Study Notes 178.307

Forestry Economics

Introduction

Forests provide a range of goods and services.  In addition to the actual wood, forests are also valuable as amenities.  People go tramping (hiking), mountain-biking, hunting or bird-watching in many forests.  Forests are also habitat for wildlife (so preserve biodiversity) and they act as a carbon store.  Generally they also reduce the frequency and severity of floods (limit erosion).  In many countries in the developing world, they provide food for subsistence consumption (bush-meat provides a significant percentage of protein in many rural communities).

This makes managing forests a difficult prospect, so in many countries forests are classed differently.  Forests may be put into reserves, where no production is allowed.  Here the primary role of the forest would be as a conservation area, with side benefits of also being a carbon-store and protector of watersheds.    Policies towards such reserves vary, with some nations permitting traditional use (hunting, gathering, firewood) by indigenous peoples (e.g. India).  Other nations may follow more rigorous exclusion of people.  Note that this is not always effective, and for this reason the term ‘paper-parks’ has been coined to describe such forests.  That is, they exist on paper (lines on a map)- but as illegal logging and poaching of wildlife still occurs- fail to protect the forests.

Other forests may be regarded as multiple-use.  These are used for production purposes as well as for amenities and conservation outputs.  For instance, Timberlands West-Coast in the late 1990s, was experimenting with such mixed uses.  It was proposed to harvest beech trees at a low rate, and simultaneously manage the forests for conservation outcomes (pest-control).  In the USA, The Nature Conservancy (TNC)- a private conservation group- has experimented with becoming ‘managers’ of private forests to achieve conservation and production outcomes.

Some forests are also regarded as pure production forests.  These are often plantation forests.  That is, forests that have been planted from seedling, rather than grown from natural seed-banks in the ‘soil’.  A good example of this is Pine plantations in New Zealand.  The species here is Monterey Pine (from California).  Its scientific name is Pinus radiata.  It forms the large majority of plantation trees in New Zealand.  With production forests, the primary focus is the value of the saleable timber produced by the trees.  Note that even with such production forests however, other valuable outputs are still generated.  Many trees have been planted on slopes in New Zealand (e.g. the East Coast) to also gain the benefits from erosion protection.  Some native species have also moved into these exotic forests and use it as a habitat.  People still go hunting or mountain-biking in these forests. 

Commercial Forestry

The starting point (often) for a private forestry company is to manage the forests as a kind of crop.  That is, the value of the forest will be a function of its wood volume.  It may help to think about NZ plantation forests as an illustration of this ‘type’ of forest.

Now, consider how the volume of wood changes over time.  When an area is planted with seedlings, growth rates tend to be high.  The seedlings have plenty of sunlight and have little competition for soil-nutrients with their neighbours.  They grow quickly.  As they get bigger, crowding starts to occur.  Neighbouring branches block sunlight from the tree, so it can’t photosynthesise as quickly.  As roots spread through the soil, they compete for the nutrients.  The tree can’t sustain its early growth rate. 

At some point in time, wood volume actually starts to decrease.  Trees are a living organism.  Some will die prematurely because of accidents (lightening strikes, storms) or disease and pests.  As these trees die, we lose this volume of wood.  Also, as one tree collapses, it often injures its neighbours (breaking off branches or damaging bark).  This also increases the risk of disease in these trees, so their mortality rate also rises.

More formally, we represent this growth path as the function f(t).  This basically means the volume of wood is a function of the age of the trees, which is t.  Seedlings have no commercial value as wood however, so there is generally some minimum age t* we need to get to, before we can harvest the trees.  There is also a breakpoint in this function at t**.  If the forest is older than t**, its growth rate f’(t) is still positive but is now declining (f”(t) is negative).

The forestry management decision is to simply find the best time to clear-fell the forest.  We will let this optimal time be T.  This may take 100 years for oak, but in NZ pine is typically harvested in a 23-28 year range.  For convenience (i.e. we can relax these assumptions but it makes the problem unnecessarily harder), assume that the price (p) of wood is a constant.  Then, assume that the only costs facing the firm are the planting costs (c)- and this is fixed.  Note that this means felling the trees occurs at zero cost.

This allows us to generate the Faustmann formula for a single rotation

This states that the harvest should be delayed until the return on the forest equals the discount rate (r).  For a private firm, this discount rate should represent its cost of capital.  In New Zealand, the CAPM model is used by many analysts to calculate this rate.

Before this point in time T, the forest is adding value at a rate greater than the discount rate.  If the firm can earn 5% elsewhere but the forest is growing at 8%, its best to keep your money in trees.  After this point, the forest is growing slower than the discount rate.  If the firm can earn 5% elsewhere and the forest is growing at 3%, it’s best to convert the trees into this alternative asset.

In short, forestry management is like any other investment decision made by a firm.  It depends on the relative rates of return on the firm’s capital.  The main difference between forests and other investment decisions is the long time lag between planting and harvest. 

Note however, that management is not quite this simple.  Forests have to be managed during their lifespan.  Juvenile trees will be thinned to reduce competition and allow faster growth to be sustained.  Pruning and pest control increases the value of the trees. 

If replanting is possible, then the optimal rotation should take into account the delay in receiving profits from subsequent fellings.  Note that replantings are not always possible.  Deforestation however, is usually a consequence of conversion of the land to agriculture, rather than forestry.

Let’s assume then, we have a set of rotations without end.  After each harvest, the area is replanted and the sequence begins again. 

This yields the Faustmann formula for a multiple rotation.

Applying the algebraic rules for discounting allows us to simplify the problem to:

We maximise this function with respect to T.  Note that this requires we use the quotient-rule.

Solving, we get

Note that the discount rate r is modified relative to the single rotation.  This expression is greater than the single rotation.  This implies harvest occurs at a point when the growth rate of wood is higher than the single rotation.  This can only be true if we have a shorter rotation cycle.  Hence, we know that where re-plantings are possible, the private forester will adopt a shorter rotation than in a single rotation. 

Technically, we should also take into account alternate uses of the land devoted to forestry as well. 

Issues

The Faustmann formula is difficult to elaborate to account for less rigid assumptions.  One problem is that the forest may have a mix of stands of different ages, so there is not one unique age to actually clearfell.  This can be solved by restricting harvesters to always clear the oldest trees first (cf. Crabbe and Long, 1989).  While this assumption is plausible, it may not always hold.  Another problem is that selective harvest based on age cohorts might result in the age-structure of the forest changing over time.  This would increase the difficulty of inferring the optimal rotation.

Market structure may also have an impact.  Suppose the firm is a monopoly.  This might mean that the firm fells the trees at a younger age.  This would reduce the supply and push up price.  Nonetheless, theoretical work shows that this intuition may not hold.  Crabbe and Long (1989) for instance, show that a monopoly might follow exactly the same harvest strategy as competitive firms.  The price of wood is also not uniform either, and varies through time.  Wood that is used for construction purposes is typically more expensive than those grades used for chipping or pulping (for paper).
Also, we have assumed that the firm is risk-neutral.  Given that forests are at risk of destruction (an introduced wood-borer could do a lot of damage, and fires or floods are other possible hazards), this also ought to be taken into account.  Not all of these risks in practice can be insured against.  Government policy often changes over the life of the forest.  For instance, felling of native trees in NZ has become increasingly more restrictive under regulation introduced in the last 20 years (leading to price surges for native timbers, and cases of ‘tree poaching’ on private land).

Another issue is the presence of non-harvest values.  These include things like the amenity values above.  Hatrman (1976) modified the basic Faustmann model to account for the presence of these values.  This is through another time dependent function- say g(t)- that represents the flow of non-timber values from the forest.  This might be increasing through time.  Some species, such as the threatened Spotted Owl in the Pacific North-West of America, are believed to depend on old-growth forests for habitat.

If the presence of these non-timber values is significant, Hartman shows that the forest rotation cycle increases.  Indeed, if these non-timber values are growing it might never be optimal to harvest.  This may create a regulatory issue.  If forest-owners are not compensated for providing these non-timber values, they will not take them into account.  That is, they are providing a positive externality.  Regulations could be used to prompt such forest-owners to lengthen this rotation cycle (e.g. a severance tax based on the area of trees cut).

Another difficulty in applying the Faustmann formula is that many forests are not owned by the private sector.  Rather they are owned by the state.  While this is one potential solution to the problem of non-timber values, governments may pursue other agendas.  For instance, rapid deforestation could be initiated to raise foreign exchange to meet a balance-of-payment crisis.  In effect, the more profitable strategy of delaying harvest is abandoned to meet this trade problem.  Perverse incentives might also exist, where landowners are subsidised to clear forests for agricultural reasons.

Conclusion

Forestry from the perspective of a firm is best viewed as an investment opportunity.  It is a peculiar investment decision, as the lag between planting and revenue from harvest, is quite lengthy.  The Faustmann formula represents the fundamental rule for harvesting trees, stating that it is essentially a timing problem.  The decision to harvest is motivated by the comparison of the return on the trees, with the discount rate (return on alternative investments) by the firm.  In practice, implementing the Faustmann formula is problematic.