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# Economics of Reforestation and Afforestation

## Summary and Keywords

Reforestation is the natural or intentional restocking of existing forests and woodlands that have been harvested or depleted, and afforestation is the establishing of a forest in an area where there were no trees. For economic and practical purposes, reforestation and afforestation have similar goals and processes and thus can be treated as identical activities. Although reforestation and afforestation have a long history, large-scale reforestation and afforestation activities started with industrialization, which caused scarcity in timber and forest-based ecosystem services. In a unified economic model of reforestation and afforestation, factors influencing investments in reforestation and in afforestation on private and public lands include timber prices, unit reforestation cost, interest rate, the responsiveness of tree growth to silviculture, and the value of nontimber benefits, such as ecosystem services. Market and public policies may facilitate, enhance, or hinder reforestation and afforestation activities, and nontimber benefits are an increasingly important motive for reforestation and, especially, afforestation efforts around the world.

# Introduction

Reforestation is a follow-up and counteraction to purposeful timber harvesting and unintentional forest destruction, and afforestation means establishing a forest in an area where no trees have existed in the immediate past. Natural and planted forests are purposefully or unintentionally harvested, degraded, or depleted in many parts of the world every year; therefore there is a need to establish new forest crops that meet individual landowners’ and societal demand for forest products and for various forest ecosystem services. The act and processes of renewing forest or tree cover either naturally or artificially are called “reforestation.” Natural reforestation is accomplished through natural seeding and coppicing or root suckers, and artificial reforestation includes direct seeding and tree planting. Similarly, because many areas that do not have trees or whose previous land uses were not forest may need tree cover for various economic and environmental purposes, afforestation ensures that these areas become forests.

Since reforestation and afforestation have the same underlying economic motives, processes, and economic and ecological impacts—they are done when forestry is the highest valued use of land, and when the present value of expected benefits of reforestation exceeds that of the costs, and they are done in the most efficient fashion. All reforestation and afforestation methods and activities—natural and artificial—can be analyzed under a profit-maximization framework to land, which is to maximize land expectation value.

# A Brief History of Reforestation and Afforestation Economics

Reforestation often occurs naturally following natural and human disturbances to forests. Thus, reforestation has a history that extends back as long as there have been forests on earth. However, reforestation and, especially, afforestation connote purposefulness and a human dimension, implying that they only started with human civilization and for human uses. Indeed, people have been planting trees for food or other nontimber forest products and for shelter, ornamental, ceremonial or religious purposes for thousands of years (Evans, 2009). Olive trees have been cultivated in Greece at least since the Minoan era (3000 bc), and fruit trees and pines were used for ornamental, religious, and ceremonial purposes in China as long ago as 2000 bc (Valder, 1999).

By contrast, large, industrial-scale reforestation and afforestation started only with industrialization process, which caused significant reduction and depletion of natural forests and timber scarcity in some parts of the world, such as England and Germany. In 1713, a German forestry administrator, Hans Carl von Carlowitz, published a book, Silvicultural Economics or the Instructions for Wild Tree Cultivation (Sylvicultura Oeconomica oder Anweisung zur wilden Baum-Zucht). Carlowitz managed the mining industry in Freiberg, Germany, on behalf of the Saxon Court, and he was responsible for ensuring the timber supply for the mining industry in the region. Despite the court’s forest order and regulations limiting timber harvesting, the impact of over-harvesting and timber shortages on Saxony’s silver mining and metallurgy industries was devastating in the early 1700s. Carlowitz thus formulated the idea for the “sustainable use” of the forest—limiting the annual quantity of the timber harvests based annual timber growth and promoting as timber growth through planned reforestation projects. Carlowitz’s idea remains an important guiding principle of modern forestry and sustainability. It also points out that reforestation is the key to increasing timber production.

In 1849, another German forestry administrator, Martin Faustmann, published a seminal article on land expectation value, “Calculation of the Value which Forest Land and Immature Stands Possess for Forestry.” Faustmann’s article defined a method for assessing the taxable value of land used for forestry purposes. He was the first person to correctly formulate a land-expectation-value formula—now called Faustmann formula—for valuing land, which is still used today. A few decades later, other scholars, notably Ohlin (1921), independently came up with the same formula. Faustmann’s article was noticed by some foresters and forest economists in the middle of 20th century (e.g., Gaffney, 1957). But it was after the article was translated into English, in 1968, that his formula really started to attract greater attention and research, first in optimal rotation age, and lately in the economics of reforestation.

Faustmann’s original formulation of land expectation value relies on natural regeneration and clearcutting, and is thus an even-aged forest management regime. In fact, he assumed that a piece of land that was unused might be used for forestry, and thus he implied an initial afforestation and follow-up reforestation after timber harvesting in the future. Hartman (1976) called on policymakers and researchers to pay attention to nontimber value, though this value had explicitly been noted in Faustmann’s original article. There may have been several publications in German that dealt with artificial regeneration in the late 19th century and the beginning of the 20th, but Hyde (1980) was the first to add a component—silvicultural investment—to the Faustmann formula in the English literature, making it suitable for analyzing artificial reforestation as well. Chang (1981) proved that Faustmann formula also applies to uneven-aged timber-stand management. Li and Zhang (2007) worked on the second derivatives of the Faustmann formula and pointed out factors influencing tree planting in the United States. Zhang and Pearse (2011) incorporated a silvicultural investment model into a forest economics textbook.

Sedjo (1980) looked empirically at the competitive and comparative advantage of planted forests in various parts of the world. Enters and Durst (2004) investigated how governments could incentivize tree planting activities in the Asia-Pacific region, and Carle, Ball, and Del Lungo (2009) summarized global planted-forest development. Zhang, Stenger, and Harou (2015) provided a unified theme of planted-forest development, derived the theoretical impacts of various policy instruments, and demonstrated the use of a planted-forest development model at a macro or country level through a comparative study of four countries on four continents—China, the United States, Brazil, and France—that collectively account for more than 40% of global planted forests in 2010. Maathai (2003) described the experience and approach of grass-roots tree planting activities in Kenya, known as the Green Belt Movement, which have economic, ecological, and political motives. In developing countries, many reforestation and afforestation activities are carried out by communities for the purposes of fuelwood production and various environmental services, not for industrial timber.

# An Economic Model for Reforestation and Afforestation

The economic model for reforestation and afforestation is based on the economic model of planted-forest development in Zhang and Pearse (2011) and Zhang, Stenger, and Harou (2015). Again, this model can be used in natural reforestation if the optimal growing stock left after partial harvests to facilitate reforestation is treated as a “tree planting cost” (Chang, 1981). In both natural and artificial regeneration, forestry is the highest and best use for land, at least until timber is harvested. If not, the land will be changed for other uses. If forestry use—for the purpose of timber production and ecosystem services—is the highest valued use, it is possible to look at the case of successive rotations on the same land, or “perpetual forestry.”

All cases of reforestation and afforestation start on bare land. Basically, reforestation (or afforestation) happens if the present value of the future benefits of reforestation (or afforestation) is greater than the costs of reforestation (or afforestation). As in Zhang and Pearse (2011), it is assumed that all additional silvicultural investment made after initial reforestation can be discounted to year 0, or the beginning of reforestation, using the interest rate of a representative landowner. In this way, all subsequent silvicultural investments can be added to and treated as part of the reforestation cost, and thus can be perceived as only occurring at the time of reforestation (year 0).

This reforestation cost variable is further broken down into two parts: total reforestation effort (E), and unit cost of reforestation effort (w). The former is a decision variable for the representative landowner; the latter is often exogenous and market-driven but may be influenced by government policies. Similarly, there is only one final harvest, and all revenues before the final harvest are compounded to and thus treated as only occurring at the time of final timber harvest. These assumptions merely make the model more flexible in derivation.

The economics of reforestation can be demonstrated using Faustmann formula. To look first at the economics of reforestation and afforestation for the purpose of timber production only: assume that the representative landowner chooses appropriate trees to plant, uses proper spacing, and understands the silvicultural options available to him: the timber-production function for a given hectare of planted forest is

$Display mathematics$
(1)

where Q is standing timber volume, which is a function of stand age, t, and the level of reforestation effort, E.

Assume that r is the discount rate for the landowner, and that P is the expected stumpage price, the net present value of the total revenue stream for each hectare becomes

$Display mathematics$
(2)

As each hectare of land used for forestry has an opportunity cost, which is the amount the owner forgoes by not renting or selling the land to someone else. The landowner expects that by using the land for growing trees, it will produce revenues sufficient to compensate him for all the forgone opportunities. In economic terms, this is the “land rent forgone.” The value of the land used to grow trees for t years is the sum of all annual land rent, R, discounted to the present:

$Display mathematics$
(3)

Thus, the complete economic model for reforestation is to maximize the land value, V, in the following equation

$Display mathematics$
(4)

In general, land rent, R, is unknown, and without it, neither optimal rotation age nor optimal reforestation investment can be determined. Where land can generate a higher and better use than forestry use (such as development) after the first rotation, a land use change and deforestation would occur. Where forestry is the highest valued use, both at the present time and in the future, there is an alternative to Equation 4, which is to deal with successive rotations on the same land, or perpetual forestry:

$Display mathematics$
(5)

Equation 5 could be simplified as

$Display mathematics$
(6)

where LEVT stands for land expectation value for timber only.

The first order condition of Equation 6 with respect to E is

$Display mathematics$
(7)

where QE is the partial derivative of Q with respect to E.

In economic terms, Equation 7 states that the optimal level of reforestation or afforestation investment is reached when the marginal revenue (or the marginal revenue product of the reforestation effort) is equal to the marginal cost of the reforestation or afforestation effort, w. Obviously, the optimal condition in Equation 7 should be satisfied at the reforestation or afforestation effort, E, as well as the optimal rotation age, t. Following a change in stumpage price, P, interest rate, r, or the growth effect of the reforestation effort, QE, both the optimal reforestation effort, E, and the optimal rotation age, t, could change. Yet, the impact of most of the economic and biological factors on the optimal E is indeterminate unless one makes additional assumptions about the growth-yield function, Q(t, E) (Chang, 1983).

Nonetheless, as Chang (1983, p. 273) notes, “on the occasions when the impacts of changes in parameters are theoretically uncertain, available empirical evidence suggested that the results generally tend to be the same as those obtained when the answers are definite.” Chang (1983) indicates that reforestation effort, E, rises with stumpage prices (P) and falls with interest rate (r) and unit reforestation cost (w) when the answers are definite. As QE and P have a multiplication relationship in Equation 7, the impact of QE on total reforestation or afforestation effort, E, should be positive as well. This is to say, when the responsiveness of timber growth to reforestation effort (QE) increases, the reforestation or afforestation effort increases. This responsiveness is mainly determined by land productivity, the genetic traits of tree species, and the reforestation techniques chosen. As the landowner is assumed to choose the right species and appropriate reforestation or afforestation techniques for a given site, QE rises along with public and private research and development investment in tree breading and reforestation techniques.

Some forests are created mostly, if not exclusively, for nontimber benefits, especially environmental benefits. Thus an economic model for reforestation that is only for nontimber values is considered.

Here nontimber values include all nontimber benefits that private landowners and the public can enjoy from a forest. The portion of these nontimber benefits that are captured mostly by the public (instead of, or in addition to, those captured by private landowners) are often called “environmental services” or “ecosystem services.” Each of these nontimber values is related to the age of the forest, but the exact relationship varies (van Kooten & Folmer, 2004). More importantly, aggregating all these benefits at various ages may produce a complicated relationship (Robert & Stenger, 2013; van Kooten & Folmer, 2004). However, these benefits must be positive in aggregate. Otherwise, there will not be such a thing as positive externality or environmental benefits associated with a forest, and there is no need to do reforestation or afforestation at all.

As in the case for timber production only, it is assumed that the landowner understands that nontimber benefits are related to a myriad of factors, such as the tree species to be planted, biodiversity and ecological impacts of tree species, the responses of trees to different silvicultural treatments and the suitability of the land for tree planting and land productivity. Timber benefits accrue only at the end of rotation when trees are harvested; whereas nontimber benefits accrue continuously or annually. Suppose that the nontimber values of a forest up to age t and reforestation effort E are given by an accumulative function, N(t, E),

$Display mathematics$
(8)

where n(t, E) is the nominal (not discounted) nontimber value at a given age, t, and given reforestation effort, E.

Our objective is to choose the level of reforestation/afforestation effort (and consequently the level of reforestation or afforestation investment) that maximizes the discounted stream of such benefits, recognizing that these benefits fall to zero each time the forest is cut.

$Display mathematics$
(9)

where Vn is capitalized, or net present value of, nontimber values in perpetuity.

The first order condition of Equation 9 is

$Display mathematics$
(10)

Equation 10 shows that when only nontimber benefits are produced from a forest, the optimal level of reforestation or afforestation effort is reached when the marginal benefit of effort is equal to the marginal cost of the effort, w.

Now, considering that the landowner receives both timber and nontimber benefits, the land expectation value becomes

$Display mathematics$
(11)

Equation 11 is an extension of the Hartman formula (Hartman, 1976), with the term representing reforestation investment added on. The optimal condition for reforestation effort (investment) is then

$Display mathematics$
(12)

Compared to Equation 7, Equation 12 means that when considering both timber and nontimber benefits, the marginal revenue of reforestation or afforestation effort increases, causing an increase in reforestation effort (investment). Further, the higher the nontimber values, the more reforestation or afforestation effort (investment) should be. This result explains where some community- or government-funded reforestation and afforestation projects are for additional, even mainly, nontimber benefits, especially environmental services. As private landowners often do not capture many parts of the nontimber benefits (the environmental benefits) of planted forests (or natural forests, for that matter) and as public demand for environmental services generally rises along with per-capita income and population, governments often step in by directly planting trees on public lands or by offering private landowners incentives to plant trees on private lands.

Although the economics of reforestation and afforestation have been illustrated by separating timber and nontimber benefits, both types of benefits are usually jointly produced from the same forests. However, the production function for nontimber benefits, especially environmental services, is often complicated and even unknown (Hyde, 2013). Furthermore, most forest-based environmental benefits are not priced. Therefore, to the extent that private or public landowners want timber benefits—a private good—some environmental services are freely supplied. In other words, a certain level of environmental services can be supplied when their prices are zero. For any amount of services that is beyond this level, there would be an opportunity cost for the landowners for sacrificing timber production. Who pays the landowners for supplying the environmental services when their opportunity costs are positive and what the prices should be are the subject of the chapter on payments for ecosystem services.

# Factors Influencing Reforestation and Afforestation on Private Lands

Equation 12 shows that reforestation or afforestation is influenced by

• expected stumpage prices, P

• unit reforestation cost, w

• interest rate, r

• the responsiveness of tree growth to silviculture, QE, and

• the value of nontimber benefits, including ecosystem services that are often external to the landowners $(d∫0tn(t,E)e−rtdE)$.

Although the first four factors are mostly market-driven and exogenous to individual landowners, various government policies can directly and indirectly influence them, and thus provide positive or pervasive incentive for these landowners to reforest. The last factor is often an externality to the individual landowners and requires even more government intervention.

This relationship is shown in Figure 1, which shows that reforestation effort (and reforestation investment) increase as stumpage prices rise. Similarly, lowering the interest rate, increasing the responsiveness of tree growth to silviculture, or adding the nontimber benefit (not shown) will also cause the marginal revenue product curve to shift to the right, thereby causing an increase in reforestation investment. At the same time, reducing the unit reforestation cost will cause the intersection point of unit reforestation cost curve and the marginal revenue product curve to move to the right, which is to say that there will be an increase in reforestation investment.

Click to view larger

Figure 1. Optimal reforestation effort, E*, changes when stumpage price increase from P0 to P1.

Stumpage prices reflect the level of timber scarcity and are mainly a market phenomenon. As a country’s natural forests decline, stumpage prices rise, which leads to more reforestation. Stumpage prices are also influenced by government taxes and fees, because private landowners are mostly interested in the after-tax prices and after-tax returns. Finally, government regulations and land withdrawal from timber production could lead to timber scarcity in the short run and in the long run, thereby raising expectations for future stumpage prices, which in turn could have a temporary or long-lasting effect on reforestation.

Government economic incentives, such as subsidies in form of direct cash payments, low-interest loans, or technical assistance, reduce the unit reforestation costs of landowners. Macroeconomic and policies may affect interest rates on the market and of private landowners. For example, government afforestation and reforestation tax credits (meaning that landowners can earn credits against their income tax liability), a policy used in the United States and other countries, reduce the interest rates of money spent in tree planting. In fact, because of the “use it or lose it” nature of the tax credits, if the money spent on tree planting is within the limit of the tax credits, from the landowners’ perspective the money spent on reforestation is free. Finally, government actions responding to rising societal demand for environmental services and private and public investment in research and development in tree breeding and silvicultural techniques could provide positive or negative incentive for landowners to develop planted forests.

Thus, reforestation (or afforestation) investment is influenced by natural and market factors and government policies. On private lands, it is influenced first by market factors (stumpage prices, unit reforestation cost, and prevailing market rate of interest), and then by government fiscal policies (tax rates, tax credits, interest rates, subsidies, technical assistance) and regulatory policies (regulations and land withdrawals). More importantly, because forestry is a long-term investment, institutional arrangements, such as secure property rights, are essential for attracting private reforestation (or afforestation) investments (Zhang & Stanturf, 2008). It is through these fiscal and regulatory policies and institutional arrangements that governments affect private investment in planted forests. The results of these comparative static analyses are applicable in dynamic settings.

# Reforestation and Afforestation Decision-Making on Public Lands

Most forests in the world are owned by public entities (Food and Agriculture Organization, 2016). Although the factors influencing private reforestation investment also influence reforestation investment on public lands in the same direction, the magnitude of these market and policy factors may be different under various institutional arrangements. More importantly, as Zhang and Pearse (2011) noted, depending on how the public forestlands are used and managed, the way that a reforestation and afforestation investment decision is made on public lands is quite different from that on private lands. Generally, reforestation and afforestation activities on public lands are made by public agencies which may do these activities themselves or by contracting with private firms or by private entities that hold tenure rights on public lands. In the latter case, the private entities may be reimbursed for their reforestation and afforestation costs or not.

First, when public forestland is directly managed by a government forest agency, the agency conducts its own reforestation and silvicultural activities. The agency may have the equipment and labor to do all of the work, or it may contract some jobs out to private firms.

When public forestland is directly managed by a government forest agency, the amount of reforestation investment is allocated through a government appropriation process: reforestation projects have to compete with all other public projects for funding. In theory, this ensures that all public expenditures—including spending on education, healthcare, and transportation infrastructure—are assessed based on identical economic and social criteria. In practice, economically beneficial reforestation projects may be sacrificed for noneconomic reasons, and reforestation may be done on land that cannot yield a net return. Stated in another way, reforestation may be done for the purpose of providing jobs and other political consideration rather than based on benefit-cost calculation. Tree planting on public forestlands in Russia and many other countries is the responsibility of government forestry agencies.

Additionally, the government forestry agency, like all government agencies, tends to maximize its budget rather than focus on economic efficiency. Empirically, governments in various parts of the world have established so-called “permanent” silvicultural programs funded by revenues from timber sales to support reforestation and other silvicultural investments. Few of these programs have lasted long, and consequently this source of reforestation funding has proven to be unstable.

Second, when public forests are used and managed by private individuals and firms through various tenure arrangements, the government may require the tenure holders, under the terms of their tenure contracts, to conduct reforestation after timber harvesting, the costs of which are reimbursed afterward. These arrangements require a process for planning, approving, and inspecting reforestation activities; the incentive for the tenure holders who conduct reforestation is to pass the inspection and get reimbursed.

Finally, governments can require tenure holders in public forests to reforest with their own money after the approved timber harvesting. Often, the tenure holders are required to make sure that trees reach certain standards (such as the “free to grow” standard, meaning that seedlings or trees free from direct competition from other vegetation) within a certain period of time. Because tenure holders are required to make the reforestation investment on public lands and cannot recoup the benefits of future timber growth, they tend to lower their bidding prices for the right to harvest public forests. These tenure holders thus treat reforestation investment as a cost of obtaining public timber. Although this approach could eliminate the need for a large public-forest bureaucracy and ensure that all cutover lands are reforested, reforestation investment is based not on the present value of the future benefits it may bring but is treated as a condition or cost to secure the right for harvesting the current timber stands. As a consequence, some inefficiency arises when reforestation investment is made in places where it should not be made based on economic principles, or when the amount of reforestation investment is not optimal. Again, since the tenure holders often do not expect to benefit much from the next forest crop, they have little incentive to invest more than the minimum required by the government regulation or that is needed to pass future government inspection.

# Conclusions and Discussion

Purposeful reforestation and afforestation through natural and artificial means has been going on for thousands of years, even though large-scale reforestation started along with industrialization that depleted of natural forests in some parts of the world. In this chapter, the framework of maximizing land expectation value is applicable to continuing and perpetual forestry and covers artificial reforestation, which gives rise to even-aged forests, and natural regeneration, which may lead to uneven-aged forests. In cases where land can generate a higher and better use than forestry use, a land-use change and deforestation would occur; and reforestation and afforestation, if they are done, are mainly for environmental services, in one full rotation or less than one full rotation.

Scarcity in timber and forest-related environmental services causes private and public landowners to reforest and afforest, and there are appropriate government policies to facilitate reforestation investment. In particular, rising stumpage prices, the responsiveness of tree growth to silviculture and, especially, demand for environmental services, and falling interest rates and unit reforestation costs can attract more reforestation. Thus, reforestation is undertaken when there are favorable market conditions and high demand for environmental services. Government fiscal, monetary, and regulatory policies affect market variables. Governments could use fiscal policies, such as tax incentives and cost-share (subsidy) programs to facilitate planted-forest development, even though the primary goal of some cost-share programs may not be forestry or reforestation per se.

Governments could also use other policies that indirectly influence planted-forest development. Fire suppression and research on tree breeding, pest and disease control, and silvicultural techniques can enhance economic returns of reforestation. Environmental regulations, too, can indirectly signal timber scarcity and raise the expectation of higher future timber prices, and thus facilitate reforestation. Most importantly, because reforestation and afforestation are a long-term investment, sound institutional arrangements such as secure property rights, a well-functioning stumpage market, and a good forestry-governance mechanism could reduce the transaction costs for landowners and facilitate their reforestation and afforestation activities. The experience of countries where a lot of reforestation and afforestation activities take place shows that market and policy factors have significant impacts on reforestation, increases in forest area and standing-timber volume, and natural forest conservation. Positive policy incentives for reforestation and afforestation need to be promoted in other parts of the world.

Although the goals of reforestation and afforestation activities and projects are timber and nontimber benefits in general, the primary motivation of each may differ. In particular, afforestation may be undertaken more for the nontimber benefits because the negative impacts of deforestation on the provision of environmental services and the need for afforestation may only be realized long after deforestation has occurred. For example, the afforestation campaign in the U.S. prairie states under the Prairie States Forestry Project in the late 1930s and early 1940s was carried out only after the Dust Bowl had caused significant ecological and economic damage in the region (Zhang, 2004). The Three-North Shelter Forest Project in China was started in 1978 when the Chinese government realized that the lack of tree cover in Northern China had disastrous consequences, such as drought and desertification (Zhang, 2003). The Great Green Wall in 11 Sahelo-Saharan states in Africa (Burkina Faso, Djibouti, Eritrea, Ethiopia, Mali, Mauritania, Niger, Nigeria, Senegal, Sudan, and Chad) is being created to combat the effects of climate change and desertification. Reforestation can also be seen as an economic and ethical decision—done if it pays and because cutting trees creates a sense of moral obligation to reforest. Thus, most reforestation activities take place in jurisdictions where timber economies are strong and land stewardship is preached and prevailing. Afforestation, on the other hand, takes on more social, ecological, and political tasks. The Great Green Wall was an initiative aiming to transform the lives of millions of people by creating a great mosaic of green and productive landscapes across North Africa, the Sahel, and the Horn. Three Green Belt Movement in Kenya (Maathai, 2003), started by Dr. Wangari Maathai in 1977, uses tree planting as a conduit for environmental conservation, community development, capacity building, and political struggle.

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