Forest Conservation and CO₂ Emissions: A Viable Approach

Abstract

We adopt viability theory to assess the sustainability of the world’s forests while taking into account some of the competing economic, social, and environmental uses of these forests, namely, timber production, poverty alleviation through agriculture, and air quality as well as the negative externalities that these uses create. We provide insights on the different trade-offs faced to achieve sustainability and draw some policy implications as to what is the path leading to sustainability in the long run.

Appendix: Variables Description

We provide in this appendix details regarding the construction and measurement of the model's variables and the estimation of parameters' values.

1.1 State Variables

F :

Forest Surface

Forest surface in the world measured in hectares. The current stock of forest is estimated by FAO [19] at 3,952 million ha in 2005. Parameter F _max has been estimated for 1750 AD at 42% of the globe's surface¹⁶ (i.e., 13,067 million ha excluding Antarctica and Greenland). This gives us a value for F _max of approximately 5,500 million ha. Consequently, we require that $F_{t}\in \left[ F_{\rm{min}}, F_{\rm{max}}\right] =\left[ 0\cdot 10^{9}\text{~ha}, 5.5\cdot 10^{9}\text{~ha}\right]$.

E :

Yearly emissions of CO₂

These are world yearly emissions of CO₂ measured in metric tons. In 2005, total CO₂ emissions amounted to 28.2 Gtons.¹⁷ Minimum emissions are set to equal 1990 emission levels, i.e., 21.4 Gtons. The value of maximum emissions used plays a minor role. It has been set to equal the double of 1990 emissions. The reason to choose a maximum is simply the need to have bounded states. Hence, the constraint reads E _t  ∈ [ E _min,E _max] = [21.4 Gtons CO₂, 42.8 Gtons CO ₂].

S :

Cumulated Quantity of CO₂ in the Atmosphere

The cumulated stock of carbon in the atmosphere is measured in gigatons. The atmospheric stock of carbon has been estimated to be approximately equal to 800 Gtons CO in 2005. The current concentration of carbon measured in parts per million was approximately 379 ppm in 2005.¹⁸ The upper bound value is set at 650 ppm i.e., 1,372 Gtons CO. The lower bound has a negligible impact on the solution. We have set it at preindustrial levels, that is 284 ppm (i.e., roughly 591 Gtons CO) in year 1832. In short, we want S _t  ∈ [ S _min,S _max] =[591 Gtons CO, 1,372 Gtons CO]≡ [2,167 Gtons CO₂, 5,031 GtCO₂].

1.2 Control Variables

ρ :

Yearly Reforestation $[\rho _{\rm{min}},\rho_{\rm{max}}]=[0\cdot 10^{6},\;3\cdot 10^{6}]$

For the period 1990–2005, FAO [19] estimates world yearly reforestation at 2.8 million ha. We let reforestation vary between no reforestation and 3 million ha/year.

d :

Yearly Deforestation $[d_{\rm{min}},d_{\max}]=[0\cdot 10^{6}, 15\cdot 10^{6}]$

For the same period, FAO [19] estimates the average global deforestation rate at 13 million ha/year. We let deforestation vary between zero and 15 million ha/year.

v :

CO ₂ Emissions Adjustment Rate [v _min,v _max] = [ − 0.015, 0.03]

During the decade going from 1990 to 2000 world's CO₂ emissions increased at roughly 1%/year.¹⁹ Only a few countries like Germany, United Kingdom, Denmark, Finland, some Eastern European countries, and former Soviet Republics were able to reduce their emissions. In particular, Germany achieved a 1.8% yearly cumulative decrease. On the other hand China's emissions increased at a rate of 3% per annum. All the other big economies lie somewhere in between. Between 2000 and 2008, however, world emissions have increased at a faster rate, 3.4% year^− 1, [24] with a probable decrease during the next 2 years (2009--2010) due to the world crisis. Following these observations we have set both the lower and upper bounds on v. As a benchmark scenario we have chosen v ∈ [v _min,v _max] = [ − 0.015,0.03].

T :

Monetary Transfers

Monetary transfers to forest owners expressed in 2005 US dollars. Unless otherwise specified, transfers are set constant and equal to zero, T = 0.

1.3 Other Parameters

η :

Natural Growth Rate of the Forest

FAO [19] gives estimates of net yearly afforestation (5.7 million ha) of which a fraction is due to human reforestation and the rest belongs to the natural renewal of the forest. Human reforestation ρ is estimated at 2.8 million ha, meaning that the term $\eta \cdot \left( 1-\frac{F}{F_{\rm{max}}}\right) \cdot F$ has been, on average, equal to 2.9 million ha during this period. If we substitute F by its value for the last years and F _max by the value pointed above we obtain η = 2.61·10^− 3.

φ :

Carbon Absorption Rate by Forests

This parameter is measured in metric tons of CO₂ equivalent absorbed per hectare of forest per year. According to Le Quéré et al. [24] during the decade from 1990--2000 forests absorbed 2.6 PgC year^− 1 (i.e., 2.6 Gtons CO) which amounts to 9.53 Gtons CO₂. Considering that world total forest surface equals 3,952 million ha, we can estimate average yearly carbon sequestration at 2.412 tons of CO₂ ha^− 1 year^− 1.

W :

Carbon Absorption Rate by Oceans

Accounts for the amount of carbon absorbed by oceans every year. According to Le Quéré et al. [24], the oceans were able to sink on average 2.2 PgC year^− 1 for the period 1990--2000, this is equivalent to 8.07 Gtons CO ₂ year^− 1.

$\underline{R}$ :

Minimal Revenue of Land Owners

Measured in US dollars. We denote $\underline{R}$ as the current or status quo revenue. We compute $\underline{R}$ by substituting in Eq. 9 the current values of all the variables and parameters in our model.

$\underline{q}$ :

Minimum Timber Supply

Minimum timber supply is measured in m³ of timber per year. Current timber supply is estimated by FAO [19] equal to 1,623 million m³ year ^− 1 of industrial roundwood and 1,777 million m³ year^− 1 of fuelwood. We estimate minimum timber supply to be equal to current timber supply, i.e., 3,400 million m³ year^− 1.

n :

Timber Yield

The timber yield is measured in m³ ha¹ year¹. We use the average world Figures given by FAO [19], i.e., n = 110/ha of growing stock.

β :

Lower Productivity due to Forest Depletion

Lower agricultural yield measured in tons per hectare. Eswaran et al. [15] estimate the loss in productivity as a consequence of land degradation, erosion and desertification. They report that the productivity loss due to such processes in Africa ranges between 2% and 40% and provide an average estimate for the whole continent to be equal to 8.2% in average. If average productivity is $\overline{Z}$ then β is equal to 0.061.

γ :

Selective Logging Yield, Fraction of Average Yield

The selective logging yield is measured as a fraction of average yield. When forests are managed for wood production they produce as much as 1--3 m³/ha (in other words n·γ = 1 − − 3 m ³). We have set the value of γ = 0.015.

δ :

Fraction of Forests Selectively Logged

Share of the world's forests selectively-logged. Following FAO [19], parameter δ has been calibrated at 30% (i.e., δ = 0.30) to fit the world yearly production of wood q.

θ :

Slope of Wood Demand

According to FAO [19], the commercial value of all wood (i.e., roundwood and fuelwood) in 2005 was $64 billion/year of which only 7 billion correspond to fuelwood. World production equals 3,400 million m³. The average price for both types of wood is $18.8/m³. FAO [16] gives the elasticity of demand for several countries and several types of wood.²⁰ A representative value of both the mean and median price elasticity of wood is −0.50. We have approximated an iso-elastic curve by a linear one in an interval of 2,000 million m³ centered at 3,400 million m³ such that the average elasticity inside the interval equals −0.50. The slope of our demand can be then computed accordingly to obtain θ = − 2.7·10⁹.

$\overline{P}$ :

Choke Price of Wood

With the average price of wood and the slope of demand computed above, we can retrieve the choke price of our inverse demand function and obtain $\overline{P}=27.98$ (US $/m ³).

ψ :

Extra Productivity of Deforested Land

Parameter ψ denotes the productivity gain of land after deforestation. It is measured as a fraction of average productivity. A reasonable range for ψ suggested in the literature is 0.2 − 0.5. We adopt ψ = 0.3.

κ ₁ :

Per-Hectare Reforestation Cost

Parameter κ ₁ denotes the reforestation cost per hectare of forest. According to the World Bank the cost for seedling is roughly $40 per thousand seedlings and the number of seedlings per hectare is equal to approximately 2,000. This amounts to approximately $80/ha of forest just for seedling. Reforestation costs, however, also include other costs such as labor costs that change with countries. The World Agroforestry Centre gives estimates for the Philippines around $1,000/ha, other NGO organizations provide estimates that range between $180/ha for Senegal and $400--500/ha for other countries in Africa such as Sudan, Madagascar and Ethiopia.²¹ We have chosen the round value of $500/ha that is representative of the average cost taking these different observations.

κ ₂ :

Per-Hectare Deforestation Cost

Parameter κ ₂ denotes the deforestation cost per hectare of forest. The Bureau of Business and Economic Research of Montana University estimates the costs of ground-based logging to be equal to $22.70 for every green ton of harvest for the year 2006.²² Considering that a green ton is equivalent to 2,000 pounds of undried biomass material (i.e., 907 kg) and that the density of wood is typically 500 kg/m³, then for a representative douglas fir plantation (530 kg/m³), we obtain that the deforestation cost is equivalent to $13.26/m³. If the yield per hectare is equal to 110 m³/ha, then we obtain an estimate of the deforestation cost per hectare of $1,459/ha.

P _A :

Average Price of Representative Agricultural Product

Measured in US dollars per metric ton. To determine the average price of the representative agricultural good, we took four representative commodities (i.e., cocoa, coffee, cotton, and sugar) from FAO [18]. Coffee and sugar in Brazil and Latin America and cotton and cacao in Africa are four crops that are related with deforestation processes. The net economic yield per hectare of crop ranges from $1,660/ha for coffee to $771/ha for cocoa. The average yield equals $1,141/ha. We have chosen the price of cotton to be the representative price of the agricultural good since its prices and economic yield ($1,467 per metric ton and $1,088/ha) are the closest to the mean.

$\overline{Z}$ :

Average Land Productivity

Measured in tons per hectare. The average yield has been computed taking into account the yield of those same four crops in metric tons per hectare and annum as mentioned before. The estimated annual yield per hectare is equal to 0.742 metric tons/ha.