Stochastic-dynamic modelling of farm-level investments under uncertainty
Section snippets
Software availability
The open source model, including a Graphical User Interface that allows straightforward changes to the initial parameters, and all related documentation are available in Spiegel et al. (2017).
State of the art
Analytical solutions for real options valuation (e.g., Black and Scholes, 1973; Geske and Johnson, 1984) are elegant from a scholarly perspective, but are often deemed inappropriate for practical application due to restrictive assumptions required (e.g., regarding stochastic processes). If such is the case, a numerical method must be employed instead (Trigeorgis, 1996; Regan et al., 2015). Cetinkaya and Thiele (2014, p. 12) distinguish between methods that approximate the underlying stochastic
General methodology
The section provides a description of the proposed method. Major equations and assumptions used for our illustrative example can be found in the next section. The method we propose includes four main steps (Fig. 1). First, we define the (state contingent) decision variables of the problem and the related real options, i.e., (multi-stage) investment with a potential positive value of waiting before exercising it. Integers, including binaries, enable differentiation among investment options with
Case study: reallocating land to perennial energy crops
We choose farm-level decisions regarding the adoption, harvest and conversion of perennial crop production in the context of farm constraints and alternative activities. Specifically, we consider investments into short rotation coppice (SRC) poplar production systems under price and opportunity costs uncertainty in Germany; the problem is characterized by limited resources, returns-to-scale, and predefined sizes of available investment options. The main characteristics of the case study are
Empirical results and related discussion
Under the baseline SRC output price scenario (i.e., observing in year one a SRC biomass output price of 50 € t−1), the farmer waits and establishes SRC in the second or third years with a probability of 23%, and in the fourth year – with a probability of 41%, depending on the SRC biomass price development in the respective years (Fig. 4). There is a chance of 13% (= 100% (in year one) − 23% (in year two) − 23% (in year three) − 41% (in year four)) that SRC would never be established, if the SRC
Implications and further research of the proposed method
The here developed methodological approach particularly advances in straightforward conversion of existing programming applications based on the net present value approach into real options framework, as well as in introducing more complex and realistic settings into existing real options models. Below, we comment on the main conversion options (A, B, and C on Fig. 6 and Table 6) for so-called “basic model” that implies investing now or never, considers investment option as standing alone,
Conclusion
This paper proposes a new method which extends the widely applied linear programming approach, for instance used in many bio-economic farm-scale models, to determine simultaneously optimal investment and management decisions and their impacts on environmental impacts. It inherits from the programing approach the possibility to address simultaneously characteristics, such as returns-to-scale, indivisibilities, quasi-fixed resources or multiple competing uses of assets, and adds two new aspects.
Funding
This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.
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2022, Agricultural SystemsCitation Excerpt :Given the empirical evidence that European farmers are typically risk-averse (Iyer et al., 2020), failing to account for uncertainty may disregard an important driver of farmers' decision-making (Castro et al., 2018; Knoke et al., 2011), especially when market risks are thought to be a major barrier to SRC adoption (Hauk et al., 2014b; Spiegel et al., 2020). One avenue of research accounting for risk in economic analyses are studies using a real options approach to evaluate SRC (e.g. Feil and Musshoff, 2018; Finger, 2016; Spiegel et al., 2021, 2020, 2018). These studies account for stochastic variation in market prices for woodchips and gross margins for annual crops, but also for the flexibility that a farmer has to postpone decisions to establish and harvest a SRC system.
Diffusion of organic farming among Dutch pig farmers: An agent-based model
2022, Agricultural SystemsCitation Excerpt :Yet, quantification of the effect usually requires quite strong assumptions on the level of risk aversion, which is rather difficult to estimate. Furthermore, even in the farm-level context, research on dynamic decisions under uncertainty and risk preferences is limited (see, e.g., Spiegel et al., 2020). Hence, including risk preferences in agent-based modelling requires, first of all, further methodological research.
A design for a generic and modular bio-economic farm model
2021, Agricultural SystemsCitation Excerpt :Other elements of decision making can be captured by constraints, such as depicting risk behaviour by a constraint restricting the probability of profits under a critical limit. In dynamic modelling, considering different financing options (equity, different loans) allows one to separate the individual discount rate of the decision maker from the market based one, an option considered in FARMDYN (see also Spiegel et al., 2020). A generic BEFM template should ideally allow flexibility in the choice of objective function (as found in FSSIM and FARMDYN) and switching between a comparative-static and a dynamic setting, and between a deterministic and stochastic one such as in FARMDYN.