Cost-effective compensation to avoid carbon emissions from forest loss: An approach to consider price–quantity effects and risk-aversion

Ecological Economics 70 (2011) 1139–1153

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Ecological Economics j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / e c o l e c o n

Analysis

Cost-effective compensation to avoid carbon emissions from forest loss: An approach to consider price–quantity effects and risk-aversion Thomas Knoke a,⁎, Otto-Emmanuel Steinbeis a, Matthias Bösch b, Rosa María Román-Cuesta c, Thomas Burkhardt d a Institute of Forest Management, Department of Ecology and Ecosystem Management, Center of Life and Food Sciences Weihenstephan, Technische Universität München, Hans-Carl-von-Carlowitz-Platz 2, 85354 Freising, Germany b Institute of Forest Economics, Technische Universität München, Hans-Carl-von-Carlowitz-Platz 2, 85354 Freising, Germany c Food and Agriculture Organization, FAO, UN-REDD Programme, Forestry Division, Viale delle Terme di Caracalla, 00100 Rome, Italy d Institute of Management, Universität Koblenz-Landau, Universitätsstraße 1, 56016 Koblenz, Germany

a r t i c l e

i n f o

Article history: Received 12 February 2010 Received in revised form 10 January 2011 Accepted 13 January 2011 Available online 23 February 2011 Keywords: Financial modeling of land-use shares Uncertainty Risk aversion Carbon compensation Land diversification Endogeneity of tropical land-use Indirect land use change (iLUC)

a b s t r a c t Analyses were carried out on financial compensation to avoid loss of tropical forests and related carbon (C) emissions when marginal financial yield declined for land-use options with extended areas, and when a riskaverting perspective (modeled according to financial theory around the capital asset pricing model) is assumed. The approach in this study was to consider natural forest, forest plantation, pasture, and cropland simultaneously to investigate how an optimized land-use distribution may reduce the amount of compensation necessary to avoid C emissions from forest loss. The financial compensations derived were as high as US$ 176 per hectare per year when comparing natural forests only with the most profitable alternative (croplands). However, compensation decreased to US$ 124 for risk-neutral decision-makers, who would strive for optimized land-use allocation, and to only US$ 47 per hectare per year for risk-avoiders, who would look to maximize the reward-to-variability ratio. Sensitivity analyses indicated that the compensation under risk-aversion increased much less than under risk-ignoring when increased productivity of agricultural land-use or growing demand for agricultural products was simulated. It was concluded that considering appropriate diversification strategies and the well documented human behavior to avoid risks is an important step in developing cost-effective compensation policies. © 2011 Elsevier B.V. All rights reserved.

1. Introduction Deforestation and forest degradation contribute 12 to 15% to the global anthropogenic carbon emissions and are, after fossil fuel combustion, the second largest anthropogenic source of carbon (van der Werf et al., 2009). The benefit of slowing or reversing deforestation and forest degradation for mitigating climate change is thus self-evident (Fearnside, 2001), and important studies, such as Stern (2006) and Eliasch (2008), identified curbing deforestation as a highly cost-effective method for reducing greenhouse gas emissions. Climate policy makers have now confirmed the need for action to reduce emissions from deforestation and forest degradation (REDD), as well as maintaining or/and enhancing forest carbon stocks (REDD+) at the UNFCCC (United Nations Framework Convention on Climate Change) meetings in Bali and Copenhagen. The Copenhagen Accord (UNFCCC, 2009) considers at COP15 two funding paths: a) The provision by developed countries of new and additional resources to

⁎ Corresponding author. Tel.: +49 8161 714700; fax: +49 8161 714616. E-mail address: [email protected] (T. Knoke). 0921-8009/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.ecolecon.2011.01.007

promote adaptation and mitigation, approaching US$ 30 billion for the period 2010–2012, and b) the developed countries commitment to a goal of mobilizing jointly US$ 100 billion a year by 2020 to address the needs of developing countries. By means of these funds tropical Nations could possibly be paid for REDD (Malhi et al., 2008; Eliasch, 2008). From the perspective of land users, payments for REDD could give standing tropical timber a financial value and thus may help in conserving tropical forests. Various studies have shown that comparatively small payments per Megagram (Mg) CO2, which is not emitted into the atmosphere through deforestation, were sufficient to compensate the opportunity costs of land users (e.g., Eliasch, 2008). However, in deriving necessary compensation payments, previous studies have often compared only two mutually exclusive land-use options, such as conservation of natural forests as one option and either of the more profitable forest or agricultural uses as the alternatives (e.g. Grieg-Gran, 2008; Knoke et al., 2008a; Butler et al., 2009; Knoke et al., 2009a). While such an approach views the difference in financial yield between the compared options (land opportunity costs) as the minimum required compensation, it ignores the option of considering various land-use types simultaneously to optimize the land-use shares according to the objective of the land-user.

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An optimized land-use distribution would possibly allow for the minimization of land opportunity costs when protecting natural forest from conversion. A mixture of various land-uses would also help to reduce through diversification uncertainties and risks. Disregarding risk diversification may be problematic due to the fact that most people show a risk-averting attitude when making decisions. Risk-aversion is well documented and mostly regarded as the normal case (Hirshleifer and Riley, 2002). Tropical land-users also tend to prefer to accept less uncertainty rather than more (Pichón, 1996). A modeling concept should, consequently, consider opportunities for diversification, for example to compensate for price uncertainty of various land-use products. Modern financial theory (e.g., Elton et al., 2007) offers a framework to, at least in part, integrate diversification effects. A modeling strategy in the sense of an “Optimized Land-Use Diversification” could apply standard financial modeling approaches adopted from the capital asset pricing theory (CAPM) to address price uncertainty for ecosystem products. Moreover, most studies assume that product prices will remain constant if carbon emissions from tropical deforestation are to be avoided. In fact, the product quantities obtained from land-use could change if land-use would be altered, with an associated impact on product prices. Assume, for example, that productive agricultural land may become scarce relative to a business as usual scenario. If we have limited supply, the agricultural products will be expensive, and, as a consequence, the high product price would stimulate additional production (to increase supply), thus increasing the pressure on land resources still under tropical forests. It thus is necessary to consider price–quantity effects when analyzing possible trends in future ecosystem areas. Only a few studies were found that considered feedback effects of quantities on prices and none that integrated into their analyses risk diversification within the context of carbon emissions through land-use change. For example, Wise et al. (2009) showed that unmanaged ecosystems and forests expand, and food crop and livestock prices rise considerably, if carbon emissions from land-use change face the same CO2 tax as emissions from fossil fuel combustion and industrial emissions. At the same time the costs for limiting atmospheric CO2 concentration would considerably sink compared to a tax scenario that ignores emissions from land-use change. The authors conclude that increasing agricultural productivity would be the challenge to be solved for the future in order to obtain successful limitation of atmospheric CO2. In their advanced modeling approach, the authors did not, however, analyze the problem from the perspective of a land user, who faces uncertainties and systematic price shifts due to country wide changes in product quantities, and who must be convinced to sacrifice deforestation. Instead a carbon tax forced land-use to change. However, it is open whether or not CO2 taxes on land-use change will ever be acceptable for tropical nations. This may be seen as critical in the context of their development opportunities. Another open question is whether or not agricultural intensification is actually a means to slow land-use change. Other authors have shown that it may well boost deforestation processes, if intensification increases the profitability of agriculture relative to the – possibly managed – natural forests (e.g., Carpentier et al., 2000). Moreover, Wise et al. (2009) based their study on a rather moderate deforestation scenario as a reference pathway, where the area of unmanaged forests decreased only by less than a third over a time period of 105 years. In contrast, we have examples from Amazonian South America in which forest cover is predicted to decline by 50% within only 12 years if landuse practices would not change (Michalski et al., 2008). One should thus test the effects of financial compensation on deforestation scenarios for a situation in which the conversion of tropical forests into agricultural land-uses is really attractive and where forests are really under pressure. South America is generally considered to be a high stress region for natural forests (FAO, 2007). Contrastingly, South America is a part of

the world where carbon pools in vegetation and soil could amount to 145 Gt, while vegetation and soils in Africa (51 Gt) and Asia (45 Gt) contain much less carbon, as reported by Tollefson (2009) from still preliminary, satellite surveys on the earth's biomass. We thus addressed the situation of a South American tropical country, where forests are under high pressure. An “Optimized Land-Use Diversification” as tested in this paper is a new approach, which considers various land-use options simultaneously to analyze the effects of considering financial carbon values as a means to reduce deforestation, here not imposed as a tax but as compensation payments. The approach has still a conceptual character and must be further developed (see discussion). It was based on standard financial modeling techniques, obtained from financial theory around the CAPM, with which we modeled future land-use shares so as to analyze possible land-use changes under various scenarios. The analyses consider price–quantity effects and options for risk diversification by mixing various land-uses, and they cover possible other land-use drivers, such as agricultural intensification, demand shifts as induced by an increasing population, or natural forest management, with sensitivity scenarios. Given a simultaneous consideration of various land-use options under quantity dependent product prices, one can expect significant differences in the costs of compensation compared to conventional approaches, which usually compare only two mutually exclusive land-use options and constant marginal financial yield. Moreover, by introducing the perspective of a risk-averter in the financial modeling concept, further changes in compensation costs and effectiveness can be assumed. The paper first describes the approach for financial modeling to obtain an “Optimized Land-Use Diversification”. Subsequently we present price and yield data for ecosystem products and assumptions for CO2 emissions in two other sections. The results address the compensation payments under various scenarios; we end with a discussion and conclusions chapter. 2. Financial Modeling Standard financial theory around portfolio selection (Markowitz, 1952; Elton et al., 2007) and related improvements by Tobin (1958) and Sharpe (1966; 1994, CAPM modeling) form the theoretical core of our approach. Portfolio theory has already proven useful in explaining aggregate land-use shifts between forest and agricultural land (Mills and Hoover, 1982), but as far as we know, it has not yet been used in the context of compensation to avoid CO2 emissions. When applying portfolio theory, the assumption of a general risk-aversion of decision-makers is fundamental. This assumption may well be justified for poor tropical farmers, our decision-makers, who must give livelihood security first priority (Vosti and Witcover, 1996; Pichón, 1996; Barrett et al., 2001; Rice, 2008). But even wealthy farmers may be risk-averters. Forster and Weiss (1998) confirmed that the degree of diversification will often increase with growing enterprise size. An increased diversification is seen as an indicator for risk-aversions, because risk-averters employ diversification strategies to compensate for uncertainties (Hirshleifer and Riley, 2002; see Di Falco and Perrings, 2005, for the case of farmers). Actually, there exists substantial evidence that diversification is generally an important and practiced strategy in land-use. For example, Mills and Hoover (1982) wanted to find out why many American farmers and landowners invest in forestry, although investment analysis often yields low profitability for this type of land-use. Their main conclusion was that farmers consider the diversification benefits of their forest land investments implicitly, indicated by low correlation coefficients to almost all other land-use options. Also, in Central Europe there exists long-standing evidence for diversification into agriculture and forestry as employed by the rural population. From a survey in 2007 it follows that 88% of German forest owners with more than 10 ha forest property are actually farmers who

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often manage mainly agricultural areas (BMELV, 2007). Moreover, the advantages of producing not only agricultural crops but also timber are already often acknowledged in shaded coffee plantations. In these systems, non-coffee products, such as fuelwood and construction materials, may account for a fifth to a third of the value realized from agroforestry (Rice, 2008). Given this evidence, the assumption of riskaversion may be seen as well founded, not only for pure financial decision-making, but also in the case of land-use. It is thus fundamental to consider this perspective in deriving compensation to avoid CO2 emissions from forest conversion. Besides the fundamental assumption of risk-aversion, the approach of an “Optimized Land-Use Diversification” provides that the future shares of ecosystems are controlled solely by financial forces and sees land-use options as risky natural assets. The decision-makers (tropical farmers) all have the same land-use options and they may organize their land-use like a portfolio of financial stocks by mixing the available options on their lands. The considered land-use options are: natural forest (managed or unmanaged), forest plantation, cropland, and pasture. The future land shares of the four land-use options, derived for various scenarios as parts of a land-use portfolio, are decision-variables, altered to maximize the objective function. Changing the initial shares of land-use options, and with this the structural composition of land-use, various portfolios were derived for a hypothetical country in South America (26 million hectare, around the size of Ecuador). The initial land-use portfolio was estimated from land cover data for South America to obtain average land-use shares for the countries here (Table 1). Aside from standard assumptions inherent in the CAPM theory, such as homogeneous expectations of decision-makers, homogeneous site quality was assumed with all land being potentially arable. While referring to the average land-use proportions in South America it is not said that the applied numerical data would prove realistic for every country in South America. This was just done to obtain a platform to start from in order to derive methodologically driven differences in compensation payments. The obtained absolute compensation payments are not a core area of concern in our “Optimized Land-Use Diversification” approach, but of interest are instead the differences between the tested methodological approaches. 2.1. Future Shares of Ecosystems When Ignoring Risk-aversion In this section preliminarily risk-aversion and uncertainties are excluded, while only decreased marginal financial yield for extended agricultural areas is considered, such that a platform for comparing the results of the alternative approaches can be established. Let it be assumed that tropical farmers may maintain natural or create artificial land-use options for alternative purposes in our hypothetical country. For the beginning, only two land-use types are considered: Natural forests as being present everywhere in the initial, virgin landscapes and

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croplands as the human-made replacement ecosystems which result from forest conversion. Croplands may only be extended at the cost of reducing natural forests, while the maintenance of natural forests means foregoing agricultural production. Let the scarcity of products from both land-uses be indicated by the prices that people are willing to pay for the associated ecosystem products, e.g. maize or tropical timber. Let us further assume that we can approximate the quantity of ecosystem products by the ecosystem area under use, an assumption that provides homogenous site conditions. With increasing area of forests and croplands, the net revenues per hectare (for simplicity denoted as financial yield from here onwards) would thus decline, because large product quantities may only be sold at decreased prices. Under these assumptions one can expect that an equilibrium distribution of land to both ecosystems would emerge under the following condition: The marginal financial yield, i.e. the yield for one additional small unit of land, is the same for both ecosystems. This point is indicated in Fig. 1 (note that curves are assumed for demonstration purposes only): Beyond the point where the marginal yield-quantity curves for both ecosystems cross, we lose more yields by foregoing one unit of natural forests compared to what we gain by having one more unit of croplands. The expansion of cropland area is thus stopped beyond the equilibrium point. The resulting land distribution to both ecosystems maximizes the total financial portfolio yield, Yp, and thus results in the equilibrium distribution of ecosystems. Land distribution was modeled by the shares, summing up to one, which the areas of both land-uses form when related to the given total country area (Eq. (1)). max Yp = yT a = ∑ yi ai i∈L

s:t: yi = f ðqi ; ni ; ci Þ

ð1Þ

T

1 a = ∑ ai = 1 i∈L

ai ≥0

In Eq. (1), y is a vector of the estimated annual financial yields per hectare for all considered land-uses, where yield of a given land-use i, yi, is a function, f(qi,ni,ci), declining with increasing country wide produced quantities (qi) and depending on productivity (ni) as well as production costs (ci). Finally a is the vector of shares (ai) of the ecosystems, the sum of which must be one (we consider the shares of all active land-uses), and L is the set of all available land-use options. 2.2. Future Shares of Ecosystems When Land-users Are Risk-averters To anticipate the future, humans must rely on earlier experiences and on their beliefs, as safe information about the future is lacking.

Table 1 Initial distribution of the considered ecosystems and financial data for initial percentages of ecosystems. Ecosystem (land-use, i)

Area (106 ha)

Percentage (%)

Source

Average financial yield (yi) at initial distribution (US$/ha/yr)

Standard deviation (si) of financial yield at initial distribution

Land opportunity costs when maintaining natural forests (ignoring decreasing marginal financial yield and possible reallocation of land) (US$/ha/yr)

Natural forests Forest plantations Croplands Pastures

832 4 158 500

47.4 0.3 9.0 (28.5 in total)

FAO (2007) FAO (2007) Biradar et al. (2009) Vera (2005) for total area (500 · 106 ha), Göttlicher et al. (2009) for separation in managed and unmanaged⁎

31.8 105.6 208.4

± 14.5 ± 30.4 ± 46.1

73.8 176.6

130.5

± 18.3

98.7

Managed pastures Unmanaged pastures Other areas

9.2 19.3 260

14.8

⁎ Values derived for a case study area in South Ecuador.

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Financial yield per additional hectare/Total financial yield per hectare (US$/ha/year)

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Yield per additional hectare natural forest Yield per additional hectare cropland Total yield per hectare

80 70 60 50 40 30 20

Equilibrium

10 0 0

20

40

60

80

100

Percentage of croplands (in %)

Fig. 1. Finding an equilibrium economic ecosystem distribution (schematic curves).

Herein, Sp is the standard deviation of the uncertain portfolio yield, ∑ is the covariance matrix that consists of the variances (vari) and covariances (covi,j) of uncertain financial yields for every land-use, i, where covariances between every possible land-use combination have to be considered. Moreover, ki,j is the correlation coefficient between yield of land-use i and j, and si the standard deviation of the yield for land-use i (assumed as normally distributed). Given classical financial theory (Elton et al., 2007), an equilibrium ecosystem distribution chosen by all risk-averting land users can be obtained, where portfolio yield, Yp, minus the yield of a riskless benchmark investment, YR, per unit of risk is at a maximum. The riskless benchmark yield, YR, was assumed as the interest yield which famers could obtain when investing in a safe financial asset. Eq. (1) has thus to be changed to consider the perspective of a risk-averting land user into the reward-to-variability ratio, Rp, introduced by Sharpe (1966; 1994) (Eq. (3)). max Rp =

Choices regarding the desirable shares of land-uses thus have to be made under uncertainty. Adverse uncertainty is commonly related to climate unpredictable events such as thunder storms that throw down trees or destroy agricultural crops, or rainfall anomalies (called event uncertainty). A second source of uncertainty is the volatility of market prices for the ecosystem products and services (if the latter have a market price). This study was focused on the price uncertainty of ecosystem products, as time series are available to quantify this type of uncertainty, and it worked with assumptions for carbon compensations. However, the effect of event uncertainty may also be strong (see Knoke and Seifert, 2008, for the example of forestry) and should thus be investigated in future studies. Following Hirshleifer and Riley (2002) the terms risk and uncertainty are used interchangeably. Estimates about future facts cannot be well quantified in an objective way, since the estimation of uncertainty is subject to uncertainty itself. The often used separation into risk (probabilities can be quantified) and uncertainty (probabilities cannot be quantified) thus depends only on our degree of belief in the available data. As a consequence, it was not distinguished between risk and uncertainty; rather the phenomenon of uncertainty was simply seen as our inability to predict something (market prices in our case) with certainty. If risk-averting farmers would mix two or more land-use options, which show independent fluctuation of yield, they may greatly benefit from risk reduction (Knoke et al., 2009a,b). That means that one land-use may generate unexpectedly great yield, while yields of the other options are less than expected and vice-versa. For example, if the milk price is down, the timber price may be high or at least moderate and if the timber price declines, the milk price may be acceptable (see Mills and Hoover, 1982, or Lönnstedt and Svensson, 2000, for empirical evidence). These financial risk interdependences were considered in the “Optimized Land-Use Diversification” to mirror the expected risk-reducing effects of diversification. For modeling convenience, the standard deviation (si) of the estimated annual yields (per hectare) was used to derive the land-use portfolio standard deviation, Sp (Eq. (2)).

Sp = s:t:

pffiffiffiffiffiffiffiffiffiffiffiffiffiffi rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi aT ∑ a = ∑ ∑ ai aj covi;j i∈L j∈L

T

1 a=1 covi;i : = vari covi; j = ki; j si sj ai; j ≥0

ð2Þ

Yp −YR Sp

ð3Þ

A similar objective function of Eq. (3) has been applied by Koellner and Schmitz (2006) to analyze issues of grassland biodiversity. For modeling a land-use the application of Eq. (3) means the following: Given the assumptions that all farmers consider the same land-use options and that they all have the same future expectations, every farmer would theoretically hold the same structural portfolio of landuses, independent from his/her individual degree of risk-aversion. This follows from Tobin's theorem of separation (Tobin, 1958). The individual degree of risk-aversion comes into play by the option to invest in risky land management and in a riskless asset. Farmers may sell or purchase land, either to distribute their financial funds between riskless (financial) and risky (natural) assets (this is the case when selling land and investing in a safe asset) or to invest borrowed money to enlarge their risky natural assets (this is the case when purchasing land). Under our approach of “Optimized Land-Use Diversification”, only selling and purchasing land depends on the individual riskaversion of land-users, but not the structural composition of the landuse portfolios. In the case that land is sold, it was assumed that the obtained land-price is invested in a safe asset so that the riskless yield is determined by land price multiplied by riskless interest. In fact, the option to invest in risky financial assets was excluded, a simplification which might be justified in a conceptual modeling approach. Provided this theoretical background, one can estimate the possible future shares of land-uses for our total hypothetical country by maximizing Eq. (3), and this with and without the inclusion of carbon compensation. 2.3. Modeling Financial Yield and Risk To maximize Eq. (1) (risk-ignoring) and Eq. (3) (risk-aversion) we used regression curves to estimate financial yield and risk. These curves model the possible feedback that product quantities may have on prices, as sketched in Section 2.1. For estimating the average financial yield per hectare per year, we formulated a regression curve with product price, pi (price for products of land-use, i), as the dependent and product quantity, qi, as the independent variable (Eq. (4)). To test for possible endogeneity problems with our data (as both prices and quantities depend on supply and demand) we used a regression technique developed for panel data. We thus analyzed price time series for various countries with the routine “proc tscsreg” (regression for time series cross sectional data, statistical program package SAS, version 9.1). A two-way analysis with random effects was carried out that included a formal “Hausman” test to identify possible significant bias in the parameter estimates. However, the routine “proc tscsreg” does not allow for residuals on a per observation basis, which we needed for the analysis of price uncertainty (see below). Also the root mean square errors as produced with this routine

T. Knoke et al. / Ecological Economics 70 (2011) 1139–1153

were extremely great and not appropriate for modeling price uncertainty. As an alternative to “proc tscsreg”, we used a first order autoregressive model (AR1 model, estimated by “proc autoreg”), which greatly reduced price residuals. However, possible country specific variables were not considered in the obtained AR1 models. Therefore, mixed models (“proc mixed”), which considered the variables “country” and “time” as random and “quantity” as fixed effects, were computed as a third option. For both the AR1 and the mixed models, the “maximum likelihood” method was applied to estimate the parameters. Only the structural parts of the regression curves obtained with the three different modeling techniques, which had the following principle form (Eq. (4)), were used. z

ð4Þ

pi = b0 + b1 qi

With pi being the predicted price for products of land-use, i, and b0, b1 and z as parameters to be derived from empirical data (see the next chapter). The annual yield per hectare, yi, was then derived as follows, with pi being the price as estimated with the price-quantity function (Eq. (4)), ni the productivity per hectare and ci the per hectare costs of land-use i (Eq. (5)): yi = pi ni −ci

ð5Þ

When estimating the parameters for Eq. (4), a certain amount of price variation remained unexplained. We used this residual variation for single observations when considering the autoregressive part (AR1 model), and random effects (mixed model) to estimate the price volatility and the related yield uncertainty. First, we computed the absolute values of the observed residuals, εi, to obtain an indicator for the price volatility, vi (Eq. (6)): vi =

qffiffiffiffiffi ε2i

ð6Þ

Later, we regressed price volatility, vi, as a dependent variable with product quantity, qi, as an independent variable. For estimating the parameters of Eq. (7) we used a logarithmic transformation of vi and the procedure “proc reg” (statistical program package SAS version 9.1). z

lnðvi Þ = b0 + b1 qi

ð7Þ

The quantity dependent volatility of financial yield, vyield,i, was finally derived as shown in Eq. (8) and then used as an approximation for the standard deviation of the yield, si, in Eq. (3): vyieldi = vi ni s:t: b vi = eð 0

+ b1 qzi Þ

ð8Þ

The above described explicit consideration of the yield uncertainty for various produced quantities was chosen due to our finding of greater price volatility when only small product quantities were sold, but lower price volatility when great quantities were sold. By means of integrating the different volatilities of the price estimations into the objective function Eq. (3) the weight of more certain yield estimates was increased (because their low volatility decreases the total standard deviation, Sp, of the portfolio), while more uncertain estimates obtained a smaller weight in financial modeling. During the financial modeling process, qi depended on the actual allocation of land to land-use i. It was derived by multiplying land-use productivity per hectare ni, and the allocated land area in hectares, hi (Eq. (9)). The area in hectares, hi, resulted as the product of land-use

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share, ai, and total available land-use area, H. qi = ni hi s:t: hi = a i H

ð9Þ

3. Prices, Quantities, Price Risks, Carbon Data, and Sensitivity Scenarios 3.1. Prices, Quantities and Price Risks To model possible future shares of land-uses under various financial assumptions, time series for various countries were used on product prices and marketed product quantities published at the websites “FAOSTAT” (FAO Statistics Division, 2009). Annual price– quantity pairs for countries of South America (timeframe 1990–2007) were analyzed. The considered countries were: Argentina, Bolivia, Brazil, Colombia, Chile, Ecuador, French Guiana, Guyana, Paraguay, Peru, Suriname, Uruguay, and Venezuela. For the forest ecosystems, price and quantity data were scarce and only data on exported timber could be used. Especially for tropical timber, the exported quantities recorded in the statistical data were particularly small. The product quantities sold in various countries and the corresponding prices achieved showed a great range and a non-linear relationship (Fig. 2) between prices and quantities as assumed with Eq. (4). Given Eq. (4) and (7) as a plausible structure for price– quantity and uncertainty–quantity curves, the SAS statistical program was used to compute regression curves (see Tables 2 and 3 for regression results). The correlation coefficients between the considered product prices (Table 4), necessary to compute the covariance matrix, ∑, were plausible when compared to other studies (for example, Lönnstedt and Svensson, 2000). Productivity and production costs were derived from existing studies or our own estimates (Table 5). The production of only one exemplary product was used to quantify the financial yields for the land-uses and thus employed highly aggregated data, as is usual, for example, in macroeconomics. This fact might be considered as an oversimplification and we shall discuss the pros and cons later. Here, it should be stressed that this simplification may be justified, as it allows for a consideration of the correlation between the product prices. Also, the conceptual character of this study focuses more on the differences between considering and ignoring options of land-use diversification, than on a comprehensive modeling of all possible land-use options and products. Despite the simplifications made, it is shown in the results section that our modeled financial yields fit well into the range of yields found in the existing literature. For natural forests sustainable management with low productivity was provided (see Knoke et al., 2009b) and tropical industrial timber as the product. Forest plantations were modeled as broadleaved forest stands with non-coniferous industrial timber as the product. Croplands were represented by maize production and for pastures the considered product was milk, as these represent important products of the region. Jones and Thornton (2003) assume as many as 40 million poor livestock keepers in mixed systems of South America, of which a substantial proportion depend on maize to a large extent. Livestock for milk is viewed a stimulus for agricultural growth and poverty reduction. Here, smallholders often tend to use their livestock as a form of insurance (FAO, 2008) rather than selling it for meat. As a risk-free annual return for Eq. (3), US$ 50 per year was used. This yield resulted from the assumption that a farmer could sell one hectare of land for a price of US$ 1000 (see, for example, Olschewski and Benitez, 2005, for likely land costs in Ecuador) and obtain a riskless interest of 5% on this amount. At the first glance this interest seems low for South America. For example, Benitez et al. (2007) listed risk-adjusted interest rates in a range of around 9% (Brazil) up to 17%

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T. Knoke et al. / Ecological Economics 70 (2011) 1139–1153

Fig. 2. Predicted and observed product prices.

(Ecuador). However, these interest rates account for the given very high country risks. As a riskless interest, Benitez et al. (2007) even considered only 3%. The assumption of 5% for risk-free interest is thus rather optimistic, and certainly not overly conservative. 3.2. Carbon Data and Necessary Compensation Pearce (2007) confirmed that the economic value resulting from carbon that is stored in natural forests, and thus not released into the atmosphere, is of utmost importance to the economic case for forest conservation. Avoided deforestation would conserve carbon values, while forest conversion into alternative land uses eliminates carbon values partly or almost totally. Given this background, data on carbon emissions caused by natural forest conversion were integrated in our financial modeling (Table 6) that were published by Pearce and Pearce (2001). In order to derive necessary compensation to avoid shrinking shares of natural forests, various compensation payments per hectare per year were added, which increased stepwise, to the financial objective

functions (Eqs. (1) and (3)) until the future land-use portfolio contained the initial share of natural forests. Note that C compensations were understood as what the tropical farmers would actually receive and thus do not cover transaction costs with the computed amounts. The actual C price must of course also cover these additional costs, which are, for example, reported by Eliasch (2008). For the case of riskaversion (Eq. (3)) a variation coefficient of 5% inherent in carbon compensation was assumed in order to consider that also carbon payments might fluctuate. The correlation coefficient between carbon payments and other financial yields was assumed to be zero. Carbon payment uncertainty was added to the product price uncertainties in Eq. (2). The necessary compensation per hectare per year was subsequently related to 1 Mg of avoided CO2 emissions. One Mg C was converted into 3.66 Mg CO2. Yearly compensation payments per Mg CO2 were appropriately capitalized to obtain present values for the costs involved using a 5% interest. For most scenarios an initial situation of a closed secondary forest was assumed instead of a closed primary forest, to

Table 2 Parameters and statistical results of price–quantity curves. Basic form of regression curve: pi = b0 + b1qzi . Note that we only used the structural parts of the models for our estimations. Parameters used for the actual land-use modeling in bold and italics. All parameters show p-values of 0.05 or lower, unless ns: not significant is indicated (p-value N 0.05). A “Hausman” p-value N 0.10 indicates that possible bias due to endogeneity of the independent variable “quantity” is not significant. Time series cross sectional model (proc tscsreg) Parameters Land use i Natural forest Forest plantation Cropland Pasture

pi (Price in US$) qi (Quantity / 1000) N 3

3

z

b0

Hausman test b1

Per m timber Per m3 timber

m timber m3 timber

145 −0.3 83 −0.4

Per ton of maize Per ton of milk

tons maize tons milk

163 −0.1 4.14(ns) 369.37 162 −0.1 −108.66 (ns) 721.27

74.05 66.40

Autoregressive model (proc autoreg) Parameters

Test statistic m p-value b0

162.84 1.46 37.64(ns) 1.57 1.41 0.20

0.23 0.21 0.24 0.66

Parameters b1

70.94 51.09

Mixed model (proc mixed)

159.72 64.19

b0

b1 74.00(ns) 162.82 67.18 38.01 (ns)

−66.76(ns) 503.70 −22.09(ns) 417.39 −113.36 728.45 −113.60(ns) 731.71

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Table 3 Parameters and statistical results for the volatility of product prices vi depending on production quantities. Basic form of regression curve: ln(vi) = b0 + b1qzi . Parameters used for the actual land-use modeling in bold and italics.

Natural forest Forest plantation Cropland Pasture

Residuals from autoregressive model

Residuals from mixed model

ln(vi) (Standard deviation of price)

qi (Quantity)

z

b0

b1

b0

b1

Per m3 timber Per m3 timber Per ton of maize Per ton of milk

m3 timber m3 timber Tons maize Tons milk

−0.3 −0.4 −0.1 −0.1

3.03 1.09 1.82 1.56

5.05 45.67 4.75 6.99

2.98 1.53 2.19 1.20

6.31 19.52 4.40 7.41

avoid overly optimistic results (Table 6). CO2 related compensation costs for primary forests and open forests were addressed in separate scenarios. Selective logging (only 0.7 m3/ha/year was assumed as harvest quantity, Table 5) was not considered as a carbon source, as the natural forest was maintained in structural and standing timber stock equilibrium (Knoke et al., 2009a). The assumption of C neutrality may be justified because mortality will be reduced due to careful timber extraction, which would, if not reduced, also cause some carbon emissions.

3.3. Sensitivity Scenarios Our sensitivity scenarios covered: (1) An increased agricultural productivity as a possible result from agricultural intensification: Agricultural productivities were increased simultaneously for cropland and pasture. Moreover, the riskless yield was increased by the same proportions to which we increased yield. This is meaningful, because an increased yield would result in higher land prices, which could possibly be invested into safe assets to obtain the riskless yield. (2) Upwardly shifted prices for given quantities as a possible result of population growth: The assumption of upwards shifted price-quantity curves means that one can achieve higher prices for given product quantities or may sell greater product quantities at given prices. This could be an effect of population growth and may have a significant effect on the necessary compensation. Wise et al. (2009) predicted price shifts for corn between 1.5 and 4.0 times the initial price over a period of 90 years, depending on various land-use scenarios, with and without the consideration of a carbon tax to limit CO2 emissions. Prices for maize and milk were increased simultaneously up to the factor of 3. Here, price risks were generally increased in the same relative proportions as prices. Also, riskless yield was increased by the same proportions as the yield1 was increased (see sensitivity scenario (1) for a justification). (3) The effect of including or excluding the sustainable management of natural forests. (4) The influence of an altered riskless yield. Given the financial modeling background explained in chapter 2 and the data we presented above (product prices, quantities, productivity, CO2 emissions when converting natural forests), Eqs. (1) and (3) were solved by means of nonlinear programming (e.g. Knoke and Moog, 2005). To avoid local optima, all optimizations were carried out for various initial shares of the considered ecosystems until stable maximum objective functions were achieved.

1 Given constant production costs, the relative increases of financial yield were greater than the relative price increases.

4. Results 4.1. Financial Yield and Uncertainty Croplands promise the greatest financial yield for the assumed initial land-use distribution, followed by pasture, forest plantations and managed natural forests respectively (Table 1). Yield uncertainty is positively correlated with yield so that cropland management is involved with the highest uncertainty. The expected financial yields of managed natural forests are by far the lowest among the considered land-uses. The assumed principle relationship, i.e. the achievable price would decline when the marketed product quantity would increase, could actually be confirmed (Table 2). The parameters obtained from the three statistical methods applied (the time series model for cross sectional data, the autoregressive model, and the mixed model) were quite similar for the land-uses “pasture”, “natural forest”, and “forest plantation”. Only the prices for maize (option “cropland”) produced considerable differences when time series models for cross sectional data and the alternatives were compared. For further modeling we decided to use the parameters obtained by the mixed model approach. Mixed model regression curves produced intermediate compensation payments and take country specific characteristics as a random effect into account. However, for the risk-avoiding perspective the differences in obtained compensations between the applied statistical modeling techniques are not large (US$ 47/ha per year as obtained with the mixed model curves versus US$ 45 produced with the autoregressive curves). The predicted prices (Fig. 2) fit well into the range of the observed prices. Correlation coefficients between residuals and the independent variable “quantity” ranged from −0.06 (forest plantations) over −0.05 (natural forests) and 0 (croplands) to 0.13 (pasture). It may thus be assumed that the requirement of residuals to be uncorrelated with the independent variable has not been violated. The results of a formal “Hausman” test also indicated the absence of significant bias in the parameter estimates (p-values between 0.21 and 0.66, see Table 2). It can thus be concluded that the parameters in the regression curves are not subject to significant bias from a possible endogeneity of the quantity variable. The regression curves to model price uncertainty delivered plausible results, too (Table 3). If observed and estimated prices were compared by computing price residuals (observed minus estimated prices), largely symmetrical distributions were obtained, with a tendency to form more or less the shape of normal distributions

Table 4 Correlation coefficients between product prices (no. of observations in parentheses, ** p-value b 0.01).

Natural forest Forest plantation Cropland

Forest plantation

Cropland

Pasture

0.19 (36)

0.014 (100) 0.25 (55)

0.035 (90) 0.11 (61) 0.21** (154)

We excluded prices for plantation timber above US$ 150/m3 as outliers.

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Table 5 Production data for the investigated ecosystems (for price estimates see Table 2). Ecosystem

Economic activity to represent ecosystem yields

Productivity

Costs

Sources used

Explanations

Natural forest

Sustainable timber harvesting in tropical forests (prices estimated from tropical timber, exported as industrial roundwood in the rough)

0.7 m3/ha/yr

39.3 US$/m3

Knoke et al. (2009b), Carpentier et al. (2000)

Forest plantation

Production of plantation timber (prices estimated from plantation timber, exported as industrial, non-coniferous roundwood in the rough), 40% saw timber, 60% firewood sold at 10 US$/m3

10 m3/ha/yr

8 US$/m3 for logging, 1000 US$/ha for establishment

Knoke et al. (2009b) and own estimation

Cropland

Production of maize (price estimates exclude green maize)

2.0 t/ha/yr

106.0 US$/ha/yr

Costs per ton: Paudel and Matsuoka (2009)

Costs: 2.62 working days per m3 at 15 US$ a day (costs per day actualized compared to Knoke et al., 2009b) Computed for Andean alder plantations, production period 20 years, financial yield computed as the annuity of the plantation net present value at an interest of 5% Productivity estimated from average harvest yield in the year 2000

Pasture

Production of milk (price estimates for fresh milk)

1.0 t/ha/yr

92 US$/ha/yr

Benitez et al. (2006), Olschewski and Benitez (2005)

(Fig. 3). However, despite the “normal” visual appearance of the residual distributions a numerical Jarque-Bera test for normality indicated a significant deviation from a normal distribution for every distribution, except that for forest plantations. Q–Q plots (where the quantiles of the empirical and an expected normal distribution were plotted against each other) made clear that the greatest deviations being caused by the very long tails of the residual distributions. One should thus interpret the results of the model that considered risks with care and keep in mind that the effects of risk were probably underrepresented with our modeling. Note that the “Optimized LandUse Diversification” approach in fact assumed a normal distribution. However, the available data are limited and the plausibility of the obtained coefficients is thus an important issue. For example, the maximum quantity of tropical timber that was marketed as industrial timber by a South American country in one year was only 200,000 m3 (Fig. 2). The obtained price–quantity curve for larger quantities thus had to be extrapolated. However, the results obtained seem realistic: The extrapolated price–quantity curve resulted in a price for tropical timber of US$ 84/m3 for the initial share of natural forests. As a tropical timber price for the example of Ecuador, we may refer to US$ 68.5/m3 (Departamento Forestal, 2005), which was observed in Ecuador for several years. This reference price is in the same order as the timber price obtained from our price model. The resulting financial yields for natural forest management (US$ 31.8/ha/year) and forest plantations (US$ 105.6/ha/year) were also plausible (Table 1, for which the initial land-use shares were assumed). For example, Knoke et al. (2009b) found values of US$ 32 (natural forest management) and 72 (forest plantations) per hectare per year for the case of Ecuador. While financial yields from sustainable management of natural forests as calculated by Carpentier et al. (2000) for Brazil (around US$ 35/ha/year) were comparable to our study's results, Turner et al. (2003) cite values for Sri Lanka (US$ 123/ha/year) and Malaysia (US$ 153/ha/year) which are even considerably greater than Table 6 Considered carbon emissions for the conversion of natural forests into alternative landuses (adopted from Pearce and Pearce, 2001, with alterations). For forest plantations we assumed carbon storage of 25 Mg C/ha. Initial ecosystem

Carbon in Mg C per hectare lost by conversion into Forest plantation

Cropland

Pasture

195

220

220

Closed secondary forest Lost carbon (Mg C/ha)

97

152

122

Open forests Lost carbon (Mg C/ha)

27

52

52

Closed primary forest Lost carbon (Mg C/ha)

our modeled financial yield. The greatest financial yield among the studies used as a reference was reported by Torras (2000) for the Amazonian basin; the author considered US$ 307/ha/year from sustainable timber use in tropical forests. Against the background of these results one can assume that the estimates presented above are rather not too optimistic for sustainable management of natural forests. Also, the financial yield for croplands (US$ 208.4/ha/year) appears realistic. Wunder (2000) presented a range from US$ 111 up to 369/ha/year for maize production. However, this range was calculated for very good production conditions in Ecuador. Our pasture management achieved US$ 130.5/ha/year, which is well inside the range of financial yields obtained from a survey of 130 Ecuadorian farms, who altogether managed an area of 7605 ha, of which 2382 ha were pasture land and the rest natural forest (Knoke et al., 2009a). Here, the median of the financial yields from pasture management was US$ 132.7/ha/year (including all products). Benitez et al. (2006) report financial yield for croplands (maize) and cattle pasture, which are even much lower than our values (US$ 108 for croplands and US$ 53/ha/year for pasture). However, at least the relation between croplands and pastures is similar in the study by Benitez et al. (2006) when compared to our study. The comparison with Benitez et al. (2006) makes also clear that the financial yield for the land-use alternatives to natural forest management were rather not underestimated. This allows the conclusion that the financial yield data reflect not a gravely atypical situation for South-American countries like Ecuador. In conclusion one can say that the opportunity costs of forest conservation were estimated in a plausible order. 4.2. Necessary Compensation under Various Scenarios 4.2.1. Compensation in a World with Only Two Mutually Exclusive Options Given the realistic nature of the estimates for financial yield used in the applied “Optimized Land-Use Diversification”, natural forests were first compared only with the most profitable single land-use option, as is often done in other studies (e.g., Butler et al., 2009). From this perspective, the minimum amount of compensation required to maintain natural forests would be US$ 176.6, as croplands must be taken as the best alternative to natural forests (see Table 1, all values per hectare per year). Below is a test for if and how this result will change under declining marginal financial yields when extending the area of agricultural land-uses, as modeled based on Eq. (4), and under the optimum mixture of land-use options from the perspective of a risk-averter. 4.2.2. Compensation in a Diversified World Even in a diversified world, the future share of natural forests reduces practically to zero (only around 900 ha remain), if compensation to avoid carbon emissions from land-use change and risk-avoidance of

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Fig. 3. Distribution of price residuals (estimated minus observed prices).

decision-makers are ignored (Eq. (1)). Under this scenario, cropland areas would extend significantly (Fig. 4). This deforestation scenario would lead to an emission of 7.0 billion (109) Mg CO2, given the assumption of closed secondary forests as the initial situation (Table 6). Also if we consider risk-aversion (Eq. (3)) the future share of natural forests declines dramatically. Given this assumption, a future share of natural forests of 1.2% (around 320,000 ha) remained unconverted (Fig. 4), and 16.9% of available land would be allocated to forest plantations. A more balanced and diversified land-use portfolio is thus obtained under the assumption of risk-aversion, yielding land-use distributions of around 18% forestry (natural and plantation), 16% cropland and 32% pasture. The risk-averting deforestation scenario reduces emissions to 5.2 billion Mg CO2, an amount considerably lower than for the risk-ignoring decisions. Under the risk-aversion scenario, tropical farmers would acknowledge the benefit of pasture and forest management to diversify their yield, while avoiding 1.8 billion Mg CO2 emissions and herewith providing a positive externality to society (see Baumgärtner and Quaas, 2010 and discussion). The risky croplands, however, would only be extended moderately compared to the scenario under risk-ignoring. Under both objective functions (risk-ignoring and risk-aversion) an appropriate compensation would lead to the conservation of the initial area of tropical forests (around 12.3 million hectares). However, the future land-use portfolios differ significantly under both objective functions, although both lead to the same area of natural forests. In contrast to the risk-ignoring scenario, which prefers risky but highly profitable croplands and thus reallocates land from pasture to this option, risk-aversion leads to greater shares of pasture (Fig. 4). Interestingly, risk-aversion has also the effect that the largest part of the natural forest would not be managed, while the total area of natural forests is under management when ignoring risks. The riskaverting farmers avoid large yield uncertainties of natural forest management when deciding to leave natural forests unmanaged in part, while receiving relatively certain compensation only for these

Fig. 4. Possible future land-use shares with and without compensation and with and without the inclusion of risk-aversion.

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natural forest areas. However, around one quarter of the natural forests would be managed to obtain (uncertain) revenues from selling tropical timber on top of the compensation payments received for maintaining the natural forest. The introduction of risk-aversion has also a fundamental effect on the totally needed compensation. The difference in the compensation per Mg CO2 (computed from yearly payments as a 5%-present value), ranging between US$ 2.16 (risk-aversion) and US$ 4.51 (riskignoring), is considerable (Table 7), while the total required compensation also differed significantly. The financial resources required to conserve the total area of natural forests is only US$ 47/ ha/year when taking the perspective of a risk-averter, while the riskignoring model requires US$ 124/ha/year to avoid conversion of the natural forests. Both compensation values are well below the yield difference between the best single land-use option (croplands) and natural forest management, which was at US$ 176.6/ha/year (Table 1). As said above this substantial amount would be the adequate compensation under a more conventional approach, when considering only two mutually exclusive land-use options and constant prices. Simultaneous consideration of several land-use options as realistic alternatives for land-users would thus result in much cheaper, and more cost-effective, compensation than for considering only the single best alternative. In addition to this compensation reducing effect, the introduction of risk-aversion (and the intensified diversification resulting from this) means that the total 5%-present-value of compensation costs is reduced from 30.3 (riskignoring) to 11.2 billion US$ (risk-aversion). Correspondingly, the necessary yearly compensation decreases from 1514 million US$ to 562 million US$, if risk-aversion is introduced. Whether the status of the natural forest is closed primary, closed secondary or open has no effect to the total necessary compensation in our calculation, because we assumed homogeneous site conditions so that the productivities of the alternative land-uses, which followed natural forest conversion, are identical. However, the compensation costs per Mg CO2 showed a considerable variation depending on what the status the converted forest is (Table 7). If closed primary forests can be protected from conversion, the compensation costs under riskaversion fall below US$ 2 per Mg CO2. If the forest is, in fact, already degraded to the status of an open forest, the compensation of avoided CO2 emission becomes much more expensive. Here, the avoidance of 1 Mg CO2 emissions would require US$ 6.13 (risk-aversion) or US$ 13.03 (risk-ignoring). To summarize, the above results indicate that consideration of more than two land use-options under declining marginal financial yield with simultaneous introduction of a risk-averting perspective has a fundamental effect on the total compensation costs. It should be stressed that effects of natural forest conservation (meaning avoiding a reduction of the share of natural forests) for much reduced compensation costs can be expected when the well documented human attitude of riskaversion is assumed, and compared to a risk-ignoring scenario. 4.2.3. Sensitivity Scenarios 4.2.3.1. Increasing Agricultural Productivity. Avoiding the conversion of natural forests is significantly more cost-effective under risk-aversion compared to risk-ignoring, even if the productivity of agricultural land-uses rises (Fig. 5). The maximum compensation was calculated for a productivity increase of 200% and with amounts to US$ 335/ha/

year (risk-ignoring) or US$ 127/ha/year (risk-aversion). Additionally, the present values of compensation costs per Mg CO2 reflect a great difference, with a maximum US$ 12.85 per Mg CO2 under riskignoring and US$ 5.04 per Mg CO2 in the case of risk-aversion. The analysis may also help to give an expression how greatly the compensations may change, if the local productivity is heterogeneous. Moreover, it shows that one has generally to consider that the intensification that leads to increased productivity will also lead to a greater pressure on natural forests, with higher compensation costs needed to avoid forest loss. 4.2.3.2. Upward Price Shifts for Agricultural Products. Upward shifted prices push necessary compensation under risk-ignoring to a value as high as US$ 640/ha/year in the extreme case. Here, the prices are 3 times the prices in the basic scenario, resulting in an increase of 200% (Fig. 6). The price per Mg avoided CO2 climbs from US$ 4.51 to 23.24 under this condition. Contrary to this development, the necessary compensation under risk-aversion rises much less. The compensation increases to US$ 210/ha/year for the greatest simulated price shift, and the maximum price per Mg avoided CO2 rises from US$ 2.16 to 8.86. The cost saving effect of considering risk-aversion is thus even more pronounced when assuming future price shifts for agricultural products. Also in this sensitivity simulation it becomes evident that altering the assumptions, for the presented case of an increased demand for agricultural products, could exert pressure on natural forests significantly. Seen from another perspective, one has to expect that strict forest conservation and population growth would make arable land relatively scarce. The consequences will be increased prices for agricultural products, a fact that could push forest conservation into ethical conflicts. The discussion addresses possible solutions for this conflict. 4.2.3.3. Effect of Natural Forest Management. Sustainable management had a significant effect under risk-ignoring. Here, the necessary compensation decreased from US$ 154 to 112/ha/year when the productivity of natural forest management increased from zero to 1.0 m3/ha/year. When assuming risk-aversion, however, we can hardly see an effect of including or excluding natural forest management. However, the reward-to-variability figure improves from US$ 4.40 per unit of risk (no management) to US$ 4.88 per unit of risk (with management of natural forest). It is thus likely that the inclusion of natural forest management makes its maintenance more attractive for farmers. Finally, it is important to note that the modeling results suggested only 2.3 million hectare under management (productivity assumption 1.0 cubic meter per hectare per year), while around 10 million hectares would remain unmanaged. Leaving a considerable portion of the forest unmanaged (and receiving only compensation for this area) is here preferred due to large price uncertainties for tropical timber. 4.2.3.4. Altered Riskless Yield. The achievable riskless yield is an important variable in the objective function to consider risk-aversion. When considerable areas of land can be bought and sold, land prices can rise or fall. In our modeling context this would have an impact on the achievable riskless yield, as it was assumed that land prices could be invested in a safe asset in the case of land being sold. The necessary compensation under the risk-aversion assumption becomes higher

Table 7 Possible CO2 emissions and compensation costs.

CO2 emission (in 109 Mg CO2) Compensation as 5% present value per Mg CO2 in US$

Closed primary forest

Closed secondary forest

Open forest

Risk-ignoring

Risk-aversion

Risk-ignoring

Risk-aversion

Risk-ignoring

Risk-aversion

9.9 3.08

9.3 1.25

7.0 4.51

5.2 2.16

2.4 13.03

1.9 6.13

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Fig. 5. Necessary compensation when agricultural productivity is increased. Fig. 7. Necessary compensation for various assumptions on riskless yield.

when assuming greater riskless yield, while it decreases considerably if lower riskless yield was assumed. Under the extreme assumption of US$ 100/year (Fig. 7), corresponding to a land price of US$ 2000/ha, the necessary compensation under risk-aversion increased to US$ 94 per hectare per year under risk-aversion, which is still less than the necessary compensation under a risk-ignoring scenario (US$ 124/ha/ year). However, 100 US$/year as riskless yield is already close to the risky yield of forest plantations, which ranges around US$ 105/ha/ year. A riskless yield of more than US$ 50 seems rather unlikely. 5. Discussion and Conclusions The tested “Optimized Land-Use Diversification” showed that a significant reduction of necessary compensation to avoid the loss of natural forests can be expected, when the shares of various land-use options under quantity dependent prices are optimized, and a riskaverting perspective is introduced into the financial model. The obtained compensation costs between US$ 2.16 and 4.51 per Mg avoided CO2 emission are very low, compared to carbon prices to be expected from officially accepted carbon markets, such as expected under the European Union Emission Trading System for 2012. These prices may range in the order of more than US$ 40 per Mg CO2 (Butler et al., 2009). Compensation costs are also low compared to discussed carbon taxes, which would possibly start with US$ 30 per Mg C (Nordhaus, 2007), corresponding to US$ 8.20 per Mg CO2, proceeding to rise continuously. The statement of low compensation costs even holds true if we consider that we would need additional compensation to cover transaction costs. However, this study should not be taken to imply that the derived average compensation values are valid for every country in South America. While the numerical results do show, at least on average, a realistic order (for example, Bellassen and Gitz, 2008), more attention should rather be paid to the differences in compensations due to the

new methodological approach of integrating risk-aversion and diversification, combined with the optimization of land-use shares. In this line the assumption of risk-aversion has actually led to intensified diversification of land-uses, which is consistent with riskaverting behavior (Hirshleifer and Riley, 2002). Combined with risk reducing land-use concepts that diversify into agriculture and natural forests, compensation policies could thus be relatively inexpensive compared to viewing land-uses as isolated investment options. The results obtained are at least in part supported by existing ecological economics literature. Baumgärtner and Quaas (2010) theoretically prove that farmers would implicitly increase on-farm agrobiodiversity with increasing private risks, thus providing higher levels of ecosystem services to society. The same effect could be shown in the “Optimized Land-Use Diversification” presented here, where risk-averse farmers' land-use strategy led to CO2 emissions which were 1.8 billion Mg lower than under the risk-ignoring landuse strategy. Risk-averse farmers would thus actually provide positive externalities to the society. Also in line with our study, Baumgärtner and Quaas (2010) conclude that farmers, who tend to be more riskaverse than society as a whole, require compensations lower than those derived under certainty. In addition, Di Falco and Perrings (2005) show those risk-averse farmers will actually choose higher levels of crop biodiversity than risk-neutral farmers. However, because financial subsidies can be seen as an alternative risk-reducing strategy these decisions may come down to trade-offs. Subsidies for one special crop can thus lead to reduced biodiversity, intensification and more risky land-uses. Similarly, payments for tropical conservation alone may reduce the perceived necessity to develop productive and risk-reducing land-use strategies (Knoke et al., 2008b). It is thus important to carefully combine optimized sustainable land-use strategies with compensation schemes as suggested by our paper. However, we obtained our results with a stylized financial model and we thus requiring discussion of its advantages, limitations, and development options. 5.1. Advantages of a Simultaneous Consideration of Land-use Options

Fig. 6. Necessary compensation when prices for agricultural products are increased (for identical quantities).

An “Optimized Land-Use Diversification”, as applied in this study, is capable of coping, at least in part, with the problem of endogeneity in land-use modeling. Endogeneity can be problematic, as the distribution of financial yields is often derived from the current land-use situation, with the obtained results then reused when extending the land area under agricultural crops. It is, however, likely that financial yield would decline with an extension of the area of agricultural croplands, such that the compensation values obtained by conventional methods would most likely overestimate realistic values (Benitez et al., 2006). The “Optimized Land-Use Diversification” addressed this by modeling declining financial yields for extended areas of the respective land-uses, caused by price–quantity effects in

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the study. This would be further pronounced if the area of agricultural crops were assumed to encompass less suitable sites, as would be the case in an extension of croplands to pasture sites (Benitez et al., 2006). This important effect was ignored when assuming homogeneous site conditions, although further investigation should be the focus of future studies. Declining financial yield with extending land-use area alone may not explain the considerable cost reduction from around US$ 176 to US$ 124/ha/year. The optimization of the distribution of land-use shares, which is inherent in the approach of this study, leads implicitly to an improved land-use allocation under the conservation scenario, helping to minimize compensation costs. Another advantage of an “Optimized Land-Use Diversification” is the consideration of risk reducing effects by adequate land-use diversification. It was found that one of only few prior studies where authors considered effects of portfolio-diversification when deriving compensation payments was the hitherto mentioned Benitez et al. (2006). The authors, however, contrastingly arrived at higher required compensation to avoid the replacement of the conservation option when considering a portfolio of several land-uses. Other than in the current study, Benitez et al. (2006) considered land-use portfolios which were not optimized but simply practiced by the land-users who were interviewed in their study. In such a case it may well be that compensation is also required to maintain a less than optimal allocation of land among the land-use options. The current study thus illustrates land-use optimization as an advantageous option, while accepting that optimized land-use must be implemented in practice before the considerable cost reducing effects eluded to herein can be realized (see below for further discussion). As a consequence, the simultaneous consideration of options to diversify land-uses is an important methodological extension compared to other studies (for example, Grieg-Gran, 2008; Eliasch, 2008; Butler et al., 2009). 5.2. Weaknesses and Limitations 5.2.1. Aggregation As a result of the arable land assumption with homogeneous site conditions being available everywhere and the high degree of aggregation, a dramatic shrinkage of natural forests was obtained in every scenario without compensation. Aggregation in national level studies is certainly a critical point (Kaimowitz and Angelsen, 1998) and may produce unrealistic results. However, national level studies, which usually have to use aggregated data, also have advantages. This perspective allows for making the prices endogenous and considering different and interacting sectors of land-use simultaneously (Angelsen and Kaimowitz, 1999). It shall be pointed out that our first focus was to demonstrate the effects of considering land-use diversification and risk aversion, which required the consideration of diversification options, where the aggregated risk of diversified land-uses reduced due to independent price fluctuations for the mixed land-uses. To cope with the aggregation problem in the future, one could classify areas with more or less homogeneous site conditions, determine productivities under these conditions and apply our model separately for those areas, thus allowing for a higher spatial resolution. This would result in a modeling approach where programming methods on a smaller spatial level are nested into the national level approach. The obtained disaggregation would certainly mean that a country wide forest elimination to a level below 1% land cover was unlikely, because for some ecosystems with very low land productivity, forest conversion into agricultural lands would not be profitable. For the current study, to test the effectiveness of compensation to avoid deforestation related CO2 emissions and methodological aspects it seemed justified, however, to use reference scenarios in which tropical forests are highly endangered, even if the extreme situation modeled here is – fortunately – not given everywhere.

5.2.2. Intertemporal Choices The comparative static modeling, as applied in the current “Optimized Land-Use Diversification” approach, addresses only two points in time: now and the future. However, one cannot say when the future point in time we are talking about will actually be achieved. In this line, the challenge of conducting more detailed modeling approaches at the micro-level is faced, for example for farmer households, which would also include dynamic conversion of land use and degradation processes. Only with a micro-level approach can one find out effective compensation for certain farms. For example, Carpentier et al. (2000) developed such a farm model that considers farm development over time. Given the beneficial effects of ecosystem diversification for natural forest conservation, it will be very important to include uncertainty and diversification aspects in micro-level models as well (see e.g., Knoke et al., 2009a,b) and to combine these approaches with economic values for ecosystem services in general. Instead of following a micro-level approach, the “Optimized Land-Use Diversification” has drawn a picture with aggregated data about which consequences several financial modeling approaches could have on average (national level) compensation costs, as information which is also valuable. Considering time dimensions is especially important at the microlevel, but it would introduce another controversially discussed aspect into the evaluation: A social discount rate has to be decided on to model intertemporal choices. Due to the static nature of our model, one can largely avoid this problem. However, to anticipate financial yields from forest plantations, to estimate the riskless yield and to compute present values of compensation costs, one also has to use a discount rate (which was 5%). Intertemporal aspects had to be modeled especially for forest plantations as a human made land-use option including very long time periods. When establishing forests, one first must invest, usually receiving the main proportion of money back after the production period (20 years in our case). Although it is technically possible to convert the net present value of forest investments into annuities (which was necessary for our modeling), the time dimensions of forestry would be unattractive for many land holders. However, the forest option may nevertheless make economic sense in a dynamic land use approach that considers degradation of agricultural lands (see below) or when option values of future forests are included. The long time periods involved in establishing new forests makes, though, clear that maintaining existing forests should have first priority, as the carbon effects and other benefits are obtainable immediately.

5.2.3. Statistical Endogeneity Problems Product prices and quantities are the result of supply and demand. The “Optimized Land-Use Diversification” covered – inter alia – product prices and risks as decisive variables for the allocation of land to various options and thus crucial for the quantities produced. The land-use modeling consequently considered that quantities are controlled to a large part by product prices. However, also a feedback of quantities to product prices was taken into account by means of regression curves. Based on various statistical techniques, correlated residuals and biased parameter estimates were avoided. An alternative to our model formulation would have been instrumental variable modeling techniques, which may be an option for future studies. However, there is actually evidence that our model structure, with the variable quantity as an independent, is appropriate particularly for the case of land-use, where decision agents can have important feedback effects on market prices, due to the quantities they produce (Angelsen and Kaimowitz, 1999). Moreover, a significant endogeneity effect by the variable quantity, in the sense that its observations were correlated with the residuals and that the estimated parameters were biased, was not given, which was proven by a formal “Hausman” test. One can thus assume that the statistical modeling has not produced great bias.

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5.2.4. Price–Quantity Effects for Carbon Information about price–quantity effects for carbon prices were excluded from the modeling. It is open whether or not such effects would come into play in future. Certainly, carbon management has to be seen in a broader context including the energy and transport sector. It is possible that scarcity issues are thus not so relevant compared to the opportunity costs involved in avoiding carbon emissions, as addressed in the current paper. 5.2.5. Risk Estimation It was already pointed out that our risk estimations are probably too optimistic so that the actual price variation may be greater than the price variations as modeled by a normal distribution. In addition, the bio-physical risks (such as lost crops due to drought, fire or winds, the variability in productivity and others) have been excluded. One may, however, expect that this underestimation of risks does not principally weaken the results. Rather, the diversification effects would be stronger, when risks are greater, as shown by Baumgärtner and Quaas (2010). If, for example, the yield volatilities were increased, the necessary compensation further declined. 5.2.6. Data Weaknesses Another point is that the study suffers from some data weaknesses involved with the statistics of the FAO. Especially for tropical timber the statistics contain only incomplete information so that some extrapolation was necessary. However, the extrapolated values produced plausible and not too optimistic yield estimates. Moreover, the FAO data were not recorded for scientific purposes and will contain some accounting errors, but we could use relatively many data (the number of observations used for the regression curves vary between 83 and 163) so that errors should cancel out. It is thus not to expect a great bias for the main result, that risk-aversion and -diversification would make compensations more cost-effective, from the poor quality of the used FAO data. In order to implement deforestation measures another requirement is to check whether the avoided deforestation that land-users are compensated for is actually being avoided. To solve this task, remote sensing methods may be of great help. It is already possible to implement biomass accounting at the regional and the national level (resolution 1000 by 1000 m down to 500 by 500 m) (Tollefson, 2009). Local deforestation processes can also be monitored with remote sensing methods, however, these techniques have to be further developed. 5.3. Future Perspectives and Further Development Even if land-use diversification into agriculture and natural forest management is up till now not extensively used in the tropics, mainly because of the low financial performance of the natural forests, we think that the model results have relevance and are actually applicable to increase the cost-effectiveness of compensation payments. In this line, Pohle et al. (2009) found a great willingness to economically use natural forests on a sustainable basis so as to diversify their land-use for various ethnic groups in Ecuador, even among cattle-ranching Mestizo communities, who have actually expanded pasture area significantly in order to sustain their livelihoods. The diversification effects can thus be expected also to be appreciated by farmers in South America more intensively under certain circumstances. If the profitability of holding natural forests would become more attractive by receiving compensation payments and money generated from sustainable management (at least in some parts of the natural forests), it is likely that forest conservation will be successful. However, knowledge transfers about diversified sustainable land-use concepts (see Knoke et al. 2009b) must accompany the compensation payments, to make the diversification concept a successful and really applicable option.

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The “Optimized Land-Use Diversification” approach seems not only applicable to analyze cost-effectiveness but could also be further developed to obtain synergies for climate change mitigation from REDD and biofuels, while utilizing synergies obtained from an optimum allocation of land-use options. Biofuels are principally seen as low C emission alternatives to fossil fuels. However, a prominent problem to be solved when implementing effective REDDmechanisms and climate friendly biofuel production is indirect landuse change (iLUC). iLUC can be attributed to the increased demand for biofuels, as a consequence of fossil fuels becoming scarce. As a response to the increased biofuel demand land that was formerly used to grow crops for food and feed are now used for biofuels. Food becomes scarce when the areas to produce food become more and more limited. The consequences of food scarcity are increased prices for the food products. Increased prices, in turn, boost further land conversion, as indicated also by highly increased necessary compensations to avoid deforestation under high price levels for crops in our study. These indirect effects on land-use change are increasingly viewed in a critical light, and can be modeled using the approach of this study in combination with land-use optimization. However, the available studies largely exclude land-use optimization. To model iLUC and its consequences, Searchinger et al. (2008) used a “world wide agricultural model” with updated historical supply and demand elasticities to model land use change. Here, new croplands created from land conversion correspond to historical proportions of each natural land converted to cultivation in the regarded countries since 1990. Fargione et al. (2008) use life cycle assessment (LCA) to compute the carbon dept incurred by iLUC and reveal how many years it will take for the carbon dept to be paid back. They based their evaluation of biofuels partly on scenarios from other studies. A recent study by Melillo et al. (2009) use a computable general equilibrium model of the world economy combined with a process-based terrestrial biogeochemistry model to obtain information about the importance of iLUC. Given these evaluations, economists say that LCA is not relevant for decision-making; rather a cost-benefit-analysis should be carried out to consider prices and intertemporal aspects. Following this argumentation and based on data by Searchinger et al. (2008), de Groter and Tsur (2010) develop a cost-benefit test for GHG emissions from biofuel production. However, the cited studies do not aim at finding appropriate compensations to achieve a desirable land-use development. To influence the decisions of land-users was thus not primarily focused on. In contrast to the cited studies, the presented “Optimized Land-Use Diversification” focused primarily on average compensations necessary to achieve a desirable (low emission) land-use change. The innovation is that land-users are seen as risk-averters, and may thus optimize their land-use portfolios, while mixing their land-use options to reduce risk through diversification. The “Optimized LandUse Diversification” approach is sensitive to price changes, which may be induced for agricultural crops when biofuels are produced. For future studies these effects (which we addressed with sensitivity tests) could be covered implicitly by considering also the quantities of or the areas used for biofuel production as an independent variable in estimating the prices for certain crops. If, in addition to this extension, it would be possible to allocate biofuel production to the manifold of degraded agricultural areas (e.g. by effective subsidies), the “Optimized Land-Use Diversification” methodology could combine effectiveness of REDD compensation schemes and positive climate effects of biofuel production. On degraded lands, diversified crops seem even more important for the livelihood of farmers in comparison to more fertile sites (Di Falco et al., 2007). In the availability of large areas of these unmanaged and degraded agricultural lands (around 20% in our initial land-use portfolio) one can generally see a large opportunity to mitigate land-use problems. This would be particularly effective, if

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biofuels will be obtainable from the cellulose that can, for example, be gained from timber. While intensification of managed agricultural lands would certainly increase the pressure on the still existing natural forests, we propose either to revitalize the abandoned lands or to reforest them with nitrogen fixing tree species and using them as rehabilitated agricultural lands after one rotation of trees (e.g. Knoke et al., 2009a). The reforestation option will help in reintegrating degraded lands back into the economic production process. However, as Knoke et al. (2009b) pointed out, this would require low-interest credits and financial incentives to bridge the first ten years, when no financial yields can be expected from forest plantations. If this problem is solved, for example by payments for carbon storage in maintained natural forests, a diversified land-use concept that builds upon reforestation of abandoned farm lands and natural forest management may even be financially superior in regards to farm net present value, when compared to a classical, deforestation based land-use systems (Knoke et al., 2009a). However, these restoration and revitalization options must also still be integrated in the modeling approach. To close our paper we shall make clear that price–quantity effects and risks so far play only a minor role in economic models that analyze land-use change and the related C emissions. For example, Upadhyay et al. (2006) reported little information regarding the relevance of price–quantity effects and risks in their comprehensive review of models used to analyze land-use change. Our study showed that the low attention that has so far been paid to these topics is inappropriate. The strong positive effect of diversification on the cost effectiveness of compensation payments, combined with restoration based sustainable land-use concepts could make concepts to reduce C emissions from deforestation really a viable option. We thus strongly support the conclusion by Wise et al. (2009, p. 1185) that: “Improved land-use management and improved agricultural practices could reduce upward pressure on crop prices and the costs of emissions mitigation. However, the allocation of scarce land resources to competing ends will remain a major challenge for the 21st century.” Acknowledgements We are grateful to the “Deutsche Forschungsgemeinschaft” (DFG) for financial support of the study (KN 586/5-2) and to the members of the research group FOR 816 whose research initiative made the study possible. We are also grateful to two anonymous reviewers and Baltazar Calvas for helpful comments as well as to Kristin Dzurella, Arman Schwarz, and Laura Carlson for the language editing. References Angelsen, A., Kaimowitz, D., 1999. Rethinking the causes of deforestation: lessons from economic models. The World Bank Research Observer 14, 73–98. Barrett, C.B., Bezuneh, M., Aboud, A., 2001. Income diversification, poverty traps and policy shocks in the Côte d'Ivoire and Kenya. Food Policy 26, 367–384. Baumgärtner, S., Quaas, M.F., 2010. Managing increasing environmental risks through agrobiodiversity and agrienvironmental policies. Agricultural Economics 41, 483–496. Bellassen, V., Gitz, V., 2008. Reducing emissions from deforestation and degradation in Cameroon — assessing costs and benefits. Ecological Economics 68, 336–344. Benitez, P.C., Kuosmanen, T., Olschewski, R., van Kooten, C., 2006. Conservation payments under risk: a stochastic dominance approach. American Journal of Agricultural Economics 88, 1–15. Benitez, P.C., McCallum, I., Obersteiner, M., Yamagata, Y., 2007. Global potential for carbon sequestration: geographical distribution, country risk and policy implications. Ecological Economics 60, 572–583. Biradar, C.M., et al., 2009. Global Map of Rainfed Cropland Areas (GMRCA) and Statistics Using Remote Sensing. In: Thenkabail, P.S., Turral, H., Biradar, C.M., Lyon, J.G. (Eds.), Remote Sensing of Global Croplands for Food Security. CRC Press, Taylor & Francis, Boca Raton, p. 373. Taylor & Francis Series in Remote Sensing Applications. BMELV (Bundesministerium für Ernährung, Landwirtschaft und Verbraucherschutz), 2007. Agrarbericht 2007. http://www.bmelv-statistik.de/fileadmin/sites/030_Agrarb/ 2007/AB07kompl.pdf. accessed 20.01.2010. Butler, R.A., Koh, Lian Pin, Ghazoul, J., 2009. REDD in the red: palm oil could undermine carbon payment schemes. Conservation Letters 2, 67–73.

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