Improving Representation of Decision Rules in LUCC-ABM: An Example with an Elicitation of Farmers’ Decision Making for Landscape Restoration in Central Malawi

: Restoring interlocking forest-agricultural landscapes— forest-agricscapes —to sustainably supply ecosystem services for socio-ecological well-being is one of Malawi’s priorities. Engaging local farmers is crucial in implementing restoration schemes. While farmers’ land-use decisions shape land-use / cover and changes (LUCC) and ecological conditions, why and how they decide to embrace restoration activities is poorly understood and neglected in forest-agricscape restoration. We analyze the nature of farmers’ restoration decisions, both individually and collectively, in Central Malawi using a mixed-method analysis. We characterize, qualitatively and quantitatively, the underlying contextual rationales, motives, beneﬁts, and incentives. Identiﬁed decision-making rules reﬂect diverse and nuanced goal frames of relative importance that are featured in various combinations. We categorize the decision-making rules as: problem-solving oriented, resource / material-constrained, beneﬁts-oriented, incentive-based, peers / leaders-inﬂuenced, knowledge / skill-dependent, altruistic-oriented, rules / norms-constrained, economic capacity-dependent, awareness-dependent, and risk averse-oriented. We link them with the corresponding vegetation- and non-vegetation-based restoration practices to depict the overall decision-making processes. Findings advance the representation of farmers’ decision rules and behavioral responses in computational agent-based modeling (ABM), through the decomposition of empirical data. The approach used can inform other modeling works attempting to better capture social actors’ decision rules. Such LUCC-ABMs are valuable for exploring spatially explicit outcomes of restoration investments by modeling such decision-making processes and policy scenarios.

Introduction
Restoring forest-agricscapes to address various environmental threats such as land degradation, deforestation, climate change, and to sustainably supply ecosystem services for socio-ecological well-being is increasingly embraced in Sub-Saharan Africa (SSA). Forest-agricscapes capture natural landscapes made of interspaced agricultural and forested lands-typical of rural areas in SSA-that should be managed holistically for landscape-scale restoration. Researchers stress that engaging local farmers and landowners is necessary for a successful implementation of forest-agricscape restoration schemes [1]. Local farmers' engagement with restoration occurs at both individual and collective Computational modeling approaches that emphasize socio-ecological interactions, specifically those that contribute to enhanced understanding of LUCC dynamics, have been widely used in recent decades [17,18]. An example is agent-based models (ABMs), which help to account for the agency of individual social actors of the socio-ecological system and their interactions with and impacts on the shared biophysical environment. The focus is on capturing actors' heterogeneity, resource constraints, interconnectedness, and interactions that conjointly constitute their decision making [19][20][21]. Recent large review studies of ABMs have focused on the representation and characterization of human (agent) decision making, including implementation frameworks for the decision architecture, generically [21,22], at the narrow farm level as potential complements to traditional farm models in policy analysis [23], and specifically to LUCC-ABMs [11,21]. We draw on these reviews which concur that understanding and representation of human decision making, including in collective action settings, in ABMs remain underexplored. Huber et al. [21] specifically decry the reduced efforts to model farmers' emotions, values, learning, risk and uncertainty, or social interactions as part of decision-making elements.
The main reasons advanced for such underexploration include the lack of context-appropriate socio-economic data and variables, and the challenging use of frameworks to parameterize those social/human behaviors properly and accurately. First, to formulate an appropriate context for the decision-making component, researchers use data from social surveys, role-playing games, semi-structured interviews, surveys, and expert knowledge to characterize and parameterize the behavioral aspects [11,18,[24][25][26]. Smajgl and Barreteau [25], in particular, offer a generic characterization and parameterization (CAP) framework "that allows for a structured and unambiguous description of the characterization and parameterization process" (p. 29), and demonstrate its use in several modeling situations. However, their framework does not illustrate explicitly how to decompose the various types of data into decisions rules and their types and how to integrate them into empirical ABMs. The provided guiding options (e.g., steps M3 and M4b in particular) remain theoretical. Second, to incorporate a relevant framework, many human decision heuristics have been employed [11,[26][27][28]. Nine types of decision models are mostly used in modeling human decisions in ABMs [26]. These Sustainability 2020, 12, 5380 4 of 33 include microeconomic models, space-theory-based models, psychosocial and cognitive models, institution-based models, experience/preference-based models, participatory agent-based modeling, empirical/heuristic rules, evolutionary programming, and assumption-and/or calibration-based rules. Some of these frameworks have been used in combination [26]. Balke and Gilbert [27] categorized 14 agent decision-making models along five main dimensions that incorporate: cognitive processes, affective aspects, social dimensions, norms, and learning. Groeneveld et al. [11] further investigated the use of theories to implement human decision making in LUCC-ABMs. They concluded that in cases where theories are used, preference is mostly given to the expected utility theory within a rational or a bounded rational paradigm. These authors suggested considering psychological theories and blending both cognitive and affective dimensions following the categories advanced by Balke and Gilbert [27]. While the challenge of behavioral theoretical grounding in LUCC-ABMs is an identified gap and barrier for the broader reusability and policy relevance of such ABMs, this study responds to the first specific need for enhancement of empirical ABM-the elicitation of decision rules from empirical multi-type data. This can contribute to easing the representation of the behavioral components.
We use insights from the GFT and the literature reviewed above to build a conceptual approach that allows us to systematically and comprehensively process and analyze data gathered from multiple sources to capture the decision making of human agents in LUCC-ABMs. Specifically, we use the approach to develop locally informed representations of farmers' restoration decision making for a future simulation of associated socio-ecological outcomes at a higher (aggregate) forest-agricscape scale in Central Malawi using an ABM. While this study is part of a larger and growing body of research on participatory modeling ranging from the effective capture of human behavior in models on socioecological problems generically [29,30] to the capture of such behavior among farmers and other environment-related land managers [31][32][33], a detailed examination of participatory modeling for ABM is beyond the scope of this paper. As explained, the focus of this paper is only on our empirical-based approach to depicting the behavioral rules.

Conceptual Approach to Develop Restoration Decision Rules
We elaborate below on the approach (Figure 1) that we followed to arrive at the restoration decision rules (RDRs, rules for short) to use later in a future empirical LUCC-ABM (not part of this article) that simulates the restoration processes in the study area.
Data used in our study come from three different sources: focus group discussions (FGDs or discussions), participatory role-playing games (RPGs or games), and a farm-household survey (FHH, survey for short). Such a mixed-method approach, detailed further below, enables us to harness the analytical power of integrating data-gathering methods, data types, and data analyses to cross-validate the findings [34]. Data from discussions and games provide in-depth qualitative contextual information for the RDRs (rules); the survey furnishes numerical variables and parameters needed in the future LUCC-ABM.
To arrive at well-defined rules, we first depict the broader mechanisms in which the rules are embedded. We call these decision-making processes (DMPs, aka processes). We define them as explicit constructs that synthesize the overarching information on decision making for forest-agricscape restoration in the study area. These processes (DMPs) are executed through rules (RDRs), which we define as procedures that result in the implementation of specific restoration activities and practices. The rules are, therefore, the drivers of the observed restoration landscape. To provide the context for the processes, we identified four groups of reasons that justify the undertaking of the various forest-agricscape restoration activities and practices: rationales, motives, benefits, and incentives. Restoration rationales are drivers of the rules that stem from logical reasoning (rational thinking). Restoration motives are more implicitly guided by worldviews, beliefs, and emotions. Benefits and incentives constitute rewards from a course of action. Benefits are endogenous (self-directed)-what individuals perceive as rewards that they generate if they undertake a specific restoration activity (e.g., economic, environmental). Incentives are exogenousthese are rewards obtained from outside sources-mainly gains (monetary and non-monetary) obtained from government programs or non-government organizations (NGO).
Separately from the context for the processes, we generated the rules from the data provided by farmers. The rules synthesize the articulated decision-making factors (factors), which we first grouped into categories representing the decision-making goal frames (goal frames). For example, Problem Solving constitutes a goal frame that reflects rational thinking to address perceived environmental problems with actions (cognitively imagined) that are adequate to meet the specified goal. To provide the context for the processes, we identified four groups of reasons that justify the undertaking of the various forest-agricscape restoration activities and practices: rationales, motives, benefits, and incentives. Restoration rationales are drivers of the rules that stem from logical reasoning (rational thinking). Restoration motives are more implicitly guided by worldviews, beliefs, and emotions. Benefits and incentives constitute rewards from a course of action. Benefits are endogenous (self-directed)-what individuals perceive as rewards that they generate if they undertake a specific restoration activity (e.g., economic, environmental). Incentives are exogenous-these are rewards obtained from outside sources-mainly gains (monetary and non-monetary) obtained from government programs or non-government organizations (NGO).
Separately from the context for the processes, we generated the rules from the data provided by farmers. The rules synthesize the articulated decision-making factors (factors), which we first grouped into categories representing the decision-making goal frames (goal frames). For example, Problem Solving constitutes a goal frame that reflects rational thinking to address perceived environmental problems with actions (cognitively imagined) that are adequate to meet the specified goal.
In this section, we have introduced our conceptual approach, unavoidably including many abbreviations for the constructs. In the consecutive sections, however, we use the alternative-simpler names provided in italics in the parentheses.

Study Area
We selected one research site in Ntchisi and one in Dedza districts in Malawi's Central Region. The sites are forest-agricscapes defined by a forest reserve (Ntchisi Forest Reserve (NFR, 9720 ha) for Ntchisi district and Mua-Livulezi Forest Reserve (MLFR, 12,147 ha) for Dedza district); the adjacent community woodlots, including formally designated village forest areas (VFAs); and the adjacent agricultural lands on customary lands. On a jurisdictional level, we cover three traditional authority areas (TAs) in Ntchisi and two TAs in Dedza ( Figure 2). The current environmental condition and potential future trajectory of each site is different, as are the underlying socio-political, cultural, and economic factors [35,36]. Both districts are part of ongoing national restoration efforts.
Sustainability 2020, 12, x FOR PEER REVIEW 6 of 35 In this section, we have introduced our conceptual approach, unavoidably including many abbreviations for the constructs. In the consecutive sections, however, we use the alternativesimpler names provided in italics in the parentheses.

Study Area
We selected one research site in Ntchisi and one in Dedza districts in Malawi's Central Region. The sites are forest-agricscapes defined by a forest reserve (Ntchisi Forest Reserve (NFR, 9720 ha) for Ntchisi district and Mua-Livulezi Forest Reserve (MLFR, 12,147 ha) for Dedza district); the adjacent community woodlots, including formally designated village forest areas (VFAs); and the adjacent agricultural lands on customary lands. On a jurisdictional level, we cover three traditional authority areas (TAs) in Ntchisi and two TAs in Dedza ( Figure 2). The current environmental condition and potential future trajectory of each site is different, as are the underlying socio-political, cultural, and economic factors [35,36]. Both districts are part of ongoing national restoration efforts.

Data Collection
We conducted seven discussions of 15-20 participants to capture the rules underlying engagement in forest-agricscape restoration. We sought four discussions per district, two with representatives of collective resource-management groups and two with representatives of farmers engaged in restoration at farm-household level in separate venues. However, in Ntchisi district one of the discussions combined the two types of representatives (hence, seven discussions in total), with

Data Collection
We conducted seven discussions of 15-20 participants to capture the rules underlying engagement in forest-agricscape restoration. We sought four discussions per district, two with representatives of collective resource-management groups and two with representatives of farmers engaged in restoration at farm-household level in separate venues. However, in Ntchisi district one of the discussions combined the two types of representatives (hence, seven discussions in total), with distinguished Sustainability 2020, 12, 5380 7 of 33 questions for individual and collective restoration. We selected the participants purposely with the help of local extension agent.
During the discussions, we used open-ended questions to gain insights into the general context for the development of the rules for both individual and collective restoration activities. Specifically, we sought farmers' perceptions of environmental restoration, the (frequency of the) restoration practices and activities they use, and the reasons underlying the restoration behaviors. Since these narratives are more reflective than actionable, we also introduced games [37,38] where the participants were actively engaged in realistic restoration action-situations to express their behaviors. Through games, we could observe and gain insights on the "whys" and the "hows" behind farmers' decisions to embark on individual and collective restoration activities under real-world circumstances. After listing their factors on colored cards, farmers ordered them by level of importance on flip charts. Sub-groups of 5-6 farmers then simulated their rules using the colored cards for ten minutes, separate from the others. The simulated rules were then subjected to plenary discussions where all the participants commented and discussed similarities or differences ( Figure 3). Finally, farmers were asked if they would change the rules in case of extreme weather events such as floods and droughts, or when government policies (affecting environmental degradation) change.
Sustainability 2020, 12, 5380 7 of 35 During the discussions, we used open-ended questions to gain insights into the general context for the development of the rules for both individual and collective restoration activities. Specifically, we sought farmers' perceptions of environmental restoration, the (frequency of the) restoration practices and activities they use, and the reasons underlying the restoration behaviors. Since these narratives are more reflective than actionable, we also introduced games [37,38] where the participants were actively engaged in realistic restoration action-situations to express their behaviors. Through games, we could observe and gain insights on the "whys" and the "hows" behind farmers' decisions to embark on individual and collective restoration activities under real-world circumstances. After listing their factors on colored cards, farmers ordered them by level of importance on flip charts. Sub-groups of 5-6 farmers then simulated their rules using the colored cards for ten minutes, separate from the others. The simulated rules were then subjected to plenary discussions where all the participants commented and discussed similarities or differences ( Figure  3). Finally, farmers were asked if they would change the rules in case of extreme weather events such as floods and droughts, or when government policies (affecting environmental degradation) change. Finally, we conducted a survey of 480 participants using a questionnaire entered into the Qualtrics software and administered in offline mode through tablets [39]. Data collected included farmers' sociodemographic characteristics, engagement (or not) in restoration and associated practices, as well as underlying rationales, motives, benefits, and incentives. We also gathered farmers' self-identified mental rules for engaging in individual-level restoration practices and for considering participation in collective action restoration activities.

Data Analysis
Our holistic analytical approach consists of complementing and cross validating the qualitative information from the discussions and games with the survey data. First, using Nvivo 12 pro, we code the text data to reveal themes related to local understandings of restoration; practices and activities; the rationales, motives, benefits, and incentives for restoration; and the restoration rules.
Second, using Stata 15, we describe the respondents' socio-demographics as reported in Appendix Table A1. We also perform descriptive analyses of variables representing the diverse restoration rationales, motives, benefits, and incentives. We compare them by gender, education level, and geographic location (i.e., TAs covered in the study) to show any statistically significant patterns. For this, we use non-parametric statistical tests of group-mean comparison including Student's t-tests or one-way ANOVAs, where relevant. For the one-way ANOVA, we check for not only independence and normality, but also for variance homogeneity to guide appropriate post hoc multiple comparison tests. Specifically, we refer to the Scheffe test when the assumption of variance Finally, we conducted a survey of 480 participants using a questionnaire entered into the Qualtrics software and administered in offline mode through tablets [39]. Data collected included farmers' sociodemographic characteristics, engagement (or not) in restoration and associated practices, as well as underlying rationales, motives, benefits, and incentives. We also gathered farmers' self-identified mental rules for engaging in individual-level restoration practices and for considering participation in collective action restoration activities.

Data Analysis
Our holistic analytical approach consists of complementing and cross validating the qualitative information from the discussions and games with the survey data. First, using Nvivo 12 pro, we code the text data to reveal themes related to local understandings of restoration; practices and activities; the rationales, motives, benefits, and incentives for restoration; and the restoration rules.
Second, using Stata 15, we describe the respondents' socio-demographics as reported in Appendix A Table A1. We also perform descriptive analyses of variables representing the diverse restoration rationales, motives, benefits, and incentives. We compare them by gender, education level, and geographic location (i.e., TAs covered in the study) to show any statistically significant patterns. For this, we use non-parametric statistical tests of group-mean comparison including Student's t-tests or one-way ANOVAs, where relevant. For the one-way ANOVA, we check for not only independence and normality, but also for variance homogeneity to guide appropriate post hoc multiple comparison tests. Specifically, we refer to the Scheffe test when the assumption of variance homogeneity is met following Bartlett's test, and the Games and Howell test when the assumption is not met, to show differences among groups being compared.
Third, we combine the qualitative insights with the survey data to enhance our analyses of the restoration factors and rules at two levels. On one hand, we categorize the factors into goal frames. We start with the goal frames generated from the discussions and account for any new goal frames included in the survey. On the other hand, we link the rules drawn from the games (Figure 4 and Table 1) to the ones captured through the survey and estimate their occurrence. We note that most farmers in the survey emulated only one main mental rule for each restoration approach, although they were given three possibilities. We thus consider their main mental rules for eliciting the potential rules from the survey.
Sustainability 2020, 12, 5380 8 of 35 homogeneity is met following Bartlett's test, and the Games and Howell test when the assumption is not met, to show differences among groups being compared. Third, we combine the qualitative insights with the survey data to enhance our analyses of the restoration factors and rules at two levels. On one hand, we categorize the factors into goal frames. We start with the goal frames generated from the discussions and account for any new goal frames included in the survey. On the other hand, we link the rules drawn from the games ( Figure 4 and Table 1) to the ones captured through the survey and estimate their occurrence. We note that most farmers in the survey emulated only one main mental rule for each restoration approach, although they were given three possibilities. We thus consider their main mental rules for eliciting the potential rules from the survey.   The rules simulated during the games showcase various combinations of 3-4 goal frames on average. Similarly, the individual mental rules from the survey are based on 2-4 goal frames on average ( Table 2).   Training, e.g., Knowledge in Tree Management Factor = decision-making factors, the initial (raw) factors that respondents use in articulating their restoration decision-making rules. (Extracted from Figure 4 above).
The rules simulated during the games showcase various combinations of 3-4 goal frames on average. Similarly, the individual mental rules from the survey are based on 2-4 goal frames on average ( Table 2). Overall, the crossed insights from the games and the survey suggest that the absence or presence of the goal frames creates distinctive rules. Therefore, in accounting for all possible rules from both types of data, we create variables consisting of 2-4 goal frames for which we fix, alternatively, the most recurrent goal frames.

Forest-Agricscape Restoration and Restoration Activities and Practices
We uncovered five different ways local farmers understand restoration of degraded forestagricscapes, including the activities and the practices they implement (Table 3). An important observation was the connections farmers made with afforestation/reforestation, soil, and water conservation, and addressing land degradation and soil fertility decline to illustrate complementarity of restoration activities for soil, water, and forest resources.

Local References to Resources Restoration Examples of Narratives a
Planting More Trees to Attract Reliable Rains "Planting more trees to attract reliable rains, and where we have cut trees, we are supposed to replace them by planting some more trees. Trees also help in preventing our buildings from heavy wind by acting as wind breaks." Using Agroforestry Systems, Including Intercropping to Restore Soil Fertility "For us agroforestry people, restoration is using fertilizer trees to conserve and improve soil fertility. Not using inorganic fertilizer that degrades soil fertility further." [ . . . ] In the past, our parents were cultivating with no fertilizer, but they were harvesting higher yields and we want to turn our soils back to that state." "Planting trees helps to ensure we are receiving reliable rains that help crops that we grow on improved soils to grow well. Some other trees act as both fertilizer trees and when they grow, they act as forests, for instance, Gliricidia."

Biodiversity Recovery
"Making sure that wildlife like birds, hares, and grasshoppers are back into the environment by planting trees. There were more wildlife animals in the past because there were more trees."

Forest Management and Protection Through Beekeeping
"Restoration is about protection of forests by keeping bees and doing all bee keeping activities; for instance, killing pests and applying oil. [ . . . ] Beehives in both village forests and forest reserves help to protect trees because people are afraid of bees." Managing Natural Regeneration " . . . after cutting down trees by making fire breaks and pruning; where there are natural regenerants, we make sure we manage." a Excerpts from all focus group discussions (FGDs).
Restoration practices were both vegetation-based and non-vegetation-based. For the former, mostly implemented for afforestation/reforestation and soil-fertility improvement, farmers cited: planting vetiver grass; practicing agroforestry with fertilizer trees; planting indigenous trees in bare areas and along rivers/stream banks; managing natural regeneration (pruning); and developing woodlots. For non-vegetation-based activities, often implemented for soil and water resource conservation on farms and forest-resource management, farmers listed: making contour, marker, and box ridges; constructing swales and water-check dams; applying manure; practicing mulching and doing no or minimum tillage as part of conservation agriculture; using intercropping and crop rotation; making fire breaks; and keeping beehives.
Furthermore, the types of collective action groups that engage in restoration endeavors ranged from tree-nursery management groups, forest-reserves management groups, village forests management groups, land and water resources conservation groups, to irrigation groups, beekeeping groups, and cookstove-making groups. Forest-related collective actions were part of the formally recognized Village Natural Resources Management Committees (VNRMCs), and the other collective actions made up what is commonly referred to as Community-based Natural Resources Management Committees and resource users' groups. Activities implemented in collective actions are illustrated below.
"We do swales making, conservation agriculture with mulching and minimum tillage, tree planting and management, vetiver planting, construction of check dams, making and applying of manure. For example, in manure making, we conduct trainings to encourage people to make and use manure. In tree management, we make tree nurseries, prepare land for tree planting; we do actual planting of trees, making firebreaks to prevent trees from uncontrolled fire." (FGD, Bwanali Community, Kachindamoto, Dedza) "As VNRMC, we do a lot of things to protect and manage trees through encouraging community members to have individual forests and protect the trees as we were trained by PERFORM [a forest project]. We also make sure that people are collecting firewood sustainably as trained by PEFORM. We also do patrols to check whosoever is illegally harvesting trees. We also use firewood-saving cookstoves as a way of reducing firewood that we use to cook." (FGD, Ntchisi) These activities epitomize and exemplify the nexuses in the restoration and management of lands, water, trees, and forests.

Farmers' Restoration Rationales, Motives, Benefits, and Incentives in Central Malawi
Farmers evoked several reasons justifying why they undertake restoration activities and practices. These provided a contextual understanding of the complex factors involved in their restoration decision making.

Farmers' Restoration Rationales and Motives
Farmers' rationales for restoration at the individual level included concerns for environmental degradation and its adverse impacts on people's lives, severe soil erosion, wind-induced destruction in treeless landscapes, changing climate, and declining soil fertility that reduces crop yields. Therefore, the aspirations and actions prescribed by logical reasoning to address those issues included keeping trees to reduce land erosion/degradation caused by runoff, improving soil fertility to harvest higher yields by using adequate fertility-enhancement farming methods, and growing trees that also served as windbreaks to protect houses and prevent other property destruction. Some farmers from both Ntchisi and Dedza (Kapenuka and Bwanali communities) illustrated these logics: "before starting restoration activities, I was experiencing heavy soil erosion but after planting vetiver grass, soil from my field has stopped eroding"; "before I started conservation agriculture, I was harvesting little"; and "with increased population growth and inadequate farmlands, this has made us to change to new farming methods that improve soil fertility, and we are restoring soil fertility to maximize yields [ . . . ] I practice crop rotation to maximize yields." Further illustrations of restoration rationales include: "we have realized that climate has changed, for instance we are receiving unreliable rains [ . . . ]".
At the collective level, objective arguments boiled down to the need to protect the environment, maintain reliable rains, conserve trees for the next generation given growing tree scarcity, sustainably use forest resources by reducing demand on forest products along with using efficient cookstoves that demand less firewood, and conserving soil and water resources that are being degraded. In terms of forest resources, farmers referred to both state-owned and community forests. The following excerpts are illustrative.
"People have interest in tree planting both individually and collectively because of scarcity of firewood and to maintain reliable rains that come when the forest is intact. We also want to conserve trees for our generation. With the pace [at which] trees are being cut down, our children will not have the chance to know some tree species, for example 'Mbawa' [Pterocarpus angolensis]." (FGD, Kapenuka Community, Kamenyagwaza, Dedza) "We get involved in community work because we have similar objectives of protecting and restoring the environment that is being degraded. We have the same purpose of forest protection [because] trees provide fresh air and can host our beehives, and people do not cut trees where there is beehive as they are afraid of bees." (FGD, Kabulika Community, Kachindamoto, Dedza) Restoration motives included influences from peers, encouragement and incitation from local authorities, and sensitization from NGOs, projects, and project funders. In both districts and across the discussions, some individuals affirmed these restoration motives in language such as: "I was also influenced by my friend who is in the scheme. I admired her harvesting more yields and she had food all the year"; and "forest officers in coordination with local leaders [Traditional Authorities and Group Village Headmen] urge us to plant trees and conserve soil." Concerning sensitization, one farmer's views from Ntchisi were representative: "People have been sensitized by NGOs on importance of restoring the environment. They tell us to conserve soil by making contour lines." The narratives were similar for collective-level restoration motives among farmers from the Kabulika community, emphasizing awareness raising by external actors: "we receive many motivations from NGOs; EU gave us beehives first before World Vision came also with beehives", observed one. Another farmer from Kapenuka voiced the widespread reliance on extension workers, along with NGOs: "we are encouraged by extension workers to work in collective action and we are also motivated by projects that require people to work in groups." We observed that the line setting apart restoration rationales and motives is not always crisp-these two underlying reasons are often interrelated. For instance, farmers from Bwanali community in Dedza explained during a discussion that "we were experiencing floods but after being trained to dig water check dams, we are able to control runoff that causes erosion also. Water is also conserved and controlled through swales and contour ridges."

Importance and Variability of Restoration Rationales and Motives by Gender, Education, and Location
The survey data reinforced the qualitative findings and revealed such interchangeability between restoration rationales and motives. On average, farmers considered 2 ± 0.9 rationales and ≈2 ± 0.9 motives. Specifically, the two most important restoration rationales were the acuteness of observed land degradation (soil erosion and formation of gullies) and low soil fertility (perceived as driving low crop yields), as mentioned by 91% and 73% of responding farmers, respectively. Other less important rationales were the difficult provision of biomass energy due to scarce firewood and scarce trees to produce charcoal (22%), and the awareness of and sensitivity to biodiversity loss (21%). The most critical restoration motives were project-based motivations, either through incentives from NGOs or government programs (52%), or through the demonstrated leadership, encouragement, and support of local authorities-the Traditional Authority-for their community (43%). Influences from either peers and friends or the media (37%), and altruistic behaviors or environmental civism in the context of scarce resources (35%) were next in importance. Specific rationales that were interchangeably considered as motives (mostly in Nthondo and Vuso Jere TAs) included severe soil erosion and land degradation, low yields, deforestation, and rainfall scarcity.
When compared by gender, education levels, and locations (Appendix A Table A2), gender did not show any statistically significant difference in terms of average numbers of rationales or motives applied. On average, both men and women consistently considered two rationales and motives each ( Figure 5, panel A). Their rationales and motives for engaging with restoration activities are like the ones described above, with similar relative importance levels ( Figure 6, panel A). Likewise, there was no statistically significant difference in the average numbers of restoration rationales and motives among the education levels attained ( Figure 5, panel B). The typical motives and rationales described above are also applicable across the different education levels ( Figure 6, panel B).
( Figure 5, panel A). Their rationales and motives for engaging with restoration activities are like the ones described above, with similar relative importance levels ( Figure 6, panel A). Likewise, there was no statistically significant difference in the average numbers of restoration rationales and motives among the education levels attained ( Figure 5, panel B). The typical motives and rationales described above are also applicable across the different education levels ( Figure 6, panel B).    In contrast, for the locations there are some statistically significant differences (p = 0.0106) for the average number of restoration motives, but not for the average number of restoration rationales advanced ( Figure 5, panel C). That the restoration motives are different across the locations is vital to underscore, and such differences lie at two levels as suggested by the post hoc comparison tests. First, across all the five TAs, farmers in Vuso Jere consider fewer motives (<2) than their peers from the other four TAs (≥2), and this is strongly apparent when compared with TA Nthondo. The second difference centers on how some motives varied in importance from one location to another (Appendix A Table A2). One prominent example is the "leadership, encouragement, and support of local authority (M3)" when compared between TA Nthondo in Ntchisi District and TAs Kachindamoto and Kamenyagwaza in Dedza District ( Figure 6, panel C). During the discussions in Ntchisi, farmers from Nthondo emphasized how their traditional authority encourages them and holds strong and respected leadership for addressing environmental degradation.

Farmers' Restoration Benefits and Incentives
Discussion participants underscored several restoration benefits and incentives. Benefits were mainly economic (honey produced and sold from beehives put in trees, timbers, selling of crops yield surplus), environmental (moisture and nutrient added to the soil, fresh air and temperature regulation, good and reliable rains), and altruistic (care for future generation and natural trees). Other benefits are food-related (fruits from trees, high crops yield), non-economic and utility-oriented (poles for constructions, coffins, firewood for cooking, and medicinal plants), and socio-cultural (sharing of tree seedlings, access to free firewood during funerals). Illustrative perspectives include: " . . . trees are used as poles for construction and are used for domestic activities such as firewood for cooking, and this reduces pressure on state-owned forest reserves." (FGD, Bwanali Community, Kachindamoto, Dedza) "Through conservation-agriculture practices, higher yields are harvested since mulching conserves moisture and adds nutrients to the soil." (FGD, Kapenuka Community, Kamenyagwaza, Dedza) "Forest and trees regulate temperature; it feels cold in hot season and it feels fresh always. I have a water point that runs from my forest. We receive reliable rains because we have more trees. [Also,] trees improve soil fertility in our fields and conserve moisture. We get manure from the tree leaves. If we plant trees, vetiver, and make contour ridges we make our lands fertile. [ . . . ] Trees act as wind break and our houses are protected from severe winds. In the end, the benefits of trees are what motivate us." (FGD, Ntchisi) Farmers participating in collective-level restoration in Kabulika community noted economic benefits and explained that "we also sell poles from the forest and we do this in collaboration with the chief. This is about our village forest which has both exotic and natural trees; people also get timber from the forest at agreed fees, poles are also harvested at a fee." In reference to social benefits, some illustrated that "we collect firewood from the forest when there is a funeral; for instance, there was a funeral in our village and women came to ask me as chairperson of the tree nursery management committee if they can go into the forest to collect firewood [and] I told the chief and we granted them permission to go and collect firewood." Another farmer added they also "share tree seedlings that [they] plant on [their] farms and house compounds, and people are motivated." In Ntchisi, farmers bundled restoration benefits that motivate them, as one illustrates: "We do receive good rains because our forest is intact and that is one reason that motivates us.
[Also], we get firewood for cooking. Other people who do not have trees in their areas use clothes and sacks for heating and cooking.
[Moreover], we are motivated by a lot of water that our mountain and forest conserve and we use the water for irrigation." (FGD, Ntchisi) Incentives and rewards in the areas varied. For individual-level restoration, many farmers indicated being recipients of both in-kind and money-based incentives from NGOs and government-led programs. One explained: "at first, people were receiving food and materials such as soybean flower, cooking oil and beans, tree seeds, hoes, and such, and after some time United Purpose started giving us money." Adding to that, another farmer noted: "MASAF was also giving us money, MK7200 [≈$9.52] for two weeks; then payment rose from MK7200 [≈$9.52] to MK21600 [≈$28.57]." Many considered the training they received on restoration matters and the perception of restoration practices as non-labor intensive, as forms of incentives. "We received training in beekeeping, and we are making money out of bee farming. Discovery project trained us in cookstoves making; we have also been trained in briquettes making and we are making money from those activities. We received training in bamboo planting although not enough. We received training from World Vision, EU, CADECOM in environment management and restoration. For example, CADECOM trained us in local tree seedlings production and we can produce own seedlings locally." (FGD, Kabulika Community, Kachindamoto, Dedza) Beside these testimonials, farmers argued why training is a critical incentive, as one farmer wrapped it up: "For us to do our work properly we need to be trained and when we are trained, we can easily pass knowledge to all the people in the community. Training is very important for a common approach and strategy to restoration activities. We can all have one common idea of the technology and there cannot be confusion. Local knowledge is not universal; some people know things differently from other people." (FGD, Bwanali Community, Kachindamoto, Dedza) Restoration incentives are not always required by farmers, and some indicated that their ongoing restoration efforts precede the renewed momentum in forest-agricscape restoration.
" . . . some of us started doing restoration activities in 2015 and 2016 when there were no projects [while] others started a long time ago when there was a project by ICRAF. Now people are used to these restoration activities and we are doing these without being paid or expecting to be paid." (FGD, Bwanali Community, Kachindamoto, Dedza) In contrast, the lack of incentives is associated with complaints. A farmer participating in collective action restoration in Ntchisi expressed long-standing resentment at such lack of incentives: "We do lots of work to conserve the forest and people come to see it because we are managing it perfectly. Unfortunately, communities are not benefiting. For instance, we do not have potable water in our community yet our forest conserves water. People from Blantyre, Mzuzu, and all over the country and even abroad come here to see this place just because the forest is well-conserved and managed, but the communities are not benefiting anything apart from good rains we receive. [ . . . ] We work in dangerous environments with no protective gear, yet we do not receive anything." (FGD, Ntchisi) Hence, many farmers made a case for incentives. They also suggested operational resources and materials as well as training and exchange visits for restoration activities as incentives. For instance, during the discussion in Kapenuka in Dedza, one farmer elaborated that "we don't receive incentives, but we would prefer being given operational resources"; another that "there has to be incentives such as fertilizer." In Ntchisi, a farmer was also specific: "incentives we need are soft loans with very low interest [and] energy-saving stoves that reduce pressure on forest resources." Other forms of suggested incentives include money as allowance for collective action tasks, such as patrolling, or in the form of recurrent salary, an important element for restoration sustainability.
"With the amount of work that we do, we are supposed to receive something in the form of money. I want to remove some perception that organizations have . . . they think on our behalf and they think we cannot conserve or manage forests if they give us money. [ . . . ] The money should be in the form of allowance and not salary. Whenever you go to patrol or do forest management activities, you should get an allowance, which is MK900 [≈$1.19] according to the government's rate." (FGD, Ntchisi) Here also, benefits and incentives for both individual farmer and collective action are intertwined and folded into the restoration motives. For instance, one farmer from the discussion in Kapenuka in Dedza advanced that "we are also motivated by the high yields we are harvesting from fields where we are practicing soil-conservation technologies. For instance, where we apply manure and use fertilizer trees, we harvest more." Some farmers from the discussions in Bwanali and Ntchisi also stressed that "benefits we realize from restoration activities are already incentives on their own [ . . . ] for example, food, firewood and water supply [ . . . ] and also the activities such as money from sales of trees and from yield surplus." An unusual perspective was underscored as follows, citing group learning and labor pooling: "working in a group is incentive already because we learn from the group and implement on our farms; for instance, planting trees and making contour ridges. It is also less laborious when working in a group [because] it reduces time and labor demand as we share responsibilities and knowledge in a group. We can easily make manure and apply on our farms."

Importance and Differences in Restoration Benefits and Incentives by Gender, Education, and Location
While substantiating the qualitative findings, the survey data depict the relative importance farmers attribute to restoration benefits and incentives. On average, farmers considered 3 ± 1 benefits and ≈1 ± 1 incentive. Specifically, crop yield improvement (96%), sustainable supply of biomass energy (firewood provision and charcoal production) (69%), positive environmental effects of reforestation (66%), and adaptation strategies to climate change impacts (59%) are the most critical benefits cited. Sustainable provision of non-timber forest products (NTFPs) was mentioned less (11%). When asked what incentives they received, "no incentives" was the most reported response (54%) by farmers, confirming the limited existence of restoration incentives in the area. The two most important incentives mentioned were knowledge and information support from extension services such as training on sustainable land management practices and supply of information on restoration matters (36%), and free or subsidized inputs such as tree seedlings and agricultural fertilizers (25%). Incentive schemes such as cash for work and credit/loan provision were less cited (6%).
The mean number of restoration benefits was significantly different (p = 0.0001) between men and women, but restoration incentives were not (Appendix A Table A3). On average, male farmers reported enjoying more benefits (>3) than female farmers (<3) (Figure 7, panel A).
Among the typical benefits described above, men perceived very strongly the positive environmental effects of reforestation and were more likely to report sustainable firewood provision and charcoal production than women. Men also referred to the sustainable provision of NTFPs as part of restoration benefits, which women barely pointed to (Figure 8, panel A). Likewise, the average number of restoration benefits was statistically different (p = 0.0003) by location, but restoration incentives were not (Figure 7, panel C). Farmers from TA Nthondo reported fewer benefits from restoration (=2) than farmers from the other TAs, who reported more (≥3). Restoration as a coping strategy for climate change and as contributing to a sustainable supply of biomass energy was not emphasized in the TAs of Ntchisi as it was in the TAs of Dedza (Figure 8, panel C). In contrast, no statistically significant difference is observed for the number of restoration benefits and incentives across education levels (Figure 7, panel B). Both types of benefits and incentives are similar across the different education levels (Figure 8, panel B). Among the typical benefits described above, men perceived very strongly the positive environmental effects of reforestation and were more likely to report sustainable firewood provision and charcoal production than women. Men also referred to the sustainable provision of NTFPs as

Farmers' Restoration Decision-Making Processes
We followed two steps to develop the overarching restoration decision-making processes in a table/matrix format. These include the depiction and description of the goal frames, and the identification and characterization of the different rules.

Restoration Decision-Making Goal Frames
We identified a total of 17 goal frames representing different categories of the registered factors (Table 4). We first identified 10 goal frames from the discussions. Further, we drew 15 goal frames from the survey that included eight of the previous goal frames uncovered from the qualitative data, thus adding seven new goal frames to the list. Together, the 17 goal frames indicate a mixture of the restoration rationales, motives, benefits, and incentives described above, to which new elements, indicating factors reflecting concerns and constrains, are added. We report their respective incidences in individual and collective-level restoration.

Restoration Decision-Making Rules
We draw out 21 distinctive rules for individual-level restoration and 19 rules for collective-level restoration. All but two rules from the discussions match those from the survey. The rules reflect how the goal frames are ordered. The highly occurring rules are displayed in Table 5 (full list in Tables A4  and A5).
Following their root goal frames, the rules that influence farmers' restoration behaviors are: problem-solving oriented, resources/materials-constrained, benefits-driven, incentive-driven, peers/ leaders-influenced, knowledge-dependent, altruistic-oriented, rules/norms-constrained, economic capacity-dependent, awareness-dependent, and risk averse-oriented. The main root goal frames for rules at the individual level were problem solving, resource/material constraints, incentives, knowledge, and benefits. When considering rules in collective actions, leadership of local authority, problem solving, benefits, and incentives stood out as highly critical root goal frames, followed by resource/material constraints.

Leadership of Local Authority OR Rules of Collective/Community Work-Resource/Material
Constraints-Economic Capacity La_Ru_McEc 8.3% a Bold denotes related goal frames as base/root for the rules; Italic denotes the related secondary goal frames, which are either absent or present in the rules, alternatively; b Number of times the rules emerged (whether with the goal frames in same order or not) expressed as % of the survey sample; * Seven respondents, among the 443 who claimed to restore land at the individual level, did not provide any factors and rules; # Two respondents, among the 268 who claimed to restore land at the collective level, did not provide any factors and rules.

Restoration Decision-Making Processes
We construct the processes as a matrix table linking each rule with the vegetation-based and/or non-vegetation-based restoration practices/activities (Tables 6 and 7; see details of their occurrences in  Appendix A Tables A6 and A7). On average, the total number of restoration practices farmers applied is 3-4 (mean 3.59) and 4-5 (mean 4.53) for individual-level and collective-level restoration, respectively. Many restoration practices/activities are common across the rules.
At the individual farm-household level, common vegetation-based restoration activities include agroforestry, farmer-managed natural regeneration (FMNR), and vetiver grass (Chrysopogon zizanioides) planting. Farmers aligned with rules #8 implement vegetation-based restoration to a lower extent. Those applying rules #12 and #18 implemented only one practice, FMNR and vetiver grass planting, respectively. Farmers associated with rules #11, #13, #20, and #21 engage with only two of the vegetation-based practices. Most recurrent non-vegetation-based restoration activities are manure application, mulching, and construction of contours ridges. For farmers following rules #8, #18, and #20 mulching comes first ahead of manure application, in contrast to the common trend. Secondary implemented practices include intercropping, swales making, markers/box ridges construction, and minimum or no tillage. Farmers utilizing rules #12, #16, and #19 strongly engage with intercropping, and a fair number of farmers following rules #11 and #18 construct swales. At the collective-action level, vegetation-based restoration activities center on tree planting and natural regeneration in forest areas. All types of rules greatly reflect those restoration activities, except rule #13 which leads to less engagement in such activities. Farmers following rule #19 plant trees also for riverbank protection. The non-vegetation-based restoration activities most encountered are activities involving firebreaks in communally held forest areas, awareness against tree cutting and deforestation in the community, and other forest protection activities such as patrolling and monitoring. Construction of swales is observed to a lower extent on communal lands. Additionally, farmers following rule #19 are involved in gully reclamation.  Vegetation-Based Restoration Activities Non-Vegetation-Based Restoration Activities

Local Perspectives on Landscape Restoration
Our findings on the local farmers' perspectives on landscape restoration reflect concerns over both adverse ecological and socioeconomic/livelihood conditions that need concurrent improvement. This dual consideration shapes the practices and activities used for restoration. These findings align with the perspective of the contemporary restoration movement, especially codified in the forest landscape restoration (FLR) paradigm being promoted widely in SSA, including Malawi. Indeed, the new wave of restoration has departed from pure eco-centric perspectives, as seen with ecological restoration, to accommodate more social dimensions, especially with regard to socio-economic well-being to which ecosystem services are a major contributor [40]. As reflected in the commonly used definition of FLR (a planned process aimed at regaining ecological integrity and functions to enhance human well-being in deforested or degraded forest landscapes, [41]), emphasis is put on social, economic, and ecological goals and outcomes.
Moreover, in a previous review, Djenontin et al. [6] pointed to considerations of local contextual factors and aspirations in defining the objectives and goals of such landscape-scale restoration as well as in choosing and promoting technological packages. In that regard, our findings can inform efforts to operationalize FLR goals and practices in mosaic forest-agricscapes, without obscuring the embedded socio-cultural context, to achieve more meaningful and sustainable outcomes. Puspitaloka et al. [42] recently attempted such contextual operationalization by rearticulating restoration in peatland ecosystems in Indonesia, following an empirical assessment of the definitions, goals, and practices of peatland restoration across four restoration interventions in Central Kalimantan.

Landscape Restoration Rationales, Motives, Benefits, and Incentives
Our study reveals that while the boundary between restoration rationales and motives remains fuzzy, their nature differs. The former follows the line of logical/causal reasoning while the latter follows affective/emotional action. The distinction is worth making as it has implications on the proper specification of behavioral paradigms and subsequent parameterizations of decision rules in modeling restoration behaviors, as we discuss below. Moreover, our findings provide justification for treating benefits and incentives as extensions of restoration motives. Benefits and incentives were regarded as personal advantages and gains, and they considerably shape restoration behaviors at individual farm-household and collective-action levels. This study confirms, empirically, the need to consider them in restoration programs and policies as observed with benefits/incentives-based interventions in enhancing restoration behaviors.
Furthermore, the motives and benefits vary significantly by location and gender. Notably, having strong leadership from local authorities who support and encourage their community members through self-engagement and exemplary actions has emerged as an integral motivational element. Ntchisi district, exemplified by TA Nthondo, holds that advantage over Dedza district. This finding confirms previous evidence of the importance of strong, engaged, and inspiring leadership in collectively addressing environmental degradation [43,44]. Further, while there were many types of perceived or actual benefits from restoring forest-agricscapes, the gender and locational differences regarding environmental and energy supply-related benefits are important to note in planning restoration interventions. Specifically, this finding can inform the design of restoration programs as to what place-specific and gender-inclusive motives to leverage, and benefits to enhance or promote.

Landscape Restoration Decision Making and Behavior
Our findings indicate that restoration rules show various combinations of goal frames, the most important ones making up the roots for the rules. This nature of rules confirms that environmental behaviors are the result of multiple goal frames with some dominating ones. This means that one or more goal frames shift to become focal goal(s) over the others in the process of cognitively constructing the decision-making rules. This corroborates the postulate of the GFT [14,15].
Furthermore, insights on the defining constituents of the goal frames themselves indicate that incentives, benefits, and knowledge could be assimilated with the gain and hedonic goal framings, following [14]. These factors also compare with some of the factors influencing land-use and environmental-management decision making, notably the consideration of economic and non-economic benefits [11]. In our study areas, incentives and benefits were primarily not expressed in monetary terms, but more as in-kind (both soft, like training incentives, and concrete, like crop yields, poles, and other tree-resource benefits), a departure from the widespread over-reliance on cash incentives in collective conservation or restoration policies and strategies (see [44]).
However, problem solving, resource constraints, and leadership of local authorities stand out as contextual types of goal frames associated with restoration behaviors. From the perspective of the GFT [14], these elements do not reflect nor qualify as normative, gain, or hedonic goal framings. Rather, they refer to environmental concerns, capability, and political impulsion. The latter is of interest as the leadership of local authorities greatly influences collective action restoration decisions. These findings underscore the need to ground understanding of restoration behaviors within their local contexts.

Representation of Restoration Decision Rules in a LUCC-ABM
We have developed a conceptual approach to depict restoration decision-making processes based on our effort to empirically depict farmers' decision-making rules and the corresponding vegetation-based and non-vegetation-based restoration practices and activities in Central Malawi. This effort is similar to Keshavarz and Karami's [45] effort to identify farmers' decision making and actions for drought management in Iran. It can serve as an input into future ABM-based restoration modeling aimed at simulating farmers' restoration behaviors, underlying decisions, and the spatially explicit socio-ecological outcomes at a higher (aggregate) forest-agricscape scale in Central Malawi. This approach can also be replicated elsewhere for similar studies attempting to ground social actors' decision rules in empirical data.
Significantly, we have uncovered that farmers incorporate both rationally grounded and motive-based goal frames in their critical decision making on using different restoration practices or getting involved in collective action restoration activities. This implies that when exploring landscape restoration using an ABM with a focus on farmers' restoration decision rules, one cannot solely espouse a rational behavior paradigm. Rather, one should also consider the role of motivational factors, including benefits and incentives. Groeneveld et al. [11] argued that the importance of such non-rational factors influencing land-use and environmental management decisions had significantly been overlooked in LUCC-ABMs, whereas they are appropriately emphasized in behavioral economics. In this regard, our findings support the adoption of a bounded rational behavior paradigm in such future modeling of restoration behaviors.
In addition, we encourage adopting a process-based decision-making model to represent human decision making and circumvent the difficulties of applying theories following previous studies [26,46]. Insights suggest that blending ideas of experience/preference-based decision models with empirical/ heuristic decision rules [26] would be an appropriate decision framework for exploring the future impact of landscape restoration in Central Malawi. Thus, our empirically grounded restoration-decision rules and processes are relevant to inform the parameterization of decision rules and representation of restoration actions for such an ABM. The occurrence of the rules could inform their respective probability distribution in the ABM and the restoration practices and activities would inform the actual actions taken by the farmer-agents.
Finally, methodologically, this study contributes to testing or putting into practice relevant recommendations on data gathering methods and processes to improve the representation of human decision making in empirical ABMs and enhance their analytical and policy value [11,18,[23][24][25]47]. Adopting mixed social science data collection methods, including semi-structured interviews through discussions and games, and a structured interview via surveys, appears useful. They can enhance understanding of the decision making underlying farmers' behaviors to characterize decision rules for further modeling processes.

Conclusions
This study sought to analyze the nature of the decisions to engage in forest-agricscape restoration through individual and collective actions in Central Malawi using a mixed-method approach to data collection and analysis. The study uncovers local farmers' perceptions of forest-agricscape restoration, and the nature of the influential factors considered when deciding to engage in restoration efforts. Furthermore, it reveals how these factors generate diverse goal frames determining restoration decision making, and ultimately the observed restoration practices and activities. Specifically, the study finds that the decision-making rules leading to restoration behaviors appear to be very diverse. They are made of goal frames that reflect nuanced considerations of environmental problems, livelihood needs and gains, constraints, socio-political influences, morals, values, and attitude to risks; all featured in diverse combinations. These restoration goal frames are categorized as problem-solving oriented, resources/materials-constrained, benefits-oriented, incentive-based, peers/leaders-influenced, knowledge/skill-dependent, altruistic-oriented, rules/norms-constrained, economic capacity-dependent, awareness-dependent, and risk averse-oriented. Improved understanding of the goal frames underscoring restoration decision-making rules is critical to inform potential management and policy mechanisms to boost restoration delivery. Finally, the study contributes a conceptual approach, with methodological application, to elicit restoration decision-making processes that associate various decision rules with the vegetation-based and non-vegetation-based restoration practices and activities undertaken by farmers. This will contribute to empirically ground the design and parameterization of farmers' restoration behaviors in an ABM that will explore effective governance modalities and spatially explicit policy options to boost landscape restoration in Malawi. Beyond that, this approach can be replicated elsewhere for similar studies attempting to ground social actors' decision rules in empirical data.

Acknowledgments:
We are grateful to the Department of Geography, Environment, and Spatial Sciences of MSU for its various institutional support. The first author thanks particularly all members of her research team in Malawi for their invaluable support in collecting the data for this research in the framework of her PhD dissertation.


Sovereign CDS Market: The Role of Dealer in Credit Events

A credit default swap (CDS) is a credit derivative that can be used as insurance against a reference entity’s credit risk, where a reference entity is either a government or corporation that has issued debt. It is formally a bilateral contract between a protection seller and protection buyer. The former is taking a short position in the CDS, while the latter is taking a long position. The protection seller compensates the protection buyer if there is a credit event with respect to any of the bonds issued by the contract’s reference entity. Credit events include bankruptcy, failure to pay, and restructuring, among other items. In exchange, the protection buyer makes periodic interest payments to the protection seller until the contract expires. As a result of their role in the 2008 financial crisis and in the sovereign debt crises in Europe, credit default swaps are among the most controversial derivative instruments. In both corporate and sovereign contexts, proponents of CDS attest to their beneficial effects in providing and transferring liquidity risk during times of distress. Critics view CDS as speculative bets, especially since CDS holders may hold more CDS than bonds with respect to the reference entity. That is, if a party owns equal amounts of bonds and CDS for a particular reference entity, then the party is completely insured against a negative credit event. In this way, a CDS works pretty much like an insurance policy on a car, house, or any other asset. However, unlike insurance, it is possible to own more CDS protection than the underlying bonds. As a result, CDS contracts make it possible to trade on

A credit default swap (CDS) is a credit derivative that can be used as insurance against a reference entity's credit risk, where a reference entity is either a government or corporation that has issued debt. It is formally a bilateral contract between a protection seller and protection buyer. The former is taking a short position in the CDS, while the latter is taking a long position. The protection seller compensates the protection buyer if there is a credit event with respect to any of the bonds issued by the contract's reference entity. Credit events include bankruptcy, failure to pay, and restructuring, among other items. In exchange, the protection buyer makes periodic interest payments to the protection seller until the contract expires.
As a result of their role in the 2008 …nancial crisis and in the sovereign debt crises in Europe, credit default swaps are among the most controversial derivative instruments. In both corporate and sovereign contexts, proponents of CDS attest to their bene…cial e¤ects in providing and transferring liquidity risk during times of distress.
Critics view CDS as speculative bets, especially since CDS holders may hold more CDS than bonds with respect to the reference entity. That is, if a party owns equal amounts of bonds and CDS for a particular reference entity, then the party is completely insured against a negative credit event. In this way, a CDS works pretty much like an insurance policy on a car, house, or any other asset. However, unlike insurance, it is possible to own more CDS protection than the underlying bonds. As a result, CDS contracts make it possible to trade on The views expressed in this article are those of the authors and do not necessarily represent those of the Federal Reserve Bank of Richmond or the Federal Reserve System. a reference entity's credit risk without having any exposure to the underlying credit, which can be interpreted as a bet on the deterioration of the reference entity's ability to repay its creditors.
In the sovereign CDS market, the reference entity is a country; as a result, increases in default risk could have signi…cant economic impact and ethical considerations. Since CDS markets tend to be more liquid and larger than the corresponding bond market, some academics and members of the media have argued that speculative bets from large traders can arti…cially drive the price of a CDS contract up. In turn, market participants observe the risk of the underlying bonds to be higher than it actually is, increasing the cost of borrowing for the distressed countries. Thus, this increases the chances of default arti…cially. In this scenario, buying CDS is functionally equivalent to short selling the bonds. Short selling bonds is nearly impossible due to the lack of liquidity in bond markets; as a result, the presence of a CDS contract allows the sovereign bond's pessimists and optimists to enter the market, increasing price stability of the underlying bond.
Previous literature has examined the role of sovereign credit default swaps and speci…cally the ban of "naked" CDS in the European Union. In Du¢ e et al. (1999), research has also been conducted on the endogenous liquidity risk of CDS. However, in the context of distressed countries, the dealer-provided liquidity that this paper introduces is a new area of study. Using our regulatory data from the Depository Trust and Clearing Corporation (DTCC), we are able to see the CDS position of market participants over time.
This paper uses a case study approach to suggest that the critics' conclusion that sovereign CDS markets drive the cost of capital up for countries may be incorrect, or at least the pressure from short positions on CDS does not seem to be coming from large dealers. To better understand the net e¤ects of sovereign CDS markets, we examine the CDS positions of major CDS dealers as risk changes. 1 Speci…cally, we use Venezuela, Ukraine, and Argentina as case studies. These three countries have experienced credit events and therefore CDS payouts since 2008.
We observe that the large CDS traders in each market, de…ned as the top ten traders of each country's CDS, tend to sell (buy) CDS as risk increases (decreases). This is the opposite direction of change one would expect if the large dealers were taking speculative bets. We leave a formal model of this mechanism to a later paper, but the basic logic of how we tie these changes in positions to market liquidity is as follows.
Large and risk-neutral dealers can take CDS positions that may result in a large loss with a nonnegligible probability so long as they perceive the position, combined with the dealer fee, to have a positive expected value. Smaller and risk-averse institutions that may not be able to sustain a large loss, rush to buy protection from the large risk-neutral dealers.
In this way, dealers provide endogenous liquidity in distressed times by market making. This may imply that sovereign CDS trading by CDS dealers can lower endogenous liquidity risk and potentially lower bond spreads during unstable …nancial periods relative to what they would have been had the sovereign CDS market not existed.

RELATED LITERATURE
Many analysts and regulators blamed the severe and widespread nature of the 2008 …nancial crisis on CDS, contending that CDS exacerbated the housing asset bubble They speci…cally argued that major …nancial institutions were using CDS for speculation and manipulation with global consequences. These criticisms of CDS were extended during the European sovereign debt crisis beginning in 2009 (Augustin et al., 2014). Sovereign CDS are insurance contracts issued against a country's public bonds. This new wave of criticism on sovereign CDS centered on the sovereign CDS market's role in price discovery and monitoring, spillover liquidity in the underlying sovereign bond markets, and hence, adjustments in borrowing costs for the country in times of distress.
Studies following the Great Recession and European sovereign debt crisis have produced mixed results on the practical uses and risks of CDS markets. We …rst discuss the structure of sovereign CDS markets and their theoretical role in bond markets. Then, we discuss the capacity of general (corporate and sovereign) CDS in contagion risk, the potential for spillover e¤ects, and price discovery/monitoring. Finally, and most relevant to this paper, we will discuss the potential for sovereign CDS to provide liquidity in their associated sovereign bond markets and what that means for a country's borrowing costs.
As insurance, CDS markets perform two basic functions. First, they allow …nancial institutions to hedge their credit risk, thereby freeing up regulatory capital to further lend. Second, they let …nancial institutions take more liquid short positions on bonds (Czech, 2019). The …rst function is of primary importance to this paper. Theoretically, by purchasing CDS contracts as hedges, …nancial institutions are potentially able to lend more capital, increasing liquidity in underlying bond markets and lowering equilibrium borrowing costs for the bond issuer in question.
However, concerns regarding the practical uses of CDS in the wake of the …nancial crises have marred their reputation. The …rst concern of CDS use is its contagion potential and spillover e¤ects into global markets. In Longsta¤ et al. (2011), the authors observe that global information shocks result in sovereign CDS spreads increasing or decreasing together. If one CDS market responds to new information, this comovement e¤ect can introduce contagion risk to other CDS markets. However, a subsequent study by Caporin et al. (2013) …nds that spillover e¤ects of reactions to large CDS spread changes in one CDS market are largely regionally contained, not global in nature. When it comes speci…cally to spillover liquidity risk, Bai et al. (2012) also did not …nd a change in the country's fundamentals.
However, having an insurance market can also provide a useful vehicle for price discovery for the underlying entity. For instance, Augustin et al. (2014) found di¤erences in CDS spreads to be useful in predicting options pricing and exchange rates up to one week in advance. A trader has a naked CDS position if it has a larger position in the CDS than the underlying bonds. Du¢ e (2010) …nds that the use of naked CDS trading data is also bene…cial to the underlying asset information and therefore increases the e¢ ciency of the bond market. This information e¢ ciency was later supported by Coudert and Gex (2013), who recognized that the derivative market provided better information than the bond market because of higher participation in CDS markets during recessionary periods. In times of distress, bond traders are likely to run from the bond market, while CDS traders stay in the market and provide pricing information.
In addition to price discovery, CDS have also been found to provide valuable information for price monitoring. Ismailescu and Phillips (2011) found CDS to be e¢ cient monitoring tools that increase the overall informational and pricing e¢ ciency in the market of the underlying entity. This can also propagate greater market participation. Portes (2012) also found CDS to be accurate, although not perfect, in pricing credit risk in the long run. However, this same relationship does not hold in the short run.
Most relevant to this paper, the presence of a CDS market on the liquidity of the associated bond market is currently being debated. Historically, a valuable instance in which the use or disuse of CDS impacted liquidity in bond markets is the European Central Bank's (ECB) gradual ban of naked CDS. A market participant owns a naked CDS if she owns more CDS than bonds in a given reference entity. It has been described by Portes (2012) as taking out life insurance on someone else's life. While this paper does not di¤erentiate between naked and nonnaked CDS trades, studying bans of general CDS can provide useful literature on CDS's role in capital markets. In the wake of the European sovereign debt crisis, the ECB temporarily banned the trade of naked CDS in 2010. The ECB later permanently banned naked CDS trading in 2011. A study by Sambalaibat (2013) found that the temporary ban increased liquidity in underlying sovereign bond markets, citing a temporary migration of CDS traders to the bond market. However, the same study found that the permanent ban of naked CDS decreased liquidity in the underlying sovereign bond markets.
This paper focuses on countries that have experienced severe defaultrisk episodes. When countries are low on cash, speculation in a CDS market, according to Che and Sethi (2011), can divert much-needed capital away from potential borrowers. The resulting rise in CDS premiums sends information to potential lenders to increase the cost of funding to the government. The government, which is unlikely to a¤ord the higher interest, will become more cash-strapped and only increases long bets in its CDS market: a self-ful…lling prophecy.
But, other literature suggests that the use of CDS can lower the probability of default. Goderis and Wagner (2011) argue that the use of nonnaked CDS can reduce risk for ex-ante default. The authors cite the existence and ownership of insurance policies on sovereign debt as an incentive for the insurance holder to reject any restructuring o¤er made by the government. Similarly, Salomao (2017) has a similar …nding: in distress, the existence of insurance contracts can increase the lender's borrowing power, which incentivizes the borrower to default less often. The author also argues that the existence of insurance contracts can raise debt levels and lower borrowing costs in equilibrium.
The liquidity bene…ts and risks of CDS have only been studied in the case of the ECB's ban of naked CDS and in theory. We try to contribute to the discussion of CDS as liquidity-providers in underlying bond markets, by analyzing how dealers trade sovereign CDS in both stable and risky time periods, to better understand how the sovereign CDS market can a¤ect liquidity in the underlying sovereign bond market. We …nd that in times of distress, big CDS dealers act as market-makers by taking shorter (longer) CDS positions as risk increases (decreases). These …ndings suggest that large dealers provide liquidity to the underlying bond market.

HISTORICAL BACKGROUND OF SOVEREIGN CREDIT EVENTS
Prior to describing the trading patterns, we review the historical and economic events that a¤ect the risk of the three countries we use as case studies: Argentina, Ukraine, and Venezuela. All three countries have defaulted on their debt in recent years; however, the reasons and economic conditions di¤er.

Ukraine
From 2001 to 2008, Ukraine experienced moderate economic growth that coincided with a global economic boom. A longstanding relationship with the former Soviet Union allowed Ukraine to import oil from Russia at approximately half the price per barrel that Western European suppliers were charging in order to power its mineral and natural resources industries, which comprise most of Ukraine's economic output. This dependency on foreign oil amounted to approximately 70 percent of its total oil usage by the mid-2000s. During this time, the Ukrainian economy averaged 7.4 percent annualized growth and large capital in ‡ows from foreign investors. However, Ukrainian economic woes began in 2006 when cheap access to Russian oil began to diminish, limiting domestic production and exports. This period of supply instability was exacerbated by the 2008 …nancial crisis, in which the International Monetary Fund (IMF) gave two stand-by disbursements that greatly helped Ukraine weather the crisis. However, increasingly unstable debt loads reached 91.5 percent of the Ukrainian GDP in 2009, and that proved critical in the coming default.
In 2013, new Russian trade restrictions and an inability to increase industrial production led to foreign investors rating default probabilities at approximately 50 percent in the swap market. Moody's Investor Service in 2013 also gave Ukraine's credit a rating of Caa1, which limited foreign investment and economic growth. Ensuing political instability, with the ousting of sitting President Viktor Yanukovych in 2014 and the annexation of Crimea by Russia, coincided with a 6.8 percent and 10.4 percent decline in GDP in 2014 and 2015, respectively. Ukraine also experienced a currency crisis in February 2014 when the government began using the hryvnia as a ‡oating currency, which caused a 70 percent depreciation against the U.S. dollar.
In December 2015, Ukraine missed interest payments on a $3 billion loan to Russia, which the International Swaps and Derivatives Association (ISDA) determined was a credit event. The IMF then o¤ered a $17.5 billion, four-year loan program in 2016 that helped stabilize the hemorrhaging economy. With a positive global economic output, a small recovery in oil prices, stronger worker productivity, and a government corruption reform program, Ukraine has experienced positive economic growth since 2016.

Venezuela
Despite having the largest proven oil reserves in the world and being the sixth largest member of the Organization of Petroleum Exporting Countries (OPEC), the Venezuelan economy has undergone signi…cant stresses in the past two decades. Petroleum accounts for approximately 95 percent of Venezuela's total exports, and its economic growth largely depends on oil prices.
The Venezuelan economy experienced signi…cant in ‡ation in the late 1990s, peaking near 100 percent in 1996. In ‡ation after the election of Hugo Chavez calmed to approximately 35 percent from 1996-2001. Further political and social unrest after the ascension of Chavez in 1998 have only exacerbated Venezuela's economic crisis. For instance, the 2002 attempted coup and the 2002-03 labor strike returned economic growth to pre-Chavez levels. The economic decline continued into the late 2000s, with a chronic housing shortage, further unsustainable in ‡ation, political unrest, and high poverty rate. In 2009, the IMF categorized the Venezuelan recovery as "weak and delayed,"especially in relation to the relative economic growth of other South American countries and its largest trading partner, the United States.
Tremors of Venezuelan economic stress occurred in early 2014 with a global depression in crude oil prices. Although Venezuela has the world's largest proven oil reserves, its economy's heavy reliance on petroleum exports makes its economic growth and prosperity largely dependent on oil prices. Preceding the mid-2014 oil glut, 96 percent of Venezuela's …scal revenue originated from oil production. An international oil glut formed after a production boost in the North American shale oil industry, lesser demand from China, and a lack of OPEC policy uniformity. At its peak, the global economy was outputting over two million barrels of oil per day. The price per barrel of Venezuelan oil fell from over $100 in 2012 to approximately $30 in 2015. As a result, Venezuela ended almost half a decade of steady economic growth with a 5 percent decline in GDP in the …rst quarter of 2014. The National Assembly of Venezuela reported in ‡ation to be approximately 4,000 percent in 2017. On December 30, 2017, ISDA declared a credit event after the Venezuelan government missed two interest payments amounting to a combined $200 million. Since the selective default, Venezuela has defaulted on eighteen other sovereign bonds. The Argentinian economy has struggled with stag ‡ation, hyperin- ‡ation, capital ‡ight, and corruption beginning with a military dictatorship that started in 1976. After a brief period of rapid economic growth under a democratic government and Minister of Economy Domingo Cavallo's anti-in ‡ation campaign, Argentina experienced another recession beginning in 1998. Regional economic crises in Brazil and commodities pricing shocks contributed to slow growth, high unemployment, and de ‡ation. The 2001 Argentinian default was framed by massive political riots in December 2001 and a struggling export economy. Consequently, the Argentinian government defaulted on $83 billion in debt after which 93 percent of investors agreed to the restructuring terms, which involved a 70 percent haircut on repayment.
Although the 2014 default was preceded by relative economic growth between 2002 and 2013, the export-dominated Argentinian economy struggled again with a sluggish world economy. Further, a unilateral devaluation of currency, as evidenced with a 1,300 percent increase in M3 money supply since 2002, has also contributed to the world's third highest in ‡ation rate in 2014 at an o¢ cial rate of approximately 10 percent. However, news sources speculate the actual in ‡ation rate more realistically hovers at 25 percent.
In this context, the remaining 7 percent of investors who did not accept the restructuring agreement in 2001 demanded to be repaid in full. Following the 2001 default, the Argentinian government declared all debt repayments to be pari passu, that is, repaid with no preference to investors. The remaining 7 percent of investors then sued in the U.S. Supreme Court, which upheld lower court rulings in Republic of Argentina v. NML Capital Ltd. that Argentina's foreign assets were not immune from discovery, which resulted in the obligation to pay all debts in full, valued at approximately $132 billion. As a result, the Argentinian government declared it would "imminently be in default" on July 30, 2014, after missing a $529 million interest payment. Standard and Poor's then declared Argentina to be in selective default in the autumn of 2014.

DATA
We obtained the dealer CDS positions using the DTCC. The Dodd-Frank Wall Street Reform and Consumer Protection Act requires realtime reporting of all swap contracts to a registered swap data repository (SDR). The DTCC operates a registered SDR on CDS. The Dodd-Frank Act also requires SDRs to make all reported data available to appropriate prudential regulators. (See Sections 727 and 728 of the Dodd-Frank Act.) As a prudential regulator, members of the Federal Reserve System have access to the transactions and positions involving individual parties, counterparties, or reference entities that are regulated by the Federal Reserve. Using the DTCC data, we recover a time series of the average CDS positions of the top ten dealers in three di¤erent countries from 2013 through 2017.
To get a measure of risk, we use both bond yields and CDS spreads. To obtain bond prices, a list of deliverable obligations from the CDS auction was obtained from the Credit Derivatives Determinations Committee for each country. These bonds were listed with a maturity date, coupon value, and CUSIP/ISIN number. Bloomberg was used to obtain historical bond prices from January 4, 2010, to February 22, 2019. Speci…cally, two sets of bond price measurements were obtained. First, the yield to maturity time series was gathered. Second, a yield to benchmark measurement was gathered, which values a bond against an internal Bloomberg benchmark. We chose to construct our own price index because the price of the deliverable bonds is the most relevant. Some outstanding sovereign bonds are included in available price indices by JPMorgan and Bloomberg, but are not deliverable in auction. Nonetheless, using these indices does not change this paper's results. Additionally, the initial issue amount was recorded for each bond.
We also collected CDS spreads from Bloomberg for each of the three countries. The correlation between CDS spreads and yields is near 1. Since Ukraine does not have bond data for most of the sample, we use the CDS spread data. Nonetheless, the results are robust to usage of either yield measures in the countries in which the yield data exists.
To create the bond indices for each country, a weighted average of the deliverable bond prices for each country was used. 2 Each date has varying numbers of bonds outstanding as the country retires and issues debt over time. As a result, the individual bond issue amount as a fraction of the total issue amount for the number of bonds available for a certain date was used to weight and standardize the bond prices. This was multiplied by the bond price, in yield-to-maturity and yield-tobenchmark, to obtain a price index of the overall deliverable obligation bond market in Argentina, Ukraine, and Venezuela. Note that a price index was not needed for CDS spreads since a CDS o¤ers protection for all deliverable bonds.

FINDINGS
In this section, we highlight how each of the three countries'…nancial crises illustrate how dealers provide liquidity during …nancial crises by selling protection. In general, we found that dealers take the opposite position of the market in times of distress, functioning as marketmakers. Speci…cally, as risk increased in a country's underlying bond market, dealers decreased their CDS positions. We de…ne big dealers as the ten largest volume traders of the speci…c CDS over our sample period. Our results are robust to using the …ve biggest dealers (another common measure). We use the CDS spread as our measure of risk, where an increasing CDS spread indicates greater risk. Our results are the same if we use bond yield. Furthermore, we often refer to long and short positions. If the big dealers have a short (long) position, they are net sellers (buyers) of CDS. We time detrended the position and CDS data. Without detrending, our results may have been skewed because the CDS market has been shrinking over the time periods considered due to changes in the regulatory landscape. However, the general …ndings from this section are robust to using the raw data without detrending it.

Ukraine
In Ukraine, the dealer positions and CDS spread show a very clear inverse relationship. From the beginning of the sample period to March 2015, risk increased as the dealer position decreased. From March 2015 to the end of the sample period, risk decreased and the dealer position rose. The latter scenario will not be seen as commonly later in the paper.
First, from January 2013 to March 2015, the CDS spread increased by 4500 basis points as Ukraine faced hyperin ‡ation and con ‡ict with Russia. During the same period, the net CDS position of big CDS dealers decreased from a $75 million long position to a $150 million short position.
Second, following the disbursement deal with the IMF, reduced tensions with Russia, and an increasingly positive economic outlook in 2015, the period from March 2015 to March 2018 shows a 4,000 basis point decrease in CDS spreads, a dramatic reduction in the country's risk. During the same period, the net CDS position of big CDS dealers increased by $230 million.
The correlation between the CDS spread and the dealer position is -0.783. The strong negative correlation is expected based on the strong inverse relationship over the entire sample period.

Venezuela
In Venezuela, the time period from the beginning of 2017 to mid-2018 strongly supports our hypothesis that big dealers reduce their position in CDS as risk increases. This time period includes Venezuela's …rst selective default in late November 2017. This selective default also caused global worries that debt repayments by the Venezuelan government would not hold. ISDA determined that a credit event took place after a missed interest payment. As a result, ratings agencies declared Venezuela to be in selective default. Venezuelan President Nicolás Maduro declared that all sovereign debts must be "re…nanced or restructured."The initial increase in bond spread beginning in June of 2017 re ‡ected a global worry that Venezuela would be imminently defaulting on its debt payments. Investors and media outlets almost unanimously anticipated this selective default would be the …rst of more than twenty defaults tha have occurred since 2017. Beginning in June 2017, the indexed Venezuelan bond spread increased almost 100 basis points.
The right side (post January 1, 2017) of Figure 2 depicts the dealer position and CDS spread over the time period in question. Once news of the selective default and its subsequent risks was evident, the CDS spread increased signi…cantly to over 6,000 basis points. As the CDS spread gradually increased in mid-2017 but prior to the sharp increase in spread, the dealers sold $400 million of CDS in just a few months, switching from a net long to a net short position. This is the opposite response expected from speculators. The Venezuela example not only demonstrates how dealers sell CDS as risk increases, but also that the action can occur prior to signi…cantly rising spreads. One possible scenario to explain this is the following. Small risk-averse …rms became concerned about the possibility of a Venezuelan default a few months prior to the default becoming extremely imminent and rushed to buy protection from the dealers. Regardless of the exact reasons, the shorting of CDS as risk increases is suggestive that dealers are providing liquidity to the market and not speculating.
While the post-2017 period is most indicative of dealers selling (buying) CDS as risk increases (decreases), the correlation between CDS and dealer position is -0.153 across the whole sample period. However, prior to 2017, there is only a slightly negative correlation. Nonetheless, this suggests that dealers taking the opposite position of speculative bettors is also true during more moderate periods of increased risk.

Argentina
For Argentina, we focus on the CDS spreads and position after July 2016, following the U.S. Supreme Court ruling in Republic of Argentina v. NML Holdings Ltd.. From 2013 to mid-2016, the Argentinian swap market was frozen from trading as the case was pending litigation. The court ruled that Argentina had the obligation to pay back all debts in full related to their earlier default, valued at approximately $132 billion.
In the period from June 2016 to December 2017, (see Figure 3) the CDS spread decreased by approximately 50 basis points. During the same period, the big CDS dealers' average position increased from a net short position of approximately $275 million to a net long position of approximately $300 million. That is, the dealers bought CDS as risk decreased.
The converse relationship is also demonstrated from January 2018 to June 2018 (see Figure 3), when the CDS spread increased by approximately 150 basis points. During the same period, the big CDS dealers' average position decreased by $875 million from a net long position of approximately $275 million to a net short position of more than $600 million.
The correlation between the CDS spread and the average big dealer position yielded a value of -0.697, which shows a strong, negative correlation. This indicates that what we have found in the two episodes discussed previously is also true in the Argentinian sample. That is, as risk increases (decreases), dealers sell (buy) CDS. Figure 4, which is extracted from Chaumont et al. (2020), displays the relationship between average yield and average dealer position aggregated by country from 2013-18. There is a downward trend in Figure  Figure 4 Cross-Country Analysis 4, with a correlation coe¢ cient of -0.2. That is, the average dealer CDS position decreases as a country's average risk increases. This mirrors our conclusions from the three case studies above, where we …nd that the dealer CDS position decreases as risk increases within each country. To the extent that the cross-country relationship is indicative of the intracountry relationship, this is evidence that our conclusion from these case studies generally applies to other countries. Nonetheless, one could be concerned that within each country represented in Figure 4, dealer positions do not decrease as risk increases. Perhaps the inverse relationship only holds when a country is signi…cantly distressed. Chaumont et al. (2020) address these concerns by using more rigorous empirical speci…cations to determine the relationship between risk and dealer position. By controlling for country, dealer, and time-…xed e¤ects, they determine the relationship between risk and dealer position within each country. Nondistressed and distressed countries are also included in the sample; as a result, they are able to determine if the e¤ect found in this paper is only true in distressed countries. In several speci…cations and robustness checks, they …nd that as risk increases (decreases), dealer CDS positions decrease (increase) within