Figure 5. Bayesian diagnostics for Biofertilizer. https://doi.org/10.36253/bae-13534 Towards a holistic approach to sustainable risk management in agriculture in the EU: a literature review Linda Arata1, Simone Cerroni2, Fabio Gaetano Santeramo3, Samuele Trestini4, Simone Severini5,* Modelling technical efficiency of horticulture farming in Kosovo: An application of data envelopment analysis Nol Krasniqi1,2,*, Stéphane Blancard1, Ekrem Gjokaj2, Giovanna Ottaviani Aalmo3 Incorporating expert knowledge in the estimate of farmers’ opportunity cost of supplying environmental services in rural Cameroon Claudiane Yanick Moukam1,*, Calvin Atewamba2 Farmers’ acceptance of a micro-irrigation system: A focus group study Maria Sabbagh1,*, Luciano Gutierrez2 Reducing food-related economic loss to improve food security and cattle trade in the Sahel: the case of agropastoral systems in Senegal Abdrahmane Wane1,*, Aliou Diouf Mballo2, Cabrelle Lauriane Dzoukou Homsi3, Pathé Diakhaté4, Rahimatou Memboup5