Afforestation as a real option with joint production of environmental services
Introduction
Around the world, many governments and non-governmental organisations have been engaged in afforesting agricultural and wasteland or reforesting harvested forest stands. There are many reasons for implementing policies, which promote this land use conversion. A range of socioeconomic benefits are expected from afforestation, for example afforestation may result in higher recreational benefits, reduce erosion and desertification problems, protect groundwater, create a supply of fuel wood and timber and contribute to carbon storing and climate change mitigation. The global investments are significant. More than 14 million hectares are annually afforested and reforested (FAO, 2015). To initiate such investment, decision makers at any level from governments to landowners, need to evaluate whether the afforestation is a financially more attractive investment than other land use alternatives. In particular when the investment is subject to great uncertainty about future costs and benefits, irreversibility in the sense of not being able to fully recover investments, and the benefits may be multiple and jointly produced (Nelson et al., 2009). This study discusses and analyses this problem of deciding for what states of nature to invest in afforestation when the values of ecosystem services from forests are stochastic and jointly produced. We analysed this in the context of real option theory and add to the research field by applying a new framework of additive real options. Our focus is in a sense the reverse of earlier studies, focused on when to intensify land use and halt conservation (e.g. Conrad, 1997; Kassar and Lasserre, 2004), as we here focus on reducing land use intensity, switching land use from agriculture to forest.
Even newly established afforestation areas quickly provide a wide range of ecosystem services such as recreation or increased quality of drinking water production (Vesterdal et al., 2002; Zandersen et al., 2007), and increasing the forest area on a property may increase hunting values (Meilby et al., 2006; Lundhede et al., 2015). Other services from afforestation may only happen in the long term, e.g. reaching a suitable habitat for important biodiversity (Hermy and Verheyen, 2007) or significant returns from timber harvest. In valuing such outputs/services of multifunctional forestry, it is important to account for the joint production of services. The joint production properties may fall into categories of fixed, complementarity, independency, and competitive relationships between the services (Randall, 2002). Ignoring these properties, any attempt to value the services provided by forest reserves may fail and inappropriate information may flow into relevant decision processes. The Sustainable Development Goals and the 2030 agenda highlight sustainable use of terrestrial ecosystems and management of forests. The EU Commission has acceded to major international declarations, recommendations, treaties or conventions of immediate relevance to sustainable forest and nature management, e.g. the EU Forest Action Plan and the Strategy of Lisbon‘s environmental pillar, the Convention on Biological Diversity, and has strongly supported the promotion of forest management through its programmes. The EU and EU member countries annually spend billions of euros on contributing to development of sustainable forest and nature management to halt the decline of biodiversity and promote the provision of ecosystem services (e.g. see the EU Natura 2000). The Millennium Ecosystem Assessment of nature's contributions to human well-being (Braat and de Groot, 2012; Carpenter et al., 2006; Pascual et al., 2017; TEEB, 2010) as well as the climate change debate and discussion on the potential roles of forests have increased the research community interest in several issues. Topics include the role of spatial correlation, spatial connection/dis-connection, and potential joint production of provisional services (e.g. forest and agricultural production, drinking water), regulatory services (e.g. carbon, nutrient cycling, biodiversity) or cultural services (e.g. hunting, recreation) and potential for win-win solutions and spin-offs of conservation and restoration projects (Bateman et al., 2013; Carpenter et al., 2006; Nelson et al., 2009; Venter et al., 2009).
From society's point of view as well as the private land owner's perspective, it is therefore an issue that the value of these possible effects and correlations are not well known. Nor are the quantitative measures of their provision. Consequently, the values associated with afforestation areas are uncertain. The expected value of e.g. future biodiversity may increase as society grows richer (Jacobsen and Hanley, 2009), as may marketed recreational services like hunting (Lundhede et al., 2015; Meilby et al., 2006). The supply of resources may become increasingly scarce (Schroter et al., 2005). On the other hand, the perceived and expected future value of a specific afforestation areas' value may also decline. An example is if e.g. biophysical limits to growth cause demand from non-consumptive benefits to decrease relative to consumptive goods. Or if changes in surrounding land use decrease the quality and value of ecosystem services provided from the afforestation area. At the same time, the afforestation investment may be seen as irreversible. Converting back to agriculture likely implies a larger cost of removing tree stumps and re-establishing the agricultural field, the more time has passed. As time passes the trees grow valuable which reduce net cost of conversion back to agriculture. However, in many instances legislation may prohibit such conversion. Thus, setting aside agricultural land for afforestation may be seen as a decision problem of when to exercise the option of not only one, but the sum of several jointly produced ecosystem services. The value of which is governed by possibly correlated stochastic processes. Here we address this problem applying two additive real options as an example, recreational hunting and forest products.
The use of real option value models and the timing of (dis-)investment decisions have been investigated in resource economics, building on e.g. McDonald and Siegel (1986) and picking up speed with Dixit and Pindyck (1994). Specifically concerning the issues of different option values and preservation, Arrow and Fisher (1974) and Henry (1974) pointed out the (quasi-) option value related to continued preservation (as opposed to development) of a resource when benefits from development are uncertain. As already mentioned, the problem we analysed here is the reverse one of earlier studies focused on when to intensify land use and halt conservation (e.g. Conrad, 1997; Kassar and Lasserre, 2004). Furthermore, the explicit attention to the joint and additive values being produced following afforestation is a novel contribution to the real option analysis in resource economics. The extension to multiple services is highly relevant, but it comes at the expense of the mathematical tractability of analysing the decision problem. We had to resort, as is often the case in such problems, to numerical solution procedures to solve explicitly defined examples.
Section snippets
State of the art
The first real-option related studies within natural resource economics were the seminal papers by Henry (1974) and Arrow and Fisher (1974), which showed in simple two period models, that with uncertain returns to irreversible development, preservation would be optimal over a larger range of expected values of development.
A different strand of work on the valuation of forest resources and exercise timing under uncertainty, which is essentially also real option problems, was developed in e.g.
The model
We developed a general model for the case where a decision maker holds the option to put down a known fixed one-off payment and in turn receive the sum of two present value processes. In the afforestation context, this has relevance. Consider for example the landowner, who faces the problem of continuing with the present agricultural system, assuming it is generating a constant return of F per unit of time to society or has the option to invest I in an afforestation project. The project will
Numerical solution procedure
Based on Malchow-Møller et al. (2004) we assumed that the value function was finite as long as δ > max {μB + μG} (McDonald and Siegel, 1986) and the problem could be solved using a value-function iteration procedure (Judd, 1998). To increase stability and iteration speed, the problem was log-normalised, which implied the variance became independent of the state, thereby standardising the calculation of the joint probability distribution. When presenting the results we converted the estimated
Empirical example of two additive ecosystem services: timber production and recreational hunting
Real options of joint production is a generic topic, and the output of our analyses covered a realistic range of possible relative states of values B and G and costs I. As such they are illustrative of the generic aspects of the decision problem. However, for further illustrative purposes, we also evaluated the question using the case of afforestation of agricultural land with jointly produced ecosystem services. We used time series data from Denmark on timber and recreational hunting to derive
Results
We started by analysing the basic properties of the decision problem and the implications of changing parameter settings on the stopping boundaries. Subsequently we estimated the optimal stopping values of the empirical case.
Concluding discussion
The current study addresses the importance of including investment theory and in particular, the implications of uncertainty of the future value of the ecosystem services when the services may rather be jointly produced than mutually exclusive. In addition, the modelling should acknowledge that a decision maker may hesitate to invest in forest and nature restoration or conservation since such decisions may be irreversible (one example is the European Natura 2000 network of set a side areas,
Acknowledgements
The authors thank the Danish National Research Foundation (grant no. DNRF96) for supporting the research at the Center for Macroecology, Evolution and Climate. The authors also thank two anonymous reviewers for their comments on earlier versions of the manuscript.
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