Regeneration decisions in forestry under climate change related uncertainties and risks: Effects of three different aspects of uncertainty

FORPOL-01184; No of Pages 9 Forest Policy and Economics xxx (2014) xxx–xxx

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Regeneration decisions in forestry under climate change related uncertainties and risks: Effects of three different aspects of uncertainty Erik Schou a,⁎, Bo Jellesmark Thorsen b,c, Jette Bredahl Jacobsen b,c a b c

Department of Geosciences and Natural Resource Management, University of Copenhagen, Rolighedsvej 23, DK-1958 Frederiksberg, Denmark Department of Food and Resource Economics, University of Copenhagen, Rolighedsvej 23, DK-1958 Frederiksberg, Denmark Centre for Macroecology, Evolution and Climate, University of Copenhagen, Rolighedsvej 23, DK-1958 Frederiksberg, Denmark

a r t i c l e

i n f o

Article history: Received 15 June 2012 Received in revised form 29 August 2014 Accepted 4 September 2014 Available online xxxx Keywords: Uncertainty Regeneration Stopping value Subjective probability Risks Climate change

a b s t r a c t Future climate development and its effects on forest ecosystems are not easily predicted or described in terms of standard probability concepts. Nevertheless, forest managers continuously make long-term decisions that will be subject to climate change impacts. The manager's assessment of possible developments and impacts and the related uncertainty will affect the combined decision on timing of final harvest and the choice of species for regeneration. We analyse harvest of a Norway spruce stand with the option to regenerate with Norway spruce or oak. We use simulated variations in biophysical risks to generate a set of alternative outcomes, investigating effects on decision making of three aspects of uncertainty: (i) the perceived time horizon before there will be certainty on outcome, (ii) the spread of impacts across the set of alternative outcomes, and (iii) the subjective probability (belief) assigned to each outcome. Results show that the later a forest manager expects to obtain certainty about climate change or the more skewed their belief distribution, the more will decisions be based on ex ante assessments — suggesting that if forest managers believe that climate change uncertainty will prevail for a longer period of time, they may make sub-optimal decisions ex ante. © 2014 Published by Elsevier B.V.

1. Introduction Large scientific efforts worldwide aim at increasing our understanding of the nature of climate change and its possible impacts. While our knowledge is steadily increasing, the issue remains nevertheless surrounded by significant uncertainty, in particular concerning long run impacts. Uncertainty is not only due to lack of knowledge about cause and effect or measurement errors, but is also due to more complex issues, like the uncertainty on political efforts to reach agreements on greenhouse gas emissions. Climate change may affect absolute and relative production performances of forest tree species, through effects on growth, health, and risk agents. Forest managers are operating under this uncertainty and routinely make decisions reaching far into the future, most prominently when deciding on species for regeneration. Because of the nature of the long term uncertainty surrounding climate change, decisions are likely to be affected not only by scientific knowledge and uncertainty, but also by public debate and information flows. As stressed by Yousefpour et al. (2012), it may be useful to address the issue of uncertainty in terms of the forest manager's belief in particular climate developments, allowing aggregation of both scientific and subjective measures of uncertainty as assessed by the manager. ⁎ Corresponding author. Tel.: +45 35336268; fax: +45 35331508. E-mail address: [email protected] (E. Schou).

Long term effects of possible climate change are a major source of uncertainty for forest management, due to the long production time in forestry. Species must not only be suitable for present, but also for future growth conditions, which in 50 years might be considerably different. Thus, the regeneration decision is important and irreversible, and highly sensitive to climate change. Mixing of species has been proposed as one way to mitigate this uncertainty, providing the forest manager with flexibility on the final choice through selective thinnings as more is learned about climate development (Jacobsen and Thorsen, 2003). However, for silvicultural reasons mixing is not always a feasible strategy, and in this paper we instead address the issue of adaptive decision making in the form of final harvest timing and subsequent species selection in forest regeneration. The purpose of this paper is to investigate how the forest manager's optimal combined decision on harvest timing and choice of species for regeneration is affected by three aspects of climate change uncertainty: 1. At what time the forest manager expects to be certain about the direction and impact of climate change 2. The spread of economic impacts across possible alternative climate change scenarios 3. The weight that the forest manager assigns to each alternative climate change scenario ex ante, i.e. the subjective probability or belief (Yousefpour et al., 2014).

http://dx.doi.org/10.1016/j.forpol.2014.09.006 1389-9341/© 2014 Published by Elsevier B.V.

Please cite this article as: Schou, E., et al., Regeneration decisions in forestry under climate change related uncertainties and risks: Effects of three different aspects of uncertainty, Forest Policy and Economics (2014), http://dx.doi.org/10.1016/j.forpol.2014.09.006

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E. Schou et al. / Forest Policy and Economics xxx (2014) xxx–xxx

We do not explicitly model climate change development and impacts over time. Rather, we rely on existing evidence, debates and prognoses in constructing a limited set of possible scenarios or outcomes of different climate change developments in order to focus on and assess how these features of uncertainty may change presentday decisions with respect to the three abovementioned aspects. To that end we assume that uncertainty about climate change and its impact is resolved at a specific point in time, using a small model with a limited set of time periods. This allows us to identify and separate the effect of the three different aspects of uncertainty from e.g. the form of the forest manager's learning or the many different specific aspects of climate change and impacts that often cloud the results of more complicated simulations (e.g. Yousefpour et al., 2013, 2014). Resolving the uncertainty gradually which is more realistic will make the effects smaller. We discuss the implications in the discussion section. The problem is illustrated using the general case of deciding simultaneously on the final harvest timing and the regeneration species, when maximising expected net present value (NPV) of timber production. We consider two alternative species that are likely to show very different climate change sensitivity, but are still possible alternatives in forest management in the Danish case that serves as our empirical fundament. These are Norway spruce (Picea abies (L.) Karst.) and Pedunculate oak (Quercus robur L.). Norway spruce is expected to suffer from health problems in a warmer climate (Larsen et al., 2011), as well as from more frequent storm damage caused by a possible higher storm frequency. According to the most recent National Forest Inventory in Denmark (Johannsen et al., 2013), Norway spruce covers 16% of the forest area. 52% of the stands are below 40 years of age, i.e. they still have at least 10 years to go before final harvest. Many stands are situated on poor soils, where oak is one of the only alternatives among species not expected to suffer from climate change. We simulated the economic consequences of changes in biophysical risks for Norway spruce and used the simulations to generate a set of illustrative alternative climate dependent outcomes for a new spruce stand — relative to a fixed performance of oak. The decision problem was thus an optimal stopping problem with fully exclusive alternatives (Malchow-Møller et al., 2004). In the decision model, the forest manager expects that within a finite number of periods, information that reveals the actual climate development will emerge. The expected NPV, conditional on each climate scenario, is known, and the manager holds a set of subjective ex ante beliefs about the likelihood of each scenario materialising, relative to the other scenarios. The expected NPV is maximised based on these subjective probabilities and hence risk neutrality is assumed. Results included the standard findings from the real option literature that the larger the spread of outcomes, the larger is the value of waiting and the bigger the impact on decisions, i.e. it becomes optimal for a larger set of states to postpone final harvest and species choice. We find that the further into the future the forest manager perceives uncertainty to be resolved, the more decisions are based on ex ante assessments and the less willing the forest manager will be to wait for ex post evidence. Finally, we show that the more skewed the forest manager's belief is towards a particular scenario, the more weight is put on ex ante assessments and the less likely the postponement of decisions becomes, essentially because the belief reflects a much lower degree of (subjective) uncertainty about future outcomes. The rest of the paper is organised as follows: In Section 2, we briefly relate our approach to the relevant part of the literature on climate change and decision making under uncertainty. In Section 3, we outline the background of our case and the material on which, we rely for simulating possible scenarios for Norway spruce. We use this in Section 4, where the model framework is set up including the simulation parameters. Results of simulations are presented in Section 5 and discussed in Section 6. We briefly conclude the study in Section 7 with some perspectives on the results from a research as well as a practical forest management point of view.

1.1. Decision making in forestry, uncertainty and climate change Reviews of decision making under climate change (Yousefpour et al., 2012), of the modelling of natural hazards in forest management (Hanewinkel et al., 2010) and of real option studies in forestry (Hildebrandt and Knoke, 2011) present a comprehensive overview of the literature on decision making under uncertainty. We do not repeat this but focus on some of the similarities and differences between our study and the studies most closely related to it. This study builds on the real option literature (Dixit and Pindyck, 1994; MacDonald and Siegel, 1986) and adds to the literature on optimal decision making under uncertainty, when forthcoming information on future states of the world may imply a real option. In forestry such studies have focused on, e.g. the use of reservation prices to handle price variation over time (Brazee and Mendelsohn, 1988), which as shown by Plantinga (1998) is a variant of the optimal stopping and real option problems addressed by McDonald and Siegel (1986). Numerous studies have addressed various real option issues in forest management, from general investment scaling and timing issues (Conrad, 1997; Insley, 2002; Thorsen, 1999a; Tee et al., 2014) to other issues of harvest timing (Malchow-Møller et al., 2004; Thorsen, 1999b). Among them we also find studies which in terms of model framework are even closer related to ours. These include Jacobsen (2007) on the regeneration decision and Jacobsen and Thorsen (2003) on the advantages of mixed species stands under climate development uncertainty. All these real option type studies, however, share the common feature of having uncertainty specified and modelled quite specifically in the form of a stochastic process, which continues to vary and evolve over time, with parameters known to the decision maker. While this may be appropriate for some types of uncertainty, e.g. on price development, it is less so for the long perspective climate development that may be better understood as uncertainty about which new dynamic climate variation pattern will be emerging (Jacobsen et al., 2010). Furthermore, by nature, it is also less feasible to rely on past experience in assessing the likelihood of alternative future climate developments. Assigning probabilities to climate change scenarios is difficult, as important conditions in classical probability theory are not met, i.e. lack of mutual exclusiveness between outcomes and a possible incomplete state space description. The use of imprecise probabilities as described by Tonn (2005) is seen as a solution to these problems. Dessai et al. (2005) describe the applicability of probability weighted scenarios in adaptation planning, stressing the importance of the decision maker's risk attitude, when investigating the sensitivity of decisions to choice of weights. According to Hall et al. (2007) it is much debated, if the use of probabilities is necessary for dealing with decision making under uncertainty, i.e. that rational decisions imply access to some probability estimates. Whether or not this is the case, it is of interest to analyse the implications if people more or less directly assign probabilities or beliefs to various outcomes — and act accordingly. Even if one rejects the use of probabilities for theoretical reasons when dealing with climate change uncertainty, subjective probabilities or perceptions of uncertainty might still to some extent explain behaviour. Thus, we follow Yousefpour et al. (2014) in addressing perceived uncertainty in terms of the beliefs, or subjective probabilities of the forest manager. The use of Bayesian updating of beliefs as a way to model and simulate a forest manager's learning on climate change development has recently been investigated in related studies (e.g. Yousefpour et al., 2013, 2014). However, to arrive at mean measures of behaviour and outcomes, the method requires the forward simulation of numerous climate development draws, combined with assumptions on initial beliefs and updating rules. This complicates the quantification of the effects of uncertainty aspects on decisions, and rules out backward induction dynamic programming solutions. The simplifying assumptions made here allow the use of this dynamic programming approach and more precisely identify the effects of the three aspects which are central to this study. Furthermore using the subjective

Please cite this article as: Schou, E., et al., Regeneration decisions in forestry under climate change related uncertainties and risks: Effects of three different aspects of uncertainty, Forest Policy and Economics (2014), http://dx.doi.org/10.1016/j.forpol.2014.09.006

E. Schou et al. / Forest Policy and Economics xxx (2014) xxx–xxx

probabilities (beliefs) of forest managers, it is possible to estimate, e.g. the value of waiting as perceived by them.

1.2. The case: climate change projections and possible impacts on forestry in Denmark Climate change uncertainty pertains both to the degree of change and to the environmental response to these changes. According to Assessment Report 4 (AR4) of the Intergovernmental Panel on Climate Change (IPCC, 2007) we may see a rise in annual global mean surface temperature over the 21st century from 2.3 to 5.3 °C for Northern Europe (48°N, 10°W to 75°N, 40°E). Annual precipitation is stated as “very likely” to increase in much of the area (though in the summer months the range is from − 21 to 16%). For Europe, it is noted that “the substantial natural variability of the European climate is a major uncertainty, particularly for short-term climate projections in the area” (Christensen et al., 2007, page 872). The IPCC SRES (Special Report on Emission Scenarios) deals with emission uncertainty and is widely used for modelling change (e.g. Albert and Schmidt, 2010; Blennow and Olufsson, 2008; Peltola et al., 2010). Scenarios are described as “plausible futures” and no probabilities are assigned to them. While this may be reasonable, it has implications on how to deal with such uncertainty in decision making. Larsen et al. (2011) assess that all the dominating species in Danish forestry will be negatively affected to some degree by climate change. Norway spruce is ranked as “very sensitive”, while oak should be less affected, or even benefit. The effect of climate change on the growth of Norway spruce has been investigated by, e.g. Albert and Schmidt (2010), Andreassen et al. (2006) and Bolte et al. (2010). They all indicate a decrease in the growth of spruce under warmer and dryer conditions. Apart from the uncertainty about climate development the risk of hazards is also considered, including its links to climate change. In

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this, we build on studies of forest management under risk of hazards like windthrow or fire (e.g. Reed, 1984; Thorsen and Helles, 1998). We consider only risk at the stand level and hence do not explicitly address the forest level and possibly spatially inter-related risks (Blennow et al., 2010; Blennow and Olufsson, 2008; Meilby et al., 2001; Reed and Errico, 1986). While the effect on growth patterns could be ambiguous and depend much on regional precipitation changes, another important concern is the impact of changes in biophysical risk. In Denmark as in Europe in general, the primary source of biophysical risk is storm (Schelhaas et al., 2003). Furthermore, insects and fungi are important risk agents (cf. Larsen and Raulund-Rasmussen, 1997). Climate change might increase the risk of damage by increasing the probability of events as well as the susceptibility of trees (Larsen et al., 2011). The influence of climate change on storm risk has been investigated by, e.g. Blennow et al. (2010), Blennow and Olufsson (2008) and Peltola et al. (2010). They all use regional projections combined with local wind models, finding increased likelihood of wind exceeding critical speeds. The influence of climate change on pests is investigated by Seidl et al. (2008) focusing on Ips typographus (L.) that primarily attacks Norway spruce. They estimate an increase in timber damage of over 300%. The beetle is also a source of concern in Denmark (Larsen et al., 2011). I. typographus may benefit from an increase in temperature as stressed by Jönsson et al. (2007). Drought stress will also make Norway spruce more susceptible to attacks (Wermelinger, 2004). In conclusion, the direction of climate change impacts may seem more certain than the levels of impacts. Notably, while most studies find that increases in risk and health problems may reduce Norway spruce performance in many regions, there could be considerable regional variation, e.g. due to local variation in precipitation. Thus, we analyse the sensitivity of the optimal decision to the variation in performance, in casu expected NPV, using illustrative scenarios of changes in growth and biophysical risk including both the possibility of increased and decreased performance of spruce relative to oak.

2. Materials and methods We investigate the decision of when to undertake final harvest of a Norway spruce stand and which species to choose for reforestation. At each decision point the forest manager must choose one of the following alternatives: - Thin the spruce stand (continue) and continue the rotation at least until next decision point - Clear cut (stop) the spruce stand and replant with spruce - Clear cut (stop) the spruce stand and replant with oak. ‘Stopping’ is an irreversible decision and the two species are exclusive options following Malchow-Møller et al. (2004) and as opposed to Jacobsen and Thorsen (2003). The decision is subject to the forest manager's perceptions of climate uncertainty and impacts. Below all possible future scenarios are concentrated into a small illustrative set of three possible climate change outcomes: a negative case, a no change case, and a positive case, as represented by the soil expectation values (SEV) of Norway spruce. For simplicity, oak is assumed to be unaffected by climate change and the forest manager to be risk neutral. Different attitudes to risk could be included, and would affect the results. This is dealt with in the discussion. 2.1. Model 1: climate uncertainty resolved within one period To solve the optimal stopping problem, a simple stochastic dynamic programming value iteration approach was used (cf. Dixit and Pindyck, 1994). The Bellmann equation (Eq. (1)) with one period to go, before uncertainty over climate change is resolved, is:

   
   V t ¼ max H t þ max ðΕt ðSEV i ÞÞ; ht þ α pt Εt V C;tþ1 þ ð1−pt Þ sHtþ1 þ max Εtþ1 ðSEV i Þ i

i

ð1Þ

where Vt is the value function at age t, which is maximised by choosing between harvesting the stand now or waiting. In case of harvest, the value of the stand is the revenue from clear-cutting at age t, Ht, plus the SEV of the species i expected to perform best at time t, SEVi. When waiting, the value is the revenue from thinning, ht, plus the future return from the stand discounted by the factor α. The stand may survive with a probability of pt or die. If it survives the manager receives VC,t + 1 which is the belief weighted expectation value over all climate change outcomes C, when making the optimal decision. If the stand dies, the manager receives the value of a final harvest, Ht + 1, reduced by the salvage factor, s, plus the SEV of the species i expected to perform best at the time of the hazard, t + 1. Please cite this article as: Schou, E., et al., Regeneration decisions in forestry under climate change related uncertainties and risks: Effects of three different aspects of uncertainty, Forest Policy and Economics (2014), http://dx.doi.org/10.1016/j.forpol.2014.09.006

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E. Schou et al. / Forest Policy and Economics xxx (2014) xxx–xxx

Assuming three possible climate development outcomes, we use the vector of normalised weights (Eq. (2)) (subjective probability mass), BC. The (belief weighted) expected VC,t + 1 is defined as: h

i

2

0

0

Εt V C;tþ1 ¼ BC V C;tþ1 ¼ ½ b1

b2

3 V 1;tþ1 b3 4 V 2;tþ1 5 V 3;tþ1

ð2Þ

C

where ∑ bc ¼ 1 and 0 ≤ bc ≤ 1. Thec¼1 decision problem in Eq. (1) is solved using finite time recursive dynamic programming, where climate uncertainty is resolved, as one of the three possible outcomes is realised. In the numerical simulations, the length of a time period was set to 10 years. 2.2. Models 2 and 3: climate uncertainty resolved after two or three periods A crucial question for timing and deciding on adaptive management strategies is assumptions on when the forest manager believes he will know, with certainty, which climate development is realised. In order to investigate this, Model 1 is expanded to models where uncertainty is resolved after two and three periods (Eq. (3)). Thus, Model 2 can be written as:
 ( " #) 39 8 2   > > ptþ1 Εtþ1 V C;tþ2 < = 6 p max Htþ1 þ max Εtþ1 ðSEV i Þ ; htþ1 þ α 7     : V t ¼ max H t þ maxðΕt ðSEV i ÞÞ; ht þ α 4 t 5 þ max Ε ð SEV Þ sH þ 1−p tþ1 tþ2 tþ2 i > >    : ; þð1−pt Þ sHtþ1 þ max Εtþ1 ðSEV i Þ

ð3Þ

Model 3 can be written with a similar extra term describing the forest manager's embedded inter-temporal optimisation. It is assumed that no additional knowledge (or change in weights of BC) will be accumulated in the period between the present time and the time of climate scenario disclosure. Finite time recursive dynamic programming is also used to solve the expanded problem. 2.3. Growth and risk dynamics in the model The analysis is carried out for even-aged stands of Norway spruce (Yield Class 13) up to age 100 years, which is assumed as the maximum rotation age, and rarely exceeded in practice. Growth and thinning is modelled over 10 year intervals, with thinning volume being a fixed proportion (20%) of stand basal area. A dynamical yield table programme, Vidar Version 1.0 (Meilby, 2009) is used to model growth. The models of the programme are based on data from species trials located all over Denmark (Nord-Larsen et al., 2009). We assume that regeneration will follow immediately upon final harvest. Regeneration for Norway spruce is based on planting, as is reforestation with oak in the first rotation followed by natural regeneration in succeeding rotations. Risk is included in the model through a risk of stand destruction, pt. Risk is defined as the probability of a risk agent damaging the stand to a degree where a total salvage harvest will be necessary. For each risk agent, a, (see Eq. (4)) this probability can be dissolved into the probability of an event occurring multiplied by the conditional probability that the stand will be damaged, given that an event occurs: a

a

a

pt ðdamageÞ ¼ pt ðevent Þ  pt ðdamagejevent Þ:

ð4Þ

For the present rotation it is assumed that risk of stand destruction can only arise from windthrow or insect pests. A possible synergy effect between storm damage and insect damage could arise (cf. Göthlin et al., 2000) but such effects are disregarded in this study. We assume insect damages to take place over the summer and storms mainly in the fall (see Eq. (5)). This means that if insect damage should occur in a given year, the stand will be removed before possible storm events could occur. The expression for total annual risk of stand destruction is then: in sect

pt ¼ pt

storm

ðdamageÞ þ pt


 in sect ðdamageÞ 1−pt ðdamageÞ :

ð5Þ

Following Thorsen and Helles (1998) the annual probability of a storm event is set at 8% for Danish conditions (Østergaard, 1988). Conditional probabilities of windthrow are calculated using an empirical model in Lohmander and Helles (1987). Using this model, current annual probabilities of destruction by storm range from 0 to 8% (depending on tree size). Concerning the risk of insect attacks, results from an Austrian study (Seidl et al., 2008) are used in the model, leading to an estimation of the annual risk of destruction of 0.5% (regardless of tree size) for the unchanged case (see Table 2). 2.4. Economic assumptions and outcomes of climate change Regeneration costs and harvest revenues are based on data from The Danish Forest Association et al. (2003) and The Danish Forest Association (2010) and adjusted for inflation (Statistics Denmark, 2010). The exchange rate is 7.45 DKK/€. As documented by Brukas et al. (2001) discount rates in comparable studies are usually set between 1 and 3%. Furthermore, Thorsen (2010) showed that using a capital asset market model, the equilibrium return rate for Danish forestry is in the range of 1–2%. Thus the discount rate used in this study is set at 1.5%. The fixed economic model parameters in the analyses are shown in Table 1. The soil expectation value of oak is calculated based on one planting intervention followed by natural regeneration in succeeding rotations. Regarding climate change scenarios, risk factors and/or levels might be affected by climate change. For example, Seidl et al. (2008) estimate a probability of destruction by insects of 1.4% at the end of the 21st century due to climate change. Apart from storms and insect attacks, drought might also become an important risk factor depending on the nature of future changes. Thus we use a sensitivity approach to model the dependence of SEV on risk, which is attributed to all the above mentioned factors. To ease computations storm risk is kept at its present level and thus only the (assumed) size independent risk factors – insects and drought – are changed in the sensitivity analysis. Based on this analysis, we present three Please cite this article as: Schou, E., et al., Regeneration decisions in forestry under climate change related uncertainties and risks: Effects of three different aspects of uncertainty, Forest Policy and Economics (2014), http://dx.doi.org/10.1016/j.forpol.2014.09.006

E. Schou et al. / Forest Policy and Economics xxx (2014) xxx–xxx

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scenarios regarding future SEV of species, which form the backbone of the study: ‘Best’, ‘Unchanged’ and ‘Worst’. The probabilities (beliefs) attached to each outcome is varied in the study. Furthermore, alternative sets of outcomes are also analysed — see Table 2. As oak is assumed to be unaffected by climate change, the scenarios only concern the future performance of Norway spruce.

Table 1 Fixed economic parameters used in the model. Variable

Norway spruce

Oak

Planting costs [€/ha] Natural regeneration [€/ha] Current SEV [€/ha] Discount rate [%]

3,100

6,700 2,000 632 1.5

807 1.5

Table 2 An overview of the scenarios for economic outcomes and belief distribution. Main outcomes Alternative outcomes Belief distribution

Best, unchanged, worst High spread, low spread Uniform, skewed

3. Results

3.2. SEV vs. risk, regeneration costs and revenue

First the simulation results are described, illustrating the possible impact of changes in biophysical risk on the SEV of Norway spruce to establish the span of possible climate impacts. Following that the results of solving the optimal harvest timing and regeneration problem under various assumptions are described.

Fig. 2 shows expected SEV for four levels of risk (in addition to storm risk which is assumed unchanged), and two levels of establishing costs and change in revenue from timber harvest. It is seen that change in revenue throughout the rotation matters much less than change in costs (due to discounting). The worst outcome illustrated is − 17,882 €/ha, noting the extreme level of risk of 7.5% p.a., while the best outcome is 7540 €/ha. A key effect observed here is the risk increase for low age classes where storm risk is low.

3.1. Conditional probability of windthrow To illustrate one of the possible indirect implications of climate change on biophysical risks, the effect of increases in the growth rate of Norway spruce on the conditional probability of storm damage, p storm (damage|event) was computed as shown in t Fig. 1. The difference in conditional probability is low for stands younger than 40 years and high for stands older than 70 years. From age 50 to 60 years, there is a considerable increase in risk in all scenarios caused by an increased height growth (thinning strategy is the same for all scenarios). Comparing the + 20% scenario with the 0% scenario, there is a risk increase in the magnitude of 100%.

1

0.9

Conditional probability

0.8 0.7 0.6 0.5

0.4 0.3 0.2 0.1 0

20

30

40

50

60

70

80

90

Age Class [years] Increase=0%

Increase=5%

Increase=10%

Increase=20%

Fig. 1. Conditional probability pstorm (damage|event) of windthrow for Norway spruce t across ages for four scenarios of increased annual volume growth. Based on windthrow damage model by Lohmander and Helles (1987).

3.3. Optimal stopping vs. expected time of climate change certainty Using the span of simulations presented in Fig. 2, the three possible economic outcomes (‘Best’, ‘Unchanged’ and ‘Worst’) of climate change impact for Norway spruce are defined. Table 3 shows the expected SEV under each outcome and the expected value in case of equal beliefs in the scenarios, i.e. a subjective probability (bC) of 1/3 prior to the climate development being resolved (‘before’). This is referred to as the baseline scenario. In these simulations, oak only performs best in the worst case, but would, ex ante, be the optimal choice based on the expected value perspective because the SEV of Norway spruce in the worst case is highly negative. If on the other hand, the option to wait until uncertainty is resolved is evaluated, then the expected SEV (‘after’) is positive and higher than either of the expected values of making the decision prior to receiving and acknowledging the information. Thus, there is a value of waiting of 2993 − 632 = 2361 €/ha. Note that the decisions underlying this expected value of waiting differ, as Norway spruce would now be chosen in two of the three possible cases. Conversion to oak would only be chosen in the worst case ex post. However, the decision to wait also implies capital costs on the existing as well as the next stand — net of further growth. Combining these two elements, we arrive at Fig. 3, which shows for a range of possible stand ages, whether it is optimal to continue for at least another 10-year period, or to harvest immediately and regenerate with oak — depending on how long the perceived time of waiting time for obtaining certainty on climate development is. Comparing the continuation value and the stopping value for Model 1 (M1), where uncertainty would be resolved within the next decision period, we found that stands of age 70 years and older should be harvested and replaced by oak. For younger stands, it would be optimal to wait one period, and hence the regeneration decision would change according to what is learnt. If uncertainty

Please cite this article as: Schou, E., et al., Regeneration decisions in forestry under climate change related uncertainties and risks: Effects of three different aspects of uncertainty, Forest Policy and Economics (2014), http://dx.doi.org/10.1016/j.forpol.2014.09.006

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E. Schou et al. / Forest Policy and Economics xxx (2014) xxx–xxx

10000

5000

0

SEV [€/ha]

-5000 -10000 4000/0

-15000

Planting costs [€/ha]/Revenue change [%]

2000/+50 -20000 0

2.5

2000/-50 5

7.5

Annual probability of destruction [%] Salvage value = 50 % Additional reg. costs = 10 % of planting costs Fig. 2. Sensitivity of soil expectation value (SEV) for Norway spruce to changes in risk (by other agents than storm), regeneration costs and revenue level. Storm risk is fixed and in addition to the levels of risk shown. Discount rate = 1.5%.

3.4. Dependence on spread of distribution In the previous analysis, a skewed set of outcomes was assumed, with a highly negative outcome in the worst case for Norway spruce. However, as these simulations rest on a set of somewhat uncertain assumptions, the results from a symmetric spread is also shown — see Fig. 4. The SEV is set to vary ±20,000 €/ha around the current expected SEV (i.e. SEV = −19,193 €/ha in the worst case and 20,807 €/ha in the best case). When uncertainty is resolved after one period (M1), it now becomes optimal to retain the stand until the maximum age of 100 years. For M2 the optimal stopping age would now be 70 years, whereas for M3 it would still be 60 years, as in the baseline scenario. Consequently, if there is a possibility of a more positive outcome for Norway spruce, then the value of waiting is higher, and in fewer cases would the forest manager decide to carry out final harvest and plant oak. There is a local minimum at age 60 years for the continuation values. This is caused by the steep increase in storm risk between ages 50 and 60 years, where trees enter high-risk classes (see also Fig. 1). The probability of continuation is thus lowered — a continuation that could be very valuable if the +20,000 €/ha outcome is realised. This large SEV lowers the relative importance of the stumpage value of the stand.

Table 3 Soil expectation values [€/ha] for simulated climate change outcomes and expected values under equal beliefs (baseline scenario). Oak is not affected by climate change. The ‘after’values are maximized values after uncertainty about climate development is resolved. Climate change outcome Species Norway spruce Oak

Worst −17,882 632

No-change 807 632

Expected value Best 7,540 632

Before −3,178 632

After 2,993 2,993

Reducing variation to ±5000 €/ha (not shown) results in a harvest age of 70 years for M1 and 60 years for the other models, corresponding to the baseline scenario. Obviously the higher the difference between climate scenarios, the larger is the value of waiting as is clearly seen in M1. However, in the case of M3, where the forest manager has to wait for three periods before uncertainty is resolved, the value of waiting cannot offset the cost of waiting. Apart from the difference in expected outcomes, the choice of discount rate will also affect the value of waiting. For the 1.5% discount rate, the discount factor for M3 over three decision periods is 0.64 compared with 0.41 for a 3% rate. Thus, only 41% of the non-discounted value of the value of waiting is retained in the case of a 3% discount rate. 3.5. Sensitivity to the distribution of beliefs In the above it was assumed that the forest manager assigns equal probabilities to the three possible climates scenarios. In this section the effects of a skewed set of probabilities is analysed. Subjective probabilities of 70% for ‘worst case’, 20% for ‘no-change’, and 10% for ‘best case’ are assumed — i.e. beliefs that are highly asymmetrical and skewed towards the negative outcome. In the baseline scenario, now, all models prescribe harvest at the present optimal rotation age (60 years). Thus, there is no longer an incentive to wait for more 20000 18000 16000 Expectation value [€/ha]

is not resolved within one period, but instead within two (M2) or three periods (M3), then this threshold age is reduced to 60 years, which is also the present optimal rotation age for Norway spruce in large parts of Denmark. Thus, the analysis shows that it is only worth to wait for additional information in case it is received within one period. After year 60, Vt for M2 and M3 are almost identical. Due to the forced stop at stand age of 100 years, the two models will always have equal Vt with two periods remaining. With one period remaining, all models have equal Vt.

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Fig. 3. Expectation values of continuation and stopping for varying expected time periods before uncertainty over the three possible climate change scenarios is resolved (Models 1, 2 and 3). Discount rate = 1.5%.

Please cite this article as: Schou, E., et al., Regeneration decisions in forestry under climate change related uncertainties and risks: Effects of three different aspects of uncertainty, Forest Policy and Economics (2014), http://dx.doi.org/10.1016/j.forpol.2014.09.006

E. Schou et al. / Forest Policy and Economics xxx (2014) xxx–xxx 20000

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Fig. 4. The same as Fig. 3 for a variation of outcome of ±20,000 €/ha around the current soil expectation value of Norway spruce. Discount rate = 1.5%.

information, as the value of waiting is reduced to a mere 726 €/ha. If the choice is made before the ‘true’ outcome is known, then oak would be chosen (E(SEV) = 636 €/ha vs. − 11,602 €/ha for Norway spruce), and with the low probability of a good outcome for Norway spruce, the risk of ‘losing out’ by choosing oak is accordingly low. If the beliefs are reversed, then tendencies are the same — except that now Norway spruce would be preferred. The central point is that the more asymmetrical the belief set, the more certain the outcome of climate development is perceived to be and the lower the value of waiting.

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base the regeneration decisions on ex ante expectations and beliefs — in our baseline case he will plant oak. This result is of clear relevance to policy makers worrying about the adaptation behaviour of forest managers and may well explain empirical observations of forest managers' adaptation decisions (Blennow et al., 2012). Furthermore, the distribution of beliefs on different climate developments and related outcomes has crucial importance. In our model, maximum uncertainty about future climate development is represented by the case where scenarios are perceived equally likely. Thus, any skewed deviations in belief patterns, or concentrations on the ‘no change’, will reduce perceived uncertainty. According to Lorenzoni and Pidgeon (2006) public views on climate change are characterised by a “perceived negativity and threat of climate change”. Thus, we tested a set of beliefs highly skewed towards a bad outcome of climate change. Clearly this functioned to reduce the incentive to wait for more information due to the assumed higher probability of a negative influence of climate change — final harvest age would decrease followed by conversion to oak. In case of skewed beliefs towards a positive outcome for Norway spruce, the forest manager would again harvest earlier, but no conversion would happen. Schneider (2001) argues that decision makers could be let to use their distribution of beliefs, when no input is available on relative likelihoods of different climate change outcomes. He argues that this might lead to the adoption of erroneous strategies for coping with change. We show that if such beliefs are furthermore skewed towards particular outcomes, the forest manager will make earlier decisions and base them on his beliefs, possibly leading to suboptimal choices. This will be exacerbated if further information is expected only to arrive in the more distant future.

4. Discussion 4.1. Species switching with climate change uncertainty as a special case of optimal stopping The stochastic decision problem analysed in this paper can be interpreted as a special case of the more general optimal stopping and real option problems, with focus on the timing of a decision (Dixit and Pindyck, 1994; McDonald and Siegel, 1986). In the model analysed here it is assumed that uncertainty will be fully resolved suddenly and in finite time and that the relevant uncertainty is that perceived by the decision maker. This differs from the real option literature in forest science, where uncertainty has been largely modelled in the form of various stochastic processes (e.g. Conrad, 1997; Brazee and Mendelsohn, 1988; Malchow-Møller et al., 2004; Thorsen, 1999a, 1999b). In these models, uncertainty prevails indefinitely and is fully described by the parameters of the stochastic processes, which are assumed to be known to the decision maker. While such models may be reasonable for e.g. the analysis of decision making under price uncertainty, they seem less relevant to the climate change case, where it is expected that the climate will not change forever (except for natural variation). This key difference allowed us to conclude on the effects of variation in the different components constituting the uncertainty related to climate change as perceived by the forest manager. The increased value of waiting (and hence delayed harvesting decision) when increasing the spread of outcomes for Norway spruce is similar to the standard finding that increasing variance in the stochastic process increases the value of waiting and the value of the asset (Dixit and Pindyck, 1994). More novel to the literature are the analyses of the role of the expected time till the perceived uncertainty on climate development will be resolved. The result suggests that if a forest manager expects that uncertainty might be resolved soon and that new information will enable him to improve his decision, then his decision, ex ante, would be to wait for this disclosure. Vice versa, if disclosure is perceived to arrive at a later time, the effect on his immediate decision decreases as the cost of waiting increases. He will harvest in more states and

4.2. Caveats, limitations and options for further improvements in the approach Several simplifying assumptions have been made in this study. Firstly, regarding the silvicultural aspect, we have assumed that final harvest and regeneration decision are linked in timing. The forest manager will have a limited legal window before he must reforest, but equally important, there are costs to be saved in preparing the area soon after harvesting to avoid costly weed control. Another silvicultural assumption is that of mono species stands, a restriction which excludes some potentially adaptive options. Jacobsen and Thorsen (2003) demonstrated the effect of mixing species on a stand level, when encountering changing growth conditions caused by climate change. Mixing allows ‘postponement’ of the choice of species for final harvest, as adjustments can occur simultaneously with knowledge gathering, thereby decreasing the probability of stand failure. As mixtures are at the core of near-natural forest management (Larsen and Nielsen, 2007) conversion into such systems might thus enlarge adaptive capabilities. Finally, scenarios have been focused on risk related to windthrow and pests like Ips typographus (L.) and Pityogenes chalcograhus (L.), which may pose a threat at various stand ages. Other risks could be relevant, including summer drought and increased susceptibility to fungi like Heterobasidion annosum ((Fr.) Bref.), which are already an important calamity in Denmark. While such risks are not additive, they may increase overall risk level. Practices might have to be revised, e.g. avoiding timber storage in the forest in certain periods to reduce bark beetle breeding material. Regarding the level of risks faced under the future climate, we had to resort to various assumptions about the possible range of annual risks faced by the stand over its life time. This is a clear drawback of the empirical simulations undertaken, but it should be noted that i) it follows from the same lack of better based information that is explicitly assumed in the model, and hence is not easily improved, and ii) the qualitative findings, which are at the core of this paper's contribution, remain valid. Turning to the behavioural and model assumptions in this study, it has been assumed that uncertainty is resolved with certainty at a

Please cite this article as: Schou, E., et al., Regeneration decisions in forestry under climate change related uncertainties and risks: Effects of three different aspects of uncertainty, Forest Policy and Economics (2014), http://dx.doi.org/10.1016/j.forpol.2014.09.006

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E. Schou et al. / Forest Policy and Economics xxx (2014) xxx–xxx

specific point in time in the future and not before. It is of course more likely that uncertainty about the direction of change is only gradually resolved, and perhaps never fully (Yousefpour et al., 2013, 2014). Both of these effects will tend to decrease the value of waiting, but the overall result will remain the same, namely that a manager is more likely to rely on ex ante expectations the further into the future, i.e. the slower, the uncertainty is resolved. Like many other studies on decision making under uncertainty, we have assumed risk neutrality and that risks are handled solely for expected return maximisation. Introducing risk aversion into the model is a functional transformation of expected pay-offs, which in this case would make it marginally more attractive to postpone decisions and wait for certainty (and vice versa for risk seeking), but will otherwise not change the key findings of the study; a result also confirmed in earlier studies on reservation prices (Gong, 1998). Risk aversion will probably be a common feature of decision makers, but behavioural economics indicate that risk seeking behaviour may occur under some conditions. Using prospect theory, Kahneman and Tversky (1979) find results that indicate that people may exhibit risk seeking behaviour when facing losses and the opposite when facing gains. In our baseline scenario, such behaviour could be incorporated by the forest manager assigning larger weight to the optimistic scenarios, and this would result in continuing with Norway spruce, putting faith in the ‘best’ outcome of the possible scenarios. According to Samuelson and Zeckhauser (1988) a status-quo bias may be present when decision makers are faced with uncertainty, i.e. that they will tend to favour the status quo over alternative courses of action. In the Danish case presented here this bias would again favour the continuation and replanting of spruce.

provide policy measures for adaptation in cases where such discrepancies between private and social payoffs to adaptation are likely to exist. 5. Conclusion As uncertain as the outcome of climate change might be, forest managers will in some way have to react to these expectations, when making the crucial choice of species selection for regeneration. In this study, we have shown the implications of the forest manager's beliefs on three distinct aspects of uncertainty about climate change and its effects, for his decision on harvest timing and subsequent choice of reforestation species. We have shown that under some combinations of assumptions, the forest manager will be willing to wait for improved knowledge on climate change developments. In this case, science has the potential to improve the basis for his decisions, provided it is able to reduce uncertainty. Based on an analysis of the resolution of uncertainty, we have shown that over a range of possible expectations, it is equally likely that the forest manager will make his decision and choice earlier and base his decisions on his current ex ante expectations, rather than wait. In such cases, he may be less likely to choose decisions implying ex ante adaptation to climate change. The important implication to realise for both policy makers and scientists is that they are able to affect decision behaviour. Political or scientific communication decreasing or increasing uncertainty about when climate change developments can be predicted better, will affect the beliefs of decision makers like forest owners in two ways: Firstly they may believe that better information will come along sooner or later into the future, the former resulting in willingness to wait, the latter in decisions based on current beliefs. Secondly, it will affect the distribution of beliefs — towards or away from measures of adaptation.

4.3. Perspectives for research, policy and practice

Acknowledgements

Clearly studies like this and those of, e.g. Jacobsen and Thorsen (2003) and Yousefpour et al. (2013, 2014) can be improved, as research produces better information on the likely economic performance of different tree species under climate change, as well as on the likelihood of these outcomes. Our results suggest why acquiring more information on these aspects, especially to reduce uncertainty on future developments, may be of paramount importance to the adaptation of future forests. We have shown that with current levels of uncertainty about the impacts (not the direction) of climate change there may be real arguments for forest owners and managers to maintain current practices and species preferences. Combining this with recent empirical knowledge about the relation between the climate change beliefs of forest owners, their experiences and their adaptation practices (Blennow et al., 2012), there is further reason to believe that forest owners may find it optimal to wait, until experiences of significant climate impacts convince them that adaptation is worthwhile. In the study we have taken the perspective of a private forest owner, but it should be acknowledged that from society's point of view, there may be two important reasons why the collective decisions of individual forest owners may not coincide with that optimal for society at large. The first reason is that society may be unlikely to share the beliefs about climate change development and impacts as suggested by Blennow et al. (2012), and is perhaps likely to find climate change more of a threat. If that is the case, measures to communicate scientific information about climate change and impacts on forestry should be supported, as well as policy measures providing incentives for adaptation decisions. The second reason is that society may be concerned with the potential externalities related to climate change impacts, e.g. large scale losses of nutrient and carbon on forest land, impacts on watersheds and biodiversity as well as recreational values. For that reason, the payoff matrix of climate change impacts as seen by society may look significantly different across species and decision alternatives. Again, while such calculations are beyond this study, our findings stress the need to

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Please cite this article as: Schou, E., et al., Regeneration decisions in forestry under climate change related uncertainties and risks: Effects of three different aspects of uncertainty, Forest Policy and Economics (2014), http://dx.doi.org/10.1016/j.forpol.2014.09.006